Relating mechanical properties of vertebral trabecular bones to osteoporosis

References

• Adams JE. 2013. Advances in bone imaging for osteoporosis. Nat Rev Endocrinol. 9(1):28–42.
   PubMed Web of Science ®Google Scholar
• Amstrup AK, Jakobsen NFB, Moser E, Sikjaer T, Mosekilde L, Rejnmark L. 2016. Association between bone indices assessed by DXA, HR-pQCT and QCT scans in post-menopausal women. J Bone Miner Metab. 34(6):638–645.
   PubMed Web of Science ®Google Scholar
• Aoubiza B, Crolet JM, Meunier A. 1996. On the mechanical characterization of compact bone structure using the homogenization theory. J Biomech. 29(12):1539–1547.
   PubMed Web of Science ®Google Scholar
• Ashman RB, Corin JD, Turner CH. 1987. Elastic properties of cancellous bone: measurement by an ultrasonic technique. J Biomech. 20(10):979–986.
   PubMed Web of Science ®Google Scholar
• Augat P, Link T, Lang TF, Lin JC, Majumdar S, Genant HK. 1998. Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations. Med Eng Phys. 20(2):124–131.
   PubMed Web of Science ®Google Scholar
• Bakhvalov N, Panasenko G. 1989. Homogenisation: averaging Processes in periodic media. Dordrecht: Springer Netherlands.
   Google Scholar
• Ballane G, Cauley JA, Luckey MM, El-Hajj Fuleihan G. 2017. Worldwide prevalence and incidence of osteoporotic vertebral fractures. Osteoporos Int. 28(5):1531–1542.
   PubMed Web of Science ®Google Scholar
• Barak MM, Black MA. 2018. A novel use of 3D printing model demonstrates the effects of deteriorated trabecular bone structure on bone stiffness and strength. J Mech Behav Biomed Mater. 78:455–464.
   PubMed Web of Science ®Google Scholar
• Basaruddin KS, Takano N. 2014. Estimation of apparent elastic moduli of trabecular bone considering biological apatite (BAp) crystallite orientation in tissue modulus. Advanced Materials Research. Vol. 894; p. 167–171.
   Google Scholar
• Borges JLC, de M Miranda IS, Lewiecki EM. 2017. The Clinical utility of vertebral fracture assessment in predicting fractures. J Clin Densitometry. 20(3):304–308.
   PubMed Web of Science ®Google Scholar
• Burr DB. 2019. Changes in bone matrix properties with aging. Bone. 120:85–93.
   PubMed Web of Science ®Google Scholar
• Cesar R, Boffa RS, Fachine LT, Leivas TP, Silva AMH, Pereira CAM, Reiff RBM, Rollo J. 2013. Evaluation of trabecular microarchitecture of normal osteoporotic and osteopenic human vertebrae. Proc Eng. 59:6–15.
   Google Scholar
• Cesar R, Leivas TP, Pereira CAM, Boffa RS, Guarniero R, Reiff RB, de M, Mandeli Netto A, Fortulan CA, Rollo JMDDA. 2017. Axial compressive strength of human vertebrae trabecular bones classified as normal, osteopenic and osteoporotic by quantitative ultrasonometry of calcaneus. Res Biomed Eng. 33(2):91–96.
   Google Scholar
• Chandran M. 2017. Fracture risk assessment in clinical practice: why do it? What to do it with? J Clin Densitometry. 20(3):274–279.
   PubMed Web of Science ®Google Scholar
• Chappard D, Baslé MF, Legrand E, Audran M. 2008. Trabecular bone microarchitecture: a review. Morphologie. 92(299):162–170.
   PubMedGoogle Scholar
• Chappard D, Baslé MF, Legrand E, Audran M. 2011. New laboratory tools in the assessment of bone quality. Osteoporos Int. 22(8):2225–2240.
   PubMed Web of Science ®Google Scholar
• Charalambakis N. 2010. Homogenization techniques and micromechanics. A survey and perspectives. Appl Mech Rev. 63(3):030803.
   Web of Science ®Google Scholar
• Chen Y, Dall׳Ara E, Sales E, Manda K, Wallace R, Pankaj P, Viceconti M. 2017. 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. 65:644–651.
   PubMed Web of Science ®Google Scholar
• Cherraf-Schweyer C, Maurice G, Taghite M, Taous K. 2007. An experimental and theoretical approach of elasticity and viscoelasticity of compact and spongy bone with periodic homogenization. Comput Methods Biomech Biomed Eng. 10(3):195–207.
   PubMedGoogle Scholar
• Chevalier Y, Charlebois M, Pahr D, Varga P, Heini P, Schneider E, Zysset P. 2008. A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads. Comput Methods Biomech Biomed Eng. 11(5):477–487.
   PubMed Web of Science ®Google Scholar
• Choi AH, Ben-Nissan B. 2018. Anatomy, modeling and biomaterial fabrication for dental and maxillofacial applications. University of Technology Sydney, Australia: Bentham Science Publishers.
   Google Scholar
• Cioranescu D, Paulin J. 1999. Homogenization of reticulated structures. Vol. 136. New York (NY): Springer-Verlag.
   Google Scholar
• Cowin S. C. 2001. Bone mechanics handbook. Vol. 2. Boca Raton, USA: CRC Press.
   Google Scholar
• Cowin SC. 1989. The mechanical properties of cancellous bone. In: Cowin SC, editor. Bone mechanics. Boca Raton (FL): CRC Press; p. 129–157.
   Google Scholar
• Crolet JM, Aoubiza B, Meunier A. 1993. Compact bone: numerical simulation of mechanical characteristics. J Biomech. 26(6):677–687.
   PubMed Web of Science ®Google Scholar
• Currey JD. 1970. The mechanical properties of bone. Clin Orthop Rel Res. 73:210–231.
   Google Scholar
• Currey JD. 2006. Bones: structure and mechanics. Princeton (NJ): Princeton University Press.
   Google Scholar
• Curtis EM, Moon RJ, Harvey NC, Cooper C. 2017. Reprint of: the impact of fragility fracture and approaches to osteoporosis risk assessment worldwide. Int J Orthopaedic Trauma Nurs. 26:7–17.
   PubMed Web of Science ®Google Scholar
• Cyganik Ł, Binkowski M, Kokot G, Rusin T, Popik P, Bolechała F, Nowak R, Wróbel Z, John A. 2014. Prediction of Young’s modulus of trabeculae in microscale using macro-scale’s relationships between bone density and mechanical properties. J Mech Behav Biomed Mater. 36:120–134.
   PubMed Web of Science ®Google Scholar
• D’Elia G, Caracchini G, Cavalli L, Innocenti P. 2009. Bone fragility and imaging techniques. Clin Cases Miner Bone Metab. 6:234–246.
   PubMedGoogle Scholar
• Damm T, Peña JA, Campbell GM, Bastgen J, Barkmann R, Glüer CC. 2019. Improved accuracy in the assessment of vertebral cortical thickness by quantitative computed tomography using the Iterative Convolution OptimizatioN (ICON) method. Bone. 120:194–203.
   PubMed Web of Science ®Google Scholar
• Dempster DW, Compston JE, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR, Parfitt AM. 2013. Standardized nomenclature, symbols, and units for bone histomorphometry: a 2012 update of the report of the ASBMR Histomorphometry Nomenclature Committee. J Bone Miner Res. 28(1):2–17.
   PubMed Web of Science ®Google Scholar
• Dimai HP. 2017. Use of dual-energy X-ray absorptiometry (DXA) for diagnosis and fracture risk assessment; WHO-criteria, T- and Z-score, and reference databases. Bone. 104:39–43.
   PubMed Web of Science ®Google Scholar
• Dos Reis F, Ganghoffer JF. 2012. Construction of micropolar continua from the asymptotic homogenization of beam lattices. Comput Struct. 112–113:354–363.
   Web of Science ®Google Scholar
• Dos Reis F, Ganghoffer JF. 2014. Homogenized elastoplastic response of repetitive 2D lattice truss materials. Comput Mater Sci. 84:145–155.
   Web of Science ®Google Scholar
• ElNady K, Goda I, Ganghoffer J-F. 2016. Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities. Comput Mech. 58(6):957–979.
   Web of Science ®Google Scholar
• Evans F.G. 1973. Mechanical properties of bone. In: Burdi AR, editor. American lecture series. Springfield (IL): Charles C. Thomas; p. 8–9.
   Google Scholar
• Fairfield H, Falank C, Farrell M, Vary C, Boucher JM, Driscoll H, Liaw L, Rosen CJ, Reagan MR. 2019. Development of a 3D bone marrow adipose tissue model. Bone. 118:77–88.
   PubMed Web of Science ®Google Scholar
• Fields AJ, Nawathe S, Eswaran SK, Jekir MG, Adams MF, Papadopoulos P, Keaveny TM. 2012. Vertebral fragility and structural redundancy. J Bone Miner Res. 27(10):2152–2158.
   PubMed Web of Science ®Google Scholar
• Fonseca H, Moreira-Gonçalves D, Coriolano HJA, Duarte JA. 2014. Bone quality: the determinants of bone strength and fragility. Sports Med. 44(1):37–53.
   PubMed Web of Science ®Google Scholar
• Galka A, Telega JJ, Tokarzewski S. 1999. Application of homogenization to evaluation of effective moduli of linear elastic trabecular bone with plate-like structure. Arch Mech. 51:335–355.
   Google Scholar
• Geers MGD, Kouznetsova VG, Matouš K, Yvonnet J. 2017. Homogenization methods and multiscale modeling: nonlinear problems. In: Encyclopedia of computational mechanics. Vol. 2, Chichester (UK): John Wiley & Sons; p. 1–34.
   Google Scholar
• Geusens P, Chapurlat R, Schett G, Ghasem-Zadeh A, Seeman E, De Jong J, Van Den Bergh J. 2014. High-resolution in vivo imaging of bone and joints: a window to microarchitecture. Nat Rev Rheumatol. 10(5):304–313.
   PubMed Web of Science ®Google Scholar
• Gibson J, Ashby MF. 1997. Cellular solids (structure and properties). Vol. 2. Cambridge: Cambridge University Press.
   Google Scholar
• Gibson LJ. 2005. Biomechanics of cellular solids. J Biomech. 38(3):377–399.
   PubMed Web of Science ®Google Scholar
• Goda I, Assidi M, Ganghoffer JF. 2014. A 3D elastic micropolar model of vertebral trabecular bone from lattice homogenization of the bone microstructure. Biomech Model Mechanobiol. 13(1):53–83.
   PubMed Web of Science ®Google Scholar
• Goda I, Ganghoffer JF. 2018. Modeling of anisotropic remodeling of trabecular bone coupled to fracture. Arch Appl Mech. 88(12):2101–2121.
   Web of Science ®Google Scholar
• Goda I, Rahouadj R, Ganghoffer JF, Kerdjoudj H, Siad L. 2016. 3D couple-stress moduli of porous polymeric biomaterials using μcT image stack and FE characterization. Int J Eng Sci. 100:25–44.
   Web of Science ®Google Scholar
• Griffith JF, Genant HK. 2008. Bone mass and architecture determination: state of the art. Best practice and research. Clin Endocrinol Metab. 22:737–764.
   Google Scholar
• Guilak F. 1994. Volume and surface area measurement of viable chondrocytes in situ using geometric modelling of serial confocal sections. J Microsc. 173(3):245–256.
   PubMedGoogle Scholar
• Hamed E, Jasiuk I, Yoo A, Lee Y, Liszka T. 2012. Multi-scale modelling of elastic moduli of trabecular bone. J R Soc Interface. 9(72):1654–1673.
   PubMed Web of Science ®Google Scholar
• Hans D, Baim S. 2017. Quantitative ultrasound (QUS) in the management of osteoporosis and assessment of fracture risk. J Clin Densitometry. 20(3):322–333.
   PubMed Web of Science ®Google Scholar
• Hill R, Hearmon R. 1964. An introduction to applied anisotropic elasticity. Math Gaz. 48(363):129.
   Google Scholar
• Hollister SJ, Brennan JM, Kikuchi N. 1994. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stress. J Biomech. 27(4):433–444.
   PubMed Web of Science ®Google Scholar
• Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. 1991. Application study of homogenization theory to the trabecular bone mechanics. J Biomech. 24:825–839.
   PubMed Web of Science ®Google Scholar
• Hollister SJ, Kikuchi N. 1992. A comparison of homogenization and standard mechanics analyses for periodic porous composites. In: Computational mechanics. Vol. 10. New York (NY): Springer-Verlag; p. 73–95.
   Google Scholar
• Hollister SJ, Kikuchi N. 1994. Homogenization theory and digital imaging: a basis for studying the mechanics and design principles of bone tissue. Biotechnol Bioeng. 43(7):586–596.
   PubMed Web of Science ®Google Scholar
• Johnson MW. Jr. 1967. Theory of elasticity of an anisotropic elastic body. SIAM Rev. 9:136–136.
   Web of Science ®Google Scholar
• Kanis J. A, Cooper C, Rizzoli R, Reginster J.-Y. 2018. Review of the guideline of the American College of Physicians on the treatment of osteoporosis. Osteoporos Int. 29(7):1505–1510.
   PubMed Web of Science ®Google Scholar
• Karaguzel G, Holick MF. 2010. Diagnosis and treatment of osteopenia. Rev Endocr Metab Disord. 11(4):237–251.
   PubMed Web of Science ®Google Scholar
• Keaveny TM, Morgan EF, Niebur GL, Yeh OC. 2001. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 3(1):307–333.
   PubMedGoogle Scholar
• Kowalczyk P. 2003. Elastic properties of cancellous bone derived from finite element models of parameterized microstructure cells. J Biomech. 36:961–972.
   PubMed Web of Science ®Google Scholar
• Liu X S, Zhang X H, Rajapakse C S, Wald M J, Magland J, Sekhon K K, Adam M F, Sajda P, Wehrli F W, Guo X E. 2010. High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone. J Bone Miner Res. 25(9):2039–2756.
   PubMedGoogle Scholar
• Lloyd AA, Wang ZX, Donnelly E. 2015. Multiscale contribution of bone tissue material property heterogeneity to trabecular bone mechanical behavior. J Biomech Eng. 137(1):010801.
   Web of Science ®Google Scholar
• Lopes DL, Martins-Cruz C, Oliveira MB, Mano JF. 2018. Bone physiology as inspiration for tissue regenerative therapies. Biomaterials. 185:240–275.
   PubMed Web of Science ®Google Scholar
• Lorensen WE, Cline HE. 1987. Marching cubes: a high resolution 3D surface construction algorithm. Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH ’87. Vol. 21. New York (NY): ACM Press; p. 163–169.
   Google Scholar
• Loures M A R, Zerbini C A F, Danowski J S, Pereira R M R, Moreira C, Paula A P d, Castro C H M, Szejnfeld V L, Mendonça L M C, Radominiski S C, et al. 2017. Guidelines of the Brazilian Society of Rheumatology for the diagnosis and treatment of osteoporosis in men. Rev Bras de Reumatologia. 57:497–514.
   PubMedGoogle Scholar
• Mahadevan V. 2018. Anatomy of the vertebral column. Surgery (Oxford). 36(7):327–332. doi:10.1016/j.mpsur.2018.05.006.
   Google Scholar
• Maquer G, Musy SN, Wandel J, Gross T, Zysset PK. 2015. Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables. J Bone Miner Res. 30(6):1000–1008. doi:10.1002/jbmr.2437.
   PubMed Web of Science ®Google Scholar
• Martin RB, Burr DB, Sharkey NA, Fyhrie DP. 2015. Mechanical properties of bone. In: Skeletal tissue mechanics. Vol. 2. New York (NY): Springer; p. 355–422.
   Google Scholar
• Metcalf L M, Dall'Ara E, Paggiosi M A, Rochester J R, Vilayphiou N, Kemp G J, McCloskey E V. 2018. Validation of calcaneus trabecular microstructure measurements by HR-pQCT. Bone. 106:69–77.
   PubMed Web of Science ®Google Scholar
• Michael Lewiecki E, Binkley N. 2017. DXA: 30 years and counting. Bone. 104:1–3.
   PubMed Web of Science ®Google Scholar
• Müller R, Rüegsegger P. 1994. Three-dimensional finite element assessed trabecular modelling of bone structures. Med Eng Phys. 17:126–133.
   Web of Science ®Google Scholar
• Nazemi SM, Cooper DML, Johnston JD. 2016. Quantifying trabecular bone material anisotropy and orientation using low-resolution clinical CT images: a feasibility study. Med Eng Phys. 38(9):978–987.
   PubMed Web of Science ®Google Scholar
• Novitskaya E, Chen P-Y, Hamed E, Jun L, Lubarda V, Jasiuk I, Mckittrick J. 2011. Recent advances on the measurement and calculation of the elastic moduli of cortical and trabecular bone: a review. Theor Appl Mech (Belgr). 38(3):209–297.
   Google Scholar
• Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. 2015. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. 137(1):010802.
   Web of Science ®Google Scholar
• Oleinik OA, Shamaev AS, Yosifian GA. 1992. Mathematical problems in elasticity and homogenization. In: Studies in mathematics and its applications. Vol. 26. Amsterdam: North-Holland; p. 1–398.
   Google Scholar
• Osterhoff G, Morgan EF, Shefelbine SJ, Karim L, McNamara LM, Augat P. 2016. Bone mechanical properties and changes with osteoporosis. Injury. 47:S11–S20.
   PubMed Web of Science ®Google Scholar
• Ott SM. 2018. Cortical or trabecular bone: what’s the difference? Am J Nephrol. 47(6):373–375.
   PubMed Web of Science ®Google Scholar
• Papanicolau G, Bensoussan A, Lions JL. 1978. Asymptotic analysis for periodic structures. In: Studies in mathematics and its applications. Vol. 1. Amsterdam: North-Holland; p. 1–699.
   Google Scholar
• Parfitt AM. 2002. Misconceptions (2): turnover is always higher in cancellous than in cortical bone. Bone. 30(6):807–809.
   PubMed Web of Science ®Google Scholar
• Parnell WJ, Grimal Q. 2009. The influence of mesoscale porosity on cortical bone anisotropy. Investigations via asymptotic homogenization. J R Soc Interface. 6(30):97–109.
   PubMed Web of Science ®Google Scholar
• Parreira PCS, Maher CG, Megale RZ, March L, Ferreira ML. 2017. An overview of clinical guidelines for the management of vertebral compression fracture: a systematic review. Spine J. 17(12):1932–1938.
   PubMed Web of Science ®Google Scholar
• Perilli E, Briggs AM, Kantor S, Codrington J, Wark JD, Parkinson IH, Fazzalari NL. 2012. Failure strength of human vertebrae: prediction using bone mineral density measured by DXA and bone volume by micro-CT. Bone. 50(6):1416–1425.
   PubMed Web of Science ®Google Scholar
• Ramchand SK, Seeman E. 2018. The influence of cortical porosity on the strength of bone during growth and advancing age. Curr Osteoporos Rep. 16(5):561–572.
   PubMed Web of Science ®Google Scholar
• Ramírez-Torres A, Penta R, Rodríguez-Ramos R, Merodio J, Sabina FJ, Bravo-Castillero J, Guinovart-Díaz R, Preziosi L, Grillo A. 2018. Three scales asymptotic homogenization and its application to layered hierarchical hard tissues. Int J Solids Struct. 130–131:190–198.
   Web of Science ®Google Scholar
• Ripamonti C, Lisi L, Buffa A, Gnudi S, Caudarella R. 2018. The trabecular bone score predicts spine fragility fractures in postmenopausal caucasian women without osteoporosis independently of bone mineral density. Med Arch. 72(1):46–50.
   PubMedGoogle Scholar
• Sanchez-Palencia E. 1980. Non-homogeneous media and vibration theory. Vol. 127. Heidelberg: Springer Berlin; p. 1–400.
   Google Scholar
• Sandino C, McErlain DD, Schipilow J, Boyd SK. 2017. Mechanical stimuli of trabecular bone in osteoporosis: a numerical simulation by finite element analysis of microarchitecture. J Mech Behav Biomed Mater. 66:19–27.
   PubMed Web of Science ®Google Scholar
• Schweser KM, Crist BD. 2017. Osteoporosis: a discussion on the past 5 years. Curr Rev Musculoskelet Med. 10(2):265–274.
   PubMed Web of Science ®Google Scholar
• Shanbhogue V V, Brixen K, Hansen S. 2016. Age and sex related changes in bone microarchitecture and estimated strength: a three-year prospective study using HRpQCT. J Bone Miner Res. 31(8):1541–1549.
   PubMed Web of Science ®Google Scholar
• Shi X, Liu XS, Wang X, Guo XE, Niebur GL. 2010. Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone. Bone. 46(5):1260–1266.
   PubMed Web of Science ®Google Scholar
• Singhal V, Bredella MA. 2019. Marrow adipose tissue imaging in humans. Bone. 118:69–76.
   PubMed Web of Science ®Google Scholar
• Sozen T, Ozisik L, Calik Basaran N. 2017. An overview and management of osteoporosis. Eur J Rheumatol. 4(1):46–56.
   PubMed Web of Science ®Google Scholar
• Stemper BD, Yoganandan N, Baisden JL, Umale S, Shah AS, Shender BS, Paskoff GR. 2015. Rate-dependent fracture characteristics of lumbar vertebral bodies. J Mech Behav Biomed Mater. 41:271–279.
   PubMed Web of Science ®Google Scholar
• Subramaniam S, Ima-Nirwana S, Chin K-Y. 2018. Performance of osteoporosis self-assessment tool (OST) in predicting osteoporosis- A review. Int J Environ Res Public Health. 15(7):1445.
   Web of Science ®Google Scholar
• Syahrom A, Abdul Kadir MR, Abdullah J, Öchsner A. 2011. Mechanical and microarchitectural analyses of cancellous bone through experiment and computer simulation. Med Biol Eng Comput. 49(12):1393–1403.
   PubMed Web of Science ®Google Scholar
• Syahrom A, Januddi M-F, bin MS, Harun M, Öchsner A. 2017. Cancellous bone. In: Advanced structured materials. Vol. 82. Singapore: Springer; p. 7–20.
   Google Scholar
• Tawara D, Sakamoto J, Murakami H, Kawahara N, Oda J, Tomita K. 2010. Mechanical evaluation by patient-specific finite element analyses demonstrates therapeutic effects for osteoporotic vertebrae. J Mech Behav Biomed Mater. 3(1):31–40.
   PubMed Web of Science ®Google Scholar
• Tjong W, Kazakia GJ, Burghardt AJ, Majumdar S. 2012. The effect of voxel size on high-resolution peripheral computed tomography measurements of trabecular and cortical bone microstructure. Med Phys. 39(4):1893–1903.
   PubMed Web of Science ®Google Scholar
• Tokarzewski S, Telega JJ, Gałka A. 1999. A contribution to evaluation of effective moduli of trabecular bone with rod-like microestructure. J Theor Appl Mech. 3:707–728.
   Google Scholar
• Tomasevic-Todorovic S, Vazic A, Issaka A, Hanna F. 2018. Comparative assessment of fracture risk among osteoporosis and osteopenia patients: a cross-sectional study. Open Access Rheumatol: Res Rev. 10:61–66.
   PubMed Web of Science ®Google Scholar
• Turner CH, Burr DB. 1993. Basic biomechanical measurements of bone: a tutorial. Bone. 14(4):595–608.
   PubMed Web of Science ®Google Scholar
• Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC. 1990. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech. 23(6):549–561.
   PubMed Web of Science ®Google Scholar
• Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. 1999. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. 32(4):437–441.
   PubMed Web of Science ®Google Scholar
• Wang J, Zhou B, Liu XS, Fields AJ, Sanyal A, Shi X, Adams M, Keaveny TM, Guo XE. 2015. Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. Bone. 72:71–80.
   PubMed Web of Science ®Google Scholar
• Weatherholt AM, Fuchs RK, Warden SJ. 2012. Specialized connective tissue: bone, the structural framework of the upper extremity. J Hand Ther. 25(2):123–132.
   PubMed Web of Science ®Google Scholar
• Zhou B, Sherry Liu X, Wang J, Lucas Lu X, Fields AJ, Edward Guo X. 2014. Dependence of mechanical properties of trabecular bone on plate-rod microstructure determined by individual trabecula segmentation (ITS). J Biomech. 47(3):702–708.
   PubMed Web of Science ®Google Scholar
• Zhou B, Wang J, Yu YE, Zhang Z, Nawathe S, Nishiyama KK, Rosete FR, Keaveny TM, Shane E, Guo XE. 2016. High-resolution peripheral quantitative computed tomography (HR-pQCT) can assess microstructural and biomechanical properties of both human distal radius and tibia: ex vivo computational and experimental validations. Bone. 86:58–67.
   PubMed Web of Science ®Google Scholar
• Zysset PK, Goulet RW, Hollister SJ. 1998. A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng. 120(5):640–640.
   PubMed Web of Science ®Google Scholar