Bio-heat response of skin tissue based on three-phase-lag model

Abstract

In this article, the thermal response of skin tissue is investigated based on three-phase-lag (TPL) model of heat conduction. The governing equation of bio-heat conduction is established by introducing both the TPL model of heat conduction and a modified energy conservation equation. The analytical solution is obtained by adopting the method of separation of variables and a parametric study on temperature responses in TPL model is carried out. It is shown that the TPL model can predict both the diffusion and wave characteristics of bio-heat conduction. Increasing the phase-lag of thermal displacement gradient would result in the rise of thermal propagation speed and decrease the temperature in affected zone. The perfusion rate of arterial blood has no obvious effect on thermal propagation velocity and thermal propagation lagging. Increasing of the rate of blood perfusion contributes to decreasing the temperature of steady state.

Three-Phase-Lag Bio-Heat Transfer Model of Cardiac Ablation

“…The developed TPL model has been validated with the results of one of the recent studies [33] that provides the analytical solution for the bio-heat response of skin tissue based on the TPL model. In particular, the same parameters and boundary conditions of [33] have been utilized, viz., outer skin surface temperature = 80 • C, arterial blood temperature = 37 • C, thickness of the tissue = 9 mm, density of the tissue = 1190 kg/m 3 , specific heat capacity of tissue = 3600 J/kg/K, density of the blood = 1060 kg/m 3 , specific heat capacity of the blood = 3770 J/kg/K, the blood perfusion rate = 1.87 × 10 −3 s −1 , thermal conductivity of the tissue = 0.235 W/m/K, the rate of thermal conductivity = 0.1 W/m/K/s, phase lag associated with heat flux = 16 s, phase lag associated with temperature gradient = 6 s, and the phase lag associated with thermal displacement gradient = 2 s. The comparative analysis of the present results with that of [33] is presented in Figure 2. As evident from Figure 2, a good agreement has been obtained between the results predicted from the present model with those reported in [33].…”

“…v = T, and k * is the rate of thermal conductivity. After some mathematical manipulations of Equation ( 7) combined with Equation (2), the following constitutive equation for TPL can be obtained [33]:…”

“…No-slip boundary conditions were imposed on the wall of the applicator in the cardiac chamber as well as the tissue-fluid interface. The thermophysical properties of cardiac tissue considered in the present study were: ρ = 1060 kg/m 3 , c = 3111 J/kg/K, ρ b = 1000 kg/m 3 , c b = 4180 J/kg/K, ω b = 0.017 s −1 , k = 0.54 W/m/K, k* = 0.1 W/m/K/s, τ q = 16 s, τ T = 6 s and τ v = 2 s [19,33,[43][44][45]58]. The computational domain presented in Figure 1b was discretized using the heterogeneous tetrahedral mesh elements with additional refinements close to the applicator where higher thermal gradients were ex-pected.…”

“…More recently, a three-phaselag (TPL) heat transfer model was applied in biological tissue, accounting for the phase lags associated with the heat flux vector, temperature gradient, and thermal displacement gradient, as proposed by Choudhuri [30], based on the thermoelasticity model developed by Green and Naghdi [31,32]. Zhang et al [33] have reported the first study utilizing the TPL model in biological tissue to quantify the heat response of the skin, adopting the method of separation of variables to obtain the analytical solution of temperature distributions. Later, the TPL bio-heat transfer model was successfully applied and reported in other recent studies [34][35][36].…”

Numerical simulation of three‐phase‐lag bio‐heat transfer model for generalized coordinate system amidst thermal ablation

“…Kumar and Rai 15 proposed a TPL heat transfer model to depict the thermal behavior inside the tissue. Recently, Zhang et al 16 studied the thermal response and parametric analysis within the skin tissue by using the TPL model of conduction. Also, Kumar et al 17 investigated the temperature profile inside the skin tissue for different coordinate systems by utilizing the DPL heat‐transmitting model amidst thermal therapy.…”