Analytical Temperature Distribution in a Multi-Layer Tissue Structure in the Presence of a Tumor

Analytical study of bioheat transfer is of significant importance for a number of biomedical applications including cryopreservation of tissue and thermal therapy for cancer. A sound fundamental understanding of thermal behavior of tissue in response to an externally applied stimulus helps design effective therapies and protocols. This paper derives an analytical solution in a multi-layer two-dimensional structure with arbitrary, space-dependent heat generation occurring in each layer. This geometry effectively models multiple layers of skin, with heat generation due to cancerous cells in the basal layer. The Pennes bioheat transfer equation is solved for the multi-layer analytically, wherein the temperature in each layer is explicitly a function of space and the thermo-physical properties of the layer. The resulting analytical temperature profile agrees well with finite-element simulations and is also in good agreement with a previously published experimental study. Results derived in this work illustrate the effect of the presence of cancerous cells on the thermal profile of the skin. Further, the model helps to understand the effect of external cooling and heating stimuli.