Analyses of non-Fourier heat conduction in 1-D spherical biological tissue based on dual-phase-lag bio-heat model using the conservation element/solution element (CE/SE) method: A numerical study

Abstract

Among the various numerical methods in solving the hyperbolic equation systems, methods that are simple, have higher accuracy, and avoid creating unwanted numerical oscillations along with having shorter runtime are preferred. In the present study, two numerical methods, space-time conservation element and solution element (CESE) as well as control volume (CV) method have been utilized to estimate temperature distribution in the spherical living tissue during laser irradiation. The results of the CESE method in simulating the non-Fourier thermal wave of the dual-phase-lag (DPL) model in spherical coordinates have been validated against the available semi-analytical results as well as the results obtained using the CV method. The good correlation between the results proved that the CESE method can be applied accurately in solving the DPL model thermal waves in spherical coordinates. In addition, the advantages of the CESE method over the CV method have been investigated. No numerical oscillations are detected in the temperature distribution obtained by the CESE method during and after exposure. Furthermore, in the same circumstances, in terms of radial grid size, a larger time step can be used in CESE method which reduces runtime. Examining the four non-Fourier models, hyperbolic, wavelike, diffusive, and over-diffusive, shows that the thermal wave occurs only in two of these models, hyperbolic and wavelike, when the phase lag of the heat flux is greater than the phase lag of the temperature gradient. After stopping laser irradiation, the maximum temperature is diffused from the surface of the tissue to its inner layers. The results proved that the speed of thermal wave progression is not only constant in hyperbolic and DPL models but also decreases in different tissues with the passage of time. Regardless of the type of tissue, the wave motion towards the center of the tissue in the hyperbolic model is greater than the DPL model. In addition, studying the thermal wave propagation speed in different tissues indicated that this parameter has a direct relationship with the thermal diffusivity of the tissues. The diffusion property caused by the temperature gradient phase lag in the DPL model is the reason why the wave expansion is greater than the hyperbolic model and why a wider range of the tissue is affected by the laser irradiation.