Chapter 4
Mathematical Models of the Interaction
of Laser Radiation with Turbid Media
Abstract We construct the mathematical model for calculating the interaction of
laser radiation with a turbid medium and the model for the prediction of the optical
characteristics of blood (refractive index and absorption coefficient) and for the
determination of the rate of blood flow in the capillary bed under irradiation of a
laser beam is proposed.
4.1 Introduction
Now we proceed to the consideration of the principles of construction of mathematical models for calculating the interaction of laser radiation with a turbid medium.
Turbid is called medium in which there is the absorption and scattering of radiation.
One example of this is human skin tissue. As was noted in Chap. 1, the skin is a live
multi-media containing various inclusions, such as, for example, blood vessels. Let’s
consider the basic periods of construction of the mathematical models describing the
interaction of laser radiation with immunocompetent multilayered turbid media, such
as human skin. (see Fig. 4.1). First we described the object of study. After that optical
and physical parameters of all its components are defined. Next step is the calculation of the radiation in the environment, and (on some models) the calculation of
the temperature fields. Distinctions between models become already appreciable at
a period geometry construction. In most cases the skin is represented in the form of
sequence of layers with various optical and thermophysical properties. The number
of layers of the skin can vary from one to seven. The simple geometry includes only
derma. The simplest geometry includes only the dermis [1]. This simplified model
is used, for example, to simulate the treatment of acne laser light with a wavelength
of 1450 nm.
The greatest number of layers of model is presented in [2]. Here, seven layers
are located in skin: a cornual layer, epidermis, the upper derma, a derma with a
superficial plexus of vessels, the lower derma, a derma with a deep plexus of vessels
© Springer International Publishing AG, part of Springer Nature 2018
K. Kulikov and T. Koshlan, Laser Interaction with Heterogeneous
Biological Tissue, Biological and Medical Physics, Biomedical Engineering,
https://doi.org/10.1007/978-3-319-94114-1_4
67
Mathematical Models of the Interaction
of Laser Radiation with Turbid Media
Abstract We construct the mathematical model for calculating the interaction of
laser radiation with a turbid medium and the model for the prediction of the optical
characteristics of blood (refractive index and absorption coefficient) and for the
determination of the rate of blood flow in the capillary bed under irradiation of a
laser beam is proposed.
4.1 Introduction
Now we proceed to the consideration of the principles of construction of mathematical models for calculating the interaction of laser radiation with a turbid medium.
Turbid is called medium in which there is the absorption and scattering of radiation.
One example of this is human skin tissue. As was noted in Chap. 1, the skin is a live
multi-media containing various inclusions, such as, for example, blood vessels. Let’s
consider the basic periods of construction of the mathematical models describing the
interaction of laser radiation with immunocompetent multilayered turbid media, such
as human skin. (see Fig. 4.1). First we described the object of study. After that optical
and physical parameters of all its components are defined. Next step is the calculation of the radiation in the environment, and (on some models) the calculation of
the temperature fields. Distinctions between models become already appreciable at
a period geometry construction. In most cases the skin is represented in the form of
sequence of layers with various optical and thermophysical properties. The number
of layers of the skin can vary from one to seven. The simple geometry includes only
derma. The simplest geometry includes only the dermis [1]. This simplified model
is used, for example, to simulate the treatment of acne laser light with a wavelength
of 1450 nm.
The greatest number of layers of model is presented in [2]. Here, seven layers
are located in skin: a cornual layer, epidermis, the upper derma, a derma with a
superficial plexus of vessels, the lower derma, a derma with a deep plexus of vessels
© Springer International Publishing AG, part of Springer Nature 2018
K. Kulikov and T. Koshlan, Laser Interaction with Heterogeneous
Biological Tissue, Biological and Medical Physics, Biomedical Engineering,
https://doi.org/10.1007/978-3-319-94114-1_4
67