Stability of a two-dimensional biomorphoelastic model for post-burn contraction

Journal article (2023)

Authors

G. Egberts Numerical Analysis - EEMCS , University of Hasselt
F.J. Vermolen University of Hasselt
Paul van Zuijlen Emma Children's Hospital Academic Medical Center, University of Amsterdam, Red Cross Hospital, Beverwijk, Amsterdam UMC
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2023 G. Egberts, F.J. Vermolen, Paul van Zuijlen
DOI
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https://doi.org/10.1007/s00285-023-01893-w
Stability Morphoelasticity Wound contraction Burns Moving-grid finite-element
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Published Date

2023

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems.