Analysis of the time-space fractional bioheat transfer equation for biological tissues during laser irradiation

Laser technology has been widely used in biomedical therapies and external surgeries. To promote its applications, a good thermal model is required to analyze the temperature distribution within the living tissues. In this paper, we develop a time-space fractional hyperbolic bioheat transfer model to study the non-Fourier bioheat transfer process within the living biological tissues during laser irradiation. Based on the the L1 approximation for the Caputo time fractional derivative and the central difference scheme for the Riesz fractional derivative, the finite difference algorithm is developed for the laser irradiation problem. The efficiency and accuracy of this method have been verified by using three numerical examples. In view of the thermophysical properties of the biological tissues, the effect of time and space fractional parameters, phase lag time and blood perfusion rate on temperature distribution within living biological tissues have been analyzed and shown graphically.