The Dynamics of a Healing Wound

Rebecca Segal, Virginia Commonwealth University

Emergency room physicians do not understand why patients with similar traumas experience different outcomes (up to and including death.) An extensive series of human subject tests are being conducted at the VCU Medical Center to improve the understanding of the complex biochemical and cellular processes which are involved in the mechanics of healing a wound. We plan to use mathematical models in conjunction with the experiments to shed light on which processes are most important in healing and why negative outcomes are observed.

Two modeling paradigms are being used to attack the problem. The first is an ODE model describing the healing of a local wound which includes a parameter for a systemic oxygen level. This is the first step to understand the role systemic parameters (such as cortisol and estrogen) will play in predicting the outcome of the wound and of the patient. The second model is a PDE based model to analyze spatial cell migration. The experimental study is using porous tubes to collect migrating cells and this model aims to capture cell migration under chemotaxis through the porous medium.