Trabecular bone modulus–density relationships depend on anatomic site

Morgan, Elise F.; Bayraktar, Harun H.; Keaveny, Tony M.

Year	Entry
2011	Aiyangar AK. Physical and Computational Modeling of Subsidence of Anterior Interbody Fusion Devices [PhD thesis]. Madison, WI: University of Wisconsin; 2011.
2019	Alexander SL, Gunnarsson CA, Weerasooriya T. Influence of the mesostructure on the compressive mechanical response of adolescent porcine cranial bone. J Mech Behav Biomed Mater. August 2019;96:96-107.
2004	Bayraktar HH, Keaveny TM. Mechanisms of uniformity of yield strains for trabecular bone. J Biomech. November 2004;37(11):1671-1678.
2007	Bevill G, Easley SK, Keaveny TM. Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site. J Biomech. 2007;40(15):3381-3388.
2008	Bevill GR. Micromechanical Modeling of Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2008.
2009	Bevill G, Eswaran SK, Farahmand F, Keaveny TM. The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties. Bone. April 2009;44(4):573-578.
2013	Boruah S, Henderson K, Subit D, Salzar RS, Shender BS, Paskoff G. Response of human skull bone to dynamic compressive loading. In: Proceedings of the 2013 International IRCOBI Conference on the Biomechanics of Injury. September 11-13, 2013; Gothenburg, Sweden.497-508.
2005	Buie HR. Use of Finite Element Method Modelling and Rapid Prototyping to Study the Effect of Trabecular Bone Architecture on Apparent Mechanical Properties [Master's thesis]. Kingston, ON: Queen's University; November 2005.
2008	Burgers TA, Mason J, Niebur G, Ploeg HL. Compressive properties of trabecular bone in the distal femur. J Biomech. 2008;41(5):1077-1085.
2008	Burgers TA. Press-Fit Fixation and Viscoelastic Response of a Bone-Implant Interface in the Distal Femur [PhD thesis]. Madison, WI: University of Wisconsin; 2008.
2009	Burgers TA, Lakes RS, García-Rodríguez S, Piller GR, Ploeg H-L. Post-yield relaxation behavior of bovine cancellous bone. J Biomech. 2009;42(16):2728-2733.
2012	Campoli G, Weinans H, Zadpoor AA. Computational load estimation of the femur. J Mech Behav Biomed Mater. June 2012;10:108-119.
2010	Chen G, Schmutz B, Epari D, Rathnayaka K, Ibrahim S, Schuetz MA, Pearcy MJ. A new approach for assigning bone material properties from CT images into finite element models. J Biomech. 2010;43(5):1011-1015.
2014	Chen Y, Pani M, Taddei F, Mazzà C, Li X, Viceconti M. Large-scale finite element analysis of human cancellous bone tissue micro computer tomography data: a convergence study. J Biomech Eng. October 2014;136(10):101013.
2017	Chen Y, Dall’Ara E, Sales E, Manda K, Wallace R, Pankaj P, Viceconti M. Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: a validation study. J Mech Behav Biomed Mater. January 2017;65:644-651.
2007	Chevalier Y, Pahr D, Allmer H, Charlebois M, Zysset P. Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation. J Biomech. 2007;40(15):3333-3340.
2011	Cole JH, van der Meulen MCH. Whole bone mechanics and bone quality. Clin Orthop Relat Res. August 2011;469(8):2139-2149.
2011	Cong A, Buijs JOD, Dragomir-Daescu D. In situ parameter identification of optimal density–elastic modulus relationships in subject-specific finite element models of the proximal femur. Med Eng Phys. March 2011;33(2):164-173.
2010	Cristofolini L, Schileo E, Juszczyk M, Taddei F, Martelli S, Viceconti M. Mechanical testing of bones: the positive synergy of finite–element models and in vitro experiments. Philos Trans R Soc A-Math Phys Eng Sci. 2010;368(1920):2725-2763.
2016	Currier EJ. Predicting Peak Load of the Femoral Neck Using Structural Parameters [Master's thesis]. Urbana, IL: University of Illinois at Urbana-Champaign; 2016.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Rotterdam, The Netherlands: Erasmus University Rotterdam; 2005.
2011	Dragomir-Daescu D, Op Den Buijs J, McEligot S, Dai Y, Entwistle RC, Salas C, Melton LJ III, Bennet KE, Khosla S, Amin S. Robust QCT/FEA models of proximal femur stiffness and fracture load during a sideways fall on the hip. Annals Biomed Eng. February 2011;39(2):742-755.
2012	Edwards WB, Troy KL. Finite element prediction of surface strain and fracture strength at the distal radius. Med Eng Phys. April 2012;34(3):290-298.
2009	Eswaran SK, Bevill G, Nagarathnam P, Allen MR, Burr DB, Keaveny TM. Effects of suppression of bone turnover on cortical and trabecular load sharing in the canine vertebral body. J Biomech. March 11, 2009;42(4):517-523.
2009	Fields AJ, Eswaran SK, Jekir MG, Keaveny TM. Role of trabecular microarchitecture in whole‐vertebral body biomechanical behavior. J Bone Min Res. September 2009;24(9):1523-1530.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
2009	García-Rodríguez S. Mechanical Behavior of Trabecular Bone [PhD thesis]. Madison, WI: University of Wisconsin-Madison; 2009.
2015	Gargac J. Evaluation of Bone Healing, Damage, and Adaptation Using Computational Modeling and Image Processing Techniques [PhD thesis]. Notre Dame, IN: University of Notre Dame; July 2015.
2010	Gong H, Zhu D, Xiao Z, Zhang X, Zhang M. Relationship between apparent elastic modulus and microstructural parameters of senile vertebral trabecular bone. In: Proceedings of the 3rd International Conference on Biomedical Engineering and Informatics (bmei 2010). October 16-18, 2010; Yantai, China.1353-1356.
2011	Grassi L, Hraiech N, Schileo E, Ansaloni M, Rochette M, Viceconti M. Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur. Med Eng Phys. 2011;33(1):112-120.
2012	Grassi L, Schileo E, Taddei F, Zani L, Juszczyk M, Cristofolini L, Viceconti M. Accuracy of finite element predictions in sideways load configurations for the proximal human femur. J Biomech. January 10, 2012;45(2):394-399.
2013	Gustafson HM, Cripton PA. Use of digital image correlation for validation of surface strain in specimen-specific vertebral finite element models. In: Proceedings of the 9th Ohio State University Injury Biomechanics Symposium. May 19-21, 2013; Columbus, OH.
2008	Harrison NM, McDonnell PF, O’Mahoney DC, Kennedy OD, O’Brien FJ, McHugh PE. Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties. J Biomech. 2008;41(11):2589-2596.
2012	Hazrati Marangalou J, Ito K, van Rietbergen B. A new approach to determine the accuracy of morphology–elasticity relationships in continuum FE analyses of human proximal femur. J Biomech. November 15, 2012;45(15):2884-2892.
2008	Helgason B, Perilli E, Schileo E, Taddei F, Brynjólfsson S, Viceconti M. Mathematical relationships between bone density and mechanical properties: a literature review. Clin Biomech (Bristol, Avon). 2008;23(2):135-146.
in press	Johnston JD, Kontulainen SA, Masri BA, Wilson DR. Predicting subchondral bone stiffness using a depth-specific CT topographic mapping technique in normal and osteoarthritic proximal tibiae. Clin Biomech (Bristol, Avon).
2010	Kadir MRA, Syahrom A, Öchsner A. Finite element analysis of idealised unit cell cancellous structure based on morphological indices of cancellous bone. Med Biol Eng Comput. May 2010;48(5):497-505.
2010	Keaveny TM, Kopperdahl DL, Melton LJ III, Hoffmann PF, Amin S, Riggs BL, Khosla S. Age‐dependence of femoral strength in white women and men. J Bone Min Res. May 2010;25(5):994-1001.
2012	Kelly N, McGarry JP. Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue. J Mech Behav Biomed Mater. May 2012;9:184-197.
2017	Kreipke TC. Structural, Mechanical, and Biological Relationships of Trabecular Bone in Osteoporosis [PhD thesis]. Notre Dame, IN: University of Notre Dame; April 2017.
2010	Lievers WB, Poljsak AS, Waldman SD, Pilkey AK. Effects of dehydration-induced structural and material changes on the apparent modulus of cancellous bone. Med Eng Phys. 2010;32(8):921-925.
2014	Martelli S, Kersh ME, Schache AG, Pandy MG. Strain energy in the femoral neck during exercise. J Biomech. June 3, 2014;47(8):1784-1791.
2008	Matsuura M, Eckstein F, Lochmüller E-M, Zysset PK. The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations. Biomech Model Mechanobiol. February 2008;7(1):27-42.
2007	McDonnell P, McHugh PE, O’Mahoney D. Vertebral osteoporosis and trabecular bone quality. Annals Biomed Eng. February 2007;35(2):170-189.
2009	Mc Donnell P, Harrison N, Liebschner MAK, Mc Hugh PE. Simulation of vertebral trabecular bone loss using voxel finite element analysis. J Biomech. 2009;42(16):2789-2796.
2016	Meyer LA. Testing and Modeling Mechanical Properties of Ex Vivo Trabecular Bone [PhD thesis]. Madison, WI: University of Wisconsin; 2016.
2004	Mittra ES. Assessment of Trabecular Bone Quality Using Microstructure, Micro-Mechanics and Micro-Finite Element Modeling [PhD thesis]. Stony Brook University; May 2004.
2016	Morales-Orcajo E, Bayod J, Barbosa de Las Casas E. Computational foot modeling: scope and applications. Arch Comput Meth Eng. September 2016;23(3):389-416.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
2008	Perilli E, Baleani M, Öhman C, Fognani R, Baruffaldi F, Viceconti M. Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur. J Biomech. 2008;41(2):438-446.
2007	Schileo E, Taddei F, Malandrino A, Cristofolini L, Viceconti M. Subject-specific finite element models can accurately predict strain levels in long bones. J Biomech. 2007;40(13):2982-2989.
2008	Schileo E, Dall’Ara E, Taddei F, Malandrino A, Schotkamp T, Baleani M, Viceconti M. An accurate estimation of bone density improves the accuracy of subject-specific finite element models. J Biomech. August 7, 2008;41(11):2483-2491.
2008	Schileo E, Taddei F, Cristofolini L, Viceconti M. Subject-specific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro. J Biomech. 2008;41(2):356-367.
2009	Schmidt JE. Biomechanical Evaluation of a Stemmed Tibial Implant [PhD thesis]. Madison, WI: University of Wisconsin; 2009.
2013	Schumacher Y. Comparison of Two Loading Surface Preparation Methods on Rat Vertebral Bodies for Compression Testing [Master's thesis]. Kingston, Ontario, Canada: Queen’s University; September 2013.
2007	Tai K, Dao M, Suresh S, Palazoglu A, Ortiz C. Nanoscale heterogeneity promotes energy dissipation in bone. Nature Mater. June 2007;6(6):454-462.
2011	Trabelsi N, Yosibash Z, Wutte C, Augat P, Eberle S. Patient-specific finite element analysis of the human femur: a double-blinded biomechanical validation. J Biomech. June 3, 2011;44(9):1666-1672.
in press	Väänänen SP, Grassi L, Venäläinen MS, Matikka H, Zheng Y, Jurvelin JS, Isaksson H. Automated segmentation of cortical and trabecular bone to generate finite element models for femoral bone mechanics. Med Eng Phys.
2011	Varghese B, Short D, Penmetsa R, Goswami T, Hangartner T. Computed-tomography-based finite-element models of long bones can accurately capture strain response to bending and torsion. J Biomech. April 29, 2011;(7):1374-1379.
2012	Vaughan TJ, McCarthy CT, McNamara LM. A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone. J Mech Behav Biomed Mater. August 2012;12:50-62.
2006	Verhulp E, van Rietbergen B, Huiskes R. Comparison of micro-level and continuum-level voxel models of the proximal femur. J Biomech. 2006;39(16):2951-2957.
2006	Verhulp E. Analyses of Trabecular Bone Failure [PhD thesis]. Eindhoven, The Netherlands: Eindhoven University of Technology; 2006.
in press	Vetter A, Witt F, Sander O, Duda GN, Weinkamer R. The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules. Biomech Model Mechanobiol.
2012	Weisse B, Aiyangar A, Affolter C, Gander R, Terrasi GP, Ploeg H. Determination of the translational and rotational stiffnesses of a L4-L5 functional spinal unit using a specimen-specific finite element model. J Mech Behav Biomed Mater. September 2012;13:45-61.
in press	Wille H, Rank E, Yosibash Z. Prediction of the mechanical response of the femur with uncertain elastic properties. J Biomech.
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.
2011	Wolfram U, Wilke H-J, Zysset PK. Damage accumulation in vertebral trabecular bone depends on loading mode and direction. J Biomech. April 7, 2011;44(7):1164-1169.
2012	Wolfram U, Gross T, Pahr DH, Schwiedrzik J, Wilke H-J, Zysset PK. Fabric-based Tsai-Wu yield criteria for vertebral trabecular bone in stress and strain space. J Mech Behav Biomed Mater. November 2012;15:218-228.
2018	Chen JTH. Alterations in Bone Tissue Properties With Parathyroid Hormone Treatment [PhD thesis]. Ithaca, NY: Cornell University; May 2018.
2011	Yan Y-B, Qi W, Wang J, Liu L-F, Teo E-C, Tianxia Q, Ba J-j, Lei W. Relationship between architectural parameters and sample volume of human cancellous bone in micro-CT scanning. Med Eng Phys. July 2011;33(6):764-769.
2018	Yan C. Effect of Fatigue Loading on Impact Response of Rat Ulna [Master's thesis]. Urbana, IL: University of Illinois at Urbana-Champaign; 2018.
2011	Yao H, Dao M, Carnelli D, Tai K, Ortiz C. Size-dependent heterogeneity benefits the mechanical performance of bone. J Mech Phys Solids. 2011;59(1):64-74.
2019	Yue Y, Yang H, Li Y, Zhong H, Tang Q, Wang J, Wang R, He H, Chen W, Chen D. Combining ultrasonic and computed tomography scanning to characterize mechanical properties of cancellous bone in necrotic human femoral heads. Med Eng Phys. April 2019;66:12-17.

Year	Entry
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
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.
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.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1999	Kabel J, van Rietbergen B, Odgaard A, Huiskes R. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. J Biomech. October 1999;25(4):481-486.
1998	Silva MJ, Keaveny TM, Hayes WC. Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections. J Orthop Res. May 1998;16(3):300-308.
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.
1994	Keaveny TM, Guo XE, Wachtel EF, McMahon TA, Hayes WC. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. J Biomech. 1994;27(9):1127-1129.
1994	Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech. 1994;27(4):375-377,
2001	Morgan EF, Yeh OC, Chang WC, Keaveny TM. Nonlinear behavior of trabecular bone at small strains. J Biomech Eng. 2001;123(1):1-9.
2000	Keyak J, Rossi S. Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories. J Biomech. 2000;33(2):209-214.
1998	Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. 1998;31(7):601-608.
1998	Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech. 1998;31(12):1187-1192.
1999	Ulrich D, van Rietbergen B, Laib A, Rüegsegger P. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone. 1999;25(1):55-60.
1987	Carter DR, Fyhrie DP, Whalen RT. Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. J Biomech. 1987;20(8):785-794.
1991	Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. J Orthop Res. 1991;9(5):674-682.
1985	Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137-147.
1994	Keller TS. Predicting the compressive mechanical behavior of bone. J Biomech. September 1994;27(9):1159-1168.
1986	Currey JD. Power law models for the mechanical properties of cancellous bone. Eng Med. July 1986;15(3):153-154.
2000	Hoffler CE, Moore KE, Kozloff K, Zysset PK, Brown MB, Goldstein SA. Heterogeneity of bone lamellar-level elastic moduli. Bone. June 2000;26(6):603-609.
1997	Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. 2nd ed. Cambridge, UK: Cambridge University Press; 1997. Cambridge Solid State Science Series.
1985	Hvid I, Jensen NC, Bünger C, Sølund K, Djurhuus JC. Bone mineral assay: its relation to the mechanical strength of cancellous bone. Eng Med. 1985;14(2):79-83.
1991	Lotz JC, Cheal EJ, Hayes WC. Fracture prediction for the proximal femur using finite element models, I: linear analysis. J Biomech Eng. 1991;113(4):353-360.
1970	Galante J, Rostoker W, Ray RD. Physical properties of trabecular bone. Calcif Tiss Res. 1970;5(1):236-246.
2002	Hengsberger S, Kulik A, Zysset P. Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions. Bone. 2002;30(1):178-184.
1994	Hollister SJ, Brennan JM, Kikuchi N. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stres. J Biomech. 1994;27(4):433-444.
1999	Hildebrand T, Laib A, Müller R, Dequeker J, Rüegsegger P. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Min Res. 1999;14(7):1167-1174.
1999	Niebur GL, Yuen JC, Hsia AC, Keaveny TM. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng. 1999;121(6):629-635.
1998	Müller R, Gerber SC, Hayes WC. Micro-compression: a novel technique for the nondestructive assessment of local bone failure. Technol Health Care. December 1998;6(5-6):433-444.
1995	van Rietbergen B, Weinans H, Huiskes R, Odgaard A. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech. 1995;28(1):69-81.
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.
2001	Morgan EF, Keaveny TM. Dependence of yield strain of human trabecular bone on anatomic site. J Biomech. 2001;34(5):569-577.
1998	Majumdar S, Kothari M, Augat P, Newitt DC, Link TM, Lin JC, Lang T, Lu Y, Genant HK. High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties. Bone. May 1998;22(5):445-454.
1988	Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.
1987	Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 1987;20(11-12):1135-1150.
2000	Fyhrie DP, Vashishth D. Bone stiffness predicts strength similarly for human vertebral cancellous bone in compression and for cortical bone in tension. Bone. February 2000;26(2):169-173.
1993	Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. February 1993;26(2):111-119.
1999	Rho J-Y, Roy ME II, Tsui TY, Pharr GM. Elastic properties of microstructural components of human bone tissue as measured by nanoindentation. J Biomed Mater Res. 1999;A45(1):48-54.