Parameter sensitivity analysis on a mathematical model of reepithelialization

Jacquelyn Dawn Parente 1 , Knut Möller 2 , Bala Amala Kannan 3 , Sabine Hensler 4 , Claudia Kuhlbach 4 , and Margareta M. Mueller 4
  • 1 Institute of Technical Medicine, Furtwangen University,, Furtwangen, Germany
  • 2 Institute of Technical Medicine, Furtwangen University,, Furtwangen, Germany
  • 3 Institute of Technical Medicine, Furtwangen University, Jakob-Kienzle-Straße 17,, Villingen-Schwenningen, Germany
  • 4 Molecular Cell Biology Laboratory and Institute of Technical Medicine, Furtwangen University,, Furtwangen, Germany

Abstract

Reepithelialization is the single requirement to define a wound as healed when the barrier function of the skin is restored. An existing reepithelialization mathematical model (RM) simulates wound healing in vitro. This work performs a parameter sensitivity analysis on an existing RM to see how robust the model is for changing wound healing rates for application to chronic wounds (inhibition) and wound healing therapies (activation). The existing RM balances the optimal distance between cells and basal membrane segments (BMs) according to the calculation of intercellular pressure and adhesion force. The RM mimics cell behavior and their interaction by passive migration, which is the displacement of cells from its initial position. First, this work reproduces the RM. The initial case recreates the interaction of a cell with its surrounding cells, while the second case recreates the interaction of the cell with its nearest BMs. These two cases were implemented in MATLAB to estimate optimal distance, intercellular pressure, an adhesive force between cells and the BMs. The analysis computes movement vectors and new positions of each cell at different time steps. Parameter sensitivity analysis was then conducted on the adhesion coefficient, where the original value in the RM was unknown. The results obtained at the assumed original parameter values are similar to the existing RM. As a result of the parameter sensitivity analysis, increasing the adhesion coefficient increases cell movement. High basal adhesion causes passive movement of cells, which in the simulation results is seen as a cellular movement towards wound closure. The existing RM is robust to changing adhesion coefficient values which change the rate of the advancing reepithelialization front. Future work includes fitting adhesion coefficient parameter values to an in vitro wounded tissue visualized by live dyes in treatment therapy experiments.

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