Modeling of heat transfer in breast by modified Pennes equation

2019 ◽  
Author(s):  
A. Rogotnev ◽  
A. Nikitiuk ◽  
O. Naimark ◽  
V. Grishko
Keyword(s):  
Heat Transfer ◽  
Pennes Equation

scholarly journals Solving bio-heat transfer multi-layer equation using Green’s Functions method

2021 ◽  
Vol 2090 (1) ◽  
pp. 012150
Author(s):  
de Oliveira Eduardo Peixoto ◽  
Gilmar Guimaräes
Keyword(s):  
Heat Transfer ◽  
Green's Functions ◽  
Green’S Functions ◽  
Transfer Problem ◽  
Blood Perfusion ◽  
The Body ◽  
Mathematical Background ◽  
Number Of Layers ◽  
Pennes Equation ◽  
Transfer Problems

Abstract An analytical method using Green’s Functions for obtaining solutions in bio-heat transfer problems, modeled by Pennes’ Equation, is presented. Mathematical background on how treating Pennes’ equation and its μ2T term is shown, and two contributions to the classical numbering system in heat conduction are proposed: inclusion of terms to specify the presence of the fin term, μ2T, and identify the biological heat transfer problem. The presentation of the solution is made for a general multi-layer domain, deriving and showing general approaches and Green’s Functions for such n number of layers. Numerical examples are presented to simplify human skin as a two-layer domain: dermis and epidermis, accounting metabolism as a heat source, and blood perfusion only at the dermis. Time-independent summations in the series-solution are written in closed forms, leading to better convergence along the boundaries. Details on obtaining the two-layer solution and its eigenvalues are presented for boundary conditions of prescribed temperature inside the body and convection at the surface, such as its intrinsic verification.

scholarly journals Modifed pennes' equation modelling bio-heat transfer in living tissues: analytical and numerical analysis

2010 ◽  
Vol 02 (12) ◽  
pp. 1375-1385 ◽  
Author(s):  
Ahmed Lakhssassi ◽  
Emmanuel Kengne ◽  
Hicham Semmaoui
Keyword(s):  
Heat Transfer ◽  
Numerical Analysis ◽  
Equation Modelling ◽  
Pennes Equation ◽  
Living Tissues

An Evaluation of the Weinbaum-Jiji Bioheat Equation for Normal and Hyperthermic Conditions

1990 ◽  
Vol 112 (1) ◽  
pp. 80-87 ◽  
Author(s):  
C. K. Charny ◽  
S. Weinbaum ◽  
R. L. Levin
Keyword(s):  
Heat Transfer ◽  
Transfer Equation ◽  
First Generation ◽  
Source Term ◽  
Equation Model ◽  
Bioheat Transfer ◽  
Bioheat Equation ◽  
Starting Point ◽  
Pennes Equation ◽  
Bioheat Transfer Equation

The predictions of the simplified Weinbaum-Jiji (WJ) bioheat transfer equation in one dimension are compared to those of the complete one-dimensional three-equation model that represented the starting point for the derivation of the WJ equation, as well as results obtained using the traditional bioheat transfer equation of Pennes [6]. The WJ equation provides very good agreement with the three-equation model for vascular generations 2 to 9, which are located in the outer half of the muscle layer, where the paired vessel diameters are less than 500 μm, under basal blood flow conditions. At the same time, the Pennes equation yields a better description of heat transfer in the first generation, where the vessels’ diameters are greater than 500 μm and ε, the vessels’ normalized thermal equilibration length, is greater than 0.3. These results were obtained under both normothermic and hyperthermic conditions. A new conceptual view of the blood source term in the Pennes equation has emerged from these results. This source term, which was originally intended to represent an isotropic heat source in the capillaries, is shown to describe instead the heat transfer from the largest countercurrent microvessels to the tissue due to small vessel bleed-off. The WJ equation includes this effect, but significantly overestimates the second type of tissue heat transfer, countercurrent convective heat transfer, when ε > 0.3. Indications are that a “hybrid” model that applies the Pennes equation in the first generation (normothermic) and first two to three generations (after onset of hyperthermia) and the Weinbaum-Jiji equation in the subsequent generations would be most appropriate for simulations of bioheat transfer in perfused tissue.

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