Analytical Solution to the Transient 1D Bioheat Equation in a Multilayer Region with Spatial Dependent Heat Sources

Dário B. Rodrigues, Pedro J. d.S. Pereira, Paulo M. Limão-Vieira, and Paolo F. Maccarini


Modelling, Bioheat transfer equation, Method of separation of variables, Magnetic fluid hyperthermia


An analytical solution given by Bessel series to the transient and one-dimensional (1D) bio heat equation in a multilayer region with spatial dependent heat sources is derived. Multilayer regions with 1D Cartesian, cylindrical or spherical geometries and composed of different types of biological tissues characterized by temperature-invariant physiological parameters are considered. Boundary conditions of first, second and third kinds to the temperature at the inner and outer surfaces are also assumed. In this work, the bio heat transfer model is applied to obtain the temperature profiles in a tumour bed and a surrounding healthy tissue using two spatial dependent heat source terms to simulate a magnetic fluid hyperthermia technique in the cancer treatment. The influence of these two heat sources, described by polynomial and exponential functions, on temperature is investigated.

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