Fractional thermal wave bio-heat equation based analysis for living biological tissue with non-Fourier Neumann boundary condition in laser pulse heating

In the present paper, the different heat transfer mechanisms in living biological tissue during pulse laser irradiation are studied with the fractional thermal wave bio-heat transfer (FTWBT) equation, the thermal wave bio-heat transfer (TWBT) equation and the Pennes bio-heat transfer (PBT) equation, respectively. The corresponding non-Fourier boundary condition is established and the analytical solutions based on the three models are obtained by employing the Fourier and Laplace transform methods. The heat wave propagation characteristics in biological tissues are revealed and discussed in detail. The results show that the FTWBT model has advantages over the others to describe the bio-heat transfer in laser therapy as long as the boundary condition is correct. The heat transfer predicted by the FTWBT model reveals the thermal diffusion feature as well as the thermal wave behavior, which is dependent on the fractional order parameter and biological tissue relaxation time.