A three dimensional model of wound healing: Analysis and computation

Avner Friedman; Bei Hu; Chuan Xue

doi:10.3934/dcdsb.2012.17.2691

Article Contents

2012, Volume 17, Issue 8: 2691-2712. Doi: 10.3934/dcdsb.2012.17.2691

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A three dimensional model of wound healing: Analysis and computation

1.
Department of Mathematics and Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210
2.
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556

Received: February 28, 2011

Revised: April 30, 2011

Published: October 2012

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Abstract

This paper is concerned with a three-dimensional model of wound healing. The boundary of the wound is a free boundary, and the region surrounding it is viewed as a partially healed tissue, satisfying a viscoelastic constitutive law for the velocity v. In the partially healed region the densities of several types of cells and the concentrations of several chemical species satisfy a coupled system of parabolic equations, whereas the tissue density satisfies a hyperbolic equation. The parabolic equations include advection by the velocity v and chemotaxis/haptotaxis terms. We prove existence and uniqueness of a smooth solution of the free boundary problem, for some time interval $0\leq t\leq T$, $T>0$. We also simulate the model equations to demonstrate the difference in the healing rate between normal wounds and chronic (or ischemic) wounds.

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Mathematics Subject Classification: Primary: 92C50, 35R35, 35B40,.

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