A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stres

Hollister, S. J.; Brennan, J. M.; Kikuchi, N.

Year	Entry
2002	Müller R. The Zürich experience: one decade of three-dimensional high-resolution computed tomography. Top Magn Reson Imaging. 2002;13(5):307-322.
2001	Guo XE. Mechanical properties of cortical and cancellous bone tissue. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:10-1–10-23.
2001	van Rietbergen B, Huiskes R. Elastic constants of cancellous bone. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:15-1–15-24.
2001	Keaveny TM. Strength of trabecular bone. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:16-1–16-42.
2009	Shi X, Wang X, Niebur GL. Effects of loading orientation on the morphology of the predicted yielded regions in trabecular bone. Ann Biomed Eng. 2009;37(2):354-362.
2001	Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001;3:307-333.
2004	Hellmich C, Ulm F-J, Dormieux L. Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? arguments from a multiscale approach. Biomech Model Mechanobiol. June 2004;2(4):219-238.
2009	Rincón-Kohli L, Zysset PK. Multi-axial mechanical properties of human trabecular bone. Biomech Model Mechanobiol. June 2009;8(3):195-208.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1997	Silva MJ, Gibson LJ. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone. 1997;21(2):191-199.
1997	Beck JD, Canfield BL, Haddock SM, Chen TJH, Kothari M, Keaveny TM. Three-dimensional imaging of trabecular bone using the computer numerically controlled milling technique. Bone. 1997;21(3):281-287.
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.
2002	Guo XE, Kim CH. Mechanical consequence of trabecular bone loss and its treatment: a three-dimensional model simulation. Bone. February 2002;30(2):404-411.
2002	Rubin C, Turner AS, Mallinckrodt C, Jerome C, Mcleod K, Bain S. Mechanical strain, induced noninvasively in the high-frequency domain, is anabolic to cancellous bone, but not cortical bone. Bone. March 2002;30(3):445-452.
2002	Homminga J, McCreadie BR, Ciarelli TE, Weinans H, Goldstein SA, Huiskes R. Cancellous bone mechanical properties from normals and patients with hip fractures differ on the structure level, not on the bone hard tissue level. Bone. May 2002;30(5):759-764.
2002	Pistoia W, van Rietbergen B, Lochmüller E-M, Lill CA, Eckstein F, Rüegsegger P. Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images. Bone. June 2002;30(6):842-848.
2003	Pistoia W, van Rietbergen B, Rüegsegger P. Mechanical consequences of different scenarios for simulated bone atrophy and recovery in the distal radius. Bone. December 2003;33(6):937-945.
2005	Shefelbine SJ, Simon U, Claes L, Gold A, Gabet Y, Bab I, Müller R, Augat P. Prediction of fracture callus mechanical properties using micro-CT images and voxel-based finite element analysis. Bone. March 2005;36(3):480-488.
2006	Stauber M, Müller R. Volumetric spatial decomposition of trabecular bone into rods and plates: a new method for local bone morphometry. Bone. 2006;38(4):475-484.
2006	Bevill G, Eswaran SK, Gupta A, Papadopoulos P, Keaveny TM. Influence of bone volume fraction and architecture on computed large-deformation failure mechanisms in human trabecular bone. Bone. December 2006;39(6):1218-1225.
2008	MacNeil JA, Boyd SK. Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite element method. Bone. June 2008;42(6):1203-1213.
2009	Liu XS, Zhang XH, Guo XE. Contributions of trabecular rods of various orientations in determining the elastic properties of human vertebral trabecular bone. Bone. August 2009;45(2):158-163.
2010	Shi X, Liu XS, Wang X, Guo XE, Niebur GL. Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone. Bone. May 2010;46(5):1260-1266.
2020	Varga P, Willie BM, Stephan C, Kozloff KM, Zysset PK. Finite element analysis of bone strength in osteogenesis imperfecta. Bone. April 2020;133:115250.
2021	Li Y, Tseng W-J, de Bakker CMJ, Zhao H, Chung R, Liu XS. Peak trabecular bone microstructure predicts rate of estrogen-deficiency-induced bone loss in rats. Bone. April 2021;145:115862.
2002	van Rietbergen B, Majumdar S, Newitt D, MacDonald B. High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment. Clin Biomech (Bristol, Avon). February 2002;17(2):81-88.
2008	Verhulp E, Van Rietbergen B, Müller R, Huiskes R. Micro-finite element simulation of trabecular-bone post-yield behaviour: effects of material model, element size and type. Comput Methods Biomech Biomed Eng. August 2008;11(4):389-395.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
2005	Morgan EF, Yeh OC, Keaveny TM. Damage in trabecular bone at small strains. Euro J Morphol. February–April 2005;42(1-2):13-21.
2019	Werner B, Ovesy M, Zysset PK. An explicit micro‐FE approach to investigate the post‐yield behaviour of trabecular bone under large deformations. Int J Num Meth Biomed Eng. May 2019;35(5):e3188.
1998	Ladd AJC, Kinney JH. Numerical errors and uncertainties in finite-element modeling of trabecular bone. J Biomech. October 1998;31(10):941-945.
1998	Hou FJ, Lang SM, Hoshaw SJ, Reimann DA, Fyhrie DP. Human vertebral body apparent and hard tissue stiffness. J Biomech. November 1998;31(11):1009-1015.
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. December 1998;31(12):1187-1192.
1999	Kabel J, van Rietbergen B, Dalstra M, Odgaard A, Huiskes R. The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. J Biomech. 1999;32(7):673-680.
1999	Jacobs CR, Davis BR, Rieger CJ, Francis JJ, Saad M, Fyhrie DP. The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling. J Biomech. November 1999;32(11):1159-1164.
2000	Charras GT, Guldberg RE. Improving the local solution accuracy of large-scale digital image-based finite element analyses. J Biomech. February 2000;33(2):255-259.
2000	Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM. High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech. December 2000;33(12):1575-1583.
2001	van der Linden JC, Birkenhäger-Frenkel DH, Verhaar JAN, Weinans H. Trabecular bone's mechanical properties are affected by its non-uniform mineral distribution. J Biomech. December 2001;34(12):1573-1580.
2002	Jaasma MJ, Bayraktar HH, Niebur GL, Keaveny TM. Biomechanical effects of intraspecimen variations in tissue modulus for trabecular bone. J Biomech. 2002;35(2):237-246.
2003	Morgan EF, Bayraktar HH, Keaveny TM. Trabecular bone modulus–density relationships depend on anatomic site. J Biomech. July 2003;36(7):897-904.
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.
2004	Verhulp E, van Rietbergen B, Huiskes R. A three-dimensional digital image correlation technique for strain measurements in microstructures. J Biomech. September 2004;37(9):1313-1320.
2004	Morgan E, Bayraktar H, Yeh O, Majumdar S, Burghardt A, Keaveny T. Contribution of inter-site variations in architecture to trabecular bone apparent yield strains. J Biomech. 2004;37(9):1413-1420.
2008	Renders GAP, Mulder L, Langenbach GEJ, van Ruijven LJ, van Eijden TMGJ. Biomechanical effect of mineral heterogeneity in trabecular bone. J Biomech. August 2008;41(13):2793-2798.
2009	Liu XS, Bevill G, Keaveny TM, Sajda P, Guo XE. Micromechanical analyses of vertebral trabecular bone based on individual trabeculae segmentation of plates and rods. J Biomech. February 9, 2009;42(3):249-256.
2010	Shi X, Liu XS, Wang X, Guo XE, Niebur GL. Type and orientation of yielded trabeculae during overloading of trabecular bone along orthogonal directions. J Biomech. September 17, 2010;43(13):2460-2466.
2011	Golden KM, Murphy NB, Cherkaev E. Spectral analysis and connectivity of porous microstructures in bone. J Biomech. 2011;44(2):337-344.
2011	Cherkaev E, Bonifasi-Lista C. Characterization of structure and properties of bone by spectral measure method. J Biomech. January 11, 2011;44(2):345-351.
1998	Guldberg RE, Hollister SJ, Charras GT. The accuracy of digital image-based finite element models. J Biomech Eng. 1998;120(2):289-295.
1998	Zysset PK, Goulet RW, Hollister SJ. A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng. October 1998;120(5):640-646.
1999	Niebur GL, Yuen JC, Hsia AC, Keaveny TM. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng. December 1999;121(6):629-635.
2001	Pistoia W, van Rietbergen B, Laib A, Rüegsegger P. High-resolution three-dimensional-pqct images can be an adequate basis for in-vivo μfe analysis of bone. J Biomech Eng. October 2001;123(2):176-183.
2001	Adachi T, Tsubota K-i, Tomita Y, Hollister SJ. Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J Biomech Eng. October 2001;123(5):403-409.
2004	Wang X, Liu X, Niebur GL. Preparation of on-axis cylindrical trabecular bone specimens using micro-CT imaging. J Biomech Eng. February 2004;126(1):122-125.
2007	Kim CH, Zhang H, Mikhail G, von Stechow D, Müller R, Kim HS, Guo XE. Effects of thresholding techniques on μCT-based finite element models of trabecular bone. J Biomech Eng. 2007;129(4):481-486.
2009	Bonifasi-Lista C, Cherkaev E, Yeni YN. Analytical approach to recovering bone porosity from effective complex shear modulus. J Biomech Eng. December 2009;131(12):121003.
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.
2021	Bennison MBL, Pilkey AK, Lievers WB. Misalignment error in cancellous bone apparent elastic modulus depends on bone volume fraction and degree of anisotropy. J Biomech Eng. February 2021;143(2):021005.
1997	Guldberg RE, Caldwell NJ, Guo XE, Goulet RW, Hollister SJ, Goldstein SA. Mechanical stimulation of tissue repair in the hydraulic bone chamber. J Bone Miner Res. August 1997;12(8):1295-1302.
2000	Borah B, Dufresne TE, Cockman MD, Gross GJ, Sod EW, Myers WR, Combs KS, Higgins RE, Pierce SA, Stevens ML. Evaluation of changes in trabecular bone architecture and mechanical properties of minipig vertebrae by three‐dimensional magnetic resonance microimaging and finite element modeling. J Bone Miner Res. September 2000;15(9):1786-1797.
2001	van der Linden JC, Homminga J, Verhaar JAN, Weinans H. Mechanical consequences of bone loss in cancellous bone. J Bone Miner Res. March 2001;16(3):457-465.
2003	Van Rietbergen B, Huiskes R, Eckstein F, Rüegsegger P. Trabecular bone tissue strains in the healthy and osteoporotic human femur. J Bone Miner Res. October 2003;18(10):1781-1788.
2003	Kim CH, Takai E, Zhou H, Von Stechow D, Müller R, Dempster DW, Guo XE. Trabecular bone response to mechanical and parathyroid hormone stimulation: the role of mechanical microenvironment. J Bone Miner Res. December 2003;18(12):2116-2125.
2006	Stauber M, Rapillard L, van Lenthe GH, Zysset P, Müller R. Importance of individual rods and plates in the assessment of bone quality and their contribution to bone stiffness. J Bone Miner Res. April 2006;21(4):586-595.
2006	Liu XS, Sajda P, Saha PK, Wehrli FW, Guo XE. Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone. J Bone Miner Res. October 2006;21(10):1608-1617.
2008	Liu XS, Sajda P, Saha PK, Wehrli FW, Bevill G, Keaveny TM, Guo XE. Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone. J Bone Miner Res. February 2008;23(2):223-235.
2010	Liu XS, Zhang XH, Sekhon KK, Adams MF, McMahon DJ, Bilezikian JP, Shane E, Guo XE. High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone. J Bone Miner Res. April 2010;25(4):746-756.
2010	Liu XS, Cohen A, Shane E, Stein E, Rogers H, Kokolus SL, Yin PT, McMahon DJ, Lappe JM, Recker RR, Guo XE. Individual trabeculae segmentation (ITS)–based morphological analysis of high‐resolution peripheral quantitative computed tomography images detects abnormal trabecular plate and rod microarchitecture in premenopausal women with idiopathic osteoporosis. J Bone Miner Res. July 2010;25(7):1496-1505.
2010	Liu XS, Cohen A, Shane E, Yin PT, Stein EM, Rogers H, Kokolus SL, McMahon DJ, Lappe JM, Recker RR, Lang T, Guo XE. Bone density, geometry, microstructure, and stiffness: relationships between peripheral and central skeletal sites assessed by DXA, HR‐pQCT, and cQCT in premenopausal women. J Bone Miner Res. October 2010;25(10):2229-2238.
2010	Stein EM, Liu XS, Nickolas TL, Cohen A, Thomas V, McMahon DJ, Zhang C, Yin PT, Cosman F, Nieves J, Guo XE, Shane E. Abnormal microarchitecture and reduced stiffness at the radius and tibia in postmenopausal women with fractures. J Bone Miner Res. December 2010;25(12):2572-2581.
2012	Liu XS, Stein EM, Zhou B, Zhang CA, Nickolas TL, Cohen A, Thomas V, McMahon DJ, Cosman F, Nieves J, Shane E, Guo XE. Individual trabecula segmentation (ITS)‐based morphological analyses and microfinite element analysis of HR‐pQCT images discriminate postmenopausal fragility fractures independent of DXA measurements. J Bone Miner Res. February 2012;27(2):263-272.
2003	van Ruijven LJ, Giesen EBW, Farella M, van Eijden TMGJ. Prediction of mechanical properties of the cancellous bone of the mandibular condyle. J Dent Res. October 2003;82(10):819-823.
2013	Depalle B, Chapurlat R, Walter-Le-Berre H, Bou-Saïd B, Follet H. Finite element dependence of stress evaluation for human trabecular bone. J Mech Behav Biomed Mater. February 2013;18:200-212.
2014	Gillard F, Boardman R, Mavrogordato M, Hollis D, Sinclair I, Pierron F, Browne M. The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression. J Mech Behav Biomed Mater. January 2014;29:480-499.
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.
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.
1998	Ladd AJC, Kinney JH, Haupt DL, Goldstein SA. Finite‐element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus. J Orthop Res. September 1998;16(5):622-628.
2007	Fritsch A, Hellmich C. “Universal” microstructural patterns in bone: micromechanics-based prediction of anisotropic material behavior. J Theo Biol. February 21, 2007;244(4):597-620.
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.
1998	Lengsfeld M, Schmitt J, Alter P, Kaminsky J, Leppek R. Comparison of geometry-based and CT voxel-based finite element modelling and experimental validation. Med Eng Phys. October 1998;20(7):515-522.
2005	Kaminsky J, Rodt T, Gharabaghi A, Forster J, Brand G, Samii M. A universal algorithm for an improved finite element mesh generation: mesh quality assessment in comparison to former automated mesh-generators and an analytic model. Med Eng Phys. 2005;27(5):383-394.
2007	MacNeil JA, Boyd SK. Accuracy of high-resolution peripheral quantitative computed tomography for measurement of bone quality. Med Eng Phys. December 2007;29(10):1096-1105.
2013	Madi K, Tozzi G, Zhang Q, Tong J, Cossey A, Au A, Hollis D, Hild F. Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis. Med Eng Phys. September 2013;35(9):1298.
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.
2003	Kim CH. In Vivo Trabecular Bone Response to Mechanical Loading and Parathyroid Hormone Stimulation [PhD thesis]. Columbia University; 2003.
2007	Liu XS. High-Resolution Image Based Micro-Mechanical Modeling of Trabecular Bone [PhD thesis]. Columbia University; 2007.
2010	Zhang XH. High Resolution Imaging Based Patient Specific Biomechanical Assessment of Bone Quality [PhD thesis]. Columbia University; 2010.
2016	Wang J. Plate-Rod Microstructural Modeling for Accurate and Fast Assessment of Bone Strength [PhD thesis]. Columbia University; 2016.
2017	Yu Y. Contributions of Anisotropic and Heterogeneous Tissue Modulus to Apparent Trabecular Bone Mechanical Properties [PhD thesis]. Columbia University; 2017.
2007	Cole JH. The Role of Architecture and Tissue Properties in the Structural Integrity of Human Vertebral Cancellous Bone [PhD thesis]. Ithaca, NY: Cornell University; May 2007.
2018	Torres AM. Fatigue Behavior of Cancellous Bone, Microdamage Accumulation, and Biologically Inspired Cellular Solids [PhD thesis]. Ithaca, NY: Cornell University; August 2018.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Erasmus University Rotterdam; 2005.
2005	Stauber M. Volumetric Spatial Decomposition of Porous Microstructures: A Framework for Element Based Analysis of Trabecular Bone [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2005.
2007	Voide R. Functional Phenotyping of Bone: A Hierarchical Assessment of Bone Failure Characteristics [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2007.
2002	Follet H. Caractérisation Biomécanique Et Modélisation 3D Par Imagerie X Et IRM Haute Résolution De L’os Spongieux Humain: Evaluation Du Risque Fracturaire [PhD thesis]. Institut national des sciences appliquées de Lyon (INSA Lyon); 2002.
2009	Moesen M. Modeling of the Geometry and Mechanical Behavior of Bone Scaffolds [PhD thesis]. Katholieke Universiteit Leuven; June 2009.
1996	Silva MJ. Predicting the Failure Behavior of the Human Vertebral Body [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1996.
2001	Arthur Moore TL. Microdamage Accumulation in Bovine Trabecular Bone [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 2001.
2004	Wang X. Measurement and Analysis of Microdamage in Bone [PhD thesis]. University of Notre Dame; December 2004.
2010	Shi X. Effects of Architecture on Microdamage Susceptibility in Trabecular Bone [PhD thesis]. University of Notre Dame; April 2010.
2015	Gargac J. Evaluation of Bone Healing, Damage, and Adaptation Using Computational Modeling and Image Processing Techniques [PhD thesis]. University of Notre Dame; July 2015.
1996	Livesay GA. Development of Homogenization Theory for Soft Tissues Undergoing Finite Elastic Deformation [PhD thesis]. University of Pittsburgh; 1996.
2019	Mustafy T. The Short and Long Term Effects of in Vivo Cyclic Axial Compression Applied During Puberty on Bone Growth, Morphometry and Biomechanics [PhD thesis]. École polytechnique de Montréal; July 2019.
2016	Chen Y. Verification and Validation of MicroCT-Based Finite Element Models of Bone Tissue Biomechanics [PhD thesis]. Sheffield, UK: University of Sheffield; July 2016.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Southern Methodist University; August 3, 2011.
2006	Verhulp E. Analyses of Trabecular Bone Failure [PhD thesis]. Eindhoven, The Netherlands: Eindhoven University of Technology; 2006.
2014	Gross T. Development and Application of 3d CT Image-Based Micro and Macro Finite Element Models for Human Bones and Orthopedic Implant Systems [PhD thesis]. Vienna University of Technology; 2014.
2007	MacNeil JAM. Clinical Assessment of Bone Quality [PhD thesis]. Calgary, AB: University of Calgary; June 2007.
2013	Enns-Bray WS. Mapping Anisotropy of the Proximal Femur for Improved Image-Based Finite Element Analysis [Master's thesis]. Calgary, AB: University of Calgary; August 2013.
2000	Nauman EA. The Analytical Design of a Hybrid Bone Substitute [PhD thesis]. Berkeley, CA: Berkeley, University of California; Spring 2000.
2002	Morgan EF-i. The Dependence on Anatomic Site of Trabecular Bone Structure-Function Relationships [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2002.
2003	Bayraktar HH. Multiaxial Strength and Micromechanics of Human Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2003.
2008	Bevill GR. Micromechanical Modeling of Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2008.
1995	Guldberg RE. Mechanical Adaptation of Trabecular Bone Formation in Vivo [PhD thesis]. University of Michigan; 1995.
1996	Lerner AL. Influence of Mechanical Stresses on Normal Bone Growth in the Developing Femur [PhD thesis]. University of Michigan; 1996.
2000	Borodkin JL. The Influence of Interface Micromechanics on the Biological Fixation of Porous-Coated Implants [PhD thesis]. University of Michigan; 2000.
2000	McCreadie BR. Structural and Material Changes in Osteoporosis: Their Impact on the Mechanical Environment of the Osteocyte [PhD thesis]. University of Michigan; 2000.
2002	Palmer ML. A Non-Linear Hierarchical Model of Stretch-Induced Injury to Skeletal Muscle Fibers [PhD thesis]. University of Michigan; 2002.
2005	Lin C-Y. Solid-Fluid Mixture Microstructure Design of Composite Materials With Application to Tissue Engineering Scaffold Design [PhD thesis]. University of Michigan; 2005.
2006	Jongpaiboonkit L. Calcium Phosphate Scaffolds for Bone Tissue Engineering and Self-Association PEG-PLLA Diblock Copolymer for Controlled Drug Delivery System [PhD thesis]. University of Michigan; 2006.
2011	Saito E. Designed Biodegradable and Osteoconductive Porous Scaffolds for Human Trabecular Bone [PhD thesis]. University of Michigan; 2011.
2010	Schwen LO. Composite Finite Elements for Trabecular Bone Microstructures [PhD thesis]. Bonn, Germany: Rheinische Friedrich-Wilhelms-Universität Bonn; July 2010.
2010	Wald MJ. Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2010.
2017	de Bakker CMJ. Structural Adaptations of the Maternal Skeleton in Response to Reproduction and Lactation [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2017.
2021	Li Y. Adaptation of Maternal Skeletal Mechano-Responsiveness, Osteocyte Microenvironment, and Bone Marrow Adipocytes in Response to Reproduction and Lactation [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2021.
2018	Hosseini Kalajahi SM. Addressing Partial Volume Artifacts With Quantitative Computed Tomography-Based Finite Element Modeling of the Human Proximal Tibia [Master's thesis]. University of Saskatchewan; April 2018.
2002	Gardiner JC. Computational Modeling of Ligament Mechanics [PhD thesis]. University of Utah; May 2002.
2000	Simmons CA. Modelling and Characterization of Mechanically Regulated Tissue Formation Around Bone-Interfacing Implants [PhD thesis]. University of Toronto; 2000.
2001	Zhang N. Investigation of Bone Mechanical Properties At the Microscopic Level Using Ultrasonic Methods and Numerical Simulation [PhD thesis]. Detroit, MI: Wayne State University; 2001.
2005	Cao KD. Development of a 4-Vertebrae, Detailed Finite Element Model of Thoracolumbar Spine [PhD thesis]. Detroit, MI: Wayne State University; August 2005.
2009	García-Rodríguez S. Mechanical Behavior of Trabecular Bone [PhD thesis]. University of Wisconsin – Madison; 2009.

Year	Entry
1987	Parfitt AM. Bone remodeling and bone loss: understanding the pathophysiology of osteoporosis. Clin Obstet Gynecol. December 1987;30(4):789-811.
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1985	Kleerekoper M, Villanueva AR, Stanciu J, Rao DS, Parfitt AM. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tiss Int. 1985;37(6):594-597.
1986	Fyhrie DP. Stress Analysis and Design of Proximal Femoral Prostheses [PhD thesis]. Stanford University; January 1986.
1973	Pugh JW, Rose RM, Radin EL. A structural model for the mechanical behavior of trabecular bone. J Biomech. 1973;6(6):657-670.
1991	Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. Application of homogenization theory to the study of trabecular bone mechanics. J Biomech. 1991;24(9):825-839.
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. April 1994;27(4):375-389.
1988	Mosekilde L. Age-related changes in vertebral trabecular bone architecture—assessed by a new method. Bone. 1988;9(4):247-250.
1989	Feldkamp LA, Goldstein SA, Parfitt MA, Jesion G, Kleerekoper M. The direct examination of three‐dimensional bone architecture in vitro by computed tomography. J Bone Miner Res. 1989;4(1):3-11.
1990	Mosekilde L. Age-related loss of vertebral trabecular bone mass and structure: biomechanical consequences. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:84-96.
1988	Mosekilde L, Mosekilde L. Iliac crest trabecular bone volume as predictor for vertebral compressive strength, ash density and trabecular bone volume in normal individuals. Bone. 1988;9(4):195-199.
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. May 1991;9(5):674-682.
1985	Beaupre GS, Hayes WC. Finite element analysis of a three-dimensional open-celled model for trabecular bone. J Biomech Eng. August 1985;107(3):249-256.
1989	Ferencz RM. Element-by-Element Preconditioning Techniques for Large-Scale, Vectorized Finite Element Analysis in Nonlinear Solid and Structural Mechanics [PhD thesis]. Stanford University; March 1989.
1986	Frost HM. Intermediary Organization of the Skeleton. Vols. 1-2. Boca Raton, FL: CRC Press; 1986.
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.
1987	Goldstein SA. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomech. 1987;20(11-12):1055-1061.
1990	Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech. 1990;23(6):549-561.
1988	Harrigan TP, Jasty M, Mann RW, Harris WH. Limitations of the continuum assumption in cancellous bone. J Biomech. 1988;21(4):269-275.
1989	Mente PL, Lewis JL. Experimental method for the measurement of the elastic modulus of trabecular bone tissue. J Orthop Res. 1989;7(3):456-461.
1982	Williams JL, Lewis JL. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. J Biomech Eng. February 1982;104(1):50-56.
1985	Cowin SC. The relationship between the elasticity tensor and the fabric tensor. Mech Mater. 1985;4(2):137-147.
1992	Hollister SJ, Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech. March 1992;10(2):73-95.
1993	Hollister SJ, Riemer BA. Digital image based finite element analysis for bone microstructure using conjugate gradient and Gaussian filter techniques. In: Wilson JN, Wilson DC, eds. Mathematical Methods in Medical Imaging II. SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation; July 11-16, 1993; San Diego, CA.95-106. Proceedings of the SPIE; vol 2035.
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.
1963	Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids. September 1963;11(5):357-372.
1991	Weinans HH. Mechanically Induced Bone Adaptations Around Orthopaedic Implants [PhD thesis]. Nijmegen, The Netherlands: Katholieke Universiteit te Nijmegen; 1991.
1990	Mosekilde L. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner. July 1990;10(1):13-35.
1993	Crolet JM, Aoubiza B, Meunier A. Compact bone: numerical simulation of mechanical characteristics. J Biomech. June 1993;26(6):677-687.
1989	Martin RB, Burr DB. Structure, Function, and Adaptation of Compact Bone. New York, NY: Raven Press; 1989.
1990	Kuhn JL, Goldstein SA, Feldkamp LA, Goulet RW, Jesion G. Evaluation of a microcomputed tomography system to study trabecular bone structure. J Orthop Res. 1990;8(6):833-842.
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.
1983	Parfitt AM, Mathews CH, Villanueva AR, Kleerekoper M, Frame B, Rao DS. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis: implications for the microanatomic and cellular mechanisms of bone loss. J Clin Invest. October 1983;72(4):1396-1409.