Mathematically modelling the role of Matrix Metalloproteinases in the development of chronic wounds #

Sonia Dari

12:10 Tuesday in 3Q68.

Part of the Mathematical medicine session.

Abstract #

Understanding the biochemistry and pharmacology that underpins chronic wounds and wound healing is of high importance as there are over 2 million people in the UK suffering from chronic wounds. In particular, chronic wounds are susceptible to high levels of Matrix Metalloproteinases (MMPs), which are responsible for the modification and proliferation of healthy tissue. High concentrations of MMPs however cease to be beneficial and can lead to the destruction of the healthy tissue. In this talk, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe a hysteresis effect when apoptotic rates are varied, providing further insight into the management (and potential reversal) of chronic wounds.