Thermal Models of Bioheat Transfer Equations in Living Tissue and Thermal Dose Equivalence Due to Hyperthermia

Abstract

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.

The Effect of Water Content on Damage Depth in Tissue Subjected to Co2 Laser, an Expermantel and Theoritcal Study

“…Cumulative Equivalent Minutes (Thermal Dose):-Sapareto and Dewey define the CEM 43 of thermal dose at 43°C which can describe the extent of thermal damage of tissue. It is a function of the temperature rise mand time, as described in equations [11] 12: Arrhenius' equation:-Arrhenius formulation, in which the thermal damage in the tissue is described as a temperature dependent rate process. Arrhenius equation 13calculates the accumulative damage in a tissue, exposed to a given temperature T for a specific time t:…”

“…The first depth of the tissue, which has 43 o C, is calculated by using equation (11), when time is equal to zero, while, the thermal diffusivity is calculated by using equation (2) [10].…”

“…Where: CEM 43: the cumulative number of equivalent minutes at 43 °C t i : the time interval [min] T: the average temperature during time interval t i.. R: related to the temperature dependence of the rate of cell death[11]. R=0.25 for T< 43 ℃ , R=0.5 for T>43 ℃ The equivalent minutes of critical thermal dose (CEM 43 ) of liver tissue is equal to 340 minutes.…”

The numerical assessment of volume averaging method in heat transfer modeling of tissue-like porous media

“…One of these differences is the absence or presence of perfusion term in blood and tissue energy equations, and the other is the consideration of blood as the integrated fluid phase or separated arterial and venous phases. Accordingly, the porous mediabased studies of living tissue heat transfer can be categorized into four groups: two equation models without perfusion term [5][6][7][8][9][10][11][12][13][14][15][16][17][18], two equation models with perfusion term [19][20][21][22][23][24][25][26][27], three equation models without perfusion term [27,28], and three equation models with perfusion [29][30][31]. For better understanding and evaluation of these important differences, this paper establishes a vascular tissue with cylindrical geometry and relative anatomical similarity to human muscle tissues.…”

Heat Exchange Within the Surrounding Biological Tissue During Magnetic Hyperthermia

“…The accurate explanation of the thermal interaction between vasculature and tissues is necessary for the development of medical technology of tumor diseases [10,11]. Thermal models of bioheat transfer equations in living tissue and thermal dose equivalence due to hyperthermia are presented in [12,13]. These works focus both on the basic formulations of the bioheat transfer equations in the living tissue and on the determination of thermal dose during thermal therapy.…”