Stability of a one-dimensional morphoelastic model for post-burn contraction

Ginger Egberts*, Fred Vermolen, Paul van Zuijlen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order O(h2). Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.
Original languageEnglish
Article number24
JournalJournal of Mathematical Biology
Volume83
Issue number3
DOIs
Publication statusPublished - 1 Sep 2021

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