{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T19:00:20Z","timestamp":1791054020194,"version":"4.1.0"},"reference-count":111,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T00:00:00Z","timestamp":1775174400000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2024.01927.BDANA"],"award-info":[{"award-number":["2024.01927.BDANA"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"unda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/00481"],"award-info":[{"award-number":["UID\/00481"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biomech Model Mechanobiol"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Background and Objective: The development of computational models for predicting bone fracture healing process holds strong potential to optimize therapeutic management in non-unions and delayed healing, reducing healthcare costs and disability-adjusted life years. The main goal of this study is to provide a thoroughly comparative analysis to computational models already proposed to predict fracture healing, including methodologies, mathematical frameworks, validation techniques, and comparative findings across different studies. Methods: This review analyzes 60 computational models selected through a systematic search in the Scopus database (2000\u20132025) using targeted keywords and rigorously screened according to predefined inclusion and exclusion criteria for simulating bone fracture healing, focusing on mechanical, biological, mechanobiological, ultrasound, and bioelectronic dynamics, employing FEM and artificial intelligence techniques. The effectiveness of each model in predicting healing progression was assessed by analyzing their computational frameworks, accuracy, and limitations. Results: Comparative analysis revealed that both mechanical and biological models provide fundamental predictions related to fracture healing (e.g., stress distribution and vascularization), but they often lack the physiological complexity demanded for clinical application. Mechanobiological models accurately predict tissue differentiation by combining mechanical stimuli, with strong qualitative agreement with in vivo histological patterns. Ultrasound models have been effective for non-invasive structural assessment, despite existing limitations due to simplified boundary conditions. Notably, the development of bioelectric models has been demonstrating a highly sensitive approach for assessing fracture healing. Conclusions:This study highlights that multidomain computational frameworks combining mechanobiological dynamics with dielectric properties hold significant potential to personalize the clinical management of delayed bone healing.<\/jats:p>","DOI":"10.1007\/s10237-026-02061-x","type":"journal-article","created":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T05:45:13Z","timestamp":1775195113000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Computational models for predicting bone fracture healing: a review of modeling approaches, predictions, and emerging strategies"],"prefix":"10.1007","volume":"25","author":[{"given":"Diogo G.","family":"Pires","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Completo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marco P. Soares dos","family":"Santos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,3]]},"reference":[{"key":"2061_CR1","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/j.jmbbm.2013.09.023","volume":"29","author":"JA Alierta","year":"2014","unstructured":"Alierta JA et al (2014) An interface finite element model can be used to predict healing outcome of bone fractures. J Mech Behav Biomed Mater 29:328\u2013338. https:\/\/doi.org\/10.1016\/j.jmbbm.2013.09.023","journal-title":"J Mech Behav Biomed Mater"},{"issue":"8","key":"2061_CR2","doi-asserted-by":"publisher","first-page":"961","DOI":"10.1016\/S0021-9290(00)00049-X","volume":"33","author":"C Ament","year":"2000","unstructured":"Ament C, Hofer EP (2000) A fuzzy logic model of fracture healing. J Biomech 33(8):961\u2013968. https:\/\/doi.org\/10.1016\/S0021-9290(00)00049-X","journal-title":"J Biomech"},{"issue":"Suppl 2","key":"2061_CR3","doi-asserted-by":"publisher","first-page":"S36","DOI":"10.1007\/s00198-004-1728-9","volume":"16","author":"P Augat","year":"2005","unstructured":"Augat P, Simon U, Liedert A, Claes L (2005) Mechanics and mechano-biology of fracture healing in normal and osteoporotic bone. Osteoporos Int 16(Suppl 2):S36\u2013S43. https:\/\/doi.org\/10.1007\/s00198-004-1728-9","journal-title":"Osteoporos Int"},{"key":"2061_CR4","doi-asserted-by":"publisher","first-page":"S78","DOI":"10.1016\/j.injury.2020.10.009","volume":"52","author":"P Augat","year":"2021","unstructured":"Augat P, Hollensteiner M, von R\u00fcden C (2021) The role of mechanical stimulation in the enhancement of bone healing. Injury 52:S78\u2013S83. https:\/\/doi.org\/10.1016\/j.injury.2020.10.009","journal-title":"Injury"},{"issue":"2","key":"2061_CR5","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.medengphy.2015.11.013","volume":"38","author":"PT Avval","year":"2016","unstructured":"Avval PT et al (2016) Long-term response of femoral density to hip implant and bone fracture plate: Computational study using a mechano-biochemical model. Med Eng Phys 38(2):171\u2013180. https:\/\/doi.org\/10.1016\/j.medengphy.2015.11.013","journal-title":"Med Eng Phys"},{"issue":"2","key":"2061_CR6","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1006\/jtbi.2001.2372","volume":"212","author":"A Bail\u00f3n-Plaza","year":"2001","unstructured":"Bail\u00f3n-Plaza A, Van Der Meulen MC (2001) A mathematical framework to study the effects of growth factor influences on fracture healing. J Theor Biol 212(2):191\u2013209. https:\/\/doi.org\/10.1006\/jtbi.2001.2372","journal-title":"J Theor Biol"},{"issue":"5","key":"2061_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1009839","volume":"18","author":"E Baratchart","year":"2022","unstructured":"Baratchart E, Lo CH, Lynch CC, Basanta D (2022) Integrated computational and in vivo models reveal key insights into macrophage behavior during bone healing. PLoS Comput Biol 18(5):1\u201333. https:\/\/doi.org\/10.1371\/journal.pcbi.1009839","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"2061_CR8","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00607-008-0004-9","volume":"82","author":"P Bastian","year":"2008","unstructured":"Bastian P, Blatt M, Dedner A, Engwer C, Kl\u00f6fkorn R, Kornhuber R, Ohlberger M, Sander O (2008) A generic grid interface for parallel and adaptive scientific computing. part ii: implementation and tests in dune. Computing 82(2):121\u2013138. https:\/\/doi.org\/10.1007\/s00607-008-0004-9","journal-title":"Computing"},{"issue":"3","key":"2061_CR9","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1111\/iwj.12231","volume":"12","author":"A Bigham-Sadegh","year":"2015","unstructured":"Bigham-Sadegh A, Oryan A (2015) Basic concepts regarding fracture healing and the current options and future directions in managing bone fractures. Int Wound J 12(3):238\u2013247. https:\/\/doi.org\/10.1111\/iwj.12231","journal-title":"Int Wound J"},{"key":"2061_CR10","doi-asserted-by":"publisher","first-page":"1231329","DOI":"10.3389\/fimmu.2023.1231329","volume":"14","author":"E Borgiani","year":"2023","unstructured":"Borgiani E et al (2023) Commbini: an experimentally-informed computational model of macrophage dynamics in the bone injury immunoresponse. Front Immunol 14:1231329. https:\/\/doi.org\/10.3389\/fimmu.2023.1231329","journal-title":"Front Immunol"},{"issue":"4","key":"2061_CR11","doi-asserted-by":"publisher","first-page":"1627","DOI":"10.1007\/s10237-021-01466-0","volume":"20","author":"E Borgiani","year":"2021","unstructured":"Borgiani E, Duda GN, Willie BM, Checa S (2021) Bone morphogenetic protein 2-induced cellular chemotaxis drives tissue patterning during critical-sized bone defect healing: an in silico study. Biomech Model Mechanobiol 20(4):1627\u20131644. https:\/\/doi.org\/10.1007\/s10237-021-01466-0","journal-title":"Biomech Model Mechanobiol"},{"issue":"7","key":"2061_CR12","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0040737","volume":"7","author":"DP Burke","year":"2012","unstructured":"Burke DP, Kelly DJ (2012) Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model. PLoS ONE 7(7):e40737. https:\/\/doi.org\/10.1371\/journal.pone.0040737","journal-title":"PLoS ONE"},{"issue":"36","key":"2061_CR13","doi-asserted-by":"publisher","first-page":"5544","DOI":"10.1016\/j.biomaterials.2007.09.003","volume":"28","author":"DP Byrne","year":"2007","unstructured":"Byrne DP, Lacroix D, Planell JA, Kelly DJ, Prendergast PJ (2007) Simulation of tissue differentiation in a scaffold as a function of porosity, young\u2019s modulus and dissolution rate: Application of mechanobiological models in tissue engineering. Biomaterials 28(36):5544\u20135554. https:\/\/doi.org\/10.1016\/j.biomaterials.2007.09.003","journal-title":"Biomaterials"},{"issue":"2","key":"2061_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.injury.2023.111203","volume":"55","author":"L Cai","year":"2024","unstructured":"Cai L, Lv Y, Yan Q, Guo W (2024) Cytokines: The links between bone and the immune system. Injury 55(2):111203. https:\/\/doi.org\/10.1016\/j.injury.2023.111203","journal-title":"Injury"},{"issue":"5","key":"2061_CR15","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1002\/jor.1100060517","volume":"6","author":"DR Carter","year":"1988","unstructured":"Carter DR, Blenman PR, Beaupr\u00e9 GS (1988) Correlations between mechanical stress history and tissue differentiation in initial fracture healing. J Orthop Res 6(5):736\u2013748. https:\/\/doi.org\/10.1002\/jor.1100060517","journal-title":"J Orthop Res"},{"issue":"9","key":"2061_CR16","doi-asserted-by":"publisher","first-page":"e535","DOI":"10.1016\/S2666-7568(21)00183-5","volume":"2","author":"JA Cauley","year":"2021","unstructured":"Cauley JA (2021) The global burden of fractures. The Lancet Healthy Longevity 2(9):e535\u2013e536. https:\/\/doi.org\/10.1016\/S2666-7568(21)00183-5","journal-title":"The Lancet Healthy Longevity"},{"issue":"1","key":"2061_CR17","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10439-008-9594-9","volume":"37","author":"S Checa","year":"2009","unstructured":"Checa S, Prendergast PJ (2009) A mechanobiological model for tissue differentiation that includes angiogenesis: a lattice-based modeling approach. Ann Biomed Eng 37(1):129\u2013145. https:\/\/doi.org\/10.1007\/s10439-008-9594-9","journal-title":"Ann Biomed Eng"},{"issue":"8","key":"2061_CR18","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2017889118","volume":"118","author":"A Cheng","year":"2021","unstructured":"Cheng A, Vantucci CE, Krishnan L, Ruehle MA, Kotanchek T, Wood LB, Roy K, Guldberg RE (2021) Early systemic immune biomarkers predict bone regeneration after trauma. Proc Natl Acad Sci USA 118(8):e2017889118. https:\/\/doi.org\/10.1073\/pnas.2017889118","journal-title":"Proc Natl Acad Sci USA"},{"issue":"3","key":"2061_CR19","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/s0021-9290(98)00153-5","volume":"32","author":"LE Claes","year":"1999","unstructured":"Claes LE, Heigele CA (1999) Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing. J Biomech 32(3):255\u2013266. https:\/\/doi.org\/10.1016\/s0021-9290(98)00153-5","journal-title":"J Biomech"},{"issue":"4","key":"2061_CR20","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1002\/jor.1100150414","volume":"15","author":"L Claes","year":"1997","unstructured":"Claes L, Augat P, Suger G, Wilke H-J (1997) Influence of size and stability of the osteotomy gap on the success of fracture healing. J Orthop Res 15(4):577\u2013584. https:\/\/doi.org\/10.1002\/jor.1100150414","journal-title":"J Orthop Res"},{"issue":"5","key":"2061_CR21","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1007\/s00423-003-0396-0","volume":"388","author":"L Claes","year":"2003","unstructured":"Claes L, Eckert-H\u00fcbner K, Augat P (2003) The fracture gap size influences the local vascularization and tissue differentiation in callus healing. Langenbecks Arch Surg 388(5):316\u2013322. https:\/\/doi.org\/10.1007\/s00423-003-0396-0","journal-title":"Langenbecks Arch Surg"},{"issue":"2","key":"2061_CR22","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/S0925-4773(00)00532-3","volume":"100","author":"CI Colnot","year":"2001","unstructured":"Colnot CI, Helms JA (2001) A molecular analysis of matrix remodeling and angiogenesis during long bone development. Mech Dev 100(2):245\u2013250. https:\/\/doi.org\/10.1016\/S0925-4773(00)00532-3","journal-title":"Mech Dev"},{"issue":"199","key":"2061_CR23","doi-asserted-by":"publisher","first-page":"20220818","DOI":"10.1098\/rsif.2022.0818","volume":"20","author":"C Concei\u00e7\u00e3o","year":"2023","unstructured":"Concei\u00e7\u00e3o C, Completo A, Soares dos Santos MP (2023) Ultrasensitive capacitive sensing system for smart medical devices with ability to monitor fracture healing stages. J R Soc Interf 20(199):20220818. https:\/\/doi.org\/10.1098\/rsif.2022.0818","journal-title":"J R Soc Interf"},{"key":"2061_CR24","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1186\/1741-7015-9-66","volume":"9","author":"R Dimitriou","year":"2011","unstructured":"Dimitriou R, Jones E, McGonagle D, Giannoudis PV (2011) Bone regeneration: current concepts and future directions. BMC Med 9:66. https:\/\/doi.org\/10.1186\/1741-7015-9-66","journal-title":"BMC Med"},{"issue":"2","key":"2061_CR25","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1038\/s41584-022-00887-0","volume":"19","author":"GN Duda","year":"2023","unstructured":"Duda GN, Geissler S, Checa S, Tsitsilonis S, Petersen A, Schmidt-Bleek K (2023) The decisive early phase of bone regeneration. Nat Rev Rheumatol 19(2):78\u201395. https:\/\/doi.org\/10.1038\/s41584-022-00887-0","journal-title":"Nat Rev Rheumatol"},{"issue":"3","key":"2061_CR26","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1055\/s-0041-1732334","volume":"35","author":"H ElHawary","year":"2021","unstructured":"ElHawary H, Baradaran A, Abi-Rafeh J, Vorstenbosch J, Xu L, Efanov JI (2021) Bone healing and inflammation: Principles of fracture and repair. Semin Plast Surg 35(3):198\u2013203. https:\/\/doi.org\/10.1055\/s-0041-1732334","journal-title":"Semin Plast Surg"},{"issue":"4","key":"2061_CR27","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.bone.2008.06.007","volume":"43","author":"DR Epari","year":"2008","unstructured":"Epari DR, Lienau J, Schell H, Witt F, Duda GN (2008) Pressure, oxygen tension and temperature in the periosteal callus during bone healing-an in vivo study in sheep. Bone 43(4):734\u2013739. https:\/\/doi.org\/10.1016\/j.bone.2008.06.007","journal-title":"Bone"},{"issue":"1","key":"2061_CR28","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/S0736-0266(02)00087-6","volume":"21","author":"JL Ford","year":"2003","unstructured":"Ford JL, Robinson DE, Scammell BE (2003) The fate of soft callus chondrocytes during long bone fracture repair. J Orthop Res 21(1):54\u201361. https:\/\/doi.org\/10.1016\/S0736-0266(02)00087-6","journal-title":"J Orthop Res"},{"issue":"6","key":"2061_CR29","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3199","volume":"35","author":"G Ganadhiepan","year":"2019","unstructured":"Ganadhiepan G, Miramini S, Patel M, Mendis P, Zhang L (2019) Bone fracture healing under Ilizarov fixator: Influence of fixator configuration, fracture geometry, and loading. Int J Numer Methods Biomed Eng 35(6):e3199. https:\/\/doi.org\/10.1002\/cnm.3199","journal-title":"Int J Numer Methods Biomed Eng"},{"issue":"7","key":"2061_CR30","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3466","volume":"37","author":"G Ganadhiepan","year":"2021","unstructured":"Ganadhiepan G, Miramini S, Mendis P, Patel M, Zhang L (2021) A probabilistic approach for modelling bone fracture healing under ilizarov circular fixator. Int J Numer Methods Biomed Eng 37(7):e3466. https:\/\/doi.org\/10.1002\/cnm.3466","journal-title":"Int J Numer Methods Biomed Eng"},{"key":"2061_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2021.104611","volume":"121","author":"G Ganadhiepan","year":"2021","unstructured":"Ganadhiepan G, Miramini S, Patel M, Mendis P, Zhang L (2021) Optimal time-dependent levels of weight-bearing for bone fracture healing under Ilizarov circular fixators. J Mech Behav Biomed Mater 121:104611. https:\/\/doi.org\/10.1016\/j.jmbbm.2021.104611","journal-title":"J Mech Behav Biomed Mater"},{"issue":"7","key":"2061_CR32","doi-asserted-by":"publisher","first-page":"1467","DOI":"10.1016\/j.jbiomech.2006.06.013","volume":"40","author":"J Garc\u00eda-Aznar","year":"2007","unstructured":"Garc\u00eda-Aznar J, Kuiper J, G\u00f3mez-Benito M, Doblar\u00e9 M, Richardson J (2007) Computational simulation of fracture healing: Influence of interfragmentary movement on the callus growth. J Biomech 40(7):1467\u20131476. https:\/\/doi.org\/10.1016\/j.jbiomech.2006.06.013","journal-title":"J Biomech"},{"issue":"8","key":"2061_CR33","doi-asserted-by":"publisher","first-page":"1256","DOI":"10.1093\/bioinformatics\/btv730","volume":"32","author":"A Ghaffarizadeh","year":"2016","unstructured":"Ghaffarizadeh A, Friedman SH, Macklin P (2016) Biofvm: an efficient, parallelized diffusive transport solver for 3-d biological simulations. Bioinformatics 32(8):1256\u20131258. https:\/\/doi.org\/10.1093\/bioinformatics\/btv730","journal-title":"Bioinformatics"},{"issue":"2","key":"2061_CR34","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005991","volume":"14","author":"A Ghaffarizadeh","year":"2018","unstructured":"Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P (2018) Physicell: An open source physics-based cell simulator for 3-d multicellular systems. PLoS Comput Biol 14(2):e1005991. https:\/\/doi.org\/10.1371\/journal.pcbi.1005991","journal-title":"PLoS Comput Biol"},{"key":"2061_CR35","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.bonr.2017.03.002","volume":"6","author":"MS Ghiasi","year":"2017","unstructured":"Ghiasi MS, Chen J, Vaziri A, Rodriguez EK, Nazarian A (2017) Bone fracture healing in mechanobiological modeling: A review of principles and methods. Bone Rep 6:87\u2013100. https:\/\/doi.org\/10.1016\/j.bonr.2017.03.002","journal-title":"Bone Rep"},{"issue":"1","key":"2061_CR36","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1186\/s12891-019-2854-z","volume":"20","author":"MS Ghiasi","year":"2019","unstructured":"Ghiasi MS, Chen JE, Rodriguez EK, Vaziri A, Nazarian A (2019) Computational modeling of human bone fracture healing affected by different conditions of initial healing stage. BMC Musculoskelet Disord 20(1):562. https:\/\/doi.org\/10.1186\/s12891-019-2854-z","journal-title":"BMC Musculoskelet Disord"},{"issue":"11","key":"2061_CR37","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1007\/s10439-018-2083-x","volume":"46","author":"S Ghimire","year":"2018","unstructured":"Ghimire S, Mu Q, Guo S, Wang B, Fan Y (2018) Role of dynamic loading on early stage of bone fracture healing. Ann Biomed Eng 46(11):1768\u20131784. https:\/\/doi.org\/10.1007\/s10439-018-2083-x","journal-title":"Ann Biomed Eng"},{"issue":"1","key":"2061_CR38","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.jtbi.2004.12.023","volume":"235","author":"MJ G\u00f3mez-Benito","year":"2005","unstructured":"G\u00f3mez-Benito MJ et al (2005) Influence of fracture gap size on the pattern of long bone healing: a computational study. J Theor Biol 235(1):105\u2013119. https:\/\/doi.org\/10.1016\/j.jtbi.2004.12.023","journal-title":"J Theor Biol"},{"issue":"5","key":"2061_CR39","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1016\/j.enganabound.2008.09.008","volume":"33","author":"Y Gonz\u00e1lez","year":"2009","unstructured":"Gonz\u00e1lez Y, Cerrolaza M, Gonz\u00e1lez C (2009) Poroelastic analysis of bone tissue differentiation by using the boundary element method. Eng Anal Boundary Elem 33(5):731\u2013740. https:\/\/doi.org\/10.1016\/j.enganabound.2008.09.008","journal-title":"Eng Anal Boundary Elem"},{"issue":"9","key":"2061_CR40","doi-asserted-by":"publisher","first-page":"1782","DOI":"10.1016\/j.jbiomech.2011.04.021","volume":"44","author":"L Gonz\u00e1lez-Torres","year":"2011","unstructured":"Gonz\u00e1lez-Torres L, G\u00f3mez-Benito M, Garc\u00eda-Aznar J (2011) Evaluation of residual stresses due to bone callus growth: A computational study. J Biomech 44(9):1782\u20131787. https:\/\/doi.org\/10.1016\/j.jbiomech.2011.04.021","journal-title":"J Biomech"},{"key":"2061_CR41","doi-asserted-by":"publisher","first-page":"2676","DOI":"10.1109\/EMBC.2013.6610091","volume":"2013","author":"KN Grivas","year":"2013","unstructured":"Grivas KN et al (2013) A meshless local boundary integral equation (lbie) method for cell proliferation predictions in bone healing. Ann Int Conf IEEE Eng Med Biol Soc 2013:2676\u20132679. https:\/\/doi.org\/10.1109\/EMBC.2013.6610091","journal-title":"Ann Int Conf IEEE Eng Med Biol Soc"},{"issue":"2","key":"2061_CR42","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1121\/1.5089221","volume":"145","author":"KN Grivas","year":"2019","unstructured":"Grivas KN, Vavva MG, Polyzos D, Carlier A, Geris L, Van Oosterwyck H, Fotiadis DI (2019) Effect of ultrasound on bone fracture healing: A computational mechanobioregulatory model. J Acoustical Soc Am 145(2):1048. https:\/\/doi.org\/10.1121\/1.5089221","journal-title":"J Acoustical Soc Am"},{"issue":"6","key":"2061_CR43","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1016\/j.injury.2011.03.035","volume":"42","author":"KD Hankenson","year":"2011","unstructured":"Hankenson KD, Dishowitz M, Gray C, Schenker M (2011) Angiogenesis in bone regeneration. Injury 42(6):556\u2013561. https:\/\/doi.org\/10.1016\/j.injury.2011.03.035","journal-title":"Injury"},{"issue":"1","key":"2061_CR44","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1097\/00005131-200301000-00003","volume":"17","author":"LJ Harrison","year":"2003","unstructured":"Harrison LJ, Cunningham JL, Str\u00f6mberg L, Goodship AE (2003) Controlled induction of a pseudarthrosis: A study using a rodent model. J Orthop Trauma 17(1):17\u201329. https:\/\/doi.org\/10.1097\/00005131-200301000-00003","journal-title":"J Orthop Trauma"},{"key":"2061_CR45","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/s10237-022-01633-x","volume":"22","author":"S Irandoust","year":"2023","unstructured":"Irandoust S, M\u00fcft\u00fc S (2023) On computational predictions of fluid flow and its effects on bone healing in dental implant treatments: an investigation of spatiotemporal fluid flow in cyclic loading. Biomech Model Mechanobiol 22:85\u2013104. https:\/\/doi.org\/10.1007\/s10237-022-01633-x","journal-title":"Biomech Model Mechanobiol"},{"issue":"8","key":"2061_CR46","doi-asserted-by":"publisher","first-page":"1507","DOI":"10.1016\/j.jbiomech.2005.01.037","volume":"39","author":"H Isaksson","year":"2006","unstructured":"Isaksson H et al (2006) Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing. J Biomech 39(8):1507\u20131516. https:\/\/doi.org\/10.1016\/j.jbiomech.2005.01.037","journal-title":"J Biomech"},{"issue":"1","key":"2061_CR47","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.jtbi.2008.07.037","volume":"255","author":"H Isaksson","year":"2008","unstructured":"Isaksson H et al (2008) Determining the most important cellular characteristics for fracture healing using design of experiments methods. J Theor Biol 255(1):26\u201339. https:\/\/doi.org\/10.1016\/j.jtbi.2008.07.037","journal-title":"J Theor Biol"},{"issue":"2","key":"2061_CR48","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.jtbi.2008.01.030","volume":"252","author":"H Isaksson","year":"2008","unstructured":"Isaksson H, van Donkelaar CC, Huiskes R, Ito K (2008) A mechano-regulatory bone-healing model incorporating cell-phenotype specific activity. J Theor Biol 252(2):230\u2013246. https:\/\/doi.org\/10.1016\/j.jtbi.2008.01.030","journal-title":"J Theor Biol"},{"issue":"20","key":"2061_CR49","doi-asserted-by":"publisher","first-page":"1742","DOI":"10.2106\/JBJS.M.00780","volume":"96","author":"HS Khanuja","year":"2014","unstructured":"Khanuja HS, Banerjee S, Jain D, Pivec R, Mont MA (2014) \u201cShort bone-conserving stems in cementless hip arthroplasty,\u2019\u2019 The Journal of Bone and Joint Surgery. American 96(20):1742\u20131752. https:\/\/doi.org\/10.2106\/JBJS.M.00780","journal-title":"American"},{"key":"2061_CR50","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/j.engreg.2020.05.003","volume":"1","author":"T Kim","year":"2020","unstructured":"Kim T, See CW, Li X, Zhu D (2020) Orthopedic implants and devices for bone fractures and defects: Past, present and perspective. Eng Regener 1:6\u201318. https:\/\/doi.org\/10.1016\/j.engreg.2020.05.003","journal-title":"Eng Regener"},{"key":"2061_CR51","doi-asserted-by":"publisher","unstructured":"Kumar R, Sporn K, Ong J, Waisberg E, Paladugu P, Vaja S, Hage T, Sekhar TC, Vadhera AS, Ngo A, Zaman N, Tavakkoli A, Masalkhi M (2025) Integrating artificial intelligence in orthopedic care: Advancements in bone care and future directions. Bioengineering 12(5). https:\/\/doi.org\/10.3390\/bioengineering12050513","DOI":"10.3390\/bioengineering12050513"},{"key":"2061_CR52","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.medengphy.2017.01.025","volume":"42","author":"Z Lihai","year":"2017","unstructured":"Lihai Z et al (2017) Computational modelling of bone fracture healing under partial weight-bearing exercise. Med Eng Phys 42:65\u201372. https:\/\/doi.org\/10.1016\/j.medengphy.2017.01.025","journal-title":"Med Eng Phys"},{"issue":"12","key":"2061_CR53","doi-asserted-by":"publisher","first-page":"2112","DOI":"10.1002\/ar.23893","volume":"301","author":"A Lipphaus","year":"2018","unstructured":"Lipphaus A, Witzel U (2018) Finite-element syntheses of callus and bone remodeling: Biomechanical study of fracture healing in long bones. Anat Rec 301(12):2112\u20132121. https:\/\/doi.org\/10.1002\/ar.23893","journal-title":"Anat Rec"},{"issue":"7","key":"2061_CR54","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1302\/2046-3758.127.BJR-2023-0111.R1","volume":"12","author":"AB Lisacek-Kiosoglous","year":"2023","unstructured":"Lisacek-Kiosoglous AB, Powling AS, Fontalis A, Gabr A, Mazomenos E, Haddad FS (2023) Artificial intelligence in orthopaedic surgery. Bone Joint Res 12(7):447\u2013454. https:\/\/doi.org\/10.1302\/2046-3758.127.BJR-2023-0111.R1","journal-title":"Bone Joint Res"},{"key":"2061_CR55","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2023.107464","volume":"233","author":"X Liu","year":"2023","unstructured":"Liu X et al (2023) Development of numerical model-based machine learning algorithms for different healing stages of distal radius fracture healing. Comput Methods Programs Biomed 233:107464. https:\/\/doi.org\/10.1016\/j.cmpb.2023.107464","journal-title":"Comput Methods Programs Biomed"},{"issue":"9","key":"2061_CR56","doi-asserted-by":"publisher","first-page":"2533","DOI":"10.1007\/s10439-021-02815-x","volume":"49","author":"X Liu","year":"2021","unstructured":"Liu X, Miramini S, Patel M, Liao J, Shidid D, Zhang L (2021) Balance between mechanical stability and mechano-biology of fracture healing under volar locking plate. Ann Biomed Eng 49(9):2533\u20132553. https:\/\/doi.org\/10.1007\/s10439-021-02815-x","journal-title":"Ann Biomed Eng"},{"key":"2061_CR57","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2022.106626","volume":"215","author":"X Liu","year":"2022","unstructured":"Liu X, Miramini S, Patel M, Liao J, Shidid D, Zhang L (2022) Influence of therapeutic grip exercises induced loading rates in distal radius fracture healing with volar locking plate fixation. Comput Methods Programs Biomed 215:106626. https:\/\/doi.org\/10.1016\/j.cmpb.2022.106626","journal-title":"Comput Methods Programs Biomed"},{"issue":"1","key":"2061_CR58","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.bone.2012.09.037","volume":"52","author":"C Lu","year":"2013","unstructured":"Lu C, Saless N, Wang X, Sinha A, Decker S, Kazakia G, Hou H, Williams B, Swartz HM, Hunt TK, Miclau T, Marcucio RS (2013) The role of oxygen during fracture healing. Bone 52(1):220\u2013229. https:\/\/doi.org\/10.1016\/j.bone.2012.09.037","journal-title":"Bone"},{"key":"2061_CR59","doi-asserted-by":"publisher","first-page":"5037578","DOI":"10.1155\/2019\/5037578","volume":"2019","author":"W Lu","year":"2019","unstructured":"Lu W, Gao B, Fan J, Cheng P, Hu Y, Jie Q, Luo Z, Yang L (2019) Mesenchymal progenitors derived from different locations in long bones display diverse characteristics. Stem Cells Int 2019:5037578. https:\/\/doi.org\/10.1155\/2019\/5037578","journal-title":"Stem Cells Int"},{"key":"2061_CR60","doi-asserted-by":"publisher","first-page":"5786089","DOI":"10.1155\/2018\/5786089","volume":"2018","author":"P Luo","year":"2018","unstructured":"Luo P, Lou J, Yang S (2018) Pain management during rehabilitation after distal radius fracture stabilized with volar locking plate: A prospective cohort study. Biomed Res Int 2018:5786089. https:\/\/doi.org\/10.1155\/2018\/5786089","journal-title":"Biomed Res Int"},{"key":"2061_CR61","doi-asserted-by":"publisher","first-page":"204173142311725","DOI":"10.1177\/20417314231172573","volume":"14","author":"Q Ma","year":"2023","unstructured":"Ma Q, Miri Z, Haugen HJ, Moghanian A, Loca D (2023) Significance of mechanical loading in bone fracture healing, bone regeneration, and vascularization. J Tissue Eng 14:20417314231172572. https:\/\/doi.org\/10.1177\/20417314231172573","journal-title":"J Tissue Eng"},{"issue":"6","key":"2061_CR62","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1002\/jor.22302","volume":"31","author":"E Miedel","year":"2013","unstructured":"Miedel E, Dishowitz MI, Myers MH, Dopkin D, Yu Y-Y, Miclau TS, Marcucio R, Ahn J, Hankenson KD (2013) Disruption of thrombospondin-2 accelerates ischemic fracture healing. J Orthop Res 31(6):935\u2013943. https:\/\/doi.org\/10.1002\/jor.22302","journal-title":"J Orthop Res"},{"key":"2061_CR63","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2019.105011","volume":"180","author":"S Miramini","year":"2019","unstructured":"Miramini S et al (2019) A probabilistic-based approach for computational simulation of bone fracture healing. Comput Methods Programs Biomed 180:105011. https:\/\/doi.org\/10.1016\/j.cmpb.2019.105011","journal-title":"Comput Methods Programs Biomed"},{"issue":"8","key":"2061_CR64","doi-asserted-by":"publisher","first-page":"900","DOI":"10.1080\/10255842.2013.855729","volume":"18","author":"S Miramini","year":"2015","unstructured":"Miramini S, Zhang L, Richardson M, Pirpiris M, Mendis P, Oloyede A, Edwards G (2015) Computational simulation of the early stage of bone healing under different configurations of locking compression plates. Comput Methods Biomech Biomed Engin 18(8):900\u2013913. https:\/\/doi.org\/10.1080\/10255842.2013.855729","journal-title":"Comput Methods Biomech Biomed Engin"},{"issue":"10","key":"2061_CR65","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1016\/j.medengphy.2016.07.007","volume":"38","author":"S Miramini","year":"2016","unstructured":"Miramini S, Zhang L, Richardson M, Mendis P, Ebeling PR (2016) Influence of fracture geometry on bone healing under locking plate fixations: A comparison between oblique and transverse tibial fractures. Med Eng Phys 38(10):1100\u20131108. https:\/\/doi.org\/10.1016\/j.medengphy.2016.07.007","journal-title":"Med Eng Phys"},{"issue":"04","key":"2061_CR66","doi-asserted-by":"publisher","first-page":"1850024","DOI":"10.1142\/S021987621850024X","volume":"15","author":"S Miramini","year":"2018","unstructured":"Miramini S, Zhang L, Richardson M, Mendis P (2018) The role of locking plate stiffness in bone fracture healing stabilized by far cortical locking technique. Int J Comput Methods 15(04):1850024. https:\/\/doi.org\/10.1142\/S021987621850024X","journal-title":"Int J Comput Methods"},{"key":"2061_CR67","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2022.105621","volume":"138","author":"S Miramini","year":"2023","unstructured":"Miramini S, Ganadhiepan G, Lin Y-C, Patel M, Richardson M, Pandy M, Zhang L (2023) Influence of muscle loading on early-stage bone fracture healing. J Mech Behav Biomed Mater 138:105621. https:\/\/doi.org\/10.1016\/j.jmbbm.2022.105621","journal-title":"J Mech Behav Biomed Mater"},{"issue":"8","key":"2061_CR68","doi-asserted-by":"publisher","first-page":"1508","DOI":"10.1002\/jor.26109","volume":"43","author":"A Misir","year":"2025","unstructured":"Misir A, Yuce A (2025) Ai in orthopedic research: A comprehensive review. J Orthop Res 43(8):1508\u20131527. https:\/\/doi.org\/10.1002\/jor.26109","journal-title":"J Orthop Res"},{"issue":"6","key":"2061_CR69","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1003604","volume":"10","author":"SR Moore","year":"2014","unstructured":"Moore SR et al (2014) Mechanistic, mathematical model to predict the dynamics of tissue genesis in bone defects via mechanical feedback and mediation of biochemical factors. PLoS Comput Biol 10(6):e1003604. https:\/\/doi.org\/10.1371\/journal.pcbi.1003604","journal-title":"PLoS Comput Biol"},{"key":"2061_CR70","doi-asserted-by":"publisher","first-page":"2024","DOI":"10.3389\/fbioe.2024.1477405","volume":"12","author":"GT Morgan","year":"2024","unstructured":"Morgan GT, Low L, Ramasamy A, Masouros SD (2024) A novel strain-based bone-fracture healing algorithm is able to predict a range of healing outcomes. Front Bioeng Biotechnol 12:2024. https:\/\/doi.org\/10.3389\/fbioe.2024.1477405","journal-title":"Front Bioeng Biotechnol"},{"issue":"2","key":"2061_CR71","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF00389747","volume":"99","author":"KH M\u00fcller","year":"1981","unstructured":"M\u00fcller KH, Witzel U (1981) Die fixateur-externe-osteosynthese ohne kn\u00f6cherne abst\u00fctzung (externe distanzosteosynthese) an der unteren gliedmasse. biomechanische, operationstechnische und osteoplastische grundlagen. Arch Orthop Trauma Surg 99(2):117\u2013130","journal-title":"Arch Orthop Trauma Surg"},{"key":"2061_CR72","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2021.106262","volume":"208","author":"JM Naveiro","year":"2021","unstructured":"Naveiro JM et al (2021) A new approach for initial callus growth during fracture healing in long bones. Comput Methods Programs Biomed 208:106262. https:\/\/doi.org\/10.1016\/j.cmpb.2021.106262","journal-title":"Comput Methods Programs Biomed"},{"issue":"5","key":"2061_CR73","doi-asserted-by":"publisher","first-page":"1279","DOI":"10.1007\/s10237-016-0759-4","volume":"15","author":"A O\u2019Reilly","year":"2016","unstructured":"O\u2019Reilly A et al (2016) A computational model to explore the role of angiogenic impairment on endochondral ossification during fracture healing. Biomech Model Mechanobiol 15(5):1279\u20131294. https:\/\/doi.org\/10.1007\/s10237-016-0759-4","journal-title":"Biomech Model Mechanobiol"},{"issue":"9","key":"2061_CR74","doi-asserted-by":"publisher","first-page":"1385","DOI":"10.1016\/j.jhsa.2007.07.005","volume":"32","author":"T Oshige","year":"2007","unstructured":"Oshige T, Sakai A, Zenke Y, Moritani S, Nakamura T (2007) A comparative study of clinical and radiological outcomes of dorsally angulated, unstable distal radius fractures in elderly patients: Intrafocal pinning versus volar locking plating. J Hand Surg 32(9):1385\u20131392. https:\/\/doi.org\/10.1016\/j.jhsa.2007.07.005","journal-title":"J Hand Surg"},{"key":"2061_CR75","doi-asserted-by":"publisher","DOI":"10.3389\/fcell.2022.856204","volume":"10","author":"GR Paul","year":"2022","unstructured":"Paul GR et al (2022) Tissue-level regeneration and remodeling dynamics are driven by mechanical stimuli in the microenvironment in a post-bridging loaded femur defect healing model in mice. Front Cell Develop Biol 10:856204. https:\/\/doi.org\/10.3389\/fcell.2022.856204","journal-title":"Front Cell Develop Biol"},{"issue":"3","key":"2061_CR76","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s10237-010-0241-7","volume":"10","author":"V Peiffer","year":"2011","unstructured":"Peiffer V et al (2011) A hybrid bioregulatory model of angiogenesis during bone fracture healing. Biomech Model Mechanobiol 10(3):383\u2013395. https:\/\/doi.org\/10.1007\/s10237-010-0241-7","journal-title":"Biomech Model Mechanobiol"},{"key":"2061_CR77","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2022.835094","volume":"10","author":"C Perier-Metz","year":"2022","unstructured":"Perier-Metz C, Cort\u00e9 L, Allena R, Checa S (2022) A 3d in silico multi-tissue evolution model highlights the relevance of local strain accumulation in bone fracture remodeling. Front Bioeng Biotechnol 10:835094. https:\/\/doi.org\/10.3389\/fbioe.2022.835094","journal-title":"Front Bioeng Biotechnol"},{"issue":"8","key":"2061_CR78","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1080\/10255842.2018.1487554","volume":"21","author":"M Pietsch","year":"2018","unstructured":"Pietsch M, Niemeyer F, Simon U, Ignatius A, Urban K (2018) Modelling the fracture-healing process as a moving-interface problem using an interface-capturing approach. Comput Methods Biomech Biomed Eng 21(8):512\u2013520. https:\/\/doi.org\/10.1080\/10255842.2018.1487554","journal-title":"Comput Methods Biomech Biomed Eng"},{"key":"2061_CR79","doi-asserted-by":"publisher","first-page":"2120240279","DOI":"10.1098\/rsif.2024.0279","volume":"21","author":"DG Pires","year":"2024","unstructured":"Pires DG, Silva NM, de Sousa BM, Marques JL, Ramos A, Ferreira JAF, Morais R, Vieira SI, Soares dos Santos MP (2024) A millimetre-scale capacitive biosensing and biophysical stimulation system for emerging bioelectronic bone implants. J R Soc Interface 21:2120240279. https:\/\/doi.org\/10.1098\/rsif.2024.0279","journal-title":"J R Soc Interface"},{"key":"2061_CR80","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1186\/s13018-025-05534-4","volume":"20","author":"DG Pires","year":"2025","unstructured":"Pires DG, Silva NM, Completo A et al (2025) Bioelectronic osteosynthesis plate to monitor the fracture bone healing using electric capacitive variations. J Orthop Surg Res 20:105. https:\/\/doi.org\/10.1186\/s13018-025-05534-4","journal-title":"J Orthop Surg Res"},{"issue":"6","key":"2061_CR81","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/S0021-9290(96)00140-6","volume":"30","author":"P Prendergast","year":"1997","unstructured":"Prendergast P, Huiskes R, S\u00f8balle K (1997) Biophysical stimuli on cells during tissue differentiation at implant interfaces. J Biomech 30(6):539\u2013548. https:\/\/doi.org\/10.1016\/S0021-9290(96)00140-6","journal-title":"J Biomech"},{"issue":"6","key":"2061_CR82","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1109\/TUFFC.2008.787","volume":"55","author":"VC Protopappas","year":"2008","unstructured":"Protopappas VC et al (2008) Ultrasonic monitoring of bone fracture healing. IEEE Trans Ultrason Ferroelectr Freq Control 55(6):1243\u20131255. https:\/\/doi.org\/10.1109\/TUFFC.2008.787","journal-title":"IEEE Trans Ultrason Ferroelectr Freq Control"},{"issue":"7","key":"2061_CR83","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.3609","volume":"38","author":"C Quinn","year":"2022","unstructured":"Quinn C, Kopp A, Vaughan TJ (2022) A coupled computational framework for bone fracture healing and long-term remodelling: Investigating the role of internal fixation on bone fractures. Int J Numer Methods Biomed Eng 38(7):e3609. https:\/\/doi.org\/10.1002\/cnm.3609","journal-title":"Int J Numer Methods Biomed Eng"},{"key":"2061_CR84","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2024.109444","volume":"184","author":"C Quinn","year":"2025","unstructured":"Quinn C, Van Gaalen K, McHugh PE, Kopp A, Vaughan TJ (2025) A multi-domain computational framework investigating the short- and long-term viability of bioabsorbable magnesium fixation for tibial fractures. Comput Biol Med 184:109444. https:\/\/doi.org\/10.1016\/j.compbiomed.2024.109444","journal-title":"Comput Biol Med"},{"issue":"1","key":"2061_CR85","doi-asserted-by":"publisher","first-page":"29826","DOI":"10.1038\/s41598-024-80502-2","volume":"14","author":"AH Razavi","year":"2024","unstructured":"Razavi AH, Nafisi N, Ghiasi MS, Oftadeh R, Hanna P, Lechtig A, Momenzadeh K, Yeritsyan D, Minassians P, Mahjoob A, Perez S, Nazarian RM, Wixted JJ, Vaziri A, Nazarian A (2024) A computational model that integrates unrestricted callus growth, mechanobiology, and angiogenesis can predict bone healing in rodents. Sci Rep 14(1):29826. https:\/\/doi.org\/10.1038\/s41598-024-80502-2","journal-title":"Sci Rep"},{"key":"2061_CR86","doi-asserted-by":"publisher","DOI":"10.1016\/j.compbiomed.2025.110683","volume":"196","author":"AH Razavi","year":"2025","unstructured":"Razavi AH, Hemmati M, Nafisi N, Mirahmadi A, Laiwala S, Keko M, Vaziri A, Rodriguez EK, Nazarian A (2025) Mechanobiology-guided machine learning models for predicting long bone fracture healing across diverse scenarios. Comput Biol Med 196:110683. https:\/\/doi.org\/10.1016\/j.compbiomed.2025.110683","journal-title":"Comput Biol Med"},{"key":"2061_CR87","doi-asserted-by":"publisher","first-page":"2307","DOI":"10.1007\/s10237-020-01340-5","volume":"19","author":"T Ren","year":"2020","unstructured":"Ren T, Dailey HL (2020) Mechanoregulation modeling of bone healing in realistic fracture geometries. Biomech Model Mechanobiol 19:2307\u20132322. https:\/\/doi.org\/10.1007\/s10237-020-01340-5","journal-title":"Biomech Model Mechanobiol"},{"issue":"9","key":"2061_CR88","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1007\/s11517-015-1285-8","volume":"53","author":"F Repp","year":"2015","unstructured":"Repp F et al (2015) The connection between cellular mechanoregulation and tissue patterns during bone healing. Med Biol Eng Comput 53(9):829\u2013842. https:\/\/doi.org\/10.1007\/s11517-015-1285-8","journal-title":"Med Biol Eng Comput"},{"issue":"3","key":"2061_CR89","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1002\/nme.4338","volume":"92","author":"A Sapotnick","year":"2012","unstructured":"Sapotnick A, Nackenhorst U (2012) A combined fic-tdg finite element approach for the numerical solution of coupled advection\u2013diffusion\u2013reaction equations with application to a bioregulatory model for bone fracture healing. Int J Numer Meth Eng 92(3):301\u2013317. https:\/\/doi.org\/10.1002\/nme.4338","journal-title":"Int J Numer Meth Eng"},{"key":"2061_CR90","unstructured":"Sheen JR, Mabrouk A, Garla VV (2023) Fracture Healing Overview. Treasure Island (FL): StatPearls Publishing. https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK551678\/"},{"key":"2061_CR91","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1016\/j.compositesb.2013.10.058","volume":"58","author":"D-S Son","year":"2014","unstructured":"Son D-S, Mehboob H, Chang S-H (2014) Simulation of the bone healing process of fractured long bones applied with a composite bone plate with consideration of the blood vessel growth. Compos B Eng 58:443\u2013450. https:\/\/doi.org\/10.1016\/j.compositesb.2013.10.058","journal-title":"Compos B Eng"},{"key":"2061_CR92","doi-asserted-by":"publisher","unstructured":"Song J, Wang G, Wang S et\u00a0al (2025) Artificial intelligence in orthopedics: fundamentals, current applications, and future perspectives, Military Med Res, 12(42). https:\/\/doi.org\/10.1186\/s40779-025-00633-z","DOI":"10.1186\/s40779-025-00633-z"},{"key":"2061_CR93","doi-asserted-by":"publisher","first-page":"20130389","DOI":"10.1098\/rsif.2013.0389","volume":"10","author":"M Steiner","year":"2013","unstructured":"Steiner M, Claes L, Ignatius A, Niemeyer F, Simon U, Wehner T (2013) Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli. J R Soc Interface 10:20130389. https:\/\/doi.org\/10.1098\/rsif.2013.0389","journal-title":"J R Soc Interface"},{"key":"2061_CR94","doi-asserted-by":"publisher","DOI":"10.1016\/j.bonr.2023.101686","volume":"19","author":"L Steppe","year":"2023","unstructured":"Steppe L, Megafu M, Tschaffon-M\u00fcller ME, Ignatius A, Haffner-Luntzer M (2023) Fracture healing research: Recent insights. Bone Rep 19:101686. https:\/\/doi.org\/10.1016\/j.bonr.2023.101686","journal-title":"Bone Rep"},{"key":"2061_CR95","doi-asserted-by":"publisher","unstructured":"Sumita M, Hanawa T, Ohnishi I, Yoneyama T (2003) \u201c9.04 - failure processes in biometallic materials,\u201d In: Comprehensive structural integrity, I.\u00a0Milne, R.\u00a0Ritchie, and B.\u00a0Karihaloo, Eds. Oxford: Pergamon. 131\u2013167. https:\/\/doi.org\/10.1016\/B0-08-043749-4\/09143-6","DOI":"10.1016\/B0-08-043749-4\/09143-6"},{"key":"2061_CR96","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2019.115212","volume":"132","author":"T Suzuki","year":"2020","unstructured":"Suzuki T et al (2020) Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis. Bone 132:115212. https:\/\/doi.org\/10.1016\/j.bone.2019.115212","journal-title":"Bone"},{"issue":"2","key":"2061_CR97","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1142\/S2424835516500193","volume":"21","author":"N Takeuchi","year":"2016","unstructured":"Takeuchi N, Hotokezaka S, Okada T, Yuge H, Mae T, Iwamoto Y (2016) Recovery of wrist function after volar locking plate fixation for distal radius fractures. J Hand Surg Asian-Pacific 21(2):199\u2013206. https:\/\/doi.org\/10.1142\/S2424835516500193","journal-title":"J Hand Surg Asian-Pacific"},{"issue":"1","key":"2061_CR98","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1186\/s44147-023-00187-8","volume":"70","author":"M Tannino","year":"2023","unstructured":"Tannino M, Mangini F, Dinia L, Frezza F (2023) A heuristic model to evaluate the dielectric properties of human tissues at microwave band based on water and solid content. J Eng Appl Sci 70(1):43. https:\/\/doi.org\/10.1186\/s44147-023-00187-8","journal-title":"J Eng Appl Sci"},{"issue":"9","key":"2061_CR99","doi-asserted-by":"publisher","first-page":"1678","DOI":"10.1016\/j.jhsa.2013.06.006","volume":"38","author":"R Tosti","year":"2013","unstructured":"Tosti R, Ilyas AM (2013) Prospective evaluation of pronator quadratus repair following volar plate fixation of distal radius fractures. J Hand Surg 38(9):1678\u20131684. https:\/\/doi.org\/10.1016\/j.jhsa.2013.06.006","journal-title":"J Hand Surg"},{"issue":"1","key":"2061_CR100","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00590-020-02749-5","volume":"31","author":"F Travascio","year":"2021","unstructured":"Travascio F, Buller LT, Milne E, Latta L (2021) Mechanical performance and implications on bone healing of different screw configurations for plate fixation of diaphyseal tibia fractures: a computational study. Eur J Orthopaedic Surg Traumatol 31(1):121\u2013130. https:\/\/doi.org\/10.1007\/s00590-020-02749-5","journal-title":"Eur J Orthopaedic Surg Traumatol"},{"key":"2061_CR101","doi-asserted-by":"publisher","unstructured":"Vavva MG, Protopappas VC, Gergidis LN, Charalambopoulos A, Fotiadis DI, Polyzos D (2008) The effect of boundary conditions on guided wave propagation in two-dimensional models of healing bone, Ultrasonics, 48(6), 598\u2013606, selected Papers from ICU 2007. https:\/\/doi.org\/10.1016\/j.ultras.2008.04.013","DOI":"10.1016\/j.ultras.2008.04.013"},{"key":"2061_CR102","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.compbiomed.2018.06.024","volume":"100","author":"MG Vavva","year":"2018","unstructured":"Vavva MG et al (2018) Effect of ultrasound on bone fracture healing: A computational bioregulatory model. Comput Biol Med 100:74\u201385. https:\/\/doi.org\/10.1016\/j.compbiomed.2018.06.024","journal-title":"Comput Biol Med"},{"issue":"1\u20132","key":"2061_CR103","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s10237-011-0299-x","volume":"11","author":"A Vetter","year":"2012","unstructured":"Vetter A et al (2012) The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules. Biomech Model Mechanobiol 11(1\u20132):147\u2013160. https:\/\/doi.org\/10.1007\/s10237-011-0299-x","journal-title":"Biomech Model Mechanobiol"},{"issue":"11","key":"2061_CR104","doi-asserted-by":"publisher","first-page":"1440","DOI":"10.1002\/jor.21175","volume":"28","author":"A Vetter","year":"2010","unstructured":"Vetter A, Epari DR, Seidel R, Schell H, Fratzl P, Duda GN, Weinkamer R (2010) Temporal tissue patterns in bone healing of sheep. J Orthop Res 28(11):1440\u20131447. https:\/\/doi.org\/10.1002\/jor.21175","journal-title":"J Orthop Res"},{"key":"2061_CR105","doi-asserted-by":"publisher","unstructured":"Wang M, Yang N (2019) Computational simulation of the influence of mechanical stability on growth factors activities during bone fracture healing. IEEE Access 7:9827\u20139835. https:\/\/doi.org\/10.1109\/ACCESS.2019.2892125","DOI":"10.1109\/ACCESS.2019.2892125"},{"issue":"5","key":"2061_CR106","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1007\/s00776-013-0415-0","volume":"18","author":"Y Watanabe","year":"2013","unstructured":"Watanabe Y, Arai Y, Takenaka N, Kobayashi M, Matsushita T (2013) Three key factors affecting treatment results of low-intensity pulsed ultrasound for delayed unions and nonunions: instability, gap size, and atrophic nonunion. J Orthop Sci 18(5):803\u2013810. https:\/\/doi.org\/10.1007\/s00776-013-0415-0","journal-title":"J Orthop Sci"},{"issue":"13","key":"2061_CR107","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1016\/j.jbiomech.2010.05.028","volume":"43","author":"T Wehner","year":"2010","unstructured":"Wehner T, Wolfram U, Henzler T, Niemeyer F, Claes L, Simon U (2010) Internal forces and moments in the femur of the rat during gait. J Biomech 43(13):2473\u20132479. https:\/\/doi.org\/10.1016\/j.jbiomech.2010.05.028","journal-title":"J Biomech"},{"issue":"12","key":"2061_CR108","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0115695","volume":"9","author":"T Wehner","year":"2014","unstructured":"Wehner T, Steiner M, Ignatius A, Claes L (2014) Prediction of the time course of callus stiffness as a function of mechanical parameters in experimental rat fracture healing studies - a numerical study. PLoS ONE 9(12):1\u201316. https:\/\/doi.org\/10.1371\/journal.pone.0115695","journal-title":"PLoS ONE"},{"issue":"1","key":"2061_CR109","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1038\/s41572-021-00289-8","volume":"7","author":"B Wildemann","year":"2021","unstructured":"Wildemann B, Ignatius A, Leung F, Taitsman LA, Smith RM, Pes\u00e1ntez R, Stoddart MJ, Richards RG, Jupiter JB (2021) Non-union bone fractures. Nat Rev Dis Primers 7(1):57. https:\/\/doi.org\/10.1038\/s41572-021-00289-8","journal-title":"Nat Rev Dis Primers"},{"issue":"9","key":"2061_CR110","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1016\/S2666-7568(21)00172-0","volume":"2","author":"A-M Wu","year":"2021","unstructured":"Wu A-M et al (2021) Global, regional, and national burden of bone fractures in 204 countries and territories, 1990\u20132019: a systematic analysis from the global burden of disease study 2019. The Lancet Healthy Longevity 2(9):580\u2013592. https:\/\/doi.org\/10.1016\/S2666-7568(21)00172-0","journal-title":"The Lancet Healthy Longevity"},{"issue":"7","key":"2061_CR111","doi-asserted-by":"publisher","first-page":"2105","DOI":"10.1109\/TBME.2024.3361893","volume":"71","author":"Y Yang","year":"2024","unstructured":"Yang Y et al (2024) Computational modeling of bone fracture healing under different initial conditions and mechanical load. IEEE Trans Biomed Eng 71(7):2105\u20132118. https:\/\/doi.org\/10.1109\/TBME.2024.3361893","journal-title":"IEEE Trans Biomed Eng"}],"container-title":["Biomechanics and Modeling in Mechanobiology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-026-02061-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10237-026-02061-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-026-02061-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T10:29:55Z","timestamp":1778754595000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10237-026-02061-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":111,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["2061"],"URL":"https:\/\/doi.org\/10.1007\/s10237-026-02061-x","relation":{},"ISSN":["1617-7959","1617-7940"],"issn-type":[{"value":"1617-7959","type":"print"},{"value":"1617-7940","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"17 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2026","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 no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"38"}}