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Melkonyan Arman
Student, National Polytechnic University of Armenia
ANALYSIS AND MODELING OF EQUIVALENT SCHEMES OF BIOLOGICAL TISSUE
Abstract: There have been observed the peculiarities of different types of biological tissue, the principles of electric circuits constructions. These principles have allowed constructing biological tissue-equivalent electrical circuits by using two, three, and four elements. There have been introduced the most commonly used electrical schemes of biological tissue, as well as their impedance phrases and application areas. An analysis of the adequate schemes and simulation of the MATLAB software environment has been performed and modelling results have been implemented.
Keywords: biological tissue, impedance, construction principle, equivalent electrical scheme, modelling.
Introduction.
By the nature of the electrical properties biological tissue is a heterogeneous environment. Organic substances (proteins, fats, carbohydrates, etc.) that make up the dense parts of tissues are dielectrics. However, all tissues and cells in the body contain fluids or are washed by them (blood, lymph, various tissue fluids), in addition to organic colloids, these fluids also contain electrolyte solutions, and therefore their resistivity to direct current is quite big.
The electrical conductivity of biological tissues (BT) is determined by the presence of free ions. The Ohm's law does not apply to BTs (due to polarization the current decreases in 2-3 ways/categories/). For the analysis of the effects of electrophysical properties of BTs on excitation processes, passive BTs are presented with equivalent electrical schemes (EESs) having alive BT impedance properties [1-6]. BT structural surveys are conducted in a wide range of frequencies (100 Hz ... 10 KHz). For this purpose, the frequency capabilities of BTs are presented in the form of EESs that correspond to the regularity of the distribution of electricity
in biological systems (the phenomenon of ionic conductivity and charge separation in BTs is caused by phase deviation of current and voltage). Tissue membranes have complicated structures, and according to Cole, they can be compared with capacitors [1]. The active ingredients of biological-electrical impedance (BEI) characterizing the flow of external and internal electrolytes (blood, lymph, interstitial fluid, etc.) are conditioned by the replacement of the amplifiers in the electric chain, and the capacitance components are characterized by separating the vacuum cleaners which is typical to the multidimensional BTs. At low frequencies (f < 100 Hz), the capability of the BT's is small, and the base deposit is an active component which is attributed to the upper layers of the skin. At high frequencies (f >10 kHz), the capacitance component of BTs decreases (decreases the impact of the discharging structures), and the active component strives for a constant value, characterizing the properties of high-definition BTs.
The nature of the problem and justification of the methodology. The construction of EES for BT is an important stage in the investigation of the given
physical phenomenon. EES should not only reflect the properties of BTs in the frequency and temperature domains that are being investigated but should also anticipate their behaviour in larger areas. From this point of view, research, comparative analysis and modelling of the principles of construction of the BTs are a topical issue.
The results of the survey.
The number of BT model circuits is determined by the approximation of the tissue characteristics. You need three rings for 10% accuracy. CF being a fre-
quency-dependent parameter allows evaluating the vitality and physiological state of the organism. The resistivity of biological tissues, determined for a given frequency of the current, can significantly change under the influence of physiological and pathophysiological factors. The non-affected BT characteristics have an exponential look, and dead BTs do not have a frequency dependency (the membrane that has the role of condensator is destroyed). The characteristic dependence of the BT impedance on the frequency, up to several tens of megahertz, is shown in Fig. 1 [10].
Fig.1. Frequency dependence of biotissue impedance
The cell is the basis of BT. The membrane is a permeable barrier to the intracellular and extracellular components and is characterized by the properties of
the dielectric. Table 1 shows typical values of the electrical resistivity of the primary biological tissues for a current frequency of 50 kHz.
Table 1
Biological tissue p, Ohmm
Muscle 2,0
Nervous tissue 14,3
Adipose tissue 33,3
Dry skin 10 5
Bone without periosteum 10 7
Cerebrospinal fluid 0,65
Blood 1,5
Neuromuscular tissue 1,6
Lungs without air 2,0
Brain (grey matter) 2,8
Skeletal muscle 3,0
Liver 4,0
skin 5,5
Brain (white matter) 6,8
Lungs on exhalation 7,0
Adipose tissue 15
lungs when inhaling 23
Bone tissue 150
The table shows that adipose and bone tissues have significantly lower electrical conductivity. Differences in resistivity can be explained, first of all, by different contents of fluid and electrolytes in organs and tissues. An important property of biological tissues is the dependence of their conductivity and relative dielectric constant on the frequency of the current.
Principles of construction of biological tissues's equivalent circuits. The construction of equivalent circuits of biological tissues is an important step in its study. The analysis of existing schemes of existing BTs shows that the composition of the elements used is limited by the use of active and reactive elements. This allows formalizing the process of analyzing and synthesis of BT schemes.
For this purpose, the mathematical theory of the multitude theory can be used to formulate the problem. Let's suppose that there is a multitude of a; elements based on which it is possible to build an equivalent scheme. The quantity of the elements in the multitude is N.Suppose that K is the minimal collection of the required blocks. In that case the multitude of the main elements can be introduced in the following way:
L; c A, i = UK.
If 1; =| L i< N, it means that there exists another implementation for the construction of the i -th version,since but for the 1 main elements,there can
also be Q = N —1; additional elements that comprise C multitude.It is obvious that Ci c A; Ci n Li = 0; Ci U Li = A. Each element of the C multitude can be included or not included in the equivalent scheme. Consequently the number of implementations in i-th version will be
C-
n- = 2 1 : The implementations of i -th version can be represented in the following way
F = {f1}, j = where f- - is the j-th implementation of the version i.
BT variants can be referred to the third type that are represented in the table 2.
Table 2
Topological variants of two, three and four element equivalent schemes of biological tissue
In the general case, the impedance Zx can contain both active - Rx and reactive Cx - capacitive resistances.
From Table 2 it can be seen that two and three elemental variants of biological tissues are realized in two sub-variants, and the four element variant is realized in three sub-variants.
The use of parallel and serial connection of active and reactive elements can be obtained various options for constructing equivalent electrical circuits of biological tissues. The resulting schemes can be considered as electrical circuits for the replacement of real biological tissue.
In the third table is given the scope of application of BTs, EESs and impedance.
Table 3
BT's known electrical equivalent schemes_
N°
model
Impedance:
Scope of application
Z = R (1 + joCR) Cole model
Low Frequency Range
Z = 1 ((1/R )+R + 1ljaC2 y ) Fricke-Morse model
Muscle BTs With Other Components (fat, blood, etc.)
Z = Ri +(1R2 + jœC2 )
A model that is based on Fricke-Morse model
Skin surface layers and hypodermic cells
Z = R:
R +(1/R2 + jmC2 )-1
Skin deep layers and internal organs
1
2
3
4
The cell membrane is normally composed of a non-conductive lipid layer which is located between the two layers of the transmitter protein molecules. In low-frequency domain (<100 Hz) power/current/ does not flow through the cell membrane, it only passes through the extracellular liquid, and the intracellular fluid does not participate in the process. In the high-frequency range (> 100 Hz), the intracellular liquid also participates in the power transmission process, which extends across the extracellular and intracellular areas. Consequently, the parallel model of Table3 does not fully reflect the BEI capabilities of the BTs.
For this reason, Fricke-Morse's model (table 3) is used to investigate the frequency characteristics of the BEI, according to which the extracellular and intracel-lular fluids are transmitters and the cell membrane is dielectric that characterizes the electrical capacity. In low and high-frequency domains, the ability to inject in the BEI strives for zero, and, in the case of elevated, the membrane does not impede the transmission. Fricke-Morse's model can be replaced by the most suitable model for analysis (table 3).
As already noted, in the study of biological tissues an important task is to consider the nature of the dependences of the frequency characteristics of the im-pedance.(full electrical resistance of an alternating current circuit) - biological tissues.
The absolute value (modulus) of the electrical impedance is determined by the expression:
|Z| =
In practice, the impedance value can be determined by measuring the amplitude (or effective) values of the voltage Uo and the current strength Io.
Z = U°/
|Z| = Uff;
eff
The phase angle 9 determines the ratio of the reactive and active components of the impedance
№ = x/R
The values of the phase angle obtained at a frequency of 1 kHz for various biological tissues are given in Table 4 [10].
Table 4
The phase angle for different types of tissues
An object 9, deg.
Human skin, frogs - 55
Frog nerve - 64
Rabbit muscle - 65
0
For qualitative and quantitative modelling of the electrical properties of individual parts of the human body, simple equivalent electrical circuits of biological tissues are widely used in Table 3, due to the presence
of active and reactive components of the impedance. Therefore, it is possible to simulate the electrical properties of biological tissues using resistors , and capaci-
tors - carriers of capacitive resistance. Due to this simulation, it is possible to evaluate the passive electrical properties of biological tissues, and the use of the MATLAB software environment to predict the behaviour of biological tissue based on the model's response [9].
These circuits were simulated using the MATLAB software at C = 8.5 ^F = 85 x 10-7 F, R1 = 120 Q, and
R2 = 100 Q. We calculated phase angle with <=an-gle(Z) formula, where angle(Z) is taken from MATLAB function list. It returns the phase angles, in radians, for each element of complex array Z.
The results of the simulation are shown in Figure
2-9.
Pic. 2 Z1 phase angle dependence of frequency and active R resistance
Pic. 3 The dependence of the Z1 Impedance module on the frequency and active R resistance
Pic.4 Z2 phase angle dependence of frequency and active R resistance
Pic. 5 Z2 Impedance module dependence on frequency and active R resistance
Pic. 6 Z3 phase angle dependence on frequency and active R resistance
-VJJ H
|Z| (Ohm)
f (Hz)
Pic. 7 Z3 The dependence of the Impedance module on the frequency and active R resistance cp(Deg.) _
Pic. 8 Z4 phase angle dependence on frequency and active R resistance
Pic. 9 Z4 Impedance module dependence on frequency and active R resistance
The results obtained give a qualitative picture of the behaviour of the absolute value of the impedance and phases with a change in the frequency of the alternating current/power/.
Conclusions:
1. Biological tissues are complex and heterogeneous. Therefore they significantly different in conductive and dielectric properties.
2. The investigations shows that the equivalent electrical circuits of most biological tissues can be devided to three types: two, three, and four elemental equivalent circuits, with their modifications.
3. Monitored equivalent electric circuits of BTs, their biological impedances and specifications can be the basis for the research and modelling of BT characteristics.
4. The obtained simulation results of the equivalent electrical circuits of biological tissues in the MATLAB environment give a qualitative picture of the behaviour of the absolute value of the impedance and the phase angle with a change in the frequency of alternating current/power/.
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Starishko O.M.
assistant of the Department of Modern Technologies of Diagnostic and Treatment Process,
Oles Honchar Dnipro National University
Lusta M. V.
student of Faculty of Medical Technologies of Diagnostics and Rehabilitation,
Oles Honchar Dnipro National University
PECULIARITIES OF MICROBIOCENOSIS COMPOSITION OF THE UROGENITAL TRACT OF WOMEN IN THE DNIPRO REGION DEFINED BY TEST SYSTEM FEMOFLORE SCREEN
Старшко Оксана МиколаХвна
асистент кафедри сучасних технологш дiагностично-лiкувального процесу, Днтровський нацюнальний утверситет iменi Олеся Гончара
Луста Максим ВШалшович студент факультету медичних технологш дiагностики та реабттацИ] Днтровський нацюнальний утверситет iменi Олеся Гончара
ОСОБЛИВОСТ1 СКЛАДУ М1КРОБ1ОЦЕНОЗУ УРОГЕН1ТАЛЬНОГО ТРАКТУ Ж1НОК ДН1ПРОВСЬКОГО РЕГ1ОНУ ЗА ДОПОМОГОЮ ТЕСТ-СИСТЕМИ ФЕМОФЛОР СКР1Н
Summary: The composition of microbiocenosis of the urogenital tract of women is determined by the polymerase chain reaction (PCR) method with real-time results detection using the Femoflore Screen test system. 120 archival data of patients were analyzed and the composition of microbiocenosis of the urogenital tract was compared, depending on the age of the patients. Comparing the data of the analyzes with the norms of microbiota and the degrees of imbalance, the regulated instructions of the Femoflore Screen were established: in 56 (46.3%) patients the most frequent infection that caused vaginal dysbiosis was Gardnerella vaginalis; in the second place -
