Hybrid integral transforms analysis of the bioheat equation with variable properties

Pennes' equation is the most frequently employed model to describe heat transfer processes within living tissues, with numerous applications in clinical diagnostics and thermal treatments. A number of analytical solutions were provided in the literature that represent the temperature distribution across tissue structures, but considering simplifying assumptions such as uniform and linear thermophysical properties and blood perfusion rates. The present work thus advances such analysis path by considering a heterogeneous medium formulation that allows for spatially variable parameters across the tissue thickness. Besides, the eventual variation of blood perfusion rates with temperature is also accounted for in the proposed model. The Generalized Integral Transform Technique (GITT) is employed to yield a hybrid numerical-analytical solution of the bioheat model in heterogeneous media, which reduces to the exact solution obtained via the Classical Integral Transform Method for a linear formulation with uniform coefficients. The open source UNIT code (“UNified Integral Transforms”) is utilized to obtain numerical results for a set of typical values of the governing parameters, in order to illustrate the convergence behavior of the proposed eigenfunction expansions and inspect the importance of accounting for spatially variable properties in predicting the thermal response of living tissues to external stimulus.