Reduced-Order Modeling of Pennes' Bioheat Equation for Thermal Dose Analysis

Abstract

Current trends in powered wearable technologies show that users are spending more time than ever in contact with their devices. Users now wear devices such as smartwatches and fitness trackers up to 24 hours per day to make use of ubiquitous health, exercise, and sleep-tracking features. Long duration contact with these heat dissipating devices increases the thermal dose delivered to user's the skin tissues. Methods for accurate, real-time prediction of the time-temperature response of the skin based on device heat dissipation and external conditions are needed to characterize and monitor the thermal dose received by the user. This article presents methods for building reduced-order models (ROMs) based on proper orthogonal decomposition (POD) for modeling transient heat transfer in partially-perfuse tissue in prolonged contact with a heat-generating wearable device. ROMs generated using this methodology are able to provide fast, accurate temperature forecasts for arbitrary time-varying boundary conditions, heat sources, and environmental conditions given an appropriate set of training data. The solution of these reduced-order models is shown to be over an order of magnitude faster than a finite-volume implementation of the same scenario, even in one spatial dimension.