Exact Analytical Formulation of Three-Dimensional Pennes Bioheat Model in Regional Hyperthermia with Modified Initial Condition

Abstract

The present research work is intended to develop an exact analytical solution of three-dimensional Pennes bioheat model subjected to regional hyperthermia. Existing literature survey indicates that a large number of research papers have been reported in one-dimensional and two-dimensional approaches, but researchers have rarely focused on three-dimensional modelling apart from a few. In practical sense, energy always propagates in multi-dimensional manner; hence, three-dimensional analysis would be considered as better approach in comparison with existing one and two-dimensional investigation particularly for living tissues. Living tissues are highly susceptible to temperature variation. As suggested by the treatment protocol of thermal therapy, regional hyperthermia occurs in large-sized organs (prostrate, breast, lung, etc.) which are deep seated inside the human body and in such cases three-dimensional analysis is essential. To solve three-dimensional Pennes bioheat model, a hybrid analytical scheme comprising of ‘shift of variables’ and ‘finite Fourier transform’ has been employed in the present research paper. The prime novelty of this research work is implementation of spatially dependent initial condition as highly non-homogeneous and non-uniform anatomical structures are observed in living tissues, whereas existing research work has been carried out on the constant temperature initial condition. The boundary conditions are imposed in the present modelling in relation with the realistic approach subjected to thermal therapies. The research output has been validated and justified with the published numerical research work, and it indicates the maximum temperature deviation of 0.215%.