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Nonlinear polarizability of erythrocytes in non-uniform alternating electric field (NUAEF) was proved theoretically and experimentally by dielectrophoresis method. The paper presents experimental evidence of the nonlinear polarizability of erythrocytes in the non-uniform alternating electric field. The rotation of erythrocyte around its own axis at more than one revolution per second in the non-uniform alternating electric field in the frequency range

The study of polarization and deformation of erythrocytes is an urgent problem in the diagnosis of some diseases. The above characteristics are interrelated in their reaction to practically any pathological process in the organism [

The aim of the work was to study the nonlinear polarizability of erythrocytes in NUAEF with an intensity ~

Human erythrocytes obtained from whole blood drawn from the donor’s vein were used in the study. To conduct the dielectrophoresis analysis, 2 ml of blood were collected with vacutainers in 3.7% citrate buffer at a ratio of 9:1. Immediately before the experiment, 10 μl of blood were diluted in ^{7} cm^{−3}. Blood collection from donors was performed with the approval of the Biomedical Ethics Committee of the Federal Budget Research Institution Research Institute of Therapy, Siberian Branch of Russian Academy of Medical Sciences (Protocol # 36 of the meeting of September 18, 2012).

Experiments were performed in a measuring cell where NUAEF was created. Detailed description of the measuring cell and the laboratory device as a whole is presented in [

Video monitoring and recording of the speed of erythrocyte rotation around its own axis were carried by the position of a typical natural reference point on its surface. The cell turnover period was measured using an electronic clock built into the computer.

Experimental observations demonstrated a slow rotation of erythrocytes around their own axes with varying frequency in the frequency range of

The dynamics of erythrocyte rotation around its own axis in non-uni- form alternating electric field. The arrow shows the position of the natural reference point on the cell membrane monitored during the rotation process

The external electric field _{}directed against the external one,

lume forms the induced dipole

NUAEF, the cell dipole is influenced by the time-averaged force vector, which makes the cell move [

where:

The vector of the cell electric field intensity _{}

The superposition of two harmonic oscillations

The condition

The nonlinear polarization of a cell requires the condition

The typical value of the erythrocyte transmembrane potential is about ^{1} (ion) should possess the energy required for overcoming the total potential barrier of the cell membrane

where:

The density of positive charges capable of overcoming the above barrier is described by Expression [

where:

The exponential function (4) can be determined using the Maclaurin series, which converges at any

If the summand

orders (starting from the third, quadratic, one) in (5) can be neglected. As a result, the density of the charges ca-

pable of overcoming the potential barrier has a linear character. If the exponent

to or more than 1, the contributions of individual summands of higher orders to nonlinearity become dominant. However, with increasing n value in (5) a general trend is observed: the values of individual summands of the series rapidly decrease.

The interrelations between Expressions (1, 3, 4, 5) allow us to consider the cell polarization process to be nonlinear, too. From the mathematical point of view, nonlinearity in Equation (5) emerges when

and

current

From Equation (6), the calculated values

on their serial numbers

where:

The calculated values of the summands of the Ma- claurin series determining the current through the cell membrane depending on and, the voltage across the membrane

The calculated values of the summands of the Ma- claurin series determining the current through the cell membrane depending on and, the voltage across the membrane

From the consideration of the first three summands of Equation (7) it follows that the alternating current of the membrane contains only the linear and the quadratic components

Taking into account that

The analysis of Expression (8) shows that the total current through the cell membrane is determined by the combination of individual harmonic components with frequencies _{ }and

nent

cell currents with the frequency

The linear model of polarization of the medium and the cell in the external alternating electric field is relatively simple. In each point, the electric field induces in their volume the dipoles with the harmonic frequency_{ }of the external field is transferred to the second and higher harmonics, and there also emerge multiple combinations between them [

The analysis of the presented known trigonometric expressions also shows that the member of the series with the serial number

Experimental data and the conducted theoretical analysis of the interaction between the cell and alternating electric field suggest that under the study conditions the erythrocyte can be presented as a nonlinear element whose membrane permeability for positive ions is higher in one direction than in the reverse direction. This is consistent with the selective permeability of the membrane, for example, for potassium ions

The conducted work allowed us to draw the following conclusions.

The nonlinear equivalent electric circuit of the cell for positive charges., and are the capacities of the membrane, cytoplasm and medium (cell suspension);, are the resistances of the membrane, cytoplasm and medium

1) The nonlinear polarizability of human erythrocytes is observed in non-uniform alternating electric field with the intensity

2) The nonlinear polarizability of erythrocytes in non-uniform alternating electric field causes their rotation around their own axes with the frequency exceeding

3) The external harmonic electric field affecting the cell is created in the cell cytoplasm in the form of a nonlinear uniform^{2} field with a constant component and a broad frequency range due to the electric properties of the cell membrane.

4) The alternating electric field from the donor erythrocyte with the amplitude exceeding

the constant component of the current

be considered as a signal one.