Mathematical Modelling of Angiogenesis in Wound Healing: Comparison of Theory and Experiment

Abstract

In this paper we present a simple mathematical model for angiogenesis in wound healing and then compare the results of theoretical predictions from computer simulations with actual experimental data. Numerical simulations of the model equations exhibit many of the characteristic features of wound healing in soft tissue. For example, the steady propagation of the wound healing unit through the wound space, the development of a dense band of capillaries near the leading edge of the unit, and the elevated vessel density associated with newly healed wounds, prior to vascular remodelling, are all discernible from the simulations. The qualitative accuracy of the initial model is assessed by comparing the numerical results with independent clinical measurements that show how the surface area of a range of wounds changes over time. The model is subsequently modified to include the effect of vascular remodelling and its impact on the spatio-temporal structure of the vascular network investigated. Predictions are made concerning the effect that changes in physical parameters have on the healing process and also regarding the manner in which remodelling is initiated.