上颈椎（C0-C3）有限元模型建立及寰椎生物力学有限元分析
|
摘要
目的：利用三维有限元方法(Three-dimensional Finite Element Method FEM)建立上颈椎(C0-C3)的三维有限元模型,并验证该模型的有效性；通过此模型对寰椎进行初步的生物力学分析。
方法：选取一名健康成年男性例行体检资料,于山西省人民医院影像科利用德国SIEMENS公司的Somatom Sensation64超高速64层螺旋CT机,以层厚0.6mm进行连续颈部扫描得到断层数据图片,以DICOM格式输出并保存；将DICOM格式CT数据图片导入医学三维重建软件MIMICS中进行处理,得到表面几何模型,以LIS格式导入到ANSYS ICEM CFD10.0前处理软件中,经过光滑处理,生成三维实体,并确定单元类型及赋予材料属性,得到实体模型。然后将实体模型导入到ANSYS10.0有限元软件中,生成上颈椎三维有限元模型。分别在整个上颈椎模型中以及单独将寰椎模型提取出的两类条件下,分析头颅位于中立位、屈曲位以及后伸位等条件下寰椎不同部位所受应力的情况。
结果：建立C0-C3的有限元模型共110105个节点,91469个单元,通过应力分析头颅不论位于中立、前屈、后伸位时,寰椎前弓受力最大,其次是后弓及侧块。
结论：(1)本研究所建的C0-C3的有限元模型外观逼真,几何相似性好,可以用来进行生物力学研究。(2)寰椎在遭受外力作用时,无论头颅位于屈曲位、中立位或者后伸位,当受纵向作用力时,首先引起的是寰椎前弓的骨折；如外力足够大或持续时间足够长,将导致Jefferson骨折产生。单纯后弓骨折是由于头部过度后伸,在上关节面受轴向压力同时,寰椎后弓受到枕骨或枢椎棘突的作用,应力集中于后弓薄弱点所致。
Objective:To construct and validate a three-dimensional upper cervical vertebrae (C0-C3) finite element model and make the first biomechanics analysis to atlas using this model.
Methods:We obtained the CT data from a healthy adult man for the regularly health examination. He was checked by radioactive and clinical examination and was proved that he has not any spinal disease. Then his cervical spine was scanned by Siemens Somatom Sensation 64 with 0.6mm thickness without any interval. We get the CT images and save the data with DICOM format. Then the CT images were inputted to the Materialise Mimics and product a 3D surface image of C0-C3 by selecting image, preconditioning and remeshing tools. The 3D image wad inputted to the ANSYS ICEM CFD10.0 with STL format and became a 3D entity, And the element type and material properties were defined at the same time. The 3D entity was inputted to the FEA software-ANSYS10.0, Based on the model of atlas and holo-model of upper cervical vertebrae(C0-C3), The stress of different position of atlas were analyzed when the skull was in neutral, flexion and posterior extension position.
Result:The model of C0-C3 was composed of 110105 node points and 91469 elements. Through the stress analysis, no matter which position the skull was, the largest Von Mises stress focused on the anterior arch and the smaller was on the posterior arch and lateral masses.
Conclusion:(1) This three-dimensional upper cervical vertebrae (C0-C3) finite element model had similar appearance with reality and can be used for biomechanical study. (2) The axial loading will cause the anterior arch fracture first no matter what position including flexion, median position or posterior extension of the head is. Enough loading or over long time of loading will beget the Jefferson's fracture; The causes for single posterior arch fractures include back extension of head, axial compression on superior joint, atlas posterior arch being pushed upward by occipital bone or axis'spinous and the stress concentrating on the Achille's heel of atlas posterior arch.
方法：选取一名健康成年男性例行体检资料,于山西省人民医院影像科利用德国SIEMENS公司的Somatom Sensation64超高速64层螺旋CT机,以层厚0.6mm进行连续颈部扫描得到断层数据图片,以DICOM格式输出并保存；将DICOM格式CT数据图片导入医学三维重建软件MIMICS中进行处理,得到表面几何模型,以LIS格式导入到ANSYS ICEM CFD10.0前处理软件中,经过光滑处理,生成三维实体,并确定单元类型及赋予材料属性,得到实体模型。然后将实体模型导入到ANSYS10.0有限元软件中,生成上颈椎三维有限元模型。分别在整个上颈椎模型中以及单独将寰椎模型提取出的两类条件下,分析头颅位于中立位、屈曲位以及后伸位等条件下寰椎不同部位所受应力的情况。
结果：建立C0-C3的有限元模型共110105个节点,91469个单元,通过应力分析头颅不论位于中立、前屈、后伸位时,寰椎前弓受力最大,其次是后弓及侧块。
结论：(1)本研究所建的C0-C3的有限元模型外观逼真,几何相似性好,可以用来进行生物力学研究。(2)寰椎在遭受外力作用时,无论头颅位于屈曲位、中立位或者后伸位,当受纵向作用力时,首先引起的是寰椎前弓的骨折；如外力足够大或持续时间足够长,将导致Jefferson骨折产生。单纯后弓骨折是由于头部过度后伸,在上关节面受轴向压力同时,寰椎后弓受到枕骨或枢椎棘突的作用,应力集中于后弓薄弱点所致。
Objective:To construct and validate a three-dimensional upper cervical vertebrae (C0-C3) finite element model and make the first biomechanics analysis to atlas using this model.
Methods:We obtained the CT data from a healthy adult man for the regularly health examination. He was checked by radioactive and clinical examination and was proved that he has not any spinal disease. Then his cervical spine was scanned by Siemens Somatom Sensation 64 with 0.6mm thickness without any interval. We get the CT images and save the data with DICOM format. Then the CT images were inputted to the Materialise Mimics and product a 3D surface image of C0-C3 by selecting image, preconditioning and remeshing tools. The 3D image wad inputted to the ANSYS ICEM CFD10.0 with STL format and became a 3D entity, And the element type and material properties were defined at the same time. The 3D entity was inputted to the FEA software-ANSYS10.0, Based on the model of atlas and holo-model of upper cervical vertebrae(C0-C3), The stress of different position of atlas were analyzed when the skull was in neutral, flexion and posterior extension position.
Result:The model of C0-C3 was composed of 110105 node points and 91469 elements. Through the stress analysis, no matter which position the skull was, the largest Von Mises stress focused on the anterior arch and the smaller was on the posterior arch and lateral masses.
Conclusion:(1) This three-dimensional upper cervical vertebrae (C0-C3) finite element model had similar appearance with reality and can be used for biomechanical study. (2) The axial loading will cause the anterior arch fracture first no matter what position including flexion, median position or posterior extension of the head is. Enough loading or over long time of loading will beget the Jefferson's fracture; The causes for single posterior arch fractures include back extension of head, axial compression on superior joint, atlas posterior arch being pushed upward by occipital bone or axis'spinous and the stress concentrating on the Achille's heel of atlas posterior arch.
引文
1 Jefferson G. Fractures of the atlas vertebrae. Report of four cases, and a review of those previously recorded [J]. Br J Surg,1920,7:407-422
2 Yoganadan N,Kumaresan S,Voo L,et al. Finite element applications in human cervical spine modeling(Review) [J]. Spine,1996,21 (15):1824-1834
3 Panjabi MM. Cervical spine models for biomechanical research[J].Spine,1998,23 (24):2684-2700
4 Yang KH, Zhu F, Luan F, et al. Development of a finite element model of the human neck[R]. Proceeding of the 42nd Stapp Car Crash Conference. SAE983157,1998,1-11
5 Jost R, Nuriek GN. Development of a finite element model of the human neck subjected to high g-level deceleration[J]. Int J Crashworthiness,2000,5:259-267
6 Karin B, Peter H. Development of a finite element mod el of the upper cervical spine an d a parameter study of ligament characteristics[J]. Spine, 2004,29(4):376-385
7 Yoganandan N, Kumaresan S, Voo L, et al. Finite element applications in human cervical spine modeling[J]. Spine,1996,21:1824-1834
8 Ha SK. Finite element modeling of multi-level cervical spinal segments(C3-C6) and biomechanical analysis of an elastomer-type prosthetic disc[J]. Med Eng Phys 2006; 28 (6):534-541
9 Ng HW, Teo EC, Lee VS. Statistical factorial analysis on the material property sensitivity of the mechanical responses of the C4-C6 under compression, anterior and posterior shear [J]. Biomech 2004;37 (5):771-777
10 夏虹,张美超,赵卫东,等.寰椎三维有限元模型的建立及其骨折机制[J].中华创伤杂志,2004,20(4)：209-212
11 Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine:A material property sensitivity study [J]. Clin Biomech,1999,14:41-53
12 夏虹.上颈椎外科疾患的解剖学与生物力学研究及临床治疗：[博士学位论文].广州：第一军医大学,2002
13 强华,贾连顺.上颈椎损伤的诊断和治疗进展[J].骨与关节损伤杂志,2000,15(1)：73-75
14 Jefferson G. Fractures of the first cervical vertebra[J]. Br Med,1927,2:153-157
15 Panjabi MM, Oda T, Crisco Ⅲ JJ, et al. Experimental study of atlas injuries I:Biomechanical analysis of their mechanisms and fracture patterns [J]. Spine,1991,16(Suppl 10):S460-S465
16 Landelis CD, Van Peteghem PK. Fractures of the atlas:classification, treatment and morbidity[J]. Spine,1987,13:450-452
17 Levine AM, Edwards CC. Treatment of injuries in the C1-C2 complex. Orthopedic Clinic of North America,1986,17:31-44
18 Segal LS, Grimm JO, Stauffer ES. Nonunion of fractures of the atlas [J]. Bone Joint Surg, 1987,69-A:1423-1434
19 An H, Simpson JM(eds). Surgery of the Cervical Spine [J]. Baltimore:Willianms & Wilkins.1994.235
20 Vaccaro AR, Colter JM. Traumatic injuries of the adult upper cervical spine. In:An HS, Simpson JM (eds). Surgery of the Cervical Spine. London:Martin Dunitz,1994.227-266
21 Brekelmans WAM, Rybicki EF, Burdeaux BD. A new method analysis the mechanical behavior of skeletal parts [J]. Acta Ortho Scand,1972,43:301-305
22 Rybicki EF, Yang KH. On the mathematical an analysis of stress in the human femur [J]. Biomech,1972,5:203-207
23 Saito T, Yamamuro T, Shikata J, et al. Analysis and prevention of spinal column deformity following cervical laminectomy, pathogenetic analysis of post laminectomy deformities [J]. Spine,1991,16:494-502
24 Kleinberger M. Application of finite element techniques to the study of cervical spine mechanics [A].37th Stapp Car Crash Couf Proe [C]. USA:SAE International.1993.261-272
25 Teo EC, Paul JP, Evans JH. Finite-element stress-analysis of a cadaver 2nd cervical vertebra [J]. Med Biol Eng Comput.1994,32(2):236-238
26 Bozic KJ, Keyak JH, Skinner HB. et al.3-dimensional finite-element modeling of a cervical vertebra-an investigation of burst fracture mechanism [J]. J Spinal Disord,1994,7(2):102-110
27 Yoganandan N, Kumaresan S, Voo L. Finite element model of the human lower cervical spine:Parametric analysis of the C4-C6 unit[J]. J Biomech Eng,1997,119(1):87-92
28 Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine:A material property sensitivity study [J]. Clin Biomech,1999,14:41-53
29 Maurel N, Lavaste F, Skalli W. A three-dimensional parameterized finite element model of the lower cervical spine:Study of the influence of the posterior articular facets [J]. J Biomech, 1997,30(9):921-931
30 Gnel VK, Clausen JD. Prediction of load sharing among spinal components of a C5-C6 motion segment using the finite element approach [J]. Spine,1998:23(6):684-691
31 Wang H, Hu B, Bai J. Computational analysis of two atlantoaxial fixation methods[A].5th IFAC Sym Model Cont Biomed Syst [C]. England:Pergamon Pr.2003.175-178
32 Punjabi MM, Oda T, Crisco JJ, et al. Experimental study of atlas injuries I:Biomechanical analysis of their mechanism and fracture patterns. Spine,1991,16(10 Suppl):S460-465
33 Teo EC, Ng HW. First cervical vertebra (atlas) fracture mechanism studies using finite element method [J]. Biomech,2001,34(1):13-21
34 Beckner MA, Heggeness MH, Doherty BJ. A biomechanical study of Jefferson Fractures[J]. Spine,1998,23(17):1832-1836
35 韩珂.寰枢椎三维有限元模型的建立及寰椎生物力学的有限元分析：[硕士学位论文]湖南：中南大学,2007
36 廖穗祥,夏虹,昌耘冰,等.上颈椎三维有限元模型的建立.中国组织工程研究与临床康复,2007,11(27)：5269-5272
37 付裕,阮狄克.颈椎生物力学中的三维有限元分析.中国脊柱脊髓杂志,2004,14(10)：632-635
38 张昊,白净.颈椎有限元模型的建立方法与进展.国外医学生物医学工程分册,2005,28 (4)：198-201
39 袁野.Hangman骨折相关有限元分析及临床治疗：[博士学位论文].广州：第一军医大学,2006
40 张美超.有限单元法在骨科生物力学中的应用：[博士学位论文].广州：第一军医大学,2002
[1]Brekelmans WAM, Rybicki EF, Burdeaux BD。A new method analysis the mechanical behavior of skeletal parts[J]. Acta Orthop Scand,1972,43:301-305.
[2]Rybicki EF, Yang KH. On the mathematical an analysis of stress in the human femur[J]. Biomech,1972,5:203-207.
[3]Goel VK, Gilbertson LG. Spine update:An applications of the finite element method to thoracolumbar spinal research-past, present and future, Spine,1995,20:1719-1727.
[4]Yoganandan N, Kum aresan S, V oo LM, etal, Finite element model of the human lower cervical spine:parametric analysis of the C4 - C6 unit. [J] Biomech Eng.1997,119:87.
[5]Wu JS, Chen JH. Clarification of the mechanical behaviour of spinal motion segments though a three-dimensional poroelastic mixed finite element model. Med Eng Phys,1996,18: 215.
[6]Miclau T, Martin RE. The evolution of modern plate osteosynthesis[J]. Injury,1997,28: SA3-6.
[7]Yoganandan N, Kumaresan S, Voo L, etal. Finite element modeling of the C4--6 cervical spine unit[J]. Med Eng Phys,1996,18(7):569 -574.
[8]Yang KH, Zhu F, Luan F, etal. Development of a finite element model of the human neck[R]. Proceeding of the 42nd Stapp Car Crash Conference. SAE983157,1998,1-11.
[9]Jost R, Nuriek GN. Development of a finite element model of the human neck subjected to high g-level deceleration[J]. Int J Crashworthiness,2000,5:259 -267.
[10]Karin B, Peter H. Development of a finite element mod el of the upper cervical spine an d a parameter study of ligament characteristics[J]. Spine,2004,29(4):376-385
[11]陈伯华,孙鹏,Natarajan N, etal.颈椎三维有限元模型的建立及意义[J].中国脊柱脊髓杂志,2002,12(2)：105-108.
[12]Bay BK, Yerby SA, McLain RF, etal. Measurement of strain distributions within vertebral body sections by texture correlation [J]. Spine,1999,24:10.17
[13]Whyne CM, Hu SS, Klishc S, etal. Effect of the pedicle and posterior arch on vertebral body strength predictions in finite element modeling[J]. Spine,1998,23(8):899-950.
[14]Smit TH,, Odgaard A, Schneider E. Structure and function of vertebral trabecular bone[J]. Spine,1997,22(24):2823-2828.
[15]silva MJ, Keaveny, ITM, Hayes Wc. load sharing between the shell and centrum in the lumbar vertebral body[J]. Spine,1997,22:140-150
[16]Cao KD, Grimm MJ, Yang KH. ad sharing within a human lumbar vertebral body using the finite element method[J]. Spine,20o1,26:E253 - E260.
[17]Goel VK, Clausen JD. Prediction of load sharing among spinal components of a C5-C6 motion segment using the finite element approach[J]. Spine,1998,23:684-691.
[18]Ng Hw, Teo EC, Lee KK, etal. Finite element analysis of cervical spinal instability under physiologic loading [J]. Journal of Spinal Disorders and Techniques,2003,16:55-65.
[19]Lu YM, Hutton MC, Gharpuray YM. Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse? a viacoelastic finite element model [J]. Spine,1996, 21:257O-2579.
[20]Natarajan RN, Andersson GBJ. The influence of lumbar disc height an d cross-sectional area on the mechanical国外医学生物医学工程分册2003年第26卷第6期response of the disc tophysiologic loading [J]spine,1999,24:1873-1881.
[21]Gole VK, Monroe BT, Gilbertson LG etal. Inter laminar shear stresses and laminae separation in a disc-finite element analysis of the L3 - L4 motion segment subjected to axial compressive loads[J]。Spine,1995,20(5):689-698.
[22]Voo LM, Kumaresan S, Yoganan dan N, etal. Finite element analysis of cervical facetectomy[J]. Spine,1997,22(9):964-969.
[23]Lu YM, Hutton WC, Gharpuray VM. Can variations in intervetebral disc heighter affect the mechanical function of the disc?[J]. Spine,1996.21(19):2208-2216.
[24]Voo LM, Kumaresan S, Yoganandan N, etal. Finite element analysis of cervical facetectomy[J]. Spine,1997,22:964-969.
[25]Lim TH, Kwon H, Joen CH, etal. Effect of endplate conditions and bone mineral density on the compressive strength of the graft-endplate interface in anterior cervical spine fusion[J]. Spine,2001,26:951-956.
[26]Lim TH, Eck JC, An HS, etal. Biomechanics of transfixation in pedicle screw instrumentation [J]. Spine,1996,21:2224-2229.
2 Yoganadan N,Kumaresan S,Voo L,et al. Finite element applications in human cervical spine modeling(Review) [J]. Spine,1996,21 (15):1824-1834
3 Panjabi MM. Cervical spine models for biomechanical research[J].Spine,1998,23 (24):2684-2700
4 Yang KH, Zhu F, Luan F, et al. Development of a finite element model of the human neck[R]. Proceeding of the 42nd Stapp Car Crash Conference. SAE983157,1998,1-11
5 Jost R, Nuriek GN. Development of a finite element model of the human neck subjected to high g-level deceleration[J]. Int J Crashworthiness,2000,5:259-267
6 Karin B, Peter H. Development of a finite element mod el of the upper cervical spine an d a parameter study of ligament characteristics[J]. Spine, 2004,29(4):376-385
7 Yoganandan N, Kumaresan S, Voo L, et al. Finite element applications in human cervical spine modeling[J]. Spine,1996,21:1824-1834
8 Ha SK. Finite element modeling of multi-level cervical spinal segments(C3-C6) and biomechanical analysis of an elastomer-type prosthetic disc[J]. Med Eng Phys 2006; 28 (6):534-541
9 Ng HW, Teo EC, Lee VS. Statistical factorial analysis on the material property sensitivity of the mechanical responses of the C4-C6 under compression, anterior and posterior shear [J]. Biomech 2004;37 (5):771-777
10 夏虹,张美超,赵卫东,等.寰椎三维有限元模型的建立及其骨折机制[J].中华创伤杂志,2004,20(4)：209-212
11 Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine:A material property sensitivity study [J]. Clin Biomech,1999,14:41-53
12 夏虹.上颈椎外科疾患的解剖学与生物力学研究及临床治疗：[博士学位论文].广州：第一军医大学,2002
13 强华,贾连顺.上颈椎损伤的诊断和治疗进展[J].骨与关节损伤杂志,2000,15(1)：73-75
14 Jefferson G. Fractures of the first cervical vertebra[J]. Br Med,1927,2:153-157
15 Panjabi MM, Oda T, Crisco Ⅲ JJ, et al. Experimental study of atlas injuries I:Biomechanical analysis of their mechanisms and fracture patterns [J]. Spine,1991,16(Suppl 10):S460-S465
16 Landelis CD, Van Peteghem PK. Fractures of the atlas:classification, treatment and morbidity[J]. Spine,1987,13:450-452
17 Levine AM, Edwards CC. Treatment of injuries in the C1-C2 complex. Orthopedic Clinic of North America,1986,17:31-44
18 Segal LS, Grimm JO, Stauffer ES. Nonunion of fractures of the atlas [J]. Bone Joint Surg, 1987,69-A:1423-1434
19 An H, Simpson JM(eds). Surgery of the Cervical Spine [J]. Baltimore:Willianms & Wilkins.1994.235
20 Vaccaro AR, Colter JM. Traumatic injuries of the adult upper cervical spine. In:An HS, Simpson JM (eds). Surgery of the Cervical Spine. London:Martin Dunitz,1994.227-266
21 Brekelmans WAM, Rybicki EF, Burdeaux BD. A new method analysis the mechanical behavior of skeletal parts [J]. Acta Ortho Scand,1972,43:301-305
22 Rybicki EF, Yang KH. On the mathematical an analysis of stress in the human femur [J]. Biomech,1972,5:203-207
23 Saito T, Yamamuro T, Shikata J, et al. Analysis and prevention of spinal column deformity following cervical laminectomy, pathogenetic analysis of post laminectomy deformities [J]. Spine,1991,16:494-502
24 Kleinberger M. Application of finite element techniques to the study of cervical spine mechanics [A].37th Stapp Car Crash Couf Proe [C]. USA:SAE International.1993.261-272
25 Teo EC, Paul JP, Evans JH. Finite-element stress-analysis of a cadaver 2nd cervical vertebra [J]. Med Biol Eng Comput.1994,32(2):236-238
26 Bozic KJ, Keyak JH, Skinner HB. et al.3-dimensional finite-element modeling of a cervical vertebra-an investigation of burst fracture mechanism [J]. J Spinal Disord,1994,7(2):102-110
27 Yoganandan N, Kumaresan S, Voo L. Finite element model of the human lower cervical spine:Parametric analysis of the C4-C6 unit[J]. J Biomech Eng,1997,119(1):87-92
28 Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine:A material property sensitivity study [J]. Clin Biomech,1999,14:41-53
29 Maurel N, Lavaste F, Skalli W. A three-dimensional parameterized finite element model of the lower cervical spine:Study of the influence of the posterior articular facets [J]. J Biomech, 1997,30(9):921-931
30 Gnel VK, Clausen JD. Prediction of load sharing among spinal components of a C5-C6 motion segment using the finite element approach [J]. Spine,1998:23(6):684-691
31 Wang H, Hu B, Bai J. Computational analysis of two atlantoaxial fixation methods[A].5th IFAC Sym Model Cont Biomed Syst [C]. England:Pergamon Pr.2003.175-178
32 Punjabi MM, Oda T, Crisco JJ, et al. Experimental study of atlas injuries I:Biomechanical analysis of their mechanism and fracture patterns. Spine,1991,16(10 Suppl):S460-465
33 Teo EC, Ng HW. First cervical vertebra (atlas) fracture mechanism studies using finite element method [J]. Biomech,2001,34(1):13-21
34 Beckner MA, Heggeness MH, Doherty BJ. A biomechanical study of Jefferson Fractures[J]. Spine,1998,23(17):1832-1836
35 韩珂.寰枢椎三维有限元模型的建立及寰椎生物力学的有限元分析：[硕士学位论文]湖南：中南大学,2007
36 廖穗祥,夏虹,昌耘冰,等.上颈椎三维有限元模型的建立.中国组织工程研究与临床康复,2007,11(27)：5269-5272
37 付裕,阮狄克.颈椎生物力学中的三维有限元分析.中国脊柱脊髓杂志,2004,14(10)：632-635
38 张昊,白净.颈椎有限元模型的建立方法与进展.国外医学生物医学工程分册,2005,28 (4)：198-201
39 袁野.Hangman骨折相关有限元分析及临床治疗：[博士学位论文].广州：第一军医大学,2006
40 张美超.有限单元法在骨科生物力学中的应用：[博士学位论文].广州：第一军医大学,2002
[1]Brekelmans WAM, Rybicki EF, Burdeaux BD。A new method analysis the mechanical behavior of skeletal parts[J]. Acta Orthop Scand,1972,43:301-305.
[2]Rybicki EF, Yang KH. On the mathematical an analysis of stress in the human femur[J]. Biomech,1972,5:203-207.
[3]Goel VK, Gilbertson LG. Spine update:An applications of the finite element method to thoracolumbar spinal research-past, present and future, Spine,1995,20:1719-1727.
[4]Yoganandan N, Kum aresan S, V oo LM, etal, Finite element model of the human lower cervical spine:parametric analysis of the C4 - C6 unit. [J] Biomech Eng.1997,119:87.
[5]Wu JS, Chen JH. Clarification of the mechanical behaviour of spinal motion segments though a three-dimensional poroelastic mixed finite element model. Med Eng Phys,1996,18: 215.
[6]Miclau T, Martin RE. The evolution of modern plate osteosynthesis[J]. Injury,1997,28: SA3-6.
[7]Yoganandan N, Kumaresan S, Voo L, etal. Finite element modeling of the C4--6 cervical spine unit[J]. Med Eng Phys,1996,18(7):569 -574.
[8]Yang KH, Zhu F, Luan F, etal. Development of a finite element model of the human neck[R]. Proceeding of the 42nd Stapp Car Crash Conference. SAE983157,1998,1-11.
[9]Jost R, Nuriek GN. Development of a finite element model of the human neck subjected to high g-level deceleration[J]. Int J Crashworthiness,2000,5:259 -267.
[10]Karin B, Peter H. Development of a finite element mod el of the upper cervical spine an d a parameter study of ligament characteristics[J]. Spine,2004,29(4):376-385
[11]陈伯华,孙鹏,Natarajan N, etal.颈椎三维有限元模型的建立及意义[J].中国脊柱脊髓杂志,2002,12(2)：105-108.
[12]Bay BK, Yerby SA, McLain RF, etal. Measurement of strain distributions within vertebral body sections by texture correlation [J]. Spine,1999,24:10.17
[13]Whyne CM, Hu SS, Klishc S, etal. Effect of the pedicle and posterior arch on vertebral body strength predictions in finite element modeling[J]. Spine,1998,23(8):899-950.
[14]Smit TH,, Odgaard A, Schneider E. Structure and function of vertebral trabecular bone[J]. Spine,1997,22(24):2823-2828.
[15]silva MJ, Keaveny, ITM, Hayes Wc. load sharing between the shell and centrum in the lumbar vertebral body[J]. Spine,1997,22:140-150
[16]Cao KD, Grimm MJ, Yang KH. ad sharing within a human lumbar vertebral body using the finite element method[J]. Spine,20o1,26:E253 - E260.
[17]Goel VK, Clausen JD. Prediction of load sharing among spinal components of a C5-C6 motion segment using the finite element approach[J]. Spine,1998,23:684-691.
[18]Ng Hw, Teo EC, Lee KK, etal. Finite element analysis of cervical spinal instability under physiologic loading [J]. Journal of Spinal Disorders and Techniques,2003,16:55-65.
[19]Lu YM, Hutton MC, Gharpuray YM. Do bending, twisting, and diurnal fluid changes in the disc affect the propensity to prolapse? a viacoelastic finite element model [J]. Spine,1996, 21:257O-2579.
[20]Natarajan RN, Andersson GBJ. The influence of lumbar disc height an d cross-sectional area on the mechanical国外医学生物医学工程分册2003年第26卷第6期response of the disc tophysiologic loading [J]spine,1999,24:1873-1881.
[21]Gole VK, Monroe BT, Gilbertson LG etal. Inter laminar shear stresses and laminae separation in a disc-finite element analysis of the L3 - L4 motion segment subjected to axial compressive loads[J]。Spine,1995,20(5):689-698.
[22]Voo LM, Kumaresan S, Yoganan dan N, etal. Finite element analysis of cervical facetectomy[J]. Spine,1997,22(9):964-969.
[23]Lu YM, Hutton WC, Gharpuray VM. Can variations in intervetebral disc heighter affect the mechanical function of the disc?[J]. Spine,1996.21(19):2208-2216.
[24]Voo LM, Kumaresan S, Yoganandan N, etal. Finite element analysis of cervical facetectomy[J]. Spine,1997,22:964-969.
[25]Lim TH, Kwon H, Joen CH, etal. Effect of endplate conditions and bone mineral density on the compressive strength of the graft-endplate interface in anterior cervical spine fusion[J]. Spine,2001,26:951-956.
[26]Lim TH, Eck JC, An HS, etal. Biomechanics of transfixation in pedicle screw instrumentation [J]. Spine,1996,21:2224-2229.