Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
LOW BACK BIOMECHANICS DURING WALKING OF INDIVIDUALS WITH A LOWER-LIMB AMPUTATION by Adam Yoder Copyright by Adam J. Yoder 2014 All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Master of Science (Engineering - Mechanical). Golden, Colorado Date ___________________________ Signed: ___________________________ Adam Yoder Signed: ___________________________ Dr. Anne Silverman Thesis Advisor Golden, Colorado Date ___________________________ Signed: ___________________________ Dr. Greg Jackson Professor and Head Department of Mechanical Engineering ii ABSTRACT Individuals with a lower-limb amputation have an increased prevalence of chronic low back pain (LBP), relative to the general adult population. Altered, dynamic whole-body biomechanics resulting from limb loss are thought to be a primary cause of the increased susceptibility. However, biomechanical LBP development is a multi-factorial problem, and a definitive cause has yet to be ascertained using only traditional, laboratory methods. Thus, the purpose of this work was to compare dynamic, in vivo low back biomechanics between individuals with and without unilateral, transtibial amputation during walking, estimated using patient-specific computational modeling and simulation. A generic, muscle-actuated whole-body model with additional detail in the L1-L5 lumbar was adjusted to represent each individual. Experimentally-measured motion capture, ground reaction force, and surface electromyography for each individual were used to simulate a gait cycle to estimate concurrent internal low back biomechanics. Results showed several group differences in computed low back metrics during particular phases of the gait cycle. Most significant in individuals with an amputation was greater lateral trunk motion towards the residual side during residual single limb stance, concurrently with greater intact-side trunk muscle forces and a greater L4L5 lumbar joint contact force. A greater range of axial trunk rotation near toe off of the residual limb was also found concurrently with greater force in residual-side erector spinae and psoas. The repetition of such abnormal biomechanics over time has potential to cause deficiencies in muscular endurance, strength asymmetries, inhibited proprioception, and myofascial pain, each associated with increased susceptibility to chronic, biomechanical LBP and other secondary musculoskeletal disorders. This work contributes to a broader goal of developing computational modeling and simulation into a supplementary clinical tool to aid in diagnosis and treatment of biomechanical disorders. iii TABLE OF CONTENTS ABSTRACT ............................................................................................................................ iii LIST OF FIGURES ....................................................................................................................... vi LIST OF ABBREVIATIONS ...................................................................................................... viii CHAPTER 1 INTRODUCTION ............................................................................................... 1 CHAPTER 2 REVIEW OF LITERATURE .............................................................................. 4 2.1. Low Back Pain ..................................................................................................... 4 2.1.1. Body Segment Kinematics .................................................................... 6 2.1.2. Muscle Function.................................................................................. 14 2.1.3. Spinal Tissue Mechanisms .................................................................. 22 2.2. Individuals with a Lower-Limb Amputation ..................................................... 30 2.3. Musculoskeletal Modeling and Simulation ....................................................... 37 2.4. Finite Element Analysis of the Spine................................................................. 48 2.5. Summary ............................................................................................................ 55 CHAPTER 3 LOW BACK KINEMATICS, MUSCLE FORCES, AND JOINT CONTACT FORCES DURING WALKING OF INDIVIDUALS WITH TRANSTIBIAL AMPUTATION ................................................................................................. 57 3.1. Abstract .............................................................................................................. 57 3.2. Introduction ........................................................................................................ 58 3.3. Methods.............................................................................................................. 60 3.4. 3.3.1. Musculoskeletal Model ....................................................................... 61 3.3.2. Simulation Framework........................................................................ 63 3.3.3. Data Analysis ...................................................................................... 64 Results ................................................................................................................ 65 3.4.1. Trunk-Pelvis Kinematics and Low Back Joint Contact Force ............ 65 iv 3.4.2. Low Back Muscle Forces.................................................................... 68 3.5. Discussion .......................................................................................................... 68 CHAPTER 4 SIMULATION AND MODEL DETAILS ........................................................ 75 4.1. Additional Musculoskeletal Model Background ............................................... 75 4.2. Simulation Settings & Parameter Optimization ................................................. 75 4.3. Muscle Fiber and Tendon Calibration ............................................................... 82 4.4. Joint Angle Conventions .................................................................................... 82 4.5. Lower Extremity EMG constraints .................................................................... 84 CHAPTER 5 FINITE ELEMENT LUMBAR SPINE GEOMETERY FOR MULTI-SCALE SIMULATION .............................................................. 86 5.1. Methods & Results ............................................................................................. 86 CHAPTER 6 GENERAL CONCLUSIONS ............................................................................ 96 6.1. Recommendations for Future Research ............................................................. 96 REFERENCES CITED ............................................................................................................... 100 APPENDIX A SUBJECT PARAMETERS ............................................................................. 113 APPENDIX B HILL MUSCLE TENDON/FIBER CALIBRATION ..................................... 114 APPENDIX C PARAMETER OPTMIZATION AND MARKER TRACKING SETTINGS ................................................................................. 116 APPENDIX D LOWER EXTREMITY EMG VALIDATION ............................................... 117 v LIST OF FIGURES Figure 1.1 Categories of, and interactions between, degenerative and biomechanical LBP ..... 3 Figure 1.2 A patient-specific, computational simulation workflow .......................................... 3 Figure 2.1 Illustration of in-phase and anti-phase modes of trunk-pelvis coordination ............ 9 Figure 2.2 Selected musculature of the hip, pelvis, and low back ........................................... 15 Figure 2.3 Representation of a scoliotic, spinal deformity ...................................................... 29 Figure 2.4 Anatomical FSU compared to a representative finite element model. ................... 49 Figure 3.1 Whole-body musculoskeletal model ...................................................................... 62 Figure 3.2 Group average results for trunk-pelvis relative angle and joint contact force ....... 66 Figure 3.3 Group average results for cumulative force within ipsilateral and contralateral low back muscle groups throughout the gait cycle ................................................ 69 Figure 4.1 The generic musculoskeletal model (MoCapModel, Model Repository v1.6, AnyBody Modeling System v6.0) .......................................................................... 76 Figure 4.2 Optimization settings for the iliac crest marker ..................................................... 79 Figure 4.3 Example of model parameters after applying the optimization sequence. ............. 80 Figure 4.4 Minimization of marker tracking errors ................................................................. 81 Figure 4.5 Frames created to measure thorax 3DOF rotation relative to pelvis ...................... 83 Figure 4.6 Joint coordinate system in the L4L5 joint .............................................................. 84 Figure 4.7 Processing steps to compute EMG-based lower bound activation constraints ...... 85 Figure 5.1 Cadaver-based L1-L5 finite element model (Huls, 2010) ...................................... 87 Figure 5.2 Bone geometry from the AnyBody model in comparison to the cadaver .............. 87 Figure 5.3 Rigid-body similarity transform for initial alignment. ........................................... 89 Figure 5.4 Representation of three-step sequential transform process .................................... 90 Figure 5.5 Lumbar muscle nodes in the AnyBody model ....................................................... 92 Figure 5.6 Bone geometry aligned after step one rigid-body registration ............................... 92 Figure 5.7 Comparison of transform methods ......................................................................... 93 Figure 5.8 Representative facet cartilage created at each of the four joint levels. .................. 94 Figure 5.9 Creation of baseline, sagittally-symmetric spinal geometry .................................. 95 vi LIST OF TABLES Table 2.1 In vivo disc pressure in the L4L5 joint measured during various activities ............ 26 Table 2.2 Total facet loads during tri-planar motions.............................................................. 28 Table 3.1 Mean (SD) of participant characteristics. ................................................................ 61 Table 3.2 Group mean (SD) of outcome metrics that were significantly different ................. 67 Table 4.1 Modeled lower extremity muscle groups in generic lower extremity model .......... 77 Table 4.2 Modeled trunk muscle groups.................................................................................. 77 Table A.1 Parameters of subjects selected for simulation. .................................................... 113 Table C.1 Settings applied in the AnyBody parameter optimization process ....................... 116 vii LIST OF ABBREVIATIONS LBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOWER BACK PAIN TFA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRANSFEMORAL AMPUTATION TTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRANSTIBIAL AMPUTATION EMG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ELECTROMYOGRAPHY ROM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RANGE OF MOTION LLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LEG LENGTH DISCREPANCY IVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTEVERTEBRAL DISC FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FINITE ELMENT METHOD FSU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FUNCTIONAL SPINAL UNIT OA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OSTEOARTHRITIS RBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RADIAL BASIS FUNCTION viii 1.CHAPTER 1 INTRODUCTION Low back pain (LBP) is a widespread clinical issue in the general population with large impacts on healthcare each year. Certain patient populations, such as lower-limb amputees, have an increased prevalence of persistent, bothersome (chronic) LBP relative to the able-bodied population. Due to the complex anatomy and physiology of the spine, diagnosing and treating the underlying etiology of a patient’s LBP is difficult, as illustrated in Figure 1.1. Experimental comparisons of chronic LBP patients with respect to LBP-free individuals have proven useful to characterize potential associations between LBP and whole-body biomechanics. In particular, abnormal posture and motion, altered muscular recruitment, and altered low back stability are often characteristic of individuals with chronic LBP. However, biomechanical and degenerative factors that may be sources of LBP are not independent (Figure 1.1), and cause/effect relationships between them are difficult to ascertain using only traditional experimental methods. However, in order to develop effective rehabilitative and therapeutic interventions to treat LBP within a particular category of patients, such as individuals with a lower limb amputation, associations between abnormal whole-body biomechanics and internal, tissue-level metrics must be established. Particular altered whole-body biomechanics of individuals with a lower-limb amputation during walking, relative to able-bodied individuals, include muscle compensations, kinematic asymmetries, and abnormal coordination between body segments. Even though these differences are frequently apparent through purely visual observations, underlying biomechanical mechanisms that contribute to increased LBP susceptibility in individuals with a lower-limb amputation have not been established. This may be due in part to limitations of traditional, 1 clinical measurement tools to fully characterize in vivo biomechanical quantities that are known or suspected tissue-level contributors to LBP, especially when these quantities must be monitored during dynamic patient motions. Advancements in computational biomechanics and simulation have recently gained attention as potential tools to address these limitations; by computing estimates of whole-body movements and accompanying, internal tissue-level mechanics that are costly, invasive, or impossible to measure in a laboratory environment. Therefore, the objective of this research was to compare the low back biomechanics of individuals with and without a lower-limb amputation during walking, using a patientspecific computational simulation workflow. The broader, long-term goal of this work is to establish baseline data, biomechanical models, and simulation tools and that will be part of a computational workflow, with potential clinical applications to aid in diagnoses and rehabilitation of patients with biomechanical LBP (Figure 1.2). 2 Figure 1.1 – Categories of, and interactions between, degenerative and biomechanical LBP. The most prevalent, competing theories of chronic LBP development are adaptation to pain versus biomechanical mechanisms that drive degeneration. Abnormal motion and muscle recruitment have been suggested as the most likely causes of LBP in individuals with a lower-limb amputation. Full background of each cited references are discussed in the Literature Review (Chapter 0), and documented in References Cited. Figure 1.2 – A patient-specific, computational simulation workflow for the evaluation of biomechanical LBP. Components developed or investigated within the scope of thesis work are designated with shading. 3 2.CHAPTER 2 REVIEW OF LITERATURE A background of low back pain (LBP) in individuals with a lower-limb amputation is available through a review of literature in the areas of low back biomechanics, clinical gait analysis, and spinal tissue degeneration. The review collectively suggests biomechanical alterations in upper and lower extremity motion, muscle function, and low back stability in individuals with a lower-limb amputation, which may be associated with increased susceptibility to chronic LBP. 2.1. Low Back Pain Low back pain is a prominent disability in the general population of the United States, with quantitative evidence suggesting that between 50-80% of all individuals will be affected by an episode of LBP at some point in their life (Rubin, 2007). More specifically, the 2006 National Health Interview Survey of U.S. adults (n=31,044) found 26% to report at least one day of LBP within the last three months (Deyo et al., 2006). Investigations of healthcare visit trends found that ~90% of cases resolved as acute instances and patients recovered quickly (Freburger et al., 2009). However, 10% of the adult population appears to develop LBP that is persistent and bothersome in excess of 3 months, at which point a chronic classification is appropriate. This category of chronic LBP is among the most common reasons to seek medical care (Becker and Stumbo, 2013), and the result each year with the United States is associated direct and indirect costs of $100-200billion, primarily due to lost time and disability wages (Freburger et al., 2009; Katz, 2006; Salzberg, 2012). 4 Recommended treatments may range from topical pain medication and therapy protocols at a minimum, to medical imaging and invasive surgery at the most severe. A review of the procedures typically followed in clinical management of LBP provides and distinguishes the generally accepted physiological links between diagnostic findings and potential etiologies (Becker and Stumbo, 2013). Examinations by physicians and physical therapists may include evaluation of standing posture and lumbar lordosis, range of motion (ROM) tests, gait analyses, supine lower extremity and low back endurance tests, and evaluation of the lower extremity neurovascular system. Immediate medical imaging has been suggested not to improve outcomes for a majority of individuals, and is thus only recommended in the presence of serious “red flag” symptoms during repeated, physical examination. Approximately 90% of LBP patients receive a nonspecific diagnosis, in which a particular etiology cannot be ascertained (van Tulder et al., 2002). Upon chronic classification after LBP persistence in excess of 3 months, injection and nerve block therapies are considered, followed by indication for surgery. Surgical intervention is a last resort in the clinical management process, although the yearly frequency of low back surgeries in the U.S. has been found to be on the increase since 1990 (Freburger et al., 2009). Difficulties in investigating complex, interrelated biomechanical and degenerative etiological factors has resulted in many studies over the past several decades seeking to determine what, if any, biomechanical factors are different between individuals with LBP relative to healthy individuals. These experimental designs generally cannot ascertain potential cause and effect relationships. Nonetheless, such findings can be valuable, and generally fall into one of three categories: (1) body-segment kinematics, (2) muscle function, and (3) lumbar tissue-level. Unless explicitly stated otherwise, the LBP subject sampling in all studies collected in this literature were individuals with clinically-nonspecific, chronic LBP. 5 2.1.1. Body Segment Kinematics Studies of whole-body movement characteristics associated with LBP have primarily focused on motions of the thorax, lumbar spine, pelvis, and thighs. Furthermore, segmental motions within a single stride, versus coordinative between-stride measures, have been characterized. Studies investigating lifting exertions and sitting postures, while a large body of the LBP literature, are not generally discussed here. Rather, the primary focus is altered body segment kinematics of individuals with LBP during walking. Distinct, angular displacements of the pelvis and lower lumbar spine in the three anatomical planes have been compared between individuals with LBP and pain-free subjects during treadmill walking (1.25m/s, angles normalized to standing) (Vogt et al., 2001). Withinstride patterns and amplitudes of segmental angular displacements were similar in subjects with chronic LBP relative to healthy subjects; however between-stride variability of lumbar and pelvic oscillations were greater in subjects with LBP. In contrast to a majority of previous work that analyzed within-stride metrics, these findings highlighted that intrasubject variability across repetitive motion may be a further important consideration with respect to chronic LBP, either as a cause or result of pain. Dynamical systems approaches use increased, between-stride variability to distinguish coordination changes and low movement stability (Hamill et al., 1999). Building on these findings, an additional similar work supplemented the experimental design of current-LBP versus no-pain, with a resolved-LBP condition (Taylor et al. 2004). The subjects used for the current-LBP condition were re-tested once the LBP had resolved. This work also concluded that distinct, segmental amplitude measurements (max minus min, all three anatomical planes, projected onto lab global) of lumbar and pelvic motion during walking were insufficient to distinguish between people with current-LBP and healthy subjects with no history 6 of LBP. However, range of lumbar bending in the frontal plane, and also of pelvic rotation in the transverse plane, were significantly reduced in paired comparisons of resolved-LBP and currentLBP. Additionally, a strong negative correlation (r=-0.74) was observed between average (between-stride) angular displacement, and subject-reported pain intensity. Subjects were seemingly modulating segmental motion to avoid aggravating pain (pain-adaptation). The collective findings of these two studies suggest that if segmental motion is being analyzed, robust, dynamic measures of relative motion are needed to distinguish between individuals with and without LBP (irrespective of acute or chronic designation). One metric commonly used to quantify dynamic coordination is continuous relative phase (CRP), which in brief summary extends calculation of joint (or segment) angle alone to also account for instantaneous velocity. The relative phase between instantaneous angle and velocity in an angle-velocity phase plane, is calculated per equation (1.1), (1.1) where ϕ is phase angle, ω is joint (or segment) angular velocity, and θ is joint (or segment) angle. Continuous relative phase between two joints (or segments) for a portion of motion is calculated by subtracting the two respective phase angles across the time duration of interest. In depth details on potential clinical uses for CRP in biomechanics are provided by (Hamill et al., 1999; Seay et al., 2011), with an example application to characterize walking stability detailed by (Hamill et al., 1999). Between-stride standard deviation of CRP has been frequently applied as a metric to quantify dynamic stability of body segment coordination. One study calculated CRP for subjects with/without nonspecific LBP (n=6), walking on an increasing-speed treadmill (0.17m/s start, to 1.5m/s finish) to investigate whether trunk-pelvis dynamic stability was associated with LBP 7 (Selles et al., 2001). In the transverse plane, pain-free individuals were found to have primarily in-phase coordination between trunk and pelvis at slow speeds, and to transition to anti-phase at faster speeds above ~1.0m/s. Anti-phase and in-phase coordination modes between the trunk and pelvis are shown in Figure 2.1. In contrast, persons with LBP had decreased CRP variability at high speeds relative to no-pain, suggesting more rigid control (increased stability) between the segments with increasingly unstable walking conditions. The frontal plane was not investigated in this study, and cause/effect for the transverse differences could not be determined. A later study improved upon the former experimental design by including a wide range of walking and running speeds (0.8m/s up to 3.8m/s), explicitly distinguishing all three anatomical planes, and recruiting subjects for three conditions (n=14 each group): current-LBP (pain >4 months), resolved-LBP (pain-free >6 months), and no history of LBP (Seay et al., 2011). Average, within-stride magnitude and variability at each speed were computed for each subject group. In agreement with the earlier work, those with current-LBP relative to pain-free had increased, dynamic trunk-pelvis stability (decreased CRP variability) in the transverse plane at higher speeds. The same increased trunk-pelvis stability was also found in the frontal plane at slow speeds (<2.8m/s). Both former studies interpreted primarily in-phase motion in either the frontal or transverse planes (Figure 2.1), in combination with a corresponding increase in dynamic stability (decrease in CRP variability), as a “guarded” gait strategy that indicated an adaptation to, rather than a cause of, the current LBP. Other, comparable work has suggested that interpreting between-stride standard deviation in CRP as a measure of coordinative stability has limitations. In particular, authors demonstrated that CRP variability is not sufficient to separate inter-subject variability from speed-induced variability if multiphasic oscillations are present in the body segments being analyzed (Lamoth et 8 Figure 2.1 – Illustration of in-phase and anti-phase modes of trunk-pelvis coordination in the frontal and transverse anatomical planes, adapted from (Seay et al., 2011). al., 2002a). With respect to the commonly studied relative trunk-pelvis motion, tri-phasic pelvis oscillations (transverse plane) have been found to develop in certain LBP-free individuals during walking at moderate to high speeds, beginning around 1.0m/s (Lamoth et al., 2002a). As only trunk-pelvis transverse plane motion was investigated in this work, whether or not similar multiphasic oscillations also develop in other segments/planes with increasing walking speed is relatively unknown. However, these findings do highlight the importance of measuring coordinative stability with between-stride standard deviation of CRP only for slow walking speeds (<~1.0m/s). An alternative method to quantify dynamic stability of segmental coordination was proposed by the same group (Lamoth et al., 2002b). Prior to calculating CRP, the raw pelvic and thoracic segment oscillation signals were decomposed into component Fourier phases. Principle frequencies were then identified, and used as filter cutoff frequencies, prior to the calculation of 9 CRP. The proposed CRFP method was applied to kinematic data collected on individuals with and without LBP, walking at incremental speeds between 0.40 and 1.94m/s (Lamoth et al., 2006b). To confirm advantages of the developed CRFP method over traditional methods, maximum minus minimum movement amplitudes (ROMs) of individual segments, and traditional CRP, were also calculated. Average, within-stride magnitude and variability of both segment ROMs, CRP, and CRFP were computed for each group-speed combination. Analyses found that segmental ROMs were comparable in all anatomical planes between groups. Transverse plane CRFP variability was decreased at faster walking speeds in persons with pain relative to without, in agreement with earlier CRP work. However, average within-stride frontal plane CRFP was more variable, particularly at higher speeds (anti-phase, Figure 2.1). Authors suggested that individuals with LBP may compensate for more-tight transverse coordination with less-tight frontal plane coordination. Less-tight frontal plane motion at higher speeds in the LBP group slightly contradicts the findings of (Seay et al., 2011), who found a tighter coordination at moderate speeds. These differences may potentially due to the aforementioned limitations of CRP (versus CRFP) to differentiate speed-induced variability from inter-subject variability. Slower walking speeds are generally preferred by individuals with LBP when asked to walk at a self-selected pace. However, a cause/effect relationship of slow walking and currentLBP is not established, and may even vary between certain patient subgroups. One theory is that slower walking results in less trunk-pelvis movement (i.e. more in-phase), resulting in less aerobic exercise of stabilizing low back musculature and by extension a gradual loss of static back endurance (SBE). Clinically, SBE is commonly used to characterize resistance of back muscle extensors to fatigue (J. H. van Dieën et al., 2003), and is quantified by performing a test of isometric opposition to a gradually increasing load imposed on the trunk, or through supine 10 leg raises. The effectiveness of diminished SBE as an LBP-identifier is generally associated with knowledge that muscular fatigue can greatly inhibit muscular proprioception (Comerford and Mottram, 2001). One study in particular showed that, in comparison to other frequently used biomechanical measures for the low back, SBE deficiency longitudinally proved to be the most accurate predictor of eventual LBP onset in originally LBP-free individuals (Luoto et al., 1995). These findings highlight that a poor capacity to withstand repetitive, irregular loading increases LBP susceptibility (even if magnitudes of the motion and loading are seemingly insignificant). Broadly, muscular fatigue may be viewed as a biomechanical mechanism of LBP (rather than an adaptation to LBP, see (Figure 1.1) Motion of body segments, other than the trunk and pelvis, far removed from the lumbar spine have also been investigated with respect to LBP. A review of walking with limited ankle dorsiflexion (functional hallux limitus) illustrates how small changes in foot kinematics can cause a cascade of biomechanical alterations throughout the body (Dananberg, 1993). When ankle dorsiflexion is less than typical during the latter half of single-limb stance, increased flexion compensations are made in the knee, hip, and lumbar spine to continue walking and ensure toe clearance during swing. Flexing the trunk requires the curvature (lordosis) of the lumbar spine to lessen, which orients passive spinal structures normally suited to cushion compression loads in a more vulnerable orientation. For example, relative to higher lumbar joint levels, the planes of facet contact in L4L5 and L5S1 are anatomically more frontal (versus transverse), but upon lordosis straightening the typical IVD-facet load sharing is altered, and disc compression is translated to more shear load along planes of facet contact (Dananberg, 1993; Skrzypiec et al., 2013). Concurrently during this phase of gait (end of stance near toe off), hip flexors are being recruited to initiate forward swing of the trailing limb, some of which are multi- 11 articular and span joints of the spine with origins on the anterior faces of the vertebral bodies (e.g., psoas). The muscle path of the psoas allows potential contributions to intervertebral compression, lateral bending, and axial twisting. Combined motion and loading of (lateral bending + twisting + compression) has been shown to produce the greatest stresses/strains within the disc relative to other combinations, suggestive of lumbar tissue injury and degeneration through repetitive application (Schmidt et al., 2007). Thus, even seemingly negligible alterations in lower-extremity biomechanics during walking can have substantial biomechanical effects at the low back, which could potentially be associated with accelerated development of degenerative LBP. In order to robustly evaluate potential associations between whole-body metrics and biomechanical LBP, in vivo spinal kinetics during walking (joint contact and muscular forces) have warranted investigation. Whole-body metrics of interest could include walking speed, trunk-pelvis coordination, lower-extremity inertial effects, and limitations in lower-extremity joint function. However, direct measurement of in vivo spinal mechanics is not currently possible in a purely clinical environment without advanced biomechanical measurement capabilities. Thus, computational tools are also needed to estimate these in vivo quantities during dynamic movements and have proven useful. To the author’s knowledge at this writing, only four studies have investigated low back in vivo joint loads of able-bodied individuals during walking by applying musculoskeletal modeling and simulation techniques (Callaghan et al., 1999; Cappozzo and Gazzani, 1982; Khoo et al., 1995; Seay et al., 2008), only one of which further investigated activities of individual muscles (Callaghan et al., 1999). The work by Callaghan and colleagues measured three-dimensional lumbar spine kinematics, surface electromyography (EMG) on several low back muscle groups, and ground 12 reactions forces for five healthy subjects walking at several different speeds, with and without arm swing restrictions. Various views exist regarding the function of arm swing during walking. The longest standing theory is that in-phase arm swing during walking is purely passive due to thorax inertia (Elftman, 1939), while a review of more recent work reports numerous studies (modeling and EMG) that have quantified muscle activities associated with dynamic, net shoulder moments (Meyns et al., 2013). Callaghan found that a combination of slow walking with restricted arm swing produced the most constant spinal joint loading, while fast walking with less arm restriction corresponded to phasic joint loading. Shear loading in the anterior/posterior direction was the only direction that was significantly correlated (positive, p<0.0003) with walking speed. Increased arm swing decreased axial and lateral lumbar spine motion, but also correlated with decreased activity in all measured (and modeled) lumbar muscle groups (peaks). This latter finding suggests that individuals who limit arm motion during walking (for whatever reason) may place elevated demand on trunk musculature. Further cause/effect implications of arm swing findings were not explored in depth, although further studies have found that arm swing decreases angular momentum about the vertical axis, and by extension, the vertical ground reaction force is also decreased, leading to a net decrease in metabolic energy consumption (~8%) (Umberger, 2008). With respect to the increasingly phasic loading with faster walking and free arm swing observed by Callaghan, more recent work discusses potential IVD-health benefits from mechanical loading afforded by walking, and these studies are reviewed in Section 2.1.3. In summary, Callaghan’s early attempt at modeling and simulating in vivo lumbar spine biomechanics during walking provides valuable insight, and demonstrated the value of computational modeling and simulation (reviewed in Section 2.3). 13 Thus, further computational investigations are warranted that both apply, and continue to verify and validate, such methodologies. The body of literature that reports associations between body segment kinematics during walking and LBP provides a strong foundation for further work. The findings collectively suggest that relative to LBP-free individuals, those with LBP have similar within-stride segmental ROMs, tighter (in-phase) transverse trunk-pelvis coordination at all speeds, different frontal trunk-pelvis coordination that may be dependent upon speed, and reduced ability to withstand continuous application of even small, abnormal motions (decreased low back muscular endurance). Also, seemingly negligible alterations in normal arm swing and lower-extremity joint kinematics have been shown have potentially large alterations on internal low back biomechanics, with further investigation required. 2.1.2. Muscle Function Muscle activity in LBP patients during walking relative to healthy individuals, has also been investigated. The motivating theory is that individuals with pain should exhibit an altered muscle coordination strategy, regardless of whether the alterations are a cause or result of the pain. Several muscle groups significant to the discussion of LBP are displayed in Figure 2.2. A broad review of trunk muscle action in LBP subjects distinguishes two prominently supported theories of LBP development in the literature; pain-spasm-pain, and pain-adaptation (J. H. van Dieën et al., 2003). The former model postulates that LBP reflexively initiates muscle activations that aggravate the pain source, which cascades into a cycle. The pain-adaptation model contrastingly postulates that LBP informs the nervous system how to alter muscle function, such that spinal tissue damage is avoided or mitigated (Figure 1.1). 14 (a) (b) (c) (d) Figure 2.2 – Selected musculature of the hip, pelvis, and low back (captured with AnyBody Modeling Software). Psoas (a), erector spinae (b), abdominal obliques (c), and quadratus lumborum (d). 15 Neither of the two theories of LBP development has garnered majority support within the biomechanics community, potentially due to the difficulty of collecting in vivo data needed to assess low back biomechanics. Surface EMG has been the most frequently applied experimental tool over the past several decades to measure low back muscle activity during dynamic movement. However, interpreting EMG as a measure of true muscle activation level, even with normalization procedures, is difficult. Further using EMG signals during dynamic activities to ascertain functional roles (agonist, antagonist, or purely postural) is generally not advised without supplemental biomechanical modeling. Lastly, the low back and abdomen relative to other body locations often have elevated levels of soft tissue that decrease signal strength. The close-knit structure of the muscles also increases potential for cross talk in surface measurement. Deep musculature such as the multifidi and psoas usually require fine wire instrumentation. As a result, the primary muscle groups discussed in the LBP literature are (in order of relative frequency): erector spinae (or paraspinal, if assumed to include the multifidi), rectus abdominus, and external/internal obliques (Figure 2.2). A generalized, functional separation of trunk musculature into three groups has been proposed: local stabilizers, which are permanently active at some low level to maintain posture, global stabilizers, which (eccentrically) modulate and limit movement, and global mobilizers, which initiate and drive movement (Comerford and Mottram, 2001). These classifications are frequently used to aid in interpretation of significant group differences in measured surface EMG, and to suggest support of either pain-adaptation or pain-spasm-pain. However, these conclusions must be taken with understanding of the discussed limitations of surface EMG for determining functional roles of muscle groups. Furthermore, for those patient groups with a suspected mechanical pain origin, rather than degenerative, a more patient-specific approach 16 may be needed. For example, a majority of the nonspecific, chronic LBP diagnosed for individuals with a lower limb amputation is suspected to have a myofascial cause associated with altered whole-body biomechanics (Kulkarni et al., 2005). A process for the development of serious, chronic LBP through repetition of slightly altered movement strategies is provided by Comerford and Mottram (2001). Spinal stability is an important concept associated with LBP, to which the relative contribution of passive spinal structures (disc, facet, ligaments) versus active musculature has been debated. Stability has numerous meanings in biomechanics, but with respect to the spinal literature, refers to the capacity under normal physiological loads to maintain normal patterns of vertebral motion that do not cause large deformity or onset of pain (Panjabi, 2003). Spinal stability has been proposed to be the sum of contributions from (1) the passive spinal column lending intrinsic stability, (2) the surrounding musculature lending dynamic stability, and (3) the neurologic control system modulating the muscular recruitment (Panjabi, 1992). One study adopting this framework, attempted to quantity the relative contributions of items (1) and (2) to stability during spinal movements about the spinal neutral posture (a range where passive contributions can be assumed negligible) (J. van Dieën et al., 2003). Matched LBP and pain-free control subjects (n=16) performed the motions while EMG amplitudes of various trunk muscle groups was recorded. Data were used to compute relative functional activation ratios during the motion. An EMG-driven computer model was used to estimate ratios of agonist/antagonist contributions to the measured total torque moment, also measured by cabled load cell. The most significant difference was a larger contribution of the lumbar erector spinae to the total torque moment, relative to the thoracic erector spinae contribution, in individuals with LBP. In Comerford’s framework (Comerford and Mottram, 2001), the lumbar erector spinae are 17 classified as local stabilizers, and the thoracic as global mobilizers. Notably, even though muscular recruitment differences were observed, the LBP subjects did not report any LBP onset during the small, slow movements. Thus, findings suggested that in the absence of large passive contributions, certain stabilizing lumbar spine segmental musculature do contribute to total spinal stability (corroborating (Panjabi, 1992)), and that alterations in normal levels of contributions are (at least in some individuals) neuromuscular adaptations to, rather than direct causes of, LBP. A later study investigated whether passive soft tissue damage (qualified by diagnosed ligamentous damage) affected total lumbar spine stability and low back muscle recruitment strategy during motion. Twenty patients with passive-damage LBP, 20 LBP-free individuals, and 12 patients with nonspecific LBP performed a slow forward flexion task around the neutral lumbar spine posture (Silfies et al., 2005). Surface EMG of five bilateral trunk muscle groups were recorded and normalized to sub-maximal isometric standing, to estimate percent activity. The two LBP subgroups (passive-damage LBP vs. nonspecific LBP) did not differ significantly relative to one another in any computed, muscular activity parameters. Upon pooling the two LBP subgroups together, a significant difference of greater activation in both the rectus abdominus and external obliques was found in the LBP group, relative to LBP-free. Furthermore, a significantly lower synergist activation ratio of (obliques / rectus abdominus) was observed in the passive-damage LBP group relative to LBP-free. The former findings indicated that individuals with LBP may over-activate trunk flexors, and also rely more heavily on the rectus abdominus (multi-segmental global mobilizer) rather than the obliques (uni-segmental local stabilizer) to perform flexion. These findings collectively suggest that abdominal muscles may play a more crucial role in spinal stability than previously thought, and also that individuals 18 with LBP have altered functional goals at the muscular level in performing certain movements, irrespective of LBP etiology. Few studies exist that have quantified low back and abdominal muscle activity during walking. One study evaluated surface EMG data on five trunk muscles for 15 healthy individuals walking at speeds between 0.6-1.7m/s (Anders et al., 2007). In general, mean muscle activity correlated positively with walking speed. Obliqus externus activity pattern changed from low continuous activity, to biphasic with increasing walking speed. Little interpretive analysis was offered, although EMG-time data for all five muscle groups were explicitly reported, providing baseline data for further work investigating the effects of LBP on muscle activity during walking. A further study investigated low back muscle activity during walking in subjects with/without chronic, nonspecific LBP. Kinematic and EMG data (erector spinae) were measured on 22 individuals with LBP and 17 with no LBP walking on a treadmill (Lamoth et al., 2006a). Biphasic lumbar erector spinae activity across the gait cycle was observed in both groups, but instances of maximum activation were significantly earlier in LBP subjects relative to LBP-free subjects. A biphasic pattern of lumbar erector spinae activity with maximum action near heel strike and negligible action during swing is understood as the norm for LBP-free subjects (Arendt-Nielsen et al., 1996; Lamoth et al., 2006b). In addition to timing differences, those with LBP also had greater within-stride variability in erector spinae activation, relative to LBP-free. Principle component analysis (PCA) of the total variance in lumbar erector spinae activity was applied to confirm that a majority of the variance was due to LBP status, over other potential sources of variability, including: walking velocity, stride length, age, and weight. 19 These findings support the concept of an anticipatory, guarded gait strategy for individuals with LBP, through altered time-dependent usage of local stabilizing trunk musculature. Two, notable works have investigated the effects of induced, acute low back pain on muscle recruitment during walking. The first collected motion and EMG data on ten subjects with LBP (nonspecific, chronic) and ten control subjects with no LBP walking at 1.1m/s (Arendt-Nielsen et al., 1996). The ten control subjects additionally agreed to experimental inducement of acute LBP via a single hypertonic saline injection. Relative to LBP-free, individuals with LBP exhibited a significant increase in EMG activity within the lumbar region during the swing phase, where normally these muscle groups should be inactive. The amount of activity increase correlated strongly with reported severity of pain. Upon inducement of LBP, the control group also developed this same altered muscle activation strategy, as well as a reduction in lumbar muscle activity during double stance, where lumbar muscle groups should be highly active. These findings strongly suggest that pain of a purely mechanical, muscular origin can affect motor coordination strategies within the lumbar region during walking, in support of a biomechanical mechanisms LBP theory (Figure 1.1). The second induced-LBP walking study investigated acute pain resulting from muscular fatigue. Low back surface EMG was recorded on 16 individuals with no prior LBP during treadmill walking, both before and after two hours of wearing a 25% body-weight waistcoat (Anders et al., 2005). Analysis of the EMG data of four subjects that developed LBP during the loading scenario, of pre-pain relative to pain-free, showed that both lumbar and abdominal muscle groups had significant deviations from normal activity, prior even to any muscle fatigue. In each case, the particular muscle differences were highly individualized; suggesting that future 20 work aimed at guiding biomechanical treatments for LBP based on muscle activity should be subject-specific. Muscle recruitment sequence between synergistic pairs of low back extensors has been investigated in individuals with LBP. Activity of both the erector spinae and gluteus maximus were recorded on 43 LBP-free subjects during trunk flexion and extension motions, before and after two hours of standing (Nelson-Wong et al., 2012). Patient-rated LBP (visual scale) during motion was used to classify each subject as either a pain or no-pain subject. In those that reported high LBP levels during motion tasks following standing, a distinct muscle recruitment sequence of lumbar erector spinae activation followed by gluteus maximus was observed (topdown), while the no-pain group exhibited the opposite sequence (bottom-up). Significantly in unplanned retrospective analyses, the top-down pattern was observed in the trials of paindeveloping individuals prior to developing any pain, suggesting that irregular recruitment strategies that correlate with elevated LBP susceptibility may be learned over time irrespective of chronic LBP. Further alterations in hip muscle recruitment have been associated with LBP development and susceptibility. Twenty-three LBP-free individuals participated in a 2-hour standing trial while hip and low back surface EMG were collected (Nelson-Wong et al., 2008). In those individuals that reported onset of LBP during standing, bilateral co-activation of the gluteus medius was found. Co-activation of unilateral lumbar erector spinae and rectus abdominus (or external obliques), which has previously proven effective as an identifier of LBPsusceptible individuals, was not different between groups. Results suggested that, at least for the sampled patient group, elevated hip muscle co-activation (rather than trunk co-activation) increased LBP susceptibility. Hip abductor function has received little attention in the LBP 21 literature, although inhibited activation of hip extensors (gluteus maximus) has been observed within current LBP patients (Leinonen and Kankaanpää, 2000; Nelson-Wong et al., 2012). In summary the collection of literature on altered muscle activity in patients with LBP leads to numerous significant findings. A functional separation (local stabilizers, global mobilizers/stabilizers) has been suggested to facilitate identification of underlying biomechanical effects of LBP. Spinal stability may have more contribution from active musculature than historically thought. While the passive subsystem does contribute to total spinal stability, damage to the passive tissue does not necessarily always cause altered neuromuscular strategies. Evaluations of standing and slow movement tasks found that, relative to LBP-free individuals, those with LBP potentially have: greater agonist/antagonist co-contraction, altered agonist (concentric) load sharing, and inhibited hip extensor activity. Additional walking evaluations found in LBP patients: a reduced tolerance to muscle fatigue, increased low back muscular activity during swing, decreased during double-limb stance, and altered erector spinae activity (earlier peak activation, greater between-stride variability). 2.1.3. Spinal Tissue Mechanisms Irrespective of altered kinematics and neuromuscular strategies that may lead to LBP, biomechanical pain is a tissue-level phenomenon. The most prevalent anatomical and physiological sources of LBP diagnosed through physician physical exams or medical imaging include spinal stenosis, osteoarthritis of the zygapophysial joints (facet OA), spondylolithesis (vertebral slippage), and damage to spinal ligaments and musculature. The intervertebral disc can be a cause of many of the above maladies (rather than a source of pain itself) when the disc, slips, or herniates, or narrows with time. The two most prominent etiologies of LBP warranting surgical interventions are IVD degeneration and facet joint OA. While degenerative biology 22 composes a large section of the LBP literature, this section will focus on review of biomechanical factors that may accelerate the degenerative timescale or cause tissue pain directly. The intervertebral disc is composed of an inner, soft nucleus pulpous surrounded by a stiff matrix of collagen fibers arranged in the annulus fibrosis. The IVD contributes damping primarily to superior/inferior (S/I) compression, followed contributions to anterior/posterior (A/P) shear load carrying, and thus these two modes have been most frequently investigated with respect to IVD degeneration. Upper limits for transverse A/P shear loading associated with tissue failure within the lumbar spine have been developed based on a compilation of in vitro cadaver and porcine studies of lumbar motion segments (Gallagher and Marras, 2012). For A/P shear, 1000N is recommended as tolerable for infrequent exposure and 700N for repetitive loading. Degeneration of the intervertebral disc over time has traditionally been thought to be driven by decreases in necessary nutrition. The small amount of nutrition that is needed (IVD is primarily avascular) has been suggested to be received primarily through passive diffusion at the vascular, cartilangeous endplates (Grunhagen et al., 2011). The former arrived at these findings by approximating a diurnal, cyclical loading as a quasi-static finite element simulation, therefore the potential for more dynamic, cyclical loading to affect transport of larger solutes throughout the disc nucleus via forced fluid flow has not been ruled out (Ferguson et al., 2004). Whether or not the increasingly in-phase trunk-pelvis coordination observed in individuals with LBP could cause more static loading that mechanically inhibits disc health over long periods of time has not been directly investigated in the literature. 23 The angle-ply composite structure of the intervertebral disc has led some investigators to apply general lamination theory to estimate safe loading of the annulus fibrosis in principal directions (Iatridis and Gwynn, 2004). A range of 8.0-10.3MPa in the fiber direction was suggested to initiate collagen fiber failure and 0.4-1.0MPa to initiate shear delamination. An average cross-sectional area for the IVD of 15.9cm2 (Sato et al., 1999) can be used to estimate a potential force range for shear delamination of 640-1600N. This range is considerably wide, although earlier cited estimates from in vitro work fall within the range: 700N (frequent) and 1000N (infrequent). The two encapsulated, synovial facet joints of a spinal motion segment are essential structural units, located posterior to the IVD. The two primary biomechanical functions of the facet joints are to limit lumbar spine extension, and to constrain medial-lateral translations and axial rotations within the plane of the IVD. The joints share considerable load with the IVD in both the S/I and A/P directions; S/I suggested to be 3-25% depending on trunk flexion (Kalichman and Hunter, 2007), and A/P 43-66% (Skrzypiec et al., 2013), both depending on overall lumbar spine posture. The facets carry greatest joint contact loads when trunk extension is combined with additional axial twisting or lateral bending. The anatomical orientation of the facet joints with respect to the transverse and frontal planes also varies by lumbar joint level (White and Panjabi, 1990). The onset of facet OA in aging individuals is clinically viewed as a consequence of unavoidable joint wear, that likely varies based upon patient-specific overall spinal morphology. A more sagittal (vs. frontal) orientation of the joint and a history of IVD complications are two potentially unavoidable factors found to correlate with accelerated facet OA (Kalichman and Hunter, 2007). IVD degeneration can narrow intervertebral spacing and decrease spinal 24 stiffness, which if present will alter the normal disc-facet load by placing increased force on the facets. A dissection of 100+ cadaver motion segments with facet joint OA observed confounding IVD degeneration to be present in a significant majority (Kalichman and Hunter, 2007), thus supporting the theory. Lastly, the L4L5 joint relative to higher levels experiences a greater, constant shearing force, due to weight of the body, lumbar lordosis curvature, and facet joint orientation. The L4L5 joint is known to be the most prevalent site of facet OA relative to other spinal levels (Fujiwara et al., 2000). Repetitive application of abnormal lumbar spine loading, even of small magnitude associated with work environment, posture, or difficulties with activities of daily living, have potential to accelerate OA development. A contrasting viewpoint is that facet OA and IVD degeneration are completely separate mechanisms. One study quantified relative levels of disc and facet damage in patients with degenerative LBP using CT and MRI (Schwarzer et al., 1994). A combination of facet OA and disc degeneration was uncommon in the subject pool of 92 patients. However, no longitudinal analyses were performed to confirm that subjects with IVD degeneration did not eventually develop facet OA if left untreated. Evidence in the literature, along with understood biomechanical function of the facets, more strongly supports that a degenerative mechanisms between the IVD and facet joints are likely coupled in a majority of individuals, although which drives the other is not established. Measured structural parameters (e.g. stiffness, centers of rotation), kinematics, and total joint contact loads in normal and degenerated conditions, from either in vitro or in vivo study are useful for validation of computational work. However, due to the difficulty in maintaining in vivo integrity in laboratory settings, these data are rare. One study reports in vivo disc pressure in an LBP-free, non-degenerated individual during 29 different tasks of daily living, measured 25 via an implanted transducer in the L4L5 joint (Wilke et al. 1999). A sampling of the data for activities most relevant to biomechanical LBP is presented in Table 2.1. Data were reported as IVD pressures from a transducer, values in Newtons to represent contact forces may be more useful. For numerous confounding factors, including that transducers only measure hydrostatic pressure in the fluid nucleus, Force = Pressure*Area can lead to errors in contact force as high as 44%. Therefore, a mean correction factor of 0.66 has been suggested, so that Force = Pressure*Area*Correction Factor (Dreischarf et al., 2013). Assuming a mean IVD cross sectional area of 1800mm2 yields the values presented in the right hand column of Table 2.1. Table 2.1 – In vivo disc pressure in the L4L5 joint measured during various activities. Pressure data may be transformed to estimates of joint contact force by use of a correction factor (c=0.66) suggested in the literature, and an average IVD cross sectional area of 1800mm2. Pressure1 [MPa] 0.50 1.10 0.53-0.65 0.50-0.70 0.38-0.60 Activity Relaxed, standing Standing, bent forward Walking Climbing stairs (one at a time) Walking down stairs (one at a time) Force2 [%BW] 87 190 92-112 87-121 66-104 1 (Wilke et al 1999) (Dreischarf 2013) 2 A similar study measured in vivo L4L5 pressures in healthy subjects and in LBP subjects with pain specific to L4L5 (Sato et al., 1999). The LBP subject pool was further subdivided into individuals with/without diagnosed L4L5 degeneration. Concurrent kinematics of the L4L5 joint measured via radiographs were also collected. Subjects reoriented the trunk to eight instructed positions of combined flexion/rotation/bending during testing. Quantitative pressures similar to those in Table 2.1 were reported and may also be useful for validation of biomechanical spine models that have confounding degeneration. The matched subject design among the LBP subgroups allowed isolation of IVD degeneration effects on resultant pressures and kinematics. Significantly, but in agreement with earlier studies, magnitude of IVD pressure was seen to 26 decrease with increasing grade of disc degeneration (quantified via MRI). The neighboring facet joints were suspected to be compensating for this load difference in response to disc narrowing, although this was not confirmed. Lastly, for any study investigating subject-specific finite element models of the spine, and desiring to compare their pressure outcome metrics to these or Wilke’s data, a robust method for computing a model-specific correction factor (rather than cavg=0.66) is detailed in the literature (Dreischarf et al., 2013). In vitro and in vivo tissue measurements of the facet joints are even less frequently reported in the literature relative to the IVD. Physically accessing the small, encapsulated joints to measure contact forces, without compromising true structural behavior, is far more difficult than measuring fluid pressure in the IVD. An early study did present load ranges measured on a cadaveric single functional spinal unit (FSU) with strain gauges on facet surfaces at the L1-L2 level, in various spinal postures (Schendel et al., 1993). However, quantitative results are likely too limited for robust validation, as only a single FSU was considered, and all musculature and passive ligaments were removed. Inclusion of physiologically realistic in vivo loading has been shown to significantly affect computational modeling outcomes on spinal loading (see Section 2.4). A majority of studies attempt to represent in vivo loading artificially; such as experimentally with a pure compressive preload on the L1 body, and in finite element models with a load in the direction directed along the lordosis (follower load). A recent, more robust cadaveric study measured facet joint contact forces, IVD pressures, and intervertebral kinematics in eight full S1-L1 spines, both with and without representative frontal plane pelvic obliquity (Popovich et al., 2013). Results for facet contact force for various loading scenarios are summarized in Table 2.2. Axial rotation produced greater loads than in flexion/extension and lateral bending, but simulated pelvic obliquity with additional rotation 27 produced the greatest facet loads. Also, IVD pressures and facet contact force were negatively correlated, further supporting the concept of passive structural load sharing, particularly for combined load scenarios. Table 2.2 – Total facet loads during tri-planar motions, measured on an S1-L1 cadaveric lumbar spine with all musculature and ligamentous structures intact. Facet Load1 [N] Motion Flexion 27±16 Extension 33±10 Ipsilateral bend 50±30 Axial rotation 95±26 Axial rotation + mild frontal pelvic obliquity 110±30 Axial rotation + large frontal pelvic obliquity 1 (Popovich et al., 2013) 124±30 A final topic relevant to low back pain in adults, and particularly individuals with a lower-limb amputation, is adult onset, idiopathic scoliosis. Scoliosis is a lateral deviation of the spine (in the frontal plane) from the normal straight alignment in the mid-sagittal plane, as represented in Figure 2.3. Clinically, a frontal angle (Cobb angle) greater than 10o diagnoses scoliosis (Hebela and Tortolani, 2009). Scoliosis alters the normal coupling between the three anatomical rotations of the spine, and can also be a direct cause of chronic, nonspecific LBP if untreated. While there are many conditions and diseases associated with scoliosis, the cause of 85-90% of cases are generally not established (White and Panjabi, 1990). However, frequently observed and/or suspected etiologies of functional scoliosis are muscle fatigue, inhibited low back proprioception (Yamada, 1971), and continuous application of altered activity in stabilizing spinal musculature (White and Panjabi, 1990). Muscle groups most associated with scoliosis and 28 targeted in chiropractic treatment are the quadratus lumborum, external obliques, and iliopsoas (Ferguson, 2014). Figure 2.3 – Representation of a scoliotic, spinal deformity (childrenshospital.org) Collective findings from literature investigating spinal tissues provide guidance for further investigations into biomechanical mechanisms that may contribute to degeneration. Combined motion and loading (lateral bending + axial rotation + compression) appears to place passive structures that contribute to spinal stability (IVD and facet) at greatest risk for accelerated degeneration. Frontal plane pelvic obliquity in particular was suggested to significantly alter facet-IVD load sharing. Also, proper interpretation of in vitro or in vivo experimental data to validate biomechanical spine models is crucial. 29 2.2. Individuals with a Lower-Limb Amputation A recent epidemiological survey within the United States recorded 1.6 million people were living with limb loss in 2005, with estimated increases to 2.2 million by 2020, and 3.6 million by 2050 (Ziegler-Graham et al., 2008). The projected growth is due to the anticipated increasing prevalence of dysvascular and diabetic conditions in aging adults, together accounting for just over half of all amputations (Ziegler-Graham et al., 2008). The remainder of amputations are due to trauma (~45%), and cancer (<2%). Diabetes remains the leading cause of amputation in the United States, although the number of traumatic amputations in 2010-2011 due to combat-related injuries was significantly greater relative to the previous decade (Krueger et al., 2012), and is also anticipated to increase. Irrespective of amputation cause, individuals with a lower-limb amputation are susceptible to a range of chronic, secondary conditions including: poor mental health, phantom limb pain, abnormal pain in both the residual and intact legs, greater prevalence of knee osteoarthritis (Burke et al., 1978), and persistent, bothersome LBP (Ehde et al., 2001; Ephraim et al., 2005; Kulkarni et al., 2005; van der Schans et al., 2002). Within the general population, the growing sub-group of individuals with lower-limb amputation has proven a distinct, elevated prevalence of LBP. Results of a comparative survey incorporating traumatic lower-limb amputees both with and without LBP, found that not only is LBP a prominent secondary disability of lower-limb amputees, but that individuals view that pain as equal to or worse than all other pain conditions affiliated with the residual limb (Kulkarni et al., 2005). Similarly, a 2004 national survey of quality of life in individuals with a lower-limb amputation recorded that 62% of respondents reported experiencing persistent, bothersome (chronic) LBP regardless of time since amputation (Ephraim et al., 2005). 30 The most frequent etiologies of LBP diagnosed in individuals with a lower-limb amputation are not made clear in reports. As a start, the work by Kulkarni and colleagues performed medical imaging diagnostics on a subset of patients that reported LBP, thus allowing characterization of concomitant degeneration. No significant correlation was found between amount of tissue degeneration quantified by medical imaging, and patient-reported severity of reported LBP. Even though perceived pain severity can be highly dependent upon the patient, these findings do suggest that a majority of individuals with a lower-limb amputation and secondary LBP, likely suffer from biomechanical LBP, rather than degenerative pain sources (Figure 1.1). In particular, the likelihood of muscular pain (myofascial) was further suggested, due to collective patient descriptions of the pain sensation (Kulkarni et al., 2005). Investigations of bone and joint changes in individuals with a lower-limb amputation also found no apparent correlation between LBP and low back degenerative changes (Burke et al., 1978), although did find a large prevalence of scoliosis (40-60%). Neither work used computed tomography as the particular imaging mode to characterize disc and facet degeneration; the former used MRI, and the latter used x-ray. This raises some concern whether level of degeneration was characterized adequately. Images from MRI and x-ray are frequently criticized in their capacity to expose disc and facet degeneration (Kalichman and Hunter, 2007). Nonetheless, former etiological investigations in combination with numerous reports of altered whole-body biomechanics in individuals with a lower-limb amputation, seem to strongly suggest pain due to biomechanical mechanisms (Figure 1.1), and the type of biomechanical LBP pathway presented by (Comerford and Mottram, 2001). An encouraging aspect of this conclusion is that, relative to degenerative LBP, biomechanical LBP (and scoliosis) can potentially be treated with therapeutic and rehabilitative interventions to motion and posture 31 habits, versus more costly and high-risk methods involving injected nerve blocks and surgery. Identification of whole-body, biomechanical alterations in individuals with a lower-limb amputation, reported in the literature, is first needed. Walking mechanics have been studied in subject pools with both transfemoral (TFA) and transtibial (TTA) amputations. Transfemoral amputation refers to amputation between the hip and the knee (or, across the femur). Transtibial amputation refers to amputation between the knee and ankle. An epidemiological study of lower-limb amputation trends in the US suggested that between 1988 and 1996, 39% of lower-limb amputee respondents (excluding toe) were transfemoral, 42% were transtibial, and the remainder were foot, ankle, or specialized type (Dillingham et al., 2002). Relative to TTA, individuals with TFA have been suggested to have even greater susceptibility to LBP, and severity of secondary disabilities (Kulkarni et al., 2005; Smith et al., 1999). In contrast, other work quantifying secondary disabilities within TFA and TTA individuals found no statistical between-group difference of LBP prevalence (Hammarlund et al., 2011). Both TTA and TFA amputation removes muscle groups that contribute to walking mechanics and are critical for body support, forward propulsion, swing initiation and mediolateral balance. As a result, walking of individuals with a lower-limb amputation in comparison to able-bodied has been characterized by numerous muscle compensations (Silverman et al., 2008), altered whole-body dynamics (Silverman and Neptune, 2011), asymmetrical coordination between body-segments (Devan et al., 2014), and a slower preferred walking speed (Kulkarni et al., 2005). These altered biomechanics of individuals with a lowerlimb amputation relative to able-bodied individuals, are similar to previously reviewed biomechanical differences between able-bodied individuals with and without LBP during 32 walking, such as: irregular coordination between pelvis and trunk (frontal and transverse), shifted phase and erratic activations of the erector spinae, abnormal swing versus stance muscle recruitment, and altered agonist/antagonist synergist ratios in the trunk-pelvis body region. A review in 2011 compiled all literature prior to time of writing that involved individuals with a lower-limb amputation, and distinguished each study based on spatiotemporal and/or physiological parameter examined (Sagawa et al., 2011). A key finding was that of 122 parameters with potential usefulness in gait analyses (Benedetti et al., 1998), 78 had yet to be investigated in individuals with a lower-limb amputation. Motion of the lower lumbar spine during walking has been compared between TFA individuals with and without LBP (occurring after amputation). Kinematic data were measured on individuals with TFA+no-LBP (n=8), TFA+LBP (n=8), and non-amputees with no LBP (n=6), walking at self-selected speeds (Morgenroth et al. 2010). Average self-selected walking speed (~1.0m/s) was not significantly different between groups. Relative to the TFA+no-LBP group, those with TFA+LBP had a greater within-stride transverse plane lumbar spine ROM. No group differences were found in the frontal or sagittal planes. In a further pooled TFA versus non-amputee comparison, those with TFA had a greater within-stride lumbar spine sagittal ROM, suggesting a reduced lumbar lordosis. Finite element analysis of the L4L5 FSU (representing all passive structures), has separately been applied to show that of the three possible tri-planar trunk motions, posterolateral IVD strain and pressure were most sensitive to base transverse rotation supplemented with additional frontal and/or sagittal bending (Schmidt et al., 2007). The facet joints do carry large load in axial rotation, but not within the ROM studied by Morgenroth. Additionally, reduced sagittal lordotic angle during gait has been suggested to place the passive spinal tissues in a more vulnerable pose to resist spinal compression generated 33 near toe off (Dananberg, 1993). The particular biomechanical differences between pooled TFA and able-bodied individuals, and also between TFA+no-LBP and TFA+LBP, have potential to be associated with accelerated degenerative mechanisms. Altered muscle recruitment in individuals with a lower-limb amputation, relative to ablebodied individuals, during walking has also been investigated. The collective literature suggests: greater residual/intact limb hip extensor moments during early stance (Grumillier et al., 2008; Silverman et al., 2008), elevated residual limb gluteus maximus activity during early/mid residual limb stance (Winter and Sienko, 1988), elevated residual limb vasti/hamstring activity during early residual-limb stance (Fey et al., 2010), and greater residual-limb hip flexor power near residual limb toe off (Sadeghi et al., 2001). Notably, the review article of amputation literature in 2011 found that of 26 amputation studies that report EMG data, all were isolated to the lower extremities. Thus, no EMG data or findings with respect to altered activity of trunk musculature in individuals with a lower-limb amputation during walking are reported in the literature. Irrespective the lack of existing low back EMG data, known biomechanical couplings between the lumbar spine and lower extremities provide a basis for developing theories of biomechanical LBP during walking of individuals with a lower limb amputation. In particular, the potential for slight limitations in normal ankle function to affect other joint angles (knee, hip, lumbar spine) via a chain of biomechanical compensations was reviewed previously (Dananberg, 1993). In individuals with lower-limb amputation, the ankle joint along with all spanning musculature is completely removed. Thus, confounding biomechanical cascades propagating from lower joints to the low back should be more severe. For example, elevated hip flexion power in response to the missing ankle plantarflexors (Sadeghi et al., 2001) could involve the 34 psoas major, which originates on anterolateral faces of the vertebral bodies (Figure 2.2). The psoas can generate significant lumbar spine compression when bilaterally activated, and slight lateral flexion when unilaterally activated (see Figure 2.2). Elevated levels of spinal load with the lumbar spine in a potentially vulnerable pose (reduced lordosis), has potential to be associated with development of LBP (Dananberg, 1993). Additionally, lateral asymmetry in the psoas muscle groups (intact hypertrophy, residual atrophy) has been observed in certain individuals with TFA (Kulkarni et al., 2005), indicating asymmetrical reliance on the intact limb psoas to perform hip flexion, and potentially less reliance on the residual side, where other hip flexors may be producing increased hip flexor power. Relative to able-bodied, individuals with a lower-limb amputation have altered spatiotemporal walking parameters. In particular, a slower self-selected walking speed (Hafner et al., 2002; Kulkarni et al., 2005), and smaller ground reaction forces on the residual limb relative to intact (Kulkarni et al., 2005), and in both limbs relative to able-bodied (Silverman and Neptune, 2011). A slower speed with lesser impulsive forces on the lower extremities has been associated with a more guarded gait strategy and greater demands to maintain balance (particularly in the frontal plane). Walking speed has been found to be the most frequently investigated gait metric in pre-2011 amputee studies; however, nearly all focused on potential causative factors of slower gait, rather than considering potential negligible affects of slower walking on other biomechanics. Associations between walking speed and trunk and pelvis kinematics during walking in individuals with lower-limb amputation has been studied on a limited basis. One study measured trunk-pelvis kinematics in individuals with TFA (n=27) across stride cycles of various speeds (Goujon-Pillet et al., 2008). Results showed that mean trunk-pelvis transverse CRP during 35 strides was significantly lower in TFA relative to able-bodied, indicating an in-phase coordination (Figure 2.1, Figure 1.1), strongly correlated with a decreased walking speed. Frontal plane pelvic obliquity during stance was also significantly different between groups, with greater inferior tilt towards the stance limb in individuals with TFA. A further similar study with nearly identical design additionally computed variability of CRP to quantify dynamic movement stability, and included TFA with/without LBP (Russell et al., 2013). In direct contrast to the former work, mean CRP was not significantly different between able-bodied and pooled TFA in the transverse plane, but was in the frontal (increased) and sagittal (lesser) (former work did not compute CRP for frontal and sagittal). Variability in CRP was not different in any group comparisons, nor did TFA with/without LBP differ in any metrics. Results of these two studies in combination suggest that, irrespective of LBP ailment, lower-limb amputation results in altered trunk-pelvis kinematics that are similar to those of able-bodied individuals with LBP. Leg length discrepancy (LLD) in individuals with a lower-limb amputation has been investigated with respect to secondary LBP. Slight LLD is common even in able-bodied individuals, and has been suggested to increase LBP susceptibility with greater discrepancy (Gailey et al., 2008), although opinions vary. How LLD contributes to LBP in individuals with a lower-limb amputation is not established, although altering length of the prosthetic pylon is common clinical practice to attempt treatment for secondary LBP. Several case studies have confirmed that LLD alteration was effective in decreasing (or eliminating) LBP for certain individuals (Illes and Maola, 2012; Morgenroth and Shakir, 2009). Biomechanically, increasing LLD can affect lateral tilting of the pelvis and frontal plane bending of the spine (Lee and Turner-Smith 2003). Abnormal pelvic posture is a known risk factor for general, mechanical LBP (Becker and Stumbo, 2013; Popovich et al., 2013). Greater medial/lateral impulsive ground 36 reaction force has also been observed in individuals with a lower-limb amputation, and has been associated with LLD and/or attempts to alleviate residual limb pain (Kulkarni et al., 2005). In summary, altered biomechanics during walking of individuals with a lower-limb amputation are apparent. Several differences are similar to those observed in able-bodied individuals with LBP, relative to LBP-free, including: tighter transverse plane trunk-pelvis coordination, greater overall trunk and pelvis transverse ROM, altered muscle recruitment strategies, and a slower self-selected walking speed. The few studies that have compared walking of individuals with lower-limb amputation with/without secondary LBP, have found no significant differences in segmental kinematics. However, forces in the low back (joint contact, muscle group effort) that are known to be primary metrics associated with spinal stability, tissue degeneration, and LBP, have not been explicitly investigated in individuals with a lower-limb amputation. Limitations in clinical and laboratory means to measure such quantities in vivo during dynamic movement have led to the lack of investigation in this area. Intriguing alternative tools that can supplement experimental methods are reviewed in Section 2.3. 2.3. Musculoskeletal Modeling and Simulation Computational modeling and rigid-body dynamic simulation of the human musculoskeletal system has seen increasing development and application over the past several decades. Broadly, the methods involve application of an interconnected system of rigid segments with anthropometry, mass/inertia, muscle anatomy, and muscle actuation properties estimated to approximate in vitro and in vivo anatomy and physiology of the human body. Experimentally collected data including motion capture, ground reaction forces, electromyography, and medical imaging can be leveraged improve confidence in solutions, and also to perform subject-specific studies. While several levels of complexity and formulation exist 37 and will be reviewed, generating a muscle-driven simulation refers to estimating a full set of muscle forces capable of reproducing (in an inverse sense), or driving (in a forward sense), an observed movement. Joint kinetics including reactions and powers may be of clinical or research interest, and are also computed in this framework. Given the breadth of methods that have been developed, a challenging task is the selection of appropriate modeling and simulation methods to answer the research question. This section first reviews relevant background, advantages, and disadvantages of the most common formulations (inverse/forward/hybrid dynamics), followed by identification of critical methodological aspects involved with simulation of walking, the complex spinal anatomy, and individuals with a lower-limb amputation. The primary advantage of musculoskeletal simulation in contrast to purely experimental laboratory methods is the ability to estimate unknown biomechanical parameters that may be costly, difficult, or impossible to measure in vitro/vivo. The basis of any muscle-driven simulation is the dynamic equations of motion for a multi-articulated system. These relations can generally be written as shown in equation (2.1), C , where , e t , (2.1) ) are generalized system position, velocity, and acceleration respectively, M(q) a collection of mass and inertial terms, coriolis and centrifugal effects, G(q) gravitational effects, R(q) a collection of muscular moment arms, FM individual muscle forces, and Fext any applied external forces (Zajac et al., 2002). Inspection of equation (2.1) reveals the complexity that any one muscle may affect the acceleration and power of any body segment, even those far removed from the muscle itself. This phenomenon is referred to as dynamic coupling, and is a consequence of a non-diagonal mass matrix upon inversion of equation (2.1). 38 Simulation frameworks are distinguished by the unknown and known quantities in solution of equation (2.1). An inverse dynamic framework assumes motion , ) and external forces are known, and computes the necessary internal forces to achieve that motion. A forward dynamic framework determines internal muscle forces through EMG-driven or optimization methods, and proceeds to simulate resulting dynamic motion and external forces due to these internal forces. Both methods have unique complexities, advantages, and disadvantages. The solution of equation (2.1) can be computed without considering individual muscles, and this is termed inverse dynamic analysis. The traditional Newton-Euler equations of motion are iteratively solved along the chain of each segment in model, using known external forces and discretely-derived joint kinematics , ). Inverse kinematics may be a pre-requisite step, in which laboratory measurements of experimental kinematic marker data are used to calculate model joint angles (q) that best reproduce the motion. A least-squares optimization to minimize the distance between virtual body markers and processed motion-capture data of optical skinmounted markers across the motion is typically sufficient to simulate whole-body walking, although more robust methods may be warranted for joint-specific investigation, such as for detailed knee study (Andersen et al., 2010a). Due to error propagation from experimental sources (noise, skin artifact) nonphysiological, external forces and moments (residuals) are required between simulated ground and the attached, proximal segment (usually the pelvis) to satisfy the dynamic equations of motion. Methods have been developed to reduce the magnitude of the non-physiological forces, such as a residual elimination algorithm (REA) (Thelen and Anderson, 2006) or a residual reduction algorithm (RRA) (Delp et al., 2007). In broad summary, the mass properties of the trunk or pelvis segment can be adjusted and the inverse kinematics solution slightly altered to 39 minimize residual forces and moments. Inverse dynamic methods are computationally efficient and are implemented in numerous software packages, but terminate at the prediction of joint intersegmental force. Inverse dynamics has proven useful in clinical settings to investigate altered biomechanics during pathologic gait. However as a descriptive rather than predictive approach, results must be interpreted carefully. Supplementing estimated joint torques with concurrently measured EMG to form clinical conclusions of individual muscle function is not recommended, due to unaccounted for dynamic coupling. Therefore, extended methods exist to estimate individual muscle forces corresponding to an inverse dynamics solution. When many muscles are added to the system, an over-determinate system with more muscles than degrees of freedom is created. Static optimization techniques are one means to resolve the redundancy problem (Tsirakos, 1997). A nonlinear, constrained optimization problem is typically formulated as, minimize G(FM) subject to (equation (2.1) (2.2) 0 < aM < 1.0 where aM represent muscular activations, and the constraint enforces that muscles can only pull, not push (Erdemir et al., 2007). To arrive at individual muscle force estimations across the movement, the optimization problem is iteratively solved at each time step. The G(FM) function is an objective criterion that should be chosen to represent a meaningful approximation of a physiologically-based goal that is relevant to the movement being studied. Various physiologic movement criteria have been proposed in the literature for certain movements and sub-systems of the body. A comprehensive review is provided by (Tsirakos, 1997). For walking, common choices include minimizations of metabolic cost (Umberger, 40 2010), or polynomial functions of muscle activations. An accepted common objective function for lower extremity walking has been the minimization of the sum of cubed muscle stresses (current force normalized by cross-sectional area), which effectively minimizes muscular fatigue, and has produced activation predictions that compare well with concurrent EMG during walking (Crowninshield and Brand, 1981). Numerous functions have been used in spinal simulation; one study compared minimization of cubed muscle stress, squared muscle stress, total joint compression, and eigenvector synergy (a proposed measure of spinal stability) and found cubed muscle stress to produce predictions in best agreement with measured EMG (Hughes and Chaffin, 1994). Without adequate EMG for validation, confidence in solution is generally limited by this step, where the unknown goals of the complex central nervous system are essentially surmised. Furthermore, selection of an appropriate motor task is increasingly difficult for individuals with pathology or pain, as an altered muscle recruitment goal is usually apparent, such as in LBP (Arendt-Nielsen et al., 1996), and in individuals with a lower-limb amputation (Fey et al., 2010). Nonetheless, static optimization approaches have proven useful in clinical applications, such as in developing design inputs for total knee replacements (Andriacchi et al., 1997). Limitations of static optimization approaches have been suggested. Firstly, inverse dynamics based static optimization is known to underestimate the total joint contact force, as muscle co-contraction about a joint is generally not a system state found to be optimal by the most popular objective criteria (Tsirakos, 1997). This is particularly significant with respect to spine modeling, as significant flexor/extensor co-contraction has been observed experimentally during demanding flexion/extension tasks (Granata et al., 2005), and also in individuals with LBP (Hall et al., 2009). Secondly, muscular activation dynamics are difficult to include in the 41 framework, as the overall solution is independent of time. However, exceptions do exist that have approximated activation dynamics in static optimization (Happee, 1994). Thirdly, forward simulation of gait has been applied to show that intrinsic force-length-velocity properties are key contributors to body support and stability during walking (Gerritsen et al., 1998). These phenomena are also difficult to include in the inverse framework and are often neglected in favor of simple muscle models, although again, exceptions do exist that have successfully approximated the three-element Hill muscle model in an inverse framework (Damsgaard et al., 2006). Static optimization has several prominent advantages relative to other methods. A distinction between the joint intersegmental (or, resultant) and the total joint contact force must be established. Joint intersegmental forces are caused by segmental accelerations and external forces (i.g. GRF), and are those computed by iterative application of the Newton-Euler equations in inverse dynamics. The joint intersegmental force underestimates the total joint contact force, which additionally accounts for compressive forces due to spanning musculature and passive structures (ligaments, cartilage). Static optimization accounts for the effect of muscles, and also any passive structures modeled, thus obtaining a better estimate of total joint contact force. Lastly, relative to forward approaches, static optimization is more computationally efficient, as multiple integrations of the system equations are not required. Forward dynamic optimization methods of simulation are different from inverse dynamics based static optimization in several key areas. Firstly, equation (2.1) is rearranged to solve for acceleration as a function of applied forces. By defining initial conditions of muscle excitations and various constraints on system parameters, the equation can be integrated to compute the resultant motion (Pandy, 2001). Development of forward dynamic methods for 42 musculoskeletal simulation began at the same time as static optimization, however forward dynamics was most hindered by computational limitations, and thus inverse dynamic based static optimization has seen more application. In contrast to static optimization, forward dynamics is time-dependent, and thus both intrinsic muscle properties and activation dynamics are easily incorporated into solution schemes (Erdemir et al., 2007). Also, the solution is less prone to propagation of experimental measurement error, although possibly at the expense of less strict kinematic tracking. Significantly, the forward dynamic versus inverse static methods have been shown to produce highly similar estimations of both muscle forces and total joint contact forces in the simulation of normal walking (Anderson and Pandy 2001). The authors also proposed that if a study aims only to estimate muscle forces and associated joint contact forces, the use of the computationally more demanding forward dynamic optimization is not currently justified. Regardless, with continually increasing computational power, forward dynamics continues to grow in popularity due to several unique analyses afforded through the problem formulation. For example, forward optimal tracking has been applied to investigate individual contributions of the biarticular gastrocnemius and uniarticular soleus to body support, forward progression, and the hip intersegmental force during walking (Neptune et al., 2001; Zajac et al., 2003). This category of analyses (induced acceleration analysis, IAA) is not possible in an inverse static optimization framework. Contribution of individual muscles to segmental power can also be elucidated with dynamic optimization. A single computed muscle power represents the net power delivered and received to/from every segment in the system by the muscle, and can be useful to assess muscle coordination principles (Zajac et al., 2002). Forward techniques using optimal control comprise a further class of musculoskeletal simulations, and require only initial muscle conditions with no experimental data. A primary benefit of optimal control is that 43 the entire motion is included in the optimization, thus, task-based optimization criteria can be enforced, such as “move the trunk as smooth as possible” (Menegaldo et al., 2003). A more in depth review of optimal control simulation is provided by (Pandy, 2001). Hybrid inverse/forward approaches have also been developed and seek a middle ground between the unique analyses afforded by through dynamic optimization, and the low computational demand of static optimization. One example is computed muscle control, developed by (Thelen et al., 2003). In brief summary, computed joint kinematics are tracked during a single forward dynamic optimization simulation solution of equation (2.1), minimizing error between experimental and predicted joint angles. At each time step, a static optimization solution is obtained to resolve muscle redundancy. Computed muscle control has proven particularly useful in the study of high pace and dynamic movements, and is also implemented open source simulation software (Delp et al., 2007). To generate muscle-driven simulations, a musculoskeletal model of the necessary portions of the body must first be soundly constructed. A developing trend in the modeling community is to share generic, whole-body models. Thus, detailed models with substantial preliminary validation have been developed for several musculoskeletal sub-systems, and can be modified with relatively minimal effort to serve the researcher’s purpose, such as subjectspecific simulation. This sharing process greatly accelerates biomechanical modeling research, and also increases confidence within the clinical and industry communities in simulation as a viable tool. Available lower extremity models differ primarily in the modeled musculature and in some cases, accompanying software package. One example is the LowerLimb2010 model, provided for free with OpenSim software and developed by (Arnold et al., 2010). The model parameters (muscle anatomy, muscle composition) are compiled from 21 cadavers to represent 44 44 Hill-type muscles. A contrasting example is the TwenteLowerExtremity model, packaged with the AnyBody Modeling System. In contrast to LowerLimb2010, all muscular and joint parameters for this model were taken from a single, consistent donor dataset (Klein Horsman, 2007). As the AnyBody Modeling System is principally an inverse dynamics based static optimization platform, increased muscle detail is represented, including 55 muscle groups separated into 159 separate actuators. Lastly, in either model, joint definitions are approximated to lesser degrees of freedom than in vivo, as is common practice in the whole-body simulation literature. Available models of the lumbar spine are much less prevalent in terms of generic availability. Early spine simulation studies developed simple EMG-assisted inverted pendulum models (Granata and Marras, 1993), and link-segment models of the low back including up to 66 muscle fascicles, to predict lumbar muscle forces (Kong et al., 1998). The most current and detailed, generic spine models available also exist in implementations of OpenSim and AnyBody (Christophy et al., 2012b; de Zee et al., 2007). Both models include the five lumbar vertebrae, and resolve the individual kinematics as a function of net trunk-pelvis motion. In contrast to the OpenSim models, the AnyBody low back model is integrated with the comprehensive TwenteLowerExtremity model, allowing whole-body studies of human movement that include the lumbar spine, and thus potentially investigations of low back biomechanics during walking. Representations of passive IVD joint stiffness in both models are simple, linear approximations. More robust, six-degree of freedom nonlinear stiffness models for use in rigid-body dynamic studies have recently been proposed (Christophy et al., 2012a). Computational modeling and simulation has been applied on several occasions to investigate the altered biomechanics of individuals with a lower-limb amputation during 45 walking. In each case, findings have provided valuable information that may otherwise have been unattainable using only traditional experimental methods. The primary focus has been lower extremity alterations, thus an even smaller selection of these works have investigated low back biomechanics. Only one study exists at the time of this writing that estimates in vivo low back biomechanics of individuals with lower-limb amputation during walking. The subject pool included 20 individuals with TTA, 20 TFA, and 20 non-amputees (Hendershot and Wolf, 2013). Three dimensional kinematics and ground reaction forces were measured, walking overground at a self-selected speed (average~1.35m/s). Intersegmental forces and moments in the L5S1 joint were computed using both top-down and bottom-up inverse dynamics, and timing and magnitude of peak forces/moments during stance of each limb were extracted. Comparing sets of results between the top-down and bottom-up inverse dynamic approaches showed the two methods were equivalent. Several significant differences in peak forces during the gait cycle were found between individuals with lower-limb amputation, relative to non-amputees. The strongest group differences were a greater maximum anterior force, and a lesser minimum posterior force, during residual swing, and also a greater maximum lateral force during residual stance. The strength of the difference increased for higher level of amputation (TFA vs TTA). As muscles were not included in the analysis, the intersegmental joint forces/moments may have underestimated the shape and magnitude of total joint contact forces/moments, due to the unaccounted for effects of whole-body musculature (Zajac et al., 2002). Also, subject parameters of age, time since amputation, prosthesis type, and self-selected walking speed may be associated with low back biomechanics, but potential effects of these parameters on the estimated metrics were not investigated. 46 Another study used forward dynamic tracking simulation (sagittal plane only) to investigate if contributions from energy storage and return prostheses (ESAR) and various muscular compensations could produce normal, symmetric gait in unilateral TTA (Zmitrewicz et al., 2007). Simulation results suggested that the prosthesis did contribute positively to trunk support, but had slight, net negative contributions to forward propulsion and swing initiation. To achieve symmetric gait, increased contributions to forward propulsion were required from the residual limb rectus femoris and gluteus maximus during residual stance, and from the intact limb soleus, gluteus maximus, and rectus femoris during early intact stance. Also, both the residual and intact limb psoas had to deliver increased energy to the respective limb to initiate swing. Since the simulation suggested a symmetric gait is physiologically attainable, but a majority of individuals with TTA still walk with asymmetric gait, muscle atrophy and inhibited sensory feedback may be more primary determinants of their gait strategy than previously thought. A further study applied forward dynamic simulations of TTA and non-amputee walking to quantify contributions of the prosthesis, and of any muscular compensations, to numerous whole-body gait parameters (Silverman and Neptune 2012). Averaged experimental data for both individuals with TTA and non-amputees were supplied as the optimal tracking targets for simulations. Simulation results suggested that the passive TTA prostheses did contribute to both body support and residual limb braking in the absence of the ankle muscles, but did not completely replace the function of the gastrocnemius to deliver energy to the residual limb for swing initiation. Contributions of the rectus femoris and vasti to braking were reduced in compensation of the elevated braking contribution from the prosthesis. Such compensations 47 have potential to be associated with LBP through dynamic coupling and unintended biomechanical cascades that propagate to the low back. In summary, the choice of framework and underlying modeling assumptions selected for a study should be based on the specific research question being investigated, type of analyses planned, and availability of experimental data. Both forward and inverse frameworks have unique advantages and limitations, but have proven utility in developing unique findings unattainable in experimental walking analyses alone. Further work investigating the associations between altered walking strategies and low back biomechanics is motivated by these previous successes. 2.4. Finite Element Analysis of the Spine Musculoskeletal dynamic simulation can estimate total joint reaction forces and rigid-body dynamics. However, with respect to the passive tissues of the spine, distributions among facet joints, the IVD, and ligaments are of interest. Finite element analysis of the spine allows such investigations. Combination of the two methods in a multi-scale sense is of primary interest to this work. To facilitate further discussion, a diagram of an anatomical FSU and a corresponding finite element model is provided in Figure 2.4. Tools for scientific investigations of the tissue-level low back biomechanics that address the issues of in vitro and in vivo study are needed. The finite element method (FEM), originally developed for civil and aeronautical structural applications, has first applications in biomechanics reported as early as 1979 by Miller. The number of biomechanical and medical studies published each year reporting FEM use has grown geometrically since initiation in the 80’s to approximately 1400 in 2009 (Erdemir et al., 2012). This growth is primarily because FEM analyses overcome many limitations of in vitro and in vivo studies, but also because 48 relative to other discrete methods, FE robustly handles the complexities of nonlinear living tissue and contact conditions. (a) (b) Figure 2.4 - Anatomical FSU (a) compared to a representative finite element model (b). Image (a) adapted from ilo.org With respect to the spine, FEM is particularly well-suited to represent the spine’s wide range of material properties, including nonlinear behavior of the IVD, complex bone geometry, and articulation of the facet joints. Other structural constituents of the spine include bony vertebral bodies, stabilizing elastic ligaments, and detailed musculature. With respect to tissue level causes of LBP in individuals with a lower limb amputation, a brief review of FEM methods that have been used to model spinal anatomy and degeneration is warranted. Recent uses of musculoskeletal simulation in combination with FEM of the spine in a multi-scale sense are also reviewed. The IVD is a frequently addressed spinal component in terms of orthopedic surgery and implantation and thus has an extensive backing in current FEM literature. The level of complexity used to model the disc varies with the specific research question. The IVD has been modeled as a single component nearly as frequently as it has been a constituent of the larger 49 spinal assembly. The IVD in vivo is known to exhibit material inhomogeneity, anisotropy, and porosity (Jones and Wilcox, 2008). Studies concerned with the dynamic response of the IVD (e.g. design of total disc replacements) have developed methods to model stress relaxation, creep, and viscoelastic effects. One study systematically compared results from three popular FEM methods to model the IVD, to experimentally measured annulus fibrosis response (Yin and Elliott, 2005). Compared methods included modeling of individual fibers within a homogenous ground material, approximating a fiber-reinforced strain energy model, and a multi-scale homogenization model of repeated volume elements. The three methods approximated experimentally measured annulus fibrosis properties equally well, and results suggested that any of the three would be adequate for use in FEM studies of disc degeneration. Studies incorporating multiple IVD’s into a complete L1-L5 lumbar spine have used other models. Constitutive relations, such as the isotropic, incompressible hyperelastic MooneyRivlin material law, supplemented with in vitro cadaveric parameters are common (Schmidt et al., 2007). The former study was able to approximate intradiscular pressures, fiber strains, and shear strains that compared well with previously reported in vitro values. The greatest stress/strain in the annulus was observed postereolaterally, elevated localized levels of which are known to correlate with disc prolapse. The geometry of the IVD is commonly simplified as axisymmetric in the sagittal plane with flat inferior/superior surfaces. Segmentation analysis of medical image data to achieve a more physiologically accurate shape is currently the state of the art (Jones and Wilcox, 2008). The prior work by Schmidt reconstructed the IVD volume geometry from 0.49mm resolution CT scan data. Current practice may be summarized as distinguishing between the nucleus, annulus ground material (various sub-compartments), and annulus collagen fibers, using a combination 50 of the documented methods for material definitions and medical images to develop volume geometry. The bony vertebrae superior and inferior to an IVD are additional, significant components of any spinal FEM model. The vertebral bodies exhibit variable bone density throughout the volume and a slight, quantifiable elastic response. Relative to the IVD, representing the complex geometry accurately is perhaps the most significant challenge to this component, and is much more crucial to resulting analyses since the geometry defines facet joints and insertion points for numerous ligaments. Development of methods to reliably reproduce vertebral geometry from medical data has resulted primarily from studies that simulate vertebral fracture and failure, where detailed response of the geometry constitutes the entirety of analyses. Methods range in complexity from manually distinguishing between cancellous and cortical density levels throughout the volume via sections of distinct elastic moduli, to automatic distribution of inhomogeneous material properties based on image analysis (Jones and Wilcox, 2008). Automatic assignment of material properties via image analysis is done by correlating a range of Young’s modulus to the range observed in a density parameter (e.g. CT Hounsfield units) of a medical image, which distinguishes between bone regions. Image-analysis has been suggested to result in a more realistic, total stiffness of the vertebral unit. The finite elements used to construct the internal volume and external surfaces can vary. Eight or twelve node brick elements appear most common in construction of bone volume (Jones and Wilcox, 2008). As with prior modeling decisions, the required level of complexity in the vertebral representation depends upon the research question being investigated. For example, in analyzing soft tissue mechanics of a functional spinal unit (FSU) under low cyclical loading, strains are likely orders of magnitude larger in the soft tissue than in the bone, and a reasonable 51 assumption may be to approximate the bones as rigid shells. Lastly, if vertebrae have been imaged individually in vitro, accurate re-alignment of multiple computerized vertebrae into original anatomical position (lordosis angle) remains a significant task. Approximation of facet joint articulation and connective ligaments are additional comple ities when modeling two or more SU’s. apid development of multi-level lumbar spine models only picked up in the last ten years (Jones and Wilcox, 2008). Therefore, methods to model facets and ligaments are less frequently documented than for the IVD and vertebral body. Experimental observations of spinal ligaments (flavum, intertransverse, interspinous, supraspinous, capsular, etc.) have revealed nonlinear behavior, thus point-to-point non-linear elastic elements connecting nodes of adjacent vertebral bodies, are common (Kurutz, 2010). For example, the black elements depicted in Figure 2.4 are of this type. Modeling facet articulation has been done using a broader range of methods. A combination of an additional cartilage layer between inferior/superior articular processes, variable-stiffness gap elements, and low-magnitude friction have all been applied in practice (Jones and Wilcox, 2008). One different approach appears in a finite element study of facet load transmission at the L2-L3 level due to axial compression (Teo et al., 2003). To reduce computational cost, the curved facet surfaces were discretized into 2D planar elements coincident with underlying continuum solid elements, allowing sliding, surface contact with a dynamically changing contact area. Frictionless, variable stiffness articular cartilage of 0.2mm was also included on each surface. The study produced results that compared well with experimentally measured facet contact force during compression, although results were highly sensitive to the simplified surface geometry in the presence of sagittal motion. Other authors have confirmed this method as adequate for spinal compression studies, but inadequate when 52 predicting A/P sagittal shear or distribution of compressive stress, and thus suggest a supplement to the method to include curvature effects (Holzapfel and Stadler, 2006). If possible, realistic in vivo facet morphology should be preserved. When modeling two or more SU’s, appropriate boundary and loading conditions to represent physiological loading become increasingly complex. The L5 joint is separated by one IVD from the relatively larger sacrum in vivo, and a fixed kinematic boundary condition applied to the inferior endplate of the L5 vertebral body reasonably approximates this connection (Kurutz, 2010). Idealized moments and force vectors are then applied to the most superior endplate of the segment chain in the simplest loading case. This method can be augmented by application of a load following lumbar spine lordosis angle (follower load), as an approximation of physiological muscle action. Attempts have been made to fully replace the idealized forces and drive the model individual muscle forces applied at anatomically relevant locations along the lumbar spine (Rohlmann et al., 2006). The former study applied a follower load and idealized moment to a lumbar spine FE model with defined muscle fascicle attachments, observing resulting forces in the muscle elements. In comparison to current optimization methods, this study is limited in that no physiologically based criterion was used to distribute muscle forces in a meaningful way. Current multi-scale methods instead use rigid-body musculoskeletal simulation and optimization to first determine muscle force profiles corresponding to an observed movement. After ensuring direct correspondence between models, individual muscle forces are subsequently applied as finite element boundary conditions. This framework was first attempted almost a decade ago (Kong et al., 1998), by determining finite element boundary conditions through minimizing squared muscle stress in inverse dynamic static optimization of a muscle-actuated, 53 rigid-body model of the thorax. Most recent applications of combined finite element and musculoskeletal simulation include analysis of: hip implant loads during stand-to-sit (Kunze et al., 2012), stresses in a femur during walking (Wagner and Divringi, 2010), cervical spine tissue mechanics in response to neck rotation (Toosizadeh and Haghpanahi, 2011), stresses in a vertebral body due to static lifting of a heavy object (Wong et al., 2011), and stresses in the IVD due to trunk posture (Gadomski et al., 2011; Zhu et al., 2013). A key consideration in multi-scale modeling is to limit error propagation due to exchange of information between the finite element and rigid body model. With respect to the spine, a source of such error may arise from applying muscle forces determined via a rigid body analysis that uses fixed centers of intervertebral rotation (CORs), to a model with non-constant CORs and elastic vertebral bodies. One study tested eight total combinations of elastic/rigid vertebrae, fixed/variable CORs, and elastic/non-elastic posterior elements in a finite element spine model, while applying muscle loads from inverse dynamics (Zhu et al., 2013). A maximum disagreement of 2o between finite element and inverse dynamic predictions of intervertebral rotation (IVR) was observed in the worst case (corresponding to 20o trunk flexion). A case with non-fixed CORs, rigid vertebral bodies, and elastic posterior elements produced IVR predictions within 0.5o. These findings are greatly beneficial to the developing area of multi-scale finite element and musculoskeletal simulation. An expansive and necessary body of work detailed in the literature, which supplements developed biomechanical finite element models, are corresponding verification and validation studies. In regards to modeling, verification questions whether the underlying theory is being solved correctly. In contrast, validation questions whether the selected theory adequately represents the real phenomena being modeled. In terms of FEM, model verification is verified 54 by how accurately the discretized equations approximate the analytical equations. When using commercial FE software, code verification is provided in the documentation as a reference, however researchers must still show that final mesh resolution produces a converged solution. Validation must be done against in vivo or in vitro measurements after producing results, in order to make any valid clinical recommendations. Indirect validation by comparing finite element results to results of other, comparable finite element studies that did validate against an experiment is also an accepted method, although is not the ideal approach. Also, uncertainties in material and boundary condition definitions for spinal finite element models typically warrant sensitivity studies of primary outcome metrics to these input parameters (Jones and Wilcox, 2008). Application of FEM to the study of spinal function is clearly an established area of work. The strengths of FEM in representing the dynamic behavior of the spine serve well the requirements of a tissue-level investigation of mechanical LBP mechanisms. Driving finite element analyses with muscle loads determined though rigid-body musculoskeletal simulation is has a short history, and maintaining model correspondence remains a current challenge. However application of methods to investigate low back loading during gait, and to investigate pain mechanisms of a patient population with altered gait (individuals with a lower limb amputation) would both be novel developments. 2.5. Summary Collective literature findings provided motivation for an investigation of low back biomechanics in individuals with a lower limb amputation during walking, via application of musculoskeletal modeling and finite element simulations. Based on discussions of LBP mechanisms, quantities of trunk-pelvis relative kinematics, muscle forces in the low back, and 55 total joint contact force were identified as metrics that could be readily compared with previous literature and clinical findings (see Sections 2.1.1, 2.1.2, and 2.1.3 respectively). Simulation literature suggested that a static optimization framework would be sufficient to reliably estimate these three metrics (Anderson and Pandy, 2001). Lastly the work performed and explained in the following chapters established baseline data, biomechanical models, and simulation tools to be part of a computational workflow with potential to be applied clinically in diagnoses and rehabilitation of patients with biomechanical LBP (Figure 1.2). 56 3.CHAPTER 3 LOW BACK KINEMATICS, MUSCLE FORCES, AND JOINT CONTACT FORCES DURING WALKING OF INDIVIDUALS WITH TRANSTIBIAL AMPUTATION A paper to be submitted to the Journal of Gait & Posture Adam J. Yoder1,2, Anthony J. Petrella, and Anne K. Silverman3 3.1. Abstract Individuals with a unilateral, below-knee amputation (TTA) have an increased susceptibility to chronic low back pain (LBP) relative to able-bodied individuals. While individuals with TTA have numerous alterations in lower extremity body segment dynamics, muscle recruitment, and joint kinetics during walking, a definitive cause of increased LBP susceptibility has not been established. Thus, the purpose of this work was to compare dynamic low back biomechanics during walking between individuals with and without unilateral, TTA using computational modeling and simulation. Experimental walking data were used to scale a generic, muscle-actuated whole body model with additional detail in the L1-L5 lumbar, and to simulate gait with concurrent estimates of dynamic internal low back biomechanics. Results showed several group differences in computed low back metrics during particular phases of the gait cycle. Most significant in individuals with an amputation was greater lateral range of axial trunk rotation near toe off of the residual limb was also found concurrently with greater force in residual-side erector spinae and psoas. Repetition of such abnormal trunk motion ________________________ 1 Graduate student, Associate Professor, and Assistant Professor, respectively, in the Department of Mechanical Engineering, Colorado School of Mines. 2 Primary researcher and author 3 Author for correspondence 57 towards the residual-side during residual single limb stance, concurrently with greater intact-side trunk muscle forces and a greater L4L5 lumbar joint contact force. A greater biomechanics over time has potential to cause deficiencies in muscular endurance, strength asymmetries, inhibited proprioception, and myofascial pain, each associated with increased susceptibility to chronic, biomechanical LBP and other secondary musculoskeletal disorders. 3.2. Introduction Individuals with unilateral lower limb amputation have a greater prevalence of low back pain (LBP) relative to the general population (Ephraim et al., 2005; Kulkarni et al., 2005). The cause of this greater prevalence is not well-understood, but is thought to be a result of biomechanical differences in the low back in contrast to potential degenerative etiologies (Burke et al., 1978; Kulkarni et al., 2005). Relative to non-amputees, individuals with transtibial amputation (TTA) walk with altered body segment kinematics (Hendershot and Wolf, 2013; Michaud et al., 2000; Rueda et al., 2013), lower extremity joint kinetics (Sadeghi et al., 2001; Silverman et al., 2008), and dynamic muscle recruitment (Winter and Sienko, 1988). Many of these reported biomechanical changes have potential to be associated with development of secondary pain conditions. Asymmetric motion between the trunk and pelvis during walking of individuals with a lower limb amputation (Hendershot and Wolf, 2013; Michaud et al., 2000; Rueda et al., 2013), has been highlighted as a potential whole-body biomechanical factor that contributes to development of biomechanical LBP (Devan et al., 2014). Biomechanical evaluation of individuals with a lower limb amputation have focused largely on lower extremity dynamics, and thus few studies reported findings of altered low back biomechanics in individuals with a lower limb amputation. Reduced relative motion between the trunk and pelvis in the transverse plane has been observed in individuals with TFA and no LBP, 58 relative to non-amputees (Goujon-Pillet et al., 2008). Individuals with TFA and concurrent secondary LBP have greater overall trunk and pelvis ROM in the transverse plane during walking, relative to TFA with no LBP (Morgenroth et al., 2010). Even fewer findings exist regarding altered low back biomechanics in individuals with TTA, although relative to nonamputees, inhibited trunk proprioception (Hendershot and Nussbaum, 2013) and reduced frontal/sagittal trunk stiffness have been found (Hendershot et al., 2013) in response to standing perturbations. Several biomechanical differences between individuals with and without an amputation are similar to biomechanical differences between able-bodied individuals with and without LBP. Tighter transverse trunk-pelvis coordination has been found in combination with more variable frontal coordination in able-bodied individuals with LBP relative to LBP-free (Lamoth et al., 2006b). Reduced low back proprioception resulting from muscular fatigue (Gandevia, 1994), and decreased static trunk extensor endurance (Luoto et al., 1995) have also been associated with increased susceptibility to biomechanical LBP in able-bodied individuals. Further characterization of dynamic, in vivo low back biomechanics in individuals with TTA during walking is needed to understand how LBP develops in this population. Dynamic lumbar joint forces in individuals with and without a lower limb amputation during walking is has only recently been explored (Hendershot and Wolf, 2013), although dynamic muscle recruitment also plays a large role in biomechanical LBP development (Comerford and Mottram, 2001; Sato et al., 1999). However, quantifying muscle and joint contact forces in vivo, particularly during dynamic motions such as walking, is challenging. Whole-body musculoskeletal modeling and simulation has proven utility in estimating biomechanical parameters that may be difficult, costly, or impossible to quantify in vivo during dynamic 59 movement, including estimates of joint contact forces and forces produced by individual muscles (Anderson and Pandy, 2001; Andriacchi et al., 1997; Sasaki and Neptune, 2010; Zajac et al., 2003). Thus, the purpose of this study was to compare low back kinematics, net lumbar joint contact forces, and forces within primary low back muscle groups between individuals with and without TTA during walking using computational modeling techniques. Based on known wholebody alterations reported in previous work, the hypothesis was that the three estimated low back metrics would be different between groups, during particular discrete phases of the gait cycle. 3.3. Methods Walking mechanics of six individuals with unilateral, traumatic TTA and six able-bodied individuals were selected from a larger, previously-collected dataset (Fey et al., 2010; Silverman et al., 2008). Group characteristics of the selected participants are provided in Table 3.1. Each individual with TTA wore their own passive prosthesis, with alignment and fit confirmed by a prosthetist prior to data collection. All participants were skilled walkers and were free of secondary musculoskeletal disorders and pain. The data collection protocol was approved by the local Institutional Review Board and all participants provided informed consent prior to participation. The experimental protocol has been previously described in detail (Fey et al., 2010; Silverman et al., 2008). Briefly, an eight-camera motion capture system (Vicon, Oxford Metrics) was used to record three-dimensional kinematics of the lower limbs, pelvis and thorax (120Hz) during overground walking. Muscle electromyography data were also recorded (1200Hz) via surface electrodes (Motion Labs Inc.) on eight intact lower extremity muscle groups, including the gluteus maximus (GMAX), gluteus medius (GMED), biceps femoris long head (BF), rectus 60 femoris (RF), vastus lateralis, soleus, medial gastrocnemius, and tibialis anterior. Electromyographic data were not collected from the soleus, gastrocnemius, and tibialis anterior of the residual limb of people with TTA. Four concealed force plates (AMTI Inc.) embedded in a 10m walkway were used to record ground reaction forces (1200Hz). Trials that fell within 0.90±0.10m/s, and that contained three consecutive force plate hits containing a residual limb gait cycle, were selected for inclusion in this work. Table 3.1 – Mean (SD) of participant characteristics. Age [years] Height [cm] Weight [kg] Time Since Amputation [years] Prosthesis Gender (male/female) Non-amputee (n=6) 35.3 (12.6) 176.2 (6.6) 71.9 (15.2) - - 5/1 TTA (n=6) 43.7 (7.7) 173.7 (9.4) 90.9 (14.7) 5.0 (1.4) 4 SACH/ 2 ESAR 5/1 3.3.1. Musculoskeletal Model A generic whole-body model was used to represent each participant and investigate low back biomechanics (AnyBody Modeling System v6.0, Model Repository v1.6, Aalborg, Denmark, Figure 3.1). The lower extremity model has been validated for prediction of muscle activity during gait, and has previously been applied to study gait of individuals with a transtibial amputation (Voinescu et al., 2012). Each leg had seven degrees of freedom (DOF) and 55 muscle groups (163 fascicles). All lower extremity muscles were modeled as three-element Hill actuators, with muscular properties (e.g., physiological cross-sectional area, optimal fiber/tendon length, pennation angle) and anatomical paths based on a single, consistent donor dataset (Klein Horsman et al., 2007). A version of the model with unilateral, transtibial amputation was created 61 (Figure 3.1) by replacing ankle musculature on the amputated side with passive ankle dorsi/plantarflexion and inversion/eversion reaction torques. Mass and inertial properties of the prosthetic shank were adjusted to represent an amputation (Mattes et al., 2000). To account for effects of lower extremity ligaments and passive structures during gait, passive torques were added at the knee, as an exponential function of knee joint angle (Audu, 1985). Figure 3.1 - Whole-body musculoskeletal model. The prosthesis is represented by removed ankle musculature and an adjusted shank center of mass location. Marker-based segment frames for HAT and pelvis with respect to the laboratory global reference are shown. The low back portion of the whole-body model contained five lumbar joints between S1 and T12, each with three DOF and fixed centers of rotation (de Zee et al., 2007). The model has previously been validated for prediction of lumbar joint contact forces, against in vivo data (Rasmussen et al., 2009). All segments superior to the L1-T12 joint were represented as a single lumped-mass head-arms-torso (HAT) segment. The five individual intervertebral rotations were constrained as a function of total, relative rotation between the HAT and pelvis segments. Eight 62 primary muscle groups (erector spinae, multifidi, semispinalis, quadratus lumborum, abdominal obliques, transversus, rectus abdominus, origins of psoas major) were modeled with 188 fascicles (de Zee et al., 2007; Hansen et al., 2006). The walking speed simulated in this work caused small ranges of lumbar segmental motion and negligible dynamic effects, thus inertial properties of the vertebrae were assumed negligible and muscles were modeled as single force elements with physiological cross-sectional area as input. Intra-abdominal pressure was modeled as a variable extension moment on the spine, computed as a function of abdominal volume (de Zee et al., 2007). Reactions due to passive spinal structures were modeled by linear reaction torques at the five lumbar joints, with properties based on average, in vitro measurements of intact spinal stiffness (Bisschop et al., 2013). 3.3.2. Simulation Framework The modified generic model was scaled to each participant’s anthropometry by optimizing model parameters (segment lengths, virtual marker set) to best fit an experimental static standing trial, similar to Anderson et al. (2010). Total tendon-fiber length was scaled with the body segments, and individual segment masses were computed as a percentage of total measured body mass (Winter, 2009). Joint angles that best reproduced the gait cycle were estimated using least-squares optimization between virtual and experimental markers across the motion (Andersen et al., 2009), with optimal segment lengths and virtual marker locations fixed from each subject’s static standing trial. Inverse kinematic solutions and processed ground reaction forces were input into a static optimization muscle recruitment simplex algorithm to compute total joint contact forces and corresponding individual muscle excitations across the gait cycle. A fatigue-based movement criteria previously validated for walking (Ackermann and van den Bogert, 2010), minimized the 63 sum of cubed muscle activations subject to dynamic equilibrium and physiological constraints on muscle activity. Lower bound activity constraints were developed using EMG measured on lower extremity muscle groups. Raw data were demeaned, rectified, and high pass filtered (20Hz). RMS envelopes were computed and low-pass filtered (6Hz) to obtain smooth estimates of excitation. To estimate activation, envelopes were uniformly shifted forward in time 15ms to account for first-order activation/deactivation dynamics (Zajac, 1989) that were not included in the muscle models. Following a preliminary analysis, residual forces and moments applied between pelvis and ground were reduced by slightly increasing/decreasing the total mass assigned to the HAT segment. The muscle recruitment algorithm was then applied to the adjusted model. 3.3.3. Data Analysis Primary outcome metrics included HAT-pelvis relative rotation, computed using an Euler Z-Y-X rotation sequence (sagittal bending - transverse rotation - frontal bending) of HAT relative to pelvis (Figure 1). Total joint contact force between the L4 and L5 vertebral segments due to all spanning musculature was resolved along each of the three anatomical directions (force on the L4 body w.r.t to L5). Modeled muscle fascicles were collected into four primary low back muscle groups (erector spinae, psoas major, internal+external obliques, quadratus lumborum), and total forces within muscle groups were computed by summing all fascicle forces. Time series of the primary outcome metrics extracted from the model (trunk-pelvis relative angles, L4L5 joint contact forces, low back muscle forces) were time-normalized to 0100% of the gait cycle. Average and range values of each outcome metric during four discrete phases of gait were computed for each individual: residual single-limb stance (~15-50%), 64 residual swing (~65-100%), and both double support phases (~0-15%,~50-65%). TTA and nonamputee outcome metrics were compared using two-sample unpaired t-tests (α 0.05) between groups, testing for significant differences in average or range values for each outcome metric within each phase of gait. 3.4. Results Across all simulations, gait cycle marker tracking errors within inverse kinematic solutions were low, with all below 2.0cm and a study RMS-gait cycle average of 9.7mm. Residual forces and moments were also low, with RMS averages across the gait cycle of 3.1, 3.5 and 5.7%BW for anterior/posterior, medial/lateral, superior/inferior forces respectively, and 2.2, 3.3 and 0.8%BW-m for frontal, sagittal, transverse moments, respectively. In review of simulated muscle activity, contractile force production of those lower extremity muscles with constrained activity showed excellent qualitative agreement with raw, filtered EMG signals. 3.4.1. Trunk-Pelvis Kinematics and Low Back Joint Contact Force Three primary kinematic differences were observed in the frontal and transverse planes (Figure 3.2, Table 3.2). Individuals with TTA had greater lateral bending toward the residual limb during residual single-limb stance (p=0.006) and second double-limb support (p=0.005), and also had a greater range of transverse rotation during both double-limb support phases (p=0.003,0.029). In general, low back joint contact forces were similar between groups in all three directions (Figure 3.2, Table 3.2). Individuals with TTA had a greater average L4L5 joint contact force in the superior/inferior direction during residual single-limb stance (p=0.022). In addition, the range of superior/inferior force during second double-limb support and residual limb swing in individuals with TTA approached significance (p<0.10). 65 Figure 3.2 - Group average results for trunk-pelvis relative angle (left), and L4L5 joint contact force (right), throughout the gait cycle. Significant group differences (p<0.05) in either average (AVG) or range (RNG) during discrete phases of gait are distinguished (*). 66 Table 3.2 - Group mean (SD) of outcome metrics that were significantly different (*), or that approached significance, in average (AVG) or range (RNG) during a phase (PHS) of gait. Phases correspond to ipsilateral (residual) limb stance (ST), swing (SW), and first/second doublesupport limb (DS1,DS2). Metric TrunkPelvis Angle Frontal Bending Transverse Rotation Superior/Inferior Ipsilateral Joint Contact Force DOF/Muscle Erector Spinae Psoas Major Obliques Contralateral Low Back Muscles Erector Spinae Psoas Major Quadratus Lumborum Obliques PHS QTY ST AVG DS2 AVG DS1 RNG DS2 RNG TTA Non-amputee [deg., %BW] [deg., %BW] p-value 3.8(1.8) 0.0(2.8) 3.3(1.1) 3.1(1.7) 0.6(1.8) -4.0(1.4) 1.4(0.8) 1.4(0.4) 0.006* 0.005* 0.003* 0.029* ST DS2 SW DS1 DS2 SW SW DS1 DS2 SW DS1 ST ST AVG RNG RNG RNG RNG RNG RNG RNG RNG AVG RNG AVG AVG 88.4(5.7) 32.7(11.3) 60.2(19.0) 18.6(8.1) 37.4(21.9) 38.7(13.7) 16.6(7.9) 13.6(6.8) 16.1(4.0) 14.7(2.4) 31.2(16.1) 22.1(7.4) 10.8(3.5) 81.3(5.0) 22.3(11.8) 45.4(8.9) 11.4(6.1) 16.4(9.8) 24.8(9.6) 8.8(1.6) 9.3(3.2) 9.4(3.5) 12.1(3.6) 15.9(10.4) 16.5(4.0) 7.6(3.5) 0.022* 0.075 0.057 0.055 0.029* 0.034* 0.029* 0.096 0.006* 0.085 0.041* 0.066 0.072 DS1 RNG 4.8(1.6) 2.1(1.2) 0.003* DS1 RNG ST AVG 13.0(2.7) 18.0(3.9) 9.6(3.7) 11.6(3.1) 0.049 0.005* 67 3.4.2. Low Back Muscle Forces There were several differences in muscle forces between groups (Figure 3.3, Table 3.2). On the ipsilateral (residual limb) side, individuals with TTA had a greater range of force within the erector spinae (p=0.029) and obliques (p=0.006) during second double-limb support. During residual limb swing, the ipsilateral erector spinae (p=0.034) and psoas major (p=0.029) also had a greater range of force production. On the contralateral side, individuals with TTA had a greater range of force within the erector spinae (p=0.041) and quadratus lumborum (p=0.003) during the first double-limb support phase. Also on the contralateral side, individuals with TTA had greater average force within the obliques during residual limb stance (p=0.005). 3.5. Discussion The purpose of this study was to compare low back kinematics, net lumbar joint contact forces, and forces within primary low back muscle groups between individuals with and without a transtibial amputation during walking. Numerous significant differences in these metrics between groups were found, and most occurred concurrently during specific phases of gait. Kinematic and joint contact force results were consistent with results from comparable modeling studies that have investigated low back kinetics during walking (Callaghan et al., 1999; Hendershot and Wolf, 2013; Khoo et al., 1995). In addition, a range for in vivo intervertebral reaction force during gait was estimated from reported in vivo L4L5 intervertebral pressures measured during walking (Wilke et al., 1999), by using a mean suggested correction factor of 0.66 for transforming between intervertebral pressures and contact force (Dreischarf et al., 2013). This yielded 91-112%BW, which supported simulated group average resultant L4L5 joint contact forces, of 91%BW (TTA) and 87%BW (non-amputee) across the gait cycle. 68 Figure 3.3 – Group average results for cumulative force within ipsilateral (top) and contralateral (bottom) low back muscle groups throughout the gait cycle. Significant group differences (p<0.05) in either average (AVG) or range (RNG) during discrete phases of gait are distinguished (*). 69 Individuals with TTA had greater lateral bending toward the residual limb throughout residual limb stance (Figure 3.2, Table 3.2). Similar results for frontal-plane bending were found in previous walking analyses of both transfemoral (Jaegers et al., 1995) and transtibial individuals (Michaud et al., 2000; Rueda et al., 2013). Prior authors suggested that greater lateral bending may be a mechanism to compensate for weak or missing hip abductors on the residual limb. However, even small lateral displacements of the trunk mass, that accounts for over half of total body weight, could place elevated demands on contralateral musculature (primarily paraspinals, obliques, quadratus lumborum) to maintain trunk posture and dynamic balance during walking. The most significant muscular difference in results of this work was a greater concurrent force from the contralateral obliques in individuals with TTA (Figure 3.3). This finding supports speculative hypotheses of previous work that found similar kinematic differences, but did not model musculature (Hendershot and Wolf, 2013; Rueda et al., 2013). Repetitive elevated muscle forces over time, may be associated with mechanical LBP, through fatigue of abdominals and resulting strength asymmetries between trunk flexors/extensors (Comerford and Mottram, 2001). Elevated activity of the external obliques in combination with normal levels of the erector spinae, has been observed in able-bodied individuals with LBP (relative to LBP-free) performing trunk sagittal flexion (Silfies et al., 2005). Such an asymmetrical recruitment strategy has potential to affect lumbar spine loading. The single group difference in joint contact force also occurred concurrently during residual stance, as a greater superior/inferior force in individuals with TTA (roughly 8%BW difference between groups, Table 3.2). A combined motion and loading scenario of (lateral bending + axial rotation + superior/inferior compression), relative to single-DOF motions and loadings, has experimentally been found to cause the greatest structural 70 stresses on passive soft tissues in cadaveric work during simulated pelvic obliquity (Popovich et al., 2013). Individuals with TTA also had concurrent, greater ranges of force within residual-side erector spinae and psoas, near toe off of the residual limb. Also near residual limb toe off, a greater range of superior/inferior force in individuals with TTA near residual limb toe off approached significance (p=0.057, Figure 3.2, Table 3.2). Greater residual limb hip flexor moments and powers near residual toe off have previously been observed in individuals with unilateral TTA (Sadeghi et al., 2001). The psoas can provide a hip flexion moment, spine compression, and spinal lateral bending, however increased force output to initiate swing in compensation of missing ankle musculature has potential to increase load on facet joints and the IVD beyond normal levels (Dananberg, 1993). Potential explanations for the elevated range of force from the intact-side erector spinae and quadratus lumborum following residual heel strike, in individuals with TTA, are less clear (Figure 3.3). Both muscles are capable of generating frontal plane moments away from the residual limb. Similar to the supposed concentric function of the contralateral obliques during residual stance, these muscles may be responsible for eccentrically modulating trunk motion as both lateral flexion and axial rotation increase towards the residual limb, more rapidly in individuals with TTA (Table 3.2). Decreased, bilaterally-asymmetric frontal plane trunk stiffness has been found in individuals with unilateral, lower limb amputation when responding to standing perturbations (Hendershot et al., 2013). Trunk stiffness is known to have dynamically changing, relative contributions from active trunk musculature and passive structures, based on posture and type of motion. Asymmetry in bi-lateral psoas muscle tone has been found in medical imaging of certain individuals with a lower limb amputation (Kulkarni et 71 al., 2005). These hip asymmetries, and other potential differences in deeper, stabilizing trunk musculature, were highlighted as potential causes of the decreased and asymmetrical trunk stiffness. Here, the asymmetrical usage of contra/ipsilateral oblique musculature during respective stance phases may also affect dynamic trunk stiffness. Later in the gait cycle, the significantly greater range of force within residual-side obliques (DS2, 6.7%BW difference, Table 3.2) may be driving the more rapid, axial rotation of the HAT back towards the intact limb during residual pre-swing. Previous work that measured, average trunk-pelvis relative ROM in the transverse plane during walking of individuals with TFA, both with/without LBP, observed no significant differences relative to LBP-free ablebodied controls (Morgenroth et al., 2010). The lack of significant differences observed by Morgenroth (2010) agrees with the findings of this work, where trunk-pelvis transverse ROM was similar between LBP-free individuals with and without TTA, throughout all four phases of gait. The numerous muscular differences found in this study have potential to be associated with development of musculoskeletal spinal disorders. An previous observation made in physical examination of individuals with lower limb amputation (n=42) was a distinct prevalence (43%) of scoliosis in medical examination of individuals with unilateral, lower limb amputation (Burke et al., 1978). Adult onset, idiopathic functional scoliosis is associated with muscle fatigue and abnormal recruitment of particular muscle groups (quadratus lumborum, psoas, external oblique), and is commonly associated with confounding chronic, nonspecific LBP. The apparent, altered muscular recruitment of individuals with TTA also supports a previous hypothesis that a majority of LBP in individuals with lower limb amputation is myofascial, rather than degenerative (Kulkarni et al., 2005). 72 A particular, comparable modeling study (Hendershot and Wolf, 2013) applied inverse dynamics to estimate intersegmental forces and moments in the low back and suggested additional, potential differences in low back biomechanics of individuals with a lower limb amputation (20 TTA, 20 TFA). Differences in peak L5S1 forces in individuals with transtibial amputation relative to able-bodied individuals, were suggested: greater anterior force and lesser posterior force during residual swing, and greater lateral force during residual stance. In results of this study, anterior/posterior forces were consistently directed anteriorly throughout the gait cycle (Figure 1), and did not differ in average value between groups. Differences in findings may due to a combination of differences in methodology and recruited subject pool. Intersegmental joint forces/moments from inverse dynamics underestimate total joint contact forces/moments from muscle-driven simulations, due to the unaccounted for effects of wholebody musculature (Zajac et al., 2002). In addition relative to this work, the recruited subject pool was notably younger with shorter time since amputation and faster self-selected walking speed of ~1.35m/s (Table 3.1). Collective differences between current and former findings suggest that low back biomechanics in individuals with a lower limb amputation are affected by dynamic muscle recruitment, age, time since amputation, and walking speed. This study had several limitations. Firstly, inverse-dynamics based static optimization does not facilitate quantification of individual muscular contributions to whole-body metrics, such as total joint forces and moments. Future work should apply a forward dynamics framework that would enable decomposition of low back joint contact forces into individual muscular contributions (e.g. Sasaki and Neptune, 2010). Secondly, while the upper extremity experimental marker protocol was sufficient to quantify overall low back kinematics, future work may consider using additional instrumentation with greater precision in measuring 73 dynamic, in vivo intervertebral kinematics, such as biplane fluoroscopy (Lin et al., 2014). Lastly, concurrent low back surface EMG was not collected as part of the experimental protocol for comparison against simulated low back muscle activity. However, lower extremity activations agreed well with corresponding EMG prior even to applying optimization constraints. Thus, there is reasonable confidence in low back muscular activity. Future work should supplement experimental lower extremity protocols with low back surface EMG measurements to include erector spinae, external obliques, and rectus abdominus. Ultimately, this study identified abnormal, dynamic biomechanics internal to the low back during walking in individuals with transtibial amputation. These findings contribute to a long-term goal to identify biomechanical mechanisms that elevate LBP susceptibility in individuals with a lower limb amputation, and ultimately to inform effective clinical interventions to rehabilitate biomechanical LBP. As the subject pool for this study excluded individuals with current LBP, the presented data can be leveraged as a baseline in future investigations that may include individuals with LBP and additional group factors of potential interest, such as time since amputation and prosthesis type. The utility of additional low back biomechanical metrics, such as distribution of total forces among passive spinal structures, to distinguish between individuals with/without a lower limb amputation and with/without secondary low back pain should also be investigated. 74 4.CHAPTER 4 SIMULATION AND MODEL DETAILS The generic, whole-body musculoskeletal model (Model Repository v1.6, AnyBody Modeling System v6.0) described in Chapter 3 required further mortifications beyond the scope of the manuscript. In depth details on these modeling and simulation components are discussed in this chapter. 4.1. Additional Musculoskeletal Model Background The lower and upper extremity models are shown in Figure 4.1. The model named “ oCap odel” in the AnyBody odel epository was used as the basis for this work. Modifications to the shank portion of the lower extremity model to represent amputation are shown, including: translation of the center of mass closer to the knee joint, reduction of the total shank mass by 25%, and removal of all ankle-spanning musculature. Also, the virtual marker set was reproduced on the AnyBody model to agree with the experimental protocol (Figure 4.1). For both parts of the model, comprehensive definition of musculature existed in the generic distribution of the repository model. A listing of the modeled muscle groups is provided in Table 4.1 for the upper extremities and Table 4.2 for the lower extremities. Also, a full reporting of individual subject parameters is provided in Table A.1 of Appendix A (expanding on (Table 3.1). 4.2. Simulation Settings & Parameter Optimization For each subject simulation, experimental data files (.c3d) with kinematic and ground reaction forces were imported directly into AnyBody. Timing of gait events for each subject were determined using automated event detection in Visual3D (Stanhope et al., 1990). For inverse kinematics and dynamics simulations, time steps were set equivalent to number of frames 75 (a) (b) (c) Figure 4.1 – The generic musculoskeletal model (MoCapModel, Model Repository v1.6, AnyBody Modeling System v6.0). The lower back model (a) and lower extremity (b) are paired together to allow whole-body simulation. The experimental marker set applied virtually to the model (c). 76 Table 4.1 – Modeled lower extremity muscle groups in generic lower extremity model. Musculature removed in the transtibial amputation version are shaded. Lower Extremity Muscles Adductor Brevis Proximal Gluteus Medius Posterior Adductor Brevis Mid Gluteus Minimus Anterior Adductor Brevis Distal Gluteus Minimus Mid Adductor Longus Gluteus Minimus Posterior Adductor Magnus Distal Gracilis Adductor Magnus Mid Iliacus Lateralis Adductor Magnus Proximal Iliacus Mid Biceps Femoris Caput. Longum Iliacus Medialis Biceps Femoris Caput. Breve Obturator Externus Inferior Extensor Digitorum Longus Obturator Externus Superior Extensor Hallucis Longus Obturator Internus Flexor Digitorum Longus Pectineus Flexor Hallucis Longus Peroneus Brevis Gastrocnemius Lateralis Peroneus Longus Gastrocnemius Medialis Peroneus Tertius Gemellus Inferior Piriformis Gemellus Superior Plantaris Gluteus Maximus Superior Popliteus Gluteus Maximus Inferior PsoasMinor Gluteus Medius Anterior Psoas Major Quadratus Femoris Rectus Femoris Sartorius Proximal Sartorius Distal Semimembranosus Semitendinosus Soleus Medialis Soleus Lateralis Tensor Fasciae Latae Tibialis Anterior Tibialis Posterior Medialis Tibialis Posterior Lateralis Vastus Intermedius Vastus Lateralis Inferior Vastus Lateralis Superior Vastus Medialis Inferior Vastus Medialis Mid Vastus Medialis Superior Table 4.2 – Modeled trunk muscle groups. Number of fascicles per group represent divisions in lines of action to represent muscle with large surface area. Muscle Group Rectus Abdominus Transversus Multifidus Erector Spinae Spinalis Iliocostalis lumborum pars lumborum Ilicostalis lumborum pars thoracis Longissimus thoracis pars lumborum Longissimus thoracis pars thoracis Psoas Major Quadratus Lumborum Obliqus Externus Obliqus Internus Thoracic Multifidi Semispinalis 77 #Fascicles 1 5 19 3 4 5 8 12 10 5 6 6 10 8 between identified start and stop times, coinciding with initial and final ipsilateral heel strike. For model parameter optimization trial runs, prior to inverse kinematics (both static standing and gait trials, for each subject), time increments were set to one-sixth of the motion frames to increase computational efficiency (Andersen et al., 2010b). The model parameter optimization procedure applied in this work is unique to the AnyBody Modeling System. An in-depth description of algorithm development is provided by (Andersen et al., 2010b). Briefly, model parameters that the researcher may have low confidence in can be optimized to obtain a robust inverse kinematic solution that improves dynamic consistency of the model with the measured experimental data; for this work, relative location of virtual motion markers within segment frames, and length of rigid body-segments. For motion markers, any of the three translational degrees of freedom can be held fixed (in directions of high confidence), or be optimized (in directions of least confidence). As an example, consider the left iliac crest marker, shown in Figure 4.2. One may be reasonably confident that the crest is near frontal-plane zero and at a fixed height superior from the anterior superior iliac spine marker. However, the position within the frontal plane may be relatively less certain, due to unknown amounts of soft tissue around the abdomen, with high variability between each individual. Therefore, the marker can essentially be constrained along a line in the frontal plane, by fixing the “X” and “Y” directions, and assigning “Z” to be optimized, as depicted in Figure 4.2. This process is highly useful for shank and thigh cluster markers, where essentially no sense of position relative to bone and joint axes are known with confidence, so all three directions can be optimized (notice the large displacements in these markers before and after optimization, Figure 4.2). Desired segment lengths can also be optimized, and all were in the static standing trial. Lastly, using this process only on the static standing trial to determine all subject parameters to 78 be held fixed for gait, mitigates to some degree potential errors from skin artifact during motion. An example for a representative subject before and after parameter optimization is shown in Figure 4.3. (a) (b) Figure 4.2 –Optimization settings for the iliac crest marker, with green representing the degree of freedom can change, and red representing a fixed condition. Little guidance is offered by the AnyBody developers on specification of optimization settings to optimize a virtual marker set (Andersen et al., 2010b). Custom, standardized optimization settings were developed based upon the experimental protocol, and applied consistently across subjects. These settings are reported in Table C.1 of Appendix C. With subject-specific, optimized parameters determined from the static trial, inverse kinematics solutions were computed as described in the manuscript (Chapter 3). To additionally mitigate error propagation in this step, tracking weights to apply during least-squares difference optimization between virtual and experimental markers were assigned for all subjects as reported in Table C.1 of Appendix C. 79 (a) (b) Figure 4.3 – Example of model parameters (a) before, and (b) after applying the optimization sequence with the optimization settings reported in Table C.1 of Appendix C. For this representative subject, notice in particular the shortening of the thigh and shank segments, and the narrowing of the pelvis. 80 (a) (b) Figure 4.4 – Minimization of marker tracking errors to <20mm, for a representative subject. Results from a static trial (a) indicate how far off markers remain after applied parameter optimization. The relatively higher errors during the gait trial (b) indicate effects of skin artifact and errors associated with modeling assumptions. 81 4.3. Muscle Fiber and Tendon Calibration The implementation of the three element Hill muscle model requires a defined length of the tendon at which force begins to develop upon stretch (tendon slack length). These parameters are defined in the generic model based on the cadaver dataset. However, tendon slack length may also be assumed to vary per individual, and for this work a suggested calibration process was applied to determine these slack lengths. This is done by, after subject specific segment lengths have been optimized and fixed, making an assumption that each muscle group should develop optimal force (or, moment about a joint) in a certain, functional joint position. This calibration process is similar to methods proposed by Delp (1990), for determining tendon slack lengths. Calibration poses and muscle groups calibrated in each pose are defined in Appendix B. 4.4. Joint Angle Conventions Rotational kinematics between the trunk and pelvis segments were computed using an Euler rotation sequence between two marker-based frames Figure 4.5. No clinically-meaningful, anatomical reference frames are defined in the generic model, so custom frames were created based on ISB recommendations (Wu et al., 2005, 2002). The pelvis frame was defined so that the +Z axis ran from the right anterior-superior iliac spine to the left anterior-superior iliac spine, +X axis point anterior along the line from midpoint of the left and right posterior superior iliac spines to the midpoint of the left and right anterior-superior iliac spines, and the +Y axis normal to the XZ plane and pointing superior. The thorax frame was defined so that the +Z axis ran from the left acromion to the right acromion, +Y axis pointing superior along the line from the midpoint of the iliac crests to the midpoint of the acromia, and +X axis normal to the ZY and pointing anterior. Resulting Euler rotation sequence of the local thorax frame relative to the 82 fixed global pelvis was then defined as Z-Y-X for flexion(-)/extension(+), followed by left(+)/right(-) axial rotation, followed by left(-)/right(+) lateral bending. As frames were based on end-position of virtual markers, naturally occurring anatomic tilt or obliquity of the pelvis could cause a static offset in the Euler angle. Therefore, angles during static trials were recorded during the parameter optimization process, and later subtracted from gait angles to normalize kinematics to quiet standing. Figure 4.5 – Representation of frames created to measure thorax 3DOF rotation relative to pelvis. Each frame is based on position of virtual markers in the model, rather than model anatomical landmarks. The L4L5 total joint contact forces were computed within the inverse-dynamics based static optimization framework by resolving translational reaction forces at the 3DOF spherical 83 joint. The effects of all spanning musculature were implicitly accounted for when solving the system equations (2.1). The joint coordinate system is shown in Figure 4.6. Joint contact forces were computed with respect to the proximal segment frame (L5), as forces applied on the distal segment (L4). Figure 4.6 – Joint coordinate system in the L4L5 joint for measurement of total joint contact force. Contact forces are measured with respect to the proximal L5 frame, as forces on the distal L4 body. The red center indicates the estimated, constant center of intervertebral rotation. 4.5. Lower Extremity EMG constraints To develop the lower bound constraints from recorded lower-extremity EMG, a custom MATLAB script was created. The open source MATLAB toolbox c3dserver was used to input analog voltage data from c3d files. Raw signals (1200Hz) were sequentially demeaned, rectified, and bi-directional high pass filtered at 20Hz. A moving RMS 80ms window (using convolution) was then applied to the partially processed data to obtain an envelope. The envelope was bidirectional low pass filtered at 4Hz to obtain a smoothed envelope acceptable as a signal for simulated activation. Lastly, the all envelopes (for all muscle groups, irrespective of fiber twitch composition) was shifted forward in time 15ms (Zajac, 1989) to represent first-order activation dynamics not accounted for in the static optimization framework. Results for a representative 84 subject’s contralateral gluteus medius are shown in Figure 4.7. Complete results for all subject simulated muscle activations compared to original EMG signals are provided in Appendix D. Smoothed and shifted envelopes were resampled for each subject to the necessary time duration corresponding to the gait cycle simulation window. As a final step, each signal was scaled to a realistic muscular activation on a 0.0-1.0 scale. To accomplish this, all static optimization simulations were completed to obtain relative estimates of activity in the muscle group with no constraints. As an initial guess, the maximum occurring voltage value in the gait cycle window was normalized to the maximum observed value in the simulated results, unless that value fell below 0.20, in which case 0.20 was used. Within the AnyBody software, constraints were applied using a parameterized beta spline function, and applied to all muscle fascicles with the muscle group. Figure 4.7 – Processing steps to compute EMG-based lower bound activation constraints, applied to a representative contralateral gluteus medius signal. 85 5.CHAPTER 5 FINITE ELEMENT LUMBAR SPINE GEOMETERY FOR MULTI-SCALE SIMULATION Attempts to perform finite element simulation in combination with muscle-actuated, rigid body dynamic simulation have previously been described in the literature, and have shown potential to facilitate investigations of total joint contact force and moment distribution among passive, structural tissues during realistic activities of daily living. A primary issue in the development of these multi-scale simulations is disagreement in predicted kinematics between the two simulations, due to a mismatch in model constituents. In particular, discrepancies in geometry, and structural parameters (e.g. total passive joint stiffness), can lead to errors (Zhu et al., 2013). Therefore, the purpose of this work was to explore subject-specific scaling of lumbar spine muscle attachments to fit generalized, vertebral geometry for the finite element portion of a multi-scale simulation framework. 5.1. Methods & Results A cadaver-based L1-L5 finite element model constructed from medical imaging data is shown in Figure 5.1. This model was part of a previous aster’s thesis in the Colorado School of Mines Department of Mechanical Engineering, within the Computational Biomechanics Group (Huls, 2010). The model contained all five vertebrae modeled as rigid shells, in addition to facet cartilage at two joint levels, nonlinear ligaments at all levels, and four intervertebral discs. The bone geometry (rigid, quadrilateral shell elements) was extracted and is shown in comparison to the generic bone geometry in the AnyBody lumbar spine model (Figure 5.2). In contrast to the cadaver-based geometry, the AnyBody geometry is based on a single sagittallysymmetric vertebrae, which is duplicated at all five vertebral levels. 86 (a) (b) Figure 5.1 – Cadaver-based L1-L5 finite element model used as the basis for multi-scale simulation work (Huls, 2010), from lateral (a) and frontal (b) views. (a) (b) Figure 5.2 – Bone geometry from the AnyBody model (a, brown) in comparison to the cadaver bone mesh (b, blue). The red spheres in the AnyBody model distinguish approximated, constant intervertebral joint centers. 87 Preliminary, qualitative comparisons of the two spinal geometries suggested significant differences in overall size, along with morphological differences in facets, spinous processes, and transverse processes (Figure 5.2). While such differences would be expected in comparison of any two individuals’ spinal geometry, to establish model correspondence for multi-scale simulation, one spine must be adjusted to agree geometrically with the other. In this case, the AnyBody generic geometry has little physiological basis in comparison to the segmented, cadaver-based geometry. Also, non-affine transformations are needed to achieve shape matching in aspects other than uniform sizing, and application of such transforms (e.g. with skew) to the cadaver mesh had high potential to create non-physiological contact planes in both the facet joints and vertebral endplates. Therefore, adjustments were made to the AnyBody geometry to match the detailed shape of the FE model derived from cadaveric image data. The AnyBody Modeling System (v6.0, Aalborg, Denmark) was used to define and apply geometry-fitting transformations. The AnyBody software implements functions of the open source Visualization Toolkit to create and apply subject-specific, three-dimensional transformations (www.vtk.org). Further information on the general use of this code package as a means to apply medical-imaging based, subject-specific scaling to the AnyBody models is openly available (anybodytech.com, Lesson 3). For this work, a sequence of three consecutive transforms was developed and applied to adjust the generic AnyBody geometry and muscular parameters (e.g. muscle path origins/insertions) to the cadaver geometry (Figure 5.4). For step one, five paired landmarks were identified on each of the L1 superior endplates, and on the L5 inferior endplates (Figure 5.3). These ten landmarks were used to define an affine, rigid-body registration (similarity transform) that relocated the cadaver L1-L5 lumbar vertebrae to the location of the generic AnyBody spine. Uniform sizing of the cadaver spine to the size of 88 the AnyBody spine was also allowed. The outcome of this step before and after performing the transformation is shown in Figure 5.3, and also in Figure 5.4 in preparation for step two. (a) (b) (c) (d) Figure 5.3 – Rigid-body similarity transform for initial alignment (step one). Paired landmark selection on the superior endplate of L1 (a,b), and outcome of transformation (c,d). 89 Step 1 (a) (b) Step 2 (c) (d) Step 3 (e) (f) Figure 5.4 – Representation of three-step sequential transform process. Step one is after the rigid-body similarity transform, step two is after the 25-landmark RBF transform, and step three is after the 1500 auto-seeded landmark STL-based transform. In each image, red landmarks correspond to the generic AnyBody vertebrae, and green landmarks to the cadaver-based vertebrae. 90 For step two, a landmark-based nonlinear radial basis function (RBF) transformation was performed to adjust shape of the AnyBody vertebrae to the cadaver geometry. Seventeen landmarks were identified per vertebrae, focused around the transverse and spinous processes of each vertebral level, where a majority of muscle origins/insertions are defined in the AnyBody model. A representation of the complete, paired sets is shown in Figure 5.4. For step three, a surface-based nonlinear RBF transformation was performed to further fit the shape of matching anatomical regions to one another. This required geometries to be nearly fit to one another through application of steps one and two. The surface-based function implemented in AnyBody automatically seeds a specified number of landmarks on the two geometries, and uses closest-point calculations to determine landmark correspondence. A set of 1500 landmarks was used, and the outcome of the surface fit is shown in step three of Figure 5.4. The implementation of subject-specific scaling functions within the AnyBody software ultimately facilitates adjustment of musculoskeletal model parameters. In terms of a multi-scale simulation framework, this allows semi-automated adjustment of muscle path origins/insertions/via-points (nodes) to fit intended finite element geometry. In the generic AnyBody lumbar model, the three-dimensional locations of muscle nodes are initially defined with respect to the generic, sagittally-symmetric bone geometry. A representation of all muscle nodes within the lumbar region is shown in Figure 5.5. To address the objective of this work, the parameterized transformations were applied simultaneously to all three-dimensional lumbar muscle nodes at each step of the three-step, bone-based transform process. The robustness of this procedure to relocate muscle nodes to the cadaver geometry was assessed for the transverse and spinous processes, as shown in Figure 5.6. The outcome for a representative transverse process (L4 level) following application of each transform step is shown in Figure 5.7. 91 Figure 5.5 – Lumbar muscle nodes in the AnyBody model, compared to target cadaver geometry (blue). All locations were initially defined with respect to the generic bone geometry (brown). Figure 5.6 - Bone geometry from the generic model (brown) and cadaver (blue) aligned after step one rigid-body registration. Anatomical regions of interest for muscle node relocation were the spinous processes (top right) and transverse process (bottom right) at each vertebral level. 92 Step 1 Step 2 Step 3 (a) (b) (c) Figure 5.7 - Comparison of transform methods, applied to AnyBody bone geometry (brown) and muscle nodes (green), performed from left to right additively. From left, rigid body registration, followed by four-landmark radial basis function, followed by automated 1500 landmark surfacebased fitting. Overall, the muscle node relocation procedure was sufficient to move generic node definitions to corresponding, relative locations on the cadaver geometry (Figure 5.7). However, bi-lateral performance in the frontal plane was not comparable. This was due to anatomical variabilty with respect to the sagittal plane. As one example, the left L4 transverse process of the cadaver spine was substantially different form the right transverse process (Figure 5.1). In view of future multi-scale analyses (Figure 1.2), such intrasubject variability would complicate baseline interpretation of outcome metrics by adding model-induced intrasubject variablity to potential, gait strategy intersubject variability. Therefore, baseline sagittaly-symmetric geometry was created using tools within HyperMesh software (Altair Hyperworks, Troy, MI). The L1-L5 vertebral geometry was first split along an approximated, mid-saggital plane. Edges of non-uniformly split elements were adjusted to lie on the resulting mid-saggital profile. The volume morphing tool in HyperMesh was used to make anatomical adjustments representative of an average L1-L5 spine, based on 93 established guidelines from the anatomical literature (Pearcy and Bogduk, 1988; White and Panjabi, 1990). Adjustments primarily included: shape and angle of the transverse process in both the frontal and sagittal planes, and anterior/posterior depth of the vertebral bodies in the frontal plane. The final, generalized bone geometry is shown in Figure 5.9. Generalized facet cartilage was also created at all lumbar joint levels on the right side, using the final bone geometry as a basis. Surface areas of the bone shell mesh to replace with cartilage were visually identified based on established anatomical guidelines (White and Panjabi, 1990). The solid layer extrusion tool was used to generate three-dimensional element layers (quadrilaterals) inward and outward from the bone surface (1.0mm each), as shown in Figure 5.8. Any interference initially created by the outward extrusion was mitigated by translating facet processes away from each other. The volume morphing tool was used to constrain translations to a single plane that was an approximate normal of each facet contact surface. In this way, the anatomically-intended contact behavior was preserved. Right side cartilage at all levels was also mirrored with the bone geometry about the mid-sagittal plane. (a) (b) Figure 5.8 – Representative facet cartilage created at each of the four joint levels. 94 (c) (a) (b) (c) (d) Figure 5.9 - Creation of baseline, sagittally-symmetric spinal geometry. The raw, segmented cadaver mesh is shown in blue (left), and the final, mirrored geometry is shown in green (right). 95 6.CHAPTER 6 GENERAL CONCLUSIONS Ultimately, this body of work identified abnormal low back biomechanics during walking of individuals with a unilateral transtibial amputation. Musculoskeletal modeling and simulation facilitated estimation of in vivo biomechanical parameters that are currently infeasible to measure in a laboratory setting. The findings of this work contribute to a goal within the biomechanical research community to better understand mechanisms that contribute to the development of LBP in individuals with a lower-limb amputation. Knowledge will be disseminated through submittal of Chapter 3 as a manuscript to the journal of Gait & Posture (April 2014). Novel, spinal geometry was also created to enable future, multi-scale finite element and rigid body dynamic simulation. Lastly, the collective biomechanical data, models, and simulations from this thesis work may serve as a baseline in future efforts to use computational tools as part of a patientspecific tool to aid in clinical rehabilitation of patients with biomechanical, musculoskeletal disorders (Figure 1.2). 6.1. Recommendations for Future Research Collective literature findings provided the initial motivation for an investigation of low back biomechanics in individuals with a lower-limb amputation. The three primary outcome metrics were also chosen to facilitate comparisons with previous work and clinical data: trunkpelvis relative kinematics, muscle forces in the low back, and total joint contact force. Small differences between groups were found in these particular three metrics; however, further differences may exist in other biomechanical metrics. For example, a dynamic phase diagram (e.g. trunk-pelvis angle versus hip angle) computed using motion capture data during walking 96 was recently shown to provide a visual description of asymmetric gait strategies between people with/without unilateral hip (Landgraeber et al., 2014). This is an example of a readily interpretable, visual metric that may be useful as an initial patient classification in the diagnosis of biomechanical disorders. Following initial diagnoses, a clinician could indicate a patient for more in-depth, biomechanical evaluation through patient-specific modeling and simulation (Figure 1.2). Also, the subject pool for this study excluded individuals with secondary LBP. Future work should leverage this baseline data to investigate potential effects of additional intersubject parameters on low back biomechanics, such as: age, time since amputation, prosthesis type, self-selected walking speed, static standing trunk-pelvis pose, and current LBP. The current state of computational modeling and simulation in biomechanics is characterized by tradeoffs between time required to develop robust, subject-specific simulations, the computational costs required to run these simulations, and sample size. As computational power continues to increase, these limitations will be mitigated. Future work should consider applying a forward dynamics framework that would allow additional investigations, such as induced acceleration analyses, segment power analyses, and joint contact force decompositions. These analyses quantify individual muscular contributions to low back joint contact forces, measures of low back dynamic stability, and trunk-pelvis kinematics. Lastly, in either a forward or inverse simulation framework, the sensitivity of whole-body, biomechanical outcome metrics to modeling assumptions and inverse kinematics/dynamics error propagation should be further established. A supplemented experimental data collection protocol could also benefit future work. Novel tools with increased precision in kinematic measurement of dynamic, in vivo vertebral body motion have recently been suggested. For example, bi-plane fluoroscopy can detect 97 millimeter-level precision of in vivo vertebral kinematics during motion (Lin et al., 2014). If using whole-body marker motion capture, additional skin markers on the lumbar region and upper extremities should be included, such as described by Armand et al, and Mason et al (both 2014) . Contributions to total body angular momentum from the arms during walking has been found to be as large as 25%, relative to pelvis (2%), thorax (5%), and legs (60%) (Bruijn et al., 2008). As individuals with lower-limb amputation have altered regulation of whole-body balance (Silverman and Neptune, 2011), accounting for the potential effects of arm swing in dynamic simulation is important. Lastly, clinical measures of subject-specific muscle group strengths and endurance, if collected could potentially be useful in making further subjectspecific model adjustments, such as representations of atrophy by adjustment of three-element Hill muscle model parameters. Future, multi-scale finite element and rigid-body dynamics simulation has potential to enable investigations of total lumbar joint contact force and moment distribution among passive soft tissues (intervertebral disc, facet joints, ligaments). However, maintaining model correspondence to avoid model-induced error propagation has been a challenge in past work (Zhu et al., 2013). Three-dimensional, spatial transformations facilitated subject-specific adjustment of generic, lumbar muscle parameters to fit medical-imaging based anatomy, in this work. Future work must investigate further challenges of dynamically communicating necessary model parameters between software packages, such as: motion and load dependent estimates of total intervertebral stiffness from finite element simulation, and dynamic muscle forces from musculoskeletal gait simulation. Lastly, collaborations between the biomechanical research and clinical communities, and discussions of findings such as those presented in this work, will be crucial to future successes in 98 patient-specific rehabilitation and treatment (Figure 1.2). Input from people that work first-hand treating and rehabilitating individuals with a lower limb amputation should become part of the future methods development. This type of cooperation should also lessen the challenge of translating estimated, biomechanical parameters (joint contact forces/moments, forces within muscle groups, trunk-pelvis coordination) to a targeted treatment plan. 99 7.REFERENCES CITED Ackermann, M., van den Bogert, A.J. (2010). "Optimality principles for model-based prediction of human gait." Journal of Biomechanics. 43(6):1055–60. Anders, C., Scholle, H.C., Wagner, H., Puta, C., Grassme, R., Petrovitch, A. (2005). "Trunk muscle coordination during gait: relationship between muscle function and acute low back pain." Pathophysiology. 12(4):243–7. Anders, C., Wagner, H., Puta, C., Grassme, R., Petrovitch, A., Scholle, H.-C. (2007). "Trunk muscle activation patterns during walking at different speeds." Journal of Electromyography and Kinesiology. 17(2):245–52. Andersen, M.S., Benoit, D.L., Damsgaard, M., Ramsey, D.K., Rasmussen, J. (2010a). "Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics." Journal of Biomechanics. 43(2):268–73. Andersen, M.S., Damsgaard, M., MacWilliams, B., Rasmussen, J. (2010b). "A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems." Computer Methods in Biomechanics and Biomedical Engineering. 13(2):171–83. Andersen, M.S., Damsgaard, M., Rasmussen, J. (2009). "Kinematic analysis of over-determinate biomechanical systems." Computer Methods in Biomechanics and Biomedical Engineering. 12(4):371–84. Anderson, F.C., Pandy, M.G. (2001). "Static and dynamic optimization solutions for gait are practically equivalent." Journal of Biomechanics. 34(2):153–61. Andriacchi, T., Natarajan, R., Hurwitz, D. (1997). "Musculoskeletal dynamics, locomotion, and clinical applications." In: Basic Orthopaedic Biomechanics., edited by Mow, V., Hayes, W., Lippincott-Raven Publishers, Philadelphia:37–68. Arendt-Nielsen, L., Graven-Nielsen, T., Svarrer, H., Svensson, P. (1996). "The influence of low back pain on muscle activity and coordination during gait: a clinical and experimental study." Pain. 64(2):231–40. Armand, S., Sangeu , ., Baker, . (2014). "Optimal markers’ placement on the thora for clinical gait analysis." Gait & Posture. 39(1):147–53. Arnold, E.M., Ward, S.R., Lieber, R.L., Delp, S.L. (2010). "A model of the lower limb for analysis of human movement." Annals of Biomedical Engineering. 38(2):269–79. Audu, M. (1985). "Optimal control modeling of lower extremity musculoskeletal motion." PhD Dissertation. Case Western University. Cleveland, Ohio. 100 Becker, J., Stumbo, J. (2013). "Back Pain in Adults." Primary Care and Clinical Practice. 40(1):1–18. Benedetti, M., Catani, F., Leardini, A., Pignotti, E., Giannini, S. (1998). "Data management applications in gait analysis for clinical." Clinical Biomechanics. 13(3):204–215. Bisschop, A., Kingma, I., Bleys, R.L. a W., Paul, C.P.L., van der Veen, A.J., van Royen, B.J., van Dieën, J.H. (2013). "Effects of repetitive movement on range of motion and stiffness around the neutral orientation of the human lumbar spine." Journal of Biomechanics. 46(1):187–91. Bruijn, S.M., Meijer, O.G., van Dieën, J.H., Kingma, I., Lamoth, C.J.C. (2008). "Coordination of leg swing, thorax rotations, and pelvis rotations during gait: the organisation of total body angular momentum." Gait & Posture. 27(3):455–62. Burke, M., Roman, V., Wright, V. (1978). "Bone and joint changes in lower limb amputees." Annals of the Rheumatic Diseases. 37:252–54. Callaghan, J., Patla, A., McGill, S. (1999). "Low back three-dimensional joint forces, kinematics, and kinetics during walking." Clinical Biomechanics. 14(3):203–16. Cappozzo, A., Gazzani, F. (1982). "Spinal loading during abnormal walking." Biomechanics: Principles and Applications. 1:141–8. Christophy, ., Curtin, ., Senan, N., Lotz, J., O’ eilly, O. (2012a). "On the modeling of the intervertebral joint in multibody models for the spine." Multibody System Dynamics. Christophy, ., Senan, N., Lotz, J., O’ eilly, O. (2012b). "A musculoskeletal model for the lumbar spine." Biomechanics and Modeling in Mechanobiology. 11(1-2):19–34. Comerford, M.J., Mottram, S.L. (2001). "Movement and stability dysfunction--contemporary developments." Manual Therapy. 6(1):15–26. Crowninshield, R.D., Brand, R. a. (1981). "A physiologically based criterion of muscle force prediction in locomotion." Journal of Biomechanics. 14(11):793–801. Damsgaard, M., Rasmussen, J., Christensen, S., Surma, E., de Zee, M. (2006). "Analysis of musculoskeletal systems in the AnyBody Modeling System." Simulation Modelling Practice and Theory. 14(8):1100–1111. Dananberg, H. (1993). "Gait style as an etiology to chronic postural pain. Part II. Postural compensatory process." Journal of the American Podiatric Medical Association. 83(11):615–24. De Zee, M., Hansen, L., Wong, C., Rasmussen, J., Simonsen, E.B. (2007). "A generic detailed rigid-body lumbar spine model." Journal of Biomechanics. 40(6):1219–27. 101 Delp, S.L. (1990). "Surgery simulation: A computer graphics system to analyze and design musculoskeletal reconstructions of the lower limb." PhD Dissertation. Stanford University. Stanford, California. Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G. (2007). "OpenSim: open-source software to create and analyze dynamic simulations of movement." IEEE Transactions on Biomedical Engineering. 54(11):1940– 50. Devan, H., Hendrick, P., Ribeiro, D.C., Hale, L.A., Carman, A. (2014). "Asymmetrical movements of the lumbopelvic region: Is this a potential mechanism for low back pain in people with lower limb amputation?" Medical Hypotheses. 82(1):77–85. Deyo, R., Mirza, S., Martin, B. (2006). "Back pain prevalence and visit rates." Spine. 31(23):2724–27. Dillingham, T.R., Pezzin, L.E., MacKenzie, E.J. (2002). "Limb amputation and limb deficiency: epidemiology and recent trends in the United States." Southern Medical Journal. 95(8):875–83. Dreischarf, M., Rohlmann, A., Zhu, R., Schmidt, H., Zander, T. (2013). "Is it possible to estimate the compressive force in the lumbar spine from intradiscal pressure measurements? A finite element evaluation." Medical Engineering & Physics. 35(9):1385–90. Ehde, D.M., Smith, D.G., Czerniecki, J.M., Campbell, K.M., Malchow, D.M., Robinson, L.R. (2001). "Back pain as a secondary disability in persons with lower limb amputations." Archives of Physical Medicine and Rehabilitation. 82(6):731–4. Elftman, H. (1939). "The function of the arms in walking." Human Biology. 11:529–39. Ephraim, P.L., Wegener, S.T., MacKenzie, E.J., Dillingham, T.R., Pezzin, L.E. (2005). "Phantom pain, residual limb pain, and back pain in amputees: results of a national survey." Archives of Physical Medicine and Rehabilitation. 86(10):1910–9. Erdemir, A., Guess, T.M., Halloran, J., Tadepalli, S.C., Morrison, T.M. (2012). "Considerations for reporting finite element analysis studies in biomechanics." Journal of Biomechanics. 45(4):625–33. Erdemir, A., McLean, S., Herzog, W., van den Bogert, A.J. (2007). "Model-based estimation of muscle forces exerted during movements." Clinical Biomechanics. 22(2):131–54. Ferguson, L. (2014). "Adult idiopathic scoliosis: the tethered spine." Journal of Bodywork and Movement Therapies. 18(1):99–111. Ferguson, S.J., Ito, K., Nolte, L. (2004). "Fluid flow and convective transport of solutes within the intervertebral disc." Journal of Biomechanics. 37(2):213–221. 102 Fey, N., Silverman, A., Neptune, R. (2010). "The influence of increasing steady-state walking speed on muscle activity in below-knee amputees." Journal of Electromyography and Kinesiology. 20(1):155–61. Freburger, J.K., Holmes, G.M., Agans, R.P., Jackman, A.M., Darter, J.D., Wallace, A.S., Castel, L.D., Kalsbeek, W.D., Carey, T.S. (2009). "The rising prevalence of chronic low back pain." Archives of Internal Medicine. 169(3):251–8. Fujiwara, A., Lim, T.H., An, H.S., Tanaka, N., Jeon, C.H., Andersson, G.B., Haughton, V.M. (2000). "The effect of disc degeneration and facet joint osteoarthritis on the segmental flexibility of the lumbar spine." Spine. 25(23):3036–44. Gadomski, B.C., Rasmussen, J., Galibarov, P., Puttlitz, C.M. (2011). "The effect of coupled motions and lifting tasks on human lumbar nucleus pressures and annulus fibrosus stresses in a muscle-loaded finite element model." In: ISB Congress XXIII. Brussels, Belgium. Gailey, R., Allen, K., Castles, J., Kucharik, J., Roeder, M. (2008). "Review of secondary physical conditions associated with lower-limb amputation and long-term prosthesis use." The Journal of Rehabilitation Research and Development. 45(1):15–30. Gallagher, S., Marras, W.S. (2012). "Tolerance of the lumbar spine to shear: A review and recommended exposure limits." Clinical Biomechanics. 27(10):973–978. Gandevia, S. (1994). "The sensation of effort co-varies with reflex effects on the motoneurone pool: evidence and implications." International Journal of Industrial Ergonomics. 13:41– 49. Gerritsen, K., Bogert, A., Hulliger, M., Zernicke, R. (1998). "Intrinsic Muscle Properties Facilitate Locomotor Control- A computer Simulation Study." Motor Control. 2:206–220. Goujon-Pillet, H., Sapin, E., Fodé, P., Lavaste, F. (2008). "Three-dimensional motions of trunk and pelvis during transfemoral amputee gait." Archives of Physical Medicine and Rehabilitation. 89(1):87–94. Granata, K.P., Lee, P.E., Franklin, T.C. (2005). "Co-contraction recruitment and spinal load during isometric trunk flexion and extension." Clinical Biomechanics. 20(10):1029–37. Granata, K.P., Marras, W.S. (1993). "An EMG-assisted model of loads on the lumbar spine during asymmetric trunk extensions." Journal of Biomechanics. 26(12):1429–38. Grumillier, C., Martinet, N., Paysant, J., André, J.M., Beyaert, C. (2008). "Compensatory mechanism involving the hip joint of the intact limb during gait in unilateral trans-tibial amputees." Journal of Biomechanics. 41(14):2926–31. 103 Grunhagen, T., Shirazi-Adl, A., Fairbank, J.C.T., Urban, J.P.G. (2011). "Intervertebral disk nutrition: a review of factors influencing concentrations of nutrients and metabolites." The Orthopedic Clinics of North America. 42(4):465–77. Hafner, B.J., Sanders, J.E., Czerniecki, J., Fergason, J. (2002). "Energy storage and return prostheses: does patient perception correlate with biomechanical analysis?" Clinical Biomechanics. 17(5):325–44. Hall, L., Tsao, H., MacDonald, D., Coppieters, M., Hodges, P.W. (2009). "Immediate effects of co-contraction training on motor control of the trunk muscles in people with recurrent low back pain." Journal of Electromyography and Kinesiology. 19(5):763–73. Hamill, J., van Emmerik, R.E., Heiderscheit, B.C., Li, L. (1999). "A dynamical systems approach to lower extremity running injuries." Clinical Biomechanics. 14(5):297–308. Hammarlund, C.S., Carlström, M., Melchior, R., Persson, B.M. (2011). "Prevalence of back pain, its effect on functional ability and health-related quality of life in lower limb amputees secondary to trauma or tumour: a comparison across three levels of amputation." Prosthetics and Orthotics International. 35(1):97–105. Hansen, L., de Zee, M., Rasmussen, J. (2006). "Anatomy and biomechanics of the back muscles in the lumbar spine with reference to biomechanical modeling." Spine. 31(17):1888–1899. Happee, R. (1994). "Inverse dynamic optimization including muscular dynamics, a new simulation method applied to goal directed movements." Journal of Biomechanics. 27(1):953–960. Hebela, N.M., Tortolani, P.J. (2009). "Idiopathic Scoliosis in Adults: Classification, Indications, and Treatment Options." Seminars in Spine Surgery. 21(1):16–23. Hendershot, B.D., Bazrgari, B., Nussbaum, M.A. (2013). "Persons with unilateral lower-limb amputation have altered and asymmetric trunk mechanical and neuromuscular behaviors estimated using multidirectional trunk perturbations." Journal of Biomechanics. 46(11):1907–12. Hendershot, B.D., Nussbaum, M.A. (2013). "Persons with lower-limb amputation have impaired trunk postural control while maintaining seated balance." Gait & Posture. 38(3):438–442. Hendershot, B.D., Wolf, E.J. (2013). "Three-dimensional joint reaction forces and moments at the low back during over-ground walking in persons with unilateral lower-extremity amputation." Clinical Biomechanics. In Press. Holzapfel, G.A., Stadler, M. (2006). "Role of facet curvature for accurate vertebral facet load analysis." European Spine Journal. 15:849–56. 104 Hughes, R., Chaffin, D. (1994). "Evaluation of muscle force prediction models of the lumbar trunk using surface electromyography." Journal of Orthopaedic Research. 12(5):689–98. Huls, K.S. (2010). "A statistical shape model for probabilistic studies of the lumbar spine." aster’s Thesis. Colorado School of ines. olden, Colorado. Iatridis, J., Gwynn, I. (2004). "Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus." Journal of Biomechanics. 37(8):1165–75. Illes, J.D., Maola, C.J. (2012). "Chiropractic management of low back pain in a patient with a transfemoral amputation." Journal of Chiropractic Medicine. 11(3):179–185. Jaegers, S.M., Arendzen, J.H., Jongh, H.J. (1995). "Prosthetic gait of unilateral transfemoral amputees: a kinematic study." Archives of Physical Medicine and Rehabilitation. 76:736– 43. Jones, A.C., Wilcox, R.K. (2008). "Finite element analysis of the spine: towards a framework of verification, validation and sensitivity analysis." Medical Engineering & Physics. 30(10):1287–304. Kalichman, L., Hunter, D.J. (2007). "Lumbar facet joint osteoarthritis: a review." Seminars in Arthritis and Rheumatism. 37(2):69–80. Katz, J.N. (2006). "Lumbar disc disorders and low-back pain: socioeconomic factors and consequences." The Journal of Bone and Joint Surgery American Volume. 88(Suppl.2):21– 4. Khoo, B.C., Goh, J.C., Bose, K. (1995). "A biomechanical model to determine lumbosacral loads during single stance phase in normal gait." Medical Engineering & Physics. 17(1):27–35. Klein Horsman, M.D. (2007). "Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity: Supplementary Web Material." Clinical Biomechanics. 22(2):S1. Klein Horsman, M.D., Koopman, H., van der Helm, F., Prosé, L., Veeger, H. (2007). "Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity." Clinical Biomechanics. 22(2):239–47. Kong, W.Z., Goel, V.K., Gilbertson, L.G. (1998). "Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting." Journal of Biomechanical Engineering. 120(2):273–80. Krueger, C., Wenke, J., Ficke, J. (2012). "Ten years at war: Comprehensive analysis of amputation trends." The Journal of Trauma and Acute Care Surgery. 73(6, Suppl.5):438– 444. 105 Kulkarni, J., Gaine, W.J., Buckley, J.G., Rankine, J.J., Adams, J. (2005). "Chronic low back pain in traumatic lower limb amputees." Clinical Rehabilitation. 19(1):81–6. Kunze, M., Schaller, A., Steinke, H., Scholz, R., Voigt, C. (2012). "Combined multi-body and finite element investigation of the effect of the seat height on acetabular implant stability during the activity of getting up." Computer Methods and Programs in Biomedicine. 105(2):175–82. Kurutz, M. (2010). "Finite Element Modeling of the Human Lumbar Spine." In: Finite Element Analysis., edited by Moratal, D., InTech, Online Open Access:209–36. Lamoth, C., Beek, P., Meijer, O. (2002a). "Pelvis-thorax coordination in the transverse plane during gait." Gait & Posture. 16(2):101–14. Lamoth, C., Daffertshofer, A., Meijer, O., Beek, P. (2006a). "How do persons with chronic low back pain speed up and slow down? Trunk-pelvis coordination and lumbar erector spinae activity during gait." Gait & Posture. 23(2):230–9. Lamoth, C., Meijer, O., Daffertshofer, A., Wuisman, P., Beek, P. (2006b). "Effects of chronic low back pain on trunk coordination and back muscle activity during walking: changes in motor control." European Spine Journal. 15(1):23–40. Lamoth, C., Meijer, O., Wuisman, P. (2002b). "Pelvis-thorax coordination in the transverse plane during walking in persons with nonspecific low back pain." Spine. 27(4):E92–99. Landgraeber, S., Rosenthal, D., Jager, M., Kecskemethy, A., Kowalczyk, W. (2014). "A new method for gait data analysis of human hip diseases." In: Annual Proceedings of the American Academy of Orthopaedic Surgeons. New Orleans, LA. Lee, R., Turner-Smith, A. (2003). "The influence of the length of lower-limb prosthesis on spinal kinematics." Archives of Physical Medicine and Rehabilitation. 84(9):1357–1362. Leinonen, V., Kankaanpää, M. (2000). "Back and hip extensor activities during trunk flexion/extension: effects of low back pain and rehabilitation." Archives of Physical Medicine and Rehabilitation. 81:32–7. Lin, C., Lu, T., Wang, T., Hsu, C., Shih, T. (2014). "Comparisons of surface vs. volumetric model-based registration methods using single-plane vs. bi-plane fluoroscopy in measuring spinal kinematics." Medical Engineering & Physics. 36(2):267–74. Luoto, S., Heliijvaara, M., Hurri, H., Alaranta, H. (1995). "Static back endurance low-back pain and the risk of low-back pain." Clinical Biomechanics. 10(6):323–324. Mason, D.L., Preece, S.J., Bramah, C.A., Herrington, L.C. (2014). "Reproducibility of kinematic measures of the thoracic spine, lumbar spine and pelvis during fast running." Gait & Posture. In Press. 106 Mattes, S.J., Martin, P.E., Royer, T.D. (2000). "Walking Symmetry and Energy Cost in Persons With Unilateral Transtibial Amputations : atching Prosthetic and Intact Limb Inertial Properties." Archives of Physical Medicine and Rehabilitation. 81:561–568. Menegaldo, L.L., Fleury, A.D.T., Weber, H.I. (2003). "Biomechanical modeling and optimal control of human posture." Journal of Biomechanics. 36(11):1701–1712. Meyns, P., Bruijn, S.M., Duysens, J. (2013). "The how and why of arm swing during human walking." Gait & Posture. 38(4):555–62. Michaud, S.B., Gard, S.A., Childress, D.S. (2000). "A preliminary investigation of pelvic obliquity patterns during gait in persons with transtibial and transfemoral amputation." Journal of Rehabilitation Research and Development. 37(1):1–10. Morgenroth, D., Orendurff, M., Shakir, A., Segal, A., Shofer, J., Czerniecki, J. (2010). "The relationship between lumbar spine kinematics during gait and low-back pain in transfemoral amputees." American Journal of Physical Medicine and Rehabilitation. 89(8):635–43. Morgenroth, D., Shakir, A. (2009). "Low-back pain in transfemoral amputees: is there a correlation with static or dynamic leg-length discrepancy?" American Journal of Physical Medicine and Rehabilitation. 88(2):108–13. Nelson-Wong, E., Alex, B., Csepe, D., Lancaster, D., Callaghan, J.P. (2012). "Altered muscle recruitment during extension from trunk flexion in low back pain developers." Clinical Biomechanics. 27(10):994–998. Nelson-Wong, E., Gregory, D.E., Winter, D. a, Callaghan, J.P. (2008). "Gluteus medius muscle activation patterns as a predictor of low back pain during standing." Clinical Biomechanics. 23(5):545–53. Neptune, R.R., Kautz, S.A., Zajac, F.E. (2001). "Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking." Journal of Biomechanics. 34(11):1387–98. Pandy, M. (2001). "Computer modeling and simulation of human movement." Annual Review of Biomedical Engineering. 3:245–73. Panjabi, M.M. (1992). "The stabilizing system of the spine. Part I. Function, dysfunction, adaptation, and enhancement." Journal of Spinal Disorders. 5(4):383–9. Panjabi, M.M. (2003). "Clinical spinal instability and low back pain." Journal of Electromyography and Kinesiology. 13(4):371–379. Pearcy, M., Bogduk, N. (1988). "Instantaneous axes of rotation of the lumbar intervertebral joints." Spine. 13(9):1033–41. 107 Popovich, J.M., Welcher, J.B., Hedman, T.P., Tawackoli, W., Anand, N., Chen, T.C., Kulig, K. (2013). "Lumbar facet joint and intervertebral disc loading during simulated pelvic obliquity." The Spine Journal. 13(11):1581–9. Rasmussen, J., de Zee, M., Carbes, S. (2009). "Validation of a biomechanical model of the lumbar spine." In: ISB Congress XXII. Cape Town, South Africa. Rohlmann, A., Bauer, L., Zander, T., Bergmann, G., Wilke, H.J. (2006). "Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data." Journal of Biomechanics. 39(6):981–9. Rubin, D. (2007). "Epidemiology and risk factors for spine pain." Neurologic Clinics. 25:353– 71. Rueda, F., Diego, I., Sánchez, A., Tejada, M., Montero, F., Page, J.C. (2013). "Knee and hip internal moments and upper-body kinematics in the frontal plane in unilateral transtibial amputees." Gait & Posture. 37(3):436–9. Russell, E.M., Whitehead, J.M.A., Wilken, J.M. (2013). "Transfemoral amputation alters pelvistrunk coordination during walking: implications for low back pain." In: 2013 Meeting of the American Society of Biomechanics. Omaha, Nebraska:#90. Sadeghi, H., Allard, P., Duhaime, P.M. (2001). "Muscle power compensatory mechanisms in below-knee amputee gait." American Journal of Physical Medicine & Rehabilitation. 80(1):25–32. Sagawa, Y., Turcot, K., Armand, S., Thevenon, A., Vuillerme, N., Watelain, E. (2011). "Biomechanics and physiological parameters during gait in lower-limb amputees: a systematic review." Gait & Posture. 33(4):511–26. Salzberg, L. (2012). "The physiology of low back pain." Primary Care and Clinical Practice. 39:487–98. Sasaki, K., Neptune, R.R. (2010). "Individual muscle contributions to the axial knee joint contact force during normal walking." Journal of Biomechanics. 43(14):2780–4. Sato, K., Kikuchi, S., Yonezawa, T. (1999). "In vivo intradiscal pressure measurement in healthy individuals and in patients with ongoing back problems." Spine. 24(23):2468–74. Schendel, M.J., Wood, K.B., Buttermann, G.R., Lewis, J.L., Ogilvie, J.W. (1993). "Experimental measurement of ligament force, facet force, and segment motion in the human lumbar spine." Journal of Biomechanics. 26(4-5):427–38. Schmidt, H., Kettler, A., Heuer, F., Simon, U., Claes, L., Wilke, H.J. (2007). "Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading." Spine. 32(7):748–55. 108 Schwarzer, A., Aprill, C., Derby, R., Fortin, J., Kine, G. (1994). "The Relative Contributions of the Disc and Zygapophyseal Joint in Chronic Low Back Pain." Spine. 19(7):801–6. Seay, J., Selbie, W., Hamill, J. (2008). "In vivo lumbo-sacral forces and moments during constant speed running at different stride lengths." Journal of Sports Sciences. 26(14):1519– 29. Seay, J.F., Van Emmerik, R.E. a, Hamill, J. (2011). "Low back pain status affects pelvis-trunk coordination and variability during walking and running." Clinical Biomechanics. 26(6):572–8. Selles, R.W., Wagenaar, R.C., Smit, T.H., Wuisman, P.I. (2001). "Disorders in trunk rotation during walking in patients with low back pain: a dynamical systems approach." Clinical Biomechanics. 16(3):175–81. Silfies, S.P., Squillante, D., Maurer, P., Westcott, S., Karduna, A.R. (2005). "Trunk muscle recruitment patterns in specific chronic low back pain populations." Clinical Biomechanics. 20(5):465–73. Silverman, A., Fey, N., Portillo, A., Walden, J., Bosker, G., Neptune, R. (2008). "Compensatory mechanisms in below-knee amputee gait in response to increasing steady-state walking speeds." Gait & Posture. 28(4):602–9. Silverman, A., Neptune, R. (2012). "Muscle and prosthesis contributions to amputee walking mechanics: a modeling study." Journal of Biomechanics. 45(13):2271–8. Silverman, A.K., Neptune, R.R. (2011). "Differences in whole-body angular momentum between below-knee amputees and non-amputees across walking speeds." Journal of Biomechanics. 44(3):379–85. Skrzypiec, D.M., Bishop, N.E., Klein, A., Püschel, K., Morlock, M.M., Huber, G. (2013). "Estimation of shear load sharing in moderately degenerated human lumbar spine." Journal of Biomechanics. 46(4):651–7. Smith, D., Ehde, D., Legro, M., Reiber, G. (1999). "Phantom limb, residual limb, and back pain after lower extremity amputations." Clinical Orthopaedics and Related Research. 361:29– 38. Stanhope, S., Kepple, T., McGuire, D., Roman, N. (1990). "A Kinematic-Based Technique for Event Time Determination During Gait." Medical and Biological Engineering and Computing. 28:355–60. Taylor, N., Goldie, P., Evans, O. (2004). "Movements of the pelvis and lumbar spine during walking in people with acute low back pain." Physiotherapy Research International. 9(2):74–84. 109 Teo, E.C., Lee, K.K., Ng, H.W., Qiu, T.X., Yang, K. (2003). "Determination of load transmission and contact force at facet joints of L2-L3 motion segment useing FE method." Journal Of Musculoskeletal Research. 7(2):97–109. Thelen, D.G., Anderson, F.C. (2006). "Using computed muscle control to generate forward dynamic simulations of human walking from experimental data." Journal of Biomechanics. 39(6):1107–15. Thelen, D.G., Anderson, F.C., Delp, S.L. (2003). "Generating dynamic simulations of movement using computed muscle control." Journal of Biomechanics. 36(3):321–328. Toosizadeh, N., Haghpanahi, M. (2011). "Generating a finite element model of the cervical spine: Estimating muscle forces and internal loads." Scientia Iranica. 18(6):1237–1245. Tsirakos, D. (1997). "Inverse optimization: functional and physiological considerations related to the force-sharing problem." Critical Reviews in Biomedical Engineering. 25(4-5):371–407. Umberger, B.R. (2008). "Effects of suppressing arm swing on kinematics, kinetics, and energetics of human walking." Journal of Biomechanics. 41:2575–85. Umberger, B.R. (2010). "Stance and swing phase costs in human walking." Journal of the Royal Society: Interface. 7(50):1329–40. Van der Schans, C.P., Geertzen, J.H.B., Schoppen, T., Dijkstra, P.U. (2002). "Phantom pain and health-related quality of life in lower limb amputees." Journal of Pain and Symptom Management. 24(4):429–36. Van Dieën, J., Cholewicki, J., Radebold, A. (2003). "Trunk muscle recruitment patterns in patients with low back pain enhance the stability of the lumbar spine." Spine. Van Dieën, J.H., Selen, L.P.J., Cholewicki, J. (2003). "Trunk muscle activation in low-back pain patients, an analysis of the literature." Journal of Electromyography and Kinesiology. 13(4):333–351. Van Tulder, M., Koes, B., Bombardier, C. (2002). "Low back pain." Best Practice & Research Clinical Rheumatology. 16(5):761–775. Vogt, L., Pfeifer, K., Portscher, M., Banzer, W. (2001). "Influences of nonspecific low back pain on three-dimensional lumbar spine kinematics in locomotion." Spine. 26(17):1910–1919. Voinescu, M., Soares, D.P., Natal Jorge, R.M., Davidescu, a, Machado, L.J. (2012). "Estimation of the forces generated by the thigh muscles for transtibial amputee gait." Journal of Biomechanics. 45(6):972–7. 110 Wagner, D.W., Divringi, K. (2010). "Combined musculoskeletal dynamics/structural finite element analysis of femur physiological loads during walking." Multidiscipline Modeling in Materials and Structures. 6(4):417–437. White, A., Panjabi, M. (1990). "Clinical biomechanics of the spine, 2nd ed." J.B. Lippincott Company, Philadelphia, PA. Wilke, H.J., Neef, P., Caimi, M., Hoogland, T., Claes, L. (1999). "New in vivo measurements of pressures in the intervertebral disc in daily life." Spine. 24(8):755–762. Winter, D., Sienko, S. (1988). "Biomechanics of below-knee amputee gait." Journal of Biomechanics. 21(5):361–67. Winter, D.A. (2009). "Biomechanics and motor control of human movement, 4th ed." Wiley & Sons, Hoboken, New Jersey. Wong, C., Rasmussen, J., Simonsen, E., Hansen, L., de Zee, M., Dendorfer, S. (2011). "The Influence of Muscle Forces on the Stress Distribution in the Lumbar Spine." The Open Spine Journal. 3:21–26. Wu, G., Siegler, S., Allard, P., Kirtley, C., Leardini, A. (2002). "ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion. Part I: ankle, hip, and spine." Journal of Biomechanics. 35:543–48. Wu, G., van der Helm, F.C.T., Veeger, H.E.J., Makhsous, M., Van Roy, P., Anglin, C., Nagels, J., Karduna, A.R., McQuade, K., Wang, X., Werner, F.W., Buchholz, B. (2005). "ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion. Part II: shoulder, elbow, wrist and hand." Journal of Biomechanics. 38(5):981–992. Yamada, K. (1971). "A neurological approach to the etiology and treatment of scoliosis." Journal of Bone and Joint Surgery. 53A:197. Yin, L., Elliott, D.M. (2005). "A homogenization model of the annulus fibrosus." Journal of Biomechanics. 38(8):1674–84. Zajac, F.E. (1989). "Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control." Critical Reviews in Biomedical Engineering. 17(4):359– 410. Zajac, F.E., Neptune, R.R., Kautz, S. a. (2002). "Biomechanics and muscle coordination of human walking. Part I: introduction to concepts, power transfer, dynamics and simulations." Gait & Posture. 16(3):215–32. 111 Zajac, F.E., Neptune, R.R., Kautz, S.A. (2003). "Biomechanics and muscle coordination of human walking: part II: lessons from dynamical simulations and clinical implications." Gait & Posture. 17(1):1–17. Zhu, R., Zander, T., Dreischarf, M., Duda, G.N., Rohlmann, A., Schmidt, H. (2013). "Considerations when loading spinal finite element models with predicted muscle forces from inverse static analyses." Journal of Biomechanics. 46(7):1376–8. Ziegler-Graham, K., MacKenzie, E.J., Ephraim, P.L., Travison, T.G., Brookmeyer, R. (2008). "Estimating the prevalence of limb loss in the United States: 2005 to 2050." Archives of Physical Medicine and Rehabilitation. 89(3):422–429. Zmitrewicz, R.J., Neptune, R.R., Sasaki, K. (2007). "Mechanical energetic contributions from individual muscles and elastic prosthetic feet during symmetric unilateral transtibial amputee walking: a theoretical study." Journal of Biomechanics. 40(8):1824–1831. 112 8. APPENDIX A SUBJECT PARAMETERS Table A.1 – Parameters of subjects selected for simulation. Time from Height Weight Amputation Subject1 Age Gender (cm) (kg) (years) Diagnosis Foot Type NonAmp1 39 M 176.5 57.2 NonAmp2 55 M 172.7 65.8 NonAmp3 28 F 180.3 66.5 NonAmp4 43 M 167.6 97.1 NonAmp5 23 M 186.7 61.7 NonAmp6 24 M 173.4 83.5 TTA1 40 M 182.9 115.2 6 Trauma ESAR TTA2 37 M 179.1 94.8 5 Trauma SACH TTA3 39 F 157.5 79.8 5 Trauma SACH TTA4 46 M 167.6 85.7 4 Traumatic SACH TTA5 42 M 177.8 96.2 3 Traumatic SACH TTA6 58 M 177.2 73.5 7 Traumatic ESAR 1 Prefi es “C” and “V” distinguish non-amputees, and “ ” distinguishes individuals with unilateral, transtibial amputation. 113 9.APPENDIX B HILL MUSCLE TENDON/FIBER CALIBRATION The six calibration poses used to determine tendon slack length for each individual are shown. Lower extremity joint angles defining the pose are also listed. Each subsequent pose overwrites the results of the previous poses for any included muscles. Muscle groups calibrated in each pose are listed under the corresponding image. Note that the visual behavior of the muscles in these images is purely a graphical artifact of the GUI. Knee = (-) extension (+) flexion Ankle = (-) plantarflexion (+) dorsiflexion Subtalar = (-) inversion (+) eversion Hip Ad/Ab = (-) ad (+) ab Hip ext/int = (-) int (+) ext Hip flex/ext = (-) extension (+) flexion 114 Ankle = 0 Subtalar = 0 Knee = 0 Hip Ad/Ab = 0 Hip ext/int = 0 Hip flex/ext = 0 Ankle = 10 Subtalar = 0 Knee = 0 Ankle = -20 Subtalar = 0 Knee = -70 Hip Ad/Ab = 0 Hip ext/int = 0 Hip flex/ext = 0 Ankle = +10 Hip Ad/Ab = 0 Subtalar = -20 Hip ext/int = 10 Knee = -50 Hip flex/ext = -60 Ankle = -5 Subtalar = 0 Knee = -80 Hip Ad/Ab = -10 Hip ext/int = 0 Hip flex/ext = -50 Ankle = +10 Hip Ad/Ab = 0 Subtalar = 0 Hip ext/int = 0 Knee = 0 Hip flex/ext = -35 115 Hip Ad/Ab = 0 Hip ext/int = 0 Hip flex/ext = -50 10. APPENDIX C PARAMETER OPTMIZATION AND MARKER TRACKING SETTINGS Table C.1 – Settings applied in the AnyBody parameter optimization process, and inverse kinematics solution Marker right anterior illiac spine left anterior illiac spine left posterior illiac spine right posterior illiac spine left illiac crest right illiac crest C7 vertebrae left acromion right acromion left lateral malleoli right lateral malleoli right medial malleoli left medial malleoli right dorsal foot right 5th metatarsal right 1st metatarsal right 2nd distal phalange left dorsal foot left 5th metatarsal left 1st metatarsal left 2nd distal phalange right heel left heel right lateral knee left lateral knee right medial knee left medial knee right greater trochanter left greater trochanter * ALL SHANK/THIGH CLUSTERS Translational DOF x y z Off Off Off Off Off Off On Off Off On Off Off Off Off On Off Off On Off Off Off Off Off On Off Off On Off Off Off Off Off Off Off Off Off Off Off Off On On On Off Off On Off Off On Off Off Off On On On Off Off On Off Off On Off Off Off Off Off Off Off Off Off Off Off Off Off Off Off Off On Off Off On Off Off Off Off Off Off Off Tracking Weight Wx Wy Wz 15.0 15.0 15.0 15.0 15.0 15.0 5.0 5.0 5.0 5.0 5.0 5.0 1.0 5.0 1.0 1.0 5.0 1.0 10.0 10.0 10.0 5.0 5.0 1.0 5.0 5.0 1.0 1.0 1.0 5.0 1.0 1.0 5.0 7.0 1.0 7.0 7.0 1.0 7.0 1.0 1.0 1.0 1.0 5.0 1.0 1.0 5.0 1.0 1.0 1.0 5.0 1.0 1.0 1.0 1.0 5.0 1.0 1.0 5.0 1.0 1.0 1.0 5.0 5.0 1.0 5.0 5.0 1.0 5.0 10.0 1.0 10.0 10.0 1.0 10.0 10.0 1.0 10.0 10.0 1.0 10.0 1.0 1.0 1.0 1.0 1.0 1.0 On 1.0 On 116 On 1.0 1.0 11. APPENDIX D LOWER EXTREMITY EMG VALIDATION Each figure represents comparison of simulated lower extremity muscle activities against the original raw EMG signals. The y-axes for each figure is plotted as force in Newtons, and xaxes are percent residual limb gait cycle. On a single muscle group subplot, each distinct curve represents a separate modeled fascicle (e.g. muscles with large surface areas were modeled as many fascicles). The titles are subject tags corresponding to Table A.1. Subplot titles are formatted with (muscle group name)_(side); where “side” is either ipsilateral (IPSI) or contralateral (CONT). Raw EMG signals are plotted in the shaded subplots directly below each muscle group subplot. 117 NonAmp1 NonAmp2 118 NonAmp3 NonAmp4 119 NonAmp5 NonAmp6 120 TTA1 TTA2 121 TTA3 TTA4 122 TTA5 TTA6 123