## On Prognosis of Distribution of Temperature During Effects of Radiation on Bio-Logical Tissues

### Pankratov EL*

*Nizhny Novgorod State Agrotechnical University, Gagarin avenue, Nizhny Novgorod, Russia*

**Submission:** June 18, 2024; **Published:** July 4, 2024

***Corresponding author:** Pankratov EL, Nizhny Novgorod State Agrotechnical University, Gagarin avenue, Nizhny Novgorod, Russia.

**How to cite this article:** Pankratov EL*. On Prognosis of Distribution of Temperature
During Effects of Radiation on Bio-Logical
Tissues. Curr Trends Biomedical Eng & Biosci. 2024; 23(1): 556102. DOI:10.19080/CTBEB.2024.23.556102

**Abstract**

In this paper we introduce a model and an analytical approach to analyze distribution of temperature at effect of radiation on biological tissues. We consider a possibility to control of heat transport in biological tissues by choosing of conditions of heating.

** Keywords: **Effect of radiation; Biological tissues; Prognosis of heat transport; Control of heat transport; Analytical approach for analysis

**Introduction**

Different types of irradiation take essential role in biological processes directly related to human health [1-6]. In the present time they are widely using in clinical practice. In this situation one can find several works to determine therapeutic effects, which were obtained by actions of the irradiation on living organisms. One type of irradiation of tissues of the considered organisms is electromagnetic radiation (including of radiation of visible range). A consequence of the radiation tis-sues of organisms is their heating. Main aim of the present paper is formulation of model for analysis of the heating of the organism. An accompany aim is formulation of analytical approach for analysis of the obtained model.

**Method and results of solution**

In this section we consider the following model of generation and redistribution of heat in tissues of an organism during and after electromagnetic irradiation. Spatiotemporal distribution of temperature in the considered case was deter-mined as solution of the following equation

where T(r,t) is the temperature of heating in tissue of an organism due to electromagnetic irradiation; ρ is the density of the above tissue; c is the specific heat of tissues; t is the current time; λ = αρc is the thermal conductivity of tissue; α is the thermal diffusivity of tissue; S_{1} = μϕE is the volumetric density of heat, which was obtained in tissue due to irradiation; μ is the absorption coefficient; ϕ is the total illumination of the tissue in the considerate area; E is the radiation energy density per unit time. Blood can absorb or release heat depending on how its temperature correlates with the temperature of the surrounding tissue. The term S_{b} is the volumetric drain or energy source and can be written as follows: S_{b} = ρc{ρ_{b}D(t)[T_{b} - T(r,t)]}, ρ_{b} is the density of blood; T_{b} is the temperature of blood; D(t) is the blood flow density. Boundary and initial conditions for the equation (1) could be written as

We solved the Eq. (1) by method of averaging of functional corrections [7-9]. In the framework of the approach, we replace the required function T(r,t) on the not yet known average value α_{1} of this function in the right side of Eq. (1). The replacement gives a possibility to obtain the following relation to determine the first-order approximation T_{1}(r,t) of the considered temperature in the following form

Approximations of temperature with larger order n could be obtained in the framework of the standard procedure [7-9], i.e. by replacement of the required function T(r,t) on the following sum in the right side of the Eq. (1). The following replacement gives a possibility to obtain the following relation to determine the second-order approximation of the considered temperature

Analysis of spatiotemporal distribution of temperature of tissue under influence of electromagnetic irradiation has been done analytically by consideration of their the second-order approximations. Analytical results were checked by com-parison with results of direct numerical simulation.

**Discussion**

In this section we analyzed dependences of temperature of tissue under influence of electromagnetic irradiation on time at different values of parameters. Figure 1 shows typical dependences of the considered temperature on time at different values of heat, which was obtained in tissue due to irradiation. Increasing of number of curves corresponds to increasing of value of the considered heat. In this case we take into account increasing of temperature of the considered tissue during irradiation and cooling of the tissue after finishing of the above irradiation. Figure 2 shows typical dependences of the considered temperature on time at different values of the considered temperature at different values of square of the irradiated part of tissue and fixed value of power of irradiation. Increasing of number of curves corresponds to increasing of value of the considered square.

**Conclusion**

In this paper we introduce a model for analysis of distribution of temperature at effect of radiation on biological tissues. We consider a possibility to control of heat transport in biological tissues by choosing of conditions of heating. Also, we introduce an analytical approach to analysis of the above temperature.

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