A revised mathematical solution to the Penne bioheat equation for deep rooted tissues using the variable separation method

Abstract

The temperature distribution of tissues under the skin surface was obtained using Penne’s bio-heat equation and the separation of variables technique. The resulting solution indicated a slight temperature difference between the recorded skin temperature and the temperature of the tissue of interest (TOI), which is a direct indication of the TOI's temperature. According to the graphical analysis, temperature is proportionally related to time and tissue distance from the skin surface. As a result, the given analytic solution may be utilized to easily analyze deeprooted tissues while accounting for thermal properties.