A wavelet approach for the variable-order fractional model of ultra-short pulsed laser therapy

Abstract

In this paper, the ultra-short pulsed laser treatment is numerically simulated for a focused laser beam applied to a cylindrical domain. To do so, the general form of the variable-order fractional-order, dual-phase lag bioheat transfer equation is implemented. To determine the major affecting parameters, the dimensionless form of the heat equation is derived and solved numerically. An efficient method based on the 2D Legendre wavelets is developed to provide a numerical solution for this variable-order time fractional model. The man advantage of the proposed algorithm is that it converts the solution of the problem into solution of a system of algebraic equations. The validity of the formulated method is investigated through one numerical example. The effect of several operational and thermo-physical properties including the phase lag time, fractional order, and the duration of active laser beam in each on/off cycle on the thermal field and heat penetration depth is examined. According to the results, it is concluded that by increasing the fractional order from 0.1 to 0.9, 65.1% increase in the penetration length occurs.