Osteoporotic and age-related fractures are a significant public health problem. The current standard of osteoporosis assessment via bone mineral density has been shown to be inadequate for fracture risk predictions highlighting the importance of material composition and structural design of bone in determining skeletal fragility. Bone is a hierarchical material that derives its fracture resistance from various mechanisms that act at length scales ranging from nano- to macroscale. Recent research efforts have focussed on the understanding of bone fracture based on this hierarchical structure to provide a more reliable assessment of fracture risk. Understanding the function, contribution and interaction of each length scale to bone toughness is a crucial step to develop new strategies for fracture risk assessment, fracture prevention, and development of therapeutic interventions for disease and age-related changes in bone. This review presents a hierarchical perspective of bone toughness ranging from nano- to macroscale and reports on the current state of knowledge in the areas of experimental and computational approaches to bone fracture.
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References
1.
MeltonL.J.3rd: ‘Adverse outcomes of osteoporotic fractures in the general population’, J. Bone Miner. Res., 2003, 18, (6), 1139–1141.
2.
RayN.F.ChanJ.K.ThamerM. and MeltonL.J.3rd: ‘Medical expenditures for the treatment of osteoporotic fractures in the United States in 1995: report from the National Osteoporosis Foundation’, J. Bone Miner. Res., 1997, 12, (1), 24–35.
3.
HuiSLSlemendaCW and JohnstonCCJr: ‘Age and bone mass as predictors of fracture in a prospective study’, J. Clin. Invest., 1988, 81,(6), 1804–1809.
4.
SeemanE: ‘Is a change in bone mineral density a sensitive and specific surrogate of anti-fracture efficacy?’, Bone, 2007, 41, (3), 308–317.
5.
StoneKLSeeleyDGLuiL.-YCauleyJAEnsrudKBrownerWSNevittMC and CummingsSR: ‘BMD at multiple sites and risk of fracture of multiple types: long-term results from the study of osteoporotic fractures’, J. Bone Miner. Res., 2003, 18, (11), 1947–1954.
6.
BouxseinML: ‘Bone quality: where do we go from here?’, Osteoporos. Int., 2003, 14, (5), 118–127.
7.
SeemanE: ‘Bone quality: the material and structural basis of bone strength’, J. Bone Miner. Metab., 2008, 26, (1), 1–8.
8.
van der MeulenMCHJepsenKJ and MikićB: ‘Understanding bone strength: size isn’t everything’,Bone, 2001, 29, (2), 101–104.
9.
RhoJYKuhn-SpearingL and ZiouposP: ‘Mechanical properties and the hierarchical structure of bone’, Med. Eng. Phys., 1998, 20, (2), 92–102.
10.
WeinerS and WagnerHD: ‘The material bone: structure-mechanical function relations’, Annu. Rev. Mater. Sci., 1998, 28, (1), 271–298.
MellonSJ and TannerKE: ‘Bone and its adaptation to mechanical loading: a review’, Int. Mater. Rev., 2012, 57, (5), 235–255.
13.
MartinRBBurrDB and SharkeyNA: ‘Skeletal tissue mechanics’; 1998, New York, Springer-Verlag.
14.
BurrDBSchafflerMB and FredericksonRG: ‘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.
15.
LandisWJ: ‘The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix’, Bone, 1995, 16, (5), 533–544.
16.
SrogaG and VashishthD: ‘Effects of bone matrix proteins on fracture and fragility in osteoporosis’, Curr. Osteoporos. Rep., 2012, 10, (2), 141–150.
17.
BaileyAJSimsTJEbbesenENMansellJPThomsenJS and MosekildeL: ‘Age-related changes in the biochemical properties of human cancellous bone collagen: relationship to bone strength’, Calcif. Tissue Int., 1999, 65, (3), 203–210.
18.
SaitoM and MarumoK: ‘Collagen cross-links as a determinant of bone quality: a possible explanation for bone fragility in aging, osteoporosis, and diabetes mellitus’, Osteoporos. Int., 2010, 21, (2), 195–214.
19.
KarimLTangSYSrogaGE and VashishthD: ‘Differences in non-enzymatic glycation and collagen cross-links between human cortical and cancellous bone’, Osteoporos. Int., 2013, 24, (9), 2441–2447.
20.
NymanJSRoyAAcunaRLGayleHJReyesMJTylerJHDeanDD and WangX: ‘Age-related effect on the concentration of collagen cross-links in human osteonal and interstitial bone tissue’, Bone, 2006, 39, (6), 1210–1217.
21.
OdettiPRossiSMonacelliFPoggiACirnigliaroMFedericiM and FedericiA: ‘Advanced glycation end products and bone loss during aging’, Ann. NY Acad. Sci., 2005, 1043, (1), 710–717.
22.
TangSY and VashishthD: ‘Non-enzymatic glycation alters microdamage formation in human cancellous bone’, Bone, 2010, 46, (1), 148–154.
23.
TangSYZeenathU and VashishthD: ‘Effects of non-enzymatic glycation on cancellous bone fragility’, Bone, 2007, 40, (4), 1144–1151.
24.
VashishthDGibsonGJKhouryJISchafflerMBKimuraJ and FyhrieDP: ‘Influence of nonenzymatic glycation on biomechanical properties of cortical bone’, Bone, 2001, 28, (2), 195–201.
25.
WangXShenXLiX and Mauli AgrawalC: ‘Age-related changes in the collagen network and toughness of bone’, Bone, 2002, 31, (1), 1–7.
26.
VashishthDWuP and GibsonGJ: ‘Age-related loss in bone: toughness is explained by non-enzymatic glycation in collagen’, 497; 2004, San Francisco, CA, Transactions of the Annual Meeting of the Orthopaedic Research Society.
27.
ZimmermannEASchaibleEBaleHBarthHDTangSYReichertPBusseBAllistonTAgerJW and RitchieRO: ‘Age-related changes in the plasticity and toughness of human cortical bone at multiple length scales’, P. Natl. Acad. Sci., 2011, 108, (35), 14416–14421.
28.
SiegmundTAllenMR and BurrDB: ‘Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking’, J. Biomech., 2008, 41, (7), 1427–1435.
29.
KarimL and VashishthD: ‘Heterogeneous glycation of cancellous bone and its association with bone quality and fragility’, PLoS One., 2012, 7, (4), e35047.
30.
SaitoMFujiiKSoshiS and TanakaT: ‘Reductions in degree of mineralization and enzymatic collagen cross-links and increases in glycation-induced pentosidine in the femoral neck cortex in cases of femoral neck fracture’, Osteoporos. Int., 2006, 17, (7), 986–995.
31.
WillettTLSuttySGasparAAveryN and GrynpasM: ‘In vitro non-enzymatic ribation reduces post-yield strain accommodation in cortical bone’, Bone, 2013, 52, (2), 611–622.
32.
ZiouposPCurreyJD and HamerAJ: ‘The role of collagen in the declining mechanical properties of aging human cortical bone’, J. Biomed. Mater. Res., 1999, 45, (2), 108–116.
33.
KafantariHKounadiEFatourosMMilonakisM and TzaphlidouM: ‘Structural alterations in rat skin and bone collagen fibrils induced by ovariectomy’, Bone, 2000, 26, (4), 349–353.
34.
PeterlikHRoschgerPKlaushoferKFratzlP: ‘Orientation dependent fracture toughness of lamellar bone’, Int. J. Fract., 2006, 139, (3–4), 395–405.
35.
FantnerGEHassenkamTKindtJHWeaverJCBirkedalHPechenikLCutroniJACidadeGAStuckyGDMorseDE and HansmaPK: ‘Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture’, Nat. Mater., 2005, 4, (8), 612–616.
36.
PoundarikAADiabTSrogaGEUralABoskeyALGundbergCM and VashishthD: ‘Dilatational band formation in bone’, P. Natl. Acad. Sci., 2012, 109, (47), 19178–19183.
37.
ThurnerP.J.ChenC.G.Ionova-MartinS.SunL.HarmanA.PorterA.AgerJ.W.3rdRitchieR.O. and AllistonT.: ‘Osteopontin deficiency increases bone fragility but preserves bone mass’, Bone, 2010, 46, (6), 1564–1573.
38.
DuvallCLTaylorWRWeissDWojtowiczAM and GuldbergRE: ‘Impaired angiogenesis, early callus formation, and late stage remodeling in fracture healing of osteopontin-deficient mice’, J. Bone Miner. Res., 2007, 22, (2), 286–297.
39.
DucyPDesboisCBoyceBPineroGStoryBDunstanCSmithEBonadioJGoldsteinSGundbergCBradleyA and KarsentyG: ‘Increased bone formation in osteocalcin-deficient mice’, Nature, 1996, 382, (6590), 448–452.
40.
SrogaGEKarimLColónW and VashishthD: ‘Biochemical characterization of major bone-matrix proteins using nanoscale-size bone samples and proteomics methodology’, Mol. Cell Proteomics, 2011, 10, (9), M110.006718.
41.
CurreyJD: ‘What determines the bending strength of compact bone?’, J. Exp. Biol., 1999, 202, (18), 2495–2503.
42.
CurreyJD: ‘Role of collagen and other organics in the mechanical properties of bone’, Osteoporos Int., 2003, 14, (5), 29–36.
43.
CurreyJDBrearK and ZiouposP: ‘The effects of ageing and changes in mineral content in degrading the toughness of human femora’, J. Biomech., 1996, 29, (2), 257–260.
44.
Gourion-ArsiquaudSLukashovaLPowerJLoveridgeNReeveJ and BoskeyAL: ‘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., 2013, 28, (1), 150–161.
45.
LauneyMEBuehlerMJ and RitchieRO: ‘On the mechanistic origins of toughness in bone’, Annu. Rev. Mater. Sci., 2010, 40, (1), 25–53.
46.
BuehlerMJ: ‘Nanomechanics of collagen fibrils under varying cross-link densities: Atomistic and continuum studies’, J. Mech. Behav. Biomed., 2008, 1, (1), 59–67.
47.
BuehlerMJ: ‘Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization’, Nanotechnology, 2007, 18, (29), 295102.
48.
ThurnerPJEricksonBJungmannRSchriockZWeaverJCFantnerGESchitterGMorseDE and HansmaPK: ‘High-speed photography of compressed human trabecular bone correlates whitening to microscopic damage’, Eng. Fract. Mech., 2007, 74, (12), 1928–1941.
49.
FantnerGEAdamsJTurnerPThurnerPJFisherLW and HansmaPK: ‘Nanoscale ion mediated networks in bone: osteopontin can repeatedly dissipate large amounts of energy’, Nano. Lett., 2007, 7, (8), 2491–2498.
50.
GuptaHSSetoJWagermaierWZaslanskyPBoeseckePFratzlP: ‘Cooperative deformation of mineral and collagen in bone at the nanoscale’, P. Natl. Acad. Sci., 2006, 103, (47), 17741–17746.
51.
TaiKDaoMSureshSPalazogluA and OrtizC: ‘Nanoscale heterogeneity promotes energy dissipation in bone’, Nat. Mater., 2007, 6, 454–462.
52.
UralA and VashishthD: ‘Interactions between microstructural and geometrical adaptation in human cortical bone’, J. Orthop. Res., 2006, 24, (7), 1489–1498.
53.
YeniYNBrownCUWangZ and NormanTL: ‘The influence of bone morphology on fracture toughness of the human femur and tibia’, Bone, 1997, 21, (5), 453–459.
54.
McCaldenRWMcGeoughJABarkerMB and Court-BrownCM: ‘Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure’, J. Bone Joint Surg. Am., 1993, 75, (8), 1193–1205.
55.
BusseBHahnMSchinkeTPüschelKDudaGN and AmlingM: ‘Reorganization of the femoral cortex due to age-, sex-, and endoprosthetic-related effects emphasized by osteonal dimensions and remodeling’, J. Biomed. Mater. Res. A, 2010, 92A, (4), 1440–1451.
56.
NallaR.K.KruzicJ.J.KinneyJ.H.BaloochM.AgerJ.W.3rd and RitchieR.O.: ‘Role of microstructure in the aging-related deterioration of the toughness of human cortical bone’, Mat. Sci. Eng. C, 2006, 26, (8), 1251–1260.
57.
Nyssen-BehetsCDuchesnePY and DhemA: ‘Structural changes with aging in cortical bone of the human tibia’, Gerontology, 1997, 43, (6), 316–325.
58.
BritzHMThomasCDLClementJG and CooperDML: ‘The relation of femoral osteon geometry to age, sex, height and weight’, Bone, 2009, 45, (1), 77–83.
59.
UralA and VashishthD: ‘Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study’, J. Biomech. Eng., 2007, 129, (5), 625–631.
60.
EvansFG and BangS: ‘Differences and relationships between the physical properties and microscopic structure of human femoral, tibial and fibular cortical bone’, Am. J. Anat., 1967, 120, 79–88.
61.
EvansFG and VincentelliR: ‘Relations of the compressive properties of human cortical bone to histological structure and calcification’, J. Biomech., 1974, 7, (1), 1–10.
62.
VincentelliR and GrigorovM: ‘The effect of Haversian remodeling on the tensile properties of human cortical bone’, J. Biomech., 1985, 18, (3), 201–207.
63.
CarterDR and HayesWC: ‘Compact bone fatigue damage: a microscopic examination’, Clin. Orthop. Relat. Res., 1977, 127, 265–274.
64.
HillerLPStoverSMGibsonVAGibelingJCPraterCSHazelwoodSJYehOC and MartinRB: ‘Osteon pullout in the equine third metacarpal bone: effects of ex vivo fatigue’, J. Orthop. Res., 2003, 21, (3), 481–488.
65.
KennedyODBrennanOMauerPRackardSMO’BrienFJTaylorD and LeeTC: ‘The effects of increased intracortical remodeling on microcrack behaviour in compact bone’, Bone, 2008, 43, (5), 889–893.
66.
O’BrienFJTaylorD and Clive LeeT: ‘The effect of bone microstructure on the initiation and growth of microcracks’, J. Orthop. Res., 2005, 23, (2), 475–480.
67.
SchafflerMBChoiK and MilgromC: ‘Aging and matrix microdamage accumulation in human compact bone’, Bone, 1995, 17, (6), 521–525.
68.
TaylorD: ‘Microcrack growth parameters for compact bone deduced from stiffness variations’, J. Biomech., 1998, 31, (7), 587–592.
69.
ZiouposP and CurreyJD: ‘Changes in the stiffness, strength, and toughness of human cortical bone with age’, Bone, 1998, 22, (1), 57–66.
70.
BoyceTMFyhrieDPGlotkowskiMCRadinEL and SchafflerMB: ‘Damage type and strain mode associations in human compact bone bending fatigue’, J. Orthop. Res., 1998, 16, (3), 322–329.
71.
NormanTL and WangZ: ‘Microdamage of human cortical bone: incidence and morphology in long bones’, Bone, 1997, 20, (4), 375–379.
72.
BurrDB: ‘The contribution of the organic matrix to bone’s material properties’, Bone, 2002, 31, (1), 8–11.
73.
SkedrosJGHolmesJLVajdaEG and BloebaumRD: ‘Cement lines of secondary osteons in human bone are not mineral-deficient: new data in a historical perspective’, Anat. Rec. A Discov. Mol. Cell. Evol. Biol., 2005, 286, (1), 781–803.
74.
ZimmermannEALauneyME and RitchieRO: ‘The significance of crack-resistance curves to the mixed-mode fracture toughness of human cortical bone’, Biomaterials, 2010, 31, (20), 5297–5305.
75.
KatsamenisOLChongHMHAndriotisOG and ThurnerPJ: ‘Load-bearing in cortical bone microstructure: Selective stiffening and heterogeneous strain distribution at the lamellar level’, J. Mech. Behav. Biomed., 2013, 17, 152–165.
76.
GuoXEHeM.-YGoldsteinSA: ‘Understanding cement line interface in bone tissue: a linear fracture mechanics approach’, ASME-BED, 1995, 29, 303–304.
77.
YeniYN and NormanTL: ‘Calculation of porosity and osteonal cement line effects on the effective fracture toughness of cortical bone in longitudinal crack growth’, J. Biomed. Mater. Res., 2000, 51, (3), 504–509.
78.
GuoXELiangLC and GoldsteinSA: ‘Micromechanics of osteonal cortical bone fracture’, J. Biomech. Eng., 1998, 120, (1), 112–117.
79.
MischinskiS and UralA: ‘Interaction of microstructure and microcrack growth in cortical bone: a finite element study’, Comput. Methods Biomech. Biomed. Engin., 2013, 16, 81–94.
80.
MischinskiS and UralA: ‘Finite element modeling of microcrack growth in cortical bone’, J. Appl. Mech., 2011, 78, (4), 041016.
81.
NajafiARArshiAREslamiMRFariborzS and MoeinzadehMH: ‘Micromechanics fracture in osteonal cortical bone: a study of the interactions between microcrack propagation, microstructure and the material properties’, J. Biomech., 2007, 40, (12), 2788–2795.
82.
AdvaniSHLeeTSMartinRB: ‘Analysis of crack arrest by cement lines in osteonal bone’, in ‘Advances in Bioengineering’, (ed. A. G. Erdman), 57–88; 1987, New York, ASME.
83.
BudynE and HocT: ‘Analysis of micro fracture in human Haversian cortical bone under transverse tension using extended physical imaging’, Int. J. Numer. Meth. Eng., 2010, 82, (8), 940–965.
84.
Abdel-WahabAAMalignoAR and SilberschmidtVV: ‘Micro-scale modelling of bovine cortical bone fracture: analysis of crack propagation and microstructure using X-FEM’, Comp. Mater. Sci., 2012, 52, (1), 128–135.
85.
LiSAbdel-WahabADemirciE and SilberschmidtV: ‘Fracture process in cortical bone: X-FEM analysis of microstructured models’, Int. J. Fract., 2013, 184, 43–55.
86.
ParsamianGP and NormanT: ‘Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness’, J. Mater. Sci. Mater. Med., 2001, 12, (9), 779–783.
87.
VashishthDBehiriJC and BonfieldW: ‘Crack growth resistance in cortical bone: concept of microcrack toughening’, J. Biomech., 1997, 30, (8), 763–769.
88.
DiabT and VashishthD: ‘Effects of damage morphology on cortical bone fragility’, Bone, 2005, 37, (1), 96–102.
89.
VashishthDKoontzJQiuSJLundin-CannonDYeniYNSchafflerMB and FyhrieDP: ‘In vivo diffuse damage in human vertebral trabecular bone’, Bone, 2000, 26, (2), 147–152.
90.
BurrDB and StaffordT: ‘Validity of the bulk-staining technique to separate artifactual from in vivo bone microdamage’, Clin. Orthop. Relat. Res., 1990, (260), 305–308.
91.
ReillyGC and CurreyJD: ‘The effects of damage and microcracking on the impact strength of bone’, J. Biomech., 2000, 33, (3), 337–343.
92.
DiabTCondonKWBurrDB and VashishthD: ‘Age-related change in the damage morphology of human cortical bone and its role in bone fragility’, Bone, 2006, 38, (3), 427–431.
93.
DiabT and VashishthD: ‘Morphology, localization and accumulation of in vivo microdamage in human cortical bone’, Bone, 2007, 40, (3), 612–618.
94.
O’BrienFJTaylorD and LeeTC: ‘Microcrack accumulation at different intervals during fatigue testing of compact bone’, J. Biomech., 2003, 36, (7), 973–980.
95.
ZiouposP: ‘Accumulation of in vivo fatigue microdamage and its relation to biomechanical properties in ageing human cortical bone’, J. Microsc., 2001, 201, (2), 270–278.
96.
NormanTLYeniYNBrownCU and WangZ: ‘Influence of microdamage on fracture toughness of the human femur and tibia’, Bone, 1998, 23, (3), 303–306.
97.
YeniYN and FyhrieDP: ‘Fatigue damage-fracture mechanics interaction in cortical bone’, Bone, 2002, 30, (3), 509–514.
98.
NallaRKKinneyJH and RitchieRO: ‘Mechanistic fracture criteria for the failure of human cortical bone’, Nat. Mater., 2003, 2, (3), 164–168.
99.
KoesterKJAgerJ and RitchieR: ‘The true toughness of human cortical bone measured with realistically short cracks’, Nat. Mater., 2008, 7, (8), 672–677.
100.
NormanTLVashishthD and BurrDB: ‘Fracture toughness of human bone under tension’, J. Biomech., 1995, 28, (3), 309–320.
101.
WangXDMasilamaniNSMabreyJDAlderME and AgrawalCM: ‘Changes in the fracture toughness of bone may not be reflected in its mineral density, porosity, and tensile properties’, Bone, 1998, 23, (1), 67–72.
102.
BonfieldWBehiriJ and CharalambidesC: ‘Orientation and age-related dependence of the fracture toughness of cortical bone’, in ‘Biomechanics: current interdisciplinary research’, (ed. S. M. Perren and E Schneider), 185–189; 1985, Springer, Netherlands.
103.
MelvinJW: ‘Fracture mechanics of bone’, J. Biomech. Eng., 1993, 115, (4B), 549–554.
104.
NallaRKKruzicJJKinneyJH and RitchieRO: ‘Effect of aging on the toughness of human cortical bone: evaluation by R-curves’, Bone, 2004, 35, (6), 1240–1246.
105.
AkkusO and RimnacCM: ‘Fracture resistance of gamma radiation sterilized cortical bone allografts’, J. Orthop. Res., 2001, 19, (5), 927–934.
106.
NormanTLNivargikarSV and BurrDB: ‘Resistance to crack growth in human cortical bone is greater in shear than in tension’, J. Biomech., 1996, 29, (8), 1023–1031.
107.
WangXMabreyJD and AgrawalCM: ‘An interspecies comparison of bone fracture properties’, Biomed. Mater. Eng., 1998, 8, (1), 1–9.
108.
ChanKSChanCK and NicolellaDP: ‘Relating crack-tip deformation to mineralization and fracture resistance in human femur cortical bone’, Bone, 2009, 45, (3), 427–434.
109.
KoesterKJBarthHD and RitchieRO: ‘Effect of aging on the transverse toughness of human cortical bone: Evaluation by R-curves’, J. Mech. Behav. Biomed. Mater., 2011, 4, (7), 1504–1513.
110.
BrownCUYeniYN and NormanTL: ‘Fracture toughness is dependent on bone location – a study of the femoral neck, femoral shaft, and the tibial shaft’, J. Biomed. Mater. Res., 2000, 49, (3), 380–389.
111.
VashishthD: ‘Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements’, J. Biomech., 2004, 37, (6), 943–946.
112.
LeeTCStainesA and TaylorD: ‘Bone adaptation to load: microdamage as a stimulus for bone remodelling’, J. Anat., 2002, 201, (6), 437–446.
113.
ZimmermannEALauneyMEBarthHD and RitchieRO: ‘Mixed-mode fracture of human cortical bone’, Biomaterials, 2009, 30, (29), 5877–5884.
114.
UralA and VashishthD: ‘Cohesive finite element modeling of age-related toughness loss in human cortical bone’, J. Biomech., 2006, 39, (16), 2974–2982.
115.
UralA and VashishthD: ‘Anisotropy of age-related toughness loss in human cortical bone: a finite element study’, J. Biomech., 2007, 40, (7), 1606–1614.
116.
UralAZiouposPBuchananD and VashishthD: ‘The effect of strain rate on fracture toughness of human cortical bone: a finite element study’, J. Mech. Behav. Biomed., 2011, 4, (7), 1021–1032.
117.
YangQDCoxBNNallaRK and RitchieRO: ‘Fracture length scales in human cortical bone: the necessity of nonlinear fracture models’, Biomaterials, 2006, 27, (9), 2095–2113.
118.
FeerickEMLiuX and McGarryP: ‘Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM)’, J. Mech. Behav. Biomed., 2013, 20, 77–89.
119.
LiSAbdel-WahabA and SilberschmidtVV: ‘Analysis of fracture processes in cortical bone tissue’,Eng. Fract. Mech., 2013, 110, 448–458.
120.
BesdoS and VashishthD: ‘Extended finite element models of introcortical porosity and heterogeneity in cortical bone’, Comp. Mater. Sci., 2012, 64, 301–305.
121.
BraidottiPBrancaFP and StagniL: ‘Scanning electron microscopy of human cortical bone failure surfaces’, J. Biomech., 1997, 30, (2), 155–162.
122.
YeniYN and FyhrieDP: ‘A rate-dependent microcrack-bridging model that can explain the strain rate dependency of cortical bone apparent yield strength’, J. Biomech., 2003, 36, (9), 1343–1353.
123.
KrugRBurghardtAJMajumdarS and LinkTM: ‘High-resolution imaging techniques for the assessment of osteoporosis’, Radiol. Clin. North Am., 2010, 48, (3), 601–621.
124.
NishiyamaK and ShaneE: ‘Clinical imaging of bone microarchitecture with HR-pQCT’, Curr. Osteoporos. Rep., 2013, 11, (2):147-55.
125.
LotzJCChealEJ and HayesWC: ‘Fracture prediction for the proximal femur using finite element models: part I – linear analysis’, J. Biomech. Eng., 1991, 113, (4), 353–360.
126.
AugatPReebH and ClaesLE: ‘Prediction of fracture load at different skeletal sites by geometric properties of the cortical shell’, J. Bone. Miner. Res., 1996, 11, (9), 1356–1363.
127.
MullerMEWebberCE and BouxseinML: ‘Predicting the failure load of the distal radius’, Osteoporos. Int., 2003, 14, (4), 345–352.
128.
SpadaroJAWernerFWBrennerRAFortinoMDFayLA and EdwardsWT: ‘Cortical and trabecular bone contribute strength to the osteopenic distal radius’, J. Orthop. Res., 1994, 12, (2), 211–218.
129.
CodyDDGrossGJHouFJSpencerHJGoldsteinSA and FyhrieDP: ‘Femoral strength is better predicted by finite element models than QCT and DXA’, J. Biomech., 1999, 32, (10), 1013–1020.
130.
MyersERHeckerATRooksDSHippJA and HayesWC: ‘Geometric variables from DXA of the radius predict forearm fracture load in vitro’, Calcif. Tissue Int., 1993, 52, (3), 199–204.
131.
KeyakJHRossiSAJonesKA and SkinnerHB: ‘Prediction of femoral fracture load using automated finite element modeling’, J. Biomech., 1997, 31, (2), 125–133.
132.
SpruijtSVan Der LindenJCSander DijkstraPDWiggersTOudkerkMSnijdersCJVan KeulenFVerhaarJANWeinansH and SwierstraBA: ‘Prediction of torsional failure in 22 cadaver femora with and without simulated subtrochanteric metastatic defects: a CT scan-based finite element analysis’, Acta Orthop., 2006, 77, (3), 474–481.
133.
YangKHShenKLDemetropoulosCKKingAIKolodziejPLevineRS and FitzgeraldRHJr: ‘The relationship between loading conditions and fracture patterns of the proximal femur’, J. Biomech. Eng., 1996, 118, (4), 575–578.
134.
WehrliFW: ‘Magnetic resonance of calcified tissues’, J. Magn. Reson., 2013, 229, 35–48.
135.
BouxseinMLMyburghKHMeulenMCHLindenbergerE and MarcusR: ‘Age-related differences in cross-sectional geometry of the forearm bones in healthy women’, Calcif. Tissue Int., 1994, 54, (2), 113–118.
136.
RuffC and HayesW: ‘Subperiosteal expansion and cortical remodeling of the human femur and tibia with aging’, Science, 1982, 217, (4563), 945–948.
137.
SteinMSThomasCDLFeikSAWarkJD and ClementJG: ‘Bone size and mechanics at the femoral diaphysis across age and sex’, J. Biomech., 1998, 31, (12), 1101–1110.
138.
DingMOdgaardALindeF and HvidI: ‘Age-related variations in the microstructure of human tibial cancellous bone’, J. Orthop. Res., 2002, 20, (3), 615–621.
139.
LochmullerEMLillCAKuhnVSchneiderE and EcksteinF: ‘Radius bone strength in bending, compression, and falling and its correlation with clinical densitometry at multiple sites’, J. Bone. Miner. Res., 2002, 17, (9), 1629–1638.
140.
AsheMCKhanKMKontulainenSAGuyPLiuDBeckTJ and McKayHA: ‘Accuracy of pQCT for evaluating the aged human radius: an ashing, histomorphometry and failure load investigation’, Osteoporos. Int., 2006, 17, (8), 1241–1251.
141.
BellKLLoveridgeNPowerJGarrahanNStantonMLuntMMeggittBF and ReeveJ: ‘Structure of the femoral neck in hip fracture: cortical bone loss in the inferoanterior to superoposterior axis’, J. Bone Miner. Res., 1999, 14, (1), 111–119.
142.
CrabtreeNLoveridgeNParkerMRushtonNPowerJBellKLBeckTJ and ReeveJ: ‘Intracapsular hip fracture and the region-specific loss of cortical bone: analysis by peripheral quantitative computed tomography’, J. Bone Miner. Res., 2001, 16, (7), 1318–1328.
143.
EswaranSKGuptaAAdamsMF and KeavenyTM: ‘Cortical and trabecular load sharing in the human vertebral body’, J. Bone Miner. Res., 2006, 21, (2), 307–314.
144.
HolzerGvon SkrbenskyGHolzerLA and PichlW: ‘Hip fractures and the contribution of cortical versus trabecular bone to femoral neck strength’, J. Bone Miner. Res., 2009, 24, (3), 468–474.
145.
PistoiaWvan RietbergenB and RuegseggerP: ‘Mechanical consequences of different scenarios for simulated bone atrophy and recovery in the distal radius’, Bone, 2003, 33, (6), 937–945.
146.
WalkerMDLiuXSSteinEZhouBBezatiEMcMahonDJUdeskyJLiuGShaneE and GuoXE: ‘Differences in bone microarchitecture between postmenopausal Chinese-American and white women’, J. Bone Miner. Res.2011, 26, (7), 1392–1398.
147.
ZebazeRMDGhasem-ZadehABohteAIuliano-BurnsSMiramsMPriceRIMackieEJ and SeemanE: ‘Intracortical remodelling and porosity in the distal radius and post-mortem femurs of women: a cross-sectional study’, Lancet, 2010, 375, (9727), 1729–1736.
148.
PistoiaWvan RietbergenBLochmullerEMLillCAEcksteinF and RuegseggerP: ‘Estimation of distal radius failure load with micro-finite element analysis models based on three-dimensional peripheral quantitative computed tomography images’, Bone, 2002, 30, (6), 842–848.
149.
LiuXSZhangXHSekhonKKAdamsMFMcMahonDJBilezikianJPShaneE and GuoXE: ‘High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone’, J. Bone Miner. Res., 2010, 25, (4), 746–756.
150.
VargaPPahrDHBaumbachS and ZyssetPK: ‘HR-pQCT based FE analysis of the most distal radius section provides an improved prediction of Colles’ fracture load in vitro’,Bone, 2010, 47, (5), 982–988.
151.
BoutroySVan RietbergenBSornay-RenduEMunozFBouxseinML and DelmasPD: ‘Finite element analysis 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), 392–399.
152.
VicoLZouchMAmiroucheAFrèreDLarocheNKollerBLaibAThomasT and AlexandreC: ‘High-resolution pQCT analysis at the distal radius and tibia discriminates patients with recent wrist and femoral neck fractures’, J. Bone Miner. Res., 2008, 23, (11), 1741–1750.
153.
VilayphiouNBoutroySSornay-RenduEvan RietbergenBMunozFDelmasPD and ChapurlatR: ‘Finite element analysis performed on radius and tibia HR-pQCT images and fragility fractures at all sites in postmenopausal women’, Bone, 2010, 46, (4), 1030–1037.
154.
MeltonL.J.3rdRiggsB.L.van LentheG.H.AchenbachS.J.MullerR.BouxseinM.L.AminS.AtkinsonE.J. and KhoslaS.: ‘Contribution of in vivo structural measurements and load/strength ratios to the determination of forearm fracture risk in postmenopausal women’, J. Bone Miner. Res., 2007, 22, (9), 1442–1448.
155.
Sornay-RenduEBoutroySMunozF and DelmasPD: ‘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), 425–433.
156.
NishiyamaKKMacdonaldHMHanleyDA and BoydSK: ‘Women with previous fragility fractures can be classified based on bone microarchitecture and finite element analysis measured with HR-pQCT’,Osteoporos. Int., 2013, 24, (5):1733–1740.
157.
BurghardtAJKazakiaGJRamachandranSLinkTM and MajumdarS: ‘Age and gender-related differences in the geometric properties and biomechanical significance of intracortical porosity in the distal radius and tibia’, J. Bone Miner. Res., 2010, 25, (5), 983–993.
158.
MacNeilJA and BoydSK: ‘Load distribution and the predictive power of morphological indices in the distal radius and tibia by high resolution peripheral quantitative computed tomography’, Bone, 2007, 41, (1), 129–137.
159.
RajapakseCSLeonardMBBhagatYASunWMaglandJF and WehrliFW: ‘Micro-MR imaging-based computational biomechanics demonstrates reduction in cortical and trabecular bone strength after renal transplantation’, Radiology, 2012, 262, (3), 912–920.
160.
WehrliFWRajapakseCSMaglandJF and SnyderPJ: ‘Mechanical implications of estrogen supplementation in early postmenopausal women’, J. Bone Miner. Res., 2010, 25, (6), 1406–1414.
161.
OrwollESMarshallLMNielsonCMCummingsSRLapidusJCauleyJAEnsrudKLaneNHoffmannPRKopperdahlDL and KeavenyTM: ‘Finite element analysis of the proximal femur and hip fracture risk in older men’, J. Bone Miner. Res., 2009, 24, (3), 475–483.
162.
MeltonLJRiggsBLKeavenyTMAchenbachSJHoffmannPFCampJJRouleauPABouxseinMLAminSAtkinsonEJRobbRA and KhoslaS: ‘Structural determinants of vertebral fracture risk’, J. Bone Miner. Res., 2007, 22, (12), 1885–1892.
163.
KeavenyTMHoffmannPFSinghMPalermoLBilezikianJPGreenspanSL and BlackDM: ‘Femoral bone strength and its relation to cortical and trabecular changes after treatment with PTH, alendronate, and their combination as assessed by finite element analysis of quantitative CT scans’, J. Bone Miner. Res., 2008, 23, (12), 1974–1982.
164.
UralA: ‘Prediction of Colles’ fracture load in human radius using cohesive finite element modeling’,J. Biomech., 2009, 42, (1), 22–28.
165.
UralABrunoPZhouBShiXT and GuoXE: ‘A new fracture assessment approach coupling HR-pQCT imaging and fracture mechanics-based finite element modeling’, J. Biomech., 2013, 46, 1305–1311.
166.
BuchananD and UralA: ‘Finite element modeling of the influence of hand position and bone properties on the Colles’ fracture load during a fall’,J. Biomech. Eng., 2010, 132, (8), 081007.
167.
TommasiniSMNasserPSchafflerMB and JepsenKJ: ‘Relationship between bone morphology and bone quality in male tibias: implications for stress fracture risk’, J. Bone Miner. Res., 2005, 20, (8), 1372–1380.
168.
JepsenK: ‘Functional interactions among morphologic and tissue quality traits define bone quality’, Clin. Orthop. Relat. Res., 2011, 469, (8), 2150–2159.
169.
TommasiniSMNasserPHuB and JepsenKJ: ‘Biological co-adaptation of morphological and composition traits contributes to mechanical functionality and skeletal fragility’, J. Bone Miner. Res., 2008, 23, (2), 236–246.
170.
YeniYNBrownCUGruenTA and NormanTL: ‘The relationships between femoral cortex geometry and tissue mechanical properties’, J. Mech. Behav. Biomed., 2013, 21, 9–16.
171.
BonadioJJepsenKJMansouraMKJaenischRKuhnJL and GoldsteinSA: ‘A murine skeletal adaptation that significantly increases cortical bone mechanical properties. Implications for human skeletal fragility’, J. Clin. Invest., 1993, 92, (4), 1697–1705.
172.
KozloffKMCardenABergwitzCForlinoAUvegesTEMorrisMDMariniJC and GoldsteinSA: ‘Brittle IV mouse model for osteogenesis imperfecta IV demonstrates postpubertal adaptations to improve whole bone strength’, J. Bone Miner. Res., 2004, 19, (4), 614–622.
173.
WallaceJMRajacharRMAllenMRBloomfieldSARobeyPGYoungMF and KohnDH: ‘Exercise-induced changes in the cortical bone of growing mice are bone- and gender-specific’, Bone, 2007, 40, (4), 1120–1127.
174.
LanyonLEHampsonWGJGoodshipAE and ShahJS: ‘Bone deformation recorded in vivo from strain gauges attached to the human tibial shaft’, Acta Orthop. Scand., 1975, 46, (2), 256–268.
175.
BurrDBMilgromCFyhrieDForwoodMNyskaMFinestoneAHoshawSSaiagE and SimkinA: ‘In vivo measurement of human tibial strains during vigorous activity’, Bone, 1996, 18, (5), 405–410.
176.
HansenUZiouposPSimpsonRCurreyJD and HyndD: ‘The effect of strain rate on the mechanical properties of human cortical bone’, J. Biomech. Eng., 2008, 130, (1), 011011.
177.
CrowninshieldR and PopeM: ‘The response of compact bone in tension at various strain rates’, Ann. Biomed. Eng., 1974, 2, (2), 217–225.
178.
EvansG.P.BehiriJ.C.VaughanL.C. and BonfieldW.‘The response of equine cortical bone to loading at strain rates experienced in vivo by the galloping horse’,Equine Vet. J., 1992, 24, (2), 125–128.
179.
PiekarskiK: ‘Fracture of bone’, J. Appl. Phys., 1970, 41, (1), 215–223.
180.
RobertsonDM and SmithDC: ‘Compressive strength of mandibular bone as a function of microstructure and strain rate’, J. Biomech., 1978, 11, (10–12), 455–471.
181.
BehiriJC and BonfieldW: ‘Crack velocity dependence of longitudinal fracture in bone’, J. Mater. Sci., 1980, 15, (7), 1841–1849.
182.
BehiriJC and BonfieldW: ‘Fracture mechanics of bone – the effects of density, specimen thickness and crack velocity on longitudinal fracture’, J. Biomech., 1984, 17, (1), 25–34.
183.
AdharapurapuRRJiangF and VecchioKS: ‘Dynamic fracture of bovine bone’, Mat. Sci. Eng. C, 2006, 26, (8), 1325–1332.
184.
KulinRJiangF and VecchioK: ‘Aging and loading rate effects on the mechanical behavior of equine bone’, JOM-J. Min. Met. Mat. S, 2008, 60, (6), 39–44.
185.
CharoenphanS and PolchaiA: ‘Finite element modeling for strain rate dependency of fracture resistance in compact bone’, J. Biomech. Eng., 2007, 129, (1), 20–25.
186.
KulinRJiangF and VecchioKS: ‘Effects of age and loading rate on equine cortical bone failure’, J. Mech. Behav. Biomed., 2011, 4, (1), 57–75.
187.
ZiouposPHansenU and CurreyJD: ‘Microcracking damage and the fracture process in relation to strain rate in human cortical bone tensile failure’, J. Biomech., 2008, 41, (14), 2932–2939.
188.
KulinRMJiangF and VecchioKS: ‘Loading rate effects on the R-curve behavior of cortical bone’, Acta Biomater., 2011, 7, (2), 724–732.
189.
TomarV: ‘Modeling of dynamic fracture and damage in two-dimensional trabecular bone microstructures using the cohesive finite element method’, J. Biomech. Eng., 2008, 130, (2), 21021.
190.
UralAZiouposPBuchananD and VashishthD: ‘Evaluation of the influence of strain rate on Colles’ fracture load’,J. Biomech., 2012, 45, (10), 1854–1857.
191.
KanisJA: ‘Diagnosis of osteoporosis and assessment of fracture risk’, Lancet, 2002, 359, (9321), 1929–1936.
192.
KanisJAOdenAJohnellOJohanssonHLaetCBrownJBurckhardtPCooperCChristiansenCCummingsSEismanJAFujiwaraSGlüerCGoltzmanDHansDKriegMACroixAMcCloskeyEMellstromDMeltonLJIIIPolsHReeveJSandersKSchottAMSilmanATorgersonDStaaTWattsNB and YoshimuraN: ‘The use of clinical risk factors enhances the performance of BMD in the prediction of hip and osteoporotic fractures in men and women’, Osteoporos. Int., 2007, 18, (8), 1033–1046.
193.
RubinKHFriis-HolmbergTHermannAPAbrahamsenB and BrixenK: ‘Risk assessment tools to identify women with increased risk of osteoporotic fracture: Complexity or simplicity? A systematic review’, J. Bone Miner. Res., 2013, 28, (8), 1701–1717.
194.
KanisJAMcCloskeyEVJohanssonHOdenAStrömO and BorgströmF: ‘Development and use of FRAX® in osteoporosis’, Osteoporos. Int., 2010, 21, (2), 407–413.
195.
WeinkamerR and FratzlP: ‘Mechanical adaptation of biological materials – the examples of bone and wood’, Mat. Sci. Eng. C, 2011, 31, (6), 1164–1173.
196.
O’BrienFJTaylorD and LeeTC: ‘An improved labelling technique for monitoring microcrack growth in compact bone’, J. Biomech., 2002, 35, (4), 523–526.
197.
VashishthD: ‘Hierarchy of bone microdamage at multiple length scales’, Int. J. Fatigue, 2007, 29, (6), 1024–1033.
