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Mathematical modelling of collagen fibres rearrangement during the tendon healing process

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cris.lastimport.scopus2024-02-12T20:20:48Z
dc.abstract.enTendon 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 asymptotic 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.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorCarrillo, Jose Antonio
dc.contributor.authorSzymańska, Zuzanna
dc.contributor.authorParisot, Martin
dc.date.accessioned2024-01-25T05:34:20Z
dc.date.available2024-01-25T05:34:20Z
dc.date.issued2021
dc.description.accesstimeAT_PUBLICATION
dc.description.financePublikacja bezkosztowa
dc.description.number2
dc.description.versionFINAL_PUBLISHED
dc.description.volume14
dc.identifier.doi10.3934/KRM.2021005
dc.identifier.issn1937-5093
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/111930
dc.identifier.weblinkhttp://aimsciences.org//article/doi/10.3934/krm.2021005?viewType=html
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofKinetic and Related Models
dc.relation.pages283
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enCollagen remodelling
dc.subject.enKinetic model
dc.subject.enTendon healing
dc.subject.enIntegro- differential equations
dc.subject.enAlignment
dc.titleMathematical modelling of collagen fibres rearrangement during the tendon healing process
dc.typeJournalArticle
dspace.entity.typePublication