scholarly journals THERMAL MODELS OF BIOHEAT TRANSFER EQUATIONS IN LIVING TISSUE AND THERMAL DOSE EQUIVALENCE DUE TO HYPERTHERMIA

2002 ◽  
Vol 14 (02) ◽  
pp. 86-96 ◽  
Author(s):  
TZU-CHING SHIH ◽  
HONG-SEN KOU ◽  
CHIHNG-TSUNG LIAUH ◽  
WIN-LI LIN
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Heating Temperature ◽  
Bioheat Transfer ◽  
Living Tissue ◽  
Thermal Dose ◽  
Bioheat Equation ◽  
Transfer Equations ◽  
Polynomial Expression

This review focuses both on the basic formulations of bioheat equation in the living tissue and on the determination of thermal dose during thermal therapy. The temperature distributions inside the heated tissues, generally controlled by heating modalities, are obtained by solving the bioheat transfer equation. However, the major criticism for the Pennes' model focused on the assumption that the heat transfer by blood flow occurs in a non-directional, heat sink- or source-like term. Several bioheat transfer models have been introduced to compare their convective and perfusive effects in vascular tissues. The present review also elucidates thermal dose equivalence that represents the extent of thermal damage or destruction of tissue in the clinical treatment of tumor with local hyperthermia. In addition, this study uses the porous medium concept to describe the heat transfer in the living tissue with the directional effect of blood flow, and the polynomial expression of thermal dose in terms of the curve fitting of the experimental isosurvival curve data by Dewey et al. Results show that the values of factor R is a function of the heating temperature instead of the two different constants suggested by Sapareto and Dewey.

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.

Analytical Solutions to the Problem of Transient Heat Transfer in Living Tissue

1978 ◽  
Vol 100 (4) ◽  
pp. 202-210 ◽  
Author(s):  
A. Shitzer ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Temperature Profile ◽  
Analytical Solutions ◽  
Biological Tissue ◽  
Geometrical Parameter ◽  
Convective Transport ◽  
Transient Heat Transfer ◽  
Living Tissue ◽  
Cylindrical Coordinates

An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the “locally fully developed” temperature profile were found to be of the order of 5–25 min. These transients are dominated by a geometrical parameter and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.

Buoyancy Effects on Human Skin Tissue Thermoregulation due to Environmental Influence

2020 ◽  
Vol 401 ◽  
pp. 107-116
Author(s):  
Lawal Hamid Adeola ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Human Skin ◽  
Environmental Influence ◽  
Saturated Porous Medium ◽  
Skin Tissue ◽  
Bioheat Equation ◽  
Biophysical Parameters ◽  
Thermal Buoyancy ◽  
The Impact

This paper theoretically examines the impact of thermal buoyancy on human skin tissue’s blood flow, heat exchange and their interaction with the surrounding environment using a two phase mathematical model that relies on continuity, momentum and energy conservation equations in continuum mechanics. The tissue blood flows and heat transfer characteristics are determined numerically based on Darcy’s Brinkman model for a saturated porous medium coupled with modified Pennes bioheat equation while analytical approach is employed to tackle the model of interacting surrounding environmental buoyancy driven air flow with heat sink. The influence of embedded biophysical parameters on the skin tissue’s blood flow rate and temperature distribution together with friction coefficient at skin tissue surface and Nusselt number are display graphically and discussed quantitatively. It is found that a boost in thermal buoyancy enhances skin tissue heat transfer and blood flow rates.

scholarly journals Analysis of non-Fourier thermal behavior for multi-layer skin model

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 61-67 ◽  
Author(s):  
Kuo-Chi Liu ◽  
Po-Jen Cheng ◽  
Yan-Nan Wang
Keyword(s):  
Heat Transfer ◽  
Wave Model ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Order Partial Differential Equation ◽  
Transfer Equations ◽  
Lag Model ◽  
Fourier Equation ◽  
Good Agreement

This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes? model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results.

Relationship Between the Nonlocal Effect and Lagging Behavior in Bioheat Transfer

2021 ◽  
Author(s):  
Xiaoya Li ◽  
Yan Li ◽  
Pengfei Luo ◽  
Xiao Geng Tian
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Order Effect ◽  
Heat Transfer Process ◽  
Bioheat Transfer ◽  
Transfer Model ◽  
Phase Lag ◽  
Medical Systems ◽  
Conduction Model ◽  
Transfer Equations

Abstract Lots of generalized heat conduction models have been developed in recent decades, such as local thermal non-equilibrium model, phase lagging model and nonlocal heat conduction model. But no attempt was made to prove which model is better (or worse) than others, or whether there is a certain relationship between these different models. With this inspiration, we establish the nonlocal bioheat transfer equations with lagging time, and the two and three-temperature bioheat transfer equations with considering all the carries' heat conduction effect are also constructed. Comparing the two (or three)-temperature equation model with the nonlocal bioheat transfer models with lagging time, one may obtain: the lagging time tt of temperature gradient and the nonlocal characteristic length ?q in the space derivative items of heat flux have the same effect on heat transfer; when the heat transport occur among N energy carriers with considering the conduction effects of all carries, the heat transfer process are depend on the high-order effect of tqN-1, ttN-1 and ?t(2N-1) in nonlocal dual phase lag bioheat transfer model. This phenomenon is very important for biological and medical systems where numerous carriers may exist on the cellular level.

Theory on Thermal Probe Arrays for the Distinction Between the Convective and the Perfusive Modalities of Heat Transfer in Living Tissues

1987 ◽  
Vol 109 (4) ◽  
pp. 346-352 ◽  
Author(s):  
H. Arkin ◽  
K. R. Holmes ◽  
M. M. Chen
Keyword(s):  
Heat Transfer ◽  
Short Pulse ◽  
Bioheat Transfer ◽  
Design Parameters ◽  
Bioheat Equation ◽  
Thermal Probe ◽  
Living Tissues ◽  
Improved Model ◽  
Important Design ◽  
Selection Of

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes’ “classic” bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.

scholarly journals Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

2021 ◽  
Vol 18 (182) ◽  
pp. 20210564
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Fractal Geometry ◽  
Tumour Growth ◽  
Fractal Dimensions ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Bioheat Equation ◽  
Cell Tissue ◽  
Transfer Equations ◽  
Spatial Dimensions ◽  
Two Parameters

In this study, the Pennes and Cattaneo–Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R 0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

Experiment-Calculated Investigation of the Forced Convection of Nanofluids Using Single Fluid Approach

2014 ◽  
Vol 348 ◽  
pp. 123-138 ◽  
Author(s):  
Andrey V. Minakov ◽  
Alexander S. Lobasov ◽  
M.I. Pryazhnikov ◽  
D.V. Guzei
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Thermal Conductivity ◽  
Experimental Determination ◽  
Forced Convection ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Hydrodynamic Description ◽  
Transfer Equations

An experiment-calculated investigation of forced convection of nanofluids based on Al2O3nanoparticles was carried out. The hydrodynamic description and a model of homogeneous nanofluids were used. The homogeneous nanofluids model assumes that the hydrodynamics and heat transfer can be described by conventional Navier-Stokes and heat transfer equations with the physical parameters corresponding to nanofluids. The results showed that this model very well described the experimental data in some cases. However, in some other cases, there are discrepancies between experiment and theory that can be explained by the real heterogeneity of nanofluids and the errors in the experimental determination of thermal conductivity and viscosity of nanofluids.

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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