Computational Modeling of Hard Tissue Response and Fracture in the Lower Cervical Spine Under Compression Including Age Effects

Almost half of motor vehicle accident (MVAs) victims experience traumatic spinal cord injuries (SCI), which are often associated with rollover accidents. Specifically, rollovers have the highest incidence rate of AIS2+ cervical spine injuries and more than half of the patients with SCIs demonstrated spine fractures with the majority being burst fractures. Detailed finite element human body models (HBMs) have been utilized to assess the safety of occupants and pedestrians in crash scenarios, augmenting the results from crash test dummies in physical tests. HBMs can predict the potential for injury and provide data such as fracture initiation and propagation that is not possible to collect experimentally. Biofidelic HBMs capable of predicting tissue-level injury require representative material properties and tissue level failure criteria. However, current HBMs use simplified constitutive models and are not capable of predicting the fracture threshold and fracture pattern for complex scenarios, such as the vertebrae in the neck. The objective of this study was to investigate constitutive models with age effect that are representative of cortical and trabecular hard tissues and assess the failure response of a C57 (C5-C6-C7) segment model under compression loading.

Two sets of material properties were identified that corresponded to the lower age of the experimental test samples (younger than 50 years old (YO)) and the higher age of the test samples (older than 70 YO). The available constitutive models in a commercial finite element code (LS-DYNA) were reviewed and the constitutive models that best represent the cortical and trabecular bone responses were analyzed. As there were no single constitutive model available that included all the key properties of hard tissues, asymmetric and anisotropic elastic-plastic (cortical) and crushable foam (trabecular) models were evaluated. Single element simulations were performed to verify the clonstitutive models. A functional spinal unit (FSU) model was extracted from a detailed 50th percentile HBM (Global Human Body Models Consortium (GHBMC) M50-O v4.3) and a centric compression simulation was performed to identify the best performing constitutive model compared to experimental data. Various eccentricity cases of the compression experiments were simulated as well such as anterior, posterior and lateral.

The anisotropic model predicted failure values and fracture patterns in better agreement with experimental data compared to an asymmetric or isotropic and symmetric model. This study showed the importance of including age effects that correspond to the age of experimental test subjects. This study also showed that simulations could provide additional insight regarding fracture initiation and progression, which is challenging to measure in dynamic experiments. Gender, segment level, and strain rate effect were not included in this work, which are limitations of the current study. In addition, the lack of human cervical spine experimental data for improved model validation is another limitation of this study. In conclusion, this study successfully utilized uncalibrated material properties of cortical and trabecular bone tissue from literature and accurately predicted failure outcomes of compression experiments with the implemented constitutive models.

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Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.

1988

Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.

1989

Ashman RB, Rho JY, Turner CH. Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J Biomech. 1989;22(8-9):895-900.

1973

Vernon-Roberts B, Pirie CJ. Healing trabecular microfractures in the bodies of lumbar vertebrae. Ann Rheum Dis. September 1973;32(5):406-412.

1984

Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.

2006

Eswaran SK, Gupta A, Adams MF, Keaveny TM. Cortical and trabecular load sharing in the human vertebral body. J Bone Miner Res. February 2006;21(2):307-314.

1998

Pintar FA, Yoganandan N, Voo L. Effect of age and loading rate on human cervical spine injury threshold. Spine. September 15, 1998;23(18):1957-1962.

2010

Charlebois M, Pretterklieber M, Zysset PK. The role of fabric in the large strain compressive behavior of human trabecular bone. J Biomech Eng. 2010;132(12):121006.

1999

Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.

2013

Harrison NM, McDonnell P, Mullins L, Wilson N, O’Mahoney D, McHugh PE. Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach. Biomech Model Mechanobiol. April 2013;12(2):225-241.

2012

Hambli R, Bettamer A, Allaoui S. Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage. Med Eng Phys. March 2012;34(2):202-210.

2002

Carter JW, Ku GS, Nuckley DJ, Ching RP. Tolerance of the cervical spine to eccentric axial compression. Stapp Car Crash J. 2002;46:441-459. SAE 2002-22-0022.

2007

Buckley JM, Loo K, Motherway J. Comparison of quantitative computed tomography-based measures in predicting vertebral compressive strength. Bone. March 2007;40(3):767-774.

2006

Ural A, Vashishth D. Cohesive finite element modeling of age-related toughness loss in human cortical bone. J Biomech. 2006;39(16):2974-2982.

1976

Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, I: theoretical considerations for hexagonal symmetry. J Biomech. 1976;9(6):407-412.

1989

Yoganandan N, Sances A, Pintar F. Biomechanical evaluation of the axial compressive responses of the human cadaveric and manikin necks. J Biomech Eng. August 1989;111(3):250-255.

2007

Hulme PA, Boyd SK, Ferguson SJ. Regional variation in vertebral bone morphology and its contribution to vertebral fracture strength. Bone. December 2007;41(6):946-957.

1983

Maiman DJ, Sances A Jr, Myklebust JB, Larson SJ, Houterman C, Chilbert M, El-Ghatit AZ. Compression injuries of the cervical spine: a biomechanical analysis. Neurosurgery. September 1983;13(3):254-260.

1995

Pintar FA, Yoganandan N, Voo L, Cusick JF, Maiman DJ, Sances A Jr. Dynamic characteristics of the human cervical spine. In: Proceedings of the 39th Stapp Car Crash Conference. November 8-10, 1995; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:195-202. SAE 952722.

1982

Allen BL Jr, Ferguson RL, Lehmann TR, O'Brien RP. A mechanistic classification of closed, indirect fractures and dislocations of the lower cervical spine. Spine. 1982;7(1):1-27.

1990

Pintar FA, Sances A Jr, Yoganandan N, Reinartz J, Maiman DJ, Suh JK, Unger G, Cusick JF, Larson SJ. Biodynamics of the total human cadaveric cervical spine. In: Proceedings of the 34th Stapp Car Crash Conference. November 4-7, 1990; Orlando, FL. Warrendale, PA: Society of Automotive Engineers:55-72. SAE 902309.

2013

Feerick EM, Liu X, McGarry P. Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM). J Mech Behav Biomed Mater. April 2013;20:77-89.

1997

Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. 2nd ed. Cambridge, UK: Cambridge University Press; 1997. Cambridge Solid State Science Series.

1981

Van Buskirk WC, Ashman RB. The elastic moduli of bone. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:131-143.

2006

Augat P, Schorlemmer S. The role of cortical bone and its microstructure in bone strength. Age Ageing. September 2006;35(suppl 2):ii27-ii31.

1993

Thurman DJ, Burnett CL, Beaudoin DE, Jeppson L, Sniezek JE. Risk factors and mechanisms of occurrence in motor-vehicle-related spinal cord injuries: Utah. In: 37th Annual Proceedings, Association for the Advancement of Automotive Medicine (AAAM). November 4-6, 1993; San Antonio, TX.201-208.

1983

McElhaney JH, Paver JG, McCrackin HJ, Maxwell GM. Cervical spine compression responses. In: Proceedings of the 27th Stapp Car Crash Conference. October 17-19, 1983; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:163-177. SAE 831615.

2018

Xie S, Wallace RJ, Callanan A, Pankaj P. From tension to compression: asymmetric mechanical behaviour of trabecular bone’s organic phase. Ann Biomed Eng. June 2018;46(6):801-809.

1993

Mosekilde L. Vertebral structure and strength in vivo and in vitro. Calcif Tiss Int. February 1993;53(suppl 1):S121-S126.

1996

Ebara S, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M. Tensile properties of nondegenerate human lumbar anulus fibrosus. Spine. March 15, 1996;21(4):452-461.

2003

Crawford RP, Cann CE, Keaveny TM. Finite element models predict in vitro vertebral body compressive strength better than quantitative computed tomography. Bone. 2003;33(4):744-750.

1991

Odgaard A, Linde F. The underestimation of Young's modulus in compressive testing of cancellous bone specimens. J Biomech. 1991;24(8):691-698.

2012

Van Toen C, Street J, Oxland TR, Cripton PA. Acoustic emission signals can discriminate between compressive bone fractures and tensile ligament injuries in the spine during dynamic loading. J Biomech. June 1, 2012;45(9):1643-1649.

1997

Ritzel H, Amling M, Pösl M, Hahn M, Delling G. The thickness of human vertebral cortical bone and its changes in aging and osteoporosis: a histomorphometric analysis of the complete spinal column from thirty‐seven autopsy specimens. J Bone Miner Res. January 1997;12(1):89-95.

1996

Amling M, Pösl M, Ritzel H, Hahn M, Vogel M, Wening VJ, Delling G. Architecture and distribution of cancellous bone yield vertebral fracture clues: a histomorphometric analysis of the complete spinal column from 40 autopsy specimens. Arch Orthop Trauma Surg. July 1996;115(5):262-269.

1999

Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ. Finite element modeling of the cervical spine: role of intervertebral disc under axial and eccentric loads. Med Eng Phys. December 1999;21(10):689-700.

1983

Denis F. The three column spine and its significance in the classification of acute thoracolumbar spinal injuries. Spine. November–December 1983;8(8):817-831.

1995

Acaroglu ER, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M. Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus. Spine. December 15, 1995;20(24):2690-2701.

1976

Burstein AH, Reilly DT, Martens M. Aging of bone tissue: mechanical properties. J Bone Joint Surg. 1976;58A(1):82-86.

1997

Keaveny TM, Pinilla TP, Crawford RP, Kopperdahl DL, Lou A. Systematic and random errors in compression testing of trabecular bone [published correction appears in J Orthop Res. 1995;17(1):151]. J Orthop Res. 1997;15(1):101-110.

2001

Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001.

2005

Iwamoto M, Miki K, Tanaka E. Ankle skeletal injury predictions using anisotropic inelastic constitutive model of cortical bone taking into account damage evolution. Stapp Car Crash J. 2005;49:133-156. SAE 2005-22-0007.

1996

Yoganandan N, Kumaresan SC, Voo L, Pintar FA, Larson SJ. Finite element modeling of the C4–C6 cervical spine unit. Med Eng Phys. October 1996;18(7):569-574.

2003

Ochia RS, Tencer AF, Ching RP. Effect of loading rate on endplate and vertebral body strength in human lumbar vertebrae. J Biomech. December 2003;36(12):1875-1881.

1996

Iatridis JC, Weidenbaum M, Setton LA, Mow VC. Is the nucleus pulposus a solid or a fluid? mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine. May 15, 1996;21(15):1174-1184.

1995

Myers BS, Winkelstein BA. Epidemiology, classification, mechanism, and tolerance of human cervical spine injuries. Crit Rev Biomed Eng. 1995;23(5-6):307-409.

2012

DeWit JA, Cronin DS. Cervical spine segment finite element model for traumatic injury prediction. J Mech Behav Biomed Mater. June 2012;10:138-150.

1998

Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.

1997

Rho J-Y, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997;18(20):1325-1330.

2003

Liebschner MAK, Kopperdahl DL, Rosenberg WS, Keaveny TM. Finite element modeling of the human thoracolumbar spine. Spine. March 15, 2003;28(6):559-565.

1974

Whitehouse WJ. The quantitative morphology of anisotropic trabecular bone. J Microsc (Oxford). July 1974;101:153-168.

1987

Mosekilde L, Mosekilde L, Danielsen CC. Biomechanical competence of vertebral trabecular bone in relation to ash density and age in normal individuals. Bone. 1987;8(2):79-85.

1985

Mosekilde L, Viidik A, Mosekilde L. Correlation between the compressive strength of iliac and vertebral trabecular bone in normal individuals. Bone. 1985;6(5):291-295.

2005

Holzapfel GA, Schulze-Bauer CAJ, Feigl G, Regitnig P. Single lamellar mechanics of the human lumbar anulus fibrosus. Biomech Model Mechanobiol. March 2005;3(3):125-140.

1995

Grote HJ, Amling M, Vogel M, Hahn M, Pösl M, Delling G. Intervertebral variation in trabecular microarchitecture throughout the normal spine in relation to age. Bone. March 1995;16(3):301-308.

1983

Goldstein SA, Wilson DL, Sonstegard DA, Matthews LS. The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J Biomech. 1983;16(12):965-969.

1998

Augat P, Link T, Lang TF, Lin JC, Majumdar S, Genant HK. Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations. Med Eng Phys. March 1998;20(2):124-131.

2013

Foster J. Injury Mechanisms and Priorities for Cervical Spine Trauma Mitigation in Rollover Crashes: The Development and Analysis of in Vitro Testing of Axial Compressive Cervical Spine Impacts [Master's thesis]. Charlottesville, VA: University of Virginia; May 2013.

1996

Adams MA, McNally DS, Dolan P. “Stress” distributions inside intervertebral discs: the effects of age and degeneration. J Bone Joint Surg. November 1996;78B(6):965-972.

2000

Carter J, Mirza S, Tencer A, Ching R. Canal geometry changes associated with axial compressive cervical spine fracture. Spine. January 2000;25(1):46-54.

2013

Ridha H, Thurner PJ. Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests. J Mech Behav Biomed Mater. November 2013;27:94-106.

1976

Saha S, Hayes WC. Tensile impact properties of human compact bone. J Biomech. 1976;9(4):243-251.

2001

Yamashita J, Furman BR, Rawls HR, Wang X, Agrawal CM. The use of dynamic mechanical analysis to assess the viscoelastic properties of human cortical bone. J Biomed Mater Res. 2001;B58(1):47-53.

1985

Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137-147.

1997

McCalden RW, McGeough JA, Court-Brown CM. Age-related changes in the compressive strength of cancellous bone: the relative importance of changes in density and trabecular architecture. J Bone Joint Surg. March 1997;79A(3):421-427.

1991

Linde F, Nørgaard P, Hvid I, Odgaard A, Søballe K. Mechanical properties of trabecular bone: dependency on strain rate. J Biomech. 1991;24(9):803-809.

1993

McCalden RW, McGeough JA, Barker MB, Court-Brown CM. Age-related changes in the tensile properties of cortical bone: the relative importance of changes in porosity, mineralization, and microstructure. J Bone Joint Surg. 1993;75A(8):1193-1205.

2006

Bouxsein ML, Melton LJ III, Riggs BL, Muller J, Atkinson EJ, Oberg AL, Robb RA, Camp JJ, Rouleau PA, McCollough CH, Khosla S. Age‐ and sex‐specific differences in the factor of risk for vertebral fracture: a population‐based study using QCT. J Bone Miner Res. September 2006;21(9):1475-1482.

2014

Ali AA, Cristofolini L, Schileo E, Hu H, Taddei F, Kim RH, Rullkoetter PJ, Laz PJ. Specimen-specific modeling of hip fracture pattern and repair. J Biomech. January 22, 2014;47(2):536-543.

1970

Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.

2009

Raddin J, Cormier J, Smyth B, Croteau J, Cooper E. Compressive neck injury and its relationship to head contact and torso motion during vehicle rollovers. In: Proceedings of the SAE World Congress & Exhibition. April 20-23, 2009; Detroit, MI. Warrendale, PA: Society of Automotive Engineers. SAE 2009-01-0829.

2012

Sanyal A, Gupta A, Bayraktar HH, Kwon RY, Keaveny TM. Shear strength behavior of human trabecular bone. J Biomech. October 11, 2012;45(15):2513-2519.

2008

Jones AC, Wilcox RK. Finite element analysis of the spine: towards a framework of verification, validation and sensitivity analysis. Med Eng Phys. December 2008;30(10):1287-1304.

1994

Silva MJ, Wang C, Keaveny TM, Hayes WC. Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate. Bone. July 8, 1994;15(4):409-414.

1999

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1996

Ford CM, Keaveny TM. The dependence of shear failure properties of trabecular bone on apparent density and trabecular orientation. J Biomech. 1996;29(10):1309-1317.

1988

Turner CH, Cowin SC. Errors induced by off-axis measurement of the elastic properties of bone. J Biomech Eng. August 1988;110(3):213-215.

1976

Hayes WC, Carter DR. Postyield behavior of subchondral trabecular bone. J Biomed Mater Res. July 1976;10(4):537-544.

2005

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1989

Yoganandan N, Haffner M, Maiman DJ, Nichols H, Pintar FA, Jentzen J, Weinshel SS, Larson SJ, Sances A Jr. Epidemiology and injury biomechanics of motor vehicle related trauma to the human spine. In: Proceedings of the 33rd Stapp Car Crash Conference. October 4-6, 1989; Washington, DC. Warrendale, PA: Society of Automotive Engineers:223-242. SAE 892438.

2006

Panzer MB. Numerical Modelling of the Human Cervical Spine in Frontal Impact [Master's thesis]. University of Waterloo; 2006.

2006

Pickett GE, Campos-Benitez M, Keller JL, Duggal N. Epidemiology of traumatic spinal cord injury in Canada. Spine. April 1, 2006;31(7):799-805.

2015

Tang T, Ebacher V, Cripton P, Guy P, McKay H, Wang R. Shear deformation and fracture of human cortical bone. Bone. February 2015;71:25-35.

1986

Yoganandan N, Sances A Jr, Maiman DJ, Myklebust JB, Pech P, Larson SJ. Experimental spinal injuries with vertical impact. Spine. November 1986;11(9):855-860.

2002

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2002

Kim HS, Al-Hassan STS. A morphological model of vertebral trabecular bone. J Biomech. August 2002;35(8):1101-1114.

1997

Cowin SC, Yang G. Averaging anisotropic elastic constant data. J Elast. February 1997;46(2):151-180.

1977

Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg. 1977;59A(7):954-962.

1984

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1994

Keaveny TM, Wachtel EF, Ford CM, Hayes WC. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. J Biomech. 1994;27(9):1137-1146.

2001

Teo EC, Ng HW. Evaluation of the role of ligaments, facets and disc nucleus in lower cervical spine under compression and sagittal moments using finite element method. Med Eng Phys. April 2001;23(3):155-164.

1990

Choi K, Kuhn JL, Ciarelli MJ, Goldstein SA. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J Biomech. 1990;23(11):1103-1113.

1999

Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.

2005

Gibson LJ. Biomechanics of cellular solids. J Biomech. 2005;38(3):377-399.

1997

Iatridis JC, Setton LA, Weidenbaum M, Mow VC. Alterations in the mechanical behavior of the human lumbar nucleus pulposus with degeneration and aging. J Orthop Res. March 1997;15(2):318-322.

2012

Mattucci SFE, Moulton JA, Chandrashekar N, Cronin DS. Strain rate dependent properties of younger human cervical spine ligaments. J Mech Behav Biomed Mater. June 2012;10:216-226.

2011

Mattucci S. Strain Rate Dependent Properties of Younger Human Cervical Spine Ligaments [Master's thesis]. University of Waterloo; 2011.

1996

Ford CM, Keaveny TM, Hayes WC. The effect of impact direction on the structural capacity of the proximal femur during falls. J Bone Miner Res. March 1996;11(3):377-383.

2013

Zysset PK, Dall'Ara E, Varga P, Pahr DH. Finite element analysis for prediction of bone strength. BoneKEy Rep. August 2013;2:386.

1994

Fyhrie DP, Schaffler MB. Failure mechanisms in human vertebral cancellous bone. Bone. 1994;15(1):105-109.

1996

Rho J-Y. An ultrasonic method for measuring the elastic properties of human tibial cortical and cancellous bone. Ultrasonics. December 1996;34(8):777-783.

1990

White AA III, Panjabi MM. Clinical Biomechanics of the Spine. 2nd ed. Philadelphia, PA: J.B. Lippincott Company; 1990.

2009

Garcia D, Zysset PK, Charlebois M, Curnier A. A three-dimensional elastic plastic damage constitutive law for bone tissue. Biomech Model Mechanobiol. April 2009;8(2):149-165.

1993

Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.

2009

Panzer MB, Cronin DS. C4–C5 segment finite element model development, validation, and load-sharing investigation. J Biomech. March 11, 2009;42(4):480-490.

1975

Runkle JC, Pugh J. The micro-mechanics of cancellous bone, II: determination of the elastic modulus of individual trabeculae by a buckling analysis. Bull Hosp Joint Dis. April 1975;36(1):2-10.

1999

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2011

Ural A, Zioupos P, Buchanan D, Vashishth D. The effect of strain rate on fracture toughness of human cortical bone: a finite element study. J Mech Behav Biomed Mater. October 2011;4(7):1021-1032.

1997

Nightingale RW, McElhaney JH, Camacho DL, Kleinberger M, Winkelstein BA, Myers BS. The dynamic responses of the cervical spine: buckling, end conditions, and tolerance in compressive impacts. In: Proceedings of the 41st Stapp Car Crash Conference. November 13-14, 1997; Lake Buena Vista, FL. Warrendale, PA: Society of Automotive Engineers:451-471. SAE 973344.

2003

Nalla RK, Kinney JH, Ritchie RO. Mechanistic fracture criteria for the failure of human cortical bone. Nat Mater. 2003;2(3):164-168.

2001

Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001;3:307-333.

2017

Barker JB, Cronin DS, Nightingale RW. Lower cervical spine motion segment computational model validation: kinematic and kinetic response for quasi-static and dynamic loading. J Biomech Eng. June 2017;139(6):061009.

1998

Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. July 1998;31(7):601-608.

1981

Kazarian L. Injuries to the human spinal column: biomechanics and injury classification. Exerc Sport Sci Rev. January 1981;9(1):297-352.

2011

Gayzik FS, Moreno DP, Vavalle NA, Rhyne AC, Stitzel JD. Development of the Global Human Body Models Consortium mid-sized male full body model. In: Proceedings of the 39th International Workshop on Human Subjects for Biomechanical Research. 2011.

2010

Wolfram U, Wilke H-J, Zysset PK. Valid μ finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions. J Biomech. 2010;43(9):1731-1737.

2004

Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.

2001

Cao KD, Grimm MJ, Yang K-H. Load sharing within a human lumbar vertebral body using the finite element method. Spine. June 5, 2001;26(12):E253-E260.

2000

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1974

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1975

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1966

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2000

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2002

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1976

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2001

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2012

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1991

Nightingale RW, Doherty BJ, Myers BS, McElhaney JH, Richardson WJ. The influence of end condition on human cervical spine injury mechanisms. In: Proceedings of the 35th Stapp Car Crash Conference. November 18-20, 1991; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:391-399. SAE 912915.

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2013

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1994

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1970

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Year	Entry
2019	Pilarczyk BM. Contributions of Muscle, Skin, and Adipose Tissue to Indentation Response, Assessed With Computational Arm Model Under Quasi-Static Conditions [Master's thesis]. University of Waterloo; 2019.
2022	Darweesh M. Evaluating Cervical Spine Response and Potential for Injury During Head-First Impact Loading Using a Finite Element Head-Neck Model [Master's thesis]. University of Waterloo; 2022.

Year

Entry

2019

Pilarczyk BM. Contributions of Muscle, Skin, and Adipose Tissue to Indentation Response, Assessed With Computational Arm Model Under Quasi-Static Conditions [Master's thesis]. University of Waterloo; 2019.

2022

Darweesh M. Evaluating Cervical Spine Response and Potential for Injury During Head-First Impact Loading Using a Finite Element Head-Neck Model [Master's thesis]. University of Waterloo; 2022.