Study and modeling of human biological tissue exposed to microwave electromagnetic waves

 

Anthony bassesuka sandoka
Electrical Engineering
ISTA Kinshasa
Kinshasa, RD Congo
bass_sandoka@yahoo.fr

 

Abstract - This article is part of an approach aimed at studying and improving the performance of existing means for interactions between electromagnetic fields and the human body. These means are the methods of characterization of the macroscopic electrical properties of biological media, and the numerical methods making it possible to model and calculate the fields induced by sources of electromagnetic radiation in the human body.

To do this, we considered a part of the physical phenomena of the propagation of a microwave electromagnetic plane wave and secondly experimental values allows us to simulate the electrical behavior of biological human tisuus. The equivalent electronic circuit model composed of capacitance, resistance and coil, assimilates biological tissues (skin, fat, blood and muscle, etc.) to a suspension of a system in a diluted medium, in order to account for the electrical behavior of these tissues organic.

To find the solutions, we used a certain method and mathematical models that govern the behavior of an electromagnetic plane wave in this biological medium.

Keywords: - Modeling, Electronic circuit equivalent, Organic Fabric, Electromagnetic microwave, Maxwell equations.

                                                                                                                                                   I.     Introduction

The techniques of microwave thermography have been used extensively in medical applications for controlling tissue temperature and detecting the electromagnetic field in biological tissues. Since the temperature increases in the resulting tissue from the deposition of energy and is proportional to the square of the electric field in the tissue; the response to thermal radiation must have the same sample[²].

In this article we presented a new behavioral model based on the physical phenomena of the propagation of an electromagnetic plane wave which assimilates biological tissues (skin, fat, blood, muscle and bone ...).

Since the dielectric properties (relative permittivity, conductivity, frequency and temperature) of a biological tissue are quite complex and vary considerably with the nature of the tissue, to make a somewhat concrete study, we considered that a tissue is divided into two broad categories, tissue with high water content such as skin, blood and muscle and tissue with low water content such as fat and bone whose characteristics vary in characteristics from one different way.

To analyze the electrical behavior of biological tissue exposed in an electromagnetic environment, we will refer to Maxwell's equations which govern the behavior of an electromagnetic plane wave in the infinite, non-magnetic, lossy, homogeneous and isotropic living biological medium, in order to to simplify the solution of telegraph equations.

The modeling and quantification of voltage and current, respectively, V (x, t) and I (x, t) is therefore to solve the wave equations for deferent models of biological tissues used. The characteristic impedance of dielectric media makes it possible to obtain the characteristics indirectly by involving the electrical parameters of the tissues.

 

                                                                                                                                                   II.    Development

To analyze the electrical behavior of biological tissue, we proceed by solving Maxwell's equations which govern the behavior of an electromagnetic plane wave in the biological medium in order to simulate the voltage and current induced by electromagnetic waves of 3,4 Gigas Hertz [Ghz] under a body temperature of 36 degrees Celsius [°C] depending on the depth of penetration into the Blood, Muscle and Skin.

To do this, this modeling will be based on the equivalent electronic circuit of human biological tissue.

The usefulness of behavioral modeling for the design of analog circuits is no longer in doubt because it allows in fact reduced design time and higher quality circuits[³]. A model reproduces the electrical behavior of a circuit, without taking into account its internal structure. There are different ways to implement a biological tissue model in the environment of a simulator, the components of which are easily found in the library of the simulator that can be easily analyzed

 

1)   The biological cell

 

The effects of electromagnetic fields in a biological cell being the target of this article, it appears to us essential to describe the biological cell and the molecular structure of the plasma membrane. The biological cell is the structural and functional unit of all living things, it is characterized by its nucleus, cytoplasm and plasma membrane[¹²]. The cell plasma membrane plays an essential role in the life of the cell, it delimits the cell and separates the cytoplasm from the external environment. It surrounds the cytosol (i.e. the liquid phase in which the cytoplasmic organelles bathe) and forms a very thin protective layer made up of lipid and protein molecules. It thus presents a heterogeneous molecular structure allowing it to play a double role: The phospholipids which are the essential constituents of its basic material, make it insulating, while the protein molecules which are scattered, ensure the exchange between the cytoplasm and the environment extra cellular[¹³].

The cell is the basic structural and functional unit of all living things. The cells are very small and very complex in organization. Knowledge of their structure, chemical composition and functioning (physiology) is very critical in biology and biomedical science. Studies of cellular functionality and behavior have been widely applied in many clinical and biomedical applications, such as disease diagnosis and knowledge of disease progression, drug development, and cancer research. [¹⁴][¹⁵].

 

2)   Electric model

 

The response of a cell in the presence of an electric field depends on two parameters which are the relative dielectric permittivity which reflects the capacity to polarize a material by accumulation of charges and the electrical conductivity which reflects the capacity to pass an electric current with minimal losses. The fundamental concepts of dielectric phenomena in biological media and their interpretation of interactions at the cellular level are well established. Based on the work of Pr. Schwan [¹⁶], [¹⁷] and Foster [¹⁸], the dielectric properties of cells depend on the frequency and exhibit relaxation and resonance phenomena, a function of different polarizations. The relaxations are named α, β et γ and are usually designated by the term dispersion for the resulting dielectric absorption is observable over a broad frequency range [¹⁶][¹⁸].

 

Different empirical models can be used to approximate the frequency variations of the electrical properties of cells. The electrical modeling of cells was first proposed by R. Höber in the 1910s, who has studied the evolution of the resistivity of a blood sample to low and high frequencies. As a result of these early observations, several electrical models of the cell were constructed in the mid-twenty-second century, such as the Fricke, Debye and Cole-Cole. These models are still widely used today in studies of the electrical behavior of biological media.

As part of our study, modeling based on the equivalent electronic circuit of human biological tissue and simulation under the Excel and Matlab environment were exploited.

Calculating the induced voltage and current, respectively V (x, t) and I (x, t), therefore amounts to solving the wave equations for the various models used. The characteristic impedance of dielectric media makes it possible to obtain the characteristics indirectly by involving the electrical parameters of the models.

V(x,t) = (R+jLw).I(x,t)                                   (1)

I(x,t) = (G+jCw).V(x,t)                                  (2)

V(x,t) =V₀ .Exp(-ax).cos(wt-bx)  (3)

I(x,t) = (I₀ /Z₀).Exp(-ax).cos(wt-bx)            (4)

g = Ö[(R+jLw)(G+jCw)  ]                               (5)

g = a+jb                                                           (6)

Z₀ = Ö[(R+jLw)/(G+jCw)]                              (7)

The bio-electronic parameters (R, L, G and C) modeled fabrics for different environments were footprints in [¹]. Where R is resistance, G is conductance, L is inductance and capacitance C. These electrical parameters will be used in our electronic equivalent circuit model of living biological tissue. The electronic circuit below is similar to any biological dielectric medium to describe and model all properties are afferent.

Fig1. Circuit électronique équivalent d’un tissu biologique.

B.    SIMULATION OF ELECTRIC BEHAVIOR

1)    Calculation of bio-electronic settings

Using Matlab for the assessment of bio-electronic parameters, we obtained the following results: a = 79; b = 81; R_e (Z₀) = 167 Ohm; Im (Z₀) = 8 Ohm; R_e(g) = 79; Im(g) = 4.

2)   Simulation Results and Discussions

Considering the frequency of 3.4 Gigas Hertz Ghz of the propagation of electromagnetic waves, the depth of penetration of electromagnetic waves in a biological medium varies from 0 to 30 millimeters.

The results of the simulation of the voltage induced by electromagnetic waves in the different biological media are:

Fig.2. Evolution of the reflected tension as a function of the depth of penetration into the Blood.

Fig.3. Evolution of the reflected tension as a function of the depth of penetration into the skin.

Fig.4Evolution of the reflected tension as a function of the depth of penetration into the muscle.

Fig.5. Superposition curve of the evolution of the reflected tensions as a function of the depth of penetration into the biological tissues under study

The results of figures 2, 3 and 4 are represented as a function of the depth which is compared to that obtained experimentally in [11]. We note from the above that the tension induced in the different biological media studied in this article, is a decreasing function of the depth of penetration.

We also notice that the induced tension is greater at the end of the biological tissue.

                                                                                                                                                    III.   Conclusion

In this article we have chosen the modeling approach based on the equivalent electronic circuit of a human biological tissue, taking into account on the one hand the physical phenomena of the propagation of a microwave electromagnetic plane wave and on the other hand the values experiments[¹] in order to simulate the electrical behavior of human biological tissues exposed in a microwave electromagnetic environment.

We have tried to take advantage of the many advantages of this method, namely the reduction of simulation time, the possibility of simulating complex systems like the one being the subject of our study.

The simulation result obtained in this article approaches that obtained experimentally in the work of M. Mimi and D.V. Land [¹¹]. We note from the above that the induced tension is important in the different biological media studied in this article, and is a decreasing function of the depth of penetration as the thickness of biological tissue is reduced.

Therefore, we therefore considered that modeling based on equivalent electronic circuit of a human biological tissue is more suitable for the study of a system as complicated and disparate that a complex biological tissue.

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