scholarly journals The Westervelt equation with a causal propagation operator coupled to the bioheat equation.

2016 ◽  
Vol 5 (3) ◽  
pp. 449-461
Author(s):  
Guy V. Norton ◽  
Robert D. Purrington
Keyword(s):  
Bioheat Equation ◽  
Causal Propagation ◽  
Westervelt Equation

A numerical comparison of the Westervelt equation with viscous attenuation and a causal propagation operator

2012 ◽  
Vol 82 (7) ◽  
pp. 1287-1297 ◽  
Author(s):  
Robert D. Purrington ◽  
Guy V. Norton
Keyword(s):  
Numerical Comparison ◽  
Causal Propagation ◽  
Westervelt Equation

The Westervelt equation with viscous attenuation versus a causal propagation operator: A numerical comparison

2009 ◽  
Vol 327 (1-2) ◽  
pp. 163-172 ◽  
Author(s):  
Guy V. Norton ◽  
Robert D. Purrington
Keyword(s):  
Numerical Comparison ◽  
Causal Propagation ◽  
Westervelt Equation

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

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.

Investigation of the Thermal and Injury Behavior During Microwave Thermal Therapy of Porcine Kidney

2002 ◽  
Author(s):  
Xiaoming He ◽  
Shawn Mcgee ◽  
James E. Coad ◽  
Paul A. Iaizzo ◽  
David J. Swanlund ◽  
...  
Keyword(s):  
Thermal Model ◽  
Histological Study ◽  
Kidney Cortex ◽  
Cellular Injury ◽  
Bioheat Equation ◽  
Tissue Slices ◽  
Thermal Histories ◽  
Microwave Probe

In this paper, we report on the characterization of microwave therapy of normal porcine kidneys both in vitro and in vivo. This technology is being developed for eventual use in the treatment of small renal cell carcinoma (RCC) by minimally invasive procedures. During experiments, microwave energy was applied through an interstitial microwave probe (Urologix, Plymouth, MN) to the kidney cortex with occasional involvement of the kidney medulla. The thermal histories at several locations were recorded. After treatment, the kidneys were bisected and small tissue slices were cut out at approximately the same depth as the thermal probes. The tissue slices were further processed for histological study. Both cellular injury and the area of microvascular stasis were quantitatively evaluated by histology. Absolute rate kinetic models of cellular injury and vascular stasis were developed and fit to this data. A 3-D finite element thermal model based on the Pennes Bioheat equation was developed and solved using a commercial software package (ANSYS, V5.7). The Specific Absorption Rate (SAR) of the microwave probe was measured experimentally in tissue equivalent gel-like solution. The thermal model was first validated by the measured in vitro thermal histories. It was then used to determine the blood perfusion term in vivo.

A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions

2018 ◽  
Vol 133 (10) ◽  
Author(s):  
R. Roohi ◽  
M. H. Heydari ◽  
M. Aslami ◽  
M. R. Mahmoudi
Keyword(s):  
Fractional Order ◽  
Numerical Study ◽  
Space Time ◽  
Legendre Functions ◽  
Bioheat Equation

Determination of a time-dependent coefficient in the bioheat equation

2014 ◽  
Vol 88 ◽  
pp. 259-266 ◽  
Author(s):  
A. Hazanee ◽  
D. Lesnic
Keyword(s):  
Time Dependent ◽  
Bioheat Equation

scholarly journals Ultrasonic Measurement of Temperature Rise in Breast Cyst and in Neighbouring Tissues as a Method of Tissue Differentiation

2016 ◽  
Vol 41 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Barbara Gambin ◽  
Michał Byra ◽  
Eleonora Kruglenko ◽  
Olga Doubrovina ◽  
Andrzej Nowicki
Keyword(s):  
Probability Density ◽  
Breast Tissue ◽  
Tissue Characterization ◽  
Heating Process ◽  
Ultrasound Images ◽  
Bioheat Equation ◽  
Acoustical Properties ◽  
Breast Cyst ◽  
Malignant Lesions ◽  
Backscattered Signals

Abstract Texture of ultrasound images contain information about the properties of examined tissues. The analysis of statistical properties of backscattered ultrasonic echoes has been recently successfully applied to differentiate healthy breast tissue from the benign and malignant lesions. We propose a novel procedure of tissue characterization based on acquiring backscattered echoes from the heated breast. We have proved that the temperature increase inside the breast modifies the intensity, spectrum of the backscattered signals and the probability density function of envelope samples. We discuss the differences in probability density functions in two types of tissue regions, e.g. cysts and the surrounding glandular tissue regions. Independently, Pennes bioheat equation in heterogeneous breast tissue was used to describe the heating process. We applied the finite element method to solve this equation. Results have been compared with the ultrasonic predictions of the temperature distribution. The results confirm the possibility of distinguishing the differences in thermal and acoustical properties of breast cyst and surrounding glandular tissues.

scholarly journals Thermal changes in Human Abdomen Exposed to Microwaves: A Model Study

2019 ◽  
Vol 8 (3) ◽  
pp. 64-75
Author(s):  
J. Kaur ◽  
S. A. Khan
Keyword(s):  
Heat Transfer ◽  
Wave Model ◽  
Biological Tissues ◽  
Bioheat Transfer ◽  
Biological Medium ◽  
Bioheat Equation ◽  
Temperature Variations ◽  
Microwave Exposure ◽  
Model Study ◽  
Speed Of Propagation

The electromagnetic energy associated with microwave radiation interacts with the biological tissues and consequently, may produce thermo-physiological effects in living beings. Traditionally, Pennes’ bioheat equation (BTE) is employed to analyze the heat transfer in biological medium. Being based on Fourier Law, Pennes’ BTE assumes infinite speed of propagation of heat transfer. However, heat propagates with finite speed within biological tissues, and thermal wave model of bioheat transfer (TWBHT) demonstrates this non-Fourier behavior of heat transfer in biological medium. In present study, we employed Pennes’ BTE and TWMBT to numerically analyze temperature variations in human abdomen model exposed to plane microwaves at 2450 MHz. The numerical scheme comprises coupling of solution of Maxwell's equation of wave propagation within tissue to Pennes’ BTE and TWMBT. Temperatures predicted by both the bioheat models are compared and effect of relaxation time on temperature variations is investigated. Additionally, electric field distribution and specific absorption rate (SAR) distribution is also studied.  Transient temperatures predicted by TWMBT are lower than that by traditional Pennes’ BTE, while temperatures are identical in steady state. The results provide comprehensive understanding of temperature changes in irradiated human body, if microwave exposure duration is short.

scholarly journals Prediction human skin temperature in comfort level

2019 ◽  
Vol 1 (3) ◽  
pp. 1-4
Author(s):  
Zaina Norhallis Zainol ◽  
Masine Md. Tap ◽  
Haslinda Mohamed Kamar
Keyword(s):  
Thermal Comfort ◽  
Skin Temperature ◽  
Human Skin ◽  
Blood Perfusion ◽  
Comfort Level ◽  
Working Environment ◽  
Percentage Error ◽  
Bioheat Equation ◽  
Acceptable Error ◽  
Human Arm

Thermal comfort is the human subject perceive satisfaction to the work environment. The thermal comfort need to be achieve towards productive working environment. The comfort level of the subject is affected by the human skin temperature. To assess the skin temperature with the sorrounding by conducting human experiment in the climatic chamber. It is rigorous and complex experiment.This study was developed to predict human skin temperature in comfort level with the finite element method and the bioheat equation. The bioheat equation is a consideration of metabolic heat generation and the blood perfusion to solve heat transfer of the living tissue. It is to determine the skin temperature focussing at the human arm. From the study, it is found that the predicted skin temperature value were in well agreement with the experimental results. The percentage error insignificant with acceptable error of 1.05%.

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