Exact analysis based on BDLTNE approach for thermal behaviour in living tissues during regional hyperthermia therapy

The present work highlights the attempt to develop a two-dimensional mathematical modelling of thermal characteristics in malignant tissues under a regional hyperthermia therapy based on the bi-dimensional local thermal non-equilibrium bioheat model. In the arena of biological heat transfer, a local thermal non-equilibrium model is preferred over a local thermal equilibrium approach, as skin tissues are a combination of highly non-uniform non-homogeneous structure of fluid and solid media (porous structure). The solution of the thermal response has been determined analytically by employing a ‘hybrid scheme’ composed of ‘shift of variables’ and ‘finite integral transform’ with the therapeutic boundary conditions and actual local coordinates dependent on the initial condition. The thermal behavioural study has been conducted with the influence of oscillating and constant heat flux imposed on the exposed surface of the diseased tissue. The results have been validated with the published experimental work. From the research output, it has been noticed that the sinusoidal therapeutic heat flux is better for the longer time of treatment in comparison with the constant heat flux heating. The treatment protocols of regional hyperthermia suggest that the size of the affected tissue (or organ) is larger in comparison with the localized hyperthermia. Hence, the multi-dimensional modelling should give better glimpse of results than the 1-D form of analysis. From the constructed 2-D thermal contours, it may be noted under the regional hyperthermia circumstance that the heat propagation in the living tissue is in two-directional nature, and thus 2-D analysis is necessary for predicting an accurate temperature response. The present analysis also highlights that a temperature range of 38–44 \(^\circ {\hbox {C}}\) is possible to maintain in a prolonged therapeutic exposure time instead of maintaining \(50\,^\circ {\hbox {C}}\) for 30 min described in the existing literature. Hence, this positive aspect obtained in the present work can avoid the collateral damage of healthy tissues in human bodies during the regional hyperthermia therapy.