Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments

First aid treatment of burn injuries reduces scarring and improves healing. Here, we quantify the efficacy of various first aid treatments by using a mathematical model to describe a suite of experimental data from a series of in vivo porcine experiments. We study a series of consistent burn injuries that are subject to first aid treatments that vary in both the temperature and duration of the first aid treatment. Calibrating the mathematical model to the experimental data provides estimates of the in vivo thermal diffusivity, the rate at which thermal energy is lost to the blood (perfusion), and the heat transfer coefficient controlling the loss of thermal energy at the interface of the fat and muscle layers. A limitation of working with in vivo animal experiments is the difficulty of resolving spatial variations in temperature across the tissues. Here, we use the solution of the calibrated mathematical model to predict and visualise the temperature distribution across the thickness of the tissue during the creation of the burn injury and the application of various first aid treatments. Using this information we propose, and report values for, a novel measure of the potential for tissue damage. This measure quantifies two important aspects that are thought to be related to thermal injury: (i) the volume of tissue that rises above the threshold temperature associated with the accumulation of tissue damage; and, (ii) the duration of time that the tissue remains above this threshold temperature. We conclude by discussing the clinical relevance of our findings.