Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source

Abstract

In this paper, the temperature distribution in a finite biological tissue in presence of metabolic and external heat source when the surface subjected to different type of boundary conditions is studied. Classical Fourier, single-phase-lag (SPL) and dual-phase-lag (DPL) models were developed for bio-heat transfer in biological tissues. The analytical solution obtained for all the three models using Laplace transform technique and results are compared. The effect of the variability of different parameters such as relaxation time, metabolic heat source, spatial heat source, different type boundary conditions on temperature distribution in different type of the tissues like muscle, tumor, fat, dermis and subcutaneous based on three models are analyzed and discussed in detail. The result obtained in three models is compared with experimental observation of Stolwijk and Hardy (Pflug Arch 291:129-162, 1966). It has been observe that the DPL bio-heat transfer model provides better result in comparison of other two models. The value of metabolic and spatial heat source in boundary condition of first, second and third kind for different type of thermal therapies are evaluated.

Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy

“…Dombrovsky et al [6] derived an advanced thermal model for indirect heating strategy for laser induced hyperthermia. Kumar et al [29] compared the results obtained by PBHT, TWBHT, DPLBHT models with experimental results of Stolwijik and Hardy [30] and found that experimental data is close with DPLBHT model. Conventionally various numerical methods [31] such as finite difference method [32] , finite difference-decom position method [33] , finite volume method [5] , smoothed particle hydrodynamics method [34] or commercial softwares like COMSOL [24] are available in literature for solving bioheat equations.…”

An improved analytical model for heat flow in cancerous tumours to avoid thermal injuries during hyperthermia

“…It might be difficult to implement a classical analytical method for solving higher-order mixed partial derivatives. 37 Hence to deal with such situations ‘hybrid’ scheme may be effective. It is a combination of two different approaches either analytical-analytical or analytical-numerical.…”

A Fibonacci Wavelet Method for Solving Dual-Phase-Lag Heat Transfer Model in Multi-Layer Skin Tissue during Hyperthermia Treatment

“…Finding the analytical and numerical solutions of the DPL model ( 3) is one of the prime research areas in mathematical, biological, and thermal sciences. Some of the commonly employed numerical techniques for obtaining the solution of model (3) include the finite volume method [16], the Laplace transform method [17], the boundary element method [18], the finite difference-decomposition method [19], the Adomian decomposition method [20], and the B-spline method [21]. Some of the compelling alternatives of the aforementioned numerical techniques include the wavelet-based numerical methods.…”