Increased calcium content and inhomogeneity of mineralization render bone toughness in osteoporosis: mineralization, morphology and biomechanics of human single trabeculae

wbldb

Busse, Björn^1,2; Hahn, Michael¹; Soltau, Markus¹; Zustin, Jozef³; Püschel, Klaus⁴; Duda, Georg N.²; Amling, Michael¹

Increased calcium content and inhomogeneity of mineralization render bone toughness in osteoporosis: mineralization, morphology and biomechanics of human single trabeculae

Bone. December 2009;45(6):1034-1043

©2009 Elsevier Inc. All rights reserved

Affiliations

¹Center for Biomechanics and Skeletal Biology, University Medical Center Hamburg‐Eppendorf, Lottestr. 59, D-22529 Hamburg, Germany

²Julius Wolff Institute and Center for Musculoskeletal Surgery, Charité-University Medicine Berlin, Augustenburger Platz 1, D-13353 Berlin, Germany

³Institute of Pathology, University Medical Center Hamburg‐Eppendorf, Martinistraβe 52, D-20246 Hamburg, Germany

⁴Institute of Legal Medicine, University Medical Center Hamburg‐Eppendorf, Martinistraβe 52, D-20246 Hamburg, Germany
Abstract and keywords

The differentiation and degree of the effects of mineral content and/or morphology on bone quality remain, to a large extent, unanswered due to several microarchitectural particularities in spatial measuring fields (e.g., force transfer, trajectories, microcalli). Therefore, as the smallest basic component of cancellous bone, we focused on single trabeculae to investigate the effects of mineralization and structure, both independently and in superposition. Transiliac Bordier bone cores and T12 vertebrae were obtained from 20 females at autopsy for specimen preparation, enabling radiographical analyses, histomorphometry, Bone Mineral Density Distribution (BMDD) analyses, and trabecular singularization to be performed. Evaluated contact X-rays and histomorphometric limits from cases with osteoporotic vertebral fractures generated two subdivisions, osteoporotic (n = 12, Ø 78 years) and non-osteoporotic (n = 8, Ø 49 years) cases, based on fracture appearance and bone volume (BV/TV). Measurements of trabecular number (Tb.N.), trabecular separation (Tb.Sp.), trabecular thickness (Tb.Th.), trabecular bone pattern factor (TBPf) and eroded surface (ES/BS) were carried out to provide detailed structural properties of the investigated groups. The mechanical properties of 400 rod-like single vertebral trabeculae, assessed by three-point bending, were matched with mineral properties as quantified by BMDD analyses of cross-sectioned rod-like and plate-like trabeculae, both in superposition and independently. Non-osteoporotic iliac crests and vertebrae displayed linear dependency on structure parameters, whereas osteoporotic compartments proved to be non-correlated with bone structure. Independent of trabecular thickness, osteoporotic rod-like trabeculae showed decreases in Young's modulus, fracture load, yield strength, ultimate stress, work to failure and bending stiffness, along with significantly increased mean calcium content and calcium width. Non-osteoporotic trabeculae showed biomechanically beneficial properties due to a homogeneous mineralization configuration, whereas osteoporotic trabeculae predominantly demonstrated various mineralized bone packets, eroded surfaces, highly mineralized cement lines and microcracks. The Young's moduli of single trabeculae exhibited significantly negative linear correlations with trabecular thickness. Because of increased, but inhomogeneously distributed, calcium content, osteoporotic trabeculae may be subject to shear stresses that render bone fragile beyond structure impairment due to cracks and lacunae.

Keywords: Osteoporosis; Biomechanics; Materials testing; Bone histomorphometry; Bone mineralization
Links

DOI: 10.1016/j.bone.2009.08.002

PubMed: 19679206

WoS: 000271916900001
History

Received: 2009-03-17

Revised: 2009-07-13

Accepted: 2009-08-03

Online: 2009-08-11

Cited Works (45)

Year	Entry
1995	Roschger P, Plenk H Jr, Klaushofer K, Eschberger J. A new scanning electron-microscopy approach to the quantification of bone-mineral distribution: backscattered electron image grey-levels correlated to calcium kα-line intensities. Scanning Microsc. March 1995;9(1):75-88.
2002	Currey JD. Bones: Structure and Mechanics. Princeton, NJ: Princeton University Press; 2002.
2003	Currey JD. Role of collagen and other organics in the mechanical properties of bone. Osteoporos Int. September 2003;14(suppl 5):S29-S36.
2004	Akkus O, Adar F, Schaffler MB. Age-related changes in physicochemical properties of mineral crystals are related to impaired mechanical function of cortical bone. Bone. March 2004;34(4):443-453.
2005	Thomsen JS, Laib A, Koller B, Prohaska S, Mosekilde L, Gowin W. Stereological measures of trabecular bone structure: comparison of 3D micro computed tomography with 2D histological sections in human proximal tibial bone biopsies. J Microsc (Oxford). 2005;218(2):171-179.
1993	Grynpas M. Age and disease-related changes in the mineral of bone. Calcif Tiss Int. February 1993;53(suppl 1):S57-S64.
2006	Hoc T, Henry L, Verdier M, Aubry D, Sedel L, Meunier A. Effect of microstructure on the mechanical properties of Haversian cortical bone. Bone. April 2006;38(4):466-474.
1996	Amling M, Herden S, Pösl M, Hahn M, Ritzel H, Delling G. Heterogeneity of the skeleton: comparison of the trabecular microarchitecture of the spine, the iliac crest, the femur, and the calcaneus. J Bone Miner Res. January 1996;11(1):36-45.
1993	Skedros JG, Bloebaum RD, Bachus KN, Boyce TM, Constantz B. Influence of mineral content and composition on graylevels in backscattered electron images of bone. J Biomed Mater Res. January 1993;27(1):57-64.
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.
2001	Laib A, Kumer JL, Majumdar S, Lane NE. The temporal changes of trabecular architecture in ovariectomized rats assessed by MicroCT. Osteoporos Int. November 2001;12(11):936-941.
1997	Mori S, Harruff R, Ambrosius W, Burr DB. Trabecular bone volume and microdamage accumulation in the femoral heads of women with and without femoral neck fractures. Bone. December 1997;21(6):521-526.
2008	Roschger P, Paschalis EP, Fratzl P, Klaushofer K. Bone mineralization density distribution in health and disease. Bone. March 2008;42(3):456-466.
1988	Burr DB, Schaffler MB, Frederickson RG. Composition of the cement line and its possible mechanical role as a local interface in human compact bone. J Biomech. 1988;21(11):939-945.
2003	Currey JD. How well are bones designed to resist fracture? J Bone Miner Res. April 2003;18(4):591-598.
1993	Vogel M, Hahn M, Delling G. Relation between 2- and 3-dimensional architecture of trabecular bone in the human spine. Bone. May–June 1993;14(3):199-203.
1989	Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS. Comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res. November 1989;7(6):876-884.
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.
1991	Hahn M, Vogel M, Delling G. Undecalcified preparation of bone tissue: report of technical experience and development of new methods. Virchows Archiv A. January 1991;418(1):1-7.
2008	Kanis JA, McCloskey EV, Johansson H, Oden A, Melton LJ III, Khaltaev N. A reference standard for the description of osteoporosis. Bone. March 2008;42(3):467-475.
1998	Roschger P, Fratzl P, Eschberger J, Klaushofer K. Validation of quantitative backscattered electron imaging for the measurement of mineral density distribution in human bone biopsies. Bone. October 1998;23(4):319-326.
1984	Currey JD. Effects of differences in mineralization on the mechanical properties of bone. Philos Trans R Soc Lond B Biol Sci. February 13, 1984;304(1121):509-518.
1998	Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.
2005	Skedros JG, Holmes JL, Vajda EG, Bloebaum AD. Cement lines of secondary osteons in human bone are not mineral‐deficient: new data in a historical perspective. Anat Rec. September 2005;286A(1):781-803.
2000	Huiskes R. If bone is the answer, then what is the question? J Anat. August 2000;197(2):145-156.
1993	Dempster DW, Ferguson-Pell MW, Mellish RWE, Cochran GVB, Xie F, Fey C, Horbert W, Parisien M, Lindsay R. Relationships between bone structure in the iliac crest and bone structure and strength in the lumbar spine. Osteoporos Int. March 1993;3(2):90-96.
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.
2004	Fratzl P, Gupta HS, Paschalis EP, Roschger P. Structure and mechanical quality of the collagen–mineral nano-composite in bone. J Mater Chem. 2004;14(14):2115-2123.
1993	Boyce TM, Bloebaum RD. Cortical aging differences and fracture implications for the human femoral neck. Bone. September–October 1993;14(5):769-778.
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.
1996	Boyde A, Jones SJ. Scanning electron microscopy of bone: instrument, specimen, and issues. Microsc Res Tech. February 1, 1996;33(2):92-120.
1992	Choi K, Goldstein SA. A comparison of the fatigue behavior of human trabecular and cortical bone tissue. J Biomech. 1992;25(12):1371-1381.
1987	Parfitt AM, Drezner MK, Glorieux FH, Kanis JA, Malluche H, Meunier PJ, Ott SM, Recker RR. Bone histomorphometry: standardization of nomenclature, symbols, and units: report of the ASBMR histomorphometry nomenclature committee. J Bone Miner Res. December 1987;2(6):595-610.
2006	McNamara LM, Van der Linden JC, Weinans H, Prendergast PJ. Stress-concentrating effect of resorption lacunae in trabecular bone. J Biomech. 2006;39(4):734-741.
1998	Boyde A, Compston JE, Reeve J, Bell KL, Noble BS, Jones SJ, Loveridge N. Effect of estrogen suppression on the mineralization density of iliac crest biopsies in young women as assessed by backscattered electron imaging. Bone. March 1998;22(3):241-250.
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.
2006	Seeman E, Delmas PD. Bone quality: the material and structural basis of bone strength and fragility. NEJM. May 25, 2006;354(21):2250-2261.
2006	McNamara LM, Ederveen AGH, 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. August 2006;39(2):392-400.
1994	Fyhrie DP, Schaffler MB. Failure mechanisms in human vertebral cancellous bone. Bone. 1994;15(1):105-109.
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.
1995	Rho JY, Hobatho MC, Ashman RB. Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys. July 1995;17(5):347-355.
1979	Currey JD. Changes in the impact energy absorption of bone with age. J Biomech. 1979;12(6):459-469.
1996	Currey JD, Brear K, Zioupos P. The effects of ageing and changes in mineral content in degrading the toughness of human femora. J Biomech. February 1996;29(2):257-260.
2000	Lucchinetti E, Thomann D, Danuser G. Micromechanical testing of bone trabeculae: potentials and limitations. J Mater Sci. December 2000;35(24):6057-6064.
1994	Zioupos P, Currey JD. The extent of microcracking and the morphology of microcracks in damaged bone. J Mater Sci. 1994;29(4):978-986.

Cited By (56)

Year	Entry
2018	Wu D, Isaksson P, Ferguson SJ, Persson C. Young’s modulus of trabecular bone at the tissue level: a review. Acta Biomater. September 15, 2018;78:1.
2010	Busse B, Djonic D, Milovanovic P, Hahn M, Püschel K, Ritchie RO, Djuric M, Amling M. Decrease in the osteocyte lacunar density accompanied by hypermineralized lacunar occlusion reveals failure and delay of remodeling in aged human bone. Aging Cell. December 2010;9(6):1065-1075.
2014	Zimmermann EA, Gludovatz B, Schaible E, Busse B, Ritchie RO. Fracture resistance of human cortical bone across multiple length-scales at physiological strain rates. Biomaterials. July 2014;35(21):5472-5481.
2015	Milovanovic P, Zimmermann EA, Riedel C, vom Scheidt A, Herzog L, Krause M, Djonic D, Djuric M, Püschel K, Amling M, Ritchie RO, Busse B. Multi-level characterization of human femoral cortices and their underlying osteocyte network reveal trends in quality of young, aged, osteoporotic and antiresorptive-treated bone. Biomaterials. March 2015;45:46-55.
2010	Thurner PJ, Chen CG, Ionova-Martin S, Sun L, Harman A, Porter A, Ager JW III, Ritchie RO, Alliston T. Osteopontin deficiency increases bone fragility but preserves bone mass. Bone. June 2010;46(6):1564-1573.
2021	Lee Y-R, Findlay DM, Muratovic D, Kuliwaba JS. Greater heterogeneity of the bone mineralisation density distribution and low bone matrix mineralisation characterise tibial subchondral bone marrow lesions in knee osteoarthritis patients. Bone. August 2021;149:115979.
2022	Liu J, Watanabe K, Dabdoub SM, Lee BS, Kim D-G. Site-specific characteristics of bone and progenitor cells in control and ovariectomized rats. Bone. October 2022;163:116501.
2020	Lerebours C, Weinkamer R, Roschger A, Buenzli PR. Mineral density differences between femoral cortical bone and trabecular bone are not explained by turnover rate alone. Bone Rep. December 1, 2020;13:100731.
2019	Shah FA, Ruscsák K, Palmquist A. 50 years of scanning electron microscopy of bone: a comprehensive overview of the important discoveries made and insights gained into bone material properties in health, disease, and taphonomy. Bone Res. 2019;7:15.
2023	Clausing RJ, Stiller A, Kuhn F, Fonseca Ulloa CA, Fölsch C, Kampschulte M, Krombach GA, Rickert M, Jahnke A. Measuring Young's modulus of single trabeculae in cancellous bone using a two-point bending test. Clin Biomech (Bristol, Avon). February 2023;102:105875.
2016	Osterhoff G, Morgan EF, Shefelbine SJ, Karim L, McNamara LM, Augat P. Bone mechanical properties and changes with osteoporosis. Injury. June 2016;47(suppl 2):S11-S20.
2012	Skedros JG, Knight AN, Farnsworth RW, Bloebaum RD. Do regional modifications in tissue mineral content and microscopic mineralization heterogeneity adapt trabecular bone tracts for habitual bending? analysis in the context of trabecular architecture of deer calcanei. J Anat. March 2012;220(3):242-255.
2010	Smith LJ, Schirer JP, Fazzalari NL. The role of mineral content in determining the micromechanical properties of discrete trabecular bone remodeling packets. J Biomech. December 1, 2010;43(16):3144-3149.
2011	Tassani S, Öhman C, Baruffaldi F, Baleani M, Viceconti M. Volume to density relation in adult human bone tissue. J Biomech. 2011;44(1):103-108.
2011	Szabó ME, Taylor M, Thurner PJ. Mechanical properties of single bovine trabeculae are unaffected by strain rate. J Biomech. March 15, 2011;44(5):962-967.
2011	Kim D-G, Shertok D, Tee BC, Yeni YN. Variability of tissue mineral density can determine physiological creep of human vertebral cancellous bone. J Biomech. June 3, 2011;44(9):1660-1665.
2011	Green JO, Nagaraja S, Diab T, Vidakovic B, Guldberg RE. Age-related changes in human trabecular bone: relationship between microstructural stress and strain and damage morphology. J Biomech. 2011;44(12):2279-2285.
2014	Yamada S, Tadano S, Fukuda S. Nanostructure and elastic modulus of single trabecula in bovine cancellous bone. J Biomech. November 7, 2014;47(14):3482-3487.
2016	Yamada S, Tadano S, Fukasaw K. Micro-cantilever bending for elastic modulus measurements of a single trabecula in cancellous bone. J Biomech. December 8, 2016;49(16):4124-4127.
2013	Hardisty MR, Zauel R, Stover SM, Fyhrie DP. The importance of intrinsic damage properties to bone fragility: a finite element study. J Biomech Eng. January 2013;135(1):011004.
2013	Gourion-Arsiquaud S, Lukashova L, Power J, Loveridge N, Reeve J, Boskey AL. Fourier transform infrared imaging of femoral neck bone: reduced heterogeneity of mineral-to-matrix and carbonate-to-phosphate and more variable crystallinity in treatment-naive fracture cases compared with fracture-free controls. J Bone Miner Res. January 2013;28(1):150-161.
2016	Boskey AL, Donnelly E, Boskey E, Spevak L, Ma Y, Zhang W, Lappe J, Recker RR. Examining the relationships between bone tissue composition, compositional heterogeneity, and fragility fracture: a matched case-controlled FTIRI study. J Bone Miner Res. May 2016;31(5):1070-1081.
2023	Wölfel EM, Lademann F, Hemmatian H, Blouin S, Messmer P, Hofbauer LC, Busse B, Rauner M, Jähn-Rickert K, Tsourdi E. Reduced bone mass and increased osteocyte tartrate-resistant acid phosphatase (TRAP) activity, but not low mineralized matrix around osteocyte lacunae, are restored after recovery from exogenous hyperthyroidism in male mice. J Bone Miner Res. January 2023;38(1):131-143.
2011	Jungmann R, Szabo ME, Schitter G, Tang RY-S, Vashishth D, Hansma PK, Thurner PJ. Local strain and damage mapping in single trabeculae during three-point bending tests. J Mech Behav Biomed Mater. May 2011;4(4):523-534.
2011	Szabó ME, Zekonyte J, Katsamenis OL, Taylor M, Thurner PJ. Similar damage initiation but different failure behavior in trabecular and cortical bone tissue. J Mech Behav Biomed Mater. November 2011;4(8):1787-1796.
2013	Carretta R, Luisier B, Bernoulli D, Stüssi E, Müller R, Lorenzetti S. Novel method to analyze post-yield mechanical properties at trabecular bone tissue level. J Mech Behav Biomed Mater. 2013;20:6-18.
2013	Carretta R, Stüssi E, Müller R, Lorenzetti S. Within subject heterogeneity in tissue-level post-yield mechanical and material properties in human trabecular bone. J Mech Behav Biomed Mater. August 2013;24:64-73.
2018	Frank M, Marx D, Nedelkovski V, Fischer J-T, Pahr DH, Thurner PJ. Dehydration of individual bovine trabeculae causes transition from ductile to quasi-brittle failure mode. J Mech Behav Biomed Mater. November 2018;87:296-305.
2022	Kuhn F, Clausing RJ, Stiller A, Fonseca Ulloa CA, Foelsch C, Rickert M, Jahnke A. Determination of E-modulus of cancellous bone derived from human humeri and validation of plotted single trabeculae: development of a standardized humerus bone model. J Orthop. September 1, 2022;33:48.
2011	Lorenzetti S, Carretta R, Müller R, Stüssi E. A new device and method for measuring the elastic modulus of single trabeculae. Med Eng Phys. October 2011;33(8):993-1000.
2020	O’Sullivan LM, Allison H, Parle EE, Schiavi J, McNamara LM. Secondary alterations in bone mineralisation and trabecular thickening occur after long-term estrogen deficiency in ovariectomised rat tibiae, which do not coincide with initial rapid bone loss. Osteoporos Int. March 2020;31(3):587-599.
2018	Suniaga S, Rolvien T, vom Scheidt A, Fiedler IAK, Bale HA, Huysseune A, Witten PE, Amling M, Busse B. Increased mechanical loading through controlled swimming exercise induces bone formation and mineralization in adult zebrafish. Sci Rep. February 26, 2018;8:3646.
2017	Heveran CM. Bone Tissue Material Properties Are Altered in Chronic Kidney Disease to Lower Fracture Resistance Determining Bone Quality [PhD thesis]. University of Colorado; 2017.
2016	Wang J. Plate-Rod Microstructural Modeling for Accurate and Fast Assessment of Bone Strength [PhD thesis]. Columbia University; 2016.
2013	Burket JC. Alterations in Tissue Composition and Nanomechanical Properties With Ageing, Osteoporosis, and Treatment [PhD thesis]. Ithaca, NY: Cornell University; January 2013.
2014	Carretta R. Post-Yield Mechanics and Material Composition of Single Trabeculae: A Combined Experimental and Modelling Approach [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2014.
2011	O'Neal JM. The Effects of Aging and Remodeling on Bone Quality and Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; August 2011.
2013	Verbruggen SW. Mechanobiological Origins of Osteoporosis [PhD thesis]. National University of Ireland Galway; September 2013.
2020	O’Sullivan LM. Time-Sequence of Biomechanical Adaption in Trabecular Tissue During Estrogen Deficiency [PhD thesis]. National University of Ireland Galway; March 2020.
2012	Tozzi G. In Vitro Studies of Bone-Cement Interface and Related Work on Cemented Acetabular Replacement [PhD thesis]. Portsmouth, England: University of Portsmouth; May 29, 2012.
2013	Morton JJ. An Investigation of Rat Vertebra Failure Behaviour Under Uniaxial Compression Through Time-Lapsed Micro-CT Imaging [Master's thesis]. Queen's University; 2013.
2013	Toal VR. The Mechanics of Microdamage and Microfracture in Trabecular Bone [PhD thesis]. Brisbane, Australia: Queensland University of Technology; September 2013.
2017	Owen R. Tissue Engineering an in Vitro Model of Osteoporosis [PhD thesis]. Sheffield, UK: University of Sheffield; October 2017.
2012	Brennan MA. Close to the Bone: Investigations Into Bone Tissue Mineralisation and Mechanobiology of Osteoporosis [PhD thesis]. University of Southampton; January 2012.
2022	Reiner E. Application of Optical Photothermal Infrared (O-PTIR) Spectroscopy to Assess Bone Composition At the Submicron Scale [Master's thesis]. Temple University; May 2022.
2021	Frank M. Mechanical Characterization of Individual Trabeculae [PhD thesis]. Vienna University of Technology; February 2021.
2019	Sadoughi S. Micromechanics of Human Bone: Role of Architecture and Tissue Material Properties [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2019.
2012	Hardisty MR. Not Tough Enough: Why Bone Turns Pale When it Feels Stressed [PhD thesis]. Davis, CA: Davis, University of California; 2012.
2012	Tjhia CKH. Bone Quality of Patients With Atypical Fractures and Severely Suppressed Bone Turnover [PhD thesis]. Davis, University of California; 2012.
2019	Nguyen C. Multiscale Network Characterization of the Strength and Robustness of Trabecular Bone [PhD thesis]. Santa Barbara, CA: Santa Barbara, University of California; September 2019.
2011	Chen CG. TGF-Β/Smad3 Regulation of Bone, Cartilage, and Tendon Matrix Composition and Material Properties [PhD thesis]. San Francisco, University of California; 2011.
2016	Arango Villegas C. Study of the Mechanical Behavior of Cortical Bone Microstructure by the Finite Element Method [PhD thesis]. Universität Politècnica de València; May 2016.
2015	Lin C-L. A Study of Human and Bovine Trabecular Bones Using Nanoindentation and Quantitative Backscattered Electron Imaging [PhD thesis]. Brisbane, Australia: University of Queensland; 2015.
2016	Lin C-l. A Study of Human and Bovine Trabecular Bones Using Nanoindentation and Quantitative Backscattered Electron Imaging [PhD thesis]. Brisbane, Australia: University of Queensland; 2016.
2023	Zhou Y. Mechanical Optimization of Orthopaedic Bone Screw Constructs [PhD thesis]. Utrecht University; 2023.
2023	Sang W. Evaluating the Role of Lacunar-Canalicular Network on Bone Mechanical Properties Using Computational Modeling [PhD thesis]. Villanova University; May 2023.