In this work we consider a recent experimental data set describing heat conduction in living porcine tissues. Understanding this novel data set is important because porcine skin is similar to human skin. Improving our understanding of heat conduction in living skin is relevant to understanding burn injuries, which are common, painful and can require prolonged and expensive treatment. A key feature of skin is that it is layered, with different thermal properties in different layers. Since the experimental data set involves heat conduction in thin living tissues of anesthetised animals, an important experimental constraint is that the temperature within the living tissue is measured at one spatial location within the layered structure. Our aim is to determine whether this data is sufficient to reliably infer the heat conduction parameters in layered skin, and we use a simplified two-layer mathematical model of heat conduction to mimic the generation of experimental data. Using synthetic data generated at one location in the two-layer mathematical model, we explore whether it is possible to infer values of the thermal diffusivity in both layers. After this initial exploration, we then examine how our ability to infer the thermal diffusivities changes when we vary the location at which the experimental data is recorded, as well as considering the situation where we are able to monitor the temperature at two locations within the layered structure. Overall, we find that our ability to parameterise a model of heterogeneous heat conduction with limited experimental data is very sensitive to the location where data is collected. Our modelling results provide guidance about optimal experimental design that could be used to guide future experimental studies.

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. Accidental burn injuries occur most frequently in children, and are a major cause of injury worldwide 1 . Burn injuries worsen after the initial insult 2 , as thermal energy and associated tissue destruction spreads into surrounding tissues. However, if first aid treatment is administered immediately at the scene or prior to qualified medical treatment, burn patients have improved healing outcomes 3 . Optimal first aid treatment conditions have been previously determined using standardised, controlled porcine burn models [4][5][6][7] . Porcine models are used because pig skin is anatomically and physiologically similar to human skin 8,9 , and pig skin responds to therapeutic agents in a similar way to human skin 10 . Recommended first aid treatment is the immediate administration of cool, running water for 20 minutes. This decreases tissue injury, increases the rate of wound healing and reduces scarring 4,6,7,11 . Ethically and morally, there is a limit to the number of different burn and treatment conditions that can be tested using live animals. Therefore, animal experiments cannot be used to examine all potential treatment temperatures and durations.In this work we use a porcine burn model, illustrated in Fig. 1, to study a series of standardised burns created by exposing the surface of the skin to a temperature of 92 °C for 15 seconds. The propagation of thermal energy through the skin is observed by measuring the temperature under the skin using a subdermal temperature probe. Using this approach we examine the effects of various first aid treatments by applying cooling water of various temperatures (0, 2 and 15 °C), for different durations (10, 20, 30 and 60 minutes). This data set provides a wealth of information about how thermal energy propagates through the skin, and clearly illustrates that different first aid treatments have a measurable effect. However, taken in isolation, even a high-quality reproducible experimental data set such as this does not provide sufficient information to quantify the efficacy of different first aid treatments as this requires more detailed spatial and temporal information about the propagation of thermal energy through the skin.To address this gap in our knowledge we examine a suite of experimental data describing the effect of various first aid treatment strategies using a mathematical model that describes the spatial and temporal distribution of thermal energy within the ski...

5In this work we consider a recent experimental data set describing heat conduction in living porcine tissues. Understanding this novel data set is important because porcine skin is similar to human skin. Improving our understanding of heat conduction in living skin is relevant to understanding burn injuries, which are common, painful and can require prolonged and expensive treatment. A key feature of skin is that it is layered, with different thermal properties in different layers. Since the experimental data set involves heat conduction in thin living tissues of anesthetised animals, an important experimental constraint is that the temperature within the living tissue is measured at one spatial location within the layered structure. Our aim is to determine whether this data is sufficient to reliably infer the heat conduction parameters in layered skin, and we use a simplified two-layer mathematical model of heat conduction to mimic the generation of experimental data. Using synthetic data generated at one location in the two-layer mathematical model, we explore whether it is possible to infer values of the thermal diffusivity in both layers. After this initial exploration, we then examine how our ability to infer the thermal diffusivities changes when we vary the location at which the experimental data is recorded, as well as considering the situation where we are able to monitor the temperature at two locations within the layered structure. Overall, we find that our ability to parameterise a model of heterogeneous heat conduction with limited experimental data is very sensitive to the location where data is collected. Our modelling results provide guidance about optimal experimental design that could be used to guide future experimental studies.Injuries caused by accidental exposure to hot liquids are common, painful and often require extensive long-term 11 treatment [1]. To improve our understanding of how thermal energy propagates through human skin, experimental 12 studies often work with porcine (pig) skin because porcine skin is anatomically similar to human skin [2][3][4][5][6][7][8]. Many 13 experimental studies deal with heat conduction in excised non-living tissues [6, 7, 9, 10]. In contrast, the experimental 14 protocols developed by Cuttle and colleagues [11][12][13][14] are unique because they quantify heat conduction in living 15 porcine tissues. Working with living tissues is far more biologically relevant than working with excised non-living 16 tissues. Cuttle's experimental protocol involves working with anesthetised living pigs that are given analgesia. A 17 thermocouple probe, referred to as the subdermal probe, is inserted obliquely under the skin of the animal at various 18 locations on the body [11][12][13][14]. To initiate an experiment, a cylindrical scald creation device is placed onto the surface 19 of the skin so that the centre of the circular scald device is above the subdermal probe. Pre-heated water is pumped 20 into the scald device and suctioned out of the device at an equal rat...

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.