(a)
THE USAGE OF
LOW-ENERGY ELECTROMAGNETIC FIELDS OF MARGINAL HIGH-FREQUENCY RANGE FOR
RECONSTRUCTION OF THE INJURED BY INFECTIOUS MICROORGANISMS ANIMAL SKIN
Taras Hutsol
State Agrarian and Engineering University in Podilya, Ukraine
E-mail: pro-gp@pdatu.edu.ua
Volodymyr Ivanyshyn
State Agrarian and Engineering University in Podilya,
Ukraine
E-mail: volodymyrivanyshyn55@gmail.com
Serhii Yermakov
State Agrarian and Engineering University in Podilya,
Ukraine
E-mail: ermkov@gmail.com
Serhii Komarnitskyi
State Agrarian and Engineering
University in Podilya, Ukraine
E-mail: sergiypetrov2207@gmail.com
Submission: 15/11/2018
Revision: 08/02/2018
Accept: 27/02/2019
ABSTRACT
The paper is concerned with the mechanism of
interaction between the electromagnetic field and the microorganisms. Currently
the issue for usage of low-energy electromagnetic fields of marginal
high-frequency range for reconstruction of the injured by infectious
microorganisms animal skin is of great interest. The use of low-energy
electromagnetic fields for restoring animal skin cover is significantly
different from the existing physical and therapy procedures.The authors made
the theoretical and the experimental research on updating and developing the
low-energy electromagnetic technology and hardware of the electromagnetic field
of high-frequency range to restore animal skin cover of infected wounds. The
process of interaction between low-energy electromagnetic fields of
high-frequency range in terms of infected animal skin cover is examined on the
basis of the mathematic model. Particular attention was paid to theoretical
aspect and cellular level analysis of the biotronic parameters of
electromagnetic fields for the oppression of infectious microorganisms in
wounds of animal skin cover and its effective reunion.
Keywords: low-energy electromagnetic field, high-frequency
range, microorganism, animal skin cover
1. INTRODUCTION
At present,
have been accumulated many facts, what indicating that, depending on the
parameters of EMF (electromagnetic field), may change many the life
activity aspects of living organisms, including farm animals (GOLANT, 1991;
CHURMASOV; ZHUKOV; KUKUSHKINA; KALININA, 1996).
Recently
has been discovered a new factor to regulate the physiological processes of EMF
of URF (ultra-radio frequency) range, which affects the biorhythms of living
organisms (ORLOV; KAZAKOV, 2000; BECKIJ; DEVYATKOV; LEBEDEVA, 2000). The use of
low-energy EMF of URF range for the recovery of animal skin attacked by
infectious microorganisms requires theoretical research on the distribution of
EMF inside the bacterial cell and its influence on the membrane of cell
cytoplasm (LACY-HULBERT; METCALFE; HESKETH, 1998; BORYSEVYCH, 1992; HUTSOL,
2017; SIMKÓ; MATTSSON, 2004).
The
main molecular components of biological membranes are proteins and lipids that
make more than a half of dry cell mass. The basic membrane-forming lipids are
the unions with the perfect combination of hydrophobic and the hydrophilous
properties. They are poorly soluble in water monomeric form, and the tendency
of their polar heads to maximize contact with water gives them the unique
ability to create multiform resistant structures in terms of aggregation of
these molecules.
An
important feature of almost all the models is the fact that the surface of cell
membranes is considered as the most probable place for such actions. Despite
some progress in the research on the action of low-energy EMF on biological
objects, most of the primary molecular mechanisms of these actions are almost
not identified.
In
our opinion, this is explained by the fact that, on the one hand, physical
approach to the living matter is insufficient, and, on the other hand, the
successful search of an appropriate simple model of processes in biological
structures is difficult and sometimes impossible.
Knowledge
of primary, physically based mechanisms of influence of low energy EMF on
microorganisms, as well as the mechanism of the relationship between molecular
and system levels will explain the phase direction of bioelectronic and
magnetic effects and give the possibility to predict their occurrence that is
especially important for the oppression of infectious microorganisms in the
wounds of animals.
2. DATA AND RESEARCH METHODOLOGY
Taking
into account the fact that the experimental investigation of the internal field
transmission is almost impossible, the only way out is solving this problem with
the help of theoretical methods.
In
mathematical modeling of the process of scattering EMF at a biological object,
suppose that it has a structure of plane parallel layers. Considering a skin
cover, we will consider the first layer to be a wool cover, the second one is
skin and the third layer is muscles.
To
solve the problem is used the equation of Maxwell in differential form, with
the help of which are determined the parameters of influence EMF and evaluated
using graphic interpretations.
3. RESULTS AND DISCUSSIONS
3.1.
Determination
of internal EMF in single-layer objects in terms of external EMF influence
Analysis
of experimental research on the EMF of SHF range influence on biological
objects of different nature shows that the following measures cause the
significant changes in the cellular level even in terms of marginal power
levels (10 microwatts/cm2). It should be noted that the degree of this action
is determined not only by the value of EMF power but also by its frequency and
modulation characteristics.
The
influence of EMF of SHF on different microorganisms and insects is well
explored from the experimental point of view, but the mechanism of this action
itself is not examined, both at the organism and at the cellular levels. The
study of the mechanism of the interaction between EMF and microorganisms is
impossible without the information about the transmission of these fields
inside the cells of microorganisms.
To
get the original expression, that allows solving the given problem, at first,
let's consider the scattering of a plane electromagnetic wave at a biological
object, that has the structure of plane-parallel layers. So, if we deal with a
skin cover, we will consider the first layer to be a wool cover, the second one
is skin and the third layer is muscles.
Let
us suppose that the irradiating area is homogeneous in planes, which are
parallel to the surface of the radiation. It will allow us to explore the
distribution of EMF only in the direction that is perpendicular to the skin
surface. In addition, let’s imagine that the EMF falls also perpendicular to
the skin surface and the irradiating area has linear dimensions and is much
longer than the wavelength (about
Let
us imagine that the wool cover is characterized by dielectric and magnetic
penetration and, skin and,
muscles and. The outer space in relation to the skin is considered to be
simple. It is characterized by a permanent electric and magnetic penetration and.
In
the case we consider the environment is air, then F/m.
It
should be noted that the biological objects are not the magnetic materials, so
for further research, we will use TR/m.
Both dielectric penetration and density of
three-layered skin surface of agricultural animals (cattle) have the following
characteristics:
·
for wool = 1,28 – 1,33 kg/m3;
·
for skin cover = 928 kg/m3;
·
for tissue muscle = 1033 – 1048 kg/m3.
To
solve the problem the equation of Maxwell in differential form is used (ILYIN;
POZNIAK, 1978; KALYNYCHENKO; HORDYICHUK, 2006; SEREDA, 2007; RUBYN, 1987).
Let’s
suppose that a flat electromagnetic wave falls on the surface of the animal
skin, which has a structure of flat parallel and isotopes homogeneous layers of
wool cover, skin and muscle d1, d2, d3 thick, and propagates in the
direction opposite to the surface of the skin, which we combine with OX and
OY axes of rectangular coordinate system (fig. 1).
Graph 1: A model
of a layered environment of particular animal skin cover: 1 – the limit of wool
cover; 2 – skin limits; 3 - muscle limits; I – the layer of wool cover; II –
the layer of the skin; III – the layer of muscles
To
make everything clear, we consider vector to be parallel
to the ОХ axis
and vector to be
parallel to an axis.
On the edge of each layer the mentioned fields must
satisfy the boundary conditions, i.e., the tangential components of the vectors
of the electric and the magnetic fields have to be continuous. The following
conditions cause the system of equations.
(1)
Superscript
Besides, the plus sign refers to a field that is
propagated in the positive OZ direction; the minus sign refers to a
field that is propagated in a negative direction of the OZ axis.
Let us take into account that:
,
– tension amplitude of
electrical component, falling from the EMF;
– unknown amplitude of the reflected
(-) and those that passed (+) on each of the three borders of layers of EMF
components;
– wave resistance of the air and
each of the three layers of the skin;
– wave numbers in the
environment and in each of the layers; - is the frequency of the
incident field.
. In the examples, the element-free multiplier for the amplitude is omitted.
Using the mentioned marks, the system (2) can be rewritten in the
following way:
(2)
So, not the uniform system of linear algebraic equations
with six unknown coefficients we have got, which characterize the passage and
reflection coefficients on each of the three boundaries between layers.
Since the determinant of the system composed of the
coefficients in the terms of the unknown is not equal to zero, the system is an
invertible and has only one solution, which can be made with the help of
Cramer’s method (KALYNYCHENKO; HORDYICHUK, 2008; KRASNOV; KYSYLOV; MAKARENKO, 1976).
In the process of solving the system of linear algebraic
equations (2), we found the following coefficients, which allow us to find the magnitude of EMF amplitudes
at each of the layers of the animal skin cover. Obviously, the magnitude of the
electric field component in the wool cover may be defined by the following
mathematical expression:
(3)
In skin cover:
(4)
In muscular tissue:
(5)
3.2.
The
distribution of the electromagnetic fields in wounds of animal skin cover
The decrease of the electric field component amplitude
over its thickness takes place in the epidermis. This will cause the emergence
of the field gradient along the cylinder axis, which corresponds to the
diffraction of the wave that has - polarization.
In the case of -
polarization it is convenient to take the incident fields, scattered and those
that passed inside the cylinder waves into cylinder functions (CHERENKOV,
2015):
(6)
(7)
where falling and scattered waves are marked by the “fall”
and “disp” indices;
the internal fields of the cylinder do not have indexes;
;
;
– unknown coefficients;
– Bessel function –of the 1st kind;
– Hankel
function of the 2nd kind;
– the amplitude of the electric
component of the field in the second layer of the skin cover.
With the help of Maxwell equations, the rest
components of an incident, scattered and those waves that passed inside the
cylinder are determined. Thus, the amplitudes of the internal fields of the
cylinder are described with the help of the following expressions:
. (8)
However, to determine the energy characteristics of
the biological object of the fields that got inside, as well as for the
definition of the main electromagnetic characteristics of the interaction
between the field and the object there is no need to take a large number of
harmonics in expressions (8). It is enough to take the zero harp. With the help
of
, we
get the formula that is suitable for practical calculations of internal fields
in bio-objects of cylindrical shape:
(9)
Where
; (10)
(11)
(12)
The expressions we obtained describe the distribution
of EMF within the biological objects of cylinder form when their characteristics
are not changed in volume.
3.3.
Multiplex
calculation of EMF inside both, the healthy animal skin cover and infected
wounds
On the basis of expressions (3) – (5) the calculations
on the distribution of the electric field component inside the animal skin
cover were worked out (graph 1). The electrophysical characteristics and
thickness of layers are taken from (LEVYTSKA; MUSHYNSKYI; HUTSOL, 2017), the
amplitude of the electric component of the incident field is taken equal to one
to make re-calculation to specific values of a field easier. Calculations are
performed for 35 GHz medium frequency, for 30 – 40 GHz frequency band.
The graphic (graph 2) shows the depth of EMF
penetration inside animal skin cover, which varies from 0 to 1 on the X-axis. The
module of the complex amplitude of the EMF electric component is given on the
Y-axis.
To make the values of dielectric permeability of
tissue layers that make a skin cover specific, the graph has the least value
inside the skin layer, moreover, it is located near the border of muscle layer.
The computations are performed for animal tissue and
their electrophysical parameters have the following value:
Wool cover skin cover muscles = 46,5 – 47,3.
The computations of electromagnetic fields inside the
infected wounds of the animal skin were performed on the basis of shown
results. The change of the electrical characteristics at the cylinder ends is
automatically taken into account by boundary conditions at the plane-parallel
layers.
First of all, the dependence of the electric field
amplitude on the cylinder axis of the infected animal skin on the frequency of
EMF incident was examined (graph 3). The calculations were made for the middle
layer of animal skin. The frequency changed from 30 to 40 GHz, and the
dielectric parameters of the epidermis and cocci colonies were equal:
.
Graph 2:
Module distribution by the electrical component of the EMF inside the healthy
animal skin: wool cover 0 –
Graph 3:
The dependence of the electric field amplitude inside the cylinder of the
infected animal skin on the frequency of incident EMF
The following chart shows that the increasing
frequency from 30 GHz to 36 GHz causes the monotonous increasing of electric
field amplitude, reaching its maximum at 36 GHz.
Further increasing of the frequency causes the
internal field amplitude loss up to 40 GHz. The obtained results prove the EMF optimal
frequency to oppress the pathogenic skin microorganisms is in the 35 – 37 GHz
frequency range.
Graph 4 represented the dependence of electric
component amplitudes of EMF inside the wound of the animal skin cover. The
change in EMF depending on the distance from the axis of the cylinder area of
the pathogenic cocci colony is shown.
Graph 4:
The dependence of the electric component amplitude of the EMF in the individual
wound of animal skin cover from the pathogenic colony of cocci for 36.0 GHz
frequency
The graphic shows that on the cylinder axis where the
infected skin area is, the amplitude is maximum and exceeds the field amplitude
of the healthy skin.
3.4.
Membrane
destruction of the pathogenic cocci cells in terms of low-energy EMF of SHF
range action
The
deflection of the membrane from the balance you can associate with the
occurrence of defects in the structure of membranes due to local compression in
longitudinal or transverse direction. Accidental reduction in the thickness of
the membrane is of local character that should be considered as the initial
phase of forming local deepening.
The
most recognized is the mechanism of destruction of the membrane, caused by defects
in the type of transverse pores. Let us suggest that in this case the formation
of the defect is accompanied by changing the lipid molecules, located near the
border of the defect with the formation of the so-called inverted pores (LEVYTSKA; MUSHYNSKYI; HUTSOL, 2017). The value of the critical radius of the defect
in the cell membrane, where the transverse pore is not closed, is demonstrated
with the help of the following correlation:
, (13)
where – is a linear pull of the length unit of the perimeter of the defect;
– the
superficial tension of the membrane;
, where – the volume of the
unit area of the membrane, – the dielectric constant of water, – the dielectric
constant of the membrane, – the critical capacity, the excess of which
leads to the destruction of the membrane.
The
value of the critical potential of breakdown can be determined from the
expression (LEVYTSKA; MUSHYNSKYI; HUTSOL, 2017).
, (14)
where – is the module of elasticity of
the membrane;
– is the thickness of the
membrane;
– is the electric constant.
According
to the theory of electrical breakdown, an average lifetime of the membrane the
EMF of SHF range can be represented by the expression
, (15)
where – is constant;
– is the maximum energy value of
the membrane in terms of irradiation in it cylinder pores;
– is the Boltzmann constant.
To
calculate the energy of the defect we should take into account the work
connected with the change in the division surface, the membrane-solution due to
the formation of the side cylinder surface and decrease division surface
section with the help of section recession that corresponds to the cylinder
sides (LEVYTSKA; MUSHYNSKYI; HUTSOL, 2017).
The
dependence of the maximum meaning of energy defect
on the critical potential value at the membrane is
determined by the expression:
(16)
The
expressions (9) – (12) allow us to estimate the voltage magnitude of the EMF
electrical component both in the cytoplasm of the microorganisms and membrane
cytoplasm attuned frequency. However, the given expressions do not give the
information about how optimal is a value of the electric voltage and what
exhibition time of EMF action is required for decomposition of cell membranes
of pathogenic cocci.
3.5.
Multiple
calculations of biotropic EMF parameters for the oppression of pathogenic
microorganisms
The
results of the study are considered to be the basis for previous determination
of biotropic EMF parameters, which affect to oppress the pathogenic organisms
in wounds of animal skin cover. In addition, these results will help to develop
appropriate technical requirements for making electronic equipment.
As a
result of the multiple calculations, the critical potential for destruction of the plasmatic membrane of pathogenic cocci
in wounds of animal skin should not be less than 110 mV. In case the potential
is 110 mV the membranes of pathogenic cocci, a critical radius of defect where transverse pore is not closed is 0,8 10-
The
shown correspondence proves (graph 5) the fact that the increase of the voltage
potential at the membrane leads to a decreasing of the critical radius of pores
and reducing the maximum importance of energy (W).
The
reduction of critical threshold power in terms of increasing the voltage
potential by the external EMF leads to increasing the reliability of
above-critical membrane defect. In case of such defect, membrane ruptures
involuntarily because the increase of the size of the defect is accompanied by
the decrease in free energy of the system.
This
fact can explain the increasing probability of rupture in pathogenic
microorganism membranes, which are influenced by EMF with optimal biotropic
options.
Graph 5:
The dependence of the critical radius of transverse pores in the membranes of
pathogenic cocci from the potential by external EMF
The
increasing voltage potential on the membrane leads to decreasing in the
critical radius of pores and reducing the maximum power (W) (graph 5).
Reduction
of critical threshold power in terms of increasing the potential by the
external EMF leads to increasing the reliability of above-critical defect of
the membrane. Such defect causes the rupture of the membrane because the
increasing size of the defect is accompanied by a decrease in the free energy
of the system.
This
explains the increasing probability of membrane rupture of pathogenic
microorganisms, which are influenced by EMF with optimal biotropic options.
Graph
6 shows the dependence of the average lifetime of the membranes of pathogenic
cocci on the difference of voltage potential on the membrane by the external
EMF.
Graph 6:
The dependence of the average lifetime of the pathogenic cocci membranes
The
shown dependence (graph 6) proves the fact that the membrane lifetime, damaged
by the cocci, influenced by external EMF, is cut in terms of the increasing
difference. When the difference between voltage potential of more than 110 V,
the lifetime of the membrane of pathogenic cocci in wounds of animal skin cover
amounts up to 1 s.
4. CONCLUSIONS
The influence
of high-frequency electromagnetic field of the radio-frequency voltage zone on
the phase of animal skin cover will slow down the inflammation process,
improving the blood circulation, microcirculation of blood and lymph,
increasing the absorption of oxygen by tissues, activation of regenerative
processes that will lead to a recovery of the animal.
The
mechanism of interaction between the electromagnetic field and the
microorganisms are studied with the help of theoretical exploration of
distribution of these fields inside the cells of microorganisms. First of all,
the scattering of a plane electromagnetic wave in biological objects that have
the structure of the plane-parallel layer of animal skin cover is concerned for
the sake of simplicity: the first layer is a wool cover, the second one is
skin, and the third one is the muscle.
To
obtain the results, the calculations of electromagnetic fields inside the
infected wounds of animal skin were done. In addition, the change of the
electrical characteristics on the sides of the cylinder zone of field action is
automatically taken into account by boundary conditions at the plane-parallel
layers. The dependence of the amplitude of the electric field on the axis of
the cylinder infected skin area on the frequency of incident electromagnetic
field was examined in the study.
To
conclude we should note that:
1) For
the calculation of the EMF distribution in wounds of animal skin cover the
expressions obtained for the plane-parallel environment should be used.
2) Oppression
of pathogenic cocci in wounds of animal skin cover should be carried out with
the use of EMF in the frequency range of 35 – 37 GHz with a power density of
not more than 5 mw/cm2 and an exhibition of 3 – 5 min.
3) A
lifetime of pathogenic cocci in wounds of animal skin cover influenced by the
action of external EMF depends on the potential of the plasmatic cocci
membrane, which critical value is 110 mw.
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