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Ready to rebuild: Modeling proliferation and remodeling stages of the wound healing process
  • Amanda Patrick,
  • Benito Chen-Charpentier
Amanda Patrick
The University of Texas Arlington Department of Mathematics

Corresponding Author:[email protected]

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Benito Chen-Charpentier
The University of Texas Arlington Department of Mathematics
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Abstract

A wound is an injury of the living tissue in the body and its integrity is compromised. The wound repair process consists of four overlapping stages: homeostasis, inflammation, proliferation, and remodeling. In this paper we propose a model for the formation of the provisional matrix in the proliferation and maturation stages. This model assumes that the cells and other factors are uniformly distributed and is based on a system of six ordinary differential equations. The real processes are very complex but the presented model includes the main assumptions and uses the parameter values found in the medical literature. Experimental values of the parameters are hard to obtain so a global sensitivity analysis is performed to determine which parameters cause the largest variations in the solutions. Numerical simulations are performed but since the reported data has large variations a system of stochastic differential equations is also introduced and solved numerically. The models can help test hypotheses about how the different species interact, and their relative importance.