Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A Mathematical Model for the Interaction of the Proteins MMP-1, TIMP-1, and ECM in a Wound
Hannah Pennington, Nitin Krishna, Richard Schugart, Canaan Coppola

Last modified: 2014-03-31


In this talk, we will discuss a mathematical model describing interactions among matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and extracellular matrix (ECM) in the healing of a diabetic foot ulcer. De-identified data for modeling were taken from Muller et al. 2008, a research outcome that collected average physiological data for two patient subgroups: “good healers” and “poor healers,” where classification was based on rate of ulcer healing. MATLAB’s GlobalSearch and fmincon routines were used to estimate parameter values by minimizing the least-squares residual between collected data and model output.  A steady-state analysis identified which end-states the proteins tended to as time approached infinity. Sensitivity analyses numerically measured to what degree the model was affected by slight changes in one or several parameter values. A Latin-Hypercube Method sensitivity analysis identified insensitive parameters, or parameters whose changes had negligible effects on the model.  The developed model has the potential for application in clinical studies, such as identifying treatment regimens for an individual patient not included in the modeling process.


Wound Healing; Sensitivity Analysis; Least-Squares Method; Protein Data; Diabetic Foot Ulcers