{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T19:06:35Z","timestamp":1784142395579,"version":"3.55.0"},"reference-count":105,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["445465815"],"award-info":[{"award-number":["445465815"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006254","name":"Ruhr-Universit\u00e4t Bochum","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006254","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BioMed Eng OnLine"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In silico models for simulating bone growth based on mechanical or non-mechanical epigenetic factors are widely used. In this study, a well-known mechanobiological model, which states that octahedral shear stress accelerates longitudinal bone growth and hydrostatic stress retards it, is applied to a finite element model of the femur of an 8-year-old boy. Proximal and distal epiphyseal plates as well as the growth plate of the greater trochanter, cartilaginous growth at the femoral isthmus, and appositional bone growth are included in the model. Furthermore, changes in the density of the cancellous bone in the metaphyses are modeled based on Wolff's law using compressive stresses as the mechanical stimulus. Muscle forces during a dynamic gait cycle were determined for nine discrete loading cases by optimizing to minimize bending stress. The highest stresses in the femoral shaft were determined as medial compressive stresses with a maximum of \u221233.2\u00a0MPa. Highest internal axial load in the shaft was 985 N during loading response. The simulated bone growth resulted in an increase in femur length of 23.7\u00a0mm and a decrease in femoral neck angle by \u22121.4\u00b0, anteversion angle by \u22122.4\u00b0, and lateral distal femur angle by \u22121.6\u00b0 per year. Growth of the apophysis of the greater trochanter resulted in an unchanged articulo-trochanteric distance. The bone remodeling led to an increase in bone density, particularly in the medial proximal metaphysis. The consideration of different growth mechanisms allowed a comprehensive simulation of femoral growth with high agreement with anthropometric data. Possible applications are the simulation of the correction of deformities.<\/jats:p>","DOI":"10.1186\/s12938-026-01598-3","type":"journal-article","created":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T17:46:26Z","timestamp":1784137586000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational mechanobiological model combining epiphyseal, apophyseal, and appositional growth and inner bone remodeling of the juvenile femur"],"prefix":"10.1186","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4428-4848","authenticated-orcid":false,"given":"Andreas","family":"Lipphaus","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ralf-Bodo","family":"Tr\u00f6bs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthias","family":"Klimek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sascha","family":"Selkmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ulrich","family":"Witzel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"key":"1598_CR1","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1159\/000327788","volume":"75","author":"J Emons","year":"2011","unstructured":"Emons J, Chagin AS, S\u00e4vendahl L, Karperien M, Wit JM. Mechanisms of growth plate maturation and epiphyseal fusion. Horm Res Paediatr. 2011;75:383\u201391.","journal-title":"Horm Res Paediatr"},{"key":"1598_CR2","doi-asserted-by":"publisher","first-page":"1851","DOI":"10.1210\/endo.143.5.8776","volume":"143","author":"V Abad","year":"2002","unstructured":"Abad V, Meyers JL, Weise M, Gafni RI, Barnes KM, Nilsson O, et al. The role of the resting zone in growth plate chondrogenesis. Endocrinology. 2002;143:1851\u20137.","journal-title":"Endocrinology"},{"key":"1598_CR3","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1677\/joe.1.06016","volume":"186","author":"O Nilsson","year":"2005","unstructured":"Nilsson O, Mitchum RD, Schrier L, Ferns SP, Barnes KM, Troendle JF, et al. Growth plate senescence is associated with loss of DNA methylation. J Endocrinol. 2005;186:241\u20139.","journal-title":"J Endocrinol"},{"key":"1598_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.matbio.2015.10.001","volume":"50","author":"C Prein","year":"2016","unstructured":"Prein C, Warmbold N, Farkas Z, Schieker M, Aszodi A, Clausen-Schaumann H. Structural and mechanical properties of the proliferative zone of the developing murine growth plate cartilage assessed by atomic force microscopy. Matrix Biol. 2016;50:1\u201315.","journal-title":"Matrix Biol"},{"key":"1598_CR5","doi-asserted-by":"publisher","first-page":"243","DOI":"10.2106\/00004623-198668020-00010","volume":"68","author":"JA Buckwalter","year":"1986","unstructured":"Buckwalter JA, Mower D, Ungar R, Schaeffer J, Ginsberg B. Morphometric analysis of chondrocyte hypertrophy. J Bone Joint Surg Am. 1986;68:243\u201355.","journal-title":"J Bone Joint Surg Am"},{"key":"1598_CR6","doi-asserted-by":"publisher","DOI":"10.1038\/s41413-018-0021-z","volume":"6","author":"P Aghajanian","year":"2018","unstructured":"Aghajanian P, Mohan S. The art of building bone: emerging role of chondrocyte-to-osteoblast transdifferentiation in endochondral ossification. Bone Res. 2018;6:19.","journal-title":"Bone Res"},{"key":"1598_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.celrep.2021.109380","volume":"36","author":"H Watanabe-Takano","year":"2021","unstructured":"Watanabe-Takano H, Ochi H, Chiba A, Matsuo A, Kanai Y, Fukuhara S, et al. Mechanical load regulates bone growth via periosteal Osteocrin. Cell Rep. 2021;36:109380.","journal-title":"Cell Rep"},{"key":"1598_CR8","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1615\/CritRevEukarGeneExpr.v19.i4.50","volume":"19","author":"AG Robling","year":"2009","unstructured":"Robling AG, Turner CH. Mechanical signaling for bone modeling and remodeling. Crit Rev Eukaryot Gene Expr. 2009;19:319\u201338.","journal-title":"Crit Rev Eukaryot Gene Expr"},{"key":"1598_CR9","first-page":"194","volume":"5","author":"F Rauch","year":"2005","unstructured":"Rauch F. Bone growth in length and width: the Yin and Yang of bone stability. J Musculoskelet Neuronal Interact. 2005;5:194\u2013201.","journal-title":"J Musculoskelet Neuronal Interact"},{"key":"1598_CR10","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1203\/01.pdr.0000214966.60416.1b","volume":"59","author":"F De Luca","year":"2006","unstructured":"De Luca F. Impaired growth plate chondrogenesis in children with chronic illnesses. Pediatr Res. 2006;59:625\u20139.","journal-title":"Pediatr Res"},{"key":"1598_CR11","doi-asserted-by":"publisher","DOI":"10.3389\/fendo.2021.720419","volume":"12","author":"MB Ranke","year":"2021","unstructured":"Ranke MB. Short and long-term effects of growth hormone in children and adolescents with GH deficiency. Front Endocrinol. 2021;12:720419.","journal-title":"Front Endocrinol"},{"key":"1598_CR12","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1111\/j.1365-2265.2007.02960.x","volume":"68","author":"RJ Perry","year":"2008","unstructured":"Perry RJ, Farquharson C, Ahmed SF. The role of sex steroids in controlling pubertal growth. Clin Endocrinol (Oxf). 2008;68:4\u201315.","journal-title":"Clin Endocrinol (Oxf)"},{"key":"1598_CR13","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1038\/nrendo.2017.178","volume":"14","author":"O Nilsson","year":"2018","unstructured":"Nilsson O. Genetic and epigenetic regulation of childhood growth. Nat Rev Endocrinol. 2018;14:70\u20132.","journal-title":"Nat Rev Endocrinol"},{"key":"1598_CR14","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1007\/BF01878009","volume":"26","author":"C Hueter","year":"1863","unstructured":"Hueter C. Anatomische Studien an den Extremit\u00e4tengelenken Neugeborener und Erwachsener. Arch Pathol Anat Physiol Klin Med. 1863;26:484\u2013519.","journal-title":"Arch Pathol Anat Physiol Klin Med"},{"key":"1598_CR15","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1016\/j.bone.2004.06.006","volume":"35","author":"A Niehoff","year":"2004","unstructured":"Niehoff A, Kersting UG, Zaucke F, Morlock MM, Br\u00fcggemann GP. Adaptation of mechanical, morphological, and biochemical properties of the rat growth plate to dose-dependent voluntary exercise. Bone. 2004;35:899\u2013908.","journal-title":"Bone"},{"key":"1598_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1002\/jmor.1052060105","volume":"206","author":"BK Hall","year":"1990","unstructured":"Hall BK, Herring SW. Paralysis and growth of the musculoskeletal system in the embryonic chick. J Morphol. 1990;206:45\u201356.","journal-title":"J Morphol"},{"key":"1598_CR17","doi-asserted-by":"publisher","first-page":"1327","DOI":"10.1002\/jor.20189","volume":"24","author":"IA Stokes","year":"2006","unstructured":"Stokes IA, Aronsson DD, Dimock AN, Cortright V, Beck S. Endochondral growth in growth plates of three species at two anatomical locations modulated by mechanical compression and tension. J Orthop Res. 2006;24:1327\u201334.","journal-title":"J Orthop Res"},{"key":"1598_CR18","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1097\/00007632-199605150-00007","volume":"21","author":"IAF Stokes","year":"1996","unstructured":"Stokes IAF, Spence H, Aronsson DD, Kilmer N. Mechanical modulation of vertebral body growth: implications for scoliosis progression. Spine. 1996;21:1162\u20137.","journal-title":"Spine"},{"key":"1598_CR19","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0047-6374(92)90073-M","volume":"66","author":"A Snyder","year":"1992","unstructured":"Snyder A, Zierath JR, Hawley JA, Sleeper MD, Craig BW. The effects of exercise mode, swimming vs. running, upon bone growth in the rapidly growing female rat. Mech Ageing Dev. 1992;66:59\u201369.","journal-title":"Mech Ageing Dev"},{"key":"1598_CR20","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1177\/036354659402200605","volume":"22","author":"H Krahl","year":"1994","unstructured":"Krahl H, Michaelis U, Pieper HG, Quack G, Montag M. Stimulation of bone growth through sports a radiologic investigation of the upper extremities in professional tennis players. Am J Sports Med. 1994;22:751\u20137.","journal-title":"Am J Sports Med"},{"key":"1598_CR21","first-page":"58","volume":"96","author":"JW Smith","year":"1962","unstructured":"Smith JW. The relationship of epiphysial plates to stress in some bones of the lower limb. J Anat. 1962;96:58\u201378.","journal-title":"J Anat"},{"key":"1598_CR22","doi-asserted-by":"publisher","first-page":"1585","DOI":"10.1007\/s10237-022-01608-y","volume":"21","author":"G Alonso","year":"2022","unstructured":"Alonso G, Yawny A, Bertolino G. How do bones grow? A mathematical description of the mechanobiological behavior of the epiphyseal plate. Biomech Model Mechanobiol. 2022;21:1585\u2013601.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR23","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1002\/jemt.1070280606","volume":"28","author":"E Hunziker","year":"1994","unstructured":"Hunziker E. Mechanism of longitudinal bone growth and its regulation by growth plate chondrocytes. Microsc Res Tech. 1994;28:505\u201319.","journal-title":"Microsc Res Tech"},{"key":"1598_CR24","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.2106\/00004623-195638050-00009","volume":"38","author":"AM Arkin","year":"1956","unstructured":"Arkin AM, Katz JF. The effects of pressure on epiphyseal growth; the mechanism of plasticity of growing bone. J Bone Joint Surg Am. 1956;38:1056\u201376.","journal-title":"J Bone Joint Surg Am"},{"key":"1598_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-86841-2","volume-title":"Gesammelte Abhandlungen zur funktionellen Anatomie des Bewegungsapparates","author":"F Pauwels","year":"1965","unstructured":"Pauwels F. Gesammelte Abhandlungen zur funktionellen Anatomie des Bewegungsapparates. Berlin: Springer; 1965."},{"key":"1598_CR26","doi-asserted-by":"publisher","first-page":"804","DOI":"10.1002\/jor.1100060604","volume":"6","author":"DR Carter","year":"1988","unstructured":"Carter DR, Wong M. The role of mechanical loading histories in the development of diarthrodial joints. J Orthop Res. 1988;6:804\u201316.","journal-title":"J Orthop Res"},{"key":"1598_CR27","first-page":"803","volume":"68","author":"SA Feik","year":"1987","unstructured":"Feik SA, Storey E, Ellender G. Stress induced periosteal changes. Br J Exp Pathol. 1987;68:803\u201313.","journal-title":"Br J Exp Pathol"},{"key":"1598_CR28","doi-asserted-by":"publisher","first-page":"982","DOI":"10.1359\/jbmr.1997.12.6.982","volume":"12","author":"TS Gross","year":"1997","unstructured":"Gross TS, Edwards JL, McLeod KJ, Rubin CT. Strain gradients correlate with sites of periosteal bone formation. J Bone Miner Res. 1997;12:982\u20138.","journal-title":"J Bone Miner Res"},{"key":"1598_CR29","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1002\/ar.24006","volume":"302","author":"A Lipphaus","year":"2019","unstructured":"Lipphaus A, Witzel U. Biomechanical study of the development of long bones: finite element structure synthesis of the human second proximal phalanx under growth conditions. Anat Rec. 2019;302:1389\u201398.","journal-title":"Anat Rec"},{"key":"1598_CR30","first-page":"73","volume":"23","author":"U Witzel","year":"2007","unstructured":"Witzel U. Eine neue Methode zur virtuellen Sch\u00e4delsynthese am Beispiel Camarasaurus. Hallesches Jahrb F\u00fcr Geowiss. 2007;23:73\u20138.","journal-title":"Hallesches Jahrb F\u00fcr Geowiss"},{"key":"1598_CR31","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1002\/ar.a.10119","volume":"275","author":"HM Frost","year":"2003","unstructured":"Frost HM. Bone\u2019s mechanostat: a 2003 update. Anat Rec A Discov Mol Cell Evol Biol. 2003;275:1081\u2013101.","journal-title":"Anat Rec A Discov Mol Cell Evol Biol"},{"key":"1598_CR32","doi-asserted-by":"publisher","first-page":"946","DOI":"10.1152\/jappl.1994.76.2.946","volume":"76","author":"AA Biewener","year":"1994","unstructured":"Biewener AA, Bertram JE. Structural response of growing bone to exercise and disuse. J Appl Physiol. 1994;76:946\u201355.","journal-title":"J Appl Physiol"},{"key":"1598_CR33","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/j.bone.2013.04.023","volume":"55","author":"BM Willie","year":"2013","unstructured":"Willie BM, Birkhold AI, Razi H, Thiele T, Aido M, Kruck B, et al. Diminished response to in vivo mechanical loading in trabecular and not cortical bone in adulthood of female C57Bl\/6 mice coincides with a reduction in deformation to load. Bone. 2013;55:335\u201346.","journal-title":"Bone"},{"key":"1598_CR34","doi-asserted-by":"publisher","DOI":"10.1002\/jbm4.10349","volume":"4","author":"T Mustafy","year":"2020","unstructured":"Mustafy T, Londono I, Moldovan F, Villemure I. Isolated cyclic loading during adolescence improves tibial bone microstructure and strength at adulthood. JBMR Plus. 2020;4:e10349.","journal-title":"JBMR Plus"},{"key":"1598_CR35","doi-asserted-by":"publisher","DOI":"10.7717\/peerj.3100","volume":"5","author":"K McCabe","year":"2017","unstructured":"McCabe K, Henderson K, Pantinople J, Richards HL, Milne N. Curvature reduces bending strains in the quokka femur. PeerJ. 2017;5:e3100.","journal-title":"PeerJ"},{"key":"1598_CR36","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1002\/ar.a.20174","volume":"283","author":"U Witzel","year":"2005","unstructured":"Witzel U, Preuschoft H. Finite-element model construction for the virtual synthesis of the skulls in vertebrates: case study of Diplodocus. Anat Rec A Discov Mol Cell Evol Biol. 2005;283:391\u2013401.","journal-title":"Anat Rec A Discov Mol Cell Evol Biol"},{"key":"1598_CR37","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1002\/jor.1100170408","volume":"17","author":"JH Heegaard","year":"1999","unstructured":"Heegaard JH, Beaupr\u00e9 GS, Carter DR. Mechanically modulated cartilage growth may regulate joint surface morphogenesis. J Orthop Res. 1999;17:509\u201317.","journal-title":"J Orthop Res"},{"key":"1598_CR38","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/s10237-009-0178-x","volume":"9","author":"RD Carpenter","year":"2010","unstructured":"Carpenter RD, Carter DR. Computational simulation of spontaneous bone straightening in growing children. Biomech Model Mechanobiol. 2010;9:317\u201328.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR39","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1016\/S8756-3282(02)00700-7","volume":"30","author":"SJ Shefelbine","year":"2002","unstructured":"Shefelbine SJ, Tardieu C, Carter DR. Development of the femoral bicondylar angle in hominid bipedalism. Bone. 2002;30:765\u201370.","journal-title":"Bone"},{"key":"1598_CR40","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1023\/B:ABME.0000012750.73170.ba","volume":"32","author":"SJ Shefelbine","year":"2004","unstructured":"Shefelbine SJ, Carter DR. Mechanobiological predictions of femoral anteversion in cerebral palsy. Ann Biomed Eng. 2004;32:297\u2013305.","journal-title":"Ann Biomed Eng"},{"key":"1598_CR41","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/s10237-019-01241-2","volume":"19","author":"SM Sadeghian","year":"2020","unstructured":"Sadeghian SM, Lewis CL, Shefelbine SJ. Predicting growth plate orientation with altered hip loading: potential cause of cam morphology. Biomech Model Mechanobiol. 2020;19:701\u201312.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR42","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1016\/j.orthres.2003.08.004","volume":"22","author":"SJ Shefelbine","year":"2004","unstructured":"Shefelbine SJ, Carter DR. Mechanobiological predictions of growth front morphology in developmental hip dysplasia. J Orthop Res. 2004;22:346\u201352.","journal-title":"J Orthop Res"},{"key":"1598_CR43","doi-asserted-by":"publisher","first-page":"3390","DOI":"10.1016\/j.jbiomech.2015.06.002","volume":"48","author":"M Giorgi","year":"2015","unstructured":"Giorgi M, Carriero A, Shefelbine SJ, Nowlan NC. Effects of normal and abnormal loading conditions on morphogenesis of the prenatal hip joint: application to hip dysplasia. J Biomech. 2015;48:3390\u20137.","journal-title":"J Biomech"},{"key":"1598_CR44","unstructured":"Lipphaus A, Tr\u00f6bs RB, Wegener-Panzer A, Witzel U. Biomechanische Simulation der Entstehung eines Genu valgum bei H\u00fcftdysplasie. In Proceedings of the Deutscher Kongress f\u00fcr Orthop\u00e4die und Unfallchirurgie, Berlin, Germany, 28 10 2021"},{"key":"1598_CR45","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1007\/s00586-007-0442-7","volume":"16","author":"IAF Stokes","year":"2007","unstructured":"Stokes IAF. Analysis and simulation of progressive adolescent scoliosis by biomechanical growth modulation. Eur Spine J. 2007;16:1621\u20138.","journal-title":"Eur Spine J"},{"key":"1598_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2020.109905","volume":"109","author":"MG Alonso","year":"2020","unstructured":"Alonso MG, Bertolino G, Yawny A. Mechanobiological based long bone growth model for the design of limb deformities correction devices. J Biomech. 2020;109:109905.","journal-title":"J Biomech"},{"key":"1598_CR47","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1007\/s10237-019-01277-4","volume":"19","author":"AF Carrera-Pinz\u00f3n","year":"2020","unstructured":"Carrera-Pinz\u00f3n AF, M\u00e1rquez-Fl\u00f3rez K, Kraft RH, Ramtani S, Garz\u00f3n-Alvarado DA. Computational model of a synovial joint morphogenesis. Biomech Model Mechanobiol. 2020;19:1389\u2013402.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR48","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1007\/s10237-017-0997-0","volume":"17","author":"JJ Vaca-Gonz\u00e1lez","year":"2018","unstructured":"Vaca-Gonz\u00e1lez JJ, Moncayo-Donoso M, Guevara JM, Hata Y, Shefelbine SJ, Garz\u00f3n-Alvarado DA. Mechanobiological modeling of endochondral ossification: an experimental and computational analysis. Biomech Model Mechanobiol. 2018;17:853\u201375.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR49","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2021.116132","volume":"153","author":"SM Sadeghian","year":"2021","unstructured":"Sadeghian SM, Shapiro FD, Shefelbine SJ. Computational model of endochondral ossification: simulating growth of a long bone. Bone. 2021;153:116132.","journal-title":"Bone"},{"key":"1598_CR50","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2021.106365","volume":"210","author":"PJ Terryn","year":"2021","unstructured":"Terryn PJ, Fernandes PR, Jo\u00e3o F, Veloso A, Baptista F. Modeling the musculoskeletal loading in bone remodeling at the hip of a child. Comput Methods Programs Biomed. 2021;210:106365.","journal-title":"Comput Methods Programs Biomed"},{"key":"1598_CR51","doi-asserted-by":"publisher","DOI":"10.1016\/j.bone.2023.116742","volume":"171","author":"D Quexada-Rodr\u00edguez","year":"2023","unstructured":"Quexada-Rodr\u00edguez D, Trabelsi O, Hobatho MC, Ramtani S, Garz\u00f3n-Alvarado D. Influence of growth plate morphology on bone trabecular groups, a framework computational approach. Bone. 2023;171:116742.","journal-title":"Bone"},{"key":"1598_CR52","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1002\/jor.1100080507","volume":"8","author":"GS Beaupr\u00e9","year":"1990","unstructured":"Beaupr\u00e9 GS, Orr TE, Carter DR. An approach for time-dependent bone modeling and remodeling-application: a preliminary remodeling simulation. J Orthop Res. 1990;8:662\u201370.","journal-title":"J Orthop Res"},{"key":"1598_CR53","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.ocl.2005.12.001","volume":"37","author":"MC Lee","year":"2006","unstructured":"Lee MC, Eberson CP. Growth and development of the child\u2019s hip. Orthop Clin North Am. 2006;37:119\u201332.","journal-title":"Orthop Clin North Am"},{"key":"1598_CR54","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1007\/s00132-016-3222-4","volume":"45","author":"B Heimkes","year":"2016","unstructured":"Heimkes B. Die gro\u00dfen Apophysen. Orthop\u00e4de. 2016;45:206\u201312.","journal-title":"Orthop\u00e4de"},{"key":"1598_CR55","doi-asserted-by":"publisher","first-page":"507","DOI":"10.3109\/17453674.2011.584210","volume":"82","author":"PA Struijs","year":"2011","unstructured":"Struijs PA, Oostra RJ, van Rijn RR, Besselaar pp. Abnormal growth of the proximal femur due to apophyseal-epiphyseal coalescence resulting in coxa valga\u2014a report of two cases in adolescents. Acta Orthop. 2011;82:507\u20139.","journal-title":"Acta Orthop"},{"key":"1598_CR56","doi-asserted-by":"publisher","first-page":"199","DOI":"10.3109\/17453676708989634","volume":"38","author":"A Langenski\u00f6ld","year":"1967","unstructured":"Langenski\u00f6ld A, Salenius P. Epiphyseodesis of the greater trochanter. Acta Orthop Scand. 1967;38:199\u2013219.","journal-title":"Acta Orthop Scand"},{"key":"1598_CR57","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.gaitpost.2024.07.120","volume":"113","author":"H Kainz","year":"2024","unstructured":"Kainz H, Koller W, Bastir M, Svehlik M, Schwartz MH. The shape and size of the femur adapts during growth to maintain a constant cartilage load. Gait Posture. 2024;113:105\u20137.","journal-title":"Gait Posture"},{"key":"1598_CR58","doi-asserted-by":"publisher","DOI":"10.3389\/fbioe.2022.914990","volume":"10","author":"N Alexander","year":"2022","unstructured":"Alexander N, Brunner R, Cip J, Viehweger E, De Pieri E. Increased femoral anteversion does not lead to increased joint forces during gait in a cohort of adolescent patients. Front Bioeng Biotechnol. 2022;10:914990.","journal-title":"Front Bioeng Biotechnol"},{"key":"1598_CR59","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2106\/00004623-196345010-00001","volume":"45-A","author":"M Anderson","year":"1963","unstructured":"Anderson M, Green WT, Messner MB. Growth and predictions of growth in the lower extremities. J Bone Joint Surg Am. 1963;45-A:1\u201314.","journal-title":"J Bone Joint Surg Am"},{"key":"1598_CR60","doi-asserted-by":"publisher","first-page":"435","DOI":"10.52628\/87.3.07","volume":"87","author":"P Van Geel","year":"2021","unstructured":"Van Geel P, Cools W, Laumen A. Evolution of head-shaft angle and neck-shaft angle in childhood. Acta Orthop Belg. 2021;87:435\u201341.","journal-title":"Acta Orthop Belg"},{"key":"1598_CR61","doi-asserted-by":"publisher","first-page":"15","DOI":"10.17816\/PTORS7315-24","volume":"7","author":"IY Pozdnikin","year":"2019","unstructured":"Pozdnikin IY, Baskov VE, Barsukov DB, Bortulev PI, Krasnov AI. Relative overgrowth of the greater trochanter and trochanteric-pelvic impingement syndrome in children: causes and X-ray anatomical characteristics. Pediatr Traumatol Orthop Reconstr Surg. 2019;7:15\u201324.","journal-title":"Pediatr Traumatol Orthop Reconstr Surg"},{"key":"1598_CR62","doi-asserted-by":"publisher","first-page":"740","DOI":"10.1097\/BPO.0b013e318186eb79","volume":"28","author":"S Sabharwal","year":"2008","unstructured":"Sabharwal S, Zhao C, Edgar M. Lower limb alignment in children: reference values based on a full-length standing radiograph. J Pediatr Orthop. 2008;28:740\u20136.","journal-title":"J Pediatr Orthop"},{"key":"1598_CR63","doi-asserted-by":"publisher","first-page":"1871","DOI":"10.1359\/jbmr.2000.15.10.1871","volume":"15","author":"M Bradney","year":"2000","unstructured":"Bradney M, Karlsson MK, Duan Y, Stuckey S, Bass S, Seeman E. Heterogeneity in the growth of the axial and appendicular skeleton in boys: implications for the pathogenesis of bone fragility in men. J Bone Miner Res. 2000;15:1871\u20138.","journal-title":"J Bone Miner Res"},{"key":"1598_CR64","first-page":"49","volume":"169","author":"SS Upadhyay","year":"1990","unstructured":"Upadhyay SS, Burwell RG, Moulton A, Small PG, Wallace WA. Femoral anteversion in healthy children application of a new method using ultrasound. J Anat. 1990;169:49\u201361.","journal-title":"J Anat"},{"key":"1598_CR65","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0235966","volume":"15","author":"H Kainz","year":"2020","unstructured":"Kainz H, Killen BA, Wesseling M, Perez-Boerema F, Pitto L, Garcia Aznar JM, et al. A multi-scale modelling framework combining musculoskeletal rigid-body simulations with adaptive finite element analyses, to evaluate the impact of femoral geometry on hip joint contact forces and femoral bone growth. PLoS ONE. 2020;15:e0235966.","journal-title":"PLoS ONE"},{"key":"1598_CR66","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/BF00174625","volume":"181","author":"M Wong","year":"1990","unstructured":"Wong M, Carter DR. A theoretical model of endochondral ossification and bone architectural construction in long bone ontogeny. Anat Embryol. 1990;181:523\u201332.","journal-title":"Anat Embryol"},{"key":"1598_CR67","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1002\/jor.1100170505","volume":"17","author":"SS Stevens","year":"1999","unstructured":"Stevens SS, Beaupr\u00e9 GS, Carter DR. Computer model of endochondral growth and ossification in long bones: biological and mechanobiological influences. J Orthop Res. 1999;17:646\u201353.","journal-title":"J Orthop Res"},{"key":"1598_CR68","doi-asserted-by":"publisher","first-page":"1869","DOI":"10.1007\/s10237-017-0925-3","volume":"16","author":"P Yadav","year":"2017","unstructured":"Yadav P, Shefelbine SJ, Pont\u00e9n E, Gutierrez-Farewik EM. Influence of muscle groups\u2019 activation on proximal femoral growth tendency. Biomech Model Mechanobiol. 2017;16:1869\u201383.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR69","doi-asserted-by":"publisher","first-page":"1613","DOI":"10.1016\/j.jbiomech.2016.03.039","volume":"49","author":"P Yadav","year":"2016","unstructured":"Yadav P, Shefelbine SJ, Gutierrez-Farewik EM. Effect of growth plate geometry and growth direction on prediction of proximal femoral morphology. J Biomech. 2016;49:1613\u20139.","journal-title":"J Biomech"},{"key":"1598_CR70","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.medengphy.2021.02.008","volume":"90","author":"P Yadav","year":"2021","unstructured":"Yadav P, Pe\u00f1a Fern\u00e1ndez M, Gutierrez-Farewik EM. Influence of loading direction due to physical activity on proximal femoral growth tendency. Med Eng Phys. 2021;90:83\u201391.","journal-title":"Med Eng Phys"},{"key":"1598_CR71","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s43465-020-00320-2","volume":"55","author":"P Naik","year":"2021","unstructured":"Naik P. Remodelling in children\u2019s fractures and limits of acceptability. Indian J Orthop. 2021;55:549\u201359.","journal-title":"Indian J Orthop"},{"key":"1598_CR72","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/j.jbiomech.2009.09.049","volume":"43","author":"NS Sverdlova","year":"2010","unstructured":"Sverdlova NS, Witzel U. Principles of determination and verification of muscle forces in the human musculoskeletal system: muscle forces to minimise bending stress. J Biomech. 2010;43:387\u201396.","journal-title":"J Biomech"},{"key":"1598_CR73","doi-asserted-by":"publisher","first-page":"1008","DOI":"10.1016\/j.medengphy.2016.05.005","volume":"38","author":"F Lutz","year":"2016","unstructured":"Lutz F, Mastel R, Runge M, Stief F, Schmidt A, Meurer A, et al. Calculation of muscle forces during normal gait under consideration of femoral bending moments. Med Eng Phys. 2016;38:1008\u201315.","journal-title":"Med Eng Phys"},{"key":"1598_CR74","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0022-5193(88)80122-X","volume":"131","author":"JE Bertram","year":"1988","unstructured":"Bertram JE, Biewener AA. Bone curvature: sacrificing strength for load predictability? J Theor Biol. 1988;131:75\u201392.","journal-title":"J Theor Biol"},{"key":"1598_CR75","doi-asserted-by":"publisher","first-page":"933","DOI":"10.1016\/S0021-9290(97)00057-2","volume":"30","author":"GN Duda","year":"1997","unstructured":"Duda GN, Schneider E, Chao EY. Internal forces and moments in the femur during walking. J Biomech. 1997;30:933\u201341.","journal-title":"J Biomech"},{"key":"1598_CR76","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1016\/S0736-0266(03)00098-6","volume":"21","author":"P Augat","year":"2003","unstructured":"Augat P, Burger J, Schorlemmer S, Henke T, Peraus M, Claes L. Shear movement at the fracture site delays healing in a diaphyseal fracture model. J Orthop Res. 2003;21:1011\u20137.","journal-title":"J Orthop Res"},{"key":"1598_CR77","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0291458","volume":"18","author":"H Kainz","year":"2023","unstructured":"Kainz H, Mindler GT, Kranzl A. Influence of femoral anteversion angle and neck-shaft angle on muscle forces and joint loading during walking. PLoS ONE. 2023;18:e0291458.","journal-title":"PLoS ONE"},{"key":"1598_CR78","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s00774-019-01079-9","volume":"38","author":"K Someya","year":"2020","unstructured":"Someya K, Mochizuki T, Hokari S, Tanifuji O, Katsumi R, Koga H, et al. Age- and sex-related characteristics in cortical thickness of femoral diaphysis for young and elderly subjects. J Bone Miner Metab. 2020;38:533\u201343.","journal-title":"J Bone Miner Metab"},{"key":"1598_CR79","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/j.jor.2025.04.014","volume":"63","author":"DQ Rodr\u00edguez","year":"2025","unstructured":"Rodr\u00edguez DQ, Ho Ba Tho MC, Trabelsi O, Garz\u00f3n-Alvarado D. Exploring the impact of mechanical stimuli on growth plate morphology and trabecular adaptation: a finite element approach. J Orthop. 2025;63:228\u201337.","journal-title":"J Orthop"},{"issue":"4","key":"1598_CR80","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1097\/01241398-198707000-00014","volume":"7","author":"SE Jordan","year":"1987","unstructured":"Jordan SE, Alonso JE, Cook FF. The etiology of valgus angulation after metaphyseal fractures of the tibia in children. J Pediatr Orthop. 1987;7(4):450\u20137.","journal-title":"J Pediatr Orthop"},{"key":"1598_CR81","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1007\/s10237-025-01942-x","volume":"24","author":"W Koller","year":"2025","unstructured":"Koller W, Svehlik M, Walln\u00f6fer E, Kranzl A, Mindler G, Baca A, et al. Femoral bone growth predictions based on personalized multi-scale simulations: validation and sensitivity analysis of a mechanobiological model. Biomech Model Mechanobiol. 2025;24:879\u201394.","journal-title":"Biomech Model Mechanobiol"},{"key":"1598_CR82","unstructured":"Lipphaus A, Wegener-Panzer A, Tr\u00f6bs, RB, Witzel U. Computational modelling of proximal and distal epiphyseal and appositional growth of the femur in children. In Proceedings of XXVIII Congress of the International Society of Biomechanics (ISB): 25\u201329 June 2021; Digital congress: A287."},{"key":"1598_CR83","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1097\/00003086-199202000-00041","volume":"275","author":"JW Pritchett","year":"1992","unstructured":"Pritchett JW. Longitudinal growth and growth-plate activity in the lower extremity. Clin Orthop Relat Res. 1992;275:274\u20139.","journal-title":"Clin Orthop Relat Res"},{"key":"1598_CR84","first-page":"22","volume":"3","author":"AA Abiodun","year":"2014","unstructured":"Abiodun AA, Falana BA, Olatunbosun A. Baseline thickness of proximal femoral epiphysis in the diagnosis of hip diseases in infants and children in Nigeria. Int J Surg Res. 2014;3:22\u20136.","journal-title":"Int J Surg Res"},{"key":"1598_CR85","doi-asserted-by":"publisher","first-page":"5982","DOI":"10.1158\/1078-0432.CCR-10-2259","volume":"17","author":"A Kim","year":"2011","unstructured":"Kim A, Dombi E, Solomon J, Fox E, Balis FM, Widemann BC. Automated volumetric growth plate measurement using magnetic resonance imaging for monitoring skeletal toxicity in children treated on investigational drug trials. Clin Cancer Res. 2011;17:5982\u201390.","journal-title":"Clin Cancer Res"},{"key":"1598_CR86","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1055\/s-2008-1039549","volume":"135","author":"B Heimkes","year":"1997","unstructured":"Heimkes B, Posel P, Plitz W, Zimmer M. Die altersabh\u00e4ngige Kr\u00e4fteverteilung am koxalen Femurende des normal wachsenden Kindes. Z Orthop Ihre Grenzgeb. 1997;135:17\u201323.","journal-title":"Z Orthop Ihre Grenzgeb"},{"key":"1598_CR87","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0124862","volume":"10","author":"J Gao","year":"2015","unstructured":"Gao J, Roan E, Williams JL. Regional variations in growth plate chondrocyte deformation as predicted by three-dimensional multi-scale simulations. PLoS ONE. 2015;10:e0124862.","journal-title":"PLoS ONE"},{"key":"1598_CR88","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1359\/jbmr.2001.16.4.597","volume":"16","author":"F Rauch","year":"2001","unstructured":"Rauch F, Schoenau E. Changes in bone density during childhood and adolescence: an approach based on bone\u2019s biological organization. J Bone Miner Res. 2001;16:597\u2013604.","journal-title":"J Bone Miner Res"},{"key":"1598_CR89","doi-asserted-by":"publisher","unstructured":"Hasgall PA, Di Gennaro F, Baumgartner C, Neufeld E, Lloyd B, Gosselin MC, Payne D, Klingenb\u00f6ck A, Kuster N, \u201cIT\u2019IS Database for thermal and electromagnetic parameters of biological tissues,\u201d Version 4.1. 2022, https:\/\/doi.org\/10.13099\/VIP21000-04-1. itis.swiss\/database","DOI":"10.13099\/VIP21000-04-1"},{"key":"1598_CR90","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1016\/j.bone.2011.06.035","volume":"49","author":"C \u00d6hman","year":"2011","unstructured":"\u00d6hman C, Baleani M, Pani C, Taddei F, Alberghini M, Viceconti M, et al. Compressive behaviour of child and adult cortical bone. Bone. 2011;49:769\u201376.","journal-title":"Bone"},{"key":"1598_CR91","first-page":"3","volume":"13","author":"S Piszczatowski","year":"2011","unstructured":"Piszczatowski S. Material aspects of growth plate modelling using Carter\u2019s and Stokes\u2019s approaches. Acta Bioeng Biomech. 2011;13:3\u201314.","journal-title":"Acta Bioeng Biomech"},{"key":"1598_CR92","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.jmbbm.2015.06.023","volume":"50","author":"LE Jansen","year":"2015","unstructured":"Jansen LE, Birch NP, Schiffman JD, Crosby AJ, Peyton SR. Mechanics of intact bone marrow. J Mech Behav Biomed Mater. 2015;50:299\u2013307.","journal-title":"J Mech Behav Biomed Mater"},{"key":"1598_CR93","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0127293","volume":"10","author":"YS Lai","year":"2015","unstructured":"Lai YS, Chen WC, Huang CH, Cheng CK, Chan KK, Chang TK. The effect of graft strength on knee laxity and graft in-situ forces after posterior cruciate ligament reconstruction. PLoS ONE. 2015;10:e0127293.","journal-title":"PLoS ONE"},{"key":"1598_CR94","doi-asserted-by":"publisher","first-page":"2318","DOI":"10.1016\/j.jbiomech.2006.10.038","volume":"40","author":"AD Speirs","year":"2007","unstructured":"Speirs AD, Heller MO, Duda GN, Taylor WR. Physiologically based boundary conditions in finite element modelling. J Biomech. 2007;40:2318\u201323.","journal-title":"J Biomech"},{"key":"1598_CR95","doi-asserted-by":"publisher","first-page":"1180","DOI":"10.1016\/j.medengphy.2015.10.002","volume":"37","author":"M Heyland","year":"2015","unstructured":"Heyland M, Trepczynski A, Duda GN, Zehn M, Schaser KD, M\u00e4rdian S. Selecting boundary conditions in physiological strain analysis of the femur: balanced loads, inertia relief method and follower load. Med Eng Phys. 2015;37:1180\u20135.","journal-title":"Med Eng Phys"},{"key":"1598_CR96","doi-asserted-by":"publisher","first-page":"2577","DOI":"10.1242\/jeb.01065","volume":"207","author":"RP Main","year":"2004","unstructured":"Main RP, Biewener AA. Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius. J Exp Biol. 2004;207:2577\u201388.","journal-title":"J Exp Biol"},{"key":"1598_CR97","doi-asserted-by":"publisher","first-page":"927","DOI":"10.1002\/jor.1100140613","volume":"14","author":"NJ Wilsman","year":"1996","unstructured":"Wilsman NJ, Farnum CE, Leiferman EM, Fry M, Barreto C. Differential growth by growth plates as a function of multiple parameters of chondrocytic kinetics. J Orthop Res. 1996;14:927\u201336.","journal-title":"J Orthop Res"},{"key":"1598_CR98","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1016\/j.dental.2006.10.004","volume":"23","author":"J Li","year":"2007","unstructured":"Li J, Li H, Shi L, Fok AS, Ucer C, Devlin H, et al. A mathematical model for simulating the bone remodeling process under mechanical stimulus. Dent Mater. 2007;23:1073\u20138.","journal-title":"Dent Mater"},{"key":"1598_CR99","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S8756-3282(99)00257-4","volume":"26","author":"FH Glorieux","year":"2000","unstructured":"Glorieux FH, Travers R, Taylor A, Bowen JR, Rauch F, Norman M, et al. Normative data for iliac bone histomorphometry in growing children. Bone. 2000;26:103\u20139.","journal-title":"Bone"},{"key":"1598_CR100","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0156222","volume":"11","author":"B Li","year":"2016","unstructured":"Li B, Sankaran JS, Judex S. Trabecular and cortical bone of growing C3H mice is highly responsive to the removal of weightbearing. PLoS ONE. 2016;11:e0156222.","journal-title":"PLoS ONE"},{"key":"1598_CR101","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1016\/j.otsr.2012.03.014","volume":"98","author":"B Guenoun","year":"2012","unstructured":"Guenoun B, Zadegan F, Aim F, Hannouche D, Nizard R. Reliability of a new method for lower-extremity measurements based on stereoradiographic three-dimensional reconstruction. Orthop Traumatol Surg Res. 2012;98:506\u201313.","journal-title":"Orthop Traumatol Surg Res"},{"key":"1598_CR102","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1080\/17453674.2019.1690873","volume":"91","author":"CS Fischer","year":"2020","unstructured":"Fischer CS, K\u00fchn JP, V\u00f6lzke H, Ittermann T, G\u00fcmbel D, Kasch R, et al. The neck-shaft angle: an update on reference values and associated factors. Acta Orthop. 2020;91:53\u20137.","journal-title":"Acta Orthop"},{"key":"1598_CR103","doi-asserted-by":"publisher","first-page":"66","DOI":"10.4055\/cios.2012.4.1.66","volume":"4","author":"PW Yoon","year":"2012","unstructured":"Yoon PW, Shin YH, Yoo JJ, Yoon KS, Kim HJ. Progression of a fracture site impaction as a prognostic indicator of impacted femoral neck fracture treated with multiple pinning. Clin Orthop Surg. 2012;4:66\u201371.","journal-title":"Clin Orthop Surg"},{"key":"1598_CR104","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1302\/2058-5241.6.210015","volume":"6","author":"N Marques Lu\u00eds","year":"2021","unstructured":"Marques Lu\u00eds N, Varatojo R. Radiological assessment of lower limb alignment. EFORT Open Rev. 2021;6:487\u201394.","journal-title":"EFORT Open Rev"},{"key":"1598_CR105","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1111\/joa.13249","volume":"237","author":"M Scorcelletti","year":"2020","unstructured":"Scorcelletti M, Reeves ND, Rittweger J, Ireland A. Femoral anteversion: significance and measurement. J Anat. 2020;237:811\u201326.","journal-title":"J Anat"}],"container-title":["BioMedical Engineering OnLine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12938-026-01598-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12938-026-01598-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12938-026-01598-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T19:01:35Z","timestamp":1784142095000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s12938-026-01598-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,15]]},"references-count":105,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["1598"],"URL":"https:\/\/doi.org\/10.1186\/s12938-026-01598-3","relation":{},"ISSN":["1475-925X"],"issn-type":[{"value":"1475-925X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,15]]},"assertion":[{"value":"27 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable.","order":1,"name":"Ethics","label":"Ethics approval and consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"94"}}