A Cut-Cell Finite-Element Method for a Discontinuous Switch Model for Wound Closure

S. V. Zemskov, F. J. Vermolen (), E. Javierre and C. Vuik
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S. V. Zemskov: Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science
F. J. Vermolen: Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science
E. Javierre: Aragón Institute of Engineering Research (I3A), Universidad de Zaragoza, Aragon Health Sciences Institute, Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Group of Structural Mechanics and Materials Modelling (GEMM)
C. Vuik: Delft University of Technology, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 929-936 from Springer

Abstract: Abstract A mathematical model for epidermal wound healing is considered. The model is based on a moving boundary problem for the wound edge in which the edge moves if a generic epidermal growth factor exceeds a given threshold value. We use a Galerkin finite-element method to solve the equations for the growth factor concentration. The moving boundary (wound edge) is tracked using a level-set method with a local adaptive mesh refinement in the interface region. To deal with the reaction-diffusion equation for the growth factor, a cut-cell method has been implemented. This cut-cell method warrants the integration over a continuous reaction term elementwisely. The results improved with respect to the results that were obtained without the use of the cut-cell method.

Keywords: Active Layer; Wound Closure; Local Curvature; Wound Edge; Move Boundary Problem (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-11795-4_100

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