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Med. Eng. Phys. Vol. Published IX. No. 7. pp. 569-574, I996 by Elsetier Science Ltd for IPEMB Printed in Great Britain PII: S13504533(96)00013-6 1X0-4.533196 $15.00 + 0.00 ELSEVIER Finite element spine unit N. Yoganandan, Department of Veterans Received modeling of the U-C6 S. C. Kumaresan, Liming Voo, F. A. Pintar and S. J. Larson of Neurosurgery, Medical College Affairs Medical Center, Milwaukee, 25 October cervical 1995, revised 18 December 1995, accepted of Wisconsin and the Department Wisconsin, USA 22 January 1996 ABSTRACT This study was conducted to develop a &tailed, three-dimensional, anatomically accurateJnite element model of the human cervical spine structure using closeup computed tomography scans and to validate against experimental data. Thefinite element model of the three vertebra segment C&C6 unit consisted of 9178 solid elements and 1193 thin shell elements. The forcedisplacement response under axial compression correlated well with expen’mental data. Because of the inclusion of three levels in the spinal structure, it was possible to determine the internal mechanics of the various components at each level. The applicability of the model was illustrated by adopting a#o@iate material properties from literature. Results indicated that, the stresses in the anterior column were higher compared to the posterior column at the infm’or level, white the opposite was found to be true at the superior level. The superior and infa’or endplate stresses were higher in the middle vertebral body compared to the adjacent vertebrae. In addition, the stresses in the cancellous core of the middle, unconstrained vertebral body were higher. The present three dimensional finite element model off em an additional facet to a better understanding of the biomechanics of the human cervical spine. Published by Elsevier Science Ltd for IPEMB. Keywords: Finite element Med. 1996, BACKGROUND Eng. Phys., method, Vol. cervical 18, 569-574, AND LITERATURF, spine, computed tomography, stress analysis October REVIEW Finite element methods of structural analysis were introduced in 1956l. The first application for the method was in the aircraft industry. One of the early a plications of the finite element technique to me cfical and biological problems was to analyse the dynamics of cardiovascular pulsatile flow in .1969l. The use of this technique to understand the behavior of the human spinal column was initiated in 1973 by Liu and Ray. Since then, there have been a plethora of finite element applications to the human low back*. In contrast, little research work has been done using the principles of the finite element technique to analyse the biomechanics of the human cervical spine. The earlier finite element models treated the cervical columns as simple rigid masses connected by beam and spring elements representing the intervertebral discs; ligaments; facet joints; and muscles. Simple rigid masses for the cervical vertebrae do not produce realistic responses. Hosey and Liu’s finite element model of the head-neck did not include the cervical posterior components, and the geometrical features such as the Correspondence to: Professor N. Yoganandan, Medical College of Wisconsin, Department of Neurosurgery, MCW Clinic at FM1.H. 9200 West Wisconsin Avenue, Milwaukee, WI 53226, USA. orientation of the disc from the anterior to the posterior and the uncinate processes’. The detailed models are by Bozic et aZ.; Kleinberger; Saito et aZ,; and Teo et ~1.~~ Bozic et al. created a finite element model of the mid cervical vertebra from a 66 year old human cadaver specimen based on computed tomography (CT) images. The actual geometry of the C4 vertebra was represented by 8590 isoparametric eight-noded brick elements. The modulus of the elasticity was based on the CT density. Traumatic loading was simulated by applying an axial compressive displacement of 4 mm through the 221 linear spring elements attached to the superior vertebral body surface such that the applied force was 3400 N. This applied force was determined from the analysis (as cited in the article). The restraint boundary was provided by 241 linear spring elements in the inferior direction. The total stiffness of the springs at the superior and inferior directions approximated the stiffness of the intervertebral disc (500 N/mm). In addition, restraints were applied in the medial, lateral and anteroposterior directions by using springs of low stiffnesses (60 N/mm). Using maximum shear stress theory, the model predicted the initiation of failure in the central cancellous core. This finding of potential failure in the central regions of the body corre- Cervical spine finite element model: N. Yoganandan et al. lates well with the findings from lumbar intervertebral joint studies (under axial compressive loading), wherein micro-trauma initiates at the central regions of the vertebral endplate as observed fluoroscopically and in cryomicrotome images, and derived from the biomedical stiffnessdeflection responses7-g. Despite the detailed finite element modeling, the isolated vertebra model has limited applications in the study of the biomechanics of the cervical column. In another investigation, Teo et aZ., developed a finite model of the second cervical vertebra (CZ) using an unembalmed adult human cadaver spine6. A coordinate measuring machine extracted the data for the finite element input. The model consisted of 328 isoparametric brick and triangle prism solid elements at 972 nodes. Material properties were obtained from literature. The vertebra was made of cortical bone and ignored the cancellous bone. Spring elements were introduced to simulate the effects of transverse ligaments; the disc; and the superior and inferior articulating facets. A force of 1 kN was applied at orientations of zero, 45” and -45” in the sagittal plane; it was distributed over a 50 mm* area on the anterior articulating surface of the dens in the anteroposterior direction. For the zero degree (e.g., head impact with windshield with an upright neck), the posterior junction at the lateral edges between the base of the odontoid process and the vertebral body and the inner lateral edges of the superior facets, experienced the highest compressive stress. For this case, maximum tensile stress occurred at the mid sagittal surface at the base of the odontoid process. With the force applied at 45” (e.g., a head impact with the neck in extension), maximum tensile stress occurred in the posterior outer lateral sides of the body and the localized compressive stress occurred on the surface of the applied force. In contrast, the force applied at an angle of -45” (e.g., boxing), resulted in high compressive stress at the posterior surface of the dens and inner lateral edges of the superior facets; the maximum tensile stress occurred at the junction of the dens and the vertebral body. Saito et al. constructed a finite element model of the ligamentous cervical column (occiput/COT2) to study the cervical deformity secondary to laminectomy5. The model simplified the vertebral geometry by dividing the spine into four sagittal slices. The first slice consisted of the spongiosa, the endplates of the bodies from Cl to T2, annulus fibrosus, and the nucleus pulposus of the discs; the laminae; the spinous processes; the anterior and posterior longitudinal ligaments; the ligamentum flavum; and the interspinous and supraspinous ligaments. The second slice consisted of the cortices of the vertebral bodies (C2-T2) and the articular facets, The third slice included the transverse processes and the intertransverse ligaments. The fourth slice simulated the lower part of the cranium and cortex of the atlas. Spanning element theory was used to connect these twodimensional slices. The lower region of T2 was fixed. TI-UP superior part of the lower cranium was 570 unconstrained in the cranio-caudal direction and restrained in the anteroposterior direction, Linear elastic material properties from literature were used. A load of 150 N applied between the hypophysial fossa and anterior to the Cl-C2 facet induced a slight displacement. The loading was repeated 13 times at the same location on the displaced model to produce a gradual deformity. A total of 1607 elements for the post laminectomy model and 1743 for the normal model were used. This model is suitable for the study of gross responses of the whole cervical column rather than the local changes at the individual spinal levels. Owing to its over-simplification of the vertebral geometry and the intervertebral joints, the load-sharing and stress distributions predicted by the model may not be realistic. Further, the model is limited to sagittal plane simulation. In a more recent study, Kleinberger developed a three-dimensional finite element model of the ligamentous cervical spine coupled with a rigid head to study the biomechanics of neck injury*. The complex anatomic structures were simplified to a combination of regularly shaped blocks such as cylinders, rectangles, and wedges. The superior and inferior surfaces of the vertebral bodies were flat. All facet angles were assumed to be 45”. The cervical lordosis was simulated by adjusting the angle between the vertebrae. Interspinous ligaments were replaced by supraspinous ligaments. The posterior and anterior disc heights were 4 mm and 5.3 mm, respectively. The material properties of the discs and the facet joints were identical. Anterior and posterior longitudinal ligaments, supraspinous ligament and ligamentum flavum were included. The effects of the capsular ligament were included in the definition of the facet joint. Cervical lordosis was maintained and Tl was fixed. Motion of the occipital condyles was constrained to z-translation (the right .handed Cartesian system of reference was used with Sx, +y and +z directions oriented along the posterior to anterior, right to left lateral and inferior to superior axes, respectively) without rotation. Lin‘ear elastic material properties were used. Loading conditions for the two simulations included the following: A 200 ms distributed pressure ramp was applied to the superior surfaces of the occipital condyles. This resulted in a total vertical force (zdirection) of 250 N. The resulting axial stiffness compared favorably with literature’&‘“. The second simulation consisted of a 10 mm axial displacement applied to Cl to determine the large strain response. The model predicted shear displacements agreed with earlier results1°-13. Currently, this is the most comprehensive finite element model of the cervical spine. As the vertebrae are considered to be rigid, material properties are linear and isotropic, and representation of the cervical spine anatomy such as the orientation of the facet joints is based on assumed geometry; the finite element model predictions are only a first approximation. The foregoing review on the finite element models of the cervical spine clearly highlights the potential of the finite element technique to inves- Cemcal spinefinite ekmrnt model: et al. A’, Yoganandan tigate the biomechanics of the human cervical spine. These studies also underscore the importance and the complexity of simulating a structure such as the human cervical spine. The above described models lack the important anatomic features, such as the articular facet variation at different spinal levels and the saddle-shapes of the superior and inferior surfaces of the cervical vertebral bodies; and, the application is limited to mostly sagittal gross motions. In other words, none of the existing cervical spine models possess the necessary detailed representation of the cervical anatomy for the study of the biomechanical responses such as the stress distribution among under real-world intervertebral components force vectors. PURPOSE A realistic model which incorporates the actual geometry and appropriate material data, and which is validated against experimental results, is of use in safety engineering and clinical medicine. For example, the model can be used to determine stress-distributions, i.e., relative contributions of each spinal component in resisting the external force vector. This output cannot be obtained easily from an experimental study. The model can also identify potential failure regions. The present study was designed to develop a detailed, threedimensional anatomically accurate finite element model of the C4-C6 human cervical spine structure using close-up CT scans and validate against of the experimental results. The applicability finite element model has been illustrated by analysing the stress distributions in the various compoems of the spinal structure. MATERIALS AND METHODS To obtain the geometrical data required for the finite element model, the cervical spine (Occiput/CO-Tl) was isolated from a 33 year old female unembalmed human cadaver. Medical records were reviewed and pre-radiography was performed to ensure the absence of bony abnormalities, spine disease or trauma. Anteroposterior, lateral and oblique radiographs were taken. The specimen was positioned in a Styrofoam container. The specimen was aligned along the anatomical axes with respect to the exterior surfaces of the container. The twodimensional sagittal and coronal CT images were obtained using a CT scanner (General Electric Model: High-Speed Advantage, Waukesha, Wisconsin, USA). They were processed using an edge-detection algorithm to extract accurate outlines of the vertebral cross-sections. By suitably combining the coronal and sagittal slices across the entire anteroposterior and leftto-right cross-sections, the solid model (for the C4-C5-C6 cervical spine structure) was developed according to the principles of three-dimensional reconstruction’4. Eight-noded isoparametric elements were chosen for the cancellous bone; transverse processes; pedicles; laminae; spinous processes; and the intervertebral discs. Thin shell Figure 1 Finite element model of the three vertebra (CPC5-C6) cervical spinal segment. The oblique frontal view demonstrates the W-5 (top) and C5-6 (bottom) discs along with the adjacent vertebral bodies (C4: top; C5: middle; C6: bottom) and the posterior elements. The arrow indicates the superior portion of the G-6 disc near the inferior endplate of the C5 vertebral body elements (1 mm thickness) were used to simulate the cortical shell and the endplates. RESULTS The finite element model of the three-segment C4-6 cervical spinal unit consisted of 9178 solid elements and 1193 thin shell elements, resulting in a total of 10 371 elements (Figure 1). Table 1 includes the material property data used in the present study. The model was validated against in vitro experimental results under axial compression. As no experimental tests were conducted in this research, data from other sources were used to define the material property information. For example, Kleinberger’s study was used to define the intervertebral disc, and Saito’s study was used to define the cortical shell and endplate characteristics4,5. The response was obtained by applying uniform axial compression at the top Table 1 Material properties used in the study Description Young’s modulus MPa Poisson’s ratio Cortical bone (5) Cancellous bone (5) Posterior elements (17) Disc - anulus (4) Disc - nucleus (4) Endplate (5) 10000 100 3500 3.4 3.4 500 0.29 0.29 0.29 0.40 0.49 0.40 Note: Numbers in parentheses denote material property data were obtained. the references from which the 571 Gruical S@W finite eknent model: N. Yoganandan et al. nodes of the model, i.e., at C4; the inferior nodes of C6 were constrained. In other words, the superior nodes of the C4 vertebral body endplate and the other components of the vertebra were displaced along the vertical direction. These boundary conditions simulated the exFerimenta1 setup reported in the Shea et al. study 5. For the applied uniform axial compressive displacement at C4, the resulting vertical reaction force at C6 was computed from the finite element analysis and this force corresponding to the applied displacement was compared with the experimental results. The finite element model forcedisplacement response shown in Figure 2 correlated well with the experimental response of Shea et aZ.15. Because of the inclusion of three levels in the spinal structure, it was possible to determine the internal mechanics of the various components at each level. Stresses were analysed to determine the biomechanical behavior of the spine under an axial compressive displacement of 1 .O mm applied to the superior nodes of the C4 vertebra of the model with the inferior nodes of the C6 vertebra constrained. Stresses in the anterior column (vertebral body-disc medium) were higher at the inferior level compared to the superior level (Figure 3~). In contrast, stresses in the posterior column (structure posterior to the body of vertebra) were higher at the superior intervertebral joint level compared to its inferior counterpart. Minimum principal compressive stresses in the middle vertebral body cancellous core were consistently higher compared to the stresses in the superior or inferior vertebral bodies (Figure 3b). Furthermore, von Mises, stresses in the endplates demonstrated a higher magnitude in the middle vertebral body compared to the proximal and distal cervical vertebrae (Figure 3~). 3 0 EZB 2 2 E E m 1 0 Anterior Experiment 0 FE Model Column Posterior Figure 3a Bar chart representation the anterior and posterior column Column of the relative stresses contribution of 1.5 c4 Figure 0 -L, C4-c5 C5-C6 3b Vertebral body c5 C6 stresses T 0 B -0.2 0.0 0.2 0.4 0.6 0.6 1.0 1.2 Displacement (mm) Figure 2 Comparison of the model output with the experimental data”. Open squares correspond to the finite element output and open circles correspond to the experimental data as reported by Shea et al. in their three-segment cervical spine axial loading study. Notice a good match between the experimental outcome and the finite element model output 572 C4 hf. c5 sup. C5 hf. C6 Sup Endplate Fiie 3c C6 superior Stresses in the C4 inferior; endplates C5 superior and inferior; and Cmvical DISCUSSION The objective of the study was to develop a detailed three-dimensional finite ,element model of the human cervical spinal structure using actual human cadaver data from CT scanned images. Both sagittal and coronal plane CT scans were used. All the important anatomic features of the cervical spine vertebrae such as the facet articulation surfaces, uncinate processes and the spinal canal were clearly defined in our model. The direct computerized process of the CT data reliably preserves the accurate topography of the original structure that is to be replicated. Principles of linear structural analysis were used in this study. It is well known that the human cervical spine is a structure with material and geometrical non linearities. Understanding the response with the linearity assumption is a first step in the process. Furthermore, the spine resists static, dynamic and fatigue loads under physiologic and traumatic situations. Our model can be extended to study the behavior under these loading situations. It should be emphasized that the principal focus of the present investigation was to develop an accurate three-dimensional model of the human cervical spine structure based on actual geometry measured from in &JO type scans (e.g., CT scans). The model was analysed under a single physiologic loading vector (axial compression) to illustrate the feasibility of our modeling technique. In the present study, the finite element model computed force-deformation responses agreed closely with experimental results of Shea et al.“. As expected, the stress distributions demonstrated - .._--_--Figure ing 4 Stress distribution pattern in the superior spine finite element model: IV. Yoganandan et al. variations indicating differences in the load-carrying capacities in the components of the cervical spine (F&ZLW 3). Because of the presence of the adjacent vertebra together with the two interconnecting intervertebral discs, and the unconstrained nature of the middle vertebra simulating a realistic physiologic situation, the present finite element model should provide better realistic biomechanical variables (e.g., stress distribution) compared to the earlier research wherein a single vertebra was used 3*6. Results from these earlier studies may be confounded due to the ‘endeffects secondary to the assumed boundary restraints at the two end surfaces of the vertebra during the execution of the finite element model. The output stress distribution in the spinal components provide insight into the internal mechanics of the cervical spine (Figure 4). The increases in the endplate stresses in the middle vertebral body may indicate a plausible mechanism of the initiation of failure from this component under compressive loads. In fact, this has been experimentally verified in lumbar functional spinal unit studies which have reported that, under axial loading, although the disc is more flexible, microtrauma initiates in the endplate resulting in a loss of integrity of the structure7s8. Furthermore, the increase in the stresses in the middle vertebral body (C5) compared to the adjacent vertebrae (C4 and C6) maysbe secondary to the inward bending (towards the vertebral centrum) of both the superior and inferior endplates of the mid-body 16. This phenomenon which occurs in viuo cannot be described using a single vertebra/vertebral body. The unconstrained, . surface of the cervical \ertehral ho+ and posterior elements under- aria1 compressivr load- 573 Cervical spine@ite element model: N. Yoganandan et al. more physiologic middle intervertebral joint can-. not be incorporated in a single-level functional unit (C4-5 or C5-6) model. From this viewpoint, the three vertebrae-two disc model is a better approximation to the spinal response than a single-level (two vertebrae-one disc) functional unit. The role of the posterior column with respect to the anterior column in terms of resisting the external load was also demonstrated by the finite element model. It should be emphasized that these results cannot be obtained by any single experimental study and consequently, the present finite element model offers an additional facet to a better understanding of the biomechanics of the human cervical spine. 6. 7. 8. 9. Analysis and prevention of spinal column deformity following cervical laminectomy, pathogenetic analysis of post laminectomy deformities. Spine 1991, 16: 494-502. Teo EC, Paul JP, Evans JH. Finite element stress analysis of a cadaver second cervical vertebra. h4ed and Biol Eng and Comput 1994, 32: 236238. Yoganandan N, Ray G, Pintar FA, Myklebust JB, Sances A, Jr. Stiffness and strain energy criteria to evaluate the threshold of injury to an intervertebral joint. J Biomech 1989; 22(2): 135-142. Yoganandan N, Maiman DJ, Pintar FA, Ray G, Myklebust JB, Sances A, Jr, Larson SJ. Microtrauma in the lumbar spine: a cause of low back pain. Neurosurm 1988; 23(2): 162-168. Yoganandan N, Larson SJ, Gallagher M, Pintar FA, Reinartz J, Droese K. Correlation of microtrauma in the lumbar spine with intraosseous pressures. Spine 1994; 19(4): 435-440. ACKNOWLEDGEMENT This study was supported in part by the PHS CDC R49-CCR 507370, DOT NHTSA Grant DTNH2293-Y-17028, and the Department of Veterans Affairs Medical Research Service. This research was presented in part at the ASME Bioengineering Conference, Beaver Creek, CO, June 1995. REFERENCES 1. Yoganandan N, Myklebust JB, Ray G, Sances A, Jr. Mathematical and finite element analysis of spinal injuries. CRC Review Biomed Eng 1987; 15(l): 29-93. 2. Hosey RR, Liu YK. A homeomorphic finite element model of the human head and neck. In RH Gallagher, BR Simon, PC Johnson, JF Gross, (Eds) . Finite Edits in Biomechanics, John Wiley & Sons, New York, 1982, pp. 379-401. 3. Bozic KJ, Keyak JH, Skinner HB, Bueff HU, Bradford DS. Three-dimensional finite element modeling of a cervical vertebra: an investigation of burst fracture mechanism. J Spinal Disorders 1994; 7(2): 102-110. 4. Kleinberger M. Application of finite element techniques to the study of cervical spine mechanics. In Proc 37th Stapp Car Crash Co@ Society of Automotive Engineers, Inc., San Antonio, TX, 1993. 5. Saito T, Yamamuro T, Shikata J, Oka M, Tsutsumi S. 574 10. Myers BS, McElhaney JH, Richardson WJ, Nightingale RW, Doherty BJ. The influence of end condition on human cervical spine injury mechanism, In Proc 35th %a@ Car Crash Con& Society of Automotive Engineers, Inc., San Diego, CA, 1991. 11. Pintar FA, Yoganandan N, Sances A, Jr, Reinartz J, Harris G, Larson SJ. Kinematic and anatomical analysis of the human cervical spinal column under axial loading. SAE Transactions 1990; 98(6): 17661789. 12. Yoganandan N, Pintar FA, Arnold P, Reinartz J, Cusick JF, Maiman DJ, Sances A, Jr. Continuous motion analysis of the head-neck complex under impact. J Spinal Dism 1994; 7(3): 420-428. 13. Yoganandan N, Sances A, Jr, Pintar FA. Biomechanical evaluation of the axial compressive responses of the human cadaveric and manikin necks. JBiomech Eng 1989; ill(3): 250-255. 14. Voo L, Denman J, Kumaresan S, Yoganandan N, Pintar FA, Cusick. Development of 3-D finite model of the cervical spine. Adu Bioeng 1995; 31: p. 13-14. 15. Shea M, Edwards WT, White AA III, Hayes WC. Variations of stiffness and strength along the human cervical spine. J Bionuxh 1991; 24(2): 95-107. 16. Sherk HH, Dunn EJ, Eismont FJ, FieldingJW, Long DM, Ono K, Penning L, Raynor R. The Cervical Spine. Second Edition. JB Lippincott Co. Philadelphia, PA, 1989, p. 881. 17. Shirazi-Ad1 SA, Ahmed AM, Shrivastava SC. A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. J Biomech 1986; 19(4): 331-350. 本文献由“学霸图书馆-文献云下载”收集自网络,仅供学习交流使用。 学霸图书馆(www.xuebalib.com)是一个“整合众多图书馆数据库资源, 提供一站式文献检索和下载服务”的24 小时在线不限IP 图书馆。 图书馆致力于便利、促进学习与科研,提供最强文献下载服务。 图书馆导航: 图书馆首页 文献云下载 图书馆入口 外文数据库大全 疑难文献辅助工具