EXACT ANALYTICAL SOLUTION OF BIOHEAT EQUATION SUBJECTED TO INTENSIVE MOVING HEAT SOURCE

2017 ◽  
Vol 17 (05) ◽  
pp. 1750081 ◽  
Author(s):  
MOHAMMAD REZA TALAEE ◽  
ALI KABIRI
Keyword(s):  
Analytical Solution ◽  
Heat Source ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Blood Perfusion ◽  
Temperature Profiles ◽  
Moving Heat Source ◽  
Bioheat Equation ◽  
Line Heat Source ◽  
Moving Line

Presented is the analytical solution of Pennes bio-heat equation, under localized moving heat source. The thermal behavior of one-dimensional (1D) nonhomogeneous layer of biological tissue is considered with blood perfusion term and modeled under the effect of concentric moving line heat source. The procedure of the solution is Eigen function expansion. The temperature profiles are calculated for three tissues of liver, kidney, and skin. Behavior of temperature profiles are studied parametrically due to the different moving speeds. The analytical solution can be used as a verification branch for studying the practical operations such as scanning laser treatment and other numerical solutions.

scholarly journals Analysis of hyperbolic Pennes bioheat equation in perfused homogeneous biological tissue subject to the instantaneous moving heat source

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Ali Kabiri ◽  
Mohammad Reza Talaee
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Method Comparison ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Profiles ◽  
Moving Heat Source ◽  
Bioheat Equation ◽  
Perfusion Rate

AbstractThe one-dimensional hyperbolic Pennes bioheat equation under instantaneous moving heat source is solved analytically based on the Eigenvalue method. Comparison with results of in vivo experiments performed earlier by other authors shows the excellent prediction of the presented closed-form solution. We present three examples for calculating the Arrhenius equation to predict the tissue thermal damage analysis with our solution, i.e., characteristics of skin, liver, and kidney are modeled by using their thermophysical properties. Furthermore, the effects of moving velocity and perfusion rate on temperature profiles and thermal tissue damage are investigated. Results illustrate that the perfusion rate plays the cooling role in the heating source moving path. Also, increasing the moving velocity leads to a decrease in absorbed heat and temperature profiles. The closed-form analytical solution could be applied to verify the numerical heating model and optimize surgery planning parameters.

Thermodynamic behaviour of microstretch viscoelastic solids with internal heat source

2014 ◽  
Vol 92 (5) ◽  
pp. 425-434 ◽  
Author(s):  
Sunita Deswal ◽  
Renu Yadav
Keyword(s):  
Heat Source ◽  
Normal Mode Analysis ◽  
Generalized Thermoelasticity ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Epoxy Material ◽  
Mech Phys Solid

The dynamical interactions caused by a line heat source moving inside a homogeneous isotropic thermo-microstretch viscoelastic half space, whose surface is subjected to a thermal load, are investigated. The formulation is in the context of generalized thermoelasticity theories proposed by Lord and Shulman (J. Mech. Phys. Solid, 15, 299 (1967)) and Green and Lindsay (Thermoelasticity, J. Elasticity, 2, 1 (1972)). The surface is assumed to be traction free. The solutions in terms of displacement components, mechanical stresses, temperature, couple stress, and microstress distribution are procured by employing the normal mode analysis. The numerical estimates of the considered variables are obtained for an aluminium–epoxy material. The results obtained are demonstrated graphically to show the effect of moving heat source and viscosity on the displacement, stresses, and temperature distribution.

Benchmark Solution for the Prediction of Temperature Distributions During Radiofrequency Ablation of Cardiac Tissue

2004 ◽  
Vol 126 (4) ◽  
pp. 519-522 ◽  
Author(s):  
Ryan T. Roper and ◽  
Matthew R. Jones
Keyword(s):  
Cardiac Tissue ◽  
Numerical Solutions ◽  
Integral Transforms ◽  
Tissue Temperature ◽  
Temperature Profiles ◽  
Bioheat Equation ◽  
Temperature Distributions ◽  
Axial Temperature ◽  
Program Temperature ◽  
Benchmark Solution

Several studies on radiofrequency (RF) ablation are aimed at accurately predicting tissue temperature distributions by numerical solution of the bioheat equation. This paper describes the development of a solution that can serve as a benchmark for subsequent numerical solutions. The solution was obtained using integral transforms and evaluated using a C program. Temperature profiles were generated at various times and for different convection coefficients. In addition, a numerical model was developed using the same assumptions made in obtaining the benchmark solution. Comparison of surface and axial temperature profiles shows that the two solutions match very closely, cross validating the numerical methods used in evaluating both solutions.

Analytical Solution for a Transient Three-Dimensional Temperature Distribution in Laser Assisted Machining Processes

Volume 3 ◽  
2004 ◽  
Author(s):  
Gustavo Gutierrez ◽  
Juan Guillermo Araya
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Heat Source ◽  
Three Dimensional ◽  
Laser Source ◽  
Finite Domain ◽  
Transient Temperature ◽  
Moving Heat Source ◽  
Infinite Domains ◽  
Laser Assisted Machining

Laser assisted machining is a recent technique for machining brittle ceramic materials by first softening them by heating the material with a laser beam, without reaching the melting point and, in this way, minimizing the damage of the workpiece and tool. The use of a laser source is a common procedure in numerous electronic and optical material processes. This research presents a new analytical solution to determine transient temperature distributions in a finite solid when it is heated by a moving heat source. The analytical solution is obtained by solving the transient three-dimensional heat conduction equation in a finite domain by the method of separation of variables. Previous studies focus on analytical solutions for semi-infinite domains. In this study, for a moving heat source, the temperature field is obtained in a finite domain. The purpose of this study is to obtain an analytical solution to predict transient temperature distribution in a finite solid due to a moving heat source.

Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

2016 ◽  
Vol 33 (1) ◽  
pp. 65-75 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction

AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

FFT Thermoelastic Solutions for Moving Heat Sources

1997 ◽  
Vol 119 (1) ◽  
pp. 156-162 ◽  
Author(s):  
Y. Ju ◽  
T. N. Farris
Keyword(s):  
Heat Source ◽  
Frequency Domain ◽  
Hot Spot ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Heat Sources ◽  
Moving Heat Source ◽  
Line Heat Source ◽  
Pass Filter ◽  
Low Pass Filter

An analytical frequency domain solution is obtained using the spatial Fourier transform for thermal and thermoelastic fields due to an arbitrary heat source or thermal distribution moving at constant speed over the surface of an insulated, traction free elastic half space. Conversions between the space and frequency domains for the input and output are performed efficiently and robustly using FFT techniques. The method is validated by comparison to the analytical result for the moving line heat source in which it is shown that numerical evaluation of the analytical solution is problematic for large speeds or distances from the heat source. The utility of the method is illustrated on the constant patch moving heat source and discretely distributed multiple heat sources known as the “hot spot” problem. It is shown, through several examples, that the effect of hot spots on surface displacement and tangential stress is small. Finally, this conclusion is generalized by quantifying the frequency domain solution for the moving heat source problem as a low pass filter.

Sign in / Sign up

Export Citation Format

Share Document