Analytical solutions of fractional bioheat model in a spherical tissue

Abstract

In this paper, the bio-heat model with fractional derivative is established to study the variations of temperature and the thermal damage in spherical tissues during thermal therapy. Easily, the exact solution in the domain of Laplace are obtained. The effects of a fractional parameter, the blood perfusion and the laser exposure time on the temperature of living tissue and the resulting of thermal damages are studied. The results display that bio-heat model with the fractional derivative is reduced to parabolic and the hyperbolic bio-heat models when the thermal relaxation time is equal to zero and the fractional parameter is equivalent to one respectively. The numerical outcomes of thermal damage and temperatures are graphically introduced.

Keywords:

• Spherical tissues
• thermal damages
• fractional derivative
• Laplace transforms

Additional information

Funding

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No (DF-431-130-1441). The authors, therefore, gratefully acknowledge the DSR technical and financial support.