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A mathematical model for the growth of elongated bones

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dc.contributor.authorFasano, A.
dc.contributor.authorHerrero, Miguel A.
dc.contributor.authorLópez, J. M.
dc.contributor.authorMedina Reus, Elena
dc.date.accessioned2023-06-20T03:34:48Z
dc.date.available2023-06-20T03:34:48Z
dc.date.issued2010
dc.description.abstractA mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling molecules. These molecules characterize the dynamics of the transition zone between the cartilage and the bone tissue. Some experimental data are needed to estimate some model parameters. We discuss how our results are essentially unaffected by small variations, and in a particular case, not necessarily small variations in the experimental values.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipMICINN Research Grant
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22554
dc.identifier.doi10.1685/2010CAIM554
dc.identifier.issn2038-0909
dc.identifier.officialurlhttp://caim.simai.eu/index.php/caim/article/view/2010CAIM554
dc.identifier.relatedurlhttp://www.simai.eu/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/43943
dc.issue.number2
dc.journal.titleCommunications in Applied and Industrial Mathematics
dc.language.isoeng
dc.page.final164
dc.page.initial153
dc.publisherItalian Society for Applied and Industrial Mathematics (SIMAI)
dc.relation.projectIDMTM2008-01867
dc.relation.projectIDFIS2008-00200
dc.rights.accessRightsopen access
dc.subject.cdu51-76
dc.subject.cdu517.9
dc.subject.cdu519.87
dc.subject.keywordGrowth plate dynamics
dc.subject.keywordmathematical model
dc.subject.keywordrobustness
dc.subject.ucmBiomatemáticas
dc.subject.ucmEcuaciones diferenciales
dc.subject.ucmInvestigación operativa (Matemáticas)
dc.subject.unesco2404 Biomatemáticas
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.subject.unesco1207 Investigación Operativa
dc.titleA mathematical model for the growth of elongated bones
dc.typejournal article
dc.volume.number1
dcterms.referencesH. Kronenberg, Developmental regulation of the growth plate, Nature, vol. 423, pp. 332-336, 2003. T. Shimo, C. Gentil, M. Iwamoto, C.Wu, E. Koyama, and M. Pacifici, Indian hedgehog and syndecans-3 coregulate chondrocyte proliferation and function during chick limb skeletogenesis, Dev. Dyn., vol. 229, pp. 607-617, 2004. E. Weir, W. Philbrick, M. Amling, L. Neff, R. Baron, and A. Broadus, Targeted overexpression of parathyroid hormone-related peptide in chondrocytes causes chondrodysplasia and delayed endochondral bone formation, Proc. Natl. Acad. Sci. USA, vol. 93, pp. 10240-10245, 1996. J. Brouwers, C. van Donkelaar, B. Sengers, and R. Huiskes, Can the growth factors pthrp, ihh and vgef, together regulate the development of a long bone?, Journal of Biomechanics, vol. 39, pp. 2774-2782, 2006. C. van Donkelaar and R. Huiskes., The pthrp-ihh fedback loop in the embryonic growth plate allows pthrp to control hypertrophy and ihh to regulate proliferation, Biomechan. Model Mechanobiol, vol. 6, pp. 55-62, 2007. G. Garzón-Alvarado, J. García-Aznar, and M. Doblaré, A reaction-diffusion model for long bones growth, Biomechan. Model Mechanobiol, vol. 8, pp. 381-395, 2009. G. Garzón-Alvarado, J. García-Aznar, and M. Doblaré, Appearance and location of secondary ossification centres may be explained by a reaction-diffusion mechanism, Comp. In Biology and Medicine, vol. 39, pp. 554-561, 2009. A. Fasano, M. Herrero, J. López, and E. Medina, On the dynamics of the growth plate in primary ossification, J. Theor. Biol., vol. 265, pp. 543-553, 2010. R. Williams, W. Zipfel, M. Tinsley, and C. Farnum, Solute transport in growth plate cartilage: In vitro and in vivo, Biophysical Journal, vol. 93, pp. 1039-1050, 2007.
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