172
11 Simulation of the Thermal Processes
organism. Thus, the problem of the thermal effect of laser radiation can be divided
into four problems to be solved successively [5]:
(1) the description of the laser radiation energy distribution;
(2) the determination of the absorption characteristics of the biological material;
(3) an analysis of the temperature distribution in irradiated tissue; and
(4) the study of the biological (biochemical, physiological) changes in the tissue
caused by an increase in the temperature.
In this chapter we construct a mathematical model that can vary the electrophysical
parameters of a biological structure (the real and imaginary parts of the refractive
indices of blood and its corpuscles, epidermis, the upper derma layer, the lower derma
layer) and the characteristic sizes of blood corpuscles and can find relations between
them and the biological properties of blood by allowing for the laser-induced heating
of biological tissue. As a result, we can perform in vivo analysis of the temperature
distribution as a function of the electrophysical parameters of the biological structure
under study. In the first part of this work, we consider the problem of the scattering of
a plane electromagnetic wave by a three-layer spherical particle simulating a blood
cell (see Chap. 3). In the second part, we analyze the more complex case of the
reflection of a plane wave using a biological sample consisting of two continuous
layers and one layer with heterogeneous inclusions that simulate blood cells with
different refractive indices and briefly examine the problem of the reflection of a
Gaussian beam with an arbitrary cross section under the conditions given above and
the problem of determining the dependence of the radiation intensity on the refractive
index for a system of blood vessels located in the upper derma layer (see Chaps. 4,
6). These parts have an auxiliary character. In the third part, we solve the problem of
the heating of a blood vessel under the action of a laser beam incident on the outer
surface of a biological structure.
Chapter is based on the results of the [6, 7].
11.2 Mathematical Model for Heating of Biological Tissue
by Laser Radiation
We propose a mathematical model for the heating of a blood vessel by laser radiation
incident on the outer skin surface. In this model, we use dimensional variables. The
laser radiation incident on the skin surface is absorbed by the biological tissue layers
(epidermis, derma) and the blood hemoglobin, increasing the temperature in the
subskin layers and inside blood vessels. In the general case, the simulation of the
thermal processes in biological tissue requires the solution of the three-dimensional
equation
(c · ρ)
−1
· div(λ · gradT (r, t)) + Q(r, m
j
τ , x
j
τ ) =
∂ T
∂t
,
(11.1)
11 Simulation of the Thermal Processes
organism. Thus, the problem of the thermal effect of laser radiation can be divided
into four problems to be solved successively [5]:
(1) the description of the laser radiation energy distribution;
(2) the determination of the absorption characteristics of the biological material;
(3) an analysis of the temperature distribution in irradiated tissue; and
(4) the study of the biological (biochemical, physiological) changes in the tissue
caused by an increase in the temperature.
In this chapter we construct a mathematical model that can vary the electrophysical
parameters of a biological structure (the real and imaginary parts of the refractive
indices of blood and its corpuscles, epidermis, the upper derma layer, the lower derma
layer) and the characteristic sizes of blood corpuscles and can find relations between
them and the biological properties of blood by allowing for the laser-induced heating
of biological tissue. As a result, we can perform in vivo analysis of the temperature
distribution as a function of the electrophysical parameters of the biological structure
under study. In the first part of this work, we consider the problem of the scattering of
a plane electromagnetic wave by a three-layer spherical particle simulating a blood
cell (see Chap. 3). In the second part, we analyze the more complex case of the
reflection of a plane wave using a biological sample consisting of two continuous
layers and one layer with heterogeneous inclusions that simulate blood cells with
different refractive indices and briefly examine the problem of the reflection of a
Gaussian beam with an arbitrary cross section under the conditions given above and
the problem of determining the dependence of the radiation intensity on the refractive
index for a system of blood vessels located in the upper derma layer (see Chaps. 4,
6). These parts have an auxiliary character. In the third part, we solve the problem of
the heating of a blood vessel under the action of a laser beam incident on the outer
surface of a biological structure.
Chapter is based on the results of the [6, 7].
11.2 Mathematical Model for Heating of Biological Tissue
by Laser Radiation
We propose a mathematical model for the heating of a blood vessel by laser radiation
incident on the outer skin surface. In this model, we use dimensional variables. The
laser radiation incident on the skin surface is absorbed by the biological tissue layers
(epidermis, derma) and the blood hemoglobin, increasing the temperature in the
subskin layers and inside blood vessels. In the general case, the simulation of the
thermal processes in biological tissue requires the solution of the three-dimensional
equation
(c · ρ)
−1
· div(λ · gradT (r, t)) + Q(r, m
j
τ , x
j
τ ) =
∂ T
∂t
,
(11.1)