Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT)

doi:10.1016/j.burns.2007.01.009

Burns

Volume 34, Issue 1, February 2008, Pages 45-49

https://doi.org/10.1016/j.burns.2007.01.009 Get rights and content

Abstract

Thermal analyses of biological tissues exposed to microwaves were studied by using thermal wave model of bio-heat transfer (TWMBT). As a model, skin stratified as three layers with various thermal physical properties were simulated and thermal wave model of bio-heat transfer equations were solved by using finite difference method. Finally, the thermal variations were simulated in the cross section of the model. Comparative studies on the traditional Pennes’ equations and thermal wave model of bio-heat transfer were performed and evaluated. Furthermore, temperature variations in the skin exposed to microwave were predicted depending on blood perfusion rate, thermal conductivity, frequency and power density of microwave, and exposure time. Thermal wave model of bio-heat transfer gives lower heat rise predictions than that of Pennes’ equation, initially. When it approaches to steady state, it overlaps with the Pennes’ equation.

Introduction

In recent years, there has been an increase in public concern about possible health risks from electromagnetic energy emitted from various sources. Common applications of RF radiation include radar, communication, navigation equipment, medical devices, industrial heating devices, and microwaves ovens [1], [2], [3]. Recently, hardware systems capable of generating microwaves have been developed and are increasingly being used for a number of applications, such as satellite communications, military radar, smart weapons, high-speed data communications, automotive anti-collisions devices, weapon detection, medical devices, and for MW practices in medicine like cryogenic surgery, frostbite, scald medicine, laser surgery, and cancer hyperthermia [3], [4].

Exposure to radio frequency radiation (RFR) at sufficiently high intensities produces perceptible increases in tissue temperature. The penetration depth of WMs is small and the heating takes place near the surface at the skin. Because of the increasing use of RF energy, sometimes at high power levels, it is becoming ever more important to identify the limits of safe exposure with respect to thermal hazards. The amount of RF energy absorbed by an organism depends on several factors, including frequency, intensity of RF radiation, and duration of exposure [5]. When the rate of energy absorption is relatively high, RF radiation produces heating in living tissue. The specific absorption rate (SAR) is a measure of the rate of energy absorption per unit mass [W/kg].

In this study, the thresholds values of incident power density given by Blick et al. [14] and Riu et al. [6], and a one-dimensional multi-layer tissue model [7] are used for simulation. Thermal analysis of heat rise in biological tissues exposed to microwaves was studied by using TWMBT. Furthermore, comparative studies were carried out by Penne's bioheat equation. The heat variations in three layer skin model were evaluated to base a model for practical applications. Related equations were solved by FDTD method and the simulation was done by using Matlab codes. In biological tissues heat transfer is generally solved by Pennes’ equation. In thermal analysis of biological tissues, TWMBT based on finite speed of heat propagation is compared with the well-known Pennes’ equation based on infinite heat propagation on biological tissues [7]. The 2.45, 7.5, and 10 GHz frequencies were chosen for simulation, since data exist in the literature to calculate the thermal relaxation time.

Section snippets

The thermal wave model of bioheat transfer (TWMBT)

Liu et al. introduced the thermal wave model of bio-heat transfer in [8], [9], the basic equation to describe TWMBT can be written as follow: $\nabla \cdot [k \nabla T (r, t)] + W_{b} C_{b} (T_{b} - T) + Q_{m} + Q_{r} + τ [- W_{b} C_{b} \frac{\partial T}{\partial t} + \frac{\partial Q_{m}}{\partial t} + \frac{\partial Q_{r}}{\partial t}] = ρ C [τ (\frac{\partial^{2} T (r, t)}{\partial t^{2}}) + \frac{\partial T (r, t)}{\partial t}]$ where ρ, C, k denote the density [kg/m³], the specific heat [J/kg °C] and thermal conductivity [W/m °C] of the tissue; C_b is specific heat of blood; W_b is blood perfusion rate [kg/m³ s]; Q_m and Q_r are volumetric heat generations due to metabolism and spatial heat source [W/m³],

Numerical method

A one-dimensional multi-layer tissue model used in this study is shown in Fig. 1. The skin is divided into three layers, epidermis, dermis, and subcutaneous. The body core is called the inner tissue. Temperature distribution within the skin tissue is calculated by using Eqs. (1), (2), (3). Incident power density of a plane wave was assumed uniform over the exposure areas. The skin model was considered as a homogenous semi-infinite medium characterized with known thermal and physical properties.

Results

Typical values of thermal properties for skin tissue and other parameters have been chosen as ρ = 1000 kg/m³, C = C_b = 4200 J/kg °C, k = 0.2 W/m °C, W_b = 0.5 kg/m³ sn, [8], T_a = 24 °C, T_b = 37 °C, however the “inner tissue” layer assumes a fairly high specific heat and conductivity. Since the main concern of this study is to understand the mechanism of injury caused by microwave exposure to skin not to deepest “inner tissue” and the microwave energy is mostly absorbed in this region, this relatively high specific

Conclusions

In bio-heat transfer, TWMBT was used as a new approach in the heat analysis of tissues exposed to microwave, and a one-dimensional three-layer skin tissue model was chosen as a biological tissue. In the heat analysis of tissues exposed to microwaves, the traditional Pennes’ equation as well as TWMBT was used and observed that same heat rises had been observed in the case of steady state.

High thermal relaxation time is stronger the thermal wave [11], and the heat will propagate mainly by the

Acknowledgements

The research is supported by the Science Research Project Support Unit (BAPYB) of Akdeniz University, Antalya, Turkey. The author is grateful to Ass. Professor Cem Hanyaloğlu from The Department of Mechanical Engineering, Akdeniz University, for his valuable discussions and suggestions.

References (15)

S.C. Jiang et al.
Effects of thermal properties geometrical dimensions on skin burn injuries
Burns
(2002)
R.F. Cleveland
Radio frequency radiation in the environment: sources, exposure standard, and related issue
World Health Organization (WHO). Environmental health criteria 137: Electromagnetic fields (300Hz–300GHz), vol. 53....
K.L. Ryan et al.
Radio frequency radiation of millimeter wave length: potential occupational safety issues relating to surface heating
Health Phys
(2000)
Ozen S. Theoretical and experimental study on thermal analysis in biological tissue which under exposure of MW...
C.H. Durney
Radio frequency radiation dosimetry handbook
(1986)
P.J. Riu et al.
A thermal model for human thresholds of microwave-evoked warmth sensations
Bioelectromagnetics
(1996)

There are more references available in the full text version of this article.

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Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer (TWMBT)

Abstract

Introduction

Section snippets

The thermal wave model of bioheat transfer (TWMBT)

Numerical method

Results

Conclusions

Acknowledgements

Burns

Radio frequency radiation in the environment: sources, exposure standard, and related issue

Radio frequency radiation of millimeter wave length: potential occupational safety issues relating to surface heating

Health Phys

Radio frequency radiation dosimetry handbook

A thermal model for human thresholds of microwave-evoked warmth sensations

Bioelectromagnetics