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

Abstract

First aid treatment of burns reduces scarring and improves healing. We quantify the efficacy of first aid treatments using a mathematical model to describe data from a series of in vivo porcine experiments. We study burn injuries that are subject to various first aid treatments. The treatments vary in the temperature and duration. Calibrating the mathematical model to the experimental data provides estimates of the thermal diffusivity, the rate at which thermal energy is lost to the blood, and the heat transfer coefficient controlling the loss of thermal energy at the interface of the fat and muscle. A limitation of working with in vivo experiments is the difficulty of measuring variations in temperature across the tissue layers. This limitation motivates us to use a simple, single layer mathematical model. Using the solution of the calibrated mathematical model we visualise the temperature distribution across the thickness of the tissue. With this information we propose a novel measure of the potential for tissue damage. This measure quantifies two important factors: (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.

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

“…We consider a stochastic model that describes the spatiotemporal diffusion of thermal energy in a heterogeneous, layered biological material. We are motivated by the experimental work of Andrews et al [21][22][23][24] who consider heat conduction through living, layered porcine skin, shown in Figure 1(a). Andrews' experiments are performed by placing a constant temperature external heat source at the surface of the skin, at the top of the epidermis.…”

“…Over time, thermal energy conducts across the epidermis and dermis, reaching the subdermal fat layer. Andrews et al [21][22][23][24] measure this heat conduction process in real time by obliquely inserting a temperature probe at the base of the fat layer. For example, the data in Figure 1(b) shows the result of an experiment where a constant heat source at 50 • C is placed at the top of the skin, and the subdermal temperature is measured at intervals of one second at the base of the fat layer.…”

“…This data suggests that the thermal disturbance at the surface of the layered skin takes approximately 14 seconds to affect the subdermal temperature. A key restriction of Andrews' experimental design is that the living tissues are relatively thin and the temperature probe can only be placed at a single location without destroying the integrity of the living tissue [21][22][23][24]. Given that Andrews' data takes the form of a time series of temperature data recorded at the base of the fat layer, a key quantity of interest is to measure the duration of time required for the temperature at the base of the fat layer to respond to the thermal disturbance at the surface of the layered skin.…”

“…Given that Andrews' data takes the form of a time series of temperature data recorded at the base of the fat layer, a key quantity of interest is to measure the duration of time required for the temperature at the base of the fat layer to respond to the thermal disturbance at the surface of the layered skin. While Andrews' experiments focus on diffusive transport of thermal energy in layered biological material [21][22][23][24], a very similar experimental design could be used to measure the chemical diffusion of dissolved solutes through skin and other heterogeneous, layered media, with broad applications including cutaneous drug delivery [26] as well as the design of landfill liners for the storage of industrial waste [27,28]. Some of our previous modelling work attempted to calibrate the solution of deterministic partial differential equation models of heat transfer to match the kind of data reported by Andrews et al [21,22].…”

“…To address this question, here we mimic the kind of data reported by Andrews et al [21] using a simple stochastic random walk model of heat conduction in a one-dimensional layered material. [23] highlighting the layered structure of the tissue, including the epidermis, dermis and fat layers, as indicated. (b) Experimental data from Andrews et al [21] showing the subdermal temperature response after a constant heat source at 50 • C is placed on the surface of the skin.…”