• 1
    Conference Report. NIH Consensus Development Panel on Osteoporosis Prevention. Consensus Development Conference. Prophylaxis and treatment of osteoporosis. Osteoporos Int. 1991; 1(2):1147.
  • 2
    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):15568.
  • 3
    Snyder BD, Piazza S, Edwards WT, Hayes WC. Role of trabecular morphology in the etiology of age-related vertebral fractures. Calcif Tissue Int. 1993; 53(Suppl 1):S1422.
  • 4
    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):37589.
  • 5
    Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001; 3:30733.
  • 6
    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):112736.
  • 7
    Morgan EF, Keaveny TM. Dependence of yield strain of human trabecular bone on anatomic site. J Biomech. 2001; 34(5):56977.
  • 8
    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. 2000; 33(12):157583.
  • 9
    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):62935.
  • 10
    Boutroy S, Bouxsein ML, Munoz F, Delmas PD. In vivo assessment of trabecular bone microarchitecture by high-resolution peripheral quantitative computed tomography. J Clin Endocrinol Metab. 2005; 90(12):650815.
  • 11
    Kazakia GJ, Hyun B, Burghardt AJ, Krug R, Newitt DC, de Papp AE, Link TM, Majumdar S. In vivo determination of bone structure in postmenopausal women: a comparison of HR-pQCT and high-field MR imaging. J Bone Miner Res. 2008; 23(4):46374.
  • 12
    Wehrli FW, Ladinsky GA, Jones C, Benito M, Magland J, Vasilic B, Popescu AM, Zemel B, Cucchiara AJ, Wright AC, Song HK, Saha PK, Peachey H, Snyder PJ. In vivo magnetic resonance detects rapid remodeling changes in the topology of the trabecular bone network after menopause and the protective effect of estradiol. J Bone Miner Res. 2008; 23(5):73040.
  • 13
    Boutroy S, van Rietbergen B, Sornay-Rendu E, Munoz F, Bouxsein ML, Delmas PD. Finite element analyses based on in vivo HR-pQCT images of the distal radius is associated with wrist fracture in postmenopausal women. J Bone Miner Res. 2008; 23(3):3929.
  • 14
    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. 2010; 25(4):74656.
  • 15
    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. 2008; 42(6):120313.
  • 16
    Liu XS, Zhang XH, Rajapakse CS, Wald MJ, Magland J, Sekhon KK, Adam MF, Sajda P, Wehrli FW, Guo XE. Accuracy of high-resolution in vivo micro magnetic resonance imaging for measurements of microstructural and mechanical properties of human distal tibial bone. J Bone Miner Res. 2010; 25(9):203950.
  • 17
    Vilayphiou N, Boutroy S, Sornay-Rendu E, Van Rietbergen B, Munoz F, Delmas PD, Chapurlat R. Finite element analysis performed on radius and tibia HR-pQCT images and fragility fractures at all sites in postmenopausal women. Bone. 2010; 46(4):10307.
  • 18
    Zhang XH, Liu XS, Vasilic B, Wehrli FW, Benito M, Rajapakse CS, Snyder PJ, Guo XE. In vivo µMRI based finite element and morphological analyses of tibial trabecular bone in eugonadal and hypogonadal men before and after testosterone treatment. J Bone Miner Res. 2008; 23(9):142634.
  • 19
    Liu XS, Walker MD, McMahon DJ, Udesky J, Liu G, Bilezikian JP, Guo XE. Better skeletal microstructure confers greater mechanical advantages in Chinese-American women versus Caucasian women. J Bone Miner Res. 2011; 26(8):178392.
  • 20
    Burghardt AJ, Kazakia GJ, Sode M, de Papp AE, Link TM, Majumdar S. A longitudinal HR-pQCT study of alendronate treatment in postmenopausal women with low bone density: Relations among density, cortical and trabecular microarchitecture, biomechanics, and bone turnover. J Bone Miner Res. 2010; 25(12):255871.
  • 21
    Melton LJ 3rd, Christen D, Riggs BL, Achenbach SJ, Muller R, van Lenthe GH, Amin S, Atkinson EJ, Khosla S. Assessing forearm fracture risk in postmenopausal women. Osteoporos Int. 2010; 21(7):11619.
  • 22
    Stein EM, Liu XS, Nickolas TL, Cohen A, McMahon DJ, Zhou B, Zhang C, Kamanda-Kosseh M, Cosman F, Nieves J, Guo XE, Shane E. Microarchitectural abnormalities are more severe in postmenopausal women with vertebral compared to nonvertebral fractures. J Clin Endocrinol Metab. 2012; 97(10):E191826.
  • 23
    Stein EM, Liu XS, Nickolas TL, Cohen A, Thomas V, McMahon DJ, Zhang C, Cosman F, Nieves J, Greisberg J, Guo XE, Shane E. Abnormal microarchitecture and stiffness in postmenopausal women with ankle fractures. J Clin Endocrinol Metab. 2011; 96(7):20418.
  • 24
    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. 2010; 25(12):2296305.
  • 25
    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. 2006; 39(6):121825.
  • 26
    Liu XS, Cohen A, Shane E, Stein E, Rogers HF, Kokolus SL, Yin PT, McMahon DJ, Lappe JM, Recker RR, Guo XE. Individual trabeculae segmentation (ITS)-based morphological analyses of high resolution peripheral quantitative computed tomography images detect abnormal trabecular plate and rod microarchitecture in premenopausal women with idiopathic osteoporosis. J Bone Miner Res. 2010; 25(7):1486505.
  • 27
    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. 2006; 21(10):160817.
  • 28
    Stauber M, Rapillard L, van Lenthe GH, Zysset P, Muller R. Importance of individual rods and plates in the assessment of bone quality and their contribution to bone stiffness. J Bone Miner Res. 2006; 21(4):58695.
  • 29
    Wehrli FW, Gomberg BR, Saha PK, Song HK, Hwang SN, Snyder PJ. Digital topological analysis of in vivo magnetic resonance microimages of trabecular bone reveals structural implications of osteoporosis. J Bone Miner Res. 2001; 16(8):152031.
  • 30
    Pialat JB, Vilayphiou N, Boutroy S, Gouttenoire PJ, Sornay-Rendu E, Chapurlat R, Peyrin F. Local topological analysis at the distal radius by HR-pQCT: Application to in vivo bone microarchitecture and fracture assessment in the OFELY study. Bone. 2012; 51(3):3628.
  • 31
    Liu XS, Sajda P, Guo XE. Specimen-specific plate-rod microstructural finite element model efficiently predicts the elastic moduli and yield strength of human vertebral trabecular bone. Trans Orthop Res Soc. 2008; 33:420.
  • 32
    Liu XS, Shane E, Guo XE. HR-pQCT-based specimen-specific plate-rod microstructural finite element model accurately and efficiently predicts the elastic modulus of human trabecular bone at distal tibia. Trans Orthop Res Soc. 2010; 35:68.
  • 33
    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. 2008; 23(2):223235.
  • 34
    Zhou B, Wang J, Sanyal A, Fields AJ, Keaveny TM, Liu XS, Guo XE. Individual trabecula segmentation (ITS)-based plate-rod microstructural finite element model predict nonlinear mechanical properties of human trabecular bone. Proceedings of the ASME 2012 Summer Bioengineering Conference, SBC2012-8065 2, June 20–23, 2012, Fajardo, Puerto Rico.
  • 35
    Lazebnik M, Madsen EL, Frank GR, Hagness SC. Tissue-mimicking phantom materials for narrowband and ultrawideband microwave applications. Phys Med Biol. 2005; 50(18):424558.
  • 36
    Viola P, Wells WM III. Alignment by maximization of mutual information. Int J Comput Vis. 1997; 24(2):13754.
  • 37
    Collignon A, Maes F, Delaere D, Vandermeulen D, Suetens P, Marchal G. Automated multi-modality image registration based on information theory. In: Bizais Y, Barillot C, di Paola R, editiors. Information processing in medical imaging. Dordrecht. The Netherlands: Kluwer Academic Publishers; p. 26374. 1995.
  • 38
    Ibáñez L, Schroeder W, Ng L, Cates J; Insight Software Consortium. The ITK Software Guide, 2nd ed, Updated for ITK version 2.4 [Internet]. Bethesda, MD: Insight Segmentation and Registration Toolkit (ITK), National Library of Medicine; 2005 [cited 2013 Mar 8]. Available from:
  • 39
    MacNeil JA, Boyd SK. Accuracy of high-resolution peripheral quantitative computed tomography for measurement of bone quality. Med Eng Phys. 2007; 29(10):1096105.
  • 40
    Liu XS, Shane E, McMahon DJ, Guo XE. Individual trabecula segmentation (ITS)-based morphological analysis of micro-scale images of human tibial trabecular bone at limited spatial resolution. J Bone Miner Res. 2011; 26(9):218493.
  • 41
    Genant HK, Wu CY, van Kuijk C, Nevitt MC. Vertebral fracture assessment using a semiquantitative technique. J Bone Miner Res. 1993; 8(9):113748.
  • 42
    Sornay-Rendu E, Boutroy S, Munoz F, Delmas PD. Alterations of cortical and trabecular architecture are associated with fractures in postmenopausal women, partially independent of decreased BMD measured by DXA: the OFELY study. J Bone Miner Res. 2007; 22(3):42533.
  • 43
    Laib A, Hauselmann HJ, Ruegsegger P. In vivo high resolution 3D-QCT of the human forearm. Technol Health Care. 1998; 6(5–6):32937.
  • 44
    Saha PK, Chaudhuri BB. Detection of 3-D simple points for topology preserving. IEEE Trans Pattern Anal Mach Intell. 1994; 16(10):102832.
  • 45
    Saha PK, Chaudhuri BB. 3D digital topology under binary transformation with applications. Comput Vis Image Underst. 1996; 63(3):41829.
  • 46
    Saha PK, Chaudhuri BB, Majumder DD. A new shape preserving parallel thinning algorithm for 3D digital images. Pattern Recogn. 1997; 30(12):193955.
  • 47
    Liu XS. High-resolution image based micro-mechanical modeling of trabecular bone [dissertation]. [New York]: Columbia University; 2007.
  • 48
    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):113746.
  • 49
    Papadopoulos P, Liu J. On the formulation and numerical solution of problems in anisotropic finite plasticity. Comp Meth Appl Mech Eng. 2001; 190(37–38):4889910.
  • 50
    Papadopoulos P, Lu J. A general framework for the numerical solution of problems in finite elasto-plasticity. Comput Methods Appl Mech Eng. 1998; 159(1–2):118.
  • 51
    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. 2004; 37(1):2735.
  • 52
    Adams MF, Bayraktar HH, Keaveny TM, Papadopoulos P. Ultrascalable implicit finite element analysis in solid mechanics with over a half a billion degrees of freedom. ACM/IEEE Proceedings of SC2004: High Performance Networking and Computing. Pittsburgh, PA; 2004.
  • 53
    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. 2010; 25(10):222938.
  • 54
    Pothuaud L, Van Rietbergen B, Charlot C, Ozhinsky E, Majumdar S. A new computational efficient approach for trabecular bone analysis using beam models generated with skeletonized graph technique. Comput Methods Biomech Biomed Engin. 2004; 7(4):20513.
  • 55
    Stauber M, Huber M, Van Lenthe GH, Boyd SK, Muller R. A finite element beam-model for efficient simulation of large-scale porous structures. Comput Methods Biomech Biomed Engin. 2004; 7(1):916.
  • 56
    van Lenthe GH, Stauber M, Muller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone. 2006; 39(6):11829.
  • 57
    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. 2009; 42(3):24956.
  • 58
    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 micro finite element analysis of HR-pQCT images discriminate postmenopausal fragility fractures independent of DXA measurements. J Bone Miner Res. 2012; 27(2):26372.
  • 59
    Wang H, Liu XS, Zhou B, Wang J, Ji B, Hwang K-C, Guo XE. Accuracy of individual trabecula segmentation based plate-rod finite element models in idealized trabecular bone microstructure. J Biomech Eng. (in press). DOI: 10.1115/1.4023983
  • 60
    Vanderoost J, Jaecques SV, Van der Perre G, Boonen S, D'Hooge J, Lauriks W, van Lenthe GH. Fast and accurate specimen-specific simulation of trabecular bone elastic modulus using novel beam-shell finite element models. J Biomech. 2010; 44(8):156672.
  • 61
    McNamara LM, Ederveen AG, Lyons CG, Price C, Schaffler MB, Weinans H, Prendergast PJ. Strength of cancellous bone trabecular tissue from normal, ovariectomized and drug-treated rats over the course of ageing. Bone. 2006; 39(2):392400.
  • 62
    Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. 1993; 26(2):1119.
  • 63
    Rho JY, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997; 18(20):132530.
  • 64
    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):6981.
  • 65
    Wolfram U, Wilke HJ, Zysset PK. Valid micro finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions. J Biomech. 2010; 43(9):17317.
  • 66
    Kim CH, Zhang H, Mikhail G, von Stechow D, Muller R, Kim HS, Guo XE. Effects of thresholding techniques on microCT-based finite element models of trabecular bone. J Biomech Eng. 2007; 129(4):4816.