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

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.

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

Advanced Electromagnetics ◽

10.7716/aem.v8i3.1092 ◽

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.

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Temperature Response in Living Skin Tissue Subject to Convective Heat Flux

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.387.1 ◽

2018 ◽

Vol 387 ◽

pp. 1-9

Author(s):

Sanatan Das ◽

Tilak Kumer Pal ◽

Rabindra Nath Jana ◽

Oluwole Daniel Makinde

Keyword(s):

Heat Transfer ◽

Biot Number ◽

Temperature Response ◽

Bioheat Transfer ◽

Heat Transfer Analysis ◽

Skin Tissue ◽

Tissue Temperature ◽

Convective Heating ◽

Transform Method ◽

Living Tissues

This paper examines the heat transfer in living skin tissue that is subjected to a convective heating. The tissue temperature evolution over time is classically described by the one-dimensional Pennes' bioheat transfer equation which is solved by applying Laplace transform method. The heat transfer analysis on skin tissue (dermis and epidermis) has only been studied defining the Biot number. The result shows that the temperature in skin tissue is less subject to the convected heating skin compared to constant skin temperature. The study also shows that the Biot number has a significant impact on the temperature distribution in the layer of living tissues. This study finds its application in thermal treatment.

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Selection of heat transfer model for describing short-pulse laser heating silica-based sensor

High Power Laser and Particle Beams ◽

10.3788/hplpb20122402.0285 ◽

2012 ◽

Vol 24 (2) ◽

pp. 285-288

Author(s):

郝向南 Hao Xiangnan ◽

聂劲松 Nie Jinsong ◽

李化 Li Hua ◽

卞进田 Bian Jintian

Keyword(s):

Heat Transfer ◽

Pulse Laser ◽

Laser Heating ◽

Short Pulse ◽

Heat Transfer Model ◽

Transfer Model ◽

Short Pulse Laser ◽

Pulse Laser Heating ◽

Selection Of

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Cycle Optimization and Comparison of Ideal Thermal Cycles for Maximum Specific Output

International Journal of Mechanical Engineering Education ◽

10.1177/030641909402200303 ◽

1994 ◽

Vol 22 (3) ◽

pp. 177-190

Author(s):

B. Agnew ◽

A. Anderson ◽

T. H. Frost

Keyword(s):

Power Generation ◽

Thermal Efficiency ◽

Design Parameters ◽

Work Output ◽

Temperature Ratio ◽

Thermodynamic Cycles ◽

Rate Processes ◽

Important Design ◽

Cycle Temperature ◽

Selection Of

The thermal efficiencies of several thermodynamic cycles are evaluated and compared for the condition of maximum specific net work output for a specified cycle temperature ratio. It is shown at this condition that the efficiencies of all of the cycles are very similar and that an objective selection of a cycle for a particular application cannot be made on the basis of thermal efficiency alone. The different cycles are then compared with respect to other important design parameters for the optimized condition and comments are made with regard to power generation and the associated controlling rate processes.

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

Biomedical Engineering Applications Basis and Communications ◽

10.4015/s1016237202000139 ◽

2002 ◽

Vol 14 (02) ◽

pp. 86-96 ◽

Cited By ~ 4

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.

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Simulations, Analysis and Thermoeconomical Synthesis of Heat Transfer Elements

10.1115/imece2001/pid-25623 ◽

2001 ◽

Author(s):

L. Reznikov ◽

T. Morosuk

Keyword(s):

Heat Transfer ◽

Temperature Fields ◽

Design Parameters ◽

Key Factors ◽

Analysis And Design ◽

Experimental Heat ◽

Experimental Heat Transfer ◽

Analysis And Synthesis ◽

Selection Of ◽

Unified Method

Abstract Problems of analysis and design of intricate heat transfer elements are traditional for various industrial and experimental heat transfer units, including multichannel heat exchangers and multi-component fins. Authors suggest and introduce unified method of analysis and synthesis for these classes of heat transfer objects. Authors’ method of simulations for such class of objects is based on step-by-step integration of local tangential and longitudinal heat flows with sequential computations of temperature fields in cycles of iterations and specific selection of boundary conditions. Variations of selected key factors provide arrays of design parameters for synthesis of new and optimized heat transfer objects.

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A Contribution to the Study of Analogies of Power Transmissions in Machines

Proceedings of the Institution of Mechanical Engineers ◽

10.1243/pime_proc_1974_188_005_02 ◽

1974 ◽

Vol 188 (1) ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

W. M. J. Schlösser

Keyword(s):

Dynamic Properties ◽

Design Parameters ◽

Force Density ◽

Effective Volume ◽

Hydraulic Power ◽

Important Design ◽

Selection Of

In this lecture an analogy is described by means of which transmissions can be analysed and compared. Two important design parameters are the force density Δ and the effective volume V*, which can be used to analyse stationary and moving methods of transmission. With this analogy a tool is given to the designer to compare transmissions with regard to performance, controllability, size and weight, intensity of loading, dynamic properties. A beginning has been made with formulating a relation between the intensity of loading and wear phenomena (II). With this work we hope to have contributed to a sounder basis for the study and development of power transmissions and their use in machines. As mechanical, electrical, pneumatic, and hydraulic power transmissions can be compared by means of this analogy, the selection of transmissions can be made on a sounder basis.

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

Journal of Biomechanical Engineering ◽

10.1115/1.2891130 ◽

1990 ◽

Vol 112 (1) ◽

pp. 80-87 ◽

Cited By ~ 50

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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