Abstract 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.

中文翻译：

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使用实验数据参数化异质活体皮肤传热的连续模型

摘要 在这项工作中，我们考虑了描述活猪组织热传导的最新实验数据集。了解这个新数据集很重要，因为猪皮肤与人类皮肤相似。提高我们对活体皮肤热传导的理解与了解烧伤有关，烧伤是常见的、痛苦的并且可能需要长期和昂贵的治疗。皮肤的一个关键特征是它是分层的，不同层具有不同的热性能。由于实验数据集涉及麻醉动物薄活组织中的热传导，一个重要的实验约束是活组织内的温度是在分层结构内的一个空间位置测量的。我们的目标是确定这些数据是否足以可靠地推断分层皮肤中的热传导参数，我们使用简化的两层热传导数学模型来模拟实验数据的生成。使用在两层数学模型中的一个位置生成的合成数据，我们探索是否可以推断出两层中的热扩散率值。在初步探索之后，我们然后检查了当我们改变记录实验数据的位置时我们推断热扩散率的能力如何变化，并考虑我们能够监测分层内两个位置的温度的情况结构体。全面的，我们发现，我们使用有限的实验数据对异质热传导模型进行参数化的能力对收集数据的位置非常敏感。我们的建模结果为优化实验设计提供了指导，可用于指导未来的实验研究。