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Form and Function of the Shoulder Girdle in Sauropod Dinosaurs A Biomechanical Investigation with the Aid of Finite Elements Dissertation to obtain the degree Doctor Rerum Naturalium (Dr. rer. nat) at the Faculty of Biology and Biotechnology International Graduate School of Biosciences Ruhr-University Bochum Department of Zoology and Neurobiology submitted by Bianca Hohn-Schulte from Dortmund Bochum, April 2010 Form und Funktion des Schultergürtels bei sauropoden Dinosauriern Eine biomechanische Untersuchung mit Hilfe finiter Elemente Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften der Fakultät für Biologie und Biotechnologie an der Internationalen Graduiertenschule Biowissenschaften der Ruhr-Universität Bochum angefertigt am Lehrstuhl für Zoologie und Neurobiologie von Bianca Hohn-Schulte aus Dortmund Bochum, im April 2010 Tag der Einreichung: 15. April 2010 Tag der mündlichen Prüfung 07. Juni 2010 1. Betreuer PD Dr. Claudia Distler-Hoffmann Lehrstuhl für Zoologie und Neurobiologie Fakultät für Biologie und Biotechnologie Ruhr-Universität Bochum 2. Betreuer: Prof. Dr. Wolfgang H. Kirchner AG Verhaltensbiologie und Didaktik der Biologie Fakultät für Biologie und Biotechnologie Ruhr-Universität Bochum Für Hannah in Liebe "An anatomist who ignores engineering mechanics is missing one of the most powerful resources of human knowledge" -R. McNeill Alexander- Contents CONTENTS ................................................................................................................................................... I CHAPTER 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 INTRODUCTION .................................................................................................................... 1 EVOLUTION OF DINOSAUR LOCOMOTION ..................................................................................................... 2 SAUROPOD LOCOMOTOR HABIT AND BODY POSTURE...................................................................................... 4 SHOULDER GIRDLE RECONSTRUCTION IN SAUROPOD DINOSAURS ...................................................................... 6 SHOULDER GIRDLE EVOLUTION AND LOCOMOTION ........................................................................................ 9 FORM AND FUNCTION IN BONES .............................................................................................................. 14 FINITE-ELEMENT METHOD (FEM) ............................................................................................................ 19 AIMS AND OBJECTIVES ........................................................................................................................... 20 CHAPTER 2 MATERIAL .......................................................................................................................... 23 CHAPTER 3 METHODS .......................................................................................................................... 25 3.1 MORPHOLOGICAL DATA ......................................................................................................................... 25 3.1.1 Relative scapular position in reptiles and mammals ............................................................... 25 3.1.2 Coracosternal joint in extant reptiles ....................................................................................... 25 3.2 MUSCLES OF THE SHOULDER GIRDLE IN ALLIGATOR MISSISSIPIENSIS ................................................................ 25 3.3 BASIC MECHANICAL PRINCIPLES ............................................................................................................... 26 3.4 FINITE-ELEMENT METHOD (FEM) ............................................................................................................ 27 3.4.1 Generation of the model .......................................................................................................... 28 3.4.2 Link elements ........................................................................................................................... 28 3.4.3 Vectorial forces ........................................................................................................................ 29 3.4.4 Bearings ................................................................................................................................... 29 3.4.5 Stress distribution .................................................................................................................... 29 3.4.6 Contact elements ..................................................................................................................... 30 3.4.7 Reduction of the bauraum ....................................................................................................... 30 3.5 3-D FE MODELS OF TWO GENERALIZED TETRAPODS ..................................................................................... 31 3.6 2-D FE MODEL OF A CROCODILIAN SHOULDER GIRDLE .................................................................................. 34 3.7 3-D FESS OF A CROCODILIAN SHOULDER GIRDLE......................................................................................... 37 3.8 3-D FESS DIPLODOCUS LONGUS ............................................................................................................. 38 3.8.1 Mechanical considerations for building the bauraum ............................................................. 39 3.8.2 Generation of the model .......................................................................................................... 41 3.8.3 Estimation and distribution of body weight ............................................................................ 42 3.8.4 Muscle reconstruction ............................................................................................................. 43 3.8.5 Calculation of static equilibrium .............................................................................................. 43 CHAPTER 4 RESULTS ............................................................................................................................. 45 4.1 MORPHOLOGY OF THE SHOULDER GIRDLE .................................................................................................. 45 4.1.1 Comparison of extant reptiles and mammals .......................................................................... 45 4.1.2 Histology of the coracosternal joint in Caiman spec. ............................................................... 49 4.2 3-D FE MODELS OF SOLID TETRAPOD BODIES ............................................................................................. 51 4.2.1 Early tetrapod .......................................................................................................................... 52 4.2.1.1 4.2.1.2 4.2.1.3 4.2.2 4.2.2.1 4.2.2.2 4.2.2.3 4.2.3 4.2.3.1 Symmetrical stance compressive stresses ........................................................................................... 52 Symmetrical stance tensile stresses .................................................................................................... 54 Asymmetrical stance compressive stresses......................................................................................... 55 Cursorial mammal ................................................................................................................... 57 Symmetrical stance compressive stresses ........................................................................................... 57 Symmetrical stance tensile stresses .................................................................................................... 59 Asymmetrical stance compressive stresses......................................................................................... 60 2-D FE model of a crocodilian shoulder girdle ......................................................................... 62 Static equilibrium ................................................................................................................................ 63 i 4.3 3-D FESS OF A CROCODILIAN SHOULDER GIRDLE......................................................................................... 64 4.3.1 Static equilibrium ..................................................................................................................... 65 4.3.2 Muscle function ....................................................................................................................... 68 4.3.3 Synthesis of the scapulocoracoid ............................................................................................. 72 4.4 3-D FESS OF THE SCAPULOCORACOID OF DIPLODOCUS LONGUS .................................................................... 74 4.4.1 Forelimb position I. .................................................................................................................. 76 4.4.2 Forelimb position II. ................................................................................................................. 78 4.4.2.1 4.4.2.2 4.4.3 4.4.3.1 4.4.3.2 CHAPTER 5 Static equilibrium ................................................................................................................................ 79 Synthesis of the scapulocoracoid in Diplodocus longus ...................................................................... 84 Reconstruction of the shoulder girdle ...................................................................................... 89 Skeletal elements of the shoulder girdle ............................................................................................. 89 Muscles of the shoulder girdle ............................................................................................................ 92 DISCUSSION ..................................................................................................................... 103 5.1 FORM AND FUNCTION OF THE TETRAPOD BODY ......................................................................................... 103 5.2 FESS OF THE CROCODILIAN SHOULDER GIRDLE .......................................................................................... 110 5.3 3-D FESS OF THE SHOULDER GIRDLE OF DIPLODOCUS LONGUS .................................................................... 113 5.3.1 Reconstruction of the shoulder girdle of Diplodocus longus. ................................................. 113 5.3.1.1 5.3.1.2 5.3.1.3 5.3.2 CHAPTER 6 6.1 6.2 Skeletal elements .............................................................................................................................. 113 Muscles of the shoulder girdle .......................................................................................................... 119 Muscle forces and dimensions .......................................................................................................... 127 FESS method .......................................................................................................................... 129 GENERAL CONCLUSIONS AND FUTURE PERSPECTIVES...................................................... 133 GENERAL CONCLUSIONS ....................................................................................................................... 133 FUTURE PERSPECTIVES ......................................................................................................................... 136 CHAPTER 7 SUMMARY ....................................................................................................................... 137 CHAPTER 8 ZUSAMMENFASSUNG ...................................................................................................... 141 CHAPTER 9 BIBLIOGRAPHY ................................................................................................................. 145 CHAPTER 10 SUPPLEMENT................................................................................................................ 160 10.1 LABORATORY MANUAL FOR HISTOLOGICAL SECTIONS OF THE CORACOSTERNAL JOINT IN CAIMAN SPEC. ................ 160 10.2 MUSCLES OF THE CROCODILIAN SHOULDER GIRDLE .................................................................................... 162 10.3 3-D FESS OF A CROCODILIAN SHOULDER GIRDLE....................................................................................... 166 10.3.1 Adjustment of static equilibrium ........................................................................................... 166 10.3.2 Reduction of the bauraum ..................................................................................................... 171 10.3.2.1 10.3.2.2 First reduction step ....................................................................................................................... 171 Second reduction step .................................................................................................................. 172 10.3.3 Technical settings .................................................................................................................. 173 10.4 3-D FESS OF THE SHOULDER GIRDLE IN DIPLODOCUS LONGUS ..................................................................... 180 10.4.1 Adjustment of static equilibrium in forelimb position I. ........................................................ 180 10.4.2 Adjustment of static equilibrium in forelimb position II. ....................................................... 189 10.4.3 Reduction of the “bauraum”.................................................................................................. 199 10.4.4 Technical settings Forelimb position I. ................................................................................... 207 10.4.5 Technical settings forelimb position II. .................................................................................. 212 CURRICULUM VITAE................................................................................................................................ 223 ii Chapter 1 Introduction Sometime in the late Devonian (380 Myr) early tetrapodomorphs began to enlarge their territory from water to land. With this evolutionary step new mechanical conditions challenge the entire body and already the first tetrapodomorphs were preadapted for these demands (Coates & Clack, 1995; Jarvik, 1996). One of the most important factors for terrestrial locomotion is the ability of the body to sustain gravitational forces. The characteristic tetrapod bauplan evolved and is basically still present in all living tetrapods. In general it consists of a head, neck, a dorsal vertebral column, dorso-lateral ribs, a tail and two pairs of fore- and hindlimbs attached to the trunk via the limb girdles. These elements are held together and moved with the aid of muscles, tendons and ligaments. During terrestrial locomotion the most critical point is the transmission of body weight from the trunk to the supporting limbs, which is always accomplished by the limb girdles. This holds true also for the biggest land living animals that ever walked on earth, the sauropod dinosaurs. Estimations of body size in sauropods ranges from 10-100 t (Alexander, 1998; Wedel, 2003; Seebacher, 2001) The biomechanical conditions and morphology of the shoulder girdle are therefore of great importance to understand the biology of an animal as they contribute to body weight support. There still is a lack of knowledge concerning the mechanics, morphology and evolution of the shoulder girdle in both extinct and extant tetrapods, especially sauropods. In contrast to the hindlimbs the shoulder girdle exhibits a unique feature, because it has no direct connection to the vertebral column and is attached to the trunk only by muscles, tendons and ligaments. Up to now research focused mainly on the hindlimbs, where osteological features and arrangements at the pelvis are commonly used to reconstruct phylogenetic relationships. The musculoskeletal system is assumed to fulfil the specific mechanical requirements by investing a minimum of energy, as evolution seems to favour structures and patterns of movement increasing the personal fitness of the animal (Alexander, 2002). A direct connection between the posture of the limbs, their biomechanics, energy saving strategies, and costs of locomotion is predicted (Reilly et al., 2007). Locomotor behaviour influences the biology of the animal as it plays a major role in foraging activities, mating and in prevention of predatory contact. 1 1.1 Evolution of dinosaur locomotion The age of dinosaurs covers almost the whole Mesozoic age from the late Triassic (230 Myr ago) until their extinction at the end of the Cretaceous (65 Myr ago). They dominated the terrestrial fauna for about 165 Myr displaying a great variety in size and locomotor behaviour (Carroll, 1987; Weishampel et al., 1990; Benton, 2005). Dinosaurs are part of the Archosauria (Fig.1), which were a highly diverse group in the Mesozoic age and at present are still represented by crown-group crocodiles and birds. In the Early Triassic archosaurs underwent a great diversification splitting into two major groups, the Crurotarsi including the ancestors of the crown-group crocodilians and the Ornithodira leading to dinosaurs and birds (Fig.1) (Sereno, 1991; Gower & Wilkinson, 1996; Benton, 1999). The evolution of archosaur locomotion is subject of ongoing discussion. One of the most important issues here is the “sprawling-to-erect-paradigm” i.e. the shift from a sprawling to an extended limb posture and the development of parasagittal gait (Hutchinson, 2006). Sprawling is the plesiomorphic limb position in reptiles, in which the femur is held more or less horizontally and directed laterally. Thus, the trunk can be elevated from the ground only to a limited extent and for a limited time. Whether the first Archosauria had an erect hindlimb position (Sereno, 1991) or were quadrupedal sprawlers (Charig, 1972; Hutchinson & Gatesy, 2000) is still debated. Nonetheless, a fully erect hindlimb postures evolved several times during the Late Triassic, first, in the crocodilian and the dinosaurian line including pterosaurs and leading to extant birds, and, second, independently in the Cynodonts and their descendants the extant mammals (Parish, 1986, 1987; Benton, 2005). The sprawling or semi-erect hindlimb posture of crown-group crocodiles therefore evolved secondarily in relation to an aquatic lifestyle (Sereno 1991; Reilly & Elias, 1998; Hutchinson & Gatesy 2000; Hutchinson, 2006). Up to now no information is available to evaluate evolution of the forelimbs in this context. Dinosaurs can be separated into Ornithischians and Saurischians, mainly or initially based on the architecture of the pelvis. In addition to morphological features of the skull, ornithischians can be distinguished from other dinosaurs by their avian-like pelvic girdle with a postero-ventrally pointing pubis. These herbivorous animals first appeared in the Upper Triassic and are represented in the fossil record by several groups until the Late Cretaceous (Fig.1). Basal ornithischians were obligate bipeds (e.g. Norman et al, 2004). With increasing body size, ornithischians evolved a facultative bipedal or obligate quadrupedal locomotor posture (Galton and Upchurch, 2004; Horner et al. 2004). The more derived Ceratopsians comprise two major groups, the Cerapoda, with the horned quadrupedal ceratopsians and facultative bipedal 2 iguanodontids, and the Thyreophora with the obligate quadrupedal armored ankylosaurs and stegosaurs (Carroll, 1987; Benton, 2005). Figure 1 Cladogram showing the relationship of the Archosauria (modified from Remes, 2008; after Benton, 2005). In contrast, saurischians have a reptile-like pelvic morphology with the pubic bone pointing antero-ventrally. The saurischian clade is subdivided into the carnivorous bipedal theropods, which comprise the ancestors of extant birds, and the quadrupedal herbivorous sauropodomorphs (Carroll, 1987; Benton, 2005; Weishampel, 1990). The sauropodomorphs, and here especially the sauropods, can be distinguished from other dinosaurs especially by their bauplan. All sauropods possess rather long necks and tails, and columnar legs and were quadrupedal herbivores (Fig.2) (Carroll, 1987; Benton, 2005; Weishampel, 1990). The basal sauropodomorphs first appear in the Upper Triassic (Fig.2). The most abundant sauropodomorph Plateosaurus is commonly known from excavation sites in southern Germany and Switzerland (Yates, 2003). Like Plateosaurus, other sauropodomorphs, such as Riojasaurus from Argentina and Melanorosaurus from South Africa, were herbivores with a body size of up to 7m long (Bonaparte, 1971; Benton, 2005). The anatomy of their forelimbs as well as the occurrence of a furcula-like clavicle inhibiting free swinging of the forelimb necessary for quadrupedal locomotion implicates that basal sauropodomorphs like Plateosaurus and Massospondylus were not able to perform effective quadrupedal locomotion (Yates & Vasconcelos, 2005; Bonnan & Senter, 2007). The just recently discovered basal sauropod Antetonitrus from South Africa was recognized as the first “true” sauropod exhibiting morphological adaptations for graviportal quadrupedalism and therefore serves as a link between basal sauropodomorphs and sauropods (Fig.2) (Yates & Kitching, 2003). 3 Figure 2 Cladogram showing the evolution of the saurischian clade (modified from Remes, 2008: after Benton, 2005). With few exceptions sauropod dinosaurs were larger than any extant tetrapod and even all contemporary dinosaurs. Whether sauropods evolved from bipedal ancestors or habitual quadrupeds is currently one of the most debated questions in sauropod locomotion research (Dzik, 2003; Fechner, 2005, 2006 a,b, 2009). Whereas theropods retained obligate bipedal locomotion and a carnivorous diet, basal sauropodomorphs are thought to have been facultatively bipedal, with some taxa more bipedal than others (e.g. Anchisaurus). The heavily-built forms such as Riojasaurus were presumably more quadrupedal (Galton, 1990; Barrett & Upchurch, 2007). With increasing body size and elongation of trunk and neck a transition to obligate quadrupedal locomotion can be observed. These assumptions, however, are inconsistent with new findings, indicating that the sauropods are the only group of saurischians with exclusively quadrupedal locomotion (Fechner 2009). 1.2 Sauropod locomotor habit and body posture Historically, the body posture and locomotor habits of sauropods was reconstructed based on observations in extant crocodiles, lizards, and mammals. A sprawling posture of the limbs, similar to that of modern crocodiles was assumed by some researchers (Hay, 1908; Tornier, 1908), even though Owen (1841) concluded from features in the limb skeleton and fossil tracks that these new species of reptiles had moved much more like mammals than living reptiles or birds. Others agreed, but hypothesized at the same time a semi-aquatic lifestyle in which buoyancy could support the animals’ enormous body weight (Marsh, 1878; Colbert, 1962; Romer, 1966; Swinton, 1970). Other researchers favoured a straight limb posture enabling swinging of the 4 limbs in the parasagittal plane during quadrupedal locomotion (Osborn, 1899; Hatcher, 1901; Matthew, 1901; Abel, 1910; Gilmore, 1932), but it was not until the seventies of the last century, that sauropods were interpreted as graviportal fully terrestrial animals (Bakker, 1971a; Coombs, 1975, 1978; Alexander, 1976). Despite of morphological differences within the various groups, sauropods share common morphological adaptations to quadrupedal locomotion in the limb skeleton and girdles (Coombs, 1978). In a first attempt dinosaurs were classified into locomotor types. Cursorial adaptations observed in extant quadrupedal tetrapods, were correlated to dinosaur anatomy to evaluate their running abilities (Coombs, 1975). Morphological evidence as the reduction of muscular attachments in the distal limbs suggests that in sauropods forelimbs are exclusively used to support the body weight. Furthermore, an extreme reduction of the phalangeals indicates a columnar support in the limb skeleton (Coombs, 1978). Further, columnar legs, an increased limb bone robusticity, and shortened limb segments in relation to an increase of body size were determined as adaptations for slow graviportal locomotion (Carrano, 2000, 2005). Presumably the gradual increase in body mass during sauropod evolution was responsible for morphological changes best observed at the limbs and limb girdles. The strengthening of the sacrum and the lengthening of the forelimbs can be viewed as adaptations to changes in locomotor posture due to increasing body size (Coombs, 1978; Alexander, 1985; Fechner, 2009). One of the advantages of an extended limb posture is the increase of stride length and thus locomotor speed (Alexander, 1985). Another advantage is the ability to support higher body weights with less energy. Since body weight increases, muscle forces can be kept low by holding the limbs in a straight position, thus lowering the rotational moments acting on the joints (Preuschoft & Christian, 1999). This is why animals with a certain body size do not display a sprawling limb posture. The correlation between acting muscles forces and lever length in the tetrapod limb further was termed the effective mechanical advantage (EMA). An increase of EMA therefore permits a lower amount of muscles forces to keep the joints in equilibrium (Biewener, 1989, 2005; Reilly et al., 2007). In case of tracks and trackways of sauropods, the problem arises to assign them to the potential trackmaker. Nevertheless there exist reliable data about trackways assigned to sauropods like Diplodocus or Brachiosaurus (Thulborn & Wade, 1984; Farlow, 1992; Lockley et al., 1994). There are currently no footprints of running sauropod dinosaurs available. Speed estimations based on the present data indicate only moderate walking speeds of about 3.96 km/h in sauropods (Alexander, 1985). For comparison, the biggest extant terrestrial tetrapod, the 5 elephant, reaches walking speeds up to 7.2 km/h (Ren et al. 2009) and maximal running speeds of about 25 km/h (Hutchinson et al., 2003). Sauropods are often compared to elephants according to their columnar limb design. With regard to speed estimations and most recent investigations on locomotor mechanics in elephants, it is suggested, that sauropods might have been more than `stiff legged' walkers (Ren et. al., 2009), which would influence further speed estimations for sauropods as well. . One crucial issue is the relative position of the limbs during standing and locomotion. Sauropods have been assumed to produce either wide or narrow gauge trackways. For example Diplodocus produced narrow gauge tracks in contrast to Brachiosaurus as a wide gauge trackway maker. The results were estimated based on the portion of total weight supported by the respective limb pair (Henderson, 2006). The proportion of weight carried by the limbs differs between dinosaur groups. Body mass estimations contribute to the reconstruction of the position of the centre of mass (COM) in the body, and the different amount of body weight supported by the hind- or forelimbs (Gunga et al., 1995, 1999, 2008; Henderson, 1999; Seebacher, 2001). In most dinosaurs a greater proportion of weight was supported by the hindlimbs (Alexander, 1989; Henderson, 1999, 2006). By contrast, Brachiosaurus and Titanosaurids like e.g. Saltasaurus and Opisthocoelocaudia supposedly enlarged their amount of weight supported by the forelimbs (Gunga et al., 1995, 1999, 2008; Henderson, 1999; Seebacher, 2001). However, the proportion of body weight supported by the forelimbs, justifies further investigations on the forelimbs and shoulder girdle to evaluate their relevance in body weight transmission. According to the former paragraph it can be noted, that investigations on archosaur and dinosaur evolution mainly refer to the hindlimbs, while the shoulder girdle and forelimbs are mainly neglected. This is probably for historical reasons, as Romer, whose studies focused mainly on the hindlimb girdle to evaluate their relevance in reconstructing phylogeny, did the first studies concerning evolution of locomotion in vertebrates during the 20th century. In none of the former described investigations on gaits and speeds of sauropod dinosaurs (Alexander, 1976, 1985, 1989; Thulborn, 1990) as well as on the posture and the evolution of the forelimbs (Christian & Preuschoft, 1996; Christian et al. 1999a, b; Christiansen 1997; Wilson & Carrano 1999; Christian, 2002; Bonnan, 2003, 2004; Bonnan & Yates, 2007; Carrano, 2005) the shoulder girdle skeleton was taken into account. 1.3 Shoulder girdle reconstruction in sauropod dinosaurs Considering the functional morphology of the shoulder girdle there still is a large gap of knowledge especially in reconstructing the position of the scapulocoracoid, the placement of the 6 sternal plate, and the orientation of the glenoid fossa. The crucial point in shoulder girdle reconstruction is the nature of the connection of these elements. In mammals no bony connection from the trunk to the scapula exists. By contrast the scapulocoracoid of extant reptiles is connected to the trunk via the coracoid to the sternal elements. Although the connection of the elements in extant reptiles therefore should be far more comprehensible than in mammals, they are rarely preserved articulated in fossils. The shoulder girdle of sauropod dinosaurs has been described for a number of species. However, few descriptions exist containing all elements. In Diplodocus (Hatcher, 1901) and Camarasaurus (Gilmore, 1932), scapula, coracoids and sternal elements were present and described in detail, as well as one pair of clavicles preserved in Diplodocus. Most findings lack at least one element, so incomplete morphological descriptions on the shoulder girdle are available for various diplodocids (McIntosh, 1988; Sereno et al. 1999; Harris & Dodson 2004; Remes 2006) and titanosaurids (Gomani, 2005; Rose, 2007). The clavicles are often identified with reservations, however a variety of investigators vote for their presence (Hatcher, 1901; Sereno et al. 1999; Michelis, 2004). Except for Hatcher (1901), Gilmore (1932) and McIntosh (1988) the anatomical position of the shoulder girdle elements in the skeleton has only been described in parts. Reconstructions of the shoulder girdle skeleton are mainly based on phylogenetic and morphological comparisons with extant archosaurs, like crocodiles and birds. As the scapular position in these species varies from a position nearly parallel to the dorsal margin of the vertebral column (birds), to a rather vertical orientation (crocodiles), present scapular reconstructions in sauropods range between 10° and 60° towards the horizontal plane (Gilmore, 1932; Bakker, 1971a; Borsuk-Bialynicka, 1977; McIntosh 1988; McIntosh et al., 1997; Wilson und Sereno, 1998; Parish & Stevens 2002; Wilhite, 2003; Bonnan, et al., 2005). The distal extent of the scapula in living birds and crocodiles is roughly oriented parallel to the neural spines. It was assumed that a similar condition in sauropods leads to a postero-dorsal inclination of scapula (Stevens and Parrish, 2002). Further the presence of flattened areas on the external surface of the dorsal ribs, termed facets, is used as an indicator for a constrained sub-vertical orientation of the pectoral girdle in sauropods (Bonnan et al. 2005). Pectoral girdle position was inferred from either death pose (Gilmore, 1932; McIntosh 1988), comparison with extant analogues (Bakker, 1971a, Borsuk-Bialynicka, 1977; Wilson & Sereno, 1998; Wilhite, 2003) or its evolution in a phylogenetic context (Bonnan et al. 2005), but none of the investigations take functional issues into consideration. 7 Sternal plates are often missing in the fossil record or were not recognized correctly. In cases in which the sternal plates are present, they were placed either far behind the coracoids, vertically in front of the ribcage (reconstruction in the Dinosaur Museum Aahtal (CH); Wilson & Sereno 1998; Wilhite, 2003) or were not placed on the mounted skeleton at all (McIntosh, 1988). Schwarz et al., (2007) were the first to present a combined approach of morphological comparison and functional considerations to reconstruct the shoulder girdle in Diplodocus, Camarasaurus and Opisthocoelocaudia. The study reveals the following constraints for scapulocoraocid reconstruction. In all amniotes the sternal plates are positioned parallel to the distal ends of the thoracic ribs so as to maintain contact to the corresponding ribs and the shoulder girdle via the coracoids. Following this, an inclination of the scapula of 60° to the vertebral column is predicted (Schwarz et al., 2007). These implications were recently adopted by Remes (2008) in his reconstruction of the shoulder girdle of sauropodomorphs. Nevertheless the mechanical background for these conclusions was not determined. In lacertilians (varanids, chameleon) the coracoid is moving translational relative to the sternal apparatus (Peterson, 1973; Jenkins & Goslow, 1985; Lilje, 2007). The junction between coracoid and sternum in these reptiles exhibits a bony” groove and tongue” mechanism, where the coracoid is acting as the tongue and the sternal elements show a groove structure. The junction is surrounded by a joint capsule embedded in connective tissue. There is currently no information available about the condition within the sternum and the coracoids in sauropod dinosaurs. The presence of a coracosternal joint influence the mobility in the shoulder girdle, as it was predicted in former studies (Bakker 1971, 1987). Therefore this issue is included in the present thesis. It is assumed that transmission of body weight depends on the position of the limbs and the direction in which they are articulated at the glenoid joint. Concerning their enormous body weights some authors recommend an orthogonal force transmission from the humerus to the scapula in sauropod dinosaurs. Assuming the humerus is positioned vertically to the glenoid joint, the scapula will be oriented nearly parallel to the dorsal margin of the vertebral column (McIntosh et al., 1997; Wilson & Sereno, 1998; Bonnan, 2001; Wilhite, 2003; Upchurch et al., 2004). These assumptions again are disputed, as other investigators argued for a moderate flexion in the limbs to reduce peak forces in the glenoid and elbow joints (Christian et al., 1999). Few descriptions exist on the dinosaur forelimb musculature in general (Raath, 1977; Coombs, 1978b; Santa Luca, 1980; Nicholls & Russell, 1985; Dilkes, 2000; Carpenter, 2002) and on sauropod dinosaurs in particular. Reconstruction of the pectoral girdle musculature in Sauropoda 8 was performed for Opistocoelocaudia (Borsuk-Bialynicka, 1977; Schwarz et al. 2007), Diplodocus (Wilhite, 2003; Schwarz et al. 2007) Camarasaurus (Wilhite, 2003; Schwarz et al. 2007) and Apatasaurus (Wilhite, 2003). All approaches rely either on muscular analogues obtained from extant lacertilians and crocodiles (Schwarz et al. 2007) or on crocodiles alone (Wilhite, 2003) and differ in terminology and number of muscles taken into account. Remes (2008) applied the extant phylogenetic bracketing (EPB) on various basal sauropodomorphs up to the basal sauropod Patagosaurus. Soft tissues like muscles, tendons and ligaments of an extinct taxon is reconstructed based on anatomical homologies observed in extant archosaurs bracketing dinosaurs (crocodiles and birds) (Bryant & Russell, 1992; Witmer, 1995). 1.4 Shoulder girdle evolution and locomotion The origin of the tetrapod shoulder girdle can best be observed in fossil stem tetrapods from the late Devonian. Similar to fishes the pectoral girdle of the first tetrapodomorphs is of dermal origin. The glenoid joint serves as the articulation site of the limbs to the pectoral girdle and is formed by the dorso-lateral scapula and the ventral coracoid. In early tetrapodomorphs the dorsal element is still covered by a pronounced dermal cleithrum. Morphological changes are clearly visible in tetrapodomorphs like Eusthenopteron, Panderichthys, Tiktaalik, and Acanthostega (Shubin et al., 2006). During the line of evolution a gradual reduction of the dermal parts and an enlargement of the enchondral elements forming the scapula and the coracoid occured. Together with the loss of the supracleithral series, connecting the skull to the limb girdle, these changes are of great importance during the evolution of the tetrapod shoulder girdle. The dermal elements except for the clavicles and interclavicles are lost in Ichthyostega, which is assumed to be the first true tetrapod (Jarvik, 1996; Clack et al. 2003; Shubin, 2006). The evolution of terrestrial activity in early tetrapods is part of an ongoing discussion. Tiktaalik roseae is currently claimed to exhibit morphological features or at least preadaptation for terrestrial locomotion in the limb girdle and cranial skeleton (Fig.3) (Shubin et al., 2006, Daeschler et al., 2006, Ahlberg & Clack, 2006; Markey et al. 2008). From the first carboniferous tetrapods to the early archosauromorphs the limbs and limb girdles are basically identical. In early reptiliomorphs like Diadectes the shoulder girdle is built of a massive bony scapulocoracoid, still retaining a cleithral part at the cranial edge, a clavicle and a ventrally positioned interclavicula (Fig. 3). The pectoral girdle shows a large scapulocoracoid bearing a screw shaped glenoid for the head of the humerus. From Diadectes to basal archosaurs as Prestosuchus the cleithrum is first reduced then completely absent, while the shoulder girdle typically retains a frontally positioned clavicle and a t-shaped interclavicula (Huene, 1935-42; 9 Benton, 2005) (Fig.3). Diadectes retained the ancestral sprawling limb posture, whereas for early archosaurs as Prestosuchus a semi-erect position of the limbs can be assumed (Benton, 2005). Up to the first archosaurs and amongst them the basal dinosaurs, the sternal elements are cartilaginous, and ossification of the breastbone is first reported in pterosaurs and dinosauria (Starck, 1979). In basal dinosauromorphs like Marasuchus some gradual changes in the pectoral girdle become visible. The whole appearance of the skeleton becomes more slender. These first dinosaurs were presumably obligate or at least facultative bipeds, adapted to fast running locomotor habits (Benton, 2005). The main elements of the shoulder girdle, scapula and coracoid, are reduced in size, the scapula becomes more slender (Fig.3). In both basal dinosauromorphs and dinosaurs like e.g. Herrerasaurus there is no evidence for a clavicle or sternal elements (Sereno, 1993), whether due to preservational reasons or functional modifications remain unclear. The pectoral girdle in “prosauropods” consists of a more or less slender scapula with moderate expansion of the distal end and a medium sized coracoid (Huene, 1926; Young, 1941; Bonaparte, 1971; Cooper, 1981; Zhang & Yang, 1995) (Fig.3). A furcula-like clavicle has been described for Massospondylus (Yates & Vasconcelos, 2005) and Plateosaurus (Huene, 1926, 1932; Galton, 2001) although a probable facet for the clavicle at the acromial process is visible in all forms. In both cases it is likely, that this v-shaped element embraced the pectoral girdle, while being attached to the frontal edge of the scapula (Yates & Vasconcelos, 2005). Ossified sternal plates are known from Plateosaurus (Huene, 1926), Massospondylus (Cooper, 1981), Lufengosaurus (Young, 1941), Jingshanosaurus (Zhang & Yang, 1995), and Yunnanosaurus (Young, 1942). Most of these sternal plates have a suboval shape with a thickened, rugose cranio-lateral border, which may indicate a connection to the adjacent coracoid plates. As it was stated before a facultative bipedal posture of the forelimbs has been assumed for basal sauropodomorph dinosaurs. In diplodoicid sauropods the scapula exhibits an enormous craniad enlargement of the proximal part, termed the acromial region, and an elongated scapula with a variably expanded distal end. The prominent acromion ridge divides a larger anterior from a smaller posterior fossa. Scapular and coracoid elements are well ossified forming together the glenoid facet, in which the scapula accounts for two thirds of the glenoid surface area (Wilhite, 2003) (Fig.3,4). The coracoids in sauropods are oval shaped, with an anterior border showing a roughened edge, indicating that it was covered by cartilage during life and may have been attached to the corresponding sternal elements. In general all these features are present in all members of this subgroup e.g. Diplodocus (Hatcher, 1901), Apatosaurus (Upchurch et al., 2004), Supersaurus (Lovelace et al., 2007), Tornieria (Remes, 2006), Suuwassea (Harris & Dodson, 2004) and other more recently described 10 diplodocoids. The pectoral girdle morphology of macronarian sauropods differs in detail. In Brachiosaurus for instance the distal end of the scapula is enlarged, while the middle part is more slender than in Diplodocus. Together with the broad proximal part the scapula assumes a barbelllike appearance (Fig.4). The most obvious difference between the two sauropod groups lies in the shape of the sternal elements. In diplodocoids the sternal plates are oval and dorso-ventrally convex, whereas in macronarians the sternal plates are more slender and elongated as in Camarasaurus or semilunar in all Titanosaurids (Fig.4). Comparison of the shoulder girdle in non-sauropodan sauropodomorphs and sauropods reveals some differences: i) the elongation of the scapula relative to the coracoid, ii) an expanded acromial region, iii) a more ventrally positioned glenoid and iv) a relative enlargement of the sternal plates (Fig.4). In contrast to the v-shaped elements described in some non-sauropodan sauropodomorphs (Yates & Vasconcelos, 2005) the clavicles in all sauropods are bilateral arched elements as described for e.g. Diplodocus (Hatcher, 1901; Holland, 1906). Further it appears that the expansion of the distal end of the scapula and therefore the cartilaginous suprascapula is reduced during sauropod evolution (Remes, 2008). As stated above a quadruped locomotor habit is assumed for all sauropod dinosaurs. In extant tetrapods the dermal elements interclavicula and clavicula persist in the shoulder girdle to varying degrees (Fig.3). The interclavicula is still present in extant archosaurs (birds, crocodilians) and reptiles, but retained in the mammalian line only in monotremes (Fig.3). The clavicle on the other hand can be observed in anurans, lacertilians, Sphenodon and in a number of mammals, while it is absent in extant crocodilians. The enchondral parts of the shoulder girdle in anurans and reptiles are represented by the scapula and the procoracoid plate (Fig.3) (Romer & Parsons 1977; Starck, 1979). During the evolution of the mammalian shoulder girdle the chondral elements receive gradual reduction as well. In monotremes the basic condition is still visible. It consists of a scapula, a procoracoid, and a metacoracoid, while the derived mammals retain only the scapula and a metacoracoid process (Fig.3) (Romer & Parsons, 1977; Starck, 1979). The sternum or sternal plates are rarely included into considerations about the shoulder girdle, even though they represent the connection between the pectoral girdle and the ribcage in tetrapods. A bony sternum is first present in basal tetrapods (Fig.3). Its evolutionary origin or possible homology remains unclear, although derivation from the ventral parts of the ribs or the pectoral girdle has been hypothesized. Embryology in reptiles and mammals indicates that the sternum develops independently and only in a second step becomes associated to the ribs and pectoral girdle (Starck, 1979; Feduccia & McCrady, 1991). Among tetrapods the degree of ossification, shape and dimensions of the sternal apparatus is extremely variable. In urodeles and 11 anurans the sternum consists of one or two cartilaginous plates, which are only connected to the pectoral girdle (Romer & Parsons, 1977; Starck, 1979). The generalized sternum in extant reptiles is represented by a ventral cartilaginous plate, which can be ossified to variable degrees. It exhibits a connection to the coracoids via a coracosternal joint, while the ventral parts of the ribs insert more or less laterally (Romer & Parsons, 1977; Starck, 1979). The mammalian sternum is reduced to a rod-like element, which consists of a ventral series of separate bones fused together to a variable degree (Fig.3) (Romer, 1977; Starck, 1979). In contrast to reptiles and birds the mammalian shoulder girdle shows no bony connections to the trunk except formammals, which retain a clavicle between the scapula and the sternum (Fig.3). 12 Figure 3 Evolution of the tetrapod shoulder girdle showing the main girdle elements in lateral view. Elements of dermal origin (yellow); Chondral elements: scapula (light grey), coracoid (dark grey). Forelimb position is displayed in frontal (left) and lateral (right) view. 13 Figure 4 Shoulder girdle elements of three major sauropod groups. Camarasauridae (Camarasaurus lentus), redrawn after Gilmore (1932); Diplodocoidea (Diplodocus longus); Brachiosauridae (Brachiosaurus brancai). Scapulocoracoids are shown in lateral view. Sternal plates are viewed ventrally, whereby the cranial border is pointing upwards. 1.5 Form and function in bones It seems obvious that form and function are closely related, as appropriate structures enable an animal to fulfill specific tasks. The basic principles of this interrelationship however are not that apparent and still subject of many discussions (Hildebrand & Goslow, 2001). According to the complexity of the vertebrate body one has to be aware to determine correlations based on simple comparison. Interrelationships between form and function of a structure should always take into account variable influences acting on the system, confirmed by empirical and experimental data (Hildebrand & Goslow, 2001). 14 The musculoskeletal system as one part of the animal body complex provides the ability to demonstrate form and function relationships in a well-arranged system, as it is "perhaps nowhere as evident as here" (Carter & Beauprè, 2001). Structural organisation of the bones, cartilage, tendons and ligaments is a result of a unique and complex phylogenetic and ontogenetic history in which genes and mechanical forces provide critical control (Carter & Beauprè, 2001). Focusing on bone, functional adaptation is not only visible in the status quo, but along the evolutionary line and during ontogenesis. The evolution of marine mammals is representative for a shift from a terrestrial to an aquatic mode of locomotion, accompanied by modification and reduction or loss of whole skeletal elements (Hildebrand & Goslow, 2001). In the early development of marsupials temporary functional elements like the metacoracoid, ontogenetically retained from former ancestors, is secondarily reduced according to locomotor changes in very early stages of postnatal development (Klima, 1987). In a macroscopic view functional adaptation of bone can be detected as alterations of bone dimensions, the development of rugosities at the insertion sites of muscles, tendons and ligaments as well as the internal distribution of osseous structures, namely compact and cancellous bone. These changes are determined as the remodelling of bone in mature stages, compared to the modelling of bone during ontogenesis. A wide range of studies reveal the strong influence of mechanical stimuli on bone formation. This contributes to reconstruction of life history in hominid remains (Preuschoft, 1970; Runestadt et al., 1993; Trinkaus et al., 1994; Larson, 1997; Orr, 2005), in orthopaedics and biomechanical engineering (Currey, 1984; Carter, 1987; Kaspar et al. 2000; Witzel 1985, 1996, 2000), as well as in zoology (Demes et al., 2001; Liebermann et al 2003; Carlson & Patel, 2006; Patel & Carlson 2007; Polk et al. 2008). All studies are based on apparent correlations between locomotor type or habitual use in the individual and detecTable alterations such as bone density and formation. During ontogenesis ossification in the developing embryo appears at about the same time as first muscle contractions are detecTable. Inhibiting muscular activity during embryonic development by either muscular disease or genetic modification results in incomplete bone formation indicated by a lower amount of bone substance, decreased diaphyseal diameters and an overall miss-shaping of the single bony elements (Lightfoot & German, 1998; Gomez et al., 2007; Jones et al., 2007). The relevance of mechanical influence on the skeletogenesis and remodelling as an epigenetic factor was recently pointed out by Newman & Müller (2005). Most of the presented studies refer to mammalian bone, but there are studies indicating a strong influence of mechanical stimuli e.g. in teleostians as well (Kranenbarg, 2005). 15 The current approach is based on two important mechanisms connected to bone morphology; bone formation during development (bone modelling), and its ability to functional adaptation according to everyday usage (bone remodelling). The relationship between function and form in bones was first noted by Wolff (1892) in his “Law of bone remodelling” and Roux (1893) predicting a causal relationship between mechanical forces and morphological modifications during life. Moreover, Wolff (1892) argued that the design of an organism is a result of both functional adaptation and natural selection according to Darwin’s evolutionary theory (Carter & Beauprè, 2001). The functional adaptation of bone was described as an auto-regulatory system responding to external stimuli, but did not explain the issue sufficiently (Roux, 1893). Later on Pauwels established the term “causal morphogenesis” to describe the functionally dependent auto-regulatory differentiation of the supporting tissue (Pauwels, 1965). Mesenchymatic stem cell tissue here is only able to detect two kinds of mechanical stimuli, elongation and compression. Elongation leads to connective tissue fibers directed to the tensional traction line, as it appears in tendons, ligaments, disci and menisci (Kummer, 1985) (Fig. 5). Under the influence of compression the cell would adapt its metabolism to produce proteoglycanes, which are basic components of the cartilage matrix. According to Pauwels (1965) bone formation is initiated by elastic deformation of the primary supporting tissue. Compression leads to chondrale ossification via a cartilaginous intermediate stage, whereas tension is responsible for desmal ossification out of connective tissue (Fig. 5) (Pauwels 1965; Kummer, 1980). Figure 5 Scheme of Pauwels “causal morphogenesis”, illustrating the influence of compression and tension on the mesenchymatic tissue. Both pathways towards lamellar bone, chondral as well as desmal ossification, are shown (Pauwels, 1965) (redrawn after Kummer, 1980). 16 Once the skeleton is fully grown each bone has to maintain its function during everyday use. Bone tissue has the ability to respond to mechanical stimuli to keep the resulting stresses constant, thus adapting its strength to the actual mechanical condition (Fig. 6) (Kummer, 1985; Roux, 1893). In an evolutionary context the ability to respond to physical stresses is determined by the genome of the individual. This leads to the conclusion that organisms possessing a highly adaptive potential could differentiate in continuous interaction with external stimuli (Pauwels, 1965). Figure 6 Functional adaptation of bone. Bone density depends upon the mechanical stress value. Stress value below the physiological level will lead to atrophic alterations of the bony. In contrast, a stress value above the physiological level causes an abnormal increase of bone (redrawn after Witzel, pers. communication). Nowadays it is widely accepted that specific mechanical stimuli have a strong influence on the differentiation of bone, cartilage and connective tissue, but whether bone modelling and remodelling is induced by compressive and tensile stresses (Biewener, 1991; Blob & Biewener, 1999, 2001; Currey 2002; Liebermann et al., 2003; Main & Biewener, 2004) or is dominated by compressive stresses alone (Sverdlova & Witzel 2010; Witzel et al., 2010) is still disputed. It has long been predicted that bone is mainly adapted to withstand high bending and torsional moments, whereas compression does only plays a minor role (Biewener et al., 1991; Carter & Beauprè, 2001; Currey 2002; Liebermann et al., 2003). The majority of these studies investigate locomotor stresses in long bones, where the resulting stresses are supposed to be mainly a result of bending. Strains hereby were determined by in vivo implanted strain gauges applied to the periost of the bone (Biewener, 1991; Blob & Biewener, 1999, 2001; Main & Biewener, 2004). Although bending induced strains are supposed to play the major role in bone loading, it was noted, that there are "noTable exceptions to the predominance of bending 17 induced bone stress at the femora of certain rodents and the metapodials of the horse, which experience primarily axial compression during steady speed locomotion" (Biewener, 1991). The absence of correlation between regional histomorphometric patterns and the measured strain environments during limb bone loading was observed in bone of goats during ontogeny. Here it was mentioned that the potential effects of other physiological and mechanical factors, such as skeletal metabolism and adjacent muscle insertions, could influence the gross and microstructural morphology of the radius during ontogeny (Main, 2007). However, there is strong evidence that in the acting musculoskeletal apparatus bending moments are reduced to a certain degree and that bone is mainly loaded by compression. According to Pauwels (1965) the femur is exposed to bending moments superimposed by compressive stresses that are always higher than the occurring tensile stresses. Such a mechanism was termed as “flexural neutralization” by Frost (1964). Kummer (1962) stated that bones are functionally adapted to minimize the occurring bending moments, thus allowing for a reduction of the required bony material. If less material can be used to gain maximal stability, this is a great advantage for the living organism, as it reduces the amount of the invested energy (Rossmann et al. 2001; Witzel & Preuschoft 2005). Bending moments can be reduced either by active structures like muscles or passive elements like tendons and ligaments (Möser & Hein, 1992; Witzel 2007; Hert, 1994; Rudman et al., 2006; Witzel & Preuschoft, 2005; Sverdlova & Witzel, 2010). The optimization of bone as a light-weight structure was recently investigated by FE analysis of the human femur. The results of this study indicate accounts for that `bone formation takes place on the pathways of the compressive stresses` (Sverdlova & Witzel, 2010). Further evidence supporting the large influence of compressive stresses is provided by experimental studies focusing on the cellular development and genetically determined mechanisms in modelling and remodelling. Recent analysis of human osteocytes reveals the nature of cell proliferation after application of cyclic tensile strain using physiological amplitudes. Cell activity associated with primary matrix formation is increased, while further differentiation of osteoblasts and matrix maturation decrease. Therefore tensile stresses play a role in initiating proliferation in osteocytes in early stages of development, but do not account for bone formation itself, as it was postulated by Pauwels (1965; see Kaspar et al., 2000). There is a close relationship between cyclic compressive strains applied to cells and the release of bone formation related substances (Rath et al., 2008). Under static compression the chondrocytes produce growth factors leading to an increase in chondrocyte differentiation as well as their maturation, leading to ossification of the tissue (Takahashi et al., 1998). In contrast, tensile stresses inhibit the release of such metabolic products and therefore inhibit proliferation and arrangement of chondrogenic 18 cells (Sato et al., 1999; Ikegame et al., 2001). These studies strongly indicate mechanisms in which cartilage as a primary supporting tissue develops under the influence of compression loading, according to Pauwels causal morphogenesis. 1.6 Finite-element method (FEM) The relationship between bone formation and mechanical stresses can be investigated using the Finite Element Method (FEM). FEM is an approach widely used in engineering design for mechanical strength analysis of machine parts and structures. FEM is a technique used for the calculation of the strain, stress, and deformation in solid and liquid structures (Zienkiewicz, 2005). The mechanical response of a structure to external loading is described by a set of differential equations. In order to solve them, the structure is divided into a finite number of geometrical elements. Each element is connected to the neighbouring elements via nodes. The elements and nodes together build a finite-element mesh of the structure. This process of subdividing a structure is called discretization, pointing out that the whole calculation of stresses and deformation occurs at a discrete number of locations instead of at every point within the original structure. The solution of the differential equations within each of these elements then leads to a highly accurate solution. The software implementation of the FEM additionally is able to visualize the solution as stress distribution and deformation (Carter & Beauprè 2001; Zienkiewicz, 2005). It has been commonly used for medical application in orthopaedics for many years (Witzel, 1985, 1996, 2000; Carter & Beauprè, 2001; Effenberger et al., 2001; Sverdlova & Witzel 2010) but is recently applied in palaeontology and zoology as well (Daniel & McHenry, 2001; Rossmann et al. 2001; Rayfield, 2004, 2005; Dumont et al., 2005; Ross et al., 2005; Huber et al. 2005; Witzel & Preuschoft, 2002, 2004, 2005; McHenry et al., 2006; 2007; Witzel & Gössling, 2006; Witzel, 2006, 2007; Wroe et al. 2008; Gössling et al. 2008; Moser et al. 2008; Fujiwara, 2009). A survey of the application of FE-methods in biology and palaeontology was recently given by Rayfield (2007). The current research using FEM can be divided into two different approaches using the method, in an inductive and a deductive approach. In the inductive approach (FEA) the structure is analyzed according to adaptation and optimization of bone to a particular function (Rayfield, 2007). In FEA in-vivo stresses and strains are calculated within a virtual structure under an applied load. The FE models are generated based on CT scans of the object. FEA is mainly used for investigations of the skull, i.e whether bone is adapted to resist bite forces and other functional forces (Daniel & McHenry, 2001; Rayfield, 2003, 2004, 2005; Dumont et al., 2005; Ross et al., 2005; McHenry et al., 2006). Other studies used the FE- method for estimation of the maximal occurring bite forces in the white 19 shark (Wroe et al., 2008) or for investigation of the bending strength of the ribcage in quadrupedal animals (Fujiwara, 2009). Studies using FE by the inductive approach reveal the stresses occurring in a priori existing structures after application of mechanical forces but do not explain the development of bone shape as a response to mechanical loading. To compensate this lack of information, a more deductive approach was developed. The finite-element structure synthesis (FESS) is an interactive procedure of the virtual synthesis of skeletal structures out of a homogeneous solid block after applying muscle forces and calculation of the stress distribution in the structure. The bone hereby is viewed as a compressive structure, in which bending loading is compensated to eliminate tensional stresses, hence, the bony elements are synthesized according to the observed compressive stress pattern. This approach is essentially based on Wolff`s law and clearly demonstrates the direct correlation between the functional loading and the biological structure and shape. It was successfully applied to the skulls of extant (Witzel & Preuschoft 2002, 2004; Witzel et al. 2004) and extinct species. These were i.e. basal archosaurs as Proterosuchus (Rossmann et al. 2001), hominids (Homo neanderthalensis) (Witzel, 2006); and the skulls of sauropod dinosaurs (Witzel 2007; Witzel & Preuschoft, 2005). Ongoing studies apply the FESS to the skull of Plateosaurus (Goessling et al. 2008) and Herrerasaurus and in an investigation of sauropod vertebrae (Moser et al. 2008). 1.7 Aims and objectives As it has been reported, reconstructions of sauropod shoulder girdles are rare and mainly based on morphological homology with extant relatives or on functional analogies with extant tetrapods. To provide ground for morphological and functional comparison a series of data is collected. Mounted skeletons of the shoulder girdle of extant reptiles and mammals are described according to their overall anatomy and relative position to the trunk. The morphology of the coracosternal joint is described using mounted skeletons of extant lacertilians and crocodiles as well as based on histological cross sections of one crocodile specimen. The development of the shoulder girdle elements during both tetrapod and dinosaurian evolution is assumed to be closely connected to the respective locomotor type. The mechanical necessities of the single elements in the tetrapod body had not been investigated in detail. With the aid of the finite-element method (FEM) the stress flow in two generalized threedimensional solid tetrapod bodies, representing either a sprawling or extended limb posture, will be analyzed to determine the influence of gravity on the body. The occurring mechanical stresses then will be correlated to the presence of structural elements of the tetrapod body. 20 The current approach is based on the prediction of Wolff´s law and Pauwels causal morphogenesis that bone formation is mainly determined by compressive stresses resulting from mechanical function of the respective element in the musculoskeletal system of the vertebrate body. Following this assumption the mechanical function in each vertebrate musculoskeletal system can be determined from the shape of its elements and vice versa. The finite element structure synthesis (FESS) is a deductive approach to synthesize the shape of the original bone out of a primary generated bauraum, and in this study was initially applied to the post-cranial skeleton of vertebrates. The novel method FESS is first adapted to the shoulder girdle and the free forelimb of an extant crocodile (Caiman crocodilus) in order to evaluate the method to assess the mechanical principles of the shoulder girdle. Sauropods are supposed to exhibit graviportal functional adaptations in the shoulder girdle skeleton similar to those observed in large extant mammals e.g. in elephants. In contrast they exhibit reptile-like osteological features and muscle equipment similar to their extant relatives. Thus, reconstruction of the shoulder girdle function, only based on comparison with extant tetrapods, is assumed to be insufficient. Sauropods are assumed to exhibit an intermediate type of force transmission in the shoulder girdle, which has to be determined in the present investigation. Then it will be compared to the conditions in extant archosaurs (crocodilians) and mammals. In this case only little information on either function or behaviour of the animal exists. The only evidence is provided by the fossil record and the previous results of the FEM in tetrapod bodies and FESS in the crocodilian shoulder girdle. This will lead to basic conclusions about the arrangement of the shoulder girdle elements and limb posture in Diplodocus longus, according to the predicted mechanical requirements for a successful force transmission from the trunk to the forelimbs. With the aid of FESS the scapulocoracoid of Diplodocus longus is synthesized by, first, reaching static equilibrium between the elements of the shoulder girdle, trunk and forelimbs. The focus will be on the static condition in one limb stance to offer a precisely defined frame for the investigation, with a minimum of boundary conditions. The resulting compressive stress patterns then will serve as the blueprint for the final synthesis of the scapulocoracoid element. If the formerly predicted boundary conditions, like positioning of the elements and applied muscle forces required to maintain equilibrium in the shoulder-trunk-forelimb system, are valid the synthesis will reflect the original shape of the scapulocoracoid of Diplodocus longus, thus confirming the previously predicted reconstruction of the acting musculature as well as the position of the pectoral girdle under a biomechanical point of view. 21 The functional conditions in the shoulder girdle of Diplodocus longus, which are revealed in the present thesis, are discussed according to their relevance for reconstructions in scientific expositions and sauropod locomotion in general. Further it will be evaluated if the shoulder girdle of Diplodocus longus shows any body weight related adaptations that allow for an increase of body size, and whether the study contributes to current discussions in context of sauropod locomotor evolution. This approach will provide insight into the biomechanical conditions of the tetrapod shoulder girdle in general and the basic principles of the construction of the shoulder girdle in sauropod dinosaurs. A mechanically plausible reconstruction of the shoulder girdle in its natural arrangement is presented to reveal mechanically based functional adaptations for locomotor habits in these extinct giants. The correlation between form and function in the musculoskeletal system should be supported, by the determination of mechanical stresses as one major influence for the formation of bone. And finally FESS should be confirmed as a powerful method to test hypotheses regarding the relationship between structure and function during the evolution of the vertebrate skeleton. 22 Chapter 2 Material Table 1 The following Table shows the species examined, as well as their part investigated and the origin of the specimen. Species Investigated part Institution Abbreviation Alligator missisipiensis (skeleton) Overall anatomy of the shoulder girdle skeleton; Relative scapular position, Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD Alligator mississipiensis (dissected specimen) Determination of the shoulder girdle musculature; Estimation of muscle forces; Overall anatomy of the pectoral girdle. Crocodile farm „Renz“, Friedberg CFR Basiliscus plumifrons Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD Caiman crocodilus (skeleton) Overall anatomy of shoulder girdle skeleton used for modelling the 3-D FESS model. Preparatory School Bochum (DE) IAS Caiman crocodilus Overall anatomy of the shoulder girdle skeleton; Relative scapular position, Anatomy of the coracosternal joint. Institute of Zoology and Neurobiology RuhrUniversity Bochum (DE) MNHB Chamaeleo jacksonii Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) IZNB Chamaeleo lateralis Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) IZUB Chamaeleo melleri Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) PSB Cordylus giganteus Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD Crocodylus niloticum Relative scapular position; Anatomy of the Museum of Natural History MNHD Extant reptiles 23 coracosternal joint. Dusseldorf/ Aquazoo (DE) Cyclura nubilis Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD Diplodocus longus Overall shoulder girdle anatomy for modelling the 3-D FESS model Senckenbergmuseum Frankfurt (DE) SMF Diplodocus spec. Shoulder girdle anatomy; Morphology of the sternal plates. Sauriermuseum Aahtal (CH) SMA Tiliqua rugosa Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD Iguana iguana Relative scapular position; Anatomy of the coracosternal joint. Museum of Natural History Dusseldorf/ Aquazoo (DE) MNHD MNHM Early tetrapod Tiktaalik roseae(NUFV 108) Pectoral girdle morphology and body measurements. University of Chicago UC MNHD Mammals Bradypus spec. Relative scapular position. Institute of Zoology University of Bonn IZB Camelus bactrianus Relative scapular position. Institute of Anatomy, Université Louis Pasteur, Strasbourg (F) IAS Equus caballus Relative scapular position. Institute of Anatomy at the Université Louis Pasteur, Strasbourg (F) IAS Leo panthera Relative scapular position. Institute of Zoology University of Bonn IZB Rupicapra rupicapra Relative scapular position. Institute of Anatomy at the Université Louis Pasteur, Strasbourg (F) IAS Vicugna vicugna Relative scapular position. Institute of Anatomy at the Université Louis Pasteur, Strasbourg (F) IAS 24 Chapter 3 3.1 Methods Morphological data All pictures of the skeletal material and muscular dissections were photographed using a digital camera and processed using Adobe CS4. In this study it should be noted, that in the following, despite its different homology, the term coracoid is used for all coracoid-, procoracoid and metacoracoid elements, according to palaeontological conventions. Homologies concerning this term will be pointed out in the text if required. 3.1.1 Relative scapular position in reptiles and mammals For determination of the scapular position relative to the trunk in extant tetrapods, pictures were taken from mounted skeletons of various reptiles and mammals. (Table 1) 3.1.2 Coracosternal joint in extant reptiles Morphology of the coracosternal joint in extant reptiles (Table 1) was documented by digital pictures. The coracosternal joint in one Caiman spec. was dissected, described and cross sections were prepared. Selected cross sections were photographed and the distribution of cartilage and bony tissue in this region was described. 3.2 Muscles of the shoulder girdle in Alligator mississipiensis Pectoral girdle morphology was documented by dissection of one female Alligator mississipiensis (CFR). Gross anatomy of the musculature, as position, origin and insertion sites of each muscle as well as their principle function were documented, digitally photographed and compared with former descriptions (Brinkmann 2000, Meers 2002). Descriptions focus mainly on the muscular lines of action and function during transmission of body weight from the trunk to the shoulder girdle and maintenance of equilibrium. Measurements include total area and crosssectional area of each muscle. Total area was estimated by drawing the muscle’s outline on millimetre paper. Cross-sections were taken through the centre of mass, perpendicular to the main fibre direction. Cross-sectional area then again was measured by drawing its outline on millimetre paper. Maximum muscle force Fmax of each shoulder girdle muscle in the alligator specimen was estimated by multiplying their anatomical cross-sectional area (A) by the specific 25 tension (Tsp) of reptiles. A specific tension of about 0.2 N/mm² in this case refers to the desert iguana (Medler 2002). 1) Fmax = A * Tsp 3.3 Basic mechanical principles Biomechanics can be viewed as the link between the engineering and biology, investigating biological problems with the aid of the mechanical principles. Before discussing the applied methods in detail, a short introduction into the basic mechanical principles is presented providing the basis for the following investigation. Force F is a measure of the intensity of the interaction of bodies. Force causes the change of velocity of a body or the deformation of a body. Force is measured in Newton (N) and has units of mass m multiplicated by acceleration a: 1 N = 1 kg * m/s² 2) F = m * a, Moment of force (M) is the product of force (F) and lever arm (l) given as kg *m/s² *m [Nm]. 3) M = F * l The system is in equilibrium when the sum of all forces and moments is zero. 4) ∑ Fi x,y,z = 0, with F acting in all directions of the coordinate system. 5) ∑ Mi x,y,z = 0, with M acting about all coordinates. In an elastic body external forces produce internal stresses and strains. Stress (σ) is the measure of local intensity of a force (F) per unit area (A) and is measured in N/mm² [MPa]. As tensile stress (σ+) leads to an increase of the initial length, it is positive by sign. Compressive stress (σ-) results in a negative elongation, therefore, it has a negative sign. 6) 26 σ=F/A Strain (ε) can be regarded as local deformations depending on the material properties of the object and describes the relative elongation (Δ l) of the body. 7) ε = (l0 – l1)/l0 Young`s modulus (E) defines the ratio of the stress σ to the strain attained by the deformation. Young`s modulus therefore is an indicator of the stiffness of the material and is given as N/mm² [MPa]. 8) E = σ/ Figure 7 Scheme showing two dinosaurs of different body weight standing on a scale in equilibrium, demonstrating the relationship between (weight) forces and moments in a static system. F1 and F2 are the acting forces, whereas Fr1 and Fr2 indicate reaction force of the same value, acting into opposite directions. L is the lever arm (distance from the insertion point of the force to the pivot of the beam). M is the resulting moment that rotates the beam. 3.4 Finite-element method (FEM) The finite element method (FEM) in this thesis is used in two different approaches. In a first step the mechanical stresses, which result from defined loading conditions after calculation, are analysed and applied to investigate mechanical stresses in solid tetrapod bodies and a 2-D FE model of the crocodilian shoulder girdle. The second approach, the finite element structure synthesis (FESS), is applied to investigate the mechanics of the crocodilian and sauropod shoulder girdle system. Both approaches share a number of methodological procedures and element descriptions, except for the synthesis in FESS. Therefore, the reduction of the bauraum is the most distinguishing part between these two approaches, and only refers to the FESS. 27 3.4.1 Generation of the model All finite element (FE) modelling and calculations in this work are carried out by the FE program ANSYS Inc. This FE program allows the attribution of different material properties to each volume of the FE model e.g. Young´s modulus, Poisson`s ratio and material density. Modelling procedure starts with creating the geometrical model with corresponding material properties, which is then subdivided into the finite elements building the FE mesh. After that the so-called boundary conditions are defined for the meshed FE model. The boundary conditions comprise the loading through the external forces and of the constraints of the free body motion in space. The external forces, which are applied in this approach indicate gravitation, body weight or are related to acting muscles. In this investigation two different approaches are used to indicate acting forces in a FE model, which are link elements and single, directed vectorial forces (Fig. 8). 3.4.2 Link elements Muscle action can be simulated by link elements, which represent the required muscles in the original anatomy of the subject. The origin and insertion sites of the considered muscles are therefore obtained from the literature. These link elements work like active springs holding each element in its relative position thus preventing large relative motion of the elements during calculation (Fig. 8). Pre-tension of each link element is defined by the link crossectional area A (mm²) and the initial strain , which is the relative elongation of the link element (Δ l/l), which depends on the Young´s modulus E (N/mm²) of the material chosen for the link elements. The forces produced by the link elements in the pre-tension in the initial state as well as in the deformed state can be calculated as follows: 9) F = σ * A, whereby σ = * E After the calculation, resulting stresses within the working links can be detected. As the applied forces are closely related to link stresses and as stress values in the links change during calculation due to the deformation of the bodies, the resulting forces differ from the initial desired values as well. To ensure the agreement of link forces with the desired external forces they have to be calculated precisely following a number of equations. As the presented approach is not suiTable for a determination of absolute muscle forces, the occurring stress values after calculation are only described qualitatively. Because of their stabilizing properties during FE calculations, which are thought to be required to reach equilibrium in the system, link elements 28 are applied in a primary investigation step. They are used to evaluate, whether the FESS could actually be applied to a multi-body system. 3.4.3 Vectorial forces Instead of link elements single forces can be used in FE calculations. Hereby defined forces are applied to the nodes in the meshed FE model. Forces are always indicated as arrows (Fig. 8). To modify the direction of the force, the node can be rotated in all directions of the coordinate system. In order to simulate muscle action, one pair of forces is required. Both forces are of the same value, but with different algebraic signs and are orthogonally directed to each other. Therefore, one acting muscle can be indicated by one single force or by a bunch of forces, which in sum refer to the total force value. 3.4.4 Bearings A FE model, which is positioned in a 2-D, or 3-D space must be restricted in all three or six degrees of freedom, respectively. Otherwise the model would move according to internal or external loading. This is accomplished by application of bearings to nodes in the model, which are indicated as triangles (Fig. 8). Bearings restrict movement in all degrees of freedom or in required directions, which refers to the actual situation. For example, if only vertically translational movements should be restricted, only y-directed bearings are required. After calculation reaction forces can be read out from some of the restricted nodes. These bearings are then termed indicator bearings, as the relative movement of the model is indicated by the direction of the resulting reaction forces at this location. This is a useful instrument to gain information about the statical situation of the model during adjustment of equilibrium in the FE model and to determine the influence of the applied link elements or forces. 3.4.5 Stress distribution After the calculation the distribution of the compressive stresses in the FE model is shown by a contour plot. The spectrum of colours in the contour legend is according to the selected numeric spread. The regions with high compressive stresses appear blue; the regions with low compressive stresses are red, tensile stresses are coded in opposite direction. Grey colours indicate regions, in which stresses are beyond the selected spectrum (Fig.8). In order to decrease areas, which are beyond the spectrum, the spread can be adapted to the maximum compressive stress value. This in turn decreases the amount of indicated lower stresses and has to be applied according to the respective situation, whereas in some cases even the lower stressed areas contain necessary information. 29 3.4.6 Contact elements To enable relative movements and transmission of mechanical stresses between the adjacent parts in the model, contact-elements were applied to the contact and target surface between the trunk and the scapulocoracoid element, as well as between the humerus and glenoid surface and within the elbow joint. Contact element properties depend on the friction coefficient, which determines the resulting friction between the adjacent areas. 3.4.7 Reduction of the bauraum The term bauraum is here used exclusively for the scapulocoracoid volume, as the synthesis refers only to this element. The other elements (trunk, humerus, antebrachium) act as surrogates for the original components. They are required to allocate the muscle forces in the 3-D space and serve as mechanical counterparts to simulate the situation in an active shoulder girdle system. In a number of iterative steps, the primary defined volume is reduced by selecting the stress bearing areas. The bauraum is modeled only in an approximation to the dimension of the original structure, and therefore leaves ample space for the spreading stresses. Consequently, the resulting stresses after calculation and before the first reduction step are below the threshold of the predicted physiological value (-2 MPa). The numeric spread of the contour legend is selected to reflect the approximate shape of the desired structure, besides the absolute stress value. As compressive stress value is defined by compression per unit area, a decrease of the area will correspondingly result in an increase of the resulting stresses, since the bauraum is reduced. As soon as the stresses are above the critical threshold of -2 MPa the regions of the geometrical model with stresses below the threshold of -2 MPa are removed simulating the atrophy of the unloaded bone. In early reduction steps, the threshold can be adapted to lower values, in order to preserve the structural integrity of the model. The reduction of the bauraum is completed for the selected cross-sections of the scapulocoracoid volume. After the reduction of the selected cross-sections, the new reduced bauraum is formed. In the next FESS iteration, the FE mesh is generated for this reduced bauraum and the stress distribution is obtained under the initial boundary conditions. The reduction and FE calculation steps are applied iteratively until a physiological level of compressive stresses is reached in the reduced model. In the present investigation, a physiological compressive stress value for bone between -2 and 20 MPa is predicted. Values betwee -2 MPa to -9 MPa corresponds to cancellous bone; for compact bone a range of -9 MPa to -20 Mpa is assumed (Witzel & Preuschoft, 2005). 30 Figure 8 2-D FE model of a simple beam (100mm x 50 mm), indicating the symbols for the boundary conditions, which are described in the text. Youngs modulus is 17 GPa, Poisson´s ratio is 0.3. A: Meshed 2-D FE model before calculation, restricted by bearings (orange triangles) at the right side; one single force (10N) is placed at the left side (red arrow). After calculation the beam is subject to bending, which compresses the ventral and stretches the dorsal side of the beam (B,C,E,F). B: 2-D FE model after calculation with the highest compressive stresses (blue-green areas) appear at the ventral side. Low compressive stresses (red) can be detected at the dorsal side. Grey areas are beyond the visible spectrum in selected spread. Numeric spread is -2.7 MPa to 0 MPa, indicated at the contour legend. Deformation is indicated by black outlines showing the situation before calculation. C: FE model after calculation with the highest tensional stresses at the dorsal side (red-orange). Numeric spread is 0 MPa- 2.7 MPa, indicated at the contour legend. Again grey areas are beyond the visible spectrum in the selected spread. D: Meshed 2-D FE model with a pre-tensioned link element (green line) instead of a directed force. Cross section of the link element is 1; Pretension is 0.1. E: Resulting compressive stress distribution after calculation. Numeric spread of the contour legend is -9 MPa to 0 MPa. F: Resulting tensional stress distribution after calculation. Numeric spread is 0 MPa- 9 MPa. Description of stress distribution is equal to B and C. 3.5 3-D FE models of two generalized tetrapods For investigation of basic stress distributions in tetrapod bodies during terrestrial locomotion and for evaluation of the predicted differences between a sprawling and extended limb positions of the forelimbs, two rather basic 3-D FE models are created. 31 Overall anatomy and relative mass distribution of the first FE model corresponds to that of Tiktaalik roseae an early Devonian tetrapod representing the sprawling-type (Fig. 9,10,11). Tiktaalik roseae was chosen by the author because of its primary morphological features and its palaeontological relevance as a basic tetrapod. The model shows only the forelimbs, whereas the hindlimb section is rested on the ground (Fig. 11). This is due to two reasons. First, the study is focused on the forelimb section and the pectoral girdle. Second, the hindlimbs of Tiktaalik roseae were not available at date, so that no reliable data could be obtained from the fossil (Shubin, personal communication). The measurements are based on own measurements of the original fossil (postcranial skeleton) completed by the author (Fig. 9); and the scaled figure reported in the original description (skull) (Daeschler et al. 2006) (Fig. 10). Figure 9 Shoulder girdle of Tiktaalik roseae (NUFV 108) in lateral (A), frontal (B) and dorsal view (C). 32 . Figure 10 Dimensions of the Devonian fossil Tiktaalik roseae (redrawn after Daeschler 2006), in lateral view (upper sketch) and in dorsal view (lower sketch). Dimensions are given in mm. The models are subjected to gravitational forces, whereas the distribution of both compressive and tensile stresses is described after calculation. First, the static condition is characterized by a symmetrical limb support at the shoulder region with both forelimbs supporting the body weight. In the second case, the asymmetrical support during consecutive phases of a movement cycle is represented by a one-limb support at the shoulder region; a situation similar to that in walking. All parts of the models possess equal material properties to ensure that the stress flow is undisturbed and not bundled in the areas with higher stiffness. Young´s modulus is 10 MPa; Poisson`s ratio is 0.3, both refer to the average values estimated for vertebrate bone (Carter & Beauprè, 2001; Kummer, 2006). Limbs with ground contact show bearings, which restrict movements in the y-axis. Forces (red arrows) applied to the models indicate the limbs held off the ground like in walking (Fig. 11, 12). The weight is defined by the model’s volume, density (equal to that of water) and the gravitational acceleration (9.82 m/s²). Figure 11 FE-model of the “sprawling” type in oblique (A) and dorsal view (B). Left forelimb is held off the ground (acting forces; red arrows), right forelimb has ground contact (bearings; yellow triangles). Hindlimb section is resting on the ground (bearings; yellow triangle). Coordinate system is placed at the right corner 33 The second model reflects the situation in extant cursorial mammals with the position of the limbs under the body (extended-type). The model is characterized by a rounded trunk, a long neck and massive head and columnar legs held under the body (Fig. 12). Overall mass distributions refer to a medium-sized equine tetrapod. Fig. 12 FE-model of the “extended” type in oblique view. Left forelimb and right hindlimb have ground contact (bearings: yellow triangles), right forelimb and left hindlimb are held off the ground (acting forces: red arrows). Coordinate system is placed at the right corner. 3.6 2-D FE model of a crocodilian shoulder girdle In order to investigate the static conditions in the crocodilian shoulder girdle an FE model is created, where the single shoulder girdle elements are placed in the observed anatomical position. Pictures in frontal and lateral view were taken in order to define the dimensions of each element. The pictures were transferred to millimetre paper in order to generate the geometrical coordinates for the FE modelling as input for the FE program, building two 2-D models in frontal and lateral view (Fig. 13). By this procedure the bauraum of the present model is defined by the dimensions of each element of the shoulder girdle system, the trunk, the scapulocoracoid, the humerus, and the antebrachium. Therefore the elements of the FE model can be viewed as substitutes for the original structure. In contrast to the finite element structure synthesis (FESS) (Witzel & Preuschoft, 2005), the compressive stress distribution in this case is only analysed, and therefore leaves out the final synthesis of the structure. Nevertheless, the basic movements and conditions in a FE multi-body system can be revealed and used for the following 3-D FESS. 34 . Figure 13 Pictures of a Caiman skeleton, in frontal (A) and lateral (C) view. Dimensions of the original, indicated as black outlines, are transferred into coordinates, in order to build the bauraum of the 2-D FE model in frontal (B) and lateral (D) view. Two 2-D FE models, one in frontal (Fig. 14), and one in lateral view of the object (Fig. 15), are calculated. The model consists of four single areas, the trunk, scapulocoracoid, humerus, and antebrachium (Fig. 14,15). As one limb stance is in the focus of the current investigation, only one-half of the body is modelled in order to minimize the calculation time. Material properties are Young`s modulus (17 GPa), which is according to cortical bone and Poisson`s ratio (0.3) (Witzel & Preuschoft, 2005). Body weight force (100 N) is applied to the trunk on one single node, which is calculated out of an assumed body weight (10 kg) supported by the forelimb in one limb stance multiplied with gravitational acceleration (9,81 m/s²). At the adjacent surfaces between the trunk and scapulocoracoid, as well as within the joints, contact-elements are applied. Considering the possible movements of each part of the model, link elements representing the relevant shoulder muscles to maintain balance are determined. Each link element exhibits a Young`s modulus, equal to vertebrate muscles, a pre-tension of 0.01 and a cross section of 0.1 mm². Relative motions of single elements are constrained by bearings. The trunk is allowed to move vertically, whereas the antebrachium is free to move sidewards (Fig.14,15). 35 Figure 14 Simplified 2-D FE model of the crocodilian shoulder girdle in frontal view. Trunk (light blue), scapulocoracoid (orange), humerus (grey), antebrachium (deep blue). Link elements representing the shoulder girdle muscles: m. pectoralis (1a,b), m. serratus (2), m. rhomboideus (3), m. subscapularis (4), m. deltoideus (5), m. coracobrachialis (6), m. triceps caput coracoideum (7), m. brachialis (8). Bearings are applied to the trunk and the antebrachium in order to allow vertical and horizontal movements, respectively. Figure 15 Simplified 2-D FE model of the crocodilian shoulder girdle in lateral view. Trunk (light blue), scapulocoracoid (orange), humerus (grey), antebrachium (deep blue). Link elements represent: m. pectoralis (1a,b), m. serratus superficialis (2a-d), m. serratus profundus (5), m. deltoideus (6), m. triceps caput humerale (7), m. triceps caput coracoideum (8), m. triceps caput scapulare (9), m. trapezius (10), m. levator scapulae (11), m. latissimus dorsi (12), m. scapulohumeralis (13), m. costo-coracoideus (14), m. brachialis (15). ). Bearings are present at the trunk and antebrachium and allow vertical and horizontal movements, respectively. 36 In this part of the approach, link elements were applied instead of the directed forces, which relate to the crocodilian shoulder girdle muscles. The origin and insertion sites of the considered muscles are obtained from the literature (Brinkmann, 200; Meers, 2003) (Table 3). In order to focus on the mechanics in the shoulder girdle system, the muscles need to be considered according to their mechanical properties. The muscle functions, which maintain balance in frontal and lateral planes, differ from each other. In frontal view, muscles are required, which act in the x,y-plane, in order to stabilize the shoulder girdle latero-medially and dorso-ventrally. In lateral view, cranio-caudal stabilization is maintained by muscular structures, which act in the y,z- plane. The calculation is finished when the equilibrium in the shoulder girdle system is established by determination of the required links, which refer to the shoulder girdle muscles. 3.7 3-D FESS of a crocodilian shoulder girdle In the synthesis part of the study the basic conditions of the frontal and lateral 2-D model are transferred into a 3-D model (Fig.16). This combination includes the coordinates (x, y, z) in space, the arrangement of the link elements, and the restriction of movements of the model in the 3-dimensional space. Again only one-half of the shoulder girdle is modelled in order to decrease calculation time. The model consists of four independent volumes, the trunk, scapulocoracoid, humerus, and antebrachium (Fig.16). Similar to the 2-D model pre-tensioned link elements are used instead of the direct force application. Body weight force refers to the 2-D FE model. Again material properties are defined as Young`s modulus (17 GPa), according to cortical bone and Poisson`s ratio (0.3) (Witzel & Preuschoft, 2005). The relative motion of each single element in the FE model corresponds to the situation in the living object. The hindlimbs prevent caudally directed movements, whereas medially directed movements are prevented by the other body half. These restrictions are realized by bearings in caudal and medial direction, respectively. The trunk should be able to move vertically and in horizontal directions, while the antebrachium is restricted to vertical movements, by bearings directed in the y-axis (Fig.16). Link elements are applied iteratively in order to determine their function in maintaining the static equilibrium in the shoulder girdle. Each link element corresponds to a shoulder girdle muscle based on the original crocodilian anatomy. Since equilibrium in the shoulder girdle is accomplished, the scapulocoracoid and the humerus are able to move free from constraints and only held in position by the acting links (Fig.16). The calculation is finished when the equilibrium in the shoulder girdle system is established by determination of the required links, which refer to the shoulder girdle muscles. 37 Figure 16 3-D FE model of the shoulder girdle region of Caiman crocodilus in oblique view. Trunk element is grey, with applied weight forces (arrows) and bearings in x-and z-direction (red triangles) up-and downward movements are possible). Scapulocoracoid element and humerus are light blue. No bearings are applied, indicating free range of movement. The element representing the antebrachium is deep blue showing bearings in y-direction (red triangles; fore-and sideward movements are possible). 3.8 3-D FESS Diplodocus longus The sauropod scapulocoracoid, which is going to be synthesized using FESS method in the present thesis, is part of the mounted skeleton of Diplodocus longus (SMF) (Fig.17a,b). The bilateral sternal plates and claviculae are missing in this mount. For completion of the sauropod shoulder girdle, the appearance and dimensions of the sternal plates and the claviculae from the Diplodocus specimen HQ1 (SMA) are included (Fig.17,c,d). Similar to the FESS of the crocodilian shoulder girdle, the investigation of the scapulocoracoid in Diplodocus longus starts by building the bauraum based on the original dimensions of the bony elements. By contrast, the FESS in this fossil requires additional considerations. As the arrangement of the shoulder girdle elements in the skeleton are in the focus of the investigation, the mechanical preconditions for this arrangement had to be expressed. Not until then, the original dimensions of the bony elements can be transferred to a 3-D FE model of the shoulder girdle system. Subsequently, the body weight force of the frontal part of the trunk is estimated, and the determination of the applied muscle forces and calculation of static equilibrium in the model are described. 38 Figure 17 Diplodocus longus (SMF) in lateral (A) and frontal view (B). Note the distance between both coracoidea in frontal view. The mount lacks the sternal elements and clavicles. Diplodocus HQ1 (SMA) in frontal (C) and lateral view (D). Sternal elements and clavicles are present. A und D in lateral view: The different positions of the scapula between the two mounts are visible. 3.8.1 Mechanical considerations for building the bauraum The construction of the model including the bauraum for the FE structure synthesis is one of the most crucial parts of the modelling, because the arrangement of the single elements has a profound impact on the equilibrium and stress distribution in the system. The arrangement of the bony elements and the musculature in FESS of the crocodilian shoulder girdle could be established based on the well-known morphological and empirical data obtained from extant species. In contrast, the shoulder girdle architecture in sauropods is largely unknown. The only elements on which one can base the investigation of the body structure is presented by single 39 bony elements. Concerning the anatomical position of the bony elements, musculature, tendons, and ligaments, or even cartilaginous parts only few information is available to date. Consequently, the shoulder girdle elements need be reconstructed based on, first, basic morphological conditions, which are valid in all extant tetrapods; and, second, based on mechanical considerations in regard to the evolution of the tetrapod shoulder girdle and its function in statical loading conditions. The morphological conditions can be obtained from the morphological comparison in extant reptiles, lacertilians, and mammals investigated in this study. The mechanical conditions refer to the results of the analysis of solid tetrapod bodies and the FESS of the crocodilian shoulder girdle. It is predicted by the basic principle in this approach that the form always follows the function. According to this, in the course of the investigation, those mechanical conditions of the shoulder girdle system are determined, which lead to the observed shape of the scapulocoracoid. As the mechanical conditions are ascertained with the aid of FESS, the anatomical position of the shoulder girdle elements as well as the required musculature is reconstructed. Furthermore, the magnitudes of forces are determined and lead to the estimation of the muscle volumes required in one limb stance. To confirm the obtained results, the reverse argument of the approach can be used. This would imply that invalid mechanical considerations would prevent static equilibrium in the shoulder girdle muscles and therefore a successful synthesis of the scapulocoracoid of Diplodocus longus. To prevent circular reasoning, the model is built using only assumptions known to fulfil the mechanical necessities required to maintain the function of the shoulder girdle during one limb stance. Function hereby means transmission of body weight from the trunk to the forelimbs, whereby each element of the multi-body system is kept in equilibrium by the acting muscles. Mechanical considerations for the arrangement affect the inclination of the scapula, the relative position of the scapulocoracoid to the ribcage, position of the sternal elements and finally the posture of the humerus at the glenoid joint. Those preconditions, which can be confirmed by the successful synthesis of the scapulocoracoid, will provide ground for reconstruction of the shoulder girdle elements. The reconstruction of the shoulder girdle in Diplodocus longus is presented in the results. The bauraum representing the scapulocoracoid is positioned more cranially in comparison to the original and lies parallel to the lateral side of the trunk. The caudal edge of the bauraum exhibits an angle of about 60° to the horizontal. The coracoid part of the bauraum contacts the most ventral part of the trunk medially. Two positions of the humerus are considered. In the first 40 limb position the humerus in frontal view is directed orthogonally to the glenoid joint, while in lateral view an angle of about 20° to the perpendicular is assumed (Fig.18a,b). In the second model, the humerus is slightly abducted in frontal view, with an angle of about 15° to the perpendicular, while lateral position is similar to the first case (Fig.18a,c). Both models reflect the static situation occurring in one limb stance. Total body weight of the frontal part of the trunk is carried by the forelimbs, while the rest is assumed to be supported by the hindlimb section. 3.8.2 Generation of the model In this part of the study, pictures were taken from the mounted skeleton in frontal and lateral view (Fig.17). Skeletal elements of the Diplodocus specimen taken into account comprise the mounted ribcage, the left scapulocoracoid, left humerus and the left lower forelimb. Dimensions were first determined by drawing the pictures of different views to millimetre paper afterwards coordinates are transferred to the FE program to generate the geometric 3D-model. Similarly, to FESS of the shoulder girdle in crocodiles only one half of the body is modelled in order to reduce calculation time (Fig. 18). The geometry of the bauraum is according to the dimensions of the original scapulocoracoid, but leaves ample space for the occurring stresses. The humerus is reduced to a rod and two spheres, which represents the humerus shaft and its proximal and distal joint surfaces, respectively and according to the original dimension of the fossil (Fig. 18). The element representing the lower forelimb is modelled as a cube with an impression for the distal humerus joint surface to serve as the elbow joint. The trunk includes the frontal part of the body stem up to the seventh cervical rib and the eighth thoracic rib. The most cranio-ventral part is extracted to provide a contact surface to the medial side of the scapulocoracoid. Young`s modulus in the model is 17 GPa, Poisson`s ratio is 0.3 (Witzel et al. 2010). Contact elements are applied to the contact areas of the shoulder and trunk, the coracoid and sternum as well as in the glenoid and elbow joint to provide force transmission. Further contact elements are applied along the adjacent areas of the scapula and the trunk.. 41 Figure 18 3-D model of the shoulder region of Diplodocus longus (A-D). In lateral view, with a flexion of the humerus relative to the glenoid joint of about 20° (A). Forelimb position one with the humerus directed vertically to the glenoid joint (C). Forelimb position two, with the humerus slightly abducted (20°) (D). Outline of the model in lateral view (E). Body weight forces (arrows) are distributed along the trunk. Bearings at the trunk are positioned in medial and anterioposterior direction to prevent relative movements; up and downward movements are enabled. Fixed bearings at the antebrachium prevent all relative movements. No bearings are applied at the scapulocoracoid and the humerus and will be held in position only by muscle forces, which are determined during the investigation in further steps. 3.8.3 Estimation and distribution of body weight For investigation of body weight transmission in the shoulder girdle, total body weight in Diplodocus has to be determined. Body weight represents the initial forces, countered by muscle forces in order to reach equilibrium in the shoulder girdle system. Determination of body weight in Diplodocus was calculated from body volume, specific density and earth acceleration. A body volume of about 13421 m3 for Diplodocus is taken from the literature (Henderson 1999). Under consideration of the assumed pneumatised postcranial bones, specific density in the living animal was supposed to be 0.8 (Wedel 2003a, 2003b, 2005; Gunga 2007). Thus, total body mass can be stated as 10,736 t. 42 In this investigation one limb stance is approximated to the situation in elephants. In elephants body weight is commonly supported by at least three limbs during locomotion; or by one forelimb support during every movement cycle (Hutchinson et al., 2007; Ren et al., 2008). According to Henderson (2006) the centre of mass in Diplodocus is located anterior to the pelvis. This is calculated for the present study as 11% of 2.5m, which is the total distance between the shoulder and pelvic joint. Therefore, average load on the forelimbs is 18% of the total body weight. In the present model this accounts to 966,24 kg acting on each forelimb in four limb support. If one forelimb is held off the ground this mass is doubled to 1932,48 kg. Multiplication with earth acceleration (9,81 kg*m s-²) results into a load of about 18957 N during one limb stance and 9478 N if both forelimbs contribute to body support, respectively. Total body load of about 18958 N is distributed evenly along the body axis of the trunk volume. 3.8.4 Muscle reconstruction Currently no complete and reliable description of the shoulder girdle musculature in sauropod dinosaurs exists. The comparison with the shoulder girdle musculature of extant crocodiles only provides basic information about the equipment and configuration of the shoulder girdle musculature applied to the FE model (Tab. 2 ). Therefore, the origins and insertions sites of the muscles, and their lines of action have to be determined during the process, according to the mechanical requirements in each calculation step. Similar to the FESS of the crocodilian shoulder girdle, the muscle forces are applied to the system in iterative steps, in order to reach equilibrium between the trunk, scapulocoracoid and humerus, whereby the situation in the elbow joint is not considered in detail. Since static equilibrium in the shoulder girdle is accomplished, muscle forces exert mechanical stresses onto the bauraum of the scapulocoracoid. As mentioned in the former paragraph, the distribution of compressive stresses should be in accordance with the fossil. Consequently, the former precluded muscle forces and the arrangement of bony elements are confirmed. 3.8.5 Calculation of static equilibrium In the following, static equilibrium of the 3-D multi-body FE model is calculated, first, with regard to the principle stress distribution within the bauraum of the scapulocoracoid. Since static equilibrium is maintained, the stresses are refined by modification of the acting forces. In the shoulder girdle system, equilibrium results from the weight force (Fg) and the ground reaction force (Fgr). Equilibrium is maintained, when the sum of forces, acting in the shoulder girdle system, is near zero. In the present case, this can be accomplished by reduction of the rotational moments at the joints and translation of the elements by means of muscle forces. The initial 43 situation, where the only applied forces relate to the body weight, is the basis for each calculation step. The relative motion of the single elements in the shoulder girdle FE model corresponds to the situation in one forelimb support. As it was described in case of the crocodilian FE model, the hindlimbs in the living animal usually prevent caudally directed movements. The medially directed movements are prevented by the contralateral body-half. The restrictions in the FE model are indicated by bearings in caudal and medial direction, respectively. The trunk element is able to move vertically, while the antebrachium is restricted to downward movements, by bearings in the y-direction. The scapulocoracoid is only restricted by indicator bearing, until equilibrium is accomplished. Then the scapulocoracoid and the humerus are free from restrictions and positioned only by the acting forces, which are related to the shoulder girdle musculature. 44 Chapter 4 4.1 Results Morphology of the shoulder girdle 4.1.1 Comparison of extant reptiles and mammals The following figures illustrate the morphology of the shoulder girdle in extant reptiles (Fig. 19,20,21) as well as in extant mammals (Fig.22). The examined reptiles belong to five different orders, Iguania, Sphenodontidae, Cordylidae, Scincidae and Crocodylia. The described mammals comprise the Artiodactyla (Equus cabalus, Rupicapra rupicapra), Felidae (Panthera leo) and one Xenarthra (Bradypus spec.). Structural relationships such as the relative position of the shoulder girdle to the ribcage and forelimbs in reptiles and mammals, as well as the morphology of the coracosternal joint in reptiles are displayed. In lateral view, the shoulder girdle in extant reptiles and mammals is always positioned cranially covering the first ribs, or even in front of the ribcage. In top view, the scapula is always positioned nearly parallel to the vertebral column. In lateral view the distal margin of the osseous scapula or the cartilaginous suprascapula extend nearly parallel to the dorsal margin of the vertebral column. The lateral inclination of the scapula, determined as the angle between the caudal margin of the scapula and the horizontal plane, ranges from 50° in crocodilians to 60° in mammals and chameleons. In all examined reptiles a ventrally positioned tongue-and-groove coracosternal joint is present. In lacertilians this joint is bony (Fig.19b,c,f; Fig.20b,c; Fig.21e,f), the sternal part is acting as the groove and the coracoid part as the tongue, together forming a sliding rim. Basiliscus plumifrons hereby makes an exception. The most cranial part of the medial side of the coracoid consists of cartilage, whereas the caudal part is osseous. The sternal element is a compact bony structure. In crocodilians those parts of the sternal and coracoid elements that form the tongue and groove system consist of cartilage, which fulfils the same function (Fig.21a,b). For a more detailed observation of the condition in crocodiles see the histological cross sections of the coracosternal joint in one caiman (Fig.22,23). 45 Figure 19 A: Cyclura nubila, shoulder girdle position in top view. B:Cyclura nubila, dorsal view of coracosternal joint, arrow points to tongue and rim structure. C: Basiliscus plumifrons, oblique view of the shoulder girdle in relation to the coracosternal joint (arrow) and the ribcage. D Basiliscus plumifrons, top view of the parallel position of the dorsal margin of the scapula. E: Iguana iguana, top view of the parallel position of the dorsal margin of the scapula. F: Iguana iguana, frontal view at the coracosternal joint (arrow). Note the most cranial part of the coracoid is cartilaginous 46 Figure 20 A:Cordylus giganteus, lateral view of the relative position of the shoulder girdle. B: Cordylus giganteus, frontal view to the coracosternal joint. C: Tiliqua rugosa, top view of the parallel position of the dorsal margin of the scapula. D: Tiliqua rugosa, dorsal view of the coracosternal joint (arrow). E: Sphenodon punctatus, lateral view showing the cranial position of the scapulocoracoid overlying the first ribs, together with a slight inclination of the scapula and parallel position of the dorsal margin of the suprascapula. 47 Figure 21 A: Crocodilus niloticus, lateral view of the overall position of the shoulder girdle, the inclination of the scapula and its orientation parallel to the ribcage. B: Crocodilus niloticus, frontal view of the cartilaginous parts of the sternocoracoid joint forming a rim and tongue structure. C: Chamaeleo jacksonii, lateral view. The shoulder girdle is positioned in parallel to the ribcage, the glenoid lies anterior to the ribcage and the scapula overlies the first ribs. D: Chamaeleo melleri, lateral view. E: Chamaeleo melleri, ventral view of the coracosternal joint. F: Chamaeleo lateralis, ventral view of the coracosternal joint. 48 Figure 22 A:Equus caballus, lateral view, The scapula covers the first ribs, while the glenoid region is positioned in front of the ribcage. B: Equus caballus, view through the ribcage from posterior showing the narrowed trunk at the level of the shoulder girdle and its parallel position relative to the ribcage. C:Bradypus spec., lateral view showing the relative position of the shoulder girdle and dorsal margin of the scapular. D: Leo panthera, lateral view of the shoulder. The scapula covers the first dorsal ribs, the glenoid is positioned shortly before the rib cage. E: Rupicapra rupicapra, lateral view displays the shoulder girdle overlying the first dorsal ribs, while the glenoid is positioned anterior to the first rib. F: Rupicapra rupicapra, dorsal view of the parallel position of the scapula relative to the ribcage. 4.1.2 Histology of the coracosternal joint in Caiman spec. The coracosternal joint in one caiman was dissected, described and a number of cross sections were taken for further preparation. The transverse sections through the coracoid and 49 sternum were stained and prepared for histological description. The pictures show the coracosternal joint consisting of cartilage. The cartilaginous part of the sternum forms a groove, while the coracoid acts as the tongue (Fig. 24). The joint is embedded in connective tissue and is surrounded by a joint capsule. Thus, the coracosternal joint exhibits all features of a real joint, compared to other joints as the glenoid joint or the knee joint. Figure 23 Shoulder girdle of Caiman spec. in ventral view. The scapula (Sc) and the coracoid (C) are drawn laterodorsally to open the coracosternal joint. The cartilaginous tongue (coracoid) and groove (sternum) are visible. For investigation of the internal structure of the coracosternal joint, transverse sections were taken in anterio-posterior direction through the articulated joint (Fig. 23). The cross sections were stained to distinguish the two types of tissue, bone and cartilage. In the coracoid tongue a proximal bony part and a distal cartilaginous part are present, whereas the distal part surrounds the bony structure of the coracoid tongue (Fig.24 a-c). In the sternal part only cartilaginous tissue can be recognized (Fig. 24 a-c). In the most anterior section the sternal rim is compact cartilage at the dorsal side of the rim and consist of connective tissue fibers at the ventral side. The connective tissue fibers surround the ventral side of the sternal rim and of the coracoid (Fig. 24 ab). In the most posterior section the entire rim consists of cartilage, which surrounds the distal coracoid tongue (Fig. 24c). 50 Figure 24 Frontal cross sections through the sternocoracoid joint in Caiman crocodilus. Cranial section (A); middle section (B) and caudal section (C). Bony tissue is stained red; cartilaginous tissue is stained light blue. The tongue (coracoid) and groove (sternum) system of the scapulocoracoid joint is clearly visible. 4.2 3-D FE models of solid tetrapod bodies The first model represents a sprawling limb position in an early tetrapod. The second refers to an extended position of the limbs as in extant cursorial mammals. In symmetrical limb support, both limbs are restricted, marked by bearings (triangles). The forces (arrows) indicate the swinging limb in asymmetrical limb support. The FE models are loaded by gravitational force, which is indicated as a single arrow at the centre of the model or at the coordinate system. 51 For each loading case, in both locomotor types, the calculations are presented in lateral, dorsal, and ventral view, showing compressive and tensile stress distributions. In asymmetrical stance, the stress distributions differ between the right and left body side, and are shown separately. To show the internal compressive stress distribution, frontal cross sections through the hindlimb region, the middle of the trunk and at the level of the forelimbs, are given. High compressive stresses are blue, low stresses are red. Colour code for tensile stresses is indicated by opposite colours. Absolute stress magnitudes can be obtained from the heading legend (DMX=total stresses, SMN=maximum tensile stresses, SMX=maximum compressive stresses). The stress distribution is related to morphological structures, which are required to sustain the mechanical demands. Compressive stresses are sustained by bony elements, whereas muscular and tendinous structures intercept the tensile stresses. Bony and muscular elements are identified and related to structural analogues, according to the amphibian, reptilian and mammal bone and muscle terminology (Starck, 1979; Romer & Parsons, 1977; Nickel et al. 1996). Although, the presence of a pectoral muscle, similar to m. pectoralis, was predicted for early tetrapods, there is little information on the shoulder girdle musculature (Diogo & Abdala 2007; Diogo et al., 2009). Therefore, with regard to the situation in early tetrapods, the description focuses on the bony elements. 4.2.1 Early tetrapod 4.2.1.1 Symmetrical stance compressive stresses During symmetrical stance the model indicates rather low maximum stress values of about 0.9 MPa. Highest compressive stresses occur at the insertion sites of the limbs, spreading dorsally over the midline of the trunk to the dorsal part of the constrained pelvic region (25a,b). The dorsal stresses indicate the presence of a vertebral column (Fig.25b), while the stresses on the lateral side refer to the presence of a scapula in extant reptiles (Starck, 1979; Romer & Parsons, 1977) or the cleithrum in early tetrapods. By contrast, the dorsal part of the neck region exhibits lower compressive stresses (Fig.25b). In ventral view compressive stresses are most visible between the supporting limbs spreading cranially to the neck region indicated by the least diameter, corresponding to the coracoid and interclavicles in extant reptiles (Starck, 1979; Romer & Parsons, 1977) or clavicle in early tetrapods, respectively (Shubin et al. 2006; Coates, 1996). 52 Figure 25 3-D FE-model based on the fossil of Tiktaalik showing the distribution of compressive stresses in lateral (A), dorsal (B) and ventral view (C). Contour legend (below) shows range of compressive stresses (colour coded); DMX=total stresses, SMN=maximum tensile stresses, SMX=maximum compressive stresses. Both limbs are constrained representing a symmetrical stance. In the frontal cross sections, the compressive stresses at the level of the supporting hindlimb run symmetrically from the fixed limbs up to the dorsal side (Fig. 26 A). At the middle of the trunk, the distribution is stratified with the highest values dorsally, to stress free regions ventrally (Fig. 26 B). Note the high stress values at the insertion site of the supporting forelimbs, spreading ventrally. Lower values are present dorsally, while the centre is free of stresses (Fig.26 C). The cross sections support the observations shown in Figure 24. Further, the stress free region in the middle of the trunk is interpreted as the body cavity, which provides space for the intestines in all extant and extinct tetrapods. 53 Figure 26 Cross sections through the FE-model in symmetrical stance showing compressive stress distribution, starting at the hindlimb section. A: At the level of the supporting hindlimb section. B: At the middle of the trunk. C: At the level of the supporting forelimbs. For convention see Fig. 24. 4.2.1.2 Symmetrical stance tensile stresses Tensile stress values reach a maximum of about 0.1 MPa and are therefore significantly lower than the occurring compressive stresses (Fig. 27). Highest values of tensile stresses are present at the ventral side of the trunk near the pelvic region representing abdominal muscles as m. rectus abdominis in extant reptiles and at the dorsal side of the neck region representing neck and shoulder muscles, as e.g. m. sternohyoideus, m. sternomastoideus, m. sternocleidomastoideus and m. spinalis capitis in extant reptiles (Starck, 1979; Romer & Parsons, 1977). No information is available about muscular structures in early tetrapods. Moderate stresses occur ventrally between the supporting limbs, which again can be sustained by pectoral muscles, such as m. pectoralis in extant reptiles (Starck, 1979; Romer & Parsons, 1977). 54 Figure 27 3-D FE-model of an early tetrapod showing tensile stresses in lateral (A), ventral (B) and dorsal (C) view. Both limbs are constrained in symmetrical stance. 4.2.1.3 Asymmetrical stance compressive stresses Maximum compressive stress values in asymmetrical support are with up to -43 MPa significantly higher than in symmetrical stance. In detail, regions showing significant compressive stresses reach values up to the 2nd power higher than in standing. Stresses are most pronounced at the insertion sites of the weight bearing limb in contrast to the swinging limb (28 A,B). At the ventral side between the forelimbs stress values increase and are most pronounced at the supporting limb spreading medially (Fig. 28 D). Stresses run from the supporting limb obliquely over the trunk to the level of the resting hindlimb, or in this case the ground-contacting belly (Fig. 28 C). The compressive part of the torsional stresses can be counteracted by compression resistant ribs, located in the body wall (Starck, 1979; Romer & Parsons, 1977). 55 Figure 28 3-D FE model of an early tetrapod showing compressive stresses in asymmetrical stance. A: right side. B: left side. C: dorsal view. D: ventral view. Again, frontal cross sections of the FE model are shown. At the level of the supporting hindlimb stresses run asymmetrically from the bearing dorsally to the anterior part of the body (Fig. 29 A). At the middle of the trunk stresses concentrate at the periphery of the trunk leaving the centre unstressed (Fig. 29 B). Note the highest stress values occur at the insertion site of the supporting limb and ventrally between the forelimbs. Stresses clearly connect both sides ventrally. There is a connection on the dorsal side as well, but to a much lower degree. The alternation of symmetrical and asymmetrical support during locomotion in reptiles therefore requires a continuous compressive resistant structure medially between the limbs, thus confirming a ventral coracoid and interclavicula for extant reptiles (Starck, 1979; Romer & Parsons, 1977) or the frontally positioned clavicles, as in early tetrapods (Shubin et al. 2006; Coates, 1996). 56 Figure 29 Frontal sections through the FE-model in asymmetrical stance showing the compressive stress distribution. Supporting limb is right, swinging limb is left. The coordinate system is visible in the middle of the trunk. A: At the level of the supporting hindlimb. B: At the middle of the trunk. C: At the level of the supporting forelimbs. 4.2.2 Cursorial mammal 4.2.2.1 Symmetrical stance compressive stresses In symmetrical stance the maximal compressive stresses in the model with an extended limb position reaches 14 MPa. High compressive stresses occur at the insertion sites of the limbs, spreading dorsally, with a slightly caudal inclination over the midline of the trunk to the hindlimbs. Compressive stresses at this location can be counteracted by the scapula in extant mammals with an extended limb position (Fig. 30 A,B). In ventral view compressive stress values between the supporting forelimbs are low and not detecTable at the hindlimb section. In extant mammals, a rod-like sternum is present at this location (Nickel et al. 1996) (Fig. 30 C). Further ventral stresses spread cranially along the neck region. These stresses can be sustained the ventral position of the cervical vertebrae, present in mammals with long necks (Fig. 30 C). The ventral part of the trunk is 57 subject to very low compressive stresses, which spread mainly from the extended forelimb to the side of the trunk (Fig. 30 A,C). Figure 30 3-D FE-model of a cursorial mammal showing compressive stresses in lateral (A), dorsal (B) and ventral view (C). All four limbs are constrained in symmetrical stance. Bearing are shown as triangles and indicate the limbs with ground contact. Coordinate system is located at the most caudal end of the model. Cross sections confirm the former results of the symmetrical stance (Fig. 31 A-C). At the middle of the trunk stresses prevail dorsally leaving the ventral side unstressed (Fig. 31 A). In both fore- and hindlimbs stresses run symmetrically from the limbs up to the dorsal side (Fig. 31 B,C). At the hindlimbs (Fig. 31 C), no ventral connection is visible, whereas at the forelimbs the cranially spreading stresses, referred to the cervical vertebrae, are visible (Fig. 31 B). 58 Figure 31 Frontal sections through the FE-model of a cursorial mammal in symmetrical stance showing compressive stress distribution. A:At the level of the supporting hindlimbs. B: In the middle of the trunk. C: At the level of the supporting forelimbs. 4.2.2.2 Symmetrical stance tensile stresses All limbs are constrained in symmetrical stance (Fig. 32 A-C). Highest values of tensile stresses occur ventrally at the belly and the dorsal side of the neck region (Fig. 32 A,B). The observed stresses can be assigned to muscular structures e.g. m. sternomastoideus, m. cleidomastoideus and m. trapezius (Nickel et al. 1996). Moderate stresses can be observed on the ventral side between the supporting limbs (Fig. 32 C). In extant mammals, the pectoral muscles can intercept the stresses at this location ((Nickel et al. 1996). 59 Figure 32 3-D FE-model of a cursorial mammal showing tensile stresses in lateral (A) ventral (B) and dorsal (C) view. 4.2.2.3 Asymmetrical stance compressive stresses In asymmetrical support the stress magnitude increases up to 35 MPa, the distribution is altered. Stresses are most pronounced at the insertion sites of the weight bearing limbs in contrast to the swinging limbs (Fig. 33 A,B). In lateral view (Fig. 33 A) the stresses at the forelimb somewhat expand cranially, but spread mainly dorsally at a slightly caudad inclination. Stresses spread dorsally from the supporting limbs to the contralateral hindlimb (Fig. 33 C). In ventral view little compressive stress connecting both sides occur between both fore-and hindlimbs (Fig. 32 D). Stress distribution in asymmetrical support corresponds to a laterally positioned scapula, in order to sustain the mechanical stresses, as it is shown before in symmetrical stance. Again, no ventral compression resistant structure is required in an extended limb position. 60 Figure 33 3-D FE model of a cursorial mammal showing compressive stresses in asymmetrical stance. The left fore- and the right hindlimbs are within ground contact (triangles). The corresponding limbs are held of the ground (arrows) (see D for description). A: right side. B: left side. C: dorsal view. D: ventral view. The cross sections support former results. At the level of the supporting hindlimbs stresses spread asymmetrically from the constrained limb dorsally to the frontal part of the body (Fig. 34 A). Similar to the sprawling limb position stresses in the middle of the trunk are concentrated at the periphery of the trunk leaving the centre unstressed (Fig. 34 B). This observation is consistent with the situation in the sprawling model. Stress free regions can be observed in both solid models, thus indicating a body cavity in tetrapods, which provides room for the intestines (Fig. 34 B). Note the highest stress values at the insertion site of the supporting limbs, where stresses spread mainly up to the lateral side of the trunk (Fig. 34 A,C). The ventral aspect shows less compression in both fore- and hindlimbs, compared to the sprawling model. 61 Figure 34 Frontal sections through the 3-D FE-model showing compressive stress distribution in asymmetrical stance. A: At the level of the supporting hindlimbs. B: At the middle of the trunk. C: At the level of the supporting forelimbs. 4.2.3 2-D FE model of a crocodilian shoulder girdle In a second approach, the mechanics and stress distribution in a crocodilian shoulder girdle are investigated. This first attempt of a 2-D multi-body FE model is used to reveal basic information about the method, the compressive stress distribution and relative movements. The calculated results are presented as one frontal (Fig. 35) and one lateral 2-D model of the pectoral girdle in a crocodilian (Fig. 36). Black outlines indicate the initial situation before calculation. In frontal view and in lateral view the trunk is restricted laterally by x-directed bearings (light blue triangles), the antebrachium is restricted in the y-direction, only capable of sideward movements. In lateral view, these constraints are likewise. Contact elements are applied to the adjacent areas of the trunk and the scapulocoracoid as well as in the glenoid and elbow joint. The required muscles, which are shown as link elements, are numbered, and indicated as black (initial situation) and as red lines (after calculation). A coordinate system is placed right at the bottom. 62 Compressive stress values can be obtained from the colour coded contour legend or from the heading legend, in which maximum and minimum stresses are recorded. High compressive stresses are blue, low stresses are red. Areas with stresses beyond the spectrum are grey. 4.2.3.1 Static equilibrium Although the relative motion of the elements is visible, the deformation remains in tolerable limits, which is a precondition for static equilibrium in the system. In frontal view, the trunk and scapulocoracoid sink downwards, while the humerus is adducted. The humerus shaft is subject to bending. The antebrachium tends to move medially. Compressive stresses within the scapulocoracoid flow from the glenoid joint medially and dorsally towards the trunk (Fig. 35). Each of the link elements corresponds to muscles in the crocodilian shoulder girdle and produces forces resulting in mechanical stresses within the predefined structure (Fig. 35). These muscles contribute to transmission of weight force from the trunk to the pectoral girdle and the supporting limb or are engaged in maintaining balance in the glenoid joint. Link elements represented are m. pectoralis (1a, b), m. serratus (2), m. rhomboideus (3), m. subscapularis (4), m. deltoideus scapularis (5), m. coracobrachialis (6), m. triceps caput coracoideum (7), m. brachialis (8). Figure 35 Frontal 2-D FE model. Distribution of compressive stresses after calculation. Black lines indicate the working link elements representing the shoulder musculature. Black outlines indicate the situation before calculation. Link elements represented are m. pectoralis (1a, b), m. serratus (2), m. rhomboideus (3), m. subscapularis (4), m. deltoideus scapularis (5), m. coracobrachialis (6), m. triceps caput coracoideum (7), m. brachialis (8). In lateral view, the relative motion of the elements is visible. Again, the deformation stays in tolerable limits. The scapulocoracoid sinks downwards, while the humerus moves caudally. 63 There is little bending of the humerus in lateral view, the shaft is mainly subject to compression. The antebrachium tends to move caudally. High stress values can be detected at the insertion site of the limb, which spread from the glenoid joint cranially and dorsally, the inclination of the stress pattern within the scapulocoracoid is clearly visible (Fig. 36). The results give a first approximation of the position of the original morphological structures in the crocodilian scapulocoraoid (Fig. 35,36). Link elements represent m. pectoralis (1 a,b), m. serratus superficialis (2 a-d), m. serratus profundus (5), m. deltoideus scapulare (6), m. triceps caput humerale (7), m. triceps caput coracoideum (8), m. triceps caput scapulare (9), m. trapezius (10), m. levator scapulae (11), m. latissimus dorsi (12), m. scapulohumeralis (13), m. costo-coracoideus (14), m. brachialis (15). Figure 36 2-D FE model in lateral view, only areas representing the scapulocoracoid, humerus and antebrachium. Black lines indicate the working link elements. Black outlines indicate the situation before calculation. Link elements represent m. pectoralis (1 a,b), m. serratus superficialis (2 a-d), m. serratus profundus (5), m. deltoideus scapulare (6), m. triceps caput humerale (7), m. triceps caput coracoideum (8), m. triceps caput scapulare (9), m. trapezius (10), m. levator scapulae (11), m. latissimus dorsi (12), m. scapulohumeralis (13), m. costo-coracoideus (14), m. brachialis (15 4.3 3-D FESS of a crocodilian shoulder girdle The present approach is the first attempt of a 3-D multi-body FESS of a crocodilian shoulder girdle. Body weight force is applied at five nodes, which are distributed over the trunk. Again, only the left side of the trunk is generated in order to minimize calculation time. Legends and symbols are similar to the 2-D FE model. Pretension of links and reaction forces within the indicator bearings for each calculation step can be obtained from the supplement. 64 In the initial situation, the trunk is restricted by bearings in x- and z-direction (triangles) to prevent medially and anteriorly directed movements, which in the living object are carried by the right supporting forelimb and the hindlimbs, respectively (Fig. 37 A,B). The antebrachium is restricted to vertical and caudad movements. To determine the function of the required muscles, they are applied to the model in iterative steps, considering their impact to the system, which can be detected as reaction forces in the indicator bearings applied to the scapulocoracoid and humerus. These indicator bearings provide stability in non-balanced calculations. Since the shoulder girdle system is balanced, the reaction forces within the indicator bearings are zero and are removed iteratively during the process. In the second setting, the trunk and the antebrachium are allowed to move in the formerly defined directions and are still supported by bearings. The scapulocoracoid and the humerus are free from restrictions and supported only by link-elements, which relate to the shoulder girdle muscles. In the following, only the final calculation step, with the shoulder girdle system in equilibrium, is presented. The entire process of equilibrium adjustment can be obtained from the supplement (Fig. 37,38). 4.3.1 Static equilibrium In the final calculation step, no bearings are required to keep the scapulocoracoid and the humerus in position. The equilibrium of the shoulder girdle was accomplished by link elements, which are related to the shoulder girdle muscles. The trunk and the antebrachium move in the predicted directions. The scapulocoracoid rotates cranially around the pivot of the glenoid joint and ventrally. The humerus rotates caudally around the pivot of the glenoid joint and cranially within the elbow joint, while it shifts the antebrachium in caudal direction. The relative motion of the elements stays in tolerable limits, which is a precondition for calculation. The relative motion of the elements in the system and the observed force transmission between the trunk, the scapulocoracoid and the humerus indicate an effective operation of the contact elements (Fig. 37,38). 65 Figure 37 Final calculation step in frontal view. Stress distribution (contour legend) and deformation (black outlines) in the crocodilian shoulder girdle are presented. Equilibrium in the shoulder girdle system is maintained by links, which relate to shoulder girdle muscles in crocodilians. Maximum and minimum stresses can be obtained from the heading legend. Force transmission between the trunk and scapulocoracoid and within the joints can be recognized. Figure 38 Final calculation step in frontal view. Stress distribution (contour legend) and deformation (black outlines) in the crocodilian shoulder girdle are presented. Equilibrium in the shoulder girdle system is maintained by links, which relate to shoulder girdle muscles in crocodilians. Maximum and minimum stresses can be obtained from the heading legend. Force transmission between the trunk and scapulocoracoid and within the joints can be recognized. 66 The distribution of compressive stresses, which appear in the bauraum after reaching equilibrium, gives a first approximation of the scapulocoracoid shape according to the original bony elements in the mounted skeleton (Fig. 39 A,B). In lateral view, the stresses spread from the glenoid joint caudad along the posterior border of the bauraum and posteriorily along the supposed area of the coracoid towards the trunk (Fig. 39 B). Medial transmission of stresses from the coracoid to the trunk again can be observed in frontal view (Fig. 39 B). Maximal compressive stress is -20 MPa, whereas the indicated threshold is between 0 and -0.09 MPa. There is a large amount of grey areas, i.e. stresses beyond the visible spectrum. The numeric spread was used to point out the areas with the highest amount of compressive stresses, because absolute values of compressive stresses are low at this point of the approach. To accumulate the stresses, the volume of the bauraum is reduced according to the stress bearing areas, while the stress free areas are removed in iterative steps. This reduction will lead to a refinement of the structure and an increase of compressive stress value. Figure 39 Comparison of the stress pattern in the final calculation step with the skeletal elements of the crocodilian shoulder girdle (black outlines). 67 4.3.2 Muscle function All links in the model relate to the shoulder girdle muscles in crocodilians (Fig.40) and are described according to their mechanical function in static equilibrium. The majority of forces exerted by the links act mainly in caudal (z-axis) and dorso-ventral (y-axis) direction, and therefore are most visible in lateral view (Fig. 40). The link elements, which connect the scapulocoracoid and the trunk, are related to m. serratus superficialis, m. trapezius, m. levator scapulae, m. costo-coracoideus, m. triceps caput scapulare and m. triceps caput coracoideum (Fig. 40). Their lines of action point mainly craniocaudally (z-axis), and in addition exert a lower amount of forces in the medio-lateral direction (xaxis). M. serratus superficialis is represented by four single links according to its distribution along the insertion site at the scapula and the thoracic ribs. The muscle transmits the body weight from the trunk to the shoulder girdle and acts as caudal rotator of the scapulocoracoid. M. trapezius, m. levator scapulae and m. costo-coracoideus contribute to static equilibrium in the shoulder girdle, as they rotate the scapulocoracoid cranially. They act as antagonists to the trunksuspending m. serratus superficialis, which rotates the scapulocoracoid caudad. M. costocoracoideus is found to contribute to static equilibrium, as it pulls the scapulocoracoid backwards. As this muscle has a smaller lever arm to the pivot of the shoulder joint compared to m. trapezius or m. levator scapulae, the main function is rather caudad translation than craniad rotation of the scapulocoracoid. To increase the amount of required forces in m. costo-coracoideus and m. trapezius, the diameter and pretension in the link elements are enlarge (Fig. 41). M. biceps brachii and m. supracoracoideus run between the scapulocoracoid and the humerus anterior to the glenoid joint and below its pivot (Fig. 40). Their line of action is directed in the x,y-and z-axis. According to the line of action these links presumably support the former muscles in cranial rotation of the scapula and the humerus. Their function cannot be determined beyond doubt, because no visible impact was detecTable during adjustment of static equilibrium. Although the function of the former muscles cannot be finally determined, they do account for a decrease of maximum stress value in the final calculation of up to -20 MPa. M. triceps caput scapulare and m. triceps caput coracoideum run between the antebrachium and the scapulocoracoid (Fig. 40). The former inserts posterior to the glenoid joint at the scapula, the latter, anterior to the glenoid at the coracoid. Functionally they rotate the scapulocoracoid caudad and craniad, respectively. Their impact on this assumed function cannot be determined during the process. In fact, they contribute to prevent a cranial translation of the antebrachium, thus supporting equilibrium in the elbow joint, while pulling the antebrachium 68 forward. Reaction forces within indicator bearings at the antebrachium still indicate a strong tendency for caudal movements, thus mm. triceps cannot account for reduction exclusively. To prevent caudad movement of the antebrachium m. brachialis, m. spiralis and m. triceps caput humerale were applied, as their line of action runs posteriorily from the antebrachium to the humerus (Fig. 40). Again, no modifications could be detected. In consequence, horizontally directed link elements were applied to the anterior border of the antebrachium to hold its position and to keep the elbow joint in equilibrium. It is assumed at this point of investigation, that further musculature, running between the antebrachium and the forefoot, is required. In frontal view, medially directed forces at the model are mainly exerted by m. pectoralis, m. rhomboideus and m. coracobrachialis. In the final calculation, the humerus moves medially towards the trunk, as indicated by deformation. This is due m. pectoralis, which acts as an adductor of the humerus (Fig. 40). Further applied links, representing m. subscapularis, m. deltoideus scapularis, m. subscapularis, m. scapulo-humeralis, m. teres major and m. latissimus dorsi show no detecTable impact for maintaining equilibrium. In fact m. teres major and m. latissimus dorsi prevent static equilibrium in any calculation step during the process, and are therefore not included in the final calculation. 69 A A B A Figure 40 Shoulder girdle muscles investigated by the former calculation in frontal (A) and in lateral view (B). Boundary conditions refer to the final calculation step. Weight forces applied to the trunk are distributed along the trunk (arrows). According to their demands under static loading conditions, the link elements exhibit a certain amount of mechanical stresses, which can be detected after calculation. In Table 8 the resulting stresses are compared to the forces initially present in the links, defined by pretension and diameter. The maximum stress values can be detected in the horizontally directed link 70 elements applied to the antebrachium. These elements have been applied to prevent caudad movements of the antebrachium, but do not influence to equilibrium in the shoulder girdle joint.The highest stresses are visible in links related to m. serratus superficialis, where the most posterior links show the highest values (250-300 N/mm²) (Fig. 41). For links representing m. triceps humerale, m. brachialis, m. deltoideus clavicularis, m. supracoracoideus and m. costocoracoideus values of >150 N/mm² can be detected (Fig. 41). Due to the requirements of static equilibrium, the forces exerted by m. costocoracoideus increased during the adjustment process. Therefore, the cross section of the link representing this muscle is 10 times the initial cross section of about 0.1mm². Further, pretension was doubled, thus leading to higher absolute stress values. To enhance cranial rotation of the scapulocoracoid the cross section of m. trapezius was increased as well, which results into significantly higher absolute stresses, than can be detected in the link after calculation (50-100 N/mm²) (Fig. 41). Therefore, m. costo-coracoideus and m. trapezius are structures in the system with the highest load. Lower stress values (100-150 N/mm²) can be viewed in m. biceps brachii, m. pectoralis major et minor, m. triceps caput scapulare, m. triceps caput coracoideum, and m. subscapularis (Fig. 41). Finally, in the links representing m. levator scapulae, m. spiralis and m. serratus profundus no stresses are detectable after calculation (Fig. 41). Figure 41 Diagram showing absolute value of link stresses after calculation in N/mm² for each link representing the involved musculature. Note the highest stress values in m. serratus superficialis 1-4, m. supracoracoideus and m. triceps caput humerale. M. levator scapulae, m. spiralis and m. serratus profundus exhibit no stresses. 71 4.3.3 Synthesis of the scapulocoracoid The resulting compressive stresses of the final calculation step are accumulated in iterative steps, in order to reduce the bauraum of the 3-D FE model. The designated shape then corresponds to the original crocodilian scapulocoracoid. First, the 3-D volume of the scapulocoraoid bauraum is dissected in antero-posterior direction (Fig. 42). Each section shows areas with more or less compressed regions. The internal stress distributions reveal the transmission of forces between the scapulocoracoid and the trunk as well as between the humerus at the level of the glenoid joint (Fig. 42). Areas with a certain amount of compressive stresses are selected. Subsequently the selected sections are spliced to form the new bauraum. After remeshing of the reduced bauraum, the model is recalculated under the predefined boundary conditions according to the final calculation step (Fig. 43). The compressive stresses are accumulated in the reduced volume, so that compressive stresses will increase until they reach physiological values according to compact bone (-2 to -20 MPa). Figure 42 Selected cross sections of the model after the final calculation step in frontal view. Virtual dissection of the model runs from anterior to posterior (1-6). Note the stress distribution in section 5 and 6, where stresses spread from the glenoid joint medially to the trunk (coracoid) and dorsally along the bauraum (scapula). 72 Figure 43 Different steps for reduction of the bauraum are presented. A: Scapulocoracoid bauraum after calculation showing the stress distribution in oblique view. White lines indicate selected areas, which show a certain amount of compressive stresses. B: Model in lateral view. Position of selected sections is indicated as vertical lines. C: Spliced areas of the selected sections, before remeshing of the new volume in lateral view. D: Remeshed new bauraum in its original position together with the trunk, humerus and antebrachium (dashed lines) in oblique view. After the 2 nd recalculation in the 3 rd reduction step an overall decrease of material in comparison to the initial bauraum can be observed (Fig. 44). The virtual synthesis of the scapulocoracoid approximately resembles the original skeletal part, as it exhibits a caudally inclined slender form, similar to the crocodilian scapulocoracoid. The coracoid part of the synthesis connects the trunk at the predicted position (Fig. 44). Further reduction steps would probably lead to a more defined structure, but the amount of additional knowledge is assumed to be insignificant. However, the investigation so far reveals necessary basic information about the application of the FESS method to a multi-body 3-D shoulder girdle system. The observed relative movements of the shoulder girdle elements, and basically defined mechanical muscle functions in this part of the study provide ground for further steps. However, no quantitative muscle values could be estimated. Consequently, in the FESS of the scapulocoraoid of Diplodocus longus the link elements are replaced by directed forces in order to gain the required information. 73 rd Figure 44 The 3 and last reduction step of the crocodilian scapulocoracoid model. A: Reduced scapulocoracoid bauraum placed within the whole model, in lateral view (A), frontal view (C), oblique view (E). Single reduced scapulocoracoid in frontal (B), lateral (D) oblique view (F). 4.4 3-D FESS of the scapulocoracoid of Diplodocus longus 3-D FESS of the scapulocoracoid of Diplodocus longus is performed via calculation of two different forelimb positions. The first FE model shows the humerus in a vertical position relative to the glenoid joint (forelimb position I.); in the second FE model (forelimb position II.) the humerus articulates at the glenoid joint with an angle of about 15° to the perpendicular. Laterally, both models exhibit an inclination angle at the humerus of about 20° to the vertical. The elements of the shoulder girdle system are held in position first, by bearings (indicated as triangles) and second, by forces preventing the movement. Therefore, two settings with different boundary conditions can be determined. The first is the initial situation, where the trunk is restricted in x- and z-direction to prevent medial and forward movements. In living animals, this function is adopted by the right supporting forelimb and hindlimb, respectively. The antebrachium is restricted by a fixed bearing. The scapulocoracoid and the humerus require 74 indicator bearings from which reaction forces can be read out after calculation. The indicator bearings will be removed iteratively, leading to the second setting in which the trunk and antebrachium are allowed to move in physiological directions. In equilibrium of the shoulder girdle system, the scapulocoracoid and the humerus are free from restrictions and held in position only by forces, which represent the shoulder girdle muscles. To determine the function of the required muscles, the forces are applied to the model in iterative steps, considering their impact on the system, which again can be detected at the indicator bearings. Changes concerning the boundary conditions (applied forces and bearings) will be described in the figure legends. Static equilibrium can not be accomplished in the first FE model. Nevertheless, this first attempt reveals basic information with regard to the method and function dependent implications of the diplodocoid shoulder girdle. To explain the consecutive nature of the method, where each result provides the basis for the following step, the most relevant information drawn from the adjustment of equilibrium in both FE models (forelimb position I and II.) is given. The entire adjustment processes can be obtained from the supplement. The results of the second FE model are presented as follows. The results comprise one frontal and lateral overview of the model, to demonstrate the applied forces representing the shoulder girdle muscles. Two contour plots, in frontal and lateral view, show the distribution and magnitude of compressive stresses after calculation. Black outlines indicate relative motion of the elements according to deformation after calculation. Contact elements are present at the adjacent areas of the trunk and the scapula, in the region of the assumed coracosternal joint and at the glenoid and elbow joints. Values of muscle forces applied to the model and reaction forces within the bearings can be obtained from the supplement. Forces are shown as arrows. The coordinate system is placed at the lower right corner. Compressive stress values can be obtained from the colour coded contour legend or from the heading legend (maximum and minimum). High compressive stresses are blue, low stresses are red. Areas with stresses beyond the spectrum are grey. After the static equilibrium in the FE model was accomplished, the scapulocoracoid of Diplodocus longus is successfully synthesized with regard to the compressive stress distribution of the second FE model. The synthesis resembles the characteristic features of the original diplodocoid scapulocoraoid. According to the successful synthesis of the scapulocoracoid, the precluded mechanical considerations concerning the shoulder girdle of Diplodocus longus are confirmed. Based on the results the shoulder girdle is reconstructed, which includes the 75 arrangement of the bony elements, and the position, function and forces of the shoulder girdle musculature. 4.4.1 Forelimb position I. In a number of iterative steps (see supplement for entire calculation steps) equilibrium was reached after completion of muscle arrangement running between trunk, scapulocoracoid, humerus, and antebrachium, except for m. latissimus and m. teres major. No arrangement could be established in which the latter muscles contributed to stability in the system. No bearings are required to keep scapula and humerus in balance, though rotation and translation of the scapulocoracoid and humerus are prevented by the applied forces. Maximum compressive stress value is -25 MPa therefore closely corresponding to the formerly predicted physiological stress values, ranging from -2 to -20MPa. Although equilibrium was maintained only by means of forces the model did not fully correspond to the original. Especially the stress distribution within the acromial region needed to be enhanced. In a first attempt, m. serratus superficialis was repositioned and forces in m. trapezius and m. triceps scapularis were enlarged. None of these approaches modified the distribution of stresses. Furthermore, the scapulocoracoid shows no rotation. The lack of rotation of the humerus within the glenoid joint can obviously not be affected by any rearrangement of muscle forces and is definitely no physiological condition. Missing rotation probably results from an inhibited sliding between the humerus and glenoid surface area. To avoid canting between the scapulocoracoid and humerus both elements were remeshed using smaller finite-elements (Fig. 45 A). Further, the friction coefficient for the contact elements was lowered from 1 to 0.1 (Fig. 45 B). Even these modifications were insufficient (Fig. 45 A,B). Nevertheless, refinement of the elements has a visible effect on the stress distribution. In consequence the refined ground model will be applied to all following calculations (see supplement). Finally the convergence criteria had been lowered from 0.1 to 0.001. To preclude any further influences the applied forces are reduced to the initial situation. Lowering convergence then results into a significant decrease of deformation and an increasing rotation and sliding between the contact areas of the scapulocoracoid and the humerus (Fig. 45 C,D; Fig. 46). Even with an enhanced sliding between the elements of the shoulder girdle, no stress distribution, resembling the shape of the original scapulocoracoid could be achieved (Fig. 45 C,D). In order to reach a more elaborate distribution of stresses, the model will be recalculated, this time with the humerus slightly abducted. As the ground reaction force supposedly flows in more medial direction, this procedure should enhance compressive stresses in the coracoid element and the acromial part of the scapula. 76 Thus, 3-D FESS was not accomplished, even though static equilibrium could be established by forces. First, convergence criteria could be revealed as the most crucial factor for a decrease of friction between areas provided with contact elements. The great numbers of contact elements applied to the joint areas are sensitive to changes in convergence criteria. Decreasing convergence criteria lead to a higher accuracy of the solution, but simultaneously increases solving time and sensitivity to model discrepancies during calculation of static equilibrium. These discrepancies are obviously responsible for the enhanced contact between the scapulocoracoid and humerus, leading to non-physiological results. As an increased convergence criteria-setting affects the distribution of stresses as well as deformation and state of equilibrium, all following calculations will be calculated using a convergence criteria of about 0.001. Figure 45 Calculations of the refined model showing a reduced amount of forces. M. serratus superficialis, m. serratus profundus, m. levator scapulae, m. trapezius and m. costo-coracoideus are reduced to a single vector respectively. Equilibrium between the trunk and scapulocoracoid is maintained, occurring stresses are plotted. The refined model was calculated with a convergence criteria of 0.1 in lateral and frontal view of the object (A, B), and, for comparison, with the convergence criteria set to 0.001. (C, D). 77 Figure 46 Magnified detail of the glenoid joint region showing the free rotation of the humerus within the glenoid fossa indicated as black outlines showing the initial situation before calculation. 4.4.2 Forelimb position II. Friction coefficient for contact elements is 0.01. Convergence criteria for calculation are 0.001. The refined model is calculated using the same boundary conditions as in forelimb position I. Again, adjustment of static equilibrium starts with forces running between the trunk and the scapulocoracoid. The scapulocoracoid is restricted to translational movements by one single indicator bearing at the distal corner. The humerus is restricted by two fixed bearings at both distal and proximal ends of the shaft. Based on this initial situation equilibrium has been reached in iterative steps (for details see supplement). Compared to the first FE model, the forces in the present steps were subdivided and placed along the predicted insertion sites at the scapulocoracoid to obtain a more distributed compressive stress pattern and to minimize stress peaks, which occur especially at insertions of high forces, while the absolute force values are kept constant. Calculation of the initial situation resulted in an increase of reaction force at the z-directed bearing at the distal edge of the scapulocoracoid, thus indicating strong forward translation, which results into imbalance of the trunk and the scapulocoracoid. Although forces and rotational moments were calculated precisely, the trunk was entraining the scapulocoraocid along its direction. Friction, even with a lowered friction coefficient of about 0.1 is beyond tolerable limits, because of the large number of contact elements between the trunk and scapulocoracoid (for details see Fig. 75, Table 14 in the supplement). To avoid misleading results from uncertain reactions between the trunk and scapulocoracoid, the trunk was removed, and the scapulocoracoid along with the humerus and 78 the antebrachium were calculated separately. The focus in this investigation is on stress distributions within the scapulocoracoid element. Areas of the trunk adjacent to the scapulocoracoid preventing medially directed movement were replaced by adequate bearings to fulfil the function. Assumed regions of main force transmission are defined at the predicted coracosternal joint and the acromial region, where the claviculae presumably contact the scapula and where forces can be transmitted. Further applied bearing should serve as indicator bearing and to provide stability until equilibrium was reached. Forces directed to the trunk maintain their line of action positioned towards the trunk. After calculation a comparison between both models reveals a reduction of translational movements at the scapulocoracoid and deformation within the model calculated without the trunk (for details see supplement, Fig. 76). Therefore, equilibrium was calculated under the described conditions. The final results include medial and caudal views in addition to the lateral and medial view to show the additional information. All steps leading to the static equilibrium can be obtained from the supplement (Table 15). 4.4.2.1 Static equilibrium Static equilibrium in the shoulder girdle system has been reached after a number of iterative steps (Fig. 47). The bearings, which were required in the initial situation, are removed and the shoulder girdle system is held in position only by forces, which refer to shoulder girdle muscles. First, equilibrium was maintained between the trunk and the scapulocoracoid by muscles running between the two elements. Indicator bearings at the scapulocoracoid were removed. The humerus then was still restricted by fixed bearings. In the following steps forces were applied by mechanical requirements to reach equilibrium not only between the trunk and the scapulocoracoid, but also within the glenoid joint. The calculations of the single iterative steps, the applied force values and reaction forces in the bearings, can be obtained from the supplement. In the final calculation all indicator bearing were removed, leaving those bearings, which provide stability in accordance to the anatomy in the sauropod shoulder girdle (Fig. 47). Therefore medially directed bearings (x-axial) at the scapulocoracoid are still present at the assumed sternocoracoid joint and the acromion, indicating the presence of the clavicle. The sum of all reaction forces, which appear at the sternocoracoid joint are high, approximately 4492 N, thus indicating strong medially directed force transmission. The reaction force, which is detected at the acromion, is less pronounced (1171 N), but still indicates medially directed force transmission at this location (for a complete list of reaction forces see supplement). The humerus is free from restrictions and therefore able to rotate within the glenoid and the elbow joint. As the resultant 79 of all forces, which act on the shoulder girdle system, runs through the pivot of the glenoid, the shaft of the humerus and the pivot of the elbow joint, rotational moments have been decreased, thus leading to a balanced system. The antebrachium is still restricted by fixed bearings. The reaction forces within the bearings indicate strong backwards and sidewards translational movements. These reaction forces can only be countered by the application of the complete limb musculature and are not considered in this study. The sum of all y-dircted forces (18387 N) is approximately the value of body weight (18956 N), which has been initially applied to the system. The difference between these two values is not significant and is referred to minor errors during calculation. The overall stress distribution of compressive stresses in the bauraum is according to the original shape of the scapulocoracoid (Fig. 47). Only the slight curvature at the caudal border of the scapula cannot be synthesised. The scapulocoracoid and the humerus are mainly subjected to compression stresses. Concurrent bending within the structures was reduced. The deformation after calculation shows the relative movements of the shoulder girdle elements, but still is in physiological limits (Fig. 47 ). The maximum value of compressive stresses is -24.7 MPa. The contour legend, which indicates the compressive stress values as different colours, was set throughout the calculation process to show a range of 0 -0.9 MPa. This was required in order to detect even low compressive stresses during the calculation. In the final calculation the numeric spread of the contour legend ranges from 0 to-1.8 MPa. The visible spectrum (orange-blue) now reflects only those areas, which provide basis for the following reduction steps. In those areas, which resemble the shape of the original scapulocoracoid, the value of compressive stresses is still lower than the precluded physiological stress value in compact bone (-2 to -20 MPa). By the reduction of the bauraum these values are then increased to a physiological value (Fig. 47). 80 Figure 47 Final calculation of the 3-D FE-model of Diplodocus longus- Outlines of the FE-model with all applied forces in lateral (A) and frontal (B) view. Distribution of compressive stresses in: lateral view (C), frontal view (D), medial view (E) and top view (F). The system is kept in equilibrium only by means of forces, which can be related to shoulder girdle muscles. All indicator bearings at the scapulocoracoid and the humerus are removed. Numeric spread of compressive stress values in the contour legend range from 0 MPa to -1.8 MPa. Stresses beyond the spectrum (grey plotted areas) are reduced. The desired stress pattern (orange-blue areas) is visible. The complete FE-model of Diplodocus longus, which includes the trunk element, is recalculated under the same boundary conditions as presented in the final calculation step (Fig. 81 48). Again, equilibrium in the shoulder girdle system was accomplished by means of forces, which refer to the shoulder girdle musculature (Fig. 49). The completion of the model shows, that the calculated muscles of the shoulder girdle not only maintain stability in the scapulocoracoid and the humerus, but also in the trunk. No vertically directed bearings are required to keep the trunk in equilibrium. Therefore the former assumed forces are confirmed. Total value of compressive stress is slightly increased. A reduction of compressive stresses and decrease of force transmission can be observed at the acromial region, which is assumed to be the contact area between the clavicles and the scapulocoracoid (Fig. 48). Nevertheless, in comparison to the former calculation, compressive stress distribution shows only little modifications. Therefore, the boundary conditions, which led to static equilibrium and distribution of compressive stresses, can be confirmed. The applied forces in the FE model are related to muscles of the shoulder girdle system and will be described according to their function. Figure 48 Stress distribution in the complete FE model of Diplodocus longus including the trunk element. Calculation is accomplished under the same boundary conditions as in the final calculation (Fig. 47) 82 Figure 49 FE-model with all muscles of the shoulder girdle, keeping the shouldergirdle -system in static equilibrium. Lateral view (A), frontal view (B). Muscles connecting the scapulocoracoid and trunk are red; muscles running from the trunk to the humerus are dark blue and muscle groups originating from the scapulocoracoid and inserting at the limb are indicated as green lines. 83 4.4.2.2 Synthesis of the scapulocoracoid in Diplodocus longus For reduction of the bauraum to the designated shape according to the diplocoid scapulocoracoid, the resulting compressive stresses are accumulated in iterative steps. Compressive stress values at this point are non-physiological, but their distribution corresponds to the original diplodocoid scapulocoracoid. Compressive stresses are concentrated within the region of the coracoid, showing transmission of stresses to the sternal region. Highest stresses can be viewed at the insertion site of the humerus at the glenoid joint. The internal compressive stress flow is undisturbed through the whole element, showing a reduction of material along the scapula. The reduction is based on the results of the single calculated model, excluding the trunk element to prevent any friction related deformations and modifications. First, the three dimensional volume of the bauraum is dissected in antero-posterior direction at eight locations (Fig. 50). Each section shows an area with more or less stressed regions. The areas with a certain amount of compressive stresses are selected (Fig. 50), retained and then spliced to form a new, reduced, bauraum. Subsequently, after remesh of the reduced bauraum, the model is recalculated under the predefined boundary conditions according to the final calculation step. By this procedure, the compressive stresses are accumulated in the reduced volume and increase until they reach a physiological stress value. Figure 50 Frontal cross sections at eight different positions through the bauraum after calculation (1-8; A). Selected areas showing a certain amount of compressive stresses, which are retained to be spliced to form the new reduced three dimensional volume (B). 84 The reduction of the original bauraum of the scapulocoracoid was accomplished in three consecutive steps. The position and orientation of the required forces are equal to the condition in the final calculation step. Insertion and origin of the forces at the bauraum are maintained throughout the reduction. In each of the steps a decrease of the structure and an increase of compressive stresses according to the shape of the scapulocoracoid can be obsereved (Fig. 51). The acromial region of the scapula became visible after the first reduction step. The numeric spread of the legends is increased stepwise according to the increased compressive stress values. Compressive stresses in the aimed regions before the first reduction range from -0.4 to -1.8 MPa. After the first and second reduction the stresses range from -0.9 to -2.7 MPa and -1.5 to -4.5 respectively. In the recalculation of the third and last reduction step the structure shows compressive stresses within a range of -2 and -9 MPa, which is in the predicted range of physiological compressive stress value of bone. In order to account for an assumed impact of acceleration during locomotion the reduced FE model was recalculated with forces, which are scaled up according to two times earth accelaration. The stresses are then within a range of -3 to 20 MPa, which is in accordance to the predicted compressive stress loading (Fig. 51). The maximum value of compressive stresses in the last reduction step is -141 MPa and is located at a small area at the most posterior border of the glenoid facet. All three reduction steps, which include frontal cross sections of the first and second reduction, can be obtained from the supplement. Figure 51 Reduction of the orignal bauraum in three consecutive steps. The range of compressive stress values is shown in the contour legends. The numeric spread of the legends is increased stepwise according to the increased compressive stress values. The reduction of the structure is visible, even in the first reduction, in which the acromial region of the scapula became visible. After reduction of the bauraum the final synthesis was smoothed by a virtual surface overlying the original mesh. By this procedure the great number of edges and nodes are reduced, emphasizing the main features of the synthesis structure (Fig. 52). Comparing the synthesized 85 finite-element model to the original fossil the main characteristics of the scapulocoracoid in Diplodocus longus can be described (Fig.53). The fossil consists of a long slender scapula with a slight impression at the anterior half of the distal end. The scapula thickens disto-proximally, and is divided in its length by a bony ridge running from the first to the last third (Fig. 53a). The described features can again be viewed in the synthesized model (Fig. 52). This holds true especially for the overall shape; the elongated scapula, the acromial region and the relative thickness of the elements (Fig. 52). Further the bony ridge and the impressions on the lateral side can be recognized (Fig. 52 A,E). The scapular body is characterized by the presence of a prominent acromial region, which forms a deep incisure between the acromion and the scapula (Fig. 52,53). The acromial region exhibits a deep impression along two thirds of its structure (Fig. 52 A). In the fossil the glenoid joint is formed by parts of the scapula and the coracoid, and is the most compact part of the scapulocoracoid (Fig.53 C). The shape of the acromion and the incisura, as well as the distribution of bony material is similar in the synthesis (Fig. 53). The most compact region again can be viewed above the glenoid joint (Fig. 52 A,C,D). The lateral impression at the acromion is not as pronounced in the FE-model, nevertheless it is marked by a slight lateral groove at this location (Fig. 52 F). The ossified epiphysis between the scapula and the coracoid is still visible in the fossil. The caudal border of the scapula is slightly convex along the whole length (Fig. 53 A). These two features cannot be synthesized in the FE-model (Fig. 52 A). The scapulocoracoid in the original is medially concave in frontal view. Both ends of the scapulocoracoid, the distal end of the scapula and the medial part of the coracoid bend towards the trunk (Fig. 53 B). The concavity is present in the FE-model as well (Fig. 52 B). The acromion forms a thin plate, which is thickened caudal-ward towards the scapula. A bony ridge running along the acromion to the glenoid joint marks the borderline between both parts of the scapula (Fig. 53 A,B). The relative thickness of the acromion and the scapula can be viewed in the FEmodel, whereby the formation of the acromial ridge is less pronounced (Fig. 52 B). The coracoid plate of the fossil is positioned fronto-ventrally to the aperture of the ribcage, its medial border shows a cranio-caudad inclination (Fig. 53 B). Considering the coracoid as a rectangular element, its frontal border has the greatest thickness, with a strong rugose structured rim. The rugosities are present along the whole frontal length, but are most visible at the first half (Fig. 53 B,C). All of these features were successfully synthesized in the FE-model. Similar to the original, the frontal border of the coracoid is most thickened, while the overall coracoid part of the model has a smooth and rounded appearance (Fig.52 B,C,F). 86 The medial view of the scapulocoracoid of Diplodocus exhibits a more or less smooth surface, which is laterally convex corresponding to the concave bending of the scapulocoracoid. The most prominent impressions of the structure are visible along the midline of the coracoid plate and in the middle part of the scapular body (Fig. 53 C). These shallow impressions, on the coracoid, the scapular body and the distal end of the scapula again are visible in the synthesis (Fig. 52 F). Figure 52 Smoothed scapulocoracoid bauraum of the final reduction step in different views. A: Lateral view. Arrows point at the long slender scapula, the prominent acromial region and the deep incisura in between them. B: In frontal view the scapulocoracoid is flexed medially concave. Arrows point at the rounded coracoid, a thin plate of the aromion, and the thickened anterior side of the scapula. C: Medial view: The most massive bony regions are located where the scapula and coracoid are forming the glenoid joint. Another arrow points at the most thickened part of the coracoid. D: Back view: Medial concavity of the scapulocoracoid is visible. Arrows point at the thin distal end of the scapula thickens along its length to the glenoid joint. E: Lateral oblique view: Arrows point to a ridge running along the last and second third of the scapula. Further arrow indicates a slight impression at the most anterior, distal end of the scapula and another shallow groove at the acromial part of the scapula. F: Medial oblique view: Arrows indicate impressions at the distal end of the scapula, superior to the glenoid joint and along the coracoid.. 87 Figure 53 .Charateristic features of the scapulocoracoid of Diplodocus longus (SMF) in lateral (A), frontal (B) and medial view (C). Lateral view (A): Long and slender scapula (I.), with a slight impression at the distal end (II.) and a bony ridge along the whole length of the scapula (III:). A prominent acromial region (IV) and a deep fossa on the lateral side of the extended part of the scapula (V) and the acromial ridge (VI). thickened bony structure above the glenoid joint (VII). Frontal view (B): The scapulocoraoid exhibits a medially convex shape. Coracoid is thickened and show a rugose structure at its medial side pointing towards the trunk (I.); Acromial ridge in frontal view (II.); The scapula is very thin, which is most pronounced at its cranial border (III.). The coracoid is positioned nearly in the same plane as the scapula (IV.) Medial side (C) Rugosities at the medial border of the coracoid (I.) and impressions at the coracoid blade (II.). Deep fossa at the medial side of the scapula (IV.). The most compact bony regions can be observed at the scapular part of the glenoid facet (V.). 88 4.4.3 Reconstruction of the shoulder girdle The reconstruction of the shoulder girdle of Diplodocus longus is based on mechanical pre-conditions for transmission of body weight from the trunk to the forelimb in one-limb stance, which are confirmed by means of the successful FESS of the scapulocoracoid. The reconstruction affects the overall position of the scapulocoracoid and the sternal plates as well as the position of the humerus (Fig. 54). The arrangement of the shoulder girdle elements allow for a closed circle of forces, kept in equilibrium by the required shoulder girdle muscles. 4.4.3.1 Skeletal elements of the shoulder girdle The scapulocoracoid is positioned parallel to the ribcage covering the first thoracic ribs in lateral view. The lateral inclination of the scapula now exhibits an angle of about 65° between the posterior side of the scapula and the horizontal plane, compared to 50° in the original mount (Fig. 54 A). The distal expansion of the scapula is slightly inclined to the dorsal margin of the vertebrate spines, leaving room for a cartilaginous suprascapula (Fig. 54 A). The coracoid plates now lie medio-frontally in the aperture of the ribcage. In contrast to the original mount they move towards each other, which results into a narrowed distance between the two halfs of the shoulder girdle (Fig. 53 B). Ample room is left for the adjacent sternal plates, which are therefore placed medio-posteriorily to the coracoids on the ventral side of the trunk (Fig. 54 B). The long axes of the paired sternal plates lie medially within the longitudinal axis of the body, firmly united by cartilage, whereas the whole plates are supposedly embedded into a cartilaginous plate, which expands at least over one half of the ventral side of the trunk (Fig. 55). The coracoid contacts the sternal plate at its short anterior border. Both elements together form the coracosternal joint (Fig. 55). This joint is assumed to exhibit a cartilaginous rim and tongue structure, where the coracoid rim moves within the sternal tongue, thus enabling relative movements between the shoulder girdle and sternum (Fig. 55). The lateral aspect of the triangular sternal element and the caudally expanding cartilaginous plate then provide room for connection to the distal ends of the thoracic ribs (Fig. 55 ). Following the reconstruction of the shoulder girdle the glenoid fossa faces slightly posteriorily (Fig. 53A). The humerus therefore articulates to the glenoid joint at a moderate angle of about 20° in lateral view, whereas the angle in frontal view is assumed to be not less than 15°. The maximal expansion of the proximal articulation facet of the humerus here is supposed to lie in the transverse plane of the glenoid facet (Fig. 53 A). 89 The position of the clavicles remains somewhat ambiguous. In the final calculation step without the trunk, one bearing was placed at the acromial region related to the contact area of the clavicle to the scapula. The reaction forces in this bearing was low compared to the sternocoracoid joint, transmitting the major amount of forces. The final calculation including the trunk shows a reduction of forces at this point, while showing constant conditions in the other regions. It is assumed, that the clavicles were positioned at the acromial regions, while their true function remains unknown. Thus, they were not included in the reconstruction. Figure 54 Shoulder girdle reconstruction of Diplodocus longus, in (A) lateral and (B) frontal view. Both situations before (black outlines) and after (grey) are shown. In lateral view the shoulder girdle is positioned more cranially covering the first rib. Inclination of the scapula is 60° after reconstruction, compared to 50° before. The humerus is rotated 45° around its y-axis; the maximal expansion of the humeral facet lies in the transverse plane of the glenoid joint. Position of the humerus is inclined 20° to the perpendicular (A). In frontal view the shoulder girdle is placed parallel to the ribcage; both coracoids are shifted medially, and contact the sternal plates. 90 Figure 55 Reconstructed shoulder girdle in ventral view (A). Coracoid plates contact the sternal plates ventro-medially. Sternal plates are embedded in a cartilaginous plate, where the distal ends of the ribs insert posterio-laterally. The coracosternal joint is built by cartilaginous parts of the coracoid and the sternal plates (A). The coracoid part is the tongue, while the sternal part builds the sliding rim or groove providing contact for the coracoid tongue (B). Circle of forces in one sauropod shoulder girdle is shown in frontal view (Fig. 56). Compressive forces in the shoulder girdle system require bony elements, while tensional stresses can be sustained by muscles or tendons. In a static system the weight forces of a body are transmitted from the trunk through the shoulder girdle elements to the supporting limb and back, while the ground reaction force acts in the opposite direction. For sauropods the circle of forces is reconstructed as follows (Fig. 56). Weight force of the body is transmitted by means of m. serratus superficialis from the trunk to the scapulocoracoid and via the glenoid joint to the supporting limb. The presumably abducted position of the limb, relative to the glenoid joint, leads to medially directed components of forces. They run from the scapulocoracoid via the sternal plates and over the ventral ribs back to the trunk, thus closing the circle of forces. In an abducted position of the humerus m. pectoralis will sustain the tensional forces, while m. deltoideus (clavicularis and scapularis) serve as the abductors of the forelimb. Further, in one limb stance tensional forces occur at the distal end of the scapula, which are taken by means of m. rhomboideus (Fig. 56). 91 Figure 56 Circle of forces in a sauropod shoulder girdle in frontal view. Compressive forces (white arrows) are taken by bony elements (black); tension (black arrows) is sustained by muscles (white). Weight force of the body (Fg) is transmitted by m. serratus from the trunk to the scapula, via the glenoid joint to the humerus. A medial component runs from the scapula to the coracoid via the sternal plates back to the trunk, closing the circle of forces. Ground reaction force (Fgr) therefore acts from the opposite direction. In an abducted position of the humerus (dashed humerus) m. pectoralis sustains the occurring tensile forces, while m. deltoideus serves as the abductor of the limb. 4.4.3.2 Muscles of the shoulder girdle The shoulder girdle muscles are reconstructed according to their mechanical function to keep the shoulder girdle in equilibrium during one limb stance (Fig. 57). Muscles are described as vectorial forces contributing to static equilibrium with regard to their line of action, whether they are single or subdivided, and their position in the model. Each force consists of components in the x-y- and z-axis, which are described separately to emphasize their contribution to movement. From this information anatomical position, origin and insertion site, as well as the function of the corresponding muscle is reconstructed. Reconstruction and determination of function was possible for all muscles running from the scapulocoracoid to the trunk, humerus, and antebrachium. Furthermore, m. pectoralis major, running between the trunk and humerus, contributes to static equilibrium. M. latissimus dorsi and m. teres major are the only muscles associated with the shoulder girdle system, which are excluded from calculation, as they supposedly play a major role during locomotion, but do not contribute to static equilibrium during one limb stance (Fig.57). Insertion sites at the model 92 compared to reconstruction can differ in some muscles. To simulate a laminar insertion at the bone, as it can be expected for m. serratus superior, m. levator scapulae or m. trapezius, the vectorial forces are shifted following their line of action. For example in m. serratus superficialis the force vectors are placed more cranially than it is described for reconstruction. This results into a homogenous distribution of stresses, the mechanical function is not affected. M. serratus superficialis- The total force of m. serratus superficialis is subdivided into a number of single vectors distributed evenly along the cranial border of the dorsal end of the scapula. In lateral view the forces are inclined posteriorily, inserting at the ventro-lateral side of the trunk. They rotate the bauraum in caudal direction. In frontal view forces are placed in the middle of the bauraum, pointing sidewards, inclination angles increase from the most cranial vectors to the vectors placed caudally. The forces draw the distal part of the scapula away from the trunk. M. serratus superficialis produces high y- and z-directional forces. Forces in x-direction are correspondingly lower. The muscle therefore originates from the fifth-eighth thoracic rib, running to the caudal border of the distal part of the scapula. M. serratus superficialis transmits body weight from the anterior part of the trunk to the scapula. As the main portion of the body weight is transmitted by this muscle, the required forces had to be correspondingly high. The determined insertion areas at both, the scapula and the ribs, provide ample space for an effective muscle diameter. M. serratus profundus- The total force is divided, with each single vector positioned at the distal end of the scapulocoracoid. The most cranial vector points to the frontal part of the trunk, the second is more or less perpendicular. The line of action in the third vector runs through the glenoid joint, while the most caudal vector is nearly parallel to the fibers of m. serratus superficialis. Altogether this muscle has a fan-shaped appearance. In frontal view the vectors point medially from the scapulocoracoid to the trunk. In sum all vectors produce zero rotational moments at the glenoid joint, while the main direction of forces lies in the y-axis. M. serratus profundus is positioned medially between the distal end of the scapula and the most anterior part of the trunk. It originates from the last cervical to the third or fourth thoracic rib. Its insertion is reconstructed at the medial side of the distal end at the scapula, ventrally to m. rhomboideus. M. serratus profundus supports the transmission of body weight and does not contribute significantly to rotation of the scapulocoracoid. As its fibers are slightly directed medially it prevents the scapula from sliding aside. The supportive nature of this muscle is most visible in its function to absorb the negative y-directional forces produced by muscles acting in cranial rotation of the scapula (i.e. m. trapezius and m. levator scapulae), while counteracting the caudal rotation of m. 93 serratus superficialis. Following this m. serratus profundus can be termed as a set-screw in this part of the shoulder-girdle system, keeping the sum of forces in equilibrium. M. trapezius- The total amount of force in this muscle is subdivided into a number of single vectors, which are positioned at the last third of the most caudal border of the scapulocoracoid. Corresponding vectors are placed at the dorsal midline of the trunk, anterior to the scapulocoracoid. All vectors are parallel to each other, their line of action is widely separated from the pivot of the glenoid joint. An increased lever arm, compared to m. serratus superficialis, allows for a decrease of forces, while countering the rotational moments at the scapulocoracoid, which are induced by the main weight bearing muscle. At the same time vectors of m. trapezius have high cranially directed z-axial components, while y-and x-axial components are low. M. trapezius originates from the dorsal midline of the trunk at the level of the last cervical and first thoracic vertebrae. Its cranial extension could be even more cranially, but this would not affect the results as forces. Its insertion is placed at the last third of the most cranial border of the scapula, dorsally to m. levator scapulae. M. trapezius is a cranial rotator of the scapula and together with m. levator scapulae serves to counteract the caudal rotation induced by m. serratus superficialis. M. levator scapulae- This muscle consists of a superior (m. levator scapulae superior) and an inferior part (m. levator scapulae), each of them subdivided into single vectors. The superior part is placed in the middle of the last third of the scapula; the inferior part is positioned below at the middle of the second third. In both parts corresponding vectors are placed at the most cranial end of the trunk. The vectors are parallel to each other, while the superior part of m. levator scapulae has a greater lever arm to the pivot of the joint than the inferior part. Muscle forces in the superior part therefore can be lowered to produce the same cranially directed rotational moments at the scapulocoracoid. As in m. trapezius high z-axial components of forces in both parts of m. levator scapulae translate the scapula cranially. The y-and x-axial components are comparably low. M. levator scapulae originates from the cranial border of the second third of the scapula to the acromial region. Its insertion is at the ventral side of the neck, presumably at the last four or five cervical vertebrae and/or adjacent cervical ribs. M. levator scapulae serves as a cranial rotator of the scapulocoracoid, supporting m. trapezius in counteracting caudal rotation. The wide distribution of this muscle along the cranial border of the scapula is reasonable as the elongated scapula acts as a long lever arm and provides ample space for m. levator scapulae in order to exert the required moments to the scapula. 94 M. rhomboideus- Vectors run parallel between the most distal end of the scapulocoracoid and the dorsal margin of the trunk. The vectors are mainly directed in the x,y-plane and consist of high x-axial forces. They prevent the most distal part of the scapula from sliding laterally. M. rhomboideus originates from the dorsal margin of the vertebral column. Its parallelly oriented fibers insert at the distal margin of the scapula and an assumed cartilaginous suprascapula. The cartilaginous part cannot be reconstructed beyond doubt. M. rhomboideus draws the distal end of the scapula towards the trunk. M. costo-coracoideus-The total force of this muscle is subdivided and runs parallel from the caudal border of the coracoid to the middle of the trunk, passing the glenoid joint ventrally. The forces exert mainly z-axial components, while x,y-components are low. It is rather close to the glenoid joint, and therefore has a short lever arm. Both cranial rotators of the scapula (m. trapezius, m. levator scapulae) produce high cranially directed z-axial forces. To establish static equilibrium not only rotational moments have to be balanced, but also the sum of forces has to be equalized. This is established by the cranially directed z-axial components of m. costocoracoideus drawing the bauraum caudally. It should be noted that without these forces no static equilibrium was reached in any calculation. M. costo-coracoideus originates from the ventral part of the first thoracic ribs, and inserts dorsally at the caudal border of the coracoid plate. It somewhat contributes to cranial rotation of the scapulocoracoid, but its major function is to draw the scapulocoracoid caudally relative to the sternum. M. costo-coracoideus pars profundus- The components of m. costo-coracoideus profundus are located in the middle of the coracoid and the ventral midline of the trunk. They are mainly directed medially, with a certain amount of z-axial forces. Components in the y-axis are low. The x-directed components draw the coracoid part of the scapulocoracoid towards the sternal part of the trunk. M. costo-coracoideus pars profundus originates from the sternum and in part from the first thoracic ribs and inserts at the dorsal side of the coracoid plate, anterior to m. costocoracoideus. This muscle serves as the main stabilizer of the coracosternal joint, as it prevents luxation of the joint by pressing the coracoid tongue towards the sternal rim. M. supracoracoideus- The total force of this muscle is subdivided and runs between the ventral side of the coracoid part of the scapulocoracoid and the anterior side of the humerus. Forces are directed mainly in the z-and x-axis, drawing the scapulocoracoid posteriorily and the humerus medially. Forces rotate the scapulocoracoid cranially, and at the same time exert posteriorily z-directed components, which are necessary to compensate for the large anteriorly directed z-components of m. levator scapulae and m.trapezius. The presence of this muscle allows 95 for reduction of forces in m. levator scapulae and m. trapezius as it serves as a support in cranial rotation. M. supracoracoideus originates from the anterior part of the ventral side of the coracoid plate and part of the most proximal border of the scapula, below the insertion of m. levator scapulae. Its insertion is on the lateral aspect of the humerus, near the glenoid joint. In one limb stance it serves as a stabilizer of the glenoid joint, playing a major role in establishing equilibrium between the scapulocoracoid and the humerus. M. coraco-brachialis brevis- The forces of m. coraco-brachialis brevis are placed at the coracoid part of the bauraum in front of the pivot of the glenoid joint and at the anterior side of the humerus. As in m. supracoracoideus the components are mainly directed in the z,x-axis, drawing the scapulocoracoid posteriorily and preventing the humerus from sliding laterally. Functionally these forces are similar, although its lever arm is longer, thus exerting higher rotational moments to the scapulocoracoid. M. coraco-brachialis brevis is reconstructed to originate from the ventral side of the coracoid plate above the insertion site of m. biceps brachii and posterior to m. supracoracoideus. Its insertion site is on the lateral side of the humerus below m. supracoracoideus. As the function is comparable to m. supracoracoideus, both muscles can be viewed as agonists during joint stabilization during one limb stance. M. biceps brachii- This muscle is positioned as one single force at the most medial part of the coracoid bauraum and the anterior part of the antebrachium. In lateral view this force runs at a far distance from the glenoid joint, but close to the pivot of the elbow joint. This results into a large rotational moment exerted on the scapulocoracoid, while expansion of forces can be kept low. At the same time the elbow joint is little affected. In frontal view distance to glenoid joint enables high rotational moments just as much as in lateral view, resulting into lateral movement of the scapulocoracoid and concurrent medial movements of the antebrachium. The laterally directed forces on the bauraum are balanced by m. costo-coracoideus pars profundus. Components are mainly y-, and x-axial, with a low portion directed posteriorily (z-axial). M. biceps brachii is reconstructed to originate from the ventro-lateral surface of the coracoid plate near the coracosternal joint. It presumably inserts on the anterior part of the antebrachium, whether on the ulna or radius cannot be determined beyond doubt. Along with m. coraco-brachialis and m. supracoracoideus it is an important stabilizer of the glenoid joint and contributes to minimize anterior movements of the scapulocoracoid in one limb stance. M. triceps caput coracoideum- It is positioned as one single force at the coracoid just in front of the pivot of the glenoid joint and at the middle of the antebrachium near the pivot of the elbow joint. In frontal view its lever arm to the glenoid joint is somewhat longer than at the elbow 96 joint, which results into moderate cranial rotation of the bauraum, while the antebrachium is not affected. Force components in the y-axis dominate, x-and z-directed components are low. M. triceps caput coracoideum originates from the medial side of the coracoid in front of the glenoid joint. It inserts on the posterior side of the ulnar element of the antebrachium. In an extend position of the humerus, as it is assumed in this reconstruction, m. triceps caput coracoideum contributes to moderate cranial rotation and backward drawing of the scapulocoracoid. M. triceps caput scapulare- This muscle originates from the lateral margin of the most proximal aspect of the scapula posterior to the glenoid joint and inserts along with m. triceps caput coracoideum behind the elbow joint in the middle of the antebrachium. In lateral view the distance to the glenoid joint is farer than to the elbow joint. The resulting force rotates the bauraum in caudal direction and contributes to posterior movements of the scapulocoracoid. In frontal view line of action runs close to the pivots of both joints, thus exerting only minor rotational moments in this plane. M. triceps caput scapulare takes its origin from the caudal border of the scapula proximal to the glenoid joint. The muscle inserts along with m. triceps caput coracoideum posteriorily at the ulna. M. triceps caput scapulare rotates the scapulocoracoid in caudal direction, while drawing it slightly backwards. Both parts of the triceps complex originate from either the posterior or anterior side of the glenoid joint. In an active muscle system they can act as mechanical antagonists, while balancing either forward or backward rotation, as needed. M. pectoralis- Total force of m. pectoralis is represented as one single vector. It is positioned at the posterior side of the humerus and near the midline at the last third of the trunk. Line of action lies mainly in the y,z-plane and exerts high z- and x-components of force, which results in posterio-medial movements of the humerus. Y-axial components of force are low. Forces applied to the anterior side of the humerus (m. supracoracoideus and m. coracobrachialis brevis) pull the humerus in cranial direction, whereas m. pectoralis counteracts these movements. M. pectoralis originates from the whole length of the ventral side of the sternal plates, at least to the level of the fifth thoracic rib. Its overall extension along the cartilaginous part of the sternum cannot be finally determined, due to lack of reliable information but it presumably does not to extend beyond the level of the fifth or sixth thoracic rib. M. pectoralis pars profundus- The establishment of static equilibrium requires a certain amount of caudally directed force components in the z-axis acting on the bauraum of the scapulocoracoid. This is due to the large amount of caudally directed z-components exhibited by m. trapezius and m. levator scapulae, which counteract the caudal rotation of the scapula. A certain portion but not all of these caudally directed z-components can be taken by m. costo97 coracoideus. M. pectoralis pars profundus was applied to produce the required z-directed components. Its line of action runs from the middle part of the trunk to the bauraum close to the glenoid joint. Main components are in z-and y-direction, whereas the x-directed component of force is low. As the force is applied close to the pivot of the glenoid joint, rotational moments exerted on the bauraum are low. M. pectoralis pars profundus originates from the medial side of the scapula, most profoundly at the glenoid joint and inserts at the second and third thoracic rib. Its main function in one limb stance is to pull the scapulocoracoid caudally. Further, it supports force transmission from the trunk to the scapulocoracoid, but only to a minor degree. M. deltoideus clavicularis- In frontal view the line of action in m. deltoideus clavicularis runs from the lateral side of the bauraum to the lateral side of the humerus. The total force is subdivided into a great number of single vectors applied to the scapulocoracoid, directed laterally, as they do at the humerus. The resulting angles between these pairs of forces are required to simulate a muscle running over the glenoid joint. By this arrangement the x-directed components of the muscle are higher, as if the pairs of forces were directed perpendicularly to each other. The sum of forces shows a high amount of medially directed forces acting on the bauraum. In order to reach equilibrium, these forces have to be countered by means of m. deltoideus clavicularis in the described modality. In lateral view line of action runs close to pivot of the glenoid joint, thus preventing lateral rotation of the scapulocoracoid bauraum. M. deltoideus clavicularis originates from the cranial edge of the scapula, in the region of the acromion and nearly the whole lateral aspect of the scapulocoracoid above the glenoid joint. In the fossil a deep impression is present at this location, providing ample space for the muscle. It inserts at the deltopectoral crest laterally at the humerus, along with m. deltoideus scapularis and m. pectoralis. Its serves as a stabilizer of the glenoid joint, as it prevents medial translation of the scapula. Further, following its line of action at the humerus, it serves as a lateral abductor of the humerus. M. deltoideus scapularis- The force of m. deltoideus scapularis is subdivided into a number of single vectors, which run from the middle of the scapula to the lateral aspect of the humerus. The arrangement is similar to m. deltoideus coracoideus. The forces are located superior to m. deltoideus coracoideus, which in comparison results into a longer lever arm and laterally directed rotational moments in frontal view. In lateral view rotational moments are lower. The forces are mainly directed in the y-axis. A certain amount of x- directed components translate the scapulocoracoid laterally. Little movement is present in the z-plane. M. deltoideus scapularis originates from the middle of the scapula. Cranially, it is positioned superior to m. deltoideus clavicularis. It runs close to the glenoid joint and inserts at the deltopectoral crest along with m. 98 deltoideus clavicularis and m. pectoralis. It stabilizes the glenoid joint, rotates the scapula laterally and, similar to m. deltoideus clavicularis, serves as a lateral adductor of the humerus. Its thickness is assumed to be lower than that of m. deltoideus clavicularis. This is because the muscle is able to exert the same amount of rotational moment with a lower amount of forces, because of the increased lever arm acting on the pivot of the glenoid joint in frontal view. M. subscapularis- The forces of m. subscapularis point from the medial side of the scapulocoracoid to the medial aspect of the humerus at the level of the glenoid joint. The arrangement of single vectors can be compared to that of m. deltoideus clavicularis and scapularis, as it is applied to balance the occurring rotational moments at the glenoid joint, but in opposite direction. The main components of this force lie in the y-and x-axis. The medially directed x-components at the scapulocoracoid provide stability as they move the scapula to the trunk, but to a lower degree than the counteracting forces exerted by the muscles of the deltoid group. M. subscapularis originates from the medial side of the scapula and covers a large area, which is provided by a bony impression at this location. It inserts deep at the medial side of the glenoid joint. Rotational moments can only be viewed in frontal view, whereas muscle actions do not affect lateral stability. This muscle is a stabilizer of the glenoid joint in one limb stance and is required to counter forces exerted by all laterally acting muscles. M. scapulo-humeralis- This muscle is applied as one single vector, pointing from the lateral side of the humerus to the second third of the scapula. The force is comparably low as laterally directed x-axial components are only required to a minor degree at this location. In frontal view it serves to pull the scapula laterally, thus minimizing bending in the scapula at this position. At the same time the forces exert moderate caudally directed rotational moments at the scapulocoracoid. M. scapulo-humeralis originates from the second third of the scapula, lying anterior to the insertion of m. serratus superficialis, below m. teres major. Its insertion is clearly separated from m. deltoideus scapularis by a prominent bony ridge running from the most distal end of the scapula to the proximal basis of the scapula near the glenoid joint. It contributes less to the establishment of static equilibrium. Considering its line of action, running from the scapula to the humerus posterior to the glenoid joint, its major function is that of a retractor of the humerus during locomotion cycles. M. teres major- This muscle is represented by one single force. Its line of action runs from the posterior, middle part of the scapulocoracoid to the posterior side of the humerus. The distance to the pivot of the glenoid joint is smaller than for m. scapulo-humeralis, therefore the resulting rotational moments are lower. The major component of force is directed to the y-axis; x99 and z-axial components are low. M. teres major was determined not to contribute to static equilibrium in one limb stance, therefore it is excluded from the muscular setting in the final calculation.M. teres major presumably originates either from the caudal border of the last third of the scapula, lying superior to m. scapulo-humeralis, or posterior to the bony ridge of the scapula, superior to m. deltoideus scapularis. As no calculation could be completed with this muscle included in the system this cannot be determined beyond doubt. M. teres major has no stabilizing function in one-limb stance, but it could in addition to m. latissimus dorsi serve in retraction of the humerus during locomotion. M. latissimus dorsi- It consists of one single force running from the dorsal margin of the trunk to the posterior side of the humerus. The line of action runs at a wide distance to the pivot of the glenoid joint, which results in high rotational moments at the humerus. The main components are in the y-and z-axis, but a certain amount of forces drags the humerus towards the trunk. The muscle is not present in the final calculation. M. latissimus dorsi presumably originates from the dorsal fascia at the thoracic vertebrae and inserts at the second third of the posterior side of the humerus. According to the long lever arm of m. latissimus dorsi at the glenoid joint, it serves as a strong retractor during locomotion, but does not contribute to static equilibrium in one limb stance. Figure 57 Reconstruction of the insertion sites of the muscles to the scapulocoracoid in lateral (left) and medial view (right). M. serratus superficialis(1), M. serratus profundus (2), M. trapezius (4), M. levator scapulae superior (5), inferior (6), M. rhomboideus (3), M. costo-coracoideus (10), M. costo-coracoideus profundus (11), M. supracoracoideus (16), M. coraco-brachialis brevis (19), M. biceps brachii (17), M. triceps caput coracoideum (18), M. triceps caput scapulare (8), M. pectoralis pars profundus (9), M. deltoideus clavicularis (15), M. deltoideus scapularis (12), M. subscapularis (7), M. scapulo-humeralis (14), M. teres major (13). 100 The cross sectional areas (CSA) of the muscles determined above is estimated by dividing muscle force by the maximal isometric stress of lacertilian skeletal musculature [0.2 N/mm² (see methods, Medler, 2002)] (Table 2). The largest CSA is present in m. serratus superficialis, formerly determined as the most weight bearing muscle in one limb stance. Large CSAs are also present in m. serratus profundus, m. trapezius, m. costo-coracoideus, m. pectoralis profundus, m. supracoracoideus, m. coracobrachialis brevis ventralis, m. deltoideus scapularis, m. deltoideus clavicularis and in both parts of m. levator scapulae (scapularis et clavicularis). CSAs estimated for m. rhomboideus, m. costo-coracoideus pars profundus, m. pectoralis, m. triceps caput coracoideum, m. biceps brachium and m. subscapularis are comparably lower (Table 2). The smallest CSAs are found in m. rhomboideus, m. triceps caput scapulare and m. scapulo-humeralis. CSAs are presented in cm² to give an impression of their overall dimensions and to be compared to the skeletal elements to which they insert (Table 2). To evaluate, whether the muscles found ample space in the skeleton or were underestimated, the dimensions of the skeletal insertion sites for some muscles are compared to the estimated CSAs. Muscular architecture differs between the respective muscles. Some of them presumably insert directly to the bone or at distinct areas via a tendon. A comparison of the insertion sites with the estimated CSAs, although only approximately, is only possible for muscles in which length and breadth of the assumed insertion sites can be measured. If the muscle inserts via a tendon to the bone, it cannot be correlated to the assumed insertion site, as it does not reflect muscle body dimension. Muscles that count for the first condition are m. serratus superficialis, m. trapezius and m. levator scapulae (superior). The insertion site of m. serratus superficialis at the scapula is assumed to be 60 cm in length and maximally 3 cm in breath, accounting to 180 cm². The area of origin at the thoracic ribs is assumed to extend over 100 cm in length and maximally 5 cm in breadth, accounting to 500 cm². A maximal CSA of about 880 cm² was estimated for this muscle. Assuming a mean value for insertion length of about 80 cm², the maximal thickness of about 11 cm² in this muscle is required. M. trapezius is assumed to insert along the scapula over a distance of 40 cm. The maximal width at the cranial border is 3 cm. Insertion area therefore would be 120 cm². The origin of this muscle extends over an assumed distance of approximately 80cm in length, its width cannot be determined beyond doubt. If the latter is assumed to be maximally 5 cm², according to the breadth of the vertebral spines, the estimated value accounts to 400 cm². The estimated CSA of m. trapezius is 215 cm², thus the formerly determined forces would be underestimated. The insertion sites of both parts of m. levator scapulae (superior) are assumed to be 30 cm and 40 cm in length, and a maximal breadth of 2 cm, respectively. M. levator scapulae therefore exhibits 60 cm² at its superior part and 80 cm² at the inferior part of the muscle. The origin extends 101 presumably 120 cm along the ventral side of the neck to insert at the cervical ribs and has a maximal breadth of about 5 cm. CSA in this case would be 600 cm². The CSAs for both muscles together has been formerly estimated as 208 cm², which is significantly lower than the CSAs provided at the muscle insertion sites. Table 2 Cross sectional areas of the shoulder girdle musculature in Diplodocus longus, calculated out of maximum muscle forces obtained from FESS. No Muscle Force (N) A (mm²) cm² 1 2 M. serratus superficialis 17603 88015 880,15 M. serratus profundus 1 301 1505 15,05 3 M. serratus profundus 2 1895 9475 94,75 4 M. trapezius 4300 21500 215 5 M. levator scapulae 3000 15000 150 6 M. levator scapulae superior 1175 5875 58,75 7 M. rhomboideus 1000 5000 50 8 M. costo-coracoideus 4800 24000 240 9 M. costo-coracoideus pars prof. 3000 15000 150 10 M. pectoralis profundus 4500 22500 225 11 M. pectoralis 3500 17500 175 12 M. triceps caput coracoideum 1900 9500 95 13 M. triceps caput scapulare 1000 5000 50 14 M. supracoracoideus 4500 22500 225 15 M. biceps brachii 2000 10000 100 16 M. coracobrachialis brevis ventralis 4000 20000 200 17 M. deltoideus scapularis 5000 25000 250 18 M. deltoideus clavicularis 6000 30000 300 19 M. subscapularis 2000 10000 100 20 M. scapulo-humeralis 500 2500 25 a with a specific tension like that of Iguana of about 0.2 N/mm² (Medler, 2002) 102 Chapter 5 5.1 Discussion Form and function of the tetrapod body The stress analysis of the 3-D FE models of solid tetrapod bodies reveals the distribution of mechanical stresses in a tetrapod-like body by the time the body is released to gravity. Two different positions of the forelimbs were investigated, the sprawling type representing the primary condition observed in early tetrapods as well as in many extinct and extant reptiles; the extended type as it is exhibited in cursorial mammals. The 3-D FE models reveal stress patterns in regions representing the limb girdles and trunk, which clearly depend on the mass distribution in the head, neck and trunk as well as the position and posture of the supporting limbs. In both the reptilian and mammalian type the compressive and tensile stresses at local regions are significantly higher during asymmetrical stance, which emphasizes the relevance of locomotion for the demands on the supporting musculoskeletal system. In the FE-models the trunk is subject to bending moments which compress the dorsal and stretch the ventral side during symmetrical support. Compression stresses spread between both fore- and hindlimbs and the dorsal side of the trunk, thus indicating a connection to the vertebral column at both regions. This has to be taken as the initial condition. In tetrapods, dorsal stresses are sustained by compression resistant structures like the vertebral column. However, no connection exists in the shoulder region of more derived tetrapods. By contrast, the mobility between the pelvic girdle and the vertebral column is restricted. During locomotion the movement of the body is accomplished by transmission of ground reaction forces resulting in forward propulsion. In tetrapods acceleration is mainly accomplished by the hindlimbs, whereas the forelimbs act in deceleration and direction changes (Hildebrand & Goslow, 2001; Alexander, 2003). In early tetrapods the shoulder region is more engaged in lifting the body off the ground than in true locomotion. A connection to the vertebral column therefore is reasonable, as the forelimbs are the first limbs to develop, carrying the entire body weight. In Tiktaalik, who supposedly represents a semi-aquatic locomotor type living in shallow water, the shoulder region shows no direct connection to the head, due to a loss of the operculum and extrascapular 103 elements, thus enabling striking head movements (Shubin et al. 2006; Downs et al. 2008). Nevertheless, it has a medio-dorsal connection via the anocleithrum and supracleithrum (Shubin et al. 2006; Downs et al. 2008). This can be regarded as an intermediate stage, where a certain stiffness is maintained via a connection to the vertebral column, but an enhanced mobility of the shoulder girdle can be established based on these preadaptations. As soon as the tetrapod hindlimbs have fully developed, the main propulsive action is transferred caudally. An enhanced mobility at the forelimbs and shoulder region still requires a connection to the vertebral column which is realized by more flexible structures as muscles and ligaments (Shubin, 1995; Coates, 1996; Shubin et al. 2006; Downs et al. 2008; Boisvert, 2008). The highest values of compressive stresses are located at the insertion sites of the limbs at the trunk, i.e. the glenoid joints. In the sprawling type two portions of maximum compressive stress patterns spread from the inserting limb, first, dorso-laterally along the trunk and, second, ventrally to the midline of the trunk. In extant reptiles the scapula (lateral aspect) and the coracoid plate along with an interclavicula connected to the sternal elements (ventral aspect) are located at this position. In early tetrapods like Tiktaalik or Acanthostega the scapula is not as developed as in later forms, additionally lacking the sternal elements, whose their function can be adopted by the cleithrum (lateral aspect) and the well developed clavicle (ventral aspect) (Shubin et al. 2006; Coates, 1996). As soon as the animal lifts one forelimb off the ground (asymmetrical support) as in walking, the stress distribution and values are modified. At the position of the scapula of the standing limb tension occurs dorsally, while compression increases ventrally. Thus, the alternation of symmetrical and asymmetrical support during sprawling locomotion confirms the relevance of a continuous compressive resistant structure medially between the limbs. This increased stresse is significantly lower in extended than in sprawling limb models. In extended limb position only minor compression is visible between the forelimbs both in symmetrical and asymmetrical support. Thus, no compression resistant structures are required. Mammals possess a sternal element, but it is reduced to a rod-like element and has no bony connection to the shoulder girdle. In the mammalian type compressive stresses concentrate dorso-laterally spreading from the inserting limb to the trunk. This inclination is more pronounced in an extended limb stance than in the sprawling model, which in fact corresponds to observations in extant cursorial mammals and lacertilians. Compression is also visible at the ventral side of the neck region, which is in accordance to the more ventral location of the cervical vertebrae, especially in mammals exhibiting a long neck. In contrast, crocodiles exhibit a more inclined position of the scapula, 104 intermediate between the condition of mammals and lacertilians. Although they are mostly engaged in aquatic locomotion, crocodiles can hold their forelimbs under the body during high speeds, termed the high walk and are able to perform gaits similar to the gallop (Zug, 1974; Webb & Gans, 1982; Renous, 2002). Crocodiles descend from quadrupedal terrestrial ancestors and therefore have a derived forelimb condition, which can not be equalized to the situation in modern lacertilians (Hutchinson & Gatesey, 2000; Benton, 2005). Additionally, in one limb support, torsional stresses occur at the surface of the trunk, which are higher and spread over larger areas than bending stresses in symmetrical stance. Stresses run obliquely from the scapula of the weight-bearing limb to the contralateral support (hindlimb). These stresses have tensile as well as compressive components. The first can be sustained by the oblique muscles of the ventro-lateral body wall; the latter necessitate segmental bony elements, namely the ribs (Preuschoft et al. 2007). The compressive stresses are concentrated in the periphery, therefore leaving the centre of the trunk without stress. Thus, the body cavity is less important to absorb mechanical stresses resulting from locomotion and therefore can provide space for the intestines. Torsional stresses increase in sprawled and extended limb positions, but are always concentrated in the periphery of the trunk. The tensile stresses have been related to appropriate muscular structures, as the m. rectus abdominis, which sustains tensile stresses along the ventral contour in animals of both sprawling and extended locomotor type. Correspondingly, on the dorsal side of the anterior trunk and posterior neck tensile stresses occur, which again can be sustained by neck and shoulder muscles connecting the head to the trunk and pectoral girdle. The corresponding muscles in extant tetrapods can be determined, although homologies differ between taxa. This will not be discussed in detail, as the aim of the study is to relate the structures due to their mechanical requirements, not their phylogenetic relationships. Shoulder girdle musculature in early tetrapods had not been described in detail by now. In Tiktaalik the adductor of the pectoral fin presumably corresponds to m. pectoralis in more derived tetrapods, as it originates at the coracoid or a more ventral element and inserts at a prominent crest at the medial side of the humerus. The only muscles considered in comparative studies on the evolution of pectoral girdle musculature in basal tetrapods are adductors and abductors of the pectoral girdle, although further muscles are supposed to be required (Shubin, 2006, Diogo & Abdala, 2007). According to the presented stress distributions at the shoulder girdle, the transmission of body weight between the trunk and the forelimbs was realized in two different ways in mammals and reptiles. In an extended limb position the weight forces of the anterior part of the body are 105 carried by the forelimbs, the scapula, the ribs, and sternum. The reaction forces expand as follows: 1. ground- forelimb- scapula via mm. serrati to the ribs and the vertebral column, 2. forelimb and scapula via the m. pectoralis profundus to the sternum (Preuschoft et al., 2007). Therefore, the first ribs are straight and strong, and the thorax is narrow. Cursorial mammals usually do not display great abduction movements of the forelimbs to prevent horizontal forces, which cannot be countered by the existing structures. The narrowness of the trunk also helps to minimize the rotational moments in one limb stance, which is essential for saving muscle energy (Preuschoft et al. 2007). A different situation is presented by living reptiles, amphibians and early tetrapods, which usually hold their limbs in a sprawling position. The weight forces are carried by the humerus, the scapulocoracoid and the ribs. The sprawling posture necessitates horizontal tensional forces which can be produced by the m. pectoralis. The resultant of ground reaction force and pull of the m. pectoralis passes through the shoulder joint. These joint forces can be separated in two components, a horizontal part and a vertical part. The ground reaction forces run through the forelimb to the shoulder joint. The horizontal part of the forces flows through the coracoid plate to the sternal apparatus, whereas the vertical part runs via the scapula, transmitted by the posterior part of m. serratus over the middle ribs to the vertebral column (Preuschoft & Gudo 2005, Preuschoft et al. 2003). Figure 58 Scheme of two basic shoulder girdle constructions. Compressive force transmission is indicated as grey vectors, tensile stresses as black arrows. A: sprawling position as in early tetrapods and recent reptiles. Compressive force transmission from the shoulder girdle to the trunk is accomplished from the coracoid via the sternal element to the ribcage. Tensile stresses are carried by the m. rhomboideus, m. serratus and m. pectoralis. B: extended position as in cursorial mammals. No bony connection is present between the shoulder girdle and trunk. Transmission of body weight force Fg and ground reaction force Fgr is solely accomplished via muscular structures. 106 The observed compressive stresses in both the sprawling and the cursorial model are in remarkable accordance with the major skeletal elements described in extant species. According to the results of the morphological comparison the position of the shoulder girdle elements is similar in all tetrapods. The scapula is always positioned parallel to the rib cage covering the first ribs latero-cranially. In addition the dorsal margin of the osseous scapula, or cartilaginous suprascapula, lies nearly parallel to the vertebral column. Lateral inclination of the scapula ranges from 50° to 60°. M. serratus has been determined to play the major role in transmission of body weight to the forelimbs (English, 1978, Jenkins & Weijs, 1979; Jenkins & Goslow, 1983; Larson & Stern, 2007). Enhanced function in body weight transmission leads to an increase of vertical compression within the ribs. Scapular position in extant quadrupeds correlates to the position of the most weight bearing ribs. Thus, all tetrapod bodies underlie the same mechanical conditions since the body is exposed to earth gravity. In case of the shoulder girdle this means that appropriate bony, muscular and tendinous structures are required for a successful transmission of body weight over the limbs to the ground to enable locomotion. These results will be the basis for the further investigation of the shoulder girdle in extant crocodiles and sauropod dinosaurs. Although sauropod dinosaurs exhibit the "typical" components of a reptile shoulder girdle, morphological changes of the shoulder girdle elements as well as in the musculature are visible and necessary. As a consequence of the presented results, further investigations should combine a functional approach with an analysis of rugose attachment sites in the fossil. The requirements of the musculo-skeletal system engaged in terrestrial locomotion could then be correlated to muscular and tendinous structures. With this approach the musculature can be reconstructed, taking into account phylogenetic as well as functional considerations for extinct animals. During evolution the number of shoulder girdle elements in both extinct and extant tetrapods underwent some alterations. The most profound changes appear at the transition from water to land, when it comes to a striking increase of element number and structural expansion, and during mammalian evolution, where a reduction of elements takes place (Romer & Parsons, 1977). With regard to the results in this study this is strongly related with fundamental changes in locomotor behaviour. Besides a variety of selective pressures like climate changes and other exogene influences (Clack, 2007; Carroll, 2005) biomechanical conditions have to be considered as selective pressures during the evolution of the tetrapod bauplan as well. This was recently pointed out in a study about body mechanics in the early tetrapod Tiktaalik roseae (Hohn et al., submitted). It was shown that Tiktaalik was able to organize its movements so as to keep the 107 necessary muscle force at the lowest possible level, because energy expenditure is proportional to the muscle forces required for movements (Alexander, 2002). Movement dependent mechanical stimulation has a significant impact on cartilage and bone remodelling during embryogenesis and postembryonic life (Carter 1987; Lightfoot & German 1998, Jones et al. 2007; Gomez et al. 2007). Influenced by epigenetic factors the structure of bone seems actually to depend on its mechanical function, its shape directly results from mechanical stress acting within the locomotor system (Müller & Streicher 1989; Newman & Müller, 2005). Thus the overall mechanical impact on bone formation is beyond discussion, but as it has been stated in the first paragraph, the major role of compressive stresses still is neglected by some authors (Biewener et al., 1991; Carter & Beauprè, 2001; Currey 2002; Liebermann et al., 2003). Mechanical stresses inducing bone formation in this approach are always compressive stresses, as predicted by Wolff (1892) Pauwels (1965) and Kummer (1962). This has been recently supported by both cell physiological studies (Kaspar et al., 2000; Rath et al., 2008, Takahashi et al. 1998, Sato et al., 1999; Ikegame et al., 2001) and biomechanical approaches using the finite-element method (Witzel, 1985, 1996, 2000, 2003, 2005a, 2005b; Sverdlova & Witzel, 2010). The origin and development of the tetrapod bauplan are widely discussed in anatomy, developmental biology, and palaeontology. The importance of epigenetic factors in ontogenetic and evolutionary processes was pointed out by Newman & Müller (2005) stating that “the increasingly autonomized skeleton continues to be reshaped and embellished by novelties that arise from the continued responsibility of chondrogenetic tissue to the biomechanical environment.” A question still unacknowledged is how the evoked stresses lead to the development of novel elements and their position in the locomotor system. One of the most dramatic changes in pectoral girdle evolution is the dissociation from the head skeleton enabling the forelimbs to move independently from the head. Studies on chicken cranial neural crest cells indicate their influence on the organisation of the skeletomuscular connectivity between the head and the trunk (Huang et al., 1999) and help to explain how skeletomuscular connectivity between the pectoral girdle and the head is maintained during tetrapod evolution, even though the pectoral girdle and the skull became dissociated during this process (Mc Gonnel et al. 2001). The repositioning of muscular attachment sites due to migrating cells during the evolution of the vertebrate skeleton could provide ground for a better understanding of the formation of novel construction within the tetrapod bauplan (McGonnel, 2001). If muscles change their position within in the musculoskeletal system, they evoke different stresses acting on the involved skeletal elements or developing tissue. This was recently pointed out by a study on hip joint 108 endoprothesis investigating physiological loading conditions in the femur in different loading cases during locomotion using finite-elements (Sverdlova & Witzel, 2010). In an evolutionary context this may result into remodelling of actually present bony tissue during ontogenesis or induce the formation of novel structures. Morphological changes occur gradually rather than suddenly. During early tetrapod evolution a striking increase of the enchondral elements (scapula, coracoid) of the shoulder girdle can be observed (Shubin et al. 2006). At the same time the dermal elements (cleithral series) of the shoulder girdle, which are functionally engaged into aquatic locomotion and feeding are reduced (Romer & Parsons, 1977; Shubin 2006; Downs et al. 2008). Enhanced terrestrial locomotion behaviour, as indicated by the fossil record, led to an increase of body weight, as a result of gravitational acceleration. This results in an increase of the counteracting muscle forces, which are required during locomotion. The gradual changes in the shoulder girdle construction, which can be observed in basal stem tetrapods, therefore indicate a close relationship between form and function in the vertebrate skeleton. However, Romer & Parsons (1977) attributed the enlargement of the ventral elements to the downwards acting body weight which otherwise would push both coracoids apart. By contrast, the results gained from the analysis of the 3-D FE models of tetrapod bodies indicate that body weight is transmitted from the trunk via muscular structures like the mm. serrati to the scapula and to the supporting forelimbs. Thus, it is suggested that the ventral elements increased as a result of the mechanical stresses occurring during terrestrial locomotion. In consequence the ventral elements provide additional attachment sites for the necessary musculature. The formerly described traits of the tetrapod bauplan can be viewed as biomechanical necessities of standing and walking on limbs. Some of these features like an enhanced development of the shoulder girdle elements especially on the ventral side and the appearance of short ribs can first be observed in Tiktaalik (Shubin et al. 2006). In marsupials, the appearance and reduction of certain elements can be observed during the individual development. In marsupials the development of the shoulder girdle consists of two parts. The embryonic and neonate stages show a strong similarity to the shoulder girdle architecture in monotremes, where the scapula, metacoracoid, procoracoid, first rib, paired sternal elements, unpaired sternal elements and clavicle together form the shoulder girdle. There is a strong functional- adaptive correlation in this temporary formation, as the neonates have to reach the mother`s pouch after birth on their own, crawling with the aid of well developed forelimbs (Klima, 1987). The stresses occurring in the marsupial pectoral girdle require structures that are able to transmit large medially directed forces, a condition which is only present in a 109 sprawling limb posture. When the neonate has reached the pouch certain elements are reduced and the tight connection between both sides is lost. In particular, the metacoracoid is reduced to the coracoid process, and the procoracoid becomes the praeclavium. The unpaired sternal element fuses with the paired elements generating the manubrium sterni (Klima, 1987). The maintenance of function in a system at all times is a precondition for morphological transformation. Even if the fossil record is often lacking gradual transitional forms along the evolutionary line between different clades, there is no doubt that function was maintained in every stage. Furthermore, a structural element can only be transformed within the constraints established by the surrounding structural elements and the organism as a whole (Gudo & Homberger, 2002). The present data are consistent with these conclusions. Indeed, our results reveal that location and shape of bony structures and associated muscles depend on the occurrence and distribution of compressive and tensile stresses, respectively. 5.2 FESS of the crocodilian shoulder girdle In the present approach, equilibrium within the 3-D finite-element model of a crocodile has been reached by application of functionally required muscular elements in iterative steps. Function here is related to the relative movements of each shoulder girdle element in the 3dimensional space. To maintain equilibrium element movement is countered by the necessary muscles, which allow determining their function in maintaining balance. In the following, muscles are discussed according to their function revealed in the study, compared to former descriptions and their impact on the system, which relates to link stresses. M. serratus superficialis transmits weight forces from the trunk to the scapulocoracoid. It supports the trunk, while simultaneously forcing the scapulocoracoid to rotate caudally. The large expansion of m. serratus superficialis from the lateral side of the trunk to the caudal border of the scapula is advantageous for transmission of large forces. Muscles are distributed over a wide area, thus producing sufficient muscle force. At the same time, these forces produce significant rotational moments at the glenoid joint, therefore, the scapula acts as a lever. The weight supporting function of m. serratus superficialis as described in the literature (Brinkmann, 2000; Meers, 2003), is consistent with the recent results. Although m. serratus profundus is supposed to support transmission of weight forces, its function cannot be determined during the process. However, it can be stated that it does not account for any rotation of the scapulocoracoid and it is less loaded after calculation compared to the resulting link stresses. 110 The rotational moments induced by m. serratus superficialis need to be compensated by appropriate muscles, which were identified as m. trapezius and m. levator scapulae. Their function as cranial rotators of the scapula has formerly been described in the literature (Brinkmann, 2000; Meers, 2003). By contrast, their function in counteracting these movements during one limb stance had yet to be determined. It became obvious during calculation that m. trapezius and m. levator are not sufficient to prevent the rotation of the scapulocoracoid. M. costo-coracoideus is required to maintain equilibrium in the shoulder joint, as it contributes to cranial rotation of the scapulocoracoid and translation of the coracoid relative to the sternal region of the trunk. Both m. trapezius and m. costo-coracoideus have been enhanced in the final calculation step by an increase of link`s cross section and pretension leading to higher forces. As no calculation was possible before, this procedure points out the importance of these structures for cranial rotation of the scapulocoracoid and caudal translation of the coracoid for static equilibrium. Although m. levator scapulae is required to maintain equilibrium during calculation, this function is not reflected by the resulting link stresses, which were near zero. In crocodiles m. pectoralis major has a broad fan-shaped appearance, originating from the most cranial aspect of the sternum almost reaching the pelvis (Meers, 2003; Brinkmann, 2000). M. pectoralis in the present approach is separated into two different functional compartments. The anterior part prevents lateral movements of the humerus and is confirmed in its role as the main humeral adductor. According to the dissection, the majority of its musclefibres are directed anterio-posteriorily, indicating its relevance as a humeral retractor. Considering the aquatic lifestyle in crocodiles, strong humeral retraction is required to support swimming motions. Based on the present results, these parts of the muscles do not contribute to static conditions. Link stresses after calculation reveal their contribution under static loading. In the course of adjusting equilibrium, m. teres minor, m. latissimus dorsi and m. scapulohumeralis were applied to the system (calculation not shown in the results). None of these calculation steps could be accomplished by any possible combination. They obviously do not contribute to static equilibrium in the shoulder girdle system and were excluded from further calculations. Muscles originate from the posterior part of the vertebral column, insert at the caudal edge of the humerus (m. latissimus) or run from the medial (m. teres minor) or caudal edge (m. scapulo-humeralis) of the scapula to the humerus. These muscles are commonly described in the literature as humeral retractors (Meers, 2003; Brinkmann, 2000), although their line of action additionally forces the scapula to rotate caudally 111 At this point of the investigation, it can be stated that function could only be determined for those muscles, which clearly contribute to static equilibrium of the shoulder girdle in one limb stance. The function of all further muscles associated with the shoulder girdle remain unclear. Nevertheless, they have a certain impact to the system as they contribute to decrease maximum compressive stresses, from -105 MPa in early stages of the process to -20 MPa in the final calculation, which is within the predicted physiological stress range of -2 to -20 MPa typical for cortical bone (Witzel & Preuschoft, 2005). As the absolute muscle forces cannot be determined at this point of investigation, they should be evaluated qualitatively, by comparison of their load after calculation. For this purpose link stresses after calculation were read out. For some of the muscles the observed stress values correlate with their functional relevance in static loading during one limb stance (e.g. m. serratus superficialis, m. costo-coracoideus, m. trapezius and m. pectoralis), while for others no functional significance was revealed during calculation (m. levator scapulae, m. serratus profundus). As for volume elements, deformation in the model after calculation is indicated by black outlines. The direction of the link elements changes their predefined position according to the relative movements of each element in the model. Consequently, the line of action of some muscles is altered. In some elements this does not lead to relevant changes, and these elements still retain their function. In case of m. levator scapulae, the trunk and scapulocoracoid movement lead to an expansion of the link element by changing its relative line of action. Expansion due to an alteration in the lines of action of the muscles is therefore the most reasonable explanation for the observed zero stresses within m. spiralis and m. serratus profundus as well. The finite-element method has been part of a number of studies investigating vertrebrate skull (Daniel & McHenry, 2001; Rayfield, 2004, 2005; Dumont et al., 2005; Ross et al., 2005; McHenry et al., 2006; Wroe et al., 2008) or rib morphology (Fujiwara, 2009), but none of them used a multi-body approach to reveal locomotion related stresses within the skeletal structure. The present study is the first attempt of a multi-body FESS applied to the shoulder girdle. Link elements were used according to former finite-element approaches, because they provide stability during calculation, especially if a number of elements act in a 3-dimensional space. Although stability was maintained, the resulting forces were found to be insTable during calculation. Again, it is emphasized that former studies never included more than two separate volumes connected by link elements (McHenry et al., 2006; Wroe et al., 2008), thus the presented difficulties had not been reported until now. It is concluded from the results that link elements are insTable during the calculation process and do not provide any information about absolute 112 force values, which can be compared to the musculature. As mechanical forces act in the x,y,zaxis, they provide detailed information, thus directed forces instead of link elements are recommended for further multi-body approaches. The maximal muscle forces, which can be determined reflect the occurring stresses in one loading case. For a reasonable comparison of muscle cross sections, as it was initially aimed at by this approach, a number of different load cases should be calculated and superimposed, as it has been performed in the FESS of a Diplodocus skull (Witzel & Preuschoft, 2005). Such an approach would lead to an overall impression of the muscular activity of the shoulder girdle musculature. Unfortunately, there are no EMG data of the crocodilian shoulder musculature available, neither in statics or during locomotion, which could provide ground for further comparison. Nevertheless the present 3-D FESS of a crocodilian shoulder girdle shows compressive stress distributions, which are near the physiological value of bone and enables the first synthesis of the main features in the scapulocoracoid of a crocodile. The function of the shoulder girdle muscles could be determined for some of the elements with special emphasis on their ability to maintain equilibrium in the glenoid joint. The findings provide the basis for the following investigation of the scapulocoracoid in sauropods. Considering the present results together with the information gained from morphological comparison in extant tetrapods, and 3-D FE analysis of solid tetrapod bodies, the preconditions for a 3-D FESS of Diplodocus longus will be configured. 5.3 3-D FESS of the shoulder girdle of Diplodocus longus 5.3.1 Reconstruction of the shoulder girdle of Diplodocus longus. 5.3.1.1 Skeletal elements One of the most debated issues in reconstruction refers to the overall position of the shoulder girdle on the trunk and especially the inclination of the scapula. Several indicators for scapula reconstruction in sauropod dinosaurs were considered in former publications. In first attempts the position was deduced from either comparison with extant reptiles without any functional considerations (Hatcher, 1901; Osborne and Mook, 1921) or refer to the "death pose" in the excavated fossil (Gilmore, 1932), leading to 60° or 45° inclination of the scapula to the horizontal plane. The taphonomic processes during the decay of a vertebrate body affect both the individual bones and the skeleton as a whole (White and Folkens, 2005). The position of the individual bone in the skeleton after decay is different from the initial situation. Each bone looses its connection to the skeletal composite at different stages of the decay, depending on the 113 strength of the adjacent ligaments and muscles. Therefore bones with predominantly muscular connections, as the scapula, are disconnected earlier from the composite than vertebraes do. Further distortions could arise from other animals feeding on the carcass and physical influences, like water, heat and geological pressure during the fossilization process (Lyman, 1994). Therefore, the scapular position deduced from "in-situ" finding is somewhat doubtful. The orientation of the glenoid joint serves as another factor affecting scapular position. The glenoid is reconstructed facing ventrally in order to allow the forelimb to articulate in an upright columnar stance, reflecting a graviportal forelimb configuration (McIntosh et al. 1997, Wilson & Sereno 1998, Bonnan 2001, Upchurch et al. 2004, Wilhite, 2003). Since the limbs in quadrupeds are straightened with increasing body size to prevent high rotational moments at the joints (Biewener, 1989, Reilly et al. 2007), highly abducted limbs in sauropods are unlikely. Our results, however, show that optimal force transmission is not limited to a strictly vertical orientation of the humerus but is also present at small angles of up to 20° between the humerus and the perpendicular in lateral view. A slight abduction of the humerus as presented in this thesis therefore is reasonable, because without any flexion in the joint, the occurring compressive stresses acting on the joint’s surface would be too high to resist (Christian et al., 1999). Furthermore, if the humerus was positioned orthogonally to the glenoid joint, the scapula would possess an inclination angle of about 40° or less (McIntosh et al. 1997, Wilson & Sereno 1998, Bonnan 2001, Upchurch et al. 2004, Wilhite 2003). According to the results of the basic finiteelement tetrapod models an inclined position of the scapula is visible in both the sprawling as well as in the extended limb stance, but it never reaches a degree of inclination below 50°. Wilhite (2003) furthermore argued that, resulting from best-fit articulation of digitized skeletal elements, the humerus has to be articulated in a ventrally facing glenoid. He assumed the thickness of cartilage to be uniform across the joint surfaces. Thus, the distances between articulating elements should be uniform as well. The distance between joint surfaces therefore should be the minimum distance required for the highest bone surface rugosities to rotate across the joint without touching the corresponding joint surface. The condition in Alligator joints is used to confirm these assumptions (Wilhite, 2003). The study provides no mechanical confirmation. Up to now, reconstruction of cartilage is not possible for fossil vertebrates because a number of yet unknown parameters to calculate material properties and structural behaviour is not available. Thus, the absolute dimensions of cartilage in extant animals remain speculative. An orthogonal position of the humerus of Diplodocus is not only assumed in lateral but in frontal view. The orientation of the maximal width of the saddle shaped humerus facet is 114 predicted to lie in the transverse plane of the glenoid joint. It was rotated along the long axis of the humerus at 45° compared to the original mount of Diplodocus longus (SMF), which is generally accepted until today (Bonnan, 2001; Wilhite, 2003, Schwarz et al. 2007; Remes et al. 2007). Following the assumption of a columnar forelimb with a posteriorily facing glenoid joint, little bending in the brachial-antebrachial joint and a restricted movement of the humerus in an anteromedial- posterolateral direction is assumed (Wilhite, 2003). By contrast, in the present study abductional movements in the forelimbs are predicted, because the enormous length and weight of the neck causes moments in the anterior part of the trunk, which can only be countered with abducted forelimbs (Preuschoft und Gudo 2005). The saddle shaped glenoid facet and the flattened caput humeri of sauropods indeed enable abduction/adduction as well as extension/flexion. Therefore, a moderately extended posture of the forelimbs, with slight flexion in the shoulder as well as in the elbow joint in lateral view, and a moderate ability for abducting movements in frontal view is assumed. In the present study the glenoid joint is represented by a simple ball and socket structure, which does not resemble the situation in the fossil. No differentiation was made between bone and cartilage at this point. This was done because of the uncertain dimensions and material properties in sauropod cartilage as stated before. Nevertheless the model was satisfactory for the present attempt as the glenoid joint is able to transmit forces and allow for rotational movements with a minimum of friction, a state which can be termed as physiological. The results reveal a concentration of stresses in the scapulocoracoid at the position of the glenoid joint. These stresses tend to spread caudally, if the bauraum would provide more space than provided in the model. An increase of contact area provided by an assumed cartilage cover would have led to caudal expansion of compressive stresses and therefore of bone material at this location. It is assumed that the missing caudal inclination of the scapula border could relate to this circumstance. Finally, this would lead only to marginal modifications. It is recommended for future investigations to take these considerations into account, thus leading to an elaborated implementation of the method. In this investigation the scapulocoracoid is positioned parallel to the rib cage, covering the first thoracic rib, whereby the glenoid is placed shortly before the ribcage. This is determined to be the basic morphological conditions as they are present in all extant quadruped tetrapods (see morphological comparison in extant tetrapods). Beside this apparent relationship a close correlation between the most weight bearing ribs and scapular position was recently described (Fujiwara et al., 2009). These ribs serve as attachments for the body weight transmitting muscle, 115 the m. serratus, and show the highest resistance against vertical compression. As these ribs lie almost beneath the scapula, scapular position was concluded based on this information (Fujiwara et al., 2009). Although the weight bearing ribs can be determined the relative position of the scapula in extinct animals remains unclear if it is deduced exclusively based on the ribs. Length of m. serratus superficialis as well as the inclination of the line of action in the fibers of the muscle is unknown in fossils. If these variables change, scapula position will change its direction as well. In the present investigation the ribs, which serve as attachment sites for m. serratus superficialis lie closely behind the scapula as it is predicted by the former approach. In contrast, their position was reconstructed based on mechanical necessities, providing a mechanically effective lever arm for the acting musculature leading to the observed shape of the scapulocoracoid. Although determination of weight bearing ribs does not allow for a final reconstruction, it contributes necessary information. At this point further investigations are contemplated including measurements on a high number of individuals to evaluate the most weight bearing ribs in sauropods. In the shoulder girdle system the position of one element has an impact on the other component. Thus the reconstruction of the coracoid position derives from former assumptions. A number of questions arise concerning the presence of any contact between the coracoids and the sternal plates, the morphology at this location, and the relative position of the elements. The sternals are often misinterpreted in the fossil record or found not to fit to any "reasonable" reconstruction and were therefore left out of the whole mount (McIntosh, 1988). The original mount of Diplodocus longus (SMF) presents no sternal plates, with the coracoids placed more laterally, thus leaving a wide gap between the coracoid plates in front of the ribcage. By contrast, in the mount of HQ1 (SMA) the sternal plates lie in front of the ribcage and in close contact to the coracoids. These two extreme positions are reflected by the literature. The mounted skeletons of a number of sauropods indicate no direct connection, in fact, the sternals were placed posterioventrally far behind the shoulder girdle. The first reconstructions of Diplodocus and Camarasaurus, although differing in many issues, recommend a possible connection between the coracoids and the sternals, but leave out any information on the definite position (Hatcher, 1901; Gilmore, 1932). As soon as the coracoids are seen as integral parts of the sternal apparatus, they should be connected with the sternal plates (Schwarz, 2007). Thus, several reconstructions recommend that the coracoids should be oriented vertically in front of the rib cage (BorsukBialynicka, 1977; McIntosh, 1997; Wilhite, 2003). 116 According to the observations in the present study and of other researchers (Schwarz et al., 2007) such a morphological condition cannot be detected in any extant tetrapod, because it would result into the loss of the ventral connection of the sternals and the distal ends of the thoracic ribs. The connection therefore can only be maintained if the coracoids are placed in the same plane as the sternal plates, thus leading to an inclination angle of the scapula of 60° to the vertebral column (Schwarz et al., 2007). This can be seen as strong morphological argument, which is confirmed by the results of the present investigation. If the scapulocoracoid is placed relative to the ribcage as it is predicted in the present study, the frontal aperture is narrowed, bringing the coracoids closer to the midline. With the assumed limb posture a medial component of forces runs through the glenoid and extends to the midline of the trunk. Therefore, the circle of forces in the horizontal plane can only be completed if the forces flow from the humerus via the coracoid to the sternals and back to the trunk via the distal ends of the ribs. This is consistent to the results of the 3-D FE models of tetrapod bodies, in that locomotion requires a compression resistant structure between both half's of the shoulder girdle in order to provide effective force transmission within the shoulder girdle system. A similar condition is present in the shoulder girdle of extant reptiles, where the transmission of forces is most visible in the FESS of the crocodilian shoulder girdle. Here high compressive stresses occur at the contact region between the trunk and the coracoid. The coracoids and sternals in sauropods do account for this function in the present case. The coracoid therefore resists the compressive stresses which occur between the shoulder joint and the sternum. In the present case the sternals lie in close medio-caudal contact to the coracoid plate to transfer the occurring forces to the ribs. Compared to the condition in extant reptiles and mammals the circle of forces in sauropods reveals an alternative way. In brief, force transmission in the mammalian shoulder girdle is accomplished only by the shoulder girdle muscles. Forces in the extended limb position flow mainly vertically, reflected by straight first ribs lying beneath the scapula, giving the thorax a narrow appearance (Preuschoft et al. 2007, Preuschoft et al. submitted). No medially directed forces occur, as mammals usually do not display significant abduction in the humerus. The sprawling limb position in extant reptiles and early tetrapods produces additional horizontal forces, which require a medially positioned compression resistant structure as stated in the former paragraph. Compared to mammals, crocodilians possess short, but stout anterior and rather strong middle ribs, where only the latter are connected to the sternum. According to the present reconstruction, the anterior trunk in sauropods is narrow like in mammals. They show particular strength of their middle ribs, while the anterior ribs are longer than in crocodiles and 117 seem to have reached the sternal elements. However, the curvature of the middle ribs is similar to cursorial mammals. The vertical portion of the occurring stresses is enhanced, while the horizontal parts are lowered. In consequence the sauropod coracoids are reduced in their dimensions and modified in shape, but still present. It can be concluded that the shoulder girdle system in sauropods was modified to the requirements of a graviportal locomotor type using their reptilian skeletal components. Like their overall position in the shoulder girdle system, the morphology of the connection between the coracoids and sternal plates is strongly debated. Two different conditions are currently assumed. In the first condition the elements are embedded in a ventral cartilaginous plate, connected to each other by sutures and/or synchondroses (Whilhite, 2003; Schwarz et al., 2007, Remes, 2008). Alternatively the elements are connected via a joint, similar to the situation in extant reptiles (Bakker, 1987). Such a condition would lead to an increase of the arc of rotation in the forelimbs and enhance mobility in the shoulder girdle. Some authors assume that the only motion within the shoulder girdle occurred in the gleno-humeral joint (Henderson 2006; Bakker 1987, Paul 1987; Christiansen 1997; Wilhite 2003). During quadrupedal locomotion translational movements of the shoulder girdle occur. In lacertilians (varanids, chameleon) the coracoid moves translational relative to the sternal apparatus (Peterson, 1973; Jenkins & Goslow, 1985; Lilje, 2007). The junction between coracoid and sternum in these reptiles exhibits a” groove and tongue” mechanism, where the bony part of the sternum acts as the groove in which the coracoid is moving. In crocodilians, these movements are enabled by rotation of the elongated coracoid relative to the sternum. Coracoid and sternum exhibit a “rim and tongue” structure as well, but consist of cartilage rather than bone. In both cases, the junction is surrounded by a joint capsule embedded in connective tissue. The condition in sauropods differs from modern lacertilians, as no bony rim and tongue structure can be detected. This holds true for the condition in crocodiles as well as the cartilaginous parts would be diminished during decay and fossilization. In fact the cartilaginous tongue and rim structure in crocodiles has been either not reported or their relevance has been underestimated in the literature. The histological cross sections of a Caiman presented here point out the structure in the coracosternal joint, which indeed holds all features of a true joint. Based on this observation a similar condition is assumed to have been realized in sauropods. In fact the mobility in the shoulder girdle becomes restricted with an increase of body size and weight. The FESS of the scapulocoracoid of Diplodocus shows a model in which the coracoid part and the sternal region are connected through contact elements enabling relative movements. The joint is hereby 118 stabilized by muscles e.g. the m. costo-coracoideus. The mobility of this joint although restricted, is indispensable for the function of the shoulder girdle, because it provides the ability for force transmission from the coracoid to the sternum and at the same time leaves a certain degree of mobility in the shoulder region. 5.3.1.2 Muscles of the shoulder girdle One major difference in the reconstruction of the shoulder girdle muscles in sauropods in this investigation compared to other attempts is the mode of determination. Muscle reconstructions were performed based on the presence and position in extant crocodilian myology, like for Opisthocoelocaudia (Borsuk-Bialinicka, 1977; Schwarz, 2007), Camarasaurus, Apatosaurus, and Diplodocus (Wilhite, 2003; Schwarz, 2007) or with the aid of the extant phylogentic bracketing (EPB) method, in which both archosaur outgroups, crocodilians and birds are considered (Remes, 2008). The latter study investigates the basal sauropods up to Patagosaurus, which is the most phylogenetically derived sauropodomorph. Except for Remes (2008), no reconstructions include all muscles acting on the shoulder girdle. In the present study the musculature was determined by its function to maintain static equilibrium and transmission of weight force from the trunk to the limbs. Although crocodilian myology serves as a basis for muscular structures suited for this function, their line of action and forces values were chosen by mechanical necessity. During the process all muscles assumed to be present in the sauropod shoulder girdle based on the terminology of Alligator mississipiensis could be determined according to their possible function in static equilibrium. This includes muscles connecting the trunk and the pectoral girdle as well as muscles running from the pectoral girdle to the humerus and the antebrachium. Additionally some muscles were included, which connect the humerus and the antebrachium. In Schwarz et al. (2007) m. serratus superficialis in Diplodocus inserts at the medial surface of the suprascapula and the caudal margin of the scapula. Orientation of the cranial bundles of muscle fibers is supposed to be ventrally, as the caudal bundles are orientated caudo-ventrally. Its origin is assumed to be at the fourth or fifth thoracic rib. An insertion at the caudal margin of the scapula is consistent with the present results. M. serratus superficialis is the main weight bearing muscle, exerting high forces on the scapula. Therefore an insertion at the cartilaginous part of the scapula is mechanically inadequate. The calculation further reveals the caudal bundles to be oriented not only caudo-ventrally but laterally to a certain degree, thus contributing to reduce bending in the long scapula. Remes (2008) suggested the muscle to insert at the first third of the 119 scapula. A placement at this location would inhibit an effective lever arm of the muscle and is inconsistent with any comparison with extant reptiles and crocodiles. In contrast, he reconstructed the m. serratus profundus in two portions inserting on the medial part of the distal scapula; one originating from the 3-6th thoracic rib, and the other part from the last cervical and first and second thoracic rib. Functionally the caudal part is equivalent to m. serratus superficialis in the present approach, while the cranial part is consistent with the results. In the present study m. serratus profundus originates from the last cervical and first to third thoracic rib, inserting at the medial part of the distal scapula. Its line of action is mainly vertical, and transmits a lower amount of weight forces than m. serratus superficialis, while rotating the scapula only to a minor degree. It contributes to equilibrium of forces in the shoulder girdle system by countering the negative vertically directed forces exerted from the cranial rotators of the scapula. This functional implication could only be revealed by a functional approach and was not documented before. However, no mechanical evidence is present to support the assumption of a cranial expansion of this muscle as predicted by Schwarz et al. (2007). In the studies by Wilhite (2003) and BorsukBialinicka (1977) this muscle was not taken into account for reconstruction. The elongation of the scapula is one apparent feature of sauropods. The scapula acts like a long lever since muscle forces insert there. In the current reconstruction the area below the scapula provides space for an effective distribution of m. serratus superficialis according to the high forces it has to exert. As rotational moments refer to the distance to the pivot, the inclination of muscles fibers and therefore the distance to the glenoid joint had to be low enough to prevent high rotation, but at the same time wide enough for an effective muscle diameter. The most reasonable placement was chosen in this calculation. If the scapula would be oriented horizontally this would not provide enough space for the muscle, meanwhile rotational moments would increase and result in larger cranial z-directional forces. Both, the rotational moment and the cranially directed z- forces would have to be countered. This would result in an unphysiological amount of forces to be produced by the antagonistic muscles. Therefore, elongation of the scapula is interpreted as an adaptation to high body weight. According to m. trapezius and m. levator scapulae a shorter lever arm could not provide sufficient area for muscle insertion to exert the forces required to counteract the high rotational forces induced by the weight bearing m. serratus superficialis. Counteracting muscles would be thickened beyond a physiological limit to produce the same forces, in order to reach sufficient counteracting rotational moments. M. rhomboideus in this study originates from the dorsal margin of the trunk and inserts medially at the most distal end of the scapula. It is assumed to have inserted in part at a 120 cartilaginous suprascapula, which was not modelled in the present case because of limitations described above. Schwarz et al. (2007) assumed a cranial expansion of this muscle, while the insertion and origin are consistent with the current results. Its main function here is to prevent lateral movements of the distal scapula, as its direction of forces is oriented in the medial plane. Again no mechanical evidence is provided in the present study to assume a different position as predicted by Remes (2008). The expansion of the suprascapula declines during sauropod phylogeny and correlates with a reduction of size and function in m. rhomboideus. This is supported by the predicted cross sections for this muscle and the provided space for a distally expanding cartilaginous part in the present model. Both m. trapezius and m. levator scapulae act as cranial rotators of the scapula, thus counteracting the caudal rotation of the scapulocoracoid resulting from m. serratus superficialis forces. The first was reconstructed to run from the last third of the scapula to the dorsal midline of the trunk at the level of the last cervical and first thoracic vertebrae. The latter expands in two portions from the cranial border of the second third of the scapula and the acromial region to the cervical ribs. The reconstruction by Remes (2008) is consistent with our results, except he assumed the muscular lines of action to be crossed, leading to a ventral insertion at the scapula of m. trapezius and dorsal insertion of m. levator scapulae, respectively. Functionally this corresponds to the present results, but anatomically makes less sense, as such a condition is absent in extant tetrapods. Reconstruction of muscle orientation in m. levator scapulae by Schwarz et al. (2007) is mainly in accordance to the present study, although the cranial expansion in the study is enhanced. The presence of m. trapezius was not considered in this investigation (Schwarz et al. 2007), or by Borsuk-Bialynicka (1977) and Wilhite (2003). The present study reveals that m. costo-coracoideus in this study has a large impact on static equilibrium in the shoulder girdle. The coracoids were reconstructed to allow for this muscle a line of action running caudally beneath the glenoid joint. Because of its small lever arm, it contributes to cranial rotation to a minor degree, but translates the coracoid caudally, which is essential in maintenance of static equilibrium. Without m. costo-coracoideus no equilibrium could be established in any calculation. The coracoid plates were reduced during sauropod evolution, but are still present, thus provide insertion areas required by this muscle. M. costo-coracoideus has been reconstructed to run from the lateral side of the coracoid anterior of the glenoid to the ventral ribs (Remes, 2008) or from the medial side of the coracoid dorsally to the ribs in front of the glenoid joint (Borsuk-Bialynicka, 1977). Both reconstructions do not contribute to the former determined function of this muscle, as the predicted line of action in that study would prevent 121 any translational movements of the coracoid relative to the sternum. The muscle has not been described by Schwarz et al. (2007) and Wilhite (2003). A differentiation in a superficial and a profund part of m. costo-coracoideus was assumed only by Meers (2002). M. costocoracoideus pars profundus in crocodiles originates from the cranial surface of the free ribs, without any fibers inserting at the sternum. In contrast, the superficial part of m. costo-coracoideus has been found to insert at the sternum (Meers, 2002), a stabilizing function of the sternum was predicted to be insignificant (Meers, 2002). The presence of m. costo-coracoideus profundus in sauropods is first described in this study. In the present investigation it has been reconstructed because of its requirement as a stabilizer of the sternocoracoid joint, as it prevents luxation of the joint under static loading conditions. If the muscle fibers of m. costo-coracoideus, which insert to the sternum, belong to a profound or superficial part of the muscle is immaterial, because the existence of such parts is supported by functional requirements. M. supracoracoideus has been decribed to originate from the lateral side of the coracoid at its distal end (Remes, 2008; Wilhite, 2003) or placed more proximally (Borsuk-Bialynicka, 1977), while its insertion is positioned at the deltopectoral crest (Remes, 2008; Wilhite, 2003) or extends to the lateral head of the humerus (Borsuk-Bialynicka, 1977), respectively. The first placement is consistent with the present study. It is defined as a humeral extensor, but no function under statical loading conditions has been mentioned. In the present study m. supracoracoideus is described as a stabilizer of the glenoid joint, as it exerts the required translational forces to keep the scapulocoracoid in equilibrium relative to the humerus. Again this muscle has not been considered in the study by Schwarz et al. (2007). Schwarz et al. (2007) do not illustrate or mention m. coraco-brachialis brevis. In the study by Borsuk-Bialynicka (1977) it was placed to originate on the distal medial bend of the coracoid and to insert at the humerus at two points, the anteroproximal surface of the humerus and anteromedial surface of the medial condyle. Further, an origin from the lateral surface of the short coracoid has been assumed or at least placed directly above the glenoid, while its insertion would have been on the cranial surface of the humerus medial to the deltopectoral crest (Wilhite, 2003; Remes, 2008). The latter reconstructions are consistent to the present strudy. M. coracobrachialis is a strong adductor in crocodiles and lacertilians, corresponding to the strong abduction of the limbs. It has been assumed to be reduced in sauropods because of their upright posture. A shift of function therefore is reasonable. In crocodiles the coracoid is positioned at an approximated angle of 90° to the scapula, therefore the origin of the muscle is far from the 122 glenoid joint and the humerus, accounting for an adductional function. In sauropods the coracoid has been shifted nearly into the same plane as the scapula, which results into a modification of the line of action of m. coraco-brachialis. In the present study its line of action runs rather anterior-posteriorily than medio-laterally. This indicates higher rotational and translational movements of the scapulocoracoid and protraction of the humerus, rather than an adduction of the humerus. Therefore its function is comparable to m. supracoracoideus, which acts as an agonist in maintaining equilibrium between the scapulocoracoid and the humerus. M. biceps brachii has not been mentioned by Schwarz et al. (2007) and Wilhite (2003). Borsuk-Bialynicka (1977) placed the origin of this muscle dorso-laterally at the coracoid, just below the assumed origin of m. coracobrachialis brevis. Its insertion is assumed to be at the distal end of the radius. Remes (2008) assumed a different insertion at the ulna and found its origin to be placed more ventrally at the lateral side of the coracoid just below the origin of m. coracobrachialis brevis (Remes, 2008). The origin at the coracoid assumed in the latter study is in accordance to the current results. The insertion site cannot be determined with certainty as ulna and radius were not differentiated in the present investigation. Referring to its line of action, m. biceps brachii serves as a protractor of the antebrachium, while rotating the scapulocoracoid caudally. Further functions revealed by this study are the prevention of craniad movements of the scapulocoracoid. Therefore it contributes to equilibrium between the scapulocoraoid and the humerus. The function as well as origin and insertion sites for the m. triceps complex have been described differently in the literature. In crocodiles this muscle complex consists of five heads, in which the first two originate from the coracoid and scapula anterior and posterior to the glenoid joint, respectively. The latter three heads are placed at the humerus. As no conditions could be evaluated by this study in which the humeral heads contribute to static equilibrium, they were not considered for reconstruction. Therefore, their presence can be neither confirmed nor excluded. In crocodiles the main function of the muscles is the extension of the antebrachium, according to the sprawling limb position. The upright posture of the limbs in sauropods, in contrast, does not correspond to this function. A reduction of the muscles is indicated by the loss of a prominent ulnar olecranon, which serves as insertion site of all triceps heads at the ulna in extant reptiles and mammals. The scapular head of the triceps complex in this study has been reconstructed to originate proximally from the caudal side of the scapula posterior to the glenoid joint. The coracoid head is placed just anterior to the glenoid joint laterally at the coracoid. In one limb stance they contribute to static equilibrium by either caudad (scapular head) or craniad 123 rotation (coracoid head) and caudad translation of the scapulocoraoid, as well as craniad translation of the antebrachium. The latter function probably plays a major role in equilibrium within the elbow joint. The triceps complex has been excluded in the study by Schwarz et al. (2007). Borsuk-Bialynicka (1977) reconstructed only two heads, a scapular and a humeral one. The origin and insertion of the scapular head is consistent with the present study, but the humeral head has been placed at the humerus just below the glenoid joint. This is not supported by any functional indication. Wilhite (2003) assumed five different heads for sauropods similar to the condition in crocodiles. No information was given about their origins at the scapulocoracoid, although a tendinous insertion at the posterior process of the ulna has been assumed. Remes (2008) reconstructed the origin of only one head at the middle of the caudal scapular border. The insertion is placed at the anterior side of the proximal humerus. Again this is in not in accordance with the function of the muscle defined in the present study. M. pectoralis in the present study orginates from the bony sternals and an assumed cartilaginous sternal plate, which extends to the position of the fifth thoracic rib. M. pectoralis contributes to retraction of the humerus during locomotion, its main function has been reconstructed according to its lever arm. It indicates an anterior-posterior translation of the humerus relative to the glenoid joint, and a caudad rotation of the humerus within the glenoid joint. Although a certain amount of force is directed medially, the function as a humeral adductor is less important in one limb stance. M. pectoralis is the main adductor in the crocodile forelimb and has been described mainly according to this function (Borsuk-Bialynicka, 1977; Wilhite, 2003; Remes, 2008). It was not included in the reconstruction by Schwarz et. al. (2007). Its origin at the sternal plates and insertion at the deltopectoral crest of the humerus is consistent with the present results (Borsuk-Bialynicka, 1977; Wilhite, 2003; Remes, 2008). An origin at the sternal plates would lead to a different function, if the sternals were oriented in front of the ribcage (Bialynicka, 1977; Wilhite, 2003). In such a position the force exerted by the muscle would run medio-dorsally from the humeral insertion. Consequently the humerus would not only be abducted, but also protracted and lifted. According to the present study such a condition would be disfunctional and cannot be observed in any other extant tetrapod. In addition this supports a more caudo-ventral position of the sternal plates. According to the limited dimensions of the sternal plates the size of this muscle seems to be reduced. In an upright limb posture the abduction of the humerus is reduced and therefore requires lower adductional forces. A correlation between size of the sternal plates and dimension of the m. pectoralis is reasonable. Nevertheless, the extension of the cartilaginous sternal plate is unknown, which could have provided insertion for part of the muscle. In the present study m. pectoralis is reduced in size 124 corresponding to former investigations. It plays an important role in static equilibium as it translates the humerus caudally. M. pectoralis pars profundus in the only muscle assumed to be present in sauropods, which is not described in crocodiles and is not mentioned in any other study. It was included for calculation, because of the requirements during static loading conditions. The muscle runs from the first thoracic ribs to the medial side of the scapula, and inserts deep above the glenoid joint. Therefore it translates the scapulocoracoid caudo-medially, without exerting any rotational moments. The presence of a profound part of m. pectoralis is currently known only for therian tetrapods (Maier, 1971). Here it is termed m. pectoralis minor, which runs from the thoracic ribs to the scapula, where it inserts deep at the glenoid joint. It has been stated before, that the archosaur musclulature remains conservative along the evolutionary line. Nevertheless, the apparent modification in the bony sauropod shoulder girdle justifies the former assumption based on functional requirements. Modifications of the musculature take place whenever the habit of locomotion has changed. The acquisition of flight in birds, for example led to alterations of the primary reptilian musculature in order to perform the new behaviour. Investigations on migrating cells associated with the shoulder girdle indicate that muscular attachement sites are repositioned during evolution, thus providing new functions (McGonnel, 2001). The homology and derivation of the assumed profound part of m. pectoralis can be disputed. The mechanical requirements of the sauropod shouler girdle indicate that such a muscle is required in the system. M. deltoideus coracoideum originates from the deep fossa and cranial border of the cranially extended part of the scapula (acromial region) and inserts proximolaterally along with m. deltoideus scapularis and m. pectoralis at the deltopectoral crest of the humerus. The line of action indicates lateral abduction of the humerus. In one limb stance this muscle prevents a medial translation of the scapula. The same term was used by Remes (2008). It was named in the literature as m. deltoideus scapularis (Wihite, 2003) or m. scapulohumeralis anterior (BorsukBialynicka, 1977). The muscle was not considered for reconstruction by Schwarz et al. (2007). Although its insertion at the humerus again is largely consistent with the present results, its scapular origin is different. Remes (2008) assumed the origin to be exclusively at the clavicles, which were positionend at the acromial region of the scapula. In basal sauropods no cranially expended part of the acromial region is present. Therefore, a comparison with Diplodocus is inadequate. A certain amount of fibers probably inserts at the clavicles in Diplodocus, which would not alter the function described above. An expansion of the muscle over the extended acromial region is suggested by the present data. The acromial ridge and the deep fossa of the 125 scapula were assumed as the scapular origin by Wilhite (2003), which is consistent to the present study. The major function here would be to draw the humerus dorsally and posteriorly. A horizontal position of the scapula was assumed in this study, leading to the described line of action for the muscle. Even in this reconstruction the muscle overlies the glenoid joint, thus leaving little lever arm for an effective protraction of the humerus. No information was given about the influence of the muscle on the scapula. The insertion of m. deltoideus scapularis was reconstructed at the deltopectoral crest along with m. deltoideus coracoideum, while the origin is placed at the middle of the scapula cranial to the scapular ridge. Similar to m. deltoideus clavicularis, the muscle serves as an abductor of the humerus and reduces bending in the elongated scapula, In contrast to the former muscles it exerts little caudal rotation to the scapula. In the literaturs it is equivalent to m. dorsalis scapulae (Wilhite, 2003; Remes, 2008) or m. deltoideus scapularis (Borsuk-Bialynicka, 1977). The muscle was excluded from the investigation by Schwarz et al. (2007). The condition in basal sauropods (Remes, 2008) is different from Diplodocus, however, the presence of such a muscle has been noted. The insertion and origin of m. deltoideus scapularis is consistent with the current results (Borsuk-Bialynicka, 1977; Wilhite, 2003), but the horizontal position of the scapula, which has been assumed in the investigations, results into different lines of action and function of the muscle. In the assumed position the muscle could neither act as an abductor of the humerus nor serve in humeral retraction, because of its small lever arm and direction of forces. M. subscapularis in the present study originates from the medial side of the scapula and inserts deep at the medial side of the glenoid joint. Its presence is required for static equilibrium in one limb stance, as it exerts medially directed rotational moments to the scapula and therefore can be termed as an antagonist of the deltoid muscles. M. subscapularis corresponds to m. subcoracoscapularis described by Borsuk-Bialynicka (1977). The assumed origin and insertion are consistent with the present study, whereas again the line of action and function in the muscle are altered due to the horizontal scapula position. The placement of the muscle and shoulder girdle position assumed by Remes (2008) are comparable to the current results. The muscle was not described by Wilhite (2003) and was omitted from reconstruction by Schwarz et al. (2007). In the present investigation m. scapulo-humeralis originates from the second third of the scapula, anterior to the insertion of m. serratus superficialis and below the m. teres major. It inserts posteriorly at the humerus below the glenoid joint. It plays a minor role for static equilibrium, although it could serve as retractor of the humerus during locomotion. In other studies the muscle was not mentioned (Borsuk-Bialynicka, 1977; Wilhite, 2003) or was excluded 126 from considerations (Schwarz et al., 2007). Remes (2008) assumed two different parts of m. scapulo-humeralis to be present in basal sauropods; m. scapulo-humeralis caudalis and cranialis. Both parts originate ventrally from m. deltoideus scapularis and insert distally at the posterior side of the humerus. While the humeral insertion is consistent with the recent findings, the origin is placed more ventrally than assumed by the present study. Retraction of the humerus is also possible in this reconstruction, but to a lower degree, as the distance to the pivot of the glenoid joint would be decreased. M. teres major in the present investigation is assumed to originate either from the caudal border of the last third of the scapula, superior to m. scapulo-humeralis, or posterior to the bony ridge of the scapula, superior to m. deltoideus scapularis. The muscle was found to have no stabilizing function in one-limb stance, but it could in addition to m. latissimus dorsi serve in retraction of the humerus during locomotion. Remes (2008) and Schwarz et al. (2007) did not mention or even excluded this muscle from reconstruction. M. latissimus dorsi presumably originates from the dorsal fascia at the thoracic vertebrae and inserts at the second third of the posterior side of the humerus. According to the long lever arm of m. latissimus dorsi relative to the glenoid joint, it serves as a strong humeral retractor during locomotion, but it does not contribute to shoulder girdle stability and static equilibrium in one limb stance. Borsuk-Bialynicka (1977) and Wilhite (2003) did not figure or reconstruct m. latissimus dorsi in their studies. Remes (2008) described a similar condition for this muscle referring to the origin and insertion sites and the predicted function. In comparison to the present results, a shoulder girdle stabilizing function is assumed for m. latissimus dorsi (m. dorsohumeralis in their study) by Schwarz et al. (2007). In the investigation the muscle overlies the scapula and inserts posteriorly to the humerus. Stability of the shoulder girdle would then be achieved by tension of the body wall musculature, which would result in a hydraulic tension of m. latissimus dorsi (m. dorsohumeralis) (Schwarz et al. 2007). Following the results obtained in this study no such stabilizing function is required, as equilibrium or stability in the shoulder girdle system can overall be maintained by means of the acting muscles determined in the present investigation. 5.3.1.3 Muscle forces and dimensions Muscle forces and dimensions were estimated for all muscles involved in static equilibrium in one limb stance. Largest cross sectional areas and consequently the highest forces can be found for m. serratus superficialis. Cross sectional areas (880 cm²) and forces (17603 N) are at least 2 or 3 times as high as was estimated for the other muscles. In comparison cross sectional 127 areas and force values for all other muscles ranged between 25 mm²-300 mm² and 500 N- 6000 N , respectively. The discrepancy between the observed values for m. serratus superficialis and the other shoulder girdle muscles can be explained. From the models, cross sectional areas can only be determined approximately as further informations are required to gain absolute values. The internal architecture of the muscles (Alexander & Ker, 1990; Payne et al., 2005) and physiological conditions of individual muscle fibers (Azizi et al, 2008) are assumed to have a large impact on the values of the exerted forces and the correlation between forces and cross sectional areas. Because of the extensive calculation process in this first attempt of a 3-D multi-body FESS only one load case was calculated. By comparison, in the synthesis of the diplodocoid skull by Witzel & Preuschoft (2005) four load cases, which refer to biting, lateral pulling to either side, gravity and opening the snout, were calculated and summarized by a load case technique (Witzel & Preuschoft, 2005). By this physiological superposition of forces, the range of motion and function of all muscles involved can be considered. The range of motion and function in the shoulder girdle musculature is usually not restricted to the situation in one limb stance, as shown before. Most muscles are able to perform a minimum of two different functions. M. serratus superficialis, therefore, is an exception. It has exclusively been described, throughout the literature, to be the main weight bearing muscle in quadruped tetrapods. Electromyographic data for an extant reptile shows activity in this muscle during the whole locomotor cycle (Jenkins & Goslow, 1983). Thus, a similar restriction of muscle function is assumed for sauropods. M. serratus superficialis is the only muscle in the shoulder girdle system, which exerts its maximal force in one limb stance, which therefore leads to a reliable estimation of its cross sectional area. The estimated dimensions of m. serratus superficialis were found to be placed at both the origin and insertion sites of the skeleton in a reasonable manner. For determination of cross sectional areas of the other shoulder girdle muscles it is recommended to calculate at least three more load cases. They should represent different stages of the locomotor cycle and in addition one single load step, in which only neck movements are considered, as they are assumed to be performed by m. trapezius and m. levator scapulae. A physiological superposition of the muscle forces then would lead to an increase of maximal muscle forces and cross sectional diameters as predicted for m. trapezius and m. levator scapulae. Although in former investigations functional aspects or mechanical advantages of a muscle were considered, the definition of function remains unclear. For instance, some muscles were supposed to stabilize a structure or not, without giving a detailed description of the 128 respective muscle function or how it can be performed. Muscle action in this study was described regarding all degrees of freedom to comprise its function as a whole, which leads to a more detailed understanding of the muscle action. Even retraction and protraction were defined as a performance in all three dimensions. Stabilizing, in this context, is therefore determined as the ability of the muscles to keep the skeletal elements in equilibrium at each point of movement by exerting the necessary amount of force components (x,y,z-axial) in the required direction. 5.3.2 FESS method The FESS method itself is an innovative technique, and has been applied to a number of anatomical features in extinct and extant species (Rossmann et al. 2001; Witzel & Preuschoft, 2002, 2004, 2005; Witzel & Gössling, 2006; Witzel, 2006, 2007; Gössling et al. 2008; Moser et al. 2008), but it was formerly not applied to a 3-D FE multi-body system of the free forelimbs. In the present thesis, the FESS method was applied to a 3-D multi body FE model of the shoulder girdle system of Diplodocus longus. Two different limb positions in frontal view were considered, the first with the humerus in a vertical position relative to the glenoid joint, and the second with the humerus slightly abducted. Using forces instead of links in the Diplodocus FE model is the major difference between both attempts of the FESS in this thesis. The link elements are less sensitive for deformation during calculation and therefore enable stability within the system. It was revealed by FESS of the crocodilian FE model, that the link elements prevent the determination of absolute muscle force and function. Link elements are widely used in FEA to simulate muscle forces, but in none of the studies the use of link elements was discussed with regard to their mechanical properties (Huber et al. 2005; McHenry et al., 2007; Wroe et al., 2008). It was shown by the present approach that using forces instead of link elements allows for a more detailed investigation. The decreased stability of the model in turn reveals a number of technically related conditions, which were not observed in the former approach of the crocodilian shoulder girdle. These issues include the size of each finite element, the convergence criteria for calculation, and the value of friction defined for the contact elements, which obviously have a great impact on stress distribution and statics in the system. Lowering the friction, refinement of the FE model, and modification of the friction coefficient for contact elements had a visible impact on stress distributions, but still did not lead to satisfactory results. Possibly an ongoing refinement of the volumes in the FE model could lead to more accuracy in calculation. Finite element number is linked to the number of nodes required in the mesh of the volume, which are 129 concurrently increased. Unfortunately, the number of nodes available in the FE Program is limited. Finally, an increase of the convergence criteria during calculation led to functional conditions in the FE model. Despite longer calculation times, the improved technical conditions were adopted for further calculation. However, the calculation of the first FE-model, in which the humerus was positioned vertically to the glenoid joint, could not be finished satisfactorily. No physiological pattern of compressive stress distribution within the bauraum could be achieved as the results lack significant compressive stresses i.e. in the coracoid region. Therefore, abduction of the humerus was proposed to increase the medially directed forces, which are necessary to maintain compressive stresses within the coracoid. Nevertheless, the performed calculations of the first attempt revealed necessary information and implications for the method. The basic movements of the multi-body system resulting from forces and bearings are demonstrated and equal to the condition in the FESS of the crocodilian shoulder girdle. Downward movements of the trunk, resulting from weight forces, rotation of the scapulocoracoid under the influence of m. serratus superficialis, and the impact of the counteracting muscles providing stability in the system could be recognized. These methodological implications were incorporated in the second FE-model. As the method is obviously sensitive to the arrangement of forces, the forces applied to the second FE model of Diplodocus longus were refined. Muscles like m. serratus superficialis, m. trapezius, and m. levator scapulae are assumed to insert along the scapula. To accommodate this, total forces are subdivided, which results into a more distributed stress pattern. This procedure also minimizes stress peaks, which occur especially at insertions of high single forces. Even though, calculation of the whole body model revealed high friction between the trunk and scapulocoracoid, which was still visible and prevented the establishment of static equilibrium. It was proposed, that the high number of contact elements between the trunk and the scapulocoracoid increases adhesion between the adjacent areas, even if friction coefficient was lowered. In consequence, a separate FE model, which consists of only the scapulocoracoid bauraum, the humerus and the antebrachium, was calculated. The mechanical function of the trunk was accomplished by bearings applied to the scapulocoracoid bauraum. After a number of iterative steps, the equilibrium in the shoulder girdle system of the second FE model was accomplished and results in a satisfying distribution of compressive stresses in the scapulocoracoid bauraum. The system is kept in equilibrium only by muscle forces, which 130 were applied to the FE model in a mechanically proper arrangement according to their function in one limb stance. The compressive stresses, which result from transmission of body weight to the scapulocoracoid serve as the blueprint for the synthesis-part of the FESS method. In three consecutive steps, the bauraum of the scapulocoracoid was then reduced, until physiological loading in the structure was achieved. The completed virtual synthesis of the scapulocoracoid of Diplodocus longus corresponds to the original fossil. With the aid of FESS the shoulder girdle of Diplodocus longus was investigated according to its function in one physiological loadcase, which here was defined as the transmission of body weight forces in one limb stance. The results of the analyis of the solid tetrapod bodies and the primary 2-D FE model of the crocodilian shoulder girdle indicate the requirement of a closed circle of forces in the shoulder girdle. Static equilibrium in the shoulder girdle can only be maintained if the weight forces are continuously transmitted through the elements of the shoulder girdle system. As compressive forces are sustained by the bony elements a ventrally closed shoulder girdle was predicted. The results in fact indicate a transmission of medially directed forces from the glenoid to the coracoid to the sternal plates via a coracosternal joint, which was considered in the reconstruction. This transmission of forces reveals an alternative way compared to extant reptiles or mammals. Therefore the shoulder girdle in dinosaurs cannot be investigated only based on functional comparison with extant tetrapods, as it was assumed in the beginning. According to Wolff`s law, bony structures are functionally adapted to mechanical loading, which is determined by mechanical stimuli, thus leading to the shape of bone. This condition is utilized by the FESS method as it allows building of virtual bony structures according to mechanical loading in a physiological loadcase (Witzel et al. 2010). The physiological loadcase is defined as mechanical loading of bone, which results from muscle and joint forces during everyday use. In a physiological loadcase bone is mainly subjected to compressive stresses. The physiological compressive stress loading presumably ranges from -2 to -20 MPa, as it can be observed for vertebrate bone (Witzel & Preuschoft, 2005; Witzel, 2007). After reaching equilibrium in the shoulder girdle of Diplodocus longus in this study, the resulting compressive stresses in the FE model range from -0.2 to 1.8 MPa. In the following three reduction steps the compressive stresses were increased to -2 to -9 MPa in the last reduction of the bauraum. After reduction a maximal value of compressive stresses (-141 MPa) is present at one discrete point at the most posterior border of the glenoid facet. This condition can be technically described as "kantenpressung" and is referred to the geometry of the FE model. To account for acceleration during locomotion the reduced model was then recalculated under loading 131 conditions according to two times earth acceleration. The resulting compressive stresses range from -3 to -20 MPa, which corresponds to the formerly predicted physiological compressive stress loading (-2 to -20 MPa) (Witzel & Preuschoft, 2005; Witzel, 2007, 2010). The synthesized scapulocoracoid resembles the original and shows a significant reduction in the structure compared to the initially generated bauraum. In comparison, the original scapulocoracoid is still thinner than the synthesis. Additional reduction steps should lead to a further decrease of the structure, which at the same time would lead to a concentration of the stressed areas. Because of the time consuming procedure the value of the additional knowledge seems doubtful. According to Pauwels (1965), bending stresses induce remodelling of bone, which results into bone formation in the compressed areas until bending is minimized (Witzel et al. 2010). This in consequence leads to the formation of a light weight structure, which is assumed to be an advantage for energy saving strategies (Alexander, 2002; Reilly et al. 2007) especially for animals with high body weights like sauropod dinosaurs. In fact, with regard to the size of the animal the dimensions of the scapula are remarkably small. The scapula of Diplodocus exhibits the greatest dimension in the lateral plane, whereas its maximal thickness ranges from approximately 10 cm at the caudal part of the glenoid facet to only 1 cm at the cranial border of the scapula. Despite its appearance the scapulocoracoid bone is able to support approximately 1/5 (2 tons) of the total body weight (10 tons) in one limb stance. In fossil remains, information about the musculature and the position of the bony elements are rare and sometimes misleading as shown in the present thesis. In this context the applied FESS method allows for the determination of the position and values of muscle forces, as they correspond to the physiological compressive stress loading in the scapulocoracoid bone. This condition makes the FESS an appropriate method for the investigation of the musculoskeletal system, especially in extant vertebrates. 132 Chapter 6 General conclusions and future perspectives 6.1 General conclusions The relationship of form and function in vertebrate bone can be sufficiently investigated by means of mechanical engineering. The form or shape of an individual bone therefore is adapted to resist the mechanical stresses, which occur under loading conditions. It is further concluded, that the major determinant of bone formation is compression stress and therefore consistent with Wolff´s law. In general, all morphological and evolutionary implications, which were drawn from the different approaches using finite element method (FEM) in the present investigation, can be referred to this circumstance. This includes the analysis of the stress distribution in two 3-D FE models of solid tetrapod bodies and the crocodilian shoulder girdle, the FESS of the crocodilian shoulder girdle and finally, the FESS of the shoulder girdle in a sauropod dinosaur (Diplodocus longus). The initial loading condition in a terrestrial vertebrate body is defined by the gravitational force. Since the animal is released to gravity, the body weight force acts towards the ground, which results into ground reaction forces. Both gravitational force and ground reaction force exert mechanical stress on the body. This primary condition reveals the most basic requirements of the presence and location of the musculoskeletal elements in a terrestrial vertebrate. Bones and muscles were found to be positioned in accordance to the observed mechanical stress patterns. The middle of the trunk is free from stresses even under loading and thus provides ample space for the intestines. The bony elements are defined to resist the compressive stresses and the musculature is able to intercept the tensional parts. The defined basic loading conditions describe two different locomotor types, one sprawling and one extended limb position. They can be distinguished by the different mechanical stress patterns reflecting the morphological structures in “lower tetrapods” (amphibians, most saurians) and dinosaurs and mammals. Furthermore, the results emphasize that the gradual changes of the shoulder girdle elements during early tetrapod 133 evolution are the result of an enhanced terrestrial locomotor behavior related to an increase of gravitational loading. FESS is based in principle on the calculation of the equilibrium of forces and moments in a mechanical system. The determination of the boundary conditions in a FE model is the most crucial point of the approach. The most basic condition of the shoulder girdle was determined with the aid of morphological comparison with tetrapod vertebrates and the stress distribution in the tetrapod body under the influence of gravitational loading. The primary approach of the 2-D and 3-D multi-body FE models of the crocodilian shoulder girdle offers the opportunity to evaluate, whether it is possible to transfer biological structures to a mechanical system. The results clearly indicate that this approach is in fact appropriate to evaluate relative movements of the skeletal elements and the function of the muscles under a functional point of view. In addition to the determination of basic functions of shoulder girdle musculature, fundamental implications related to the method could be revealed. Although the results provide a first insight into the shoulder girdle mechanics, the use of link elements for this approach could not be approved. In consequence, directed forces instead of link elements were applied in the final approach of the 3-D FESS of the sauropod shoulder girdle. As the analysis of the 2-D model leads to implications for the relative movements in the shoulder girdle system, the results of the 3-D FESS reach further. The alteration of each value, position and direction of the forces lead to visible changes of stress distribution and static condition, pointing out that with these iterative steps a more detailed investigation of muscle function can be established. As forces are related to muscle function, investigations therefore should aim to determine function in all three dimensions. The results obtained by the FESS of the crocodilian and Diplodocus shoulder girdle lead to the further conclusion that in a functional shoulder girdle, a closed circle of mechanical forces is required. The relationship of form and function of bone is the central aspect of the FESS method. With a mechanical equilibrium in the shoulder girdle system achieved, the distribution of compressive stresses in the predefined bauraum resembles the shape of the original model. A physiological stress distribution then could be accomplished by iterative reduction of the bauraum according to the stress bearing areas. Although the results of the FESS of the Diplodocus longus shoulder girdle are more developed than in case of the crocodilian shoulder girdle, both 134 approaches reveal the compressive stresses to be the major determinants of bone formation and therefore support the primary results obtained from the solid tetrapod FE models. Because the system is in equilibrium, the mechanical stress patterns can again be related to the bony structures and in turn allow for the deduction of the mechanical function of the shoulder girdle muscles. The predefined basic mechanical conditions in the tetrapod shoulder girdle in general and the shoulder girdle of Diplodocus longus in particular. The deductive nature of the FESS method accounts for its capacity to investigate the mechanics of the musculoskeletal system in extant animals. Although there is a lack of information of soft tissue in fossil remains, muscle structures and the relative position of the elements can be reconstructed by their function. A number of initially defined morphological and functional considerations, such as a closed circle of forces, and the most cranially position of the shoulder girdle, in which the scapula is lying parallel to the ribcage, were found to be present in all extant tetrapods. Other features, such as the number of shoulder girdle elements and their relative position in the forelimb girdle system are different. The function, which was determined as the transmission of body weight from the trunk to the shoulder girdle, is consistent for all taxa included in this investigation. According to the transmission of body weight, the shoulder girdle of Diplodocus longus was found to fulfill the mechanical requirements of an extended limb position, similar to a mammalian-like locomotor type but with the components of a modified reptile-like shoulder girdle. These results account for a careful evaluation of comparisons with extant homologues and functional analogues; they cannot be applied to extinct ancestors regardless the individual functional adaptations. Nevertheless morphological comparison is necessary, and was also included in this approach, but always with regard to the locomotor behavior between the object of interest and the extant analogue. In general the results emphasize the highly adaptive nature of bone in order to maintain function during the evolution of sauropod dinosaurs. In both FESS approaches the structure of the primary generated bauraum was significantly reduced in iterative steps. The resulting physiological loading condition of bone was established most successfully for the scapulocoracoid of Diplodocus longus. Under physiological conditions, bending in the scapulocoracoid synthesis was significantly reduced. A minimization of bending in bone leads to an overall reduction of the material, which can be observed in the synthesis and in the original fossil. It can be concluded that the maximal function of the bone is maintained by the investment of the minimum of material. A light weight 135 construction in sauropod bones was also assumed for the vertebrae and is here shown to be realized in the shoulder girdle skeleton as well. A minimization of energy expenditure can be achieved by an extended position of the forelimbs and a light weight construction of the shoulder girdle skeleton, which are therefore determined to be preconditions for an increase of body size in sauropod dinosaurs. Light weight construction in the remaining skeletal parts has to be tested but seems reasonable. This would be a strong argument for their success and is probably a precondition for gigantism. FESS is an innovative approach using the FE method, and an appropriate tool not only to study the maximal strength of bone, but to explain the nature of bone according to its mechanical function and to shed light on the mechanisms of evolution of the great diversity in vertebrate bones. 6.2 Future perspectives The present study provides ground for further investigations on the evolution of the shoulder girdle in the dinosaurs as well as for the development of the forelimb girdle along tetrapod evolution. As evolutionary changes in the musculoskeletal system were referred to be locomotion related changes, its impact for the reconstruction of early tetrapod behaviour should be investigated further on. The formation of bone was determined to be influenced by mechanical signals as a result of its function in the musculoskeletal system. To evaluate the relative impact on the remodelling as well as on the modelling of bone these two pathways should be investigated by means of mechanical, physiological and ontogenetical methods in an interdisciplinary approach. Such an approch would clearly provide insight to the mechanisms of inidvidual bone formation and vertebrate skeleton evolution. 136 Chapter 7 Summary There is a lack of knowledge about the functional morphology of the shoulder girdle in both extinct and extant tetrapods. This in particular holds true for the sauropod dinosaurs, which were the biggest land living animals. Locomotor behaviour directly influences the biology of the animal, and therefore provides the opportunity to investigate possible correlations between the morphology of the forelimb girdle, its biomechanics and energy saving adaptations. The obtained information could then provide further insight into the biology of these extinct giants, especially with regard to the evolution of sauropod gigantism. The current investigation is mainly based on Wolff´s law and Pauwels causal morphogenesis, which predicts that the formation of bone is highly influenced by mechanical stresses, as a result of mechanical loading conditions in the vertebrate body. The finite element method (FEM) allows for the investigation of stresses and deformation in solid structures and is applied in this thesis in two different approaches. In the first step mechanical stresses in vertebrate tetrapod bodies were analyzed to reveal the basic functional conditions under gravitational loading. The second approach is termed the Finite-Element Structure Synthesis (FESS), in which the shape of the original bone can be virtually synthesized from a primary generated bauraum according to the mechanical stresses under loading conditions. Both approaches were applied to investigate the musculoskeletal system of extant and extinct vertebrates under defined biomechanical conditions. The current study starts with basic morphological and functional considerations about the shoulder girdle of extant tetrapods to provide ground for the investigation of the sauropod shoulder girdle. Morphological comparison between extant lacertilians and mammals reveals a similar relative position of the shoulder girdle in both groups. This includes a cranially positioned shoulder girdle covering the first ribs, and a scapula, which is positioned nearly parallel to the vertebral column in lateral and dorsal view of the ribcage. In addition, all observed reptiles exhibit a ventrally positioned tongue-and-groove coracosternal joint, in which the sternal part acts as the groove and the coracoid part acts as the tongue. In lacertilians both parts consist of compact bone 137 except for Basiliscus plumifrons, where the coracoid tongue is only partly ossified. In contrast, the tongue-and-groove structure in all observed crocodilians is built of cartilage, which was examined by observations of macerated skeletons and of histological sections. For the investigation of the mechanical stress distribution in two different limb positions under the influence of gravitational loading, two simplified solid 3-D FE models of tetrapod bodies were analysed. Here, the sprawling limb position reflects the primitive condition, which is predicted for early tetrapods and is observed in all extant lacertilians and crocodiles. The extended limb position, in which the limbs are held under the body, refers to the situation in extant mammalians. The analysis reveals stress patterns in regions, which represent the limb girdles and the vertebral column and depend on the mass distribution in the body segments as well as the position and posture of the supporting limbs. The major difference between both limb conditions was in the orientation of the scapula, which is more inclined in an extended limb position, and in the presence of a coracoid between both supporting forelimbs. The latter is only required in a sprawling limb position in order to sustain the medially directed compressive forces. Morphological observations of the shoulder girdle in extant tetrapods and the analysis of mechanical stresses in the simplified 3-D FE models lead to the following conclusions. First, all tetrapod bodies underlie the same basic mechanical conditions since the body is exposed to earth acceleration, which require appropriate bony and muscular structures to sustain the occuring stresses, which is precondition for a successful transmission of body weight from the trunk to the supporting forelimbs. Further, the transmission of body weight and the resulting mechanical stresses depend on the position and posture of the forelimbs, which is realized in mammals and reptiles in different ways. To evaluate the relative movements of the shoulder girdle elements in one-limb stance and the occurring mechanical stress flow in the shoulder girdle region a simplified 2- D multi-body FE model of the crocodilian shoulder girdle was built. Based on the obtained information a a multi-body 3-D FE model of the crocodilian shoulder girdle was created and investigated with the FESS method. The virtual synthesis of the crocodilian scapulocoracoid resembles basic features of the original structure, like the position of the scapulocoracoid, the long slender shape of the scapula and the connection of the coracoid to the sternal region. The results allow for the evaluation of the FESS method, revea implications for the function and relative movements in the shoulder girdle system, and finally lead to determine the basic shoulder girdle muscle function during one limb stance. 138 Finally, the 3-D FESS method was applied to the shoulder girdle of a sauropod dinosaur, Diplodocus longus. After establishing the static equilibrium in the shoulder girdle system by means of muscle forces, the scapulocoracoid was synthesized according to the distribution of physiological compressive stresses at the bauraum. The virtual synthesis of the scapulocoracoid exhibits a variety of features, which can be observed in the original fossil, like e.g. the prominent acromial region, a long and slender scapula, the overall convex shape of the scapulocoracoid and the most compact structures at the level of the glenoid. According to the mechanical conditions in the sauropod shoulder girdle system, which were determined by this FESS approach, a mechanically reasonable reconstruction of the shoulder girdle of Diplodocus longus was accomplished. This includes the position of the skeletal elements and the acting musculature. The scapulocoracoid exhibits a lateral inclination of about 60° relative to the vertebral column. It is positioned parallel to the ribcage, which results into a narrowed frontal aperture compared to the original mount. This in consequence enables a direct contact of the coracoids to the sternal plates, which were placed medio-caudally to the coracoids. Following the results of the FESS a moderate extended posture of the forelimbs is reconstructed. This includes a slight flexion in the shoulder and the elbow joint in lateral view, and a moderate abduction of the humerus in frontal view. The position, function and force values of the musculature were determined according to the requirements of static equilibrium in one limb stance. The reconstruction comprises all muscles running between the trunk and the shoulder girdle, as well as from the shoulder girdle to the humerus and the antebrachium. The results reveal the adaptation of a reptile-like shoulder girdle in sauropods to an extended limb posture. It therefore presents an alternative way of function compared to extant mammals on the one hand and extant lacertilians and crocodiles on the other hand. The present study indicates that mechanical stress patterns can be related to the position, form and function of the elements in the musculoskeletal system of tetrapod vertebrates. Furthermore, with the successful virtual synthesis of the scapulocoracoid of Diplodocus longus, carried out by the FESS method, the close relationship of mechanical function and form in a limbgirdle system was pointed out for the first time In addition, bending moments in the virtual synthesis of the diplodocid scapulocoracoid are minimized, while the structure is mainly loaded under compression. This in turn results into an overall reduction of the material, in the virtual synthesis and in the original fossil. The musculoskeletal system is predicted to be optimized as a light-weight construction, in which the maximal function of bone is maintained by the investment of the minimum of material. These 139 considerations are supported by the results of the 3-D FESS of Diplodocus longus. According to the situation in Diplodocus longus a light weight construction of the shoulder girdle skeleton is assumed to be one precondition for an increase of body size in sauropod dinosaurs. Finally the FE method in general and the FESS method in particular are appropriate tools to investigate the mechanics of the musculoskeletal system in extinct and extant tetrapod vertebrates under a functional point of view. 140 Chapter 8 Zusammenfassung Die funktionelle Morphologie des Schultergürtels wurde bisher sowohl für fossile als auch rezente Tetrapoden nur unzureichend untersucht. Dies gilt insbesondere für die größten jemals lebenden Landlebewesen, die Sauropoden. Da die Fortbewegung eines Tieres einen direkten Einfluss auf seine Lebensweise hat, bietet sich hier die Möglichkeit, die Morphologie und Mechanik des Schultergürtels in Bezug auf geeignete Strategien zur Optimierung des Energieverbrauchs hin zu untersuchen. Mit der vorliegenden Dissertation werden neue Erkenntnisse in Bezug auf die Schultergürtelmechanik der Sauropoden aufgezeigt, welche dazu beitragen die Biologie dieser fossilen Giganten zu untersuchen und mögliche Anpassungen des Schultergürtels als Voraussetzung des sauropoden Gigantismus zu definieren. Die Grundlage für die mechanischen Überlegungen dieser Untersuchung beruhen auf dem Wolff`schen Transformationsgesetz und Pauwels `Kausaler Morphogenese`, welche besagen, dass sowohl die Bildung als auch der Erhalt knöcherner Strukturen von mechanischen Spannungen beeinflusst werden. Mit Hilfe der Finite- Element Methode (FEM) ist es möglich, mechanische Spannungen und Verformungen in festen Körpern zu untersuchen und bildlich darzustellen. Die FEM wurde in der vorliegenden Arbeit in zwei unterschiedlichen Ansätzen verwendet. Um den Einfluss der Schwerkraft auf die Spannungsverteilung im Wirbeltierkörper zu untersuchen, wurden zunächst Spannungsanalysen an vereinfachten Finite-Element Modellen vierbeiniger Wirbeltierkörper durchgeführt. Mit Hilfe der Finiten-Element Struktur Synthese (FESS) ließen sich anschließend virtuelle Synthesen knöcherner Strukturen auf der Basis der beobachteten mechanischen Spannungen erzeugen. Diese Vorgehensweise erlaubte sowohl die Untersuchung des Zusammenhangs zwischen der Form und Funktion von Knochen, als auch die Bestimmung mechanischer Funktionen im Schultergürtel rezenter und fossiler tetrapoder Wirbeltiere. Die Untersuchung begann mit einer Reihe funktionsmorphologischer Überlegungen zum Schultergürtel rezenter und fossiler Tetrapoden, welche die Grundlage für die Untersuchung des Schultergürtels von Diplodocus longus bildeten. Im morphologischen Vergleich zwischen rezenten Lacertiliern und Säugetieren zeigen sich große Übereinstimmungen in der relativen Position des Schultergürtels. In beiden Gruppen liegt 141 der Schultergürtel weit kopfwärts auf Höhe der ersten Rippen, und ist von dorsal gesehen parallel zum Rippenkorb angeordnet. Der distale Rand der knöchernen Scapula beziehungsweise der knorpeligen Suprascapula zeigt ebenfalls eine parallele Ausrichtung zur Wirbelsäule. Desweiteren besitzen alle untersuchten Reptilien ein Coracosternalgelenk, welches aus einer sternalen Gleitrinne und dem sich darin gleitenden Coracoid gebildet wird. Diese Nut-und Feder Konstruktion zeigt sich bei allen untersuchten Lazertiliern vollständig verknöchert, mit Ausnahme von Basiliskus plumifrons, bei dem der entsprechende Anteil des Coracoids teilweise knorpelig ausgebildet ist. Im Gegensatz dazu wird bei den Krokodilen sowohl die sternale Gleitrinne als auch der Anteil des Coracoids ausschließlich aus Knorpelgewebe gebildet, was an mazerierten Skeletten und histologischen Querschnitten durch das Coracosternalgelenk verdeutlicht werden konnte. Um den Einfluss der Schwerkraft auf die Spannungsverteilung zwischen zwei unterschiedlichen Gliedmaßenstellungen zu analysieren, wurden zwei vereinfachte 3-D FE Tetrapodenmodelle erstellt. Die abgespreizte Gliedmaßenstellung stellt die ursprüngliche Kondition dar, wie sie für basale Tetrapoden angenommen wird und auch bei allen rezenten Lacertiliern und Krokodilen beobachtet werden kann. Eine gestreckte Gliedmaßenstellung hingegen reflektiert die Situation bei rezenten Säugetieren, insbesondere großen Lauftieren. Die größten Spannungen zeigen sich in den Regionen, die mit der Position der Gliedmaßengürtel und der Wirbelsäule übereinstimmen. Die Position und Orientierung der Spannungsverläufe werden von der Massenverteilung innerhalb des Körpers und der Stellung der Gliedmaßen beeinflusst. Die größten Unterschiede zwischen beiden Gliedmaßenstellungen zeigen sich in der Orientierung der Scapula, welche im Fall der gestreckten Gliedmaßen eine stärkere Neigung nach caudal aufweist, und in der Präsenz eines ventral gelegenen Coracoids zwischen den Vorderextremitäten. Ein Coracoid, welches in der Lage ist, hohe medial gerichtete Druckspannungen aufzunehmen, lässt sich ausschließlich bei einer abgespreizten Gliedmaßenstellung annehmen. Die morphologische Betrachtung rezenter Tetrapoden und die Spannungsanalysen anhand der basalen 3-D FE Modelle lässt folgende Rückschlüsse zu. Unter dem Einfluss der Schwerkraft lassen sich für alle Wirbeltierkörper grundsätzliche mechanische Belastungen beobachten. Diese können nur durch die Ausbildung geeigneter knöcherner und muskulärer Strukturen kompensiert werden, um somit eine Übertragung des Körpergewichts vom Rumpf auf die unterstützenden Gliedmaßen zu gewährleisten. Die Kraftübertragung und die resultierenden mechanischen Spannungen sind hierbei abhängig von der Stellung der Gliedmaßen, und werden von Säugetieren als auch Reptilien in unterschiedlicher Weise realisiert. 142 Um die Bewegungen der einzelnen Elemente des Schultergürtels während des Einbeinstandes zu bestimmen und die daraus resultierenden Spannungsverteilungen zu analysieren, wurde zunächst ein vereinfachtes 2-D FE Mehrkörpermodel eines Krokodilschultergürtels modelliert. Basierend auf den gewonnenen Erkenntnissen wurde die Untersuchung um ein 3-D FE Mehrkörpermodell erweitert und mit Hilfe der FESS Methode untersucht. Die virtuelle Synthese des Scapulocoracoids zeigt in wesentlichen Merkmalen Übereinstimmung mit dem Original. Dies betrifft die Position des Scapulocoracoids, die elongierte Scapula und die Verbindung zwischen Coracoid und der Sternalregion. Die 3-D FESS des Scapulocoracoids eines Krokodils erlaubt die Evaluation der verwendeten Methode und die Bestimmung der grundlegenden mechanischen Bewegungen innerhalb des Schultergürtels unter statischen Bedingungen im Einbeinstand. Im letzten Teil der Dissertation wurde die FESS auf den Schultergürtel von Diplodocus longus angewandt und ein 3-D FE Modell erstellt. Nach der Einstellung des statischen Gleichgewichts im Einbeinstand mit Hilfe von Muskelkräften wurde der primäre Bauraum des Scapulocoraocoids unter Berücksichtigung der beobachteten physiologischen Druckspannungsverteilung reduziert. Die virtuelle Synthese des Scapulocoracoids zeigt eine Vielzahl von Merkmalen des originalen Fundes. Dies sind insbesondere die ausgeprägte Acromialregion, eine lange schlanke Form der Scapula, die konvexe Form des Scapulocoraocoids und die größte Knochendicke im Bereich des Glenoids. Auf der Basis der ermittelten mechanischen Bedingungen, wurde eine Rekonstruktion des Schultergürtels unter funktionellen Gesichtspunkten durchgeführt. Die Rekonstruktion beinhaltet die Position der Skelettelemente und der im vorliegenden Lastfall wirkenden Muskulatur. Das Scapulocoracoid zeigt eine laterale Neigung zur Wirbelsäule von 60° und ist parallel zum Rippenkorb ausgerichtet, was in einer Verschmälerung der frontalen Öffnung im Vergleich zur ursprünglichen Montage des Skeletts resultiert. Dies ermöglicht einen direkten Kontakt der Coracoidea und der Sternalplatten, welche medio-caudal den Coracoidea positioniert werden. Basierend auf den Ergebnissen der FESS wird für Diplodocus longus eine gestreckte Extremitätenstellung angenommen, die jedoch in der Lateralen eine moderate Flexion im Schulter- als auch im Ellenbogengelenk zeigt und in der Frontalen eine Abduktion des Humerus um 20° zeigt. Die Position und Funktion der Muskeln sowie der Muskelkräfte wurden ausschließlich anhand der mechanischen Funktion bei der Einstellung des statischen Gleichgewichts im Einbeinstand bestimmt. Die Rekonstruktion umfasst alle Muskeln, welche vom Rumpf zum 143 Schultergürtel, bzw. vom Schultergürtel zum Humerus und Antebrachium verlaufen. Die Ergebnisse zeigen desweiteren eine Anpassungen des sauropoden Schultergürtels mit seiner ursprünglichen Reptilienmorphologie an eine gestreckte Gliedmaßenstellung, welcher somit einen funktionell alternativen Weg im Vergleich zu rezenten Reptilien und Säugtieren darstellt. Es konnte gezeigt werden, dass mechanische Spannungen als Folge der Einwirkung von Kräften auf den Wirbeltierkörper sowohl die Position, als auch die Form und Funktion der Elemente des Skelettapparats reflektieren. Schließlich wurde mit Hilfe der virtuellen Synthese des Scapulocoraocoids von Diplodocus longus erstmals der Zusammenhang zwischen mechanischen Spannungen und der Form und Funktion am Beispiel eines Gliedmaßengürtels dargestellt. Zudem konnten die in der Synthese des Scapulocoracoids auftretenden Biegespannungen minimiert werden, wodurch die Struktur hauptsächlich unter Druckspannung belastet wird. Die Minimierung von Biegespannungen gilt als die Grundvoraussetzung für die Leichtbauweise von Knochen, welche in dieser Dissertation mit Hilfe der FESS für das Scapulocoracoid von Diplodocus longus nachgewiesen werden konnte. Diese Optimierung im Schultergürtelskelett kann somit als eine Präadaptation für die Größenzunahme bei sauropoden Dinosauriern interpretiert werden. 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Dehydration and embedding Ethanol 70%, as long as deserved, minimum 24h; Change 2 times Ethanol 95% 24h; Change 2 times Isopropanol 24h; Change 2 times; last 2h at 60° in a heated chamber. Mix the warm Isopropanol 1:1 with Paraplast Leave overnight Isopropanol will vaporize. 2h Paraplast 1 at 60° 2h Paraplast 2 2-4h Paraplast 3 Embedding in fresh Paraplast and cool down. Deparaffinise After drying and before dying, paraffin should be removed from the sections. 10 min Rotihistol I at 45° 10 min Rotihistol II at 45° 10 min Isopropanol 10 min Ethanol 95% 10 min Ethanol 70% 4 times 2 min. distilled water (change with high frequency) Dyeing Dyeing process Sections were dyed using Aldehydfuchsin Goldner (AFG) solution, resulting in red-green dyeing for bony tissue and green-violet dyeing for cartilaginous tissue. Deparaffinise and rinse with distilled water min. oxidation preparation until sections turn brown Reductional preparation until section is colourless Rinse with water. 160 times in Ethanol 70% Leave 5 min. in Aldehydfuchsin 2 times in Ethanol 70% 2 times in distilled water 2-5 min. Hämatooxylin-Weigert 10 min. under flowing water 10 min. Säurefuchsin-Ponceau-Azophloxin times vinegar acid 1% (change frequently) 30 sec. Orange G (moving) 3 times vinegar acid 1% (change frequently min. in Lightgreen 3 times vinegar acid 1% (short) 2 times Isopropanol Leave in Isopropanol Cover the sections in Euparal 161 10.2 Muscles of the crocodilian shoulder girdle Table 3 Muscles of the shoulder girdle in crocodiles. Description of the anatomical position, origin and insertion sites and the muscle function during locomotion are described (Brinkmann 2000; Meers 2002). Muscle Position Origin Insertion M. serratus superficialis (Fürbringer 1902) Deep at the posterior part of the shoulder flank Last cervical rib and processus uncinati of the first thoracic ribs. Caudal border scapula. the Transmitting body weight from the trunk to the shoulder girdle. M. serratus profundus (Fürbringer 1876) Completely covered by the scapula and the adjacent musculature, between scapula and trunk. Ribs of the last four cervical vertebrae. Dorso-medial part of the scapular head. Supports transmission of body weight. M. trapezius (Buttmann 1826) Superficial at the anterior part of the neck and thorax. From the thoraco-dorsal fascia ventro-lateral along the surface of the trunk. Along the cranial edge of the scapula, dorsal to the acromion. Rotates the scapula cranially and assists during protraction. M. levator scapulae (Fürbringer 1876) Superficial at the lateral side of the neck, completely covered by m. trapezius. First two cervical ribs and processi transversi of the rd th 3 -6 cervical ribs. Almost along the whole cranial margin of the scapula. Cranial rotator of the scapula. M. rhomboideus (Fürbringer 1876) Deep under the distal end of the scapula and suprascapula. Dorso-lateral to the thoracic fascia at the last cervical and first thoracic ribs. Medial distal part of the scapular head and part of the suprascapula; ventral to m. serratus profundus. Pulls the medially. 162 Function of scapula Muscle Position Origin Insertion Function M. costo-coracoideus (Fürbringer 1976) Deep to m. pectoralis, between coracoid plate and rib cage. At the last cervical rib and the first lower thoracic ribs. Dorsal area and caudal margin of the coracoid plate. Pulls the coracoid caudally relative to the sternum. Acts as a caudal rotator of the coracoid. M. deltoideus clavicularis (Romer 1977) Lateral part of the scapula and upper humerus, running over the glenoid joint. at the ventral two third of the frontal part of the scapula. At the processus lateralis humeri and the most proximal third of the humerus shaft. Protracts the humerus and stabilises the glenoid joint. M. deltoideus scapularis (Fürbringer 1876) Positioned below m. trapezius at the lateral side of the scapula Lateral surface of the scapula, cranial to m. teres major. at the proximal processus lateralis humeri. Stabiliser of the glenoid joint, adductor of the humerus. M. subscapularis (Fürbringer 1876) Deep at the medial side of the scapula. Originates fleshy from the second third part of the medial side of the scapula, whereby it covers most of the cranial to caudal area. Has a tendinous insertion at processus medialis humeri. Adductor of humerus draws scapula medially. M. scapulo-humeralis (Fürbringer 1900) Deep muscle, above the glenoid joint. Takes it origin from the last third of the caudal ridge of the scapula. Dorsal side of the most proximal end of the humerus and glenoid joint capsule. Draws the scapulacoracoid caudally. Mm. supracoracoidea (Fürbringer 1876) Muscle complex divided into three distinct parts (M. supracoracoideus longus, intermedius and brevis) cover nearly the whole area of the coracoid, deep at the glenoid joint. Cranial edge and medial surface of the coracoid near to the glenoid joint. M. supracoracoideus intermedius: Lateral side at the apex of the most ventral part of the scapular body cranial to the glenoid joint; M. supracoracoideus brevis runs from below m. supracoracoideus to the most dorsal part of the coracoid body. Insertion: portions processus humeri. Function: Primary protractor of the humerus, secondly acting as an adductor of the humerus. 163 All three insert at lateralis the the Muscle Position Origin Insertion Function M. coracobrachialis brevis dorsalis (Fürbringer 1876) Deep at the glenoid joint. Dorso-lateral cranial portion of the scapula, ventral to the acromion and caudal to the m. supracoracoideus brevis. Cranio-ventral aspect of the joint capsule and the deltopectoral crest. Stabilizer of the humerus head; may assists in protraction and flexion of the humerus. Mm. triceps brachii (Starck 1978-82) Large complex consists of five muscle independent heads, lying superficial at the dorsal side of the humerus drawing over the olecranon to the ulna. s All three parts insert in a common tendon at the olecranon of the ulna. Flexors of the humerus as well as extensors of the antebrachium, serving as stabilisers of the glenoid joint. M. triceps caput scapulare See above Lower portion of the lower third of the scapula, dorsal to the glenoid joint. See above See above M. triceps caput coracoideum See above Consists of a tendinous arc. First originates from the caudal edge of the scapula, dorsal to the glenoid rim. Second from the caudal border of the coracoid, immediately dorsal to m. costo-coracoideus. See above See above Mm. triceps caput humerale lateralis, medialis & posticum Position: Surrounding the middle and distal part of the humerus shaft. Humerus shaft See above Serves as extensors of the antebrachium. M. brachialis (Fürbringer 1876) Superficial at the ventral side of the humerus and the elbow joint. Cranio-dorsal surface of the proximal humerus distal to the deltopectoral crest. At the most proximal end of ulna and radius, just below the elbow joint. Strong flexor of the antebrachium. M. spiralis (Fürbringer, 1876) On the ventral side of the elbow joint, running between humerus and antebrachium. At the ventral side of the most distal part of the humerus. Proximal radius. Flexor of antebrachium. 164 end of the the M. teres major (Fürbringer 1876) Superficial at the shoulder blade. Caudal to m. deltoideus scapularis at the lateral side of the shoulder blade. 165 In a common tendon with m. latissimus dorsi dorsolateral at the proximal end of the humerus. Serves together with m. latissimus dorsi as an elevator of the humerus and flexor of the glenoid joint. 10.3 3-D FESS of a crocodilian shoulder girdle 10.3.1 Adjustment of static equilibrium 1. M. serratus superficialis transmits the body weight forces from the trunk to the shoulder girdle; m. pectoralis prevents the humerus from sliding aside. The trunk is free to move up and downwards, the scapulocoracoid is restricted by applied bearings in z and x direction. Both the humerus and the antebrachium exhibit fixed-bearings preventing any movement. The indicator bearings applied to the scapulocoracoid show reaction forces indicating a caudal rotation and downward movements, which are prevented by pushing the humerus into the glenoid joint. The humerus is tending to rotate cranially within the ulnar joint, pushing the antebrachium caudally. Humerus is exhibiting high bending forces in the shaft. For pretension and reaction forces see Table 4. Figure 59 3-D model in the initial situation in frontal (above) and lateral view (below). In addition to the initial body weight force (red arrows) m. serratus superficialis and m. pectoralis are applied to the system. 166 2. Scapulocoracoid is only restricted in the cranio-caudally direction, by bearings at the right distal edge and left proximal corner, able to move in vertical directions. Bearings in x,y,zdirection are applied to humerus at the distal end, while the proximal part is now free from restrictions, thus allow free movement in the glenoid joint and rotation in the elbow joint. Applied muscles in this step are m. trapezius and levator scapulae acting in opposite direction to m. serratus superior rotating the scapulocoracoid cranially. Further applied muscles are m. rhomboideus, exerting forces medial directed forces towards the trunk, and m. costo-coracoideus to support the m. serratus and m. trapezius in cranial rotation of the scapula. The trunk element and scapulocoracoid again move downwards, while bending in the humerus shaft is reduced. Reaction forces in the scapulocoracoid bearings still indicate a caudalward rotation. Note the increase of maximum stress value compared to the first calculation step. Distribution of stresses has modified, resulting from the reduction of applied bearings. Stresses concentrate mainly at the coracoid position and at the caudal edge of the scapulocoracoid. For pretension and reaction forces see Table 5. 167 Figure 60 3-D model of the object in frontal (above) and lateral view (below). Muscles added in this step are m. trapezius, m. levator scapulae, m. costo-coracoideus and m. rhomboideus. The bearing at the left distal end of the scapulocoracoid was removed. 3. In the following step, distribution of the applied links and restriction of movements is modified. M. deltoideus scapularis und clavicularis are applied to the system. The scapulocoracoid is restricted by one bearing, which is positioned at the proximo-cranial corner. M. costocoracoideus prevents caudal rotation of the scapula by pulling the coracoid region backward and counter wise rotation. Reaction force in the scapular bearing indicates a shift from caudal to cranial rotation, which indicates that m. costo-coracoideus overcompensates the movement of the scapulocoracoid. M. deltoideus act in the opposite direction, but has no visible impact on the results. Total stress value is decreases in comparison to the former calculation step. With regard 168 to the stress distribution, no major modifications can be observed. For pretension and reaction forces see Table 6 Figure 61 One bearing at the distal corner of the scapula was removed. M. deltoideus scapularis and clavicularis are placed in the system to counter cranial rotation of the scapulocoracoid. 4. In the present calculation m. triceps caput coracoideum, caput scapulare, caput humerale and m. supracoracoideus were applied to the FE model, in order to counter the cranial rotation of the scapula. To support this action, m. costo-coracoideus was removed. Reaction forces value in the bearing at the scapulocoracoid is increased. The additionally applied muscles are not sufficient to keep the system in equilibrium. The maximum stress value is increases, while the overall distribution of stresses is not affected. Reaction forces within the bearings applied to the antebrachium element and the distal part of the humerus indicate posterior movement of the antebrachium. To investigate static equilibrium in the elbow joint as well, the model would require the entire set of muscles and structures reaching from the limb to the forefoot. This is not 169 in the focus of this work. Distribution of stresses within the antebrachium or humerus and the equilibrium within the ulnar joint will not be taken into account. Muscle related links and pretension of link elements can be obtained from Table 7. Figure 62 Boundary conditions are equal to the former step. Here m. triceps caput coracoideum, caput scapulare and m. supracoracoideus were added to the model. 170 10.3.2 Reduction of the bauraum 10.3.2.1 First reduction step st Figure 63 1 reduction step of the FE model in lateral (A) and frontal (C) view. Single reduction of the scapulocoracoid in lateral (B) and frontal (D) view. Boundary conditions (links, bearings and weight forces) are equal to the final calculation step. Insertion sites of the links is maintained. Reduction of the initial bauraum is most present in lateral view. In frontal view the outlines of the model are more rounded than in the original bauraum. The overall structure is still massive. Figure 64 Calculation of the 1st reduction step with all applied bearings and link elements, which equal to the boundary condition in the final calculation step. The distribution of compressive stresses in lateral (A) and frontal (C) view. Compressive stress pattern in the single reduced bauraum of the scapulocoracoid, in lateral (B) and frontal (D) view. Black outlines in (B) and (D) indicate the selected contours for the next reduction step, according to the selected stress bearing areas. 171 Figure 65 Anterio-posterior cross sections of the first reduction step. Sections are at the same level compared to the final calculation. Selected frontal cross sections show thecompressive stressed regions of the scapulocoracoid bauraum. Compressive stresses spread from the glenoid joint medio-dorsally and are undistrubed throughout the bauraum. 10.3.2.2 Second reduction step Figure 66 Second reduction step of the FE model in lateral (A) and frontal (C) view. Single bauraum, which refers to the scapulocoracoid in lateral (B) and frontal (D) view. Reduction at this point is showing a heavy decrease of the primary structure compared to the first reduction. The shape of the bauraum is in approximation to the original scapulocoracoid. The outlines of the bauraum are still edged. 172 10.3.3 Technical settings Table 4 Applied links for the actual calculation step, which refer to muscles or muscle groups in crocodiles. Link diameter and pretension of the link element. F x,y,z are reaction forces, detected at the bearings after calculation. The first three bearings are the right and left distal bearings, 21921 the proximal bearing at the scapula, respectively. No. Muscle Link diameter (mm) Pretension (mm) NODE FX 1a M. pectoralis major 0,1 0,01 21074 13.627 -9.905 1b M. pectoralis minor 0,1 0,01 21132 15.574 12.372 2 M. rhomboideus 21921 12.023 -0.86006E01 3a M. serratus superficialis 1 0,1 0,01 24336 20.593 -35.828 3b M. serratus superficialis 2 0,1 0,01 3c M. serratus superficialis 3 0,1 0,01 3d M. serratus superficialis 4 0,1 0,01 VALUE 49.553 4 M. serratus profundus 5 M. subscapularis 6 M. coracobrachialis brevis 7 M. scapulo-humeralis 8 M. biceps brachii 9 M. brachialis 10 M. latissimus dorsi 11 M. teres major 12 M. trapezius 13 M. levator scapulae 14 M. deltoideus clavicularis 173 FY 0.0000 FZ -32.632 15 M. deltoideus scapularis 16 M. triceps caput scapulare 17 M. triceps caput coracoideum 18 M. triceps caput humerale 19 M. costocoracoideus 20 M. spiralis 21 M. supracoracoideus Table 5 Applied links for the actual calculation step, which refer to muscles or muscle groups in crocodiles. Link diameter and pretension of the link element. F x,y,z are reaction forces, detected at the bearings after calculation. Node number 21074 is the distal bearing at the scapula, node 21921 is the proximal bearing. No. Muscle Link diameter (mm) Pretension (mm) NODE 1a M. pectoralis major 0,1 0,01 21074 -117.47 1b M. pectoralis minor 0,1 0,01 21921 -24.933 2 M. rhomboideus 0,1 0,01 49327 -61.131 18.213 3a M. serratus superficialis 1 0,1 0,01 49328 30.040 11.062 3b M. serratus superficialis 2 0,1 0,01 49815 35.367 -22.453 3c M. serratus superficialis 3 0,1 0,01 72120 -59.656 -97.608 53.934 3d M. serratus superficialis 4 0,1 0,01 72128 -80.453 14.425 -62.266 4 M. serratus profundus 72212 -22.452 0.45032 -0.12602E01 5 M. subscapularis 72220 -11.304 22.276 10.653 6 M. coracobrachialis brevis 76204 -31.395 80.842 140.51 174 FX FY FZ 7 M. scapulo-humeralis 8 M. biceps brachii 9 M. brachialis 10 M. latissimus dorsi 11 M. teres major 12 M. trapezius 0,1 0,01 13 M. levator scapulae 0,1 0,01 14 M. deltoideus clavicularis 15 M. deltoideus scapularis 16 M. triceps caput scapulare 17 M. triceps caput coracoideum 18 M. triceps caput humerale 19 M. costocoracoideus 0,1 0,01 20 M. spiralis 21 M. supracoracoideus 76533 -0.33880 TOTAL VALUES 0.71294E05 -73.323 -14.737 100.00 0.47307E05 Table 6 Applied links for the actual calculation step, which refer to muscles or muscle groups in crocodiles. Link diameter and pretension of the link element. F x,y,z are reaction forces, detected at the bearings after calculation. No. Muskel Link diameter (mm) Pretension (mm) NODE 1a M. pectoralis major 0,1 0,01 21074 1b M. pectoralis minor 0,1 0,01 2 M. rhomboideus 0,1 0,01 TOTAL VALUES 3a M. serratus superficialis 1 0,1 0,01 VALUE 0.0 175 FX FY FZ 113.22 0 0.0000 113.22 3b M. serratus superficialis 2 0,1 0,01 3c M. serratus superficialis 3 0,1 0,01 3d M. serratus superficialis 4 0,1 0,01 4 M. serratus profundus 0,1 0,01 5 M. subscapularis 6 M. coracobrachialis brevis 7 M. scapulo-humeralis 8 M. biceps brachii 9 M. brachialis 10 M. latissimus dorsi 11 M. teres major 12 M. trapezius 0,1 0,01 13 M. levator scapulae 0,1 0,01 14 M. deltoideus clavicularis 0,1 0,01 15 M. deltoideus scapularis 0,1 0,01 16 M. triceps caput scapulare 17 M. triceps caput coracoideum 18 M. triceps caput humerale 19 M. costocoracoideus 0,1 0,01 20 M. spiralis 21 M. supracoracoideus 176 Table 7 Applied links for the actual calculation step, which refer to muscles or muscle groups in crocodiles. Link diameter and pretension of the link element. F x,y,z are reaction forces, detected at the bearings after calculation. No. Muskel Link diameter (mm) Pretension (mm) NODE 1a M. pectoralis major 0,1 0,01 21074 1b M. pectoralis minor 0,1 0,01 2 M. rhomboideus 0,1 0,01 TOTAL V ALUES 3a M. serratus superficialis 1 0,1 0,01 VALUE 0.0 3b M. serratus superficialis 2 0,1 0,01 3c M. serratus superficialis 3 0,1 0,01 3d M. serratus superficialis 4 0,1 0,01 4 M. serratus profundus 0,1 0,01 5 M. subscapularis 6 M. coracobrachialis brevis 7 M. scapulo-humeralis 8 M. biceps brachii 9 M. brachialis 10 M. latissimus dorsi 11 M. teres major 12 M. trapezius 0,1 0,01 13 M. levator scapulae 0,1 0.01 14 M. deltoideus clavicularis 15 M. deltoideus scapularis 0,1 0.01 177 FX FY FZ 130.53 0 0.0000 130.53 16 M. triceps caput scapulare 0,1 0.01 17 M. triceps caput coracoideum 0,1 0.01 18 M. triceps caput humerale 19 M. costocoracoideus 20 M. spiralis 21 M. supracoracoideus 0,1 0.01 Table 8 Link diameters, pretension, acting forces and stresses within the link elements according to the shoulder girdle musculature in the final calculation step. No. Muskel M. pectoralis major Link diameter (mm) 0,1 Pretension (mm) 0.01 Force (N) 10 Link stress (N/mm²) after calculation 150 1a 1b M. pectoralis minor 0,1 0.01 10 129 2 M. rhomboideus Not defined 3a M. serratus superficialis 1 M. serratus superficialis 2 M. serratus superficialis 3 M. serratus superficialis 4 M. serratus profundus M. subscapularis 0,1 0.01 10 137 0,1 0.01 10 196 0,1 0.01 10 290 0,1 0.01 10 315 0,1 0.01 10 0 0,1 0.01 10 92 Not defined 8 M. coracobrachialis brevis M. scapulohumeralis M. biceps brachii 0,1 0.01 10 130 9 M. brachialis 0,1 0.01 10 169 10 M. latissimus dorsi Not defined 11 M. teres major Not defined 12 M. trapezius 1 0.01 100 69 13 M. levator scapulae 0,1 0.01 10 0 14 M. deltoideus clavicularis 0,1 0.01 10 157 3b 3c 3d 4 5 6 7 Not defined 178 15 16 17 18 19 20 21 M. deltoideus scapularis M. triceps caput scapulare M. triceps caput coracoideum M. triceps caput humerale M. costocoracoideus M. spiralis 0,1 0.01 10 70 0,1 0.01 10 128 0,2 0.01 20 135 0,1 0.01 10 205 1 0.02 200 147 0,1 0.01 10 0 M. supracoracoideus Antebrachium 0,1 0.01 10 196 0,1 0,01 10 803 179 10.4 3-D FESS of the shoulder girdle in Diplodocus longus 10.4.1 Adjustment of static equilibrium in forelimb position I. In the following, the outlines of the FE-model in frontal and lateral view demonstrate the applied forces representing the shoulder girdle muscles (above). The contour plot in frontal and lateral view shows the distribution and magnitude of compressive stresses after calculation; black outlines indicate deformation after calculation showing the initial situation. Contact elements are applied to the adjacent areas of the trunk and the scapula, at the region of the assumed coracosternal joint and at the glenoid and elbow joint. Values of muscle forces applied to the model and reaction forces within the bearings can be obtained from the supplement. Forces are shown as arrows. The coordinate system is placed right at the bottom. Compressive stress values can be obtained from the contour legend (colour coded) or from the heading legend (maximum and minimum). High compressive stresses are blue, low stresses are red. Areas with stresses beyond the spectrum are grey. The elements of the shoulder girdle system can be held in position by first, bearings (indicated as triangles) and second, by forces preventing the movement. Therefore, two settings with different boundary conditions can be determined. The first is the initial situation, whereas the trunk is restricted in x- and z-direction to prevent medial and forward movements. In living animals, this function is adopted by the right supporting forelimb and hindlimbs, respectively. A fixed bearing restricts the antebrachium. The scapulocoracoid and the humerus require indicator bearings from which reaction forces can be read-out. These indicator bearings should be near zero if the elements are balanced out and provide stability in non-balanced calculations. They will be removed iteratively, leading to the second setting in which the trunk and antebrachium are allowed to move in physiological directions. The scapulocoracoid and the humerus are free from restrictions and held in position only by the applied forces representing the shoulder girdle muscles. To determine the function of the required forces (muscles), they are applied to the model in iterative steps, considering their impact to the system, which again can be detected at the indicator bearings. Changes concerning the boundary conditions (applied forces and bearings) will be described in the figure legends. 1. Basic movements of the multi-body model can be shown. The trunk is sinking downwards, while the scapulocoracoid is tending to rotate caudally around the pivot of the glenoid joint under the influence of the forces transmitted by m. serratus superficialis. Concurrently the scapulocoracoid is sinking downwards and is translated in cranialward direction, while the humerus rotates around the pivot of the elbow joint cranially as well. Stress distribution 180 within the scapulocoracoid shows a non-physiological pattern. The antebrachium is restricted for movements in all directions. For boundary conditions see Table 9. Figure 67 Distribution and deformation in the FE model after calculation. Applied muscles are m. serratus superficialis, m. serratus profundus and m. trapezius. Bearings are applied to the distal end of the scapulocoracoid in z-direction and to both ends of the humerus in x,y,z-direction. 2. Equilibrium between the scapulocoracoid and the trunk is reached. The scapulocoracoid is held in position only by the applied forces, while sinking downwards but shows no rotational movements. The trunk is sinking downwards and the humerus is subject to bending. Stress pattern is non-physiological, spreading from the glenoid joint to the caudal edge of the scapula. Transmission of forces can be detected between the coracoid and sternal elements and at the glenoid joint. In the next step, the equilibrium should be reached between scapulocoracoid and humerus by removing bearings from the humerus. For boundary conditions see Table 10. 181 Figure 68 Show the results after calculation, while reaching equilibrium without any restrictions at the scapulocoracoid. Muscles added to the model are, m. levator scapulae, m. costo-coracoideus and m. rhomboideus. No bearings at the scapulocoracoid are present. 182 3. The present figure is showing the calculated model adding m. triceps caput coracoideum and caput scapulae in order to attain balance of the humerus by pushing it into the glenoid joint. Balance in the scapulocoracoid should not be affected, as both part of the triceps complex act as functional antagonists, producing the same rotational moments referring to their line of action. One indicator bearing is applied to the humerus shaft in z-direction, not affecting the balance of the scapulocoracoid. Reaction force is high, indicating a strong forward direction, even with the actual applied forces in this step. Relative movement of the humerus and antebrachium to the medial side is shown. Stress distribution within the scapulocoracoid is slightly modified compared to former calculation steps. For boundary conditions see Table 11. Figure 69 Bearings are removed from the distal and proximal humerus joints, leaving one z-directed bearing at the humerus shaft. Further m. triceps caput coracoideum and caput scapulae were added to the model. 183 4. As the former calculation did not prevent the humerus from forward movement, the m. pectoralis complex is added to the model, instead of mm. triceps. One bearing is again placed at the distal end of the scapula, as without any calculation can be realized. Reaction force at the bearing is high pointing out that addition of m. pectoralis has a destabilizing effect to the scapulocoracoid in this arrangement. The humerus is free from restrictions, but shows high bending in medial direction, as a result of applied m. pectoralis. Stress distribution shows a decrease of compressive stresses in the cranial part of the scapulocoracoid and is therefore not physiological. For boundary conditions see Table 12. Figure 70 Position of bearings equals to the former step. M. pectoralis is applied to the model instead of m. triceps caput scapulare and caput coracoideum. 5. In a number of iterative steps equilibrium was reached. No bearings are required to keep scapula and humerus in balance. Maximum compressive stress value is -25 MPa. 184 Compressive stresses spread from the glenoid joint to the caudal border of the scapula, to the coracoid and sternal element. There still is no fully accordance to the original. Stress distribution within the acromial region has to be enhanced. In a next step modification of stress distribution is aimed due to repositioning of m. serratus superficialis. For boundary conditions see Table 13. Figure 71 No bearing are applied to the scapulocoracoid and humerus. Equilibrium is maintained only by means of forces. All muscles of the shoulder girdle system are applied, except for m. latissimus and m. teres major. 6. Boundary conditions in this calculation step are equal to the final calculation step except for m. serratus superficialis (Table 13).The upper picture shows the origin of m. serratus superficialis at the most caudal ribs. In the lower picture m. serratus superficialis is shifted cranially. As rotational moments result from the forces, they should increase in the upper configuration, because of the greater lever arm they exhibit in this arrangement. Concurrently the stability of equilibrium within the model is not affected by these modifications. The distribution of stresses within the scapulocoracoid bauraum cannot be modified essentially. 185 Figure 72 Two different calculation steps of the FE model. In the above shown calculation m. serratus superficialis originates most caudally from the trunk; In the calculation below the origin of m. serratus superficialis is placed more cranially. 7. The concentration of compressive stresses at the caudal border of the scapula superior to the glenoid joint is a result of strong bending moments at this area. To reduce bending in the scapulocoracoid, the forces values of m. trapezius and m. triceps scapularis are increased. Note the unusual deformation of the humerus shaft. Although strong forces are applied to diminish bending in the scapula, no reduction can be observed. Instead a heavy increase of compressive stresses at the proximal part of the scapulocoracoid can be observed. Further the scapula was aimed to rotate cranially, as a result only -y-directed translation can be detected. 186 Figure 73 Boundary conditions equal to the former calculations. The forces values of m. trapezius and m. triceps scapulae were increased. 8. The meshed scapulocoracoid bauraum and the humerus are refined to reduce canting in between these elements. This is not leading to a sufficient result, although stress distribution is approximating to the predicted distribution. The humerus exhibit great deformation in the proximal section, resulting from entrainment by the scapulocoracoid during movement. Minor rotation is visible around the restricted distal scapular edge. Further, the equilibrium is affected and no longer maintained. To enable calculation one bearing is applied to the distal edge of the bauraum. Lowering the friction coefficient from 1 to 0.1, diminish the unusual deformation in the humerus shaft, but neither rotation of the scapulocoracoid is visible nor free rotation within the glenoid joint is achieved. It can be concluded that a refinement of the elements and an increased friction do not account for free rotational movements between areas provided with contact elements. Boundary conditions can be obtained from Table 13. 187 Figure 74 Ground model with refined elements, calculated under the same boundary conditions as in Fig. 57 (A). Calculation of (A) shows alteration in stress distribution and equilibrium in the system, while the humerus shows no undisturbed movement within the glenoid joint (B). Friction coefficient for contact elements is lowered from .1 to 0.1, again no detecTable changes towards the desired status in the glenoid region were achieved (C). 188 10.4.2 Adjustment of static equilibrium in forelimb position II. The model shows a slight abduction of the humerus, whereas all other parts refer to the former defined model. Friction coefficient for contact elements has been kept. Convergence criteria for calculation is 0.001. The refined model is calculated under the same boundary conditions as in forelimb position I. Again adjusting of static equilibrium starts by forces running between the trunk and the scapulocoracoid. The scapulocoracoid is restricted to translational movements by one single indicator bearing at the distal corner. The humerus is restricted by two fixed bearings applied to both distal and proximal end of the shaft. Out of this initial situation, equilibrium is reached in iterative steps. 1. M. serratus superficialis here is the initial force rotating the scapulocoracoid caudally. M. trapezius and m. levator scapulae are counteracting the rotation in cranial direction, but at the same time adding high z-directional forces to the system, moving the scapulocoracoid cranially. M. costo-coracoideus produces z-directional forces into the opposite direction, but not to a great extent. Forces value of m. serratus profundus is here first calculated in order to transfer the +y dues of the acting vector forces resulting from m. trapezius and m.levator scapulae. In the following calculation steps forces value of m. serratus profundus will be calculated out of the summation of all y-dues of the acting vector forces running between the trunk and the scapulocoracoid, in order to keep the sum of forces=0, which is a precondition for equilibrium. Indicator bearing at the distal end of the scapula shows a moderate cranial rotation. Sum of ydirceted forces within the bearing located at the glenoid is near the initial forces value of about 18956N, denotes that the sum of weight force is actually completely transferred to this point. Distribution of compressive stresses is showing high values within the former aimed regions, like the acromial region, the scapula and within the coracoid region. For boundary conditions and reaction forces see Table 14. Compared to the first FE model, the forces in the present steps were subdivided and placed along the predicted insertion sites at the scapulocoracoid to obtain a more distributed compressive stress pattern and to minimize stress peaks, which occur especially at insertions of high forces, while the aabsolute force values are kept constant. Calculation of the initial situation resulted in an increase of reaction force at the z-directed bearing at the distal edge of the scapulocoracoid, thus indicating strong forward translation, which results into imbalance of the trunk and the scapulocoracoid. Although forces and rotational moments were calculated precisely, the trunk was entraining the scapulocoraocid along its direction. Friction, even with a 189 lowered friction coefficient of about 0.1 is beyond tolerable limits, because of the large number of contact elements between the trunk and scapulocoracoid. Figure 75 First calculation of the refined model. The applied force were reduced to an initial situaltion. Single forces are subdivided and distributed along the assumed insertion sites. For boundary conditions see Table 14. 2. To avoid misleading results from uncertain reactions between the trunk and scapulocoracoid, the trunk was removed, and the scapulocoracoid along with the humerus and the antebrachium were calculated separately. The focus in this investigation is on stress distributions within the scapulocoracoid element. Areas of the trunk adjacent to the scapulocoraoid preventing medial directed movement were replaced by adequate bearings to fulfil the function. Assumed regions of main force transmission are defined at the predicted 190 coracosternal joint and the acromial region, where the claviculae presumably contact the scapula and where forces can be transmitted. Further applied bearing should serve as indicator bearing and to provide stability until equilibrium was reached. Forces directed to the trunk remain their line of action positioned towards the trunk. (for reaction forces and boundary condition see Table 15). Figure 76 Calculation without the trunk element under the same boundary conditions as in the former steps, which includes the trunk (Table 15). Lateral movements of the scapulocoracoid, which formerly were prevented by the adjacent trunk element are transferred by applied x-dirceted bearings. The bearing at the distal end of the scapulocoracoid shows indicates low translational movements of the scapulocoracoid. 3. In the next calculations, views of the medial and caudal side are presented in addition to the lateral and medial view to gain necessary information. In the present calculation m. serratus superficialis, m. serratus profundus, m trapezius, m. levator scapulae and m. costocoracoideus are applied to the system. They run between the scapulocoracoid and the trunk, while m. triceps caput scapulare and m. triceps caput coracoideum run between the antebrachium and the scapulocoracoid. Medially directed movements of the scapulocoracoid are inhibited by application of x-directed bearings at the coracoid and the acromial region. To support stability one x-directed bearing is placed at the caudal edge near the glenoid joint. Indicator bearing in zdirection is applied to the distal edge of the scapulocoracoid. The humerus is restricted in all 191 directions at both the proximal and distal end. One fixed bearing is placed at the antebrachium fixed bearing to inhibit any movement. For reaction forces and forces values see Table 16. Figure 77 M. serratus superficialis, m. serratus profundus, m trapezius, m. levator scapulae and m. costo-coracoideus are applied to the FE model. M. triceps caput scapulare and caput coracoideum run between the antebrachium and the scapulocoracoid. One x-directed bearing is placed at the coracoid and the acromial region. One x-directed bearing is placed at the caudal edge near the glenoid joint. One indicator bearing in z-direction is applied to the distal edge of the scapulocoracoid. The humerus is restricted in all directions at both the proximal and distal end. A fixed bearing is placed at the antebrachium. 4. No restriction is required at the distal end of the scapula, because z- directed reaction forces within this bearing are low. Reaction force within the bearing at the glenoid joint indicates translation of the scapulocoracoid in cranial direction, which cannot be diminished by the applied forces of m. supracoracoideus, m. biceps brachii, m. coraco-brachialis brevis, m. deltoideus pars scapularis et clavicularis, m. subscapularis and m. scapulo-humeralis. Another force is required to 192 counter the high z-directed forces of m. trapezius and m. levator scapulae. Compressive stresses are increasing at the glenoid region, resulting from m. deltoideus clavicularis. High stress magnitudes can be observed at the medial side of the scapula as result of medial bending. For reaction forces and boundary conditions see Table 17. Figure 78 Forces added to the system are m. supracoracoideus, m. biceps brachii, m. coraco-brachialis brevis, m. deltoideus pars scapularis et clavicularis, m. subscapularis and m. scapulo-humeralis. No bearing are placed at thedistal end of the scapulocoraoid. Medial bending of the scapulocoracoid is indicated by black outlines 5. In order to counteract the cranialward translation of the scapulocoracoid, m. pectoralis profundus is applied to the system, originating from the ventral side of the trunk inserting profund at the medial side of the glenoid joint. To eliminate influence of further forces, m. triceps scapulare, m. deltoideus scapularis, m. deltoideus clavicularis, m. subscapularis and m. scapulo193 humeralis are temporary removed. Reaction force within the bearing at the distal end of the scapula is increased, while reaction force value of the bearing located at the glenoid is highly decreased, showing the great benefit of m. pectoralis profundus in preventing cranialward translation. For reaction forces and boundary conditions see Table 18. Figure 79 M. triceps scapulare, m. deltoideus scapularis, m. deltoideus clavicularis, m. subscapularis and m. scapulohumeralis are temporary removed. M. pectoralis profundus was applied to the system to counter caudally directed translational movements. 6. M. triceps scapulare, m. deltoideus clavicularis and m. subscapularis are applied to the system including an enhanced m. pectoralis major. M. levator scapulae has been divided into a superior and inferior portion for a refinement of the resulting stresses. The occuring reaction forces within the proximal bearing of the scapulocoracoid indicate high translational forces in 194 directed caudally, thus pushing the humerus into the glenoid joint. Although reaction forces at the proximal part as well as at the distal end are not eliminated, calculation could be accomplished without any restriction at the scapulocoracoid and proximal end of the humerus. For reaction forces values and boundary conditions for this calculation see Table 19. Figure 80 M. triceps scapulare, m. deltoideus clavicularis and m. subscapularis are applied to the system including an enhanced m. pectoralis major. M. levator scapulae has been divided into a superior and inferior portion for a refinement of the resulting stresses. 7. Medially directed movements of the scapulocoracoid are indicated at the bearing, which is located at the caudal border of the scapula. In order to minimize these deformations, m. costo-coracoideus pars profundus is applied. It originates from the ventral surface of the coracoid to the medial part of the sternal region. Further m. deltoideus scapularis and m. deltoideus clavicularis are slightly enhanced. Medial directed forces are now flowing medially from the 195 coracoid to the sternal region, while the indicator bearing at the caudal border is released (see Table 20). Stress distribution has not been modified essentially. Figure 81 M. costo-coracoideus pars profundus is applied to the system. It originates from the ventral surface of the coracoid to the medial part of the sternal region. Further forces for m. deltoideus scapularis and m. deltoideus clavicularis are increased. 8. Moderate modifications are executed in the present calculation step. Forces value in m. trapezius and m. levator scapulae are decreased. The calculation is accomplished without any restrictions at the scapulocoracoid and proximal humerus. The stress distribution in lateral view is sufficient, while the medial side is still affected by bending and shows high stresses and an unphysiological stress pattern. For boundary conditions and reaction forces see Table 21. 196 Figure 82 Forces value in m. trapezius and m. levator scapulae has been decreased. No restrictions at the scapulocoracoid and proximal humerus are necessary for calculation. 9. In order to modify the occurring compressive stresses m. serratus superficialis is positioned more laterally at the scapula compared to the former steps (see frontal view). The boundary conditions and reaction forces can be obtained from Table 22. As a result the compressive stress flow is modified. The compressive stresses are lowered at the medial side and concurrently increased at the lateral side. The static equilibrium is not affected, but the 197 caudalmost bearing at the scapula shows highly increased reaction forces, which indicate a medialward direction at this location. Figure 83 M. serratus superficialis is positioned more laterally at the scapula (frontal view) compared to the former steps. The boundary conditions are consistent. M. serratus superficialis are shifted to the middle of the scapulocoracoid bauraum. M. deltoideus clavicularis, m. deltoideus scapularis and m. subscapularis are repositioned. Their vector forces are directed more laterally. This results into higher laterally x-directional components of vector force in m. deltoideus clavicularis and m. deltoideus scapularis and medially x-directed components of force in m. subscapularis. The stress 198 distribution is modified. The medial side shows a decline of compressive stresses. In lateral view stresses are within the acromial region, the coracoid part and the scapula. The reaction forces are low at the indicator bearing, which is positioned at the distal end of the scapula. The calculation could be accomplished in addition without any restrictions at the scapulocorcoid and the proximal end of the humerus (not shown here). For reaction forces and boundary conditons see Table 23. Figure 84 M. serratus superficialis has been shifted to the middle of the scapulocoracoid bauraum. The boundary conditions are consistent. The medial side of the scapulocoracoid shows a decrease of bending , indicated by a reduction of compressive stresses. 10.4.3 Reduction of the “bauraum” After the first reduction the new bauraum still displays only the rough dimensions of the original, but is yet clearly reduced compared to the former bauraum. The bauraum shows compressive stresses ate the prominent acromial region at the cranial border of the scapulocoraoid. The scapula is more slender and the coracoid region has been rounded compared 199 to the original bauraum. A reduction of the material can also be viewed in frontal view as the breadth of the scapula is reduced. The contour legend is set to range from 0 to -2.7, which indicate an increase of compressive stresses in the bauraum. Maximum compressive stress increase (-111 N), but can only be detected at a sinlge location at the caudal border of the glenoid joint. The internal distribution of compressive stresses is shown in frontal cross sections. The stresses flow mainly undisturbed through the structure of the bauraum (Fig.). Fi gure 85 Pictures A-D FE model after the first reduction step, recalculated under the same boundary conditions as in the final calculation step. 200 Figure 86 Figure A-H are showing cross sections at the same location as in the final calculation step. The stressed areas are accumulating in the bauraum, while the overall structure is reduced. This leads to a thinning of the former bauraum. 201 In the second reduction step the main features of the scapulocoracoid again are visible, whereas the whole structure is refined compared to the original bauraum. The element is now exhibiting a more slender appearance, with a medially dished scapula. The acromial region of the scapula is clearly visible. At the distal end of the scapula the stresses are accumulating at the medial side. The contour plot is set to range from 0 to-4.5. The main part of the reduced bauraum now shows compressive stresses, which are within the range of physiological stress value (-2 to 20 MPa). Again, the maximum of compressive stresses is increased (-280 N), but still present at one distinct location at the caudal border of the glenoid joint. For a more detailed examination see cross sections of this reduction step (Fig. 82) Figure 87 FE model after the second reduction step. Compressive stress distribution after recalculation under constant boundary conditions. 202 Figure 88 Frontal cross sections of the second reduction step after calculation. Again sections were taken at the same position as in figure 71. Distribution of stresses along the bauraum are in accordance to the original. Features do not alter, but shows an ongoing refinement of the structure. 203 After the third and last reduction step the thinning of the whole structure is clearly visible and most pronounced at the most cranial border of the scapula. The prominent acromial region is present and in accordance to the orginal. The reduced bauraum is medially concave (Fig. B). The most compact structures can be obsereved in the coracoid at the position of the assumed coracosternal joint and dorso-caudally to the glenoid joint. Figure 89 Figure FE model after the third reduction step and before recalculation. Lateral view (A), frontal view (B), medial view (C), back view (D). The forces required under statical loading are present (arrows). The scapulocoracoid and humerus are free from restrictions. Bearings at the position of the coracosternal joint are inidicated as triangles. In the recalculation of the third and last reduction step the stressed regions are still in accordance to the original and exhibit physiological stress values in the structure,which range from -2 to -9 MPa. The amount of areas with show stresses below the physiological value is reduced. The compressive stresses concentrate within the aimed regions of the scapulocoraoid. A further reduction step could lead to a more defined structures, but is not considered at this point 204 of investigation. No additional information are expected. Contour legend has been set ranging from 0 to -9. Maximum compressive stress value again can be detected only at one distinct area at the caudal border of the glenoid joint. Figure 90 FE model after the third reduction step, recalculated under the former boundary conditions. is pointing out the stressed regions in accordance to the original, exhibit mostly physiological stress value in the structure. Contour legend has been set to -9. Maximum compressive stress value again can be detected at the caudal border of the glenoid joint and at the coracosternal joint. 205 In order to simulate acceleration under locomotor related conditions, the third reduction step was recalculated with all forces scaled two times as high as in the initial load case, according to 2 times earth acceleration. Compressive stress values in the relevant part of the structure are between -2 and -20 MPa. Figure 91 Calculation of the 3rd reduction step according to 2 times earth acceleration. The amount of compressive stresses in the relavent parts of the scapulocoracoid are between -3 and -20 MPa.. 206 10.4.4 Technical settings Forelimb position I. Table 9 Applied forces, which refer to muscles or muscle groups. Muscle Muscle force (N) Fg body weight 18956 M. serratus superficialis 15800 M. serratus profundus 3160 M. trapezius 10354 M. levator scapulae M. costo-coracoideus M. rhomboideus M. pectoralis posterior M. pectoralis anterior M. triceps caput coracoideum M. triceps caput scapulare M. supracoracoideus M. biceps brachii M. coracobrachialis brevis ventralis M. deltoideus scapularis M. deltoideus clavicularis M. subscapularis M. scapulo-humeralis M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis M. latissimus dorsi M. teres major 207 Table 10 Showing the applied forces referring to muscles or muscle groups. F x,y,z are reaction forces ,which can be detected at supported nodes after calculation. Muscle Muscle force (N) NODE FX FY FZ Fg body weight 18956 228 -100.49 286.89 130.21 M. serratus superficialis 15800 344 -60.062 126.09 -53.008 M. serratus profundus 3160 462 32.473 85.347 -56.963 M. trapezius 6902 73725 -3675.2 -942.35 M. levator scapulae 6360 78115 3216.0 -166.78 M. costo-coracoideus 13516 83886 1713.1 -49.955 M. rhomboideus 1400 141302 43.812 1370.5 728.29 141424 -1169.7 17087. 410.56 Total value -0.37996E-02 18956. -0.92033E-05 M. pectoralis posterior M. pectoralis anterior M. triceps caput coracoideum M. triceps caput scapulare M. supracoracoideus M. biceps brachii M. coracobrachialis brevis ventralis M. deltoideus scapularis M. deltoideus clavicularis M. subscapularis M. scapulo-humeralis M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis M. latissimus dorsi M. teres major 208 Table 11 Values of applied forces refer to muscles or muscle groups. F z is reaction force, which can be detected at supported nodes located at the humerus after calculation. Muscle Muscle force (N) NODE Fg body weight 18956 141623 M. serratus superficialis 15800 M. serratus profundus 3160 M. trapezius 6902 M. levator scapulae 6360 M. costo-coracoideus 13516 M. rhomboideus 1400 VALUE M. pectoralis posterior M. pectoralis anterior M. triceps caput coracoideum 9332 M. triceps caput scapulare 7466 M. supracoracoideus M. biceps brachii M. coracobrachialis brevis ventralis M. deltoideus scapularis M. deltoideus clavicularis M. subscapularis M. scapulo-humeralis M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis M. latissimus dorsi M. teres major 209 FX FY FZ -3173.1 0.0000 0.0000 -3173.1 Table 12 Values of applied forces refer to muscles or muscle groups. Muscle Muscle force (N) Fg body weight 18956 M. serratus superficialis 15800 M. serratus profundus 3160 M. trapezius 3543,77 M. levator scapulae 7633,56 M. costo-coracoideus 13904 M. rhomboideus 1400 M. pectoralis anterior M. pectoralis posterior 14964 M. triceps caput coracoideum M. triceps caput scapulare M. supracoracoideus M. biceps brachii M. coracobrachialis brevis ventralis M. deltoideus scapularis M. deltoideus clavicularis M. subscapularis M. scapulo-humeralis M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis M. latissimus dorsi M. teres major 210 Table 13 Values of applied forces refer to muscles or muscle groups. Muscle Muscle force (N) Fg body weight 18956 M. serratus superficialis 15800 M. serratus profundus 3160 M. trapezius 6902 M. levator scapulae 6360 M. costo-coracoideus 13644 M. rhomboideus 1400 M. pectoralis anterior 1800 M. pectoralis posterior 3640 M. triceps caput coracoideum 1500 M. triceps caput scapulare 2000 M. supracoracoideus 1000 M. biceps brachii 1500 M. coracobrachialis brevis ventralis 2000 M. deltoideus scapularis 100 M. deltoideus clavicularis 2000 M. subscapularis 5000 M. scapulo-humeralis 2000 M. triceps caput humerale laterale 500 M. triceps capita humerale mediale 500 M. triceps capita humerale posticum 500 M. spiralis 500 M. brachialis 500 M. latissimus dorsi M. teres major 211 10.4.5 Technical settings forelimb position II. Table 14 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr NODE FX FY FZ M. serratus superficialis 19058 12551 -606.35 15226. -6577.1 M. serratus profundus 5707 122396 -3120.4 970.99 M. trapezius 8550 122708 3735.3 1447.6 M. levator scapulae 6464 122730 1026.0 3620.8 M. costo-coracoideus 7880 123301 -48.179 -249.01 186985 165.12 M. triceps caput coracoideum 0 186991 -11.561 190.52 M. triceps caput scapulare 0 187047 80.003 507.73 305.28 M. supracoracoideus 0 187145 439.19 192.74 M. biceps brachii 0 193046 -1054.8 2427.2 878.78 M. coracobrachialis brevis ventralis 0 M. deltoideus scapularis 0 M. deltoideus clavicularis 0 Total values 0.28684E04 18956. 0.60038E04 M. subscapularis 0 M. scapulo-humeralis 0 M. rhomboideus M. pectoralis 1 M. pectoralis 2 M. pectoralis 3 M. pectoralis 4 M. latissimus dorsi M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis 212 Table 15 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr NODE FX M. serratus superficialis 19058 1287 M. serratus profundus 5707 1312 6420.5 M. trapezius 8550 5541 2976.5 M. levator scapulae 6464 12585 1124.1 M. costo-coracoideus 7880 186985 FY FZ 60.484 15143. 6155.8 167.02 186991 86.684 200.41 93.814 529.01 304.21 444.85 189.63 M. triceps caput coracoideum 0 187047 M. triceps caput scapulare 0 187145 M. supracoracoideus 0 193046 991.00 2004.8 774.34 M. biceps brachii 0 M. coracobrachialis brevis ventralis 0 M. deltoideus scapularis 0 TOTAL VALUES 8866.1 18489. 4948.1 M. deltoideus clavicularis 0 M. subscapularis 0 M. scapulo-humeralis 0 M. rhomboideus M. pectoralis 1 M. pectoralis 2 M. pectoralis 3 M. pectoralis 4 M. latissimus dorsi M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis 213 Table 16 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX M. serratus superficialis 19058 1287 M. serratus profundus 5707 1312 8479.9 M. trapezius 8550 5541 4563.3 M. levator scapulae 6464 12551 -3343.2 M. costo-coracoideus 7880 186985 FY FZ -432.77 18855. -4966.8 -110.84 186991 100.57 -197.29 184.68 42.130 -95.471 147.49 -91.053 M. triceps caput coracoideum 30000 187047 M. triceps caput scapulare 2000 187145 M. supracoracoideus 0 193046 -754.57 1545.0 488.34 TOTAL VALUES 6253.4 20282. -5097.8 M. biceps brachii M. coracobrachialis brevis ventralis 0 M. deltoideus scapularis 0 M. deltoideus clavicularis 0 M. subscapularis 0 M. scapulo-humeralis 0 M. rhomboideus 0 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 M. pectoralis 4 0 M. latissimus dorsi 0 M. triceps capita humerale mediale 0 M. triceps capita humerale posticum 0 M. spiralis 0 M. brachialis 0 214 Table 17 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX FY FZ M. serratus superficialis 19058 2 2567.4 M. serratus profundus 4040 1287 M. trapezius 7650 1312 8666.5 M. levator scapulae 6464 5541 3962.4 M. costo-coracoideus 7800 12551 5156.2 M. triceps caput coracoideum 2000 186985 M. triceps caput scapulare 3000 186991 177.97 331.34 M. supracoracoideus 2000 187047 303.40 534.91 455.66 M. biceps brachii 3000 187145 391.00 256.81 M. coracobrachialis brevis ventralis 2000 193046 399.42 634.16 436.64 M. deltoideus scapularis 3500 M. deltoideus clavicularis 3500 M. subscapularis 3500 TOTAL VALUE 5786.1 20275. 4267.1 M. scapulo-humeralis 4000 M. rhomboideus 0 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 M. pectoralis 4 0 M. latissimus dorsi 0 M. triceps capita humerale mediale 0 M. triceps capita humerale posticum 0 M. spiralis 0 M. brachialis 0 15.515 215 22393 3119.5 226.73 Table 18 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX M. serratus superficialis 1958 2 2379.5 M. serratus profundus 2123 1287 M. trapezius 6000 1312 7887.0 M. levator scapulae 7000 5541 3833.4 M. costo-coracoideus 5000 12551 3299.3 M. pectoralis profundus 5000 186985 M. triceps caput coracoideum 2000 187047 M. triceps caput scapulare 0 187145 M. supracoracoideus 2500 193046 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 2500 M. deltoideus scapularis 0 TOTAL VALUE M. deltoideus clavicularis 0 M. subscapularis 0 M. scapulo-humeralis 0 M. rhomboideus 0 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 M. pectoralis 4 0 M. latissimus dorsi 0 M. triceps capita humerale mediale 0 M. triceps capita humerale posticum 0 M. spiralis 0 FY FZ 597.16 216 18150. 847.52 85.090 91.135 10.622 79.529 119.14 99.542 30.515 2542.1 194.76 6245.1 20565. 624.19 Table 19 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z Fg Summe NODE FX 444 3451.7 FY FZ M. serratus superficialis 19058 1287 M. serratus profundus 446 5565 4342.4 M. trapezius 5500 10124 8752.2 M. levator scapulae 3500 12551 5160.0 M. levator scapulae superior 1500 186985 M. rhomboideus 1000 186991 195.27 290.65 M. costo-coracoideus 5000 187047 152.24 625.67 1008.6 M. pectoralis profundus 6000 187145 237.44 691.05 M. triceps caput coracoideum 1900 M. triceps caput scapulare 1000 M. supracoracoideus 3500 19132. 6266.8 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 4000 M. deltoideus scapularis 0 M. deltoideus clavicularis 2660 M. subscapularis 2000 M. scapulo-humeralis 0 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 M. pectoralis 4 3300 M. latissimus dorsi 0 200.05 TOTAL VALUE M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis 217 17409. 6400.3 459.46 5077.0 Table 20 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX FY FZ M. serratus superficialis 19058 444 4879.7 M. serratus profundus 542 1287 M. trapezius 5500 5565 2039.2 M. levator scapulae 3500 5764 2152.7 M. levator scapulae superior 1500 5830 581.46 M. rhomboideus 1000 10124 4132.7 M. costo-coracoideus 4000 186985 M. costo-coracoideus pars prof. 3500 186991 35.459 761.37 M. pectoralis profundus 4500 187047 16.848 1858.9 937.35 M. pectoralis 1 500 187145 1931.9 474.33 M. pectoralis 2 500 193046 4161.8 13910. 5248.3 M. pectoralis 3 500 M. pectoralis 4 3500 M. latissimus dorsi 0 TOTAL VALUE 9676.3 19323. 6501.5 M. triceps caput coracoideum 1900 M. triceps caput scapulare 1000 M. supracoracoideus 4500 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 4000 M. deltoideus scapularis 0 M. deltoideus clavicularis inferior 0 M. deltoideus clavicularis 2000 M. subscapularis 2000 M. scapulo-humeralis 0 158.48 M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis 218 860.58 M. brachialis Table 21 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX FY FZ M. serratus superficialis 19058 444 4879.7 M. serratus profundus 542 1287 M. trapezius 5500 5565 2039.2 M. levator scapulae 3500 5764 2152.7 M. levator scapulae superior 1500 5830 581.46 M. rhomboideus 1000 10124 4132.7 M. costo-coracoideus 4000 186985 M. costo-coracoideus pars prof. 3500 186991 35.459 761.37 M. pectoralis profundus 4500 187047 16.848 1858.9 937.35 M. pectoralis 1 500 187145 1931.9 474.33 M. pectoralis 2 500 193046 4161.8 13910. 5248.3 M. pectoralis 3 500 M. pectoralis 4 3500 M. latissimus dorsi 0 TOTAL VALUE 9676.3 19323. 6501.5 M. triceps caput coracoideum 1900 M. triceps caput scapulare 1000 M. supracoracoideus 4500 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 4000 M. deltoideus scapularis 0 M. deltoideus clavicularis inferior 0 M. deltoideus clavicularis 2000 M. subscapularis 2000 M. scapulo-humeralis 0 158.48 M. triceps caput humerale laterale M. triceps capita humerale mediale M. triceps capita humerale posticum 219 860.58 M. spiralis M. brachialis Table 22 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX FY FZ M. serratus superficialis 19057 444 181.93 M. serratus profundus 354 1287 M. trapezius 5100 5565 4569.6 M. levator scapulae 3100 10124 8638.2 M. levator scapulae superior 1500 186985 M. rhomboideus 40 186991 46.329 686.25 M. costo-coracoideus 4000 187047 109.57 1770.8 1087.8 M. costo-coracoideus pars prof. 3000 187145 1869.6 718.24 M. pectoralis profundus 4500 193046 4118.2 14028. 4323.8 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 TOTAL VALUE 8970.9 19187. 6116.4 M. pectoralis 4 3500 M. latissimus dorsi 0 M. triceps caput coracoideum 1900 M. triceps caput scapulare 1000 M. supracoracoideus 4500 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 2000 M. deltoideus scapularis 0 M. deltoideus clavicularis inferior 0 M. deltoideus clavicularis 6000 M. subscapularis 2000 M. scapulo-humeralis 0 13.439 M. triceps caput humerale laterale M. triceps capita humerale mediale 220 832.29 M. triceps capita humerale posticum M. spiralis M. brachialis Table 23 Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muskel Fr x/y/z NODE FX M. serratus superficialis 19057 444 2506.1 M. serratus profundus 354 Scapula M. trapezius 5100 5565 5822.5 M. levator scapulae 3100 10124 4531.4 M. levator scapulae superior 1500 186985 M. rhomboideus 40 186991 -65.951 655.40 M. costo-coracoideus 4000 187047 104.03 1761.0 1096.9 M. costo-coracoideus pars prof. 3000 187145 1872.5 737.45 M. pectoralis profundus 4500 193046 -4093.5 14098. 4279.1 M. pectoralis 1 0 M. pectoralis 2 0 M. pectoralis 3 0 TOTAL VALUE 8804.6 19204. 6050.4 M. pectoralis 4 3500 M. latissimus dorsi 0 M. triceps caput coracoideum 1900 M. triceps caput scapulare 1000 M. supracoracoideus 4500 M. biceps brachii 2000 M. coracobrachialis brevis ventralis 2000 M. deltoideus scapularis 0 M. deltoideus clavicularis inferior 0 M. deltoideus clavicularis 6000 M. subscapularis 2000 M. scapulo-humeralis 0 M. triceps caput humerale laterale 221 FY FZ -63.120 816.65 M. triceps capita humerale mediale M. triceps capita humerale posticum M. spiralis M. brachialis Table 24 Final calculation. Values of applied forces refer to muscles or muscle groups. F x,y,z are reaction forces, which can be detected at supported nodes after calculation. Muscle Fr x/y/z NODE M. serratus superficialis 17603 Sternocoracoid joint M. serratus profundus 1 FX FY FZ 2 683.14 301 12 -19.819 M. serratus profundus 2 2140 18 1519.2 M. trapezius 4300 25 1016.7 M. levator scapulae 3000 32 445.13 M. levator scapulae superior 1175 425 464.48 M. rhomboideus 1000 447 1233.9 M. costo-coracoideus 4800 553 -507.90 M. costo-coracoideus pars prof. 3000 557 -712.87 M. pectoralis profundus 4500 565 735.69 M. pectoralis 3500 570 314.88 M. triceps caput coracoideum 1900 576 -179.77 M. triceps caput scapulare 1000 Acromion 10124 1171.8 M. supracoracoideus 4500 Antebrachium 186985 M. biceps brachii 2000 186991 -2325.6 1090.8 M. coracobrachialis brevis ventralis 4000 187047 -2709.8 3730.7 2518.0 M. deltoideus scapularis 5000 187145 8529.8 3329.2 M. deltoideus clavicularis 6000 M. subscapularis 2000 M. scapulo-humeralis 500 18387. 5847.1 TOTAL VALUE 222 5035.7 1129.2 Curriculum Vitae Date of birth 14.02.1974, in Dortmund Marital status married, one child Education Since 02/05 PhD student at the Ruhr-University; Faculty of Biology and Biotechnology, Department of Zoology and Neurobiology, Bochum; Thesis: Biomechanics of the shoulder girdle in sauropod dinosaurs 10/00 bis 12/03 Biology at the University of Mainz, Diploma 10/95 bis 07/00 Biology at the Ruhr-University Bochum 10/94 bis 07/95 Biology at the University Göttingen 1993 Abitur Professional Experience Since 15/02/10 Project coordinator at the Ruhr-University Research School, Bochum 10/05-10/08 Scientific assistant of Prof. Dr. Dr. h.c. H. Preuschoft, formerly Institute of Anatomy, Medical Faculty, Ruhr-University Bochum 01/04-06/04 Institute of Anthropology, University Mainz Publications Hohn-Schulte B, Preuschoft H & Witzel U (submitted) Biomechanics of the tetrapod shoulder girdle with special emphasis on the early tetrapod Tiktaalik roseae. PLoS ONE. Hohn-Schulte B (in press) Walking with the Shoulder of Giants: Biomechanical Conditions in the Tetrapod Shoulder Girdle as a Basis for Sauropod Shoulder Reconstruction In: Biology of the Sauropod Dinosaurs: Understanding the life of giants. Klein N, Remes K, Gee C (eds.) James Farlow, Indiana University Press, 513-551. Hohn B, Witzel U & Preuschoft H (2008) 3-D Finite-Element Structure Synthesis of the shoulder girdle in Diplodocus longus. Journal of Vertebrate Palaeontology 28 (3) 88A. 223 Hohn B, Witzel U & Preuschoft H (2006) Functional morphology of the shoulder girdle and the forelimbs in sauropod dinosaurs under consideration of 3-D finite-element structure synthesis (FESS). Journal of Vertebrate Palaeontology 26(3): 77A. Preuschoft H, Hohn-Schulte B, Stoinski S & Witzel U (in press) Why so huge? Biomechanical reasons for the acquisition of large size in sauropod and theropod dinosaurs. In: Biology of the Sauropod Dinosaurs: Understanding the life of giants. Klein N, Remes K, Gee C (eds.) James Farlow, Indiana University Press. Preuschoft H, Hohn-Schulte B, Scherf H, Schmidt M, Krause C & Witzel U (2010) Functional analysis of the primate shoulder. International Journal of Primatology 31: 301-320. Preuschoft H, Witzel U, Hohn B, Distler C & Schulte D (2007) Biomechanics of locomotion and body structure in varanids with special emphasis on the forelimbs. Mertensiella 16, 59-78. Congresses and Workshops 2008 1st International Workshop” The Evolution of Gigantism in Sauropod dinosaurs”, Bonn 2008 68th Annual meeting of the “Society of Vertebrate Palaeontologists” (SVP), Cleveland (USA) 2007 „International Congress of Vertebrate Morphologists“(ICVM), Paris (F) 2006 66th Annual meeting of the “Society of Vertebrate Palaeontologists” (SVP), Ottawa (CA) 2006 8th Congress of the “Society of Vertebrate Palaeontology and Comparative Anatomy” (SVPCA), Paris (F) Grants 10/08-03/09 PhD Grant Wilhelm und Günter Esser-Stiftung, Gesellschaft der Freunde der Ruhr-Universität Bochum (GdF) 10/2008 Womens support grant of the Faculty of Biology and Biotechnology, RuhrUniversity Bochum Memberships in professional associations DFG-Forschergruppe 533 „Biologie der Sauropoden- Evolution des Gigantismus“ Society of Vertebrate Palaeontology (SVP) 224 Acknowledgements I first express my gratitude to Dr. C. Distler-Hoffmann for her guidance, support and encouragement throughout the thesis. I wish to thank Prof. Dr. H. Preuschoft for assignment of this work, all the beneficial discussions and advices and for the opportunity to join the Research group “Biology of the Sauropod Dinosaurs: The Evolution of Gigantism. For his extensive support and advice my thanks go to Prof. Dr. U. Witzel. I have greatly benefited from discussions, guidance and overall support from R. Gössling and Dr. N. Sverdlova. Further thanks go to all members of the LMK. I am also indebted to Prof. M. Sander, Dr. C. Gee, Dr. A. Christian, N. Pajor, T. Bräuer, K. Moser, Dr. K. Remes, Dr. O. Rauhut, Dr. H. Mallison, Dr. N. Klein, J.-T. Möller, Dr. T. Suthau, S. Stoinski, Dr. T. Tütken, and the remaining members of the Research group for discussions on sauropods and locomotion. Special thanks goes to K. Heitplatz for organization and help, whenever it was needed. This thesis could never have been completed without Dr. R. Fechner, and I am grateful for her support and encouragement. For access to the wonderful fossil of Tiktaalik roseae many thanks go to Dr. Shubin and K. Monoyios, University of Chicago. For access to the specimens and assistance I thank the staff of the following institutions: Institute d´Anatomie Normale, Strassbourg, Senckenberg museum of natural history, Frankfurt; Natural museum of history, Berlin; Saurier museum Aathal; Bayrische Staatsammlung, München. Many thanks go to my colleagues at the Ruhr-University Research School. I am overall grateful to my family and friends who never stopped supporting me through the long years to finish this project. This research project was funded by the DFG and a PhD grant of the Wilhelm & Günther Esser Stiftung. 225 Erklärung Hiermit erkläre ich, dass ich die Arbeit selbstständig verfasst und bei keiner anderen Fakultät eingereicht und dass ich keine anderen als die angegebenen Hilfsmittel verwendet habe. Es handelt sich bei der heute von mir eingereichen Dissertation um fünf in Wort und Bild völlig übereinstimmende Exemplare. Weiterhin erkläre ich, dass digitale Abbildungen nur die orginalen Daten enthalten und in keinem Fall inhaltsverändernde Bidbearbeitung vorgenommen wurde. Bochum, im April 2010 _______________________________ (Unterschrift) 226