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Investigation of bio-relaxation mechanism in human blood.


The electric field's applications are mainly related to inanimate nature of material. Nevertheless, the universal character of the phenomenon of electric polarization of substances presumes that the dielectric effect significantly influences metabolism. The study of field induced contraction in blood cell is very important to understand the relaxation mechanism.

Blood is a highly functional body fluid, it delivers oxygen to the vital parts, it transports nutrients, vitamins, and metabolites and it also is a fundamental part of the immune system. Therefore, the precise knowledge of its constituents, its physical, biological, and chemical properties and its dynamics is of great importance. Especially its dielectric parameters are of relevance for various medical applications such as cell separation (e.g., cancer cells from normal blood cells), checking the deterioration of preserved blood, and dielectric coagulometry, research in the field of artificial blood (1-9).

In addition, the precise knowledge of the dielectric properties of blood is prerequisite for fixing limiting values for electromagnetic pollution (via the conductivity in the specific absorption rate (SAR)). Early measurements of the electrical properties of blood contributed significantly to unravel the constitution of red blood cells (RBC). For example, the results by Hober, provided the first indications of dispersion (i.e. frequency dependence), caused by the membrane of RBCs, in the radio frequency (RF) spectrum of the dielectric properties of blood. This relaxation process is now a days identified as being of Maxwell-Wagner type and termed [alpha]-relaxation in biophysical literature (10-12).

To study the electrical properties of the human erythrocytes and whole blood have been a challenge under alternating current in the frequency domain (13). The investigation of fundamental electrical properties made it possible to derive the thickness of a biological membrane by a physical method (14). The frequency dependence of the dielectric properties of the RBC in suspension has been reported (15-17).

Several approaches have been proposed to model the blood dielectric properties. Grosse used a simple counterion model, in which the fluid is treated as a suspension of cells inside an electrolyte solution (the plasma). Also, Grosse and Schwan have proposed that a microscopic model of potentials induced by alternating electrical fields, applied on cells, must include additional information such as membrane conductance and surface admittance (16). A different approach based on the Maxwell-Wagner model has been used for analyzing the dielectric properties of suspensions of erythrocytes (5-6).

Some researchers have reported a study of the dielectric properties of blood as a function of temperature. They found a weak dependence of the permittivity and conductivity as a function of temperature variations. More recently Jaspard et al. have also published a study of the dielectric properties of blood as a function of the hematocrit percentage, where they found a strong dependence on the concentration. In these works a frequency range from 1 MHz to 1 GHz was swept, and measurements were performed on blood of humans, cows, and sheep.


Nano and microparticles are the constituents of human blood; they drastically affect the charge transfer (CT) through the viable fluid. The frequency dependent dielectric properties of the blood are characterized by charge transfer of [alpha]-relaxation type, are widely investigated with special stress on physical mechanism. In the present study, we will investigate the relaxation mechanism associated with human blood group A+ at different conditions of experiment.

Experimental Details

We have taken blood sample for the measurement of dielectric properties of A+ human blood group of normal person. First of all we have analyzed that experimental blood sample is normal or malignant with some pathological measurements. Pathological report confirms the experimental blood is normal with respect to all parameters. The blood sample kept into Ethylene Diamene Tetra Acetic acid (EDTA) voil for protecting it from coagulations of blood. The real and imaginary parts of dielectric constant, dissipation factor and A. C. conductivity of normal human blood of A+ blood group were investigated in the frequency range from 42 Hz to 5 MHz by using LCR HiTESTER meter (Hioki 3532-50) at different temperature in vacuum (i.e. 10-2 Torr). It is based on the polarization of biological molecule with frequency. The LCR meter, was connected with the computer and the data were collected as a function of different frequencies (Figure 1).




The dielectric properties of human blood were studied by using temperature dependent dielectric spectroscopy under frequency range from 42 Hz to 5 MHz. We have investigated the variation of dielectric properties with temperature and frequency in "A" positive blood group in vacuum.

Figure 2 and 3 shows the frequency dependent real and imaginary part of dielectric constant at different temperature. The decay trends of dielectric constant with frequency are same at all temperature. The dielectric constant is decaying rapidly upto 10 kHz and then constant above this frequency. The dielectric loss is characterized by a sharp peak (Figure 4) at the frequency of 500 Hz and 100 kHz. Slight shifting of peak is being observed at different temperature.



The absorption constant, relaxation time and AC conductivity is maximum at room temperature and minimum at 70[degrees]C (Figure 5, 6 and 7). The decay nature of absorption constant is similar to dielectric loss.

The behavior of dielectric properties was explained on the basis of relaxation mechanism of blood. The dielectric spectra show that dielectric parameters (dielectric constant, dissipation factor and impedance) are the function of frequency. We also observed two typical relaxations in this process.


The behavior of dielectric properties was explained on the basis of relaxation mechanism of blood. The dielectric spectra show that dielectric parameters (dielectric constant, dissipation factor and impedance) are the function of frequency. Dielectric constant indicates the relative charge storage capability of material as compared with free space. The equation, = [[epsilon].sup.*] = j[epsilon]", was used to calculate the complex dielectric constant, where [epsilon]', [epsilon]" are the real, imaginary parts of dielectric constant & j is the imaginary root of -1 (i.e. j= [check]--l), and were determine from equations (1) and (2).

[epsilon]' = [c.sub.m]/[c.sub.0], where [c.sub.0] = 4[pi] [[epsilon].sub.0] (ab/b-a) (1)

[epsilon]" = [epsilon]' tan [delta] (2)

where, a and b are inner and outer radius of sample holder respectively.

(8.85 x [10.sup.-12] F/m) is free space dielectric constant.

[c.sub.m] is capacitance of a capacitor with a medium (blood sample).

[c.sub.0] is capacitance of a capacitor in free space or vacuum.



The tangential loss is a measure of energy loss in the dielectric during A.C. operation, which is a material property and does not depend on the geometry of dielectric. In general, the tangential loss (tan [delta]), expressed as dissipation factor can be defined as

tan [delta] = [epsilon]"/[epsilon]' + [sigma]/2[pi]f[epsilon]' (3)

Where [epsilon]", [epsilon]', [sigma] and f are real, imaginary parts of dielectric constant, conductivity and frequency respectively.

The dielectric properties of blood are caused by several factors such as blood cells, proteins etc. In blood the main factors may influence the aggregation process: the structure of blood cells and the concentration of certain high molecular plasma proteins. Generally, the blood cells are negatively charged and repel each other, whereas many plasma proteins are positively charged and neutralize the surface charges of erythrocytes, reducing the repulsive forces and promoting aggregation. In blood the large cells have a small surface-to-volume ratio, and therefore have less charge in relation to their mass and hence adhere together more easily than small cells; the exact mechanism of dielectric properties of blood is not yet fully understood.



The possibility of manipulating the living cells in electric field is explained by their dielectric properties or dielectrophoresis. It is defined as the lateral motion imparted on the uncharged but polarizable blood cells or particles as a result of polarization induced by nonuniform electric fields. When a polarizable blood cell (or particle) is exposed to an electric field, the particle polarizes, giving rise to an induced dipole moment (18). The value of the dipole moment depends on the particle volume, its permittivity relative to that of the surrounding medium, and the electric field intensity, E. In the case of a spherical homogeneous blood cell of radius r the effective dipole moment, m, can be expressed by Sauer (19).

m = 4[pi][[epsilon].sub.m]f([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m]])[r.sup.3] (4)

wheref([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m]) = ([[epsilon].sup.*.sub.p]--[[epsilon].sup.*.sub.m])/( [[epsilon].sup.*.sub.p]--2[[epsilon].sup.*.sub.m]) is called Clausious Mosotti factor and [[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m] are the complex pennitivities of medium and the particle or cell. Generally, the complex permittivity is given by

[[epsilon].sup.*] = [epsilon]--j ([sigma]/[omega]) (5)

where [epsilon] is the real permittivity, [sigma] is the conductivity, [j.sup.2] = -1 and [omega] is the angular frequency. When Re {f([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m])} > 0 the effective dipole moment is aligned with the electric field E. However, if Re {f ([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m]}}<0, then effective dipole moment act against the applied field vector.

The dielectrophoretic force F acting on a dipole can be generally expressed as follows:

F = Re {m [nabla] E} (6)

Combining equation (4) and (6) the equation for dielectrophoretic force can be written as :

F = 2[pi][r.sup.3][[epsilon].sub.m] Re {f ([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m])[nabla][E.sup.2]} (7)

It is to be noted that for the case of the sphere the Clausius

Mosotti factor is bounded by the limits.

1 [greater than or equal to] Re {f {[[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m])} [greater than or equal to] - 1/2. 8)

As stated above, the Clausius Mosotti factor can be either positive or negative (or zero); so the force on a blood cell can act to direct a cell either towards or away from a region of high electric field strength. These two conditions are shown in Figure 8.

Figure 8 shows the cell on the left is more polarizable than the surrounding medium and is attracted towards the strong field at the electrode; however, the cell of low polarizability on the right is directed away from the strong field region.

In fact equation (7) is valid for a homogeneous cell or particle. However, we know that living cells are far from homogeneous. The living cell consists of cellular membrane and cytoplasm. Assume that a spherical living cell consists of a cytoplasm with permittivity [[epsilon].sub.p], conductivity [[sigma].sub.p] and radius r enclosed by cellular membrane of permittivity [[epsilon].sub.c], and thickness [delta]. As shown by Kaler and Jones (20) at frequencies higher than 10 kHz the sinusoidal steady-state dielectric response of a spherical living cell can be represented by an equivalent homogeneous sphere of radius r + [delta] and the complex permittivity [[epsilon].sup.*sub.cell].

[[epsilon].sup.*sub.cell] = [c.sub.m] (j[omega][r.sub.1] + 1)/[j[omega]([[tau].sub.1] + [[tau].sub.2])+ 1] (9)

Hence, [c.sub.m] = [[epsilon].sub.c]/[delta] is the cell membrane capacitance per unit area, and [[tau].sub.1] = [[epsilon].sub.p]/[[sigma].sub.p] and [[tau].sub.2] = [c.sub.m] r/[[sigma].sub.p] are the times constant.

Equation (7) depict the force acting on a cell in a nonuniform electric field is dependent on its dimensions. Besides, as derived from the definition of the Clausius-Mosotti factor, the force depends on dielectric properties of cytoplasm as well. Thus, mobility of cells in the electric field is a rather complex function of their dimensions and shape as well as of dielectric parameters of cytoplasm and cellular membrane. Thereby, the dependence of the Clausius-Mosotti factor on the electric field frequency allows for a wide range variation of the force acting on a cell.

When blood is subjected to alternating electric field, the rotation torque is exerted on cell

[tau] = m x E (10)

This shows that the torque depends only on the electric field vector and not on the field gradient. The value of the phase difference between the induced dipole moment m, and the field vector E controls the magnitude of the torque, reaching maximum when the phase difference is 9"", and zero when the phase is zero. Thus a cell in a rotating electric field will rotate asynchronously with the field. It can be shown that the torque depends only on the imaginary component of the dipole moment and so the time-averaged torque on a cell of radius r is:

[tau]([omega]) = -4[pi][[epsilon].sub.m][r.sup.3]Im {f([[epsilon].sup.*.sub.p], [[epsilon].sup.*.sub.m])}[E.sup.2] (11)

For example, if the imaginary component of m is positive, then the torque exerted will be negative and cause the particle to rotate in antifield direction.

It follows from equation (11) that if a cell is placed between electrodes and the angular rate of rotation of cells in the rotating field is measured, the dependence of the angular rate on electric field frequency will coincide with the frequency dependence of the imaginary part of the Clausius-Mosotti factor.

There appears an interaction (dipolar or ionic) between the two types of molecules such as RBC and WBC. This is particularly reflected in various physical properties: (a) change in regular arrangement of blood cells, (b) increase in conductivity, (c) decrease in activation energy for carrier transport, (d) enhancement in the intensity of secondary relaxation processes.

The increase in dielectric constant with temperature may be due to the increase in cell mobility and also may be partly due to expansion of cell boundaries. Infact the cells are immobile at lower temperature and dipolar orientation is less but at higher temperature dipolar motion and mobility of cell play significant role into total polarization of blood cells.

The magnitude of loss peak decreases with increasing frequency and temperature. The dielectric parameters at high temperature are generally appearing by rotatory diffusional motion of biomolecules from one quasi--stable position to another. This is known as [alpha]-relaxation. The dielectric parameter appears at low temperature are mainly due to small movements of dipolar cells.

The [alpha]-relaxation located in the low-frequency regime (i.e. 100 kHz) was detected in some biological materials. However, interestingly, an [alpha]-relaxation seems to be absent in whole blood (15) and only is found in hemolyzed blood cells. This was speculated to be due to a higher ion permeability of the membranes in the latter case, shifting the relaxation spectrum into the experimental frequency window. The origin of the [alpha]-relaxation is a matter of controversy; most commonly, it is assumed to arise from counterion diffusion effects.

The blood cells adjust their position themselves under application of A.C. electric field, (of frequency), and have minimum energies against the applied electric field by forming dipoles opposite to. The time for dipoles to return to their initial position is called relaxation time. Each micro-dipole has its own relaxation time depending on its physical characteristics. Thus, in blood wide spectra of relaxation times should exist as shown in Figure 6. This relaxation time distribution behavior is due to the increase in mobility of free charges between different microcomponants through blood which causes dielectric relaxation with definite period. This process provides the conducting path for charge carriers and hence A. C. conductivity increases with (Figure 7) frequency and temperature. Further, the analysis of the temperature-dependent AC conductivity and its comparison with the relaxation time reveals a charge transport is governed by different energy barriers than the motions of the solution molecules or reorientation of bound water molecules (21-22).

It is clear from Fig. 6, the relaxation time increase with temperature, it is characteristics time of the involved dynamics of the relaxing entities. All relaxation times reveal straight-line behavior in the Arrhenius representation of, indicating thermally activated behavior (23).

[tau] = [[tau].sub.0] exp([[epsilon].sub.[tau]]/[k.sub.B]T) (12)

where, [[tau].sub.0] is an inverse attempt frequency, often assumed to be of the order of a typical phonon frequency and [E.sub.[tau]] is the activation energy for the relaxation.

The two mechanisms are likely to be involved when blood is subject to field and temperature; aggregation and interfacial polarization. Generally, blood cells are liable to aggregate when certain plasma proteins are present. This aggregation of blood cells changes the distribution of the cells in a suspension, which alters the distribution of the electrical field when an electrical current is applied, and hence changes the measured resistance, impedance and capacitance values. The results shown in the present study indicate that the aggregation of blood cell might increase both resistance and capacitance. Therefore, higher the concentration of certain plasma proteins, the faster and stronger is the aggregation and the greater are the resistance and capacitance. The aggregation of blood cells might be the cause of their increased capacitance as observed in present study. Our results are comparable with the results reported in literature (24-26).

The possibility of Interfacial polarization cannot fully ignored, when an external electric field in the frequency range used in the present study is applied, two changes take place; (i) charges with opposite signs normally accumulate on both sides of a cell membrane, the centers of these charges would separate in the radial direction, modifying the apparent dipole moments and (ii) certain macromolecules accumulated in the interfacial region would orient so as to reduce their potential energy (27-29). Fibrinogens and other plasma proteins, as charged, could be adsorbed to the interface and hence affect the measured effective resistance and capacitance. It is very clear from histogram that only two type of relaxation mechanism are responsible for dielectric properties of A+ blood group (Figure 9). Therefore, dipolar and interfacial polarization are the possible relaxation mechanism of human blood.


It is concluded that the effect of alternating field and temperature causes the relaxation of blood. Furthermore, the dielectric behavior of human blood under present investigation is followed by dipolar and interfacial types of relaxations. It is concluded that the permittivity and loss of whole blood is significantly affected by frequency of field and temperature. The distribution of relaxation time shows the similar behavior. The A. C. conductivity of whole blood is modified by application of A.C. field and temperature, which does not allow for storage of charge carriers. This measurement will certainly enrich the area of biosensors research. This basic study applies to distinguish the malignant blood and normal blood as well as blood groups. Finally, it is concluded that the application of dielectric measurement method in biomaterial is very accurate, affordable, harmless, portable, and rapid when used noninvasively. The future work is extended to apply this method on malignant blood.

Received 16 March 2016; Accepted 7 June 2016; Published online 10 June 2016


We are thankful to Prof. B.B. Dzantiev Dy Director, A. N. Bach Institute of Biochemistry, Russian Academy of Sciences, Moscow (Russia) for discussion and suggestion to improve the quality of work.


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M.S. Gaur *, Dayal Saran

Department of Physics, Hindustan College of Science and Technology, Farah, Mathura 281 122, Uttar Pradesh, India (affiliated to Dr. A.P.J. Abdul Kalam Technical University, Lucknow, Uttar Pradesh)

* Coresponding author: Dr. M.S. Gaur; E-mail:
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Title Annotation:Original Article
Author:Gaur, M.S.; Saran, Dayal
Publication:Trends in Biomaterials and Artificial Organs
Article Type:Report
Date:Jan 1, 2016
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