Iterative Rational Krylov Algorithm (IRKA) for Modelling Dynamic Temperature Distribution in Epidermal Temperature Sensors

Abstract

Accurate skin temperature measurement can offer clinically useful data regarding cardiovascular health, cognitive function, cancer risk, and many other aspects of human physiology together with other measurements [36]. Skin thermometry has several uses in medicine, athletics, and research. Subsequently understanding the skin structure and its response to diverse sorts of signals is essential to design efficient and robust skin sensors. There are various devices available for skin temperature measurement for example contact thermometers, infrared cameras, surface probes and others but they offer limitations like discomfort, thermal loading, limited accuracy, one-point measurement, longer response time, are invasive and others. Epidermal sensors are a type of non-invasive wearable sensors that are designed to be placed onto the skin’s surface, and are flexible, thin, that are attached to the skin like a temporary tattoo or bandage without any thermal and mechanical burden. They utilise temperature coefficient of resistance (TCR) to monitor temperature of the human skin. The TCR sensor comprises gold elements encapsulated between two layers of polyimide thin films integrated onto a thin elastomeric sheet. The design of a high performance TCR sensor requires modelling of temperature distribution and the response time. Analytical solutions of partial differential equations (PDEs) are only available for simple geometries while for complex structures like the TCR sensor numerical approach (finite difference/finite element) for solving the governing equation is used. Though finite element method (FEM) simulations provide an effective tool for modelling purposes, they are computationally complex, in particular, for spatial mapping of temperature using sensor arrays. Therefore, for an effective and time-efficient design of TCR sensors, model order reduction (MOR) of the heat equation offers an alternative approach. Here, in order to circumvent the challenge, we propose Iterative Rational Krylov Algorithm (IRKA) based MOR for modelling the temperature distribution and the time response of the epidermal TCR sensors. The comparison with xii List of Tables FEM simulations reveals that the IRKA based MOR offers similar accuracy with much lower computational cost as it remarkably computes the temperature distribution in a 3 orders of magnitude lesser time than the FEM simulations. IRKA based modelling of the temperature dynamics presents a promising approach for time efficient design of epidermal TCR sensors for biomedical applications.