Mathematical modelling of collagen fibres rearrangement during the tendon healing process

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dc.contributor.authorCarrillo, José Antonio
dc.contributor.authorParisot, Martin
dc.contributor.authorSzymańska, Zuzanna
dc.contributor.organizationMathematical Institute, University of Oxford, Oxford, United Kingdomen
dc.contributor.organizationInria-Bordeaux, Team CARDAMOM, Talence Cedex, Franceen
dc.contributor.organizationInstitute of Mathematics, Polish Academy of Sciences, Warsaw, Polanden
dc.contributor.organizationInterdisciplinary Centre for Mathematical and Computational Modelling, University of Warsawen
dc.date.accessioned2022-04-04T10:40:44Z
dc.date.available2022-04-04T10:40:44Z
dc.date.issued2021
dc.description.abstractTendon injuries present a clinical challenge to modern medicine as they heal slowly and rarely is there full restoration to healthy tendon structure and mechanical strength. Moreover, the process of healing is not fully elucidated. To improve understanding of tendon function and the healing process, we propose a new model of collagen fibres rearrangement during tendon healing. The model consists of an integro-differential equation describing the dynamics of collagen fibres distribution. We further reduce the model in a suitable asym-ptotic regime leading to a nonlinear non-local Fokker-Planck type equation for the spatial and orientation distribution of collagen fibre bundles. Due to its simplicity, the reduced model allows for possible parameter estimation based on data. We showcase some of the qualitative properties of this model simulating its long time asymptotic behaviour and the total time for tendon fibres to align in terms of the model parameters. A possible biological interpretation of the numerical experiments performed leads us to the working hypothesis of the importance of tendon cell size in patient recovery.en
dc.identifier.citationJosé Antonio Carrillo, Martin Parisot, Zuzanna Szymańska. Mathematical modelling of collagen fibres rearrangement during the tendon healing process. Kinetic & Related Models, 2021, 14 (2) : 283-301. doi: 10.3934/krm.2021005en
dc.identifier.doi10.3934/krm.2021005
dc.identifier.issn1937-5093
dc.identifier.urihttps://open.icm.edu.pl/handle/123456789/21225
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciencesen
dc.rightsUznanie autorstwa 4.0 Międzynarodowe*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectcollagen remodellingen
dc.subjectkinetic modelen
dc.subjecttendon healingen
dc.subjectintegro-differential equationsen
dc.subjectalignmenten
dc.titleMathematical modelling of collagen fibres rearrangement during the tendon healing processen
dc.typearticleen
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