{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:24:44Z","timestamp":1792783484132,"version":"4.5.0"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11772240, 11720101002, 11542001, 11502175"],"award-info":[{"award-number":["11772240, 11720101002, 11542001, 11502175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20150381"],"award-info":[{"award-number":["BK20150381"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central University"},{"name":"Translational Medicine and Interdisciplinary Research Joint Fund of Zhongnan Hospital of Wuhan University","award":["ZNJC201927"],"award-info":[{"award-number":["ZNJC201927"]}],"id":[{"id":"https:\/\/ror.org\/01v5mqw79","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Innovative Group Development Program at School of Civil Engineering, Wuhan University","id":[{"id":"https:\/\/ror.org\/033vjfk17","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biomech Model Mechanobiol"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s10237-021-01491-z","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T07:02:37Z","timestamp":1627282957000},"page":"2013-2030","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Loss of longitudinal superiority marks the microarchitecture deterioration of osteoporotic cancellous bones"],"prefix":"10.1007","volume":"20","author":[{"given":"Zhenzi","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanan","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoxiao","family":"Liang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Lei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobin","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2688-8960","authenticated-orcid":false,"given":"Zuoqi","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Cai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"1491_CR1","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.jmbbm.2017.12.010","volume":"78","author":"MM Barak","year":"2018","unstructured":"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 78:455\u2013464. https:\/\/doi.org\/10.1016\/j.jmbbm.2017.12.010","journal-title":"J Mech Behav Biomed"},{"key":"1491_CR2","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1007\/s11926-010-0097-y","volume":"12","author":"DJ Becker","year":"2010","unstructured":"Becker DJ, Kilgore ML, Morrisey MA (2010) The societal burden of osteoporosis. Curr Rheumatol Rep 12:186\u2013191","journal-title":"Curr Rheumatol Rep"},{"key":"1491_CR3","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/j.bone.2008.11.020","volume":"44","author":"G Bevill","year":"2009","unstructured":"Bevill G, Keaveny TM (2009) Trabecular bone strength predictions using finite element analysis of micro-scale images at limited spatial resolution. Bone 44:579\u2013584. https:\/\/doi.org\/10.1016\/j.bone.2008.11.020","journal-title":"Bone"},{"key":"1491_CR4","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.jmbbm.2007.04.001","volume":"1","author":"MJ Buehler","year":"2008","unstructured":"Buehler MJ (2008) Nanomechanics of collagen fibrils under varying cross-link densities: Atomistic and continuum studies. J Mech Behav Biomed 1:59\u201367. https:\/\/doi.org\/10.1016\/j.jmbbm.2007.04.001","journal-title":"J Mech Behav Biomed"},{"key":"1491_CR5","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/j.bone.2007.07.007","volume":"41","author":"HR Buie","year":"2007","unstructured":"Buie HR, Campbell GM, Klinck RJ, MacNeil JA, Boyd SK (2007) Automatic segmentation of cortical and trabecular compartments based on a dual threshold technique for in vivo micro-CT bone analysis. Bone 41:505\u2013515. https:\/\/doi.org\/10.1016\/j.bone.2007.07.007","journal-title":"Bone"},{"key":"1491_CR6","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.morpho.2008.10.003","volume":"92","author":"D Chappard","year":"2008","unstructured":"Chappard D, Basl\u00e9 M-F, Legrand E, Audran M (2008) Trabecular bone microarchitecture: a review. Morphologie 92:162\u2013170","journal-title":"Morphologie"},{"key":"1491_CR7","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1359\/jbmr.2000.15.1.32","volume":"15","author":"TE Ciarelli","year":"2000","unstructured":"Ciarelli TE, Fyhrie DP, Schaffler MB, Goldstein SA (2000) Variations in three-dimensional cancellous bone architecture of the proximal femur in female hip fractures and in controls. J Bone Miner Res 15:32\u201340. https:\/\/doi.org\/10.1359\/jbmr.2000.15.1.32","journal-title":"J Bone Miner Res"},{"key":"1491_CR8","doi-asserted-by":"publisher","first-page":"115126","DOI":"10.1016\/j.bone.2019.115126","volume":"130","author":"A Creecy","year":"2020","unstructured":"Creecy A et al (2020) The age-related decrease in material properties of BALB\/c mouse long bones involves alterations to the extracellular matrix. Bone 130:115126","journal-title":"Bone"},{"key":"1491_CR9","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1016\/S0002-9343(01)01124-X","volume":"112","author":"SR Cummings","year":"2002","unstructured":"Cummings SR, Karpf DB, Harris F, Genant HK, Ensrud K, LaCroix AZ, Black DM (2002) Improvement in spine bone density and reduction in risk of vertebral fractures during treatment with antiresorptive drugs. Am J Med 112:281\u2013289. https:\/\/doi.org\/10.1016\/S0002-9343(01)01124-X","journal-title":"Am J Med"},{"key":"1491_CR10","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1243\/EMED_JOUR_1986_015_039_02","volume":"15","author":"JD Currey","year":"1986","unstructured":"Currey JD (1986) Power law models for the mechanical properties of cancellous bone. Eng Med 15:153\u2013154","journal-title":"Eng Med"},{"key":"1491_CR11","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1016\/j.bone.2003.12.022","volume":"34","author":"PD Delmas","year":"2004","unstructured":"Delmas PD, Seeman E (2004) Changes in bone mineral density explain little of the reduction in vertebral or nonvertebral fracture risk with anti-resorptive therapy. Bone 34:599\u2013604. https:\/\/doi.org\/10.1016\/j.bone.2003.12.022","journal-title":"Bone"},{"key":"1491_CR12","doi-asserted-by":"publisher","first-page":"2128","DOI":"10.1007\/s11999-010-1702-0","volume":"469","author":"E Donnelly","year":"2011","unstructured":"Donnelly E (2011) Methods for assessing bone quality: a review. Clin Orthop Relat R 469:2128\u20132138. https:\/\/doi.org\/10.1007\/s11999-010-1702-0","journal-title":"Clin Orthop Relat R"},{"key":"1491_CR13","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.jbiomech.2018.04.042","volume":"75","author":"WS Enns-Bray","year":"2018","unstructured":"Enns-Bray WS, Ferguson SJ, Helgason B (2018) Strain rate dependency of bovine trabecular bone under impact loading at sideways fall velocity. J Biomech 75:46\u201352. https:\/\/doi.org\/10.1016\/j.jbiomech.2018.04.042","journal-title":"J Biomech"},{"key":"1491_CR14","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1364\/JOSAA.1.000612","volume":"1","author":"LA Feldkamp","year":"1984","unstructured":"Feldkamp LA, Davis LC, Kress JW (1984) Practical cone-beam algorithm. Josa A 1:612\u2013619","journal-title":"Josa A"},{"key":"1491_CR15","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1016\/j.bone.2003.12.012","volume":"34","author":"H Follet","year":"2004","unstructured":"Follet H, Boivin G, Rumelhart C, Meunier PJ (2004) The degree of mineralization is a determinant of bone strength: a study on human calcanei. Bone 34:783\u2013789. https:\/\/doi.org\/10.1016\/j.bone.2003.12.012","journal-title":"Bone"},{"key":"1491_CR16","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s40279-013-0100-7","volume":"44","author":"H Fonseca","year":"2014","unstructured":"Fonseca H, Moreira-Goncalves D, Coriolano HJA, Duarte JA (2014) Bone quality: the determinants of bone strength and fragility. Sports Med 44:37\u201353. https:\/\/doi.org\/10.1007\/s40279-013-0100-7","journal-title":"Sports Med"},{"key":"1491_CR17","first-page":"270","volume":"28","author":"LJ Gibson","year":"2003","unstructured":"Gibson LJ (2003) Cellular solids. Mrs. Bulletin 28:270\u2013274","journal-title":"Bulletin"},{"key":"1491_CR18","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.jbiomech.2004.09.027","volume":"38","author":"LJ Gibson","year":"2005","unstructured":"Gibson LJ (2005) Biomechanics of cellular solids. J Biomech 38:377\u2013399. https:\/\/doi.org\/10.1016\/j.jbiomech.2004.09.027","journal-title":"J Biomech"},{"key":"1491_CR19","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1007\/s10237-012-0443-2","volume":"12","author":"T Gross","year":"2013","unstructured":"Gross T, Pahr DH, Zysset PK (2013) Morphology-elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations. Biomech Model Mechan 12:793\u2013800. https:\/\/doi.org\/10.1007\/s10237-012-0443-2","journal-title":"Biomech Model Mechan"},{"key":"1491_CR20","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1002\/jor.1100180224","volume":"18","author":"XE Guo","year":"2000","unstructured":"Guo XE, Goldstein SA (2000) Vertebral trabecular bone microscopic tissue elastic modulus and hardness do not change in ovariectomized rats. J Orthop Res 18:333\u2013336","journal-title":"J Orthop Res"},{"key":"1491_CR21","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/j.bone.2013.06.028","volume":"56","author":"R Hambli","year":"2013","unstructured":"Hambli R (2013a) Micro-CT finite element model and experimental validation of trabecular bone damage and fracture. Bone 56:363\u2013374. https:\/\/doi.org\/10.1016\/j.bone.2013.06.028","journal-title":"Bone"},{"key":"1491_CR22","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s11517-012-0986-5","volume":"51","author":"R Hambli","year":"2013","unstructured":"Hambli R (2013b) A quasi-brittle continuum damage finite element model of the human proximal femur based on element deletion. Med Biol Eng Comput 51:219\u2013231. https:\/\/doi.org\/10.1007\/s11517-012-0986-5","journal-title":"Med Biol Eng Comput"},{"key":"1491_CR23","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.medengphy.2011.07.011","volume":"34","author":"R Hambli","year":"2012","unstructured":"Hambli R, Bettamer A, Allaoui S (2012) Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage. Med Eng Phys 34:202\u2013210. https:\/\/doi.org\/10.1016\/j.medengphy.2011.07.011","journal-title":"Med Eng Phys"},{"key":"1491_CR24","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1016\/j.jbiomech.2008.05.014","volume":"41","author":"NM Harrison","year":"2008","unstructured":"Harrison NM, McDonnell PF, O\u2019Mahoney DC, Kennedy OD, O\u2019Brien FJ, McHugh PE (2008) Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties. J Biomech 41:2589\u20132596. https:\/\/doi.org\/10.1016\/j.jbiomech.2008.05.014","journal-title":"J Biomech"},{"key":"1491_CR25","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10237-012-0394-7","volume":"12","author":"NM Harrison","year":"2013","unstructured":"Harrison NM, McDonnell P, Mullins L, Wilson N, O\u2019Mahoney D, McHugh PE (2013) Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach. Biomech Model Mechan 12:225\u2013241. https:\/\/doi.org\/10.1007\/s10237-012-0394-7","journal-title":"Biomech Model Mechan"},{"key":"1491_CR26","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/S8756-3282(01)00624-X","volume":"30","author":"S Hengsberger","year":"2002","unstructured":"Hengsberger S, Kulik A, Zysset P (2002) Nanoindentation discriminates the elastic properties of individual human bone lamellae under dry and physiological conditions. Bone 30:178\u2013184. https:\/\/doi.org\/10.1016\/S8756-3282(01)00624-X","journal-title":"Bone"},{"key":"1491_CR27","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1016\/S8756-3282(02)00693-2","volume":"30","author":"J Homminga","year":"2002","unstructured":"Homminga J, McCreadie BR, Ciarelli TE, Weinans H, Goldstein SA, Huiskes R (2002) Cancellous bone mechanical properties from normals and patients with hip fractures differ on the structure level, not on the bone hard tissue level. Bone 30:759\u2013764. https:\/\/doi.org\/10.1016\/S8756-3282(02)00693-2","journal-title":"Bone"},{"key":"1491_CR28","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/S8756-3282(02)00920-1","volume":"32","author":"GR Jordan","year":"2003","unstructured":"Jordan GR et al (2003) Increased femoral neck cancellous bone and connectivity in coxarthrosis (hip osteoarthritis). Bone 32:86\u201395. https:\/\/doi.org\/10.1016\/S8756-3282(02)00920-1","journal-title":"Bone"},{"key":"1491_CR29","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1016\/S8756-3282(99)00190-8","volume":"25","author":"J Kabel","year":"1999","unstructured":"Kabel J, van Rietbergen B, Odgaard A, Huiskes R (1999) Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone 25:481\u2013486. https:\/\/doi.org\/10.1016\/S8756-3282(99)00190-8","journal-title":"Bone"},{"key":"1491_CR30","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/j.bone.2015.09.009","volume":"81","author":"K Karasuyama","year":"2015","unstructured":"Karasuyama K, Yamamoto T, Motomura G, Sonoda K, Kubo Y, Iwamoto Y (2015) The role of sclerotic changes in the starting mechanisms of collapse: a histomorphometric and FEM study on the femoral head of osteonecrosis. Bone 81:644\u2013648. https:\/\/doi.org\/10.1016\/j.bone.2015.09.009","journal-title":"Bone"},{"key":"1491_CR31","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.1016\/0021-9290(94)90053-1","volume":"27","author":"TM Keaveny","year":"1994","unstructured":"Keaveny TM, Guo XE, Wachtel EF, Mcmahon TA, Hayes WC (1994) Trabecular bone exhibits fully linear elastic behavior and yields at low strains. J Biomech 27:1127\u20131136. https:\/\/doi.org\/10.1016\/0021-9290(94)90053-1","journal-title":"J Biomech"},{"key":"1491_CR32","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1146\/annurev.bioeng.3.1.307","volume":"3","author":"TM Keaveny","year":"2001","unstructured":"Keaveny TM, Morgan EF, Niebur GL, Yeh OC (2001) Biomechanics of trabecular bone. Annu Rev Biomed Eng 3:307\u2013333. https:\/\/doi.org\/10.1146\/annurev.bioeng.3.1.307","journal-title":"Annu Rev Biomed Eng"},{"key":"1491_CR33","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1146\/annurev-matsci-070909-104427","volume":"40","author":"ME Launey","year":"2010","unstructured":"Launey ME, Buehler MJ, Ritchie RO (2010) On the Mechanistic origins of toughness in bone. Annu Rev Mater Res 40:25\u201353. https:\/\/doi.org\/10.1146\/annurev-matsci-070909-104427","journal-title":"Annu Rev Mater Res"},{"key":"1491_CR34","doi-asserted-by":"publisher","first-page":"331","DOI":"10.3949\/ccjm.76a.08041","volume":"76","author":"A Licata","year":"2009","unstructured":"Licata A (2009) Bone density versus bone quality: What\u2019s a clinician to do? Clev Clin J Med 76:331\u2013336","journal-title":"Clev Clin J Med"},{"key":"1491_CR35","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1097\/01.blo.0000132404.30139.f2","volume":"27","author":"JT Lin","year":"2004","unstructured":"Lin JT, Lane JM (2004) Osteoporosis\u2013a review. Clin Orthop Relat R 27:126\u2013134. https:\/\/doi.org\/10.1097\/01.blo.0000132404.30139.f2","journal-title":"Clin Orthop Relat R"},{"key":"1491_CR36","doi-asserted-by":"publisher","first-page":"107436","DOI":"10.1016\/j.compositesb.2019.107436","volume":"177","author":"P Liu","year":"2019","unstructured":"Liu P, Liang X, Li Z, Zhu X, Zhang Z, Cai L (2019) Decoupled effects of bone mass, microarchitecture and tissue property on the mechanical deterioration of osteoporotic bones. Compos Part B-Eng 177:107436","journal-title":"Compos Part B-Eng"},{"key":"1491_CR37","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1359\/Jbmr.071009","volume":"23","author":"XS Liu","year":"2008","unstructured":"Liu XS, Sajda P, Saha PK, Wehrli FW, Bevill G, Keaveny TM, Guo XE (2008) 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 23:223\u2013235. https:\/\/doi.org\/10.1359\/Jbmr.071009","journal-title":"J Bone Miner Res"},{"key":"1491_CR38","doi-asserted-by":"publisher","first-page":"1190","DOI":"10.1016\/j.bone.2006.06.008","volume":"39","author":"BR McCreadie","year":"2006","unstructured":"McCreadie BR, Morris MD, Chen TC, Rao DS, Finney WF, Widjaja E, Goldstein SA (2006) Bone tissue compositional differences in women with and without osteoporotic fracture. Bone 39:1190\u20131195. https:\/\/doi.org\/10.1016\/j.bone.2006.06.008","journal-title":"Bone"},{"key":"1491_CR39","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1098\/rsif.2009.0282","volume":"7","author":"LM McNamara","year":"2010","unstructured":"McNamara LM (2010) Perspective on post-menopausal osteoporosis: establishing an interdisciplinary understanding of the sequence of events from the molecular level to whole bone fractures. J R Soc Interface 7:353\u2013372. https:\/\/doi.org\/10.1098\/rsif.2009.0282","journal-title":"J R Soc Interface"},{"key":"1491_CR40","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1016\/S0021-9290(03)00071-X","volume":"36","author":"EF Morgan","year":"2003","unstructured":"Morgan EF, Bayraktar HH, Keaveny TM (2003) Trabecular bone modulus-density relationships depend on anatomic site. J Biomech 36:897\u2013904. https:\/\/doi.org\/10.1016\/S0021-9290(03)00071-X","journal-title":"J Biomech"},{"key":"1491_CR41","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1016\/S0021-9290(00)00149-4","volume":"33","author":"GL Niebur","year":"2000","unstructured":"Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM (2000) High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech 33:1575\u20131583","journal-title":"J Biomech"},{"key":"1491_CR42","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1002\/9781119266594.ch12","volume-title":"Primer on the metabolic bone diseases and disorders of mineral metabolism","author":"JS Nyman","year":"2018","unstructured":"Nyman JS, Vashishth D (2018) Assessment of bone mass, structure, and quality in rodents. In: Bilezkian JP (ed) Primer on the metabolic bone diseases and disorders of mineral metabolism. Wiley, New York, pp 93\u2013100"},{"key":"1491_CR43","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/s00466-016-1301-3","volume":"58","author":"DT O\u2019Connor","year":"2016","unstructured":"O\u2019Connor DT et al (2016) Modeling orthotropic elasticity, localized plasticity and fracture in trabecular bone. Comput Mech 58:423\u2013439. https:\/\/doi.org\/10.1007\/s00466-016-1301-3","journal-title":"Comput Mech"},{"key":"1491_CR44","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1016\/S0140-6736(10)62349-5","volume":"377","author":"TD Rachner","year":"2011","unstructured":"Rachner TD, Khosla S, Hofbauer LC (2011) Osteoporosis: now and the future. Lancet 377:1276\u20131287. https:\/\/doi.org\/10.1016\/S0140-6736(10)62349-5","journal-title":"Lancet"},{"key":"1491_CR46","doi-asserted-by":"publisher","first-page":"S505","DOI":"10.1016\/8756-3282(95)00258-4","volume":"17","author":"BL Riggs","year":"1995","unstructured":"Riggs BL, Melton LJ (1995) The worldwide problem of osteoporosis\u2013insights afforded by epidemiology. Bone 17:S505\u2013S511. https:\/\/doi.org\/10.1016\/8756-3282(95)00258-4","journal-title":"Bone"},{"key":"1491_CR47","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1007\/s00296-010-1542-y","volume":"30","author":"R Rizzoli","year":"2010","unstructured":"Rizzoli R, Laroche M, Krieg MA, Frieling I, Thomas T, Delmas P, Felsenberg D (2010) Strontium ranelate and alendronate have differing effects on distal tibia bone microstructure in women with osteoporosis. Rheumatol Int 30:1341\u20131348. https:\/\/doi.org\/10.1007\/s00296-010-1542-y","journal-title":"Rheumatol Int"},{"key":"1491_CR48","doi-asserted-by":"publisher","DOI":"10.1098\/rsfs.2015.0055","author":"FA Sabet","year":"2016","unstructured":"Sabet FA, Najafi AR, Hamed E, Jasiuk I (2016) Modelling of bone fracture and strength at different length scales: a review. Interface Focus. https:\/\/doi.org\/10.1098\/rsfs.2015.0055","journal-title":"Interface Focus"},{"key":"1491_CR49","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.jmbbm.2016.10.005","volume":"66","author":"C Sandino","year":"2017","unstructured":"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 66:19\u201327. https:\/\/doi.org\/10.1016\/j.jmbbm.2016.10.005","journal-title":"J Mech Behav Biomed"},{"key":"1491_CR50","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s10237-012-0392-9","volume":"12","author":"JJ Schwiedrzik","year":"2013","unstructured":"Schwiedrzik JJ, Zysset PK (2013) An anisotropic elastic-viscoplastic damage model for bone tissue. Biomech Model Mechan 12:201\u2013213. https:\/\/doi.org\/10.1007\/s10237-012-0392-9","journal-title":"Biomech Model Mechan"},{"key":"1491_CR51","doi-asserted-by":"publisher","first-page":"2250","DOI":"10.1056\/NEJMra053077","volume":"354","author":"E Seeman","year":"2006","unstructured":"Seeman E, Delmas PD (2006) Mechanisms of disease\u2013bone quality\u2013the material and structural basis of bone strength and fragility. New Engl J Med 354:2250\u20132261","journal-title":"New Engl J Med"},{"key":"1491_CR52","doi-asserted-by":"publisher","first-page":"1618","DOI":"10.1359\/Jbmr.090316","volume":"24","author":"MJ Silva","year":"2009","unstructured":"Silva MJ, Brodt MD, Lynch MA, McKenzie JA, Tanouye KM, Nyman JS, Wang XD (2009) Type 1 diabetes in young rats leads to progressive trabecular bone loss, cessation of cortical bone growth, and diminished whole bone strength and fatigue life. J Bone Miner Res 24:1618\u20131627. https:\/\/doi.org\/10.1359\/Jbmr.090316","journal-title":"J Bone Miner Res"},{"key":"1491_CR53","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1007\/s10237-019-01254-x","volume":"19","author":"M Stipsitz","year":"2020","unstructured":"Stipsitz M, Zysset PK, Pahr DH (2020) Efficient materially nonlinear mu FE solver for simulations of trabecular bone failure. Biomech Model Mechan 19:861\u2013874. https:\/\/doi.org\/10.1007\/s10237-019-01254-x","journal-title":"Biomech Model Mechan"},{"key":"1491_CR54","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1038\/nmat4719","volume":"15","author":"OA Tertuliano","year":"2016","unstructured":"Tertuliano OA, Greer JR (2016) The nanocomposite nature of bone drives its strength and damage resistance. Nat Mater 15:1195\u20131202","journal-title":"Nat Mater"},{"key":"1491_CR55","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/abdd9d","volume":"16","author":"OA Tertuliano","year":"2021","unstructured":"Tertuliano OA, Edwards BW, Meza LR, Deshpande VS, Greer JR (2021) Nanofibril-mediated fracture resistance of bone Bioinspir Biomim 16:035001. https:\/\/doi.org\/10.1088\/1748-3190\/abdd9d","journal-title":"Bioinspir Biomim"},{"key":"1491_CR56","doi-asserted-by":"publisher","first-page":"1928","DOI":"10.1016\/j.engfracmech.2006.05.024","volume":"74","author":"PJ Thurner","year":"2007","unstructured":"Thurner PJ et al (2007) High-speed photography of compressed human trabecular bone correlates whitening to microscopic damage. Eng Fract Mech 74:1928\u20131941","journal-title":"Eng Fract Mech"},{"key":"1491_CR57","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1016\/0021-9290(90)90048-8","volume":"23","author":"CH Turner","year":"1990","unstructured":"Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC (1990) The fabric dependence of the orthotropic elastic-constants of cancellous bone. J Biomech 23:549\u2013561. https:\/\/doi.org\/10.1016\/0021-9290(90)90048-8","journal-title":"J Biomech"},{"key":"1491_CR58","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1002\/jor.1100160105","volume":"16","author":"B Van Rietbergen","year":"1998","unstructured":"Van Rietbergen B, Odgaard A, Kabel J, Huiskes R (1998) Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions. J Orthop Res 16:23\u201328. https:\/\/doi.org\/10.1002\/jor.1100160105","journal-title":"J Orthop Res"},{"key":"1491_CR59","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1080\/10255840701848756","volume":"11","author":"E Verhulp","year":"2008","unstructured":"Verhulp E, Van Rietbergen B, Muller R, Huiskes R (2008) Micro-finite element simulation of trabecular-bone post-yield behaviour\u2013effects of material model, element size and type. Comput Method Biomec 11:389\u2013395. https:\/\/doi.org\/10.1080\/10255840701848756","journal-title":"Comput Method Biomec"},{"key":"1491_CR60","doi-asserted-by":"publisher","first-page":"044502","DOI":"10.1115\/1.4023983","volume":"135","author":"H Wang","year":"2013","unstructured":"Wang H et al (2013) Accuracy of individual trabecula segmentation based plate and rod finite element models in idealized trabecular bone microstructure. J Biomech Eng-T Asme 135:044502. https:\/\/doi.org\/10.1115\/1.4023983","journal-title":"J Biomech Eng-T Asme"},{"key":"1491_CR61","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.bone.2014.11.006","volume":"72","author":"J Wang","year":"2015","unstructured":"Wang J et al (2015) Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. Bone 72:71\u201380. https:\/\/doi.org\/10.1016\/j.bone.2014.11.006","journal-title":"Bone"},{"key":"1491_CR62","doi-asserted-by":"publisher","first-page":"40265","DOI":"10.1038\/srep40265","volume":"7","author":"ZW Wang","year":"2017","unstructured":"Wang ZW et al (2017) Unique local bone tissue characteristics in iliac crest bone biopsy from adolescent idiopathic scoliosis with severe spinal deformity. Sci Rep-Uk 7:40265. https:\/\/doi.org\/10.1038\/srep40265","journal-title":"Sci Rep-Uk"},{"key":"1491_CR63","doi-asserted-by":"publisher","first-page":"e3188","DOI":"10.1002\/cnm.3188","volume":"35","author":"B Werner","year":"2019","unstructured":"Werner B, Ovesy M, Zysset P (2019) An explicit microFE approach to investigate the post-yield behaviour of trabecular bone under large deformations. Int J Numer Meth Bio 35:e3188","journal-title":"Int J Numer Meth Bio"},{"key":"1491_CR64","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1115\/1.2834756","volume":"120","author":"P Zysset","year":"1998","unstructured":"Zysset P, Goulet R, Hollister S (1998a) A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng 120:640\u2013646","journal-title":"J Biomech Eng"},{"key":"1491_CR65","doi-asserted-by":"publisher","first-page":"429","DOI":"10.3233\/THC-1998-65-615","volume":"6","author":"PK Zysset","year":"1998","unstructured":"Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA (1998b) Mechanical properties of human trabecular bone lamellae quantified by nanoindentation. Technol Health Care 6:429\u2013432","journal-title":"Technol Health Care"}],"container-title":["Biomechanics and Modeling in Mechanobiology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-021-01491-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10237-021-01491-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-021-01491-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,19]],"date-time":"2021-09-19T13:05:52Z","timestamp":1632056752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10237-021-01491-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,26]]},"references-count":64,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1491"],"URL":"https:\/\/doi.org\/10.1007\/s10237-021-01491-z","relation":{},"ISSN":["1617-7959","1617-7940"],"issn-type":[{"value":"1617-7959","type":"print"},{"value":"1617-7940","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,26]]},"assertion":[{"value":"26 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}