A novel distributed-order time fractional derivative model of laser-induced thermal therapy for deep-lying tumor

The laser-induced thermal therapy (LITT) scheme has proved great efficacy in tumor treatment. Therefore, the research between the heat conduction problems of LITT has become a hot topic in recent years. To seek rational constitutive relations of heat flux and temperature which can describe the heat transfer behavior of LITT, we develop a novel distributed-order time fractional derivative model based on the dual-phase-lag (DPL) model and Pennes bio-heat conduction model in this paper. Physical parameters of the governing equation are approximated using experimental data. Formulated model considers a spectrum of memory and nonlocal characteristics based on the DPL model. Distributed-order integrals are approximated by the summation of multi-fractional terms and fractional derivatives are discretized by the L1 scheme. Source item is introduced into the governing equation to verify the correctness of the numerical methods. The influences of the physical parameters on the tissue temperature are discussed and analyzed in details. Results demonstrate that the proposed model truly performs better compared to the classical Fourier's law and DPL model in describing the heat conduction behavior of LITT.