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Theoretical aspects of measuring input resistance in syncytial tissue by means of double-barreled electrode/Iejimo varzos matavimo sincitiniame audinyje dvikanaliu elektrodu teoriniai aspektai.

Introduction

Investigation of the intercellular electric communication is of utmost importance for the explanation of the mechanisms of excitation wave spread in the cardiac tissue. Measurement of the input resistance presents one of possibilities to evaluate the intercellular electric coupling. In the syncytial structure, the input resistance can be measured by using double-microelectrode technique [1-3], when one barrel of the microelectrode is used for delivering a rectangular jump of current, and the other one is used for recording the intracellular potential. However, when introduced to cell, such microelectrodes, because of their large dimensions, may damage the membrane to a greater extent than single-barrel microelectrodes used exclusively for recording the intracellular potential or for delivering the current [4,5]. Also, the possibility that the current leakage via the damaged membrane may exert a considerable effect during the measurement of the input resistance by means of a double-barreled microelectrode cannot be rejected.

In the present work, the results of input resistance measurement in the rabbit's right auricle endocardium by means of a double-barreled microelectrode, under normal conditions and under heptanol-induced blockade, are presented. Mathematical model for determination of input resistance was constructed and experimental data were analysed on theoretical basis.

Methods

Measurements were performed on rabbit's right atrium preparations in vitro. Preparation involving crista terminalis and trabecular area were perfused by Tyrode solution of the following composition (in mM): NaCl 136; KCl - 2.7; Ca[Cl.sub.2] - 1.8; MgS[O.sub.4] - 0.5; Na[H.sub.2]P[O.sub.4] 4.6; NaHC[O.sub.3]--up to pH=7.35; glucose--2 g/l; temperature--37 [+ or -] 0.5[degrees]C. The input resistance measurements were performed in the trabecular area of isolated preparations from the rabbit right atrium. The preparation was stimulated at the rate of 3 Hz, with the bipolar electrode placed on crista terminalis. A double microelectrode was used for recording the input resistance, one barrel serving for delivering the current jump [I.sub.o], and the other one for recording the jump of the intracellular potential ([DELTA][V.sub.i]) and extracellular potential ([DELTA][V.sub.e]). The input resistance ([R.sub.in]) was calculated according to Ohm's law:

[R.sub.in] = [DELTA][V.sub.i] - [DELTA][V.sub.e]/[I.sub.o]. (1)

The measurement was first performed under normal conditions, then 3.5 mM heptanol, an efficient inhibitor of electric coupling [6], was added to the normal Tyrode. The electric coupling used to deteriorate (while the input resistance increased) within 10-15 min, a complete blockade being reached, as indicated by the absence of action potentials at the recording site, with the ensuring cessation of the input resistance increase.

Simulating measurement of the input resistance

When the input resistance is measured by double-barreled microelectrode, current [I.sub.o] flows through resistance of the myoplasm [r.sub.pl], resistance of intercellular contacts [r.sub.k] and resistance of the electrogenic membrane [r.sub.m] (electric diagram in Fig. 1a). In reality the cell is injured when microelectrode is inserted and leakage current flows through the leakage resistance [r.sub.d] at the damaged site (Fig.1b).

According to theoretical models [7], the input resistance ([R.sub.in]) in three dimensional isotropic syncytial tissue, which consists of spherical tightly packed cells with intercellular contacts of high conductivity, depends on resistances of intercellular contacts and myoplasm:

[R.sub.in] = ([[rho].sub.pl] - [[rho].sub.T]/4[pi][r.sub.o] + [pi][R.sub.k]/32[r.sup.2.sub.c], (2)

where [[rho].sub.pl]--resistivity of myoplasm, [[rho].sub.T]--resistivity of Tyrode solution, [r.sub.o]--distance between tips of double-barreled microelectrode, [R.sub.k]--resistivity of intercellular contacts, [r.sub.c]--radius of cell.

[FIGURE 1 OMITTED]

Considering (1) in future we will assume that

[r.sub.pl] = ([[rho].sub.pl] - [[rho].sub.T])/4[pi][r.sub.o], (3)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]--the input resistance of Tyrode solution.

According to [8], the resistance [r.sub.m] has no influence on the input resistance of the tissue. Therefore the resistance of the electrogenic membrane [r.sub.m] may be removed out of the equivalent diagram (Fig. 1c).

In the ideal case if the cells membrane is not injured by microelectrode impalement, there is no current flow through the site of impalement ([r.sub.d] [right arrow] [infinity]). If the [r.sub.m] is neglected, then the input resistance of the tissue [R.sub.in] is

[R.sub.in] = [r.sub.pl] + [r.sub.k].

However in reality the insertion of the microelectrode into the cell causes the leakage current through the site of impalement [8-11]. Therefore the measured input resistance [R.sub.im] in that case is

[R.sub.im] = [r.sub.pl] + [r.sub.k] x [r.sub.d]/([r.sub.k] + [r.sub.d]) (5)

If the intercellular contacts are blocked (by the heptanol) the resistance of the intercellular contacts [r.sub.k] [right arrow] [infinity] and experimentally obtained input resistance ([R.sub.H]) is described by (6)

[R.sub.H] = [r.sub.pl] + [r'.sub.d], (6)

where [r'.sub.d]--the leakage resistance of the damaged tissue by microelectrode impalement.

Eq. (2-6) form the system of equations where some quantities or their range are known ([[rho].sub.pl], [[rho].sub.T], [r.sub.o], [R.sub.im], [R.sub.H]), and some are unknown ([R.sub.in], [r.sub.pl], [r.sub.k], [r.sub.d], [r'.sub.d]].

Supposing the leakage resistance of the damaged tissue does not changes after impalement of the microelectrode under control conditions and under influence of heptanol, i.e. [r'.sub.d] = [r.sub.d], the solution of equations (2-6) leads to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

The results of mathematical simulation will be used analyzing measurements of input resistance in the rabbit's right atrium under control and influence of heptanol.

Results of experimentally measured input resistance

In all 15 experiments were carried out. In different experiments, the measured input resistance values, [R.sub.im], ranged, under normal conditions from 0.47 MOhms to 0.95 MOhms. Under heptanol-induced blockade of the intercellular electric coupling, the input resistance values, [R.sub.H], ranged from 1.17 to 2.59 MOhms, i.e. they were 1.5 to 4.5 times higher than those under normal conditions (Table 1).

[FIGURE 2 OMITTED]

The analysis of [R.sub.H] dependency on [R.sub.im] (Fig. 2) shows there is a weak relation between these quantities: the coefficient of determination [R.sup.2] is 0.1243.

Results and Discussion

It is known that heptanol blocks the intercellular electric communication in myocardium without exerting any effect on the resistance of the electrogenic membrane [6, 12]. Therefore, the input resistance of the tissue would be the same as the input resistance of isolated cell.

[FIGURE 3 OMITTED]

All calculations were made assuming that the resistivities of the intercellular medium of the myocardial tissue ([r.sub.pl]) and Tyrode solution ([[rho].sub.T]) are respectively 120 Ohms-cm [15] and 64 Ohms-cm [16], also [R.sub.im] and RH do not depend on the distance [r.sub.o] between the tips of a double-barreled microelectrode. We obtained that the resistance of the myoplasm ([r.sub.pl]) increases and the resistance of intercellular contacts ([r.sub.k]) decreases considerably when the dimensions of the microelectrode [r.sub.o] are smaller. In our experiments the input resistance measured in Tyrode solution was 50-100 KOhm.

For instance, the input resistance obtained by the whole cell patch clamp method in the isolated ventricular cell of guinea-pig was 25.9 MOhms [13]. The input resistance measured by the single-barrel microelectrode in the same object was 12.4 MOhms [14]. Therefore the total block of the intercellular electric communication in the rabbit's atrium may lead to an increase of the input resistance by many times. In reality the input resistance of myocardial tissue under influence of heptanol on the average increases only by 2.67 times and reaches 1.84 MOhms. This inadequacy between theoretical hypothesis and our experimental data may be explained by the emerging of the leakage current through the resistance [r.sub.d] at the injured site of the cell (Fig.1c). The degree of injury depends on the method the input resistance is measured: the membrane is injured more when the input resistance is measured by double-barreled microelectrode than by whole cell patch clamp method. On the base of our model and experimentally obtained values of the input resistance under control ([R.sub.im]) and under heptanol ([R.sub.H]) we can assess the values of the real input resistance ([R.sub.in]), the leakage resistance of the damaged site ([r.sub.d]), contribution of the intercellular contacts ([r.sub.k]) and myoplasm ([r.sub.pl]) into the input resistance of myocardial tissue when microelectrodes of different dimensions are used for measurements. Minimum, maximum and average values of the real input resistance are presented on the Fig. 3a.

According to equation (3) the dimensions of such microelectrode's tip are 0.5 / 1.0 [micro]m and therefore have a small influence on the [R.sub.in] (Fig. 3b).

Positive correlation exists between experimentally obtained input resistance [R.sub.im] and [R.sub.in] derived from equation (7): [R.sub.im] increases with the increase of [R.sub.in] (Fig. 4a). For instance, the coefficient of determination ([R.sup.2]) is 0.654, when [r.sub.o] = 0.5 [micro]m.

However, the relation between the input resistance ([R.sub.im]) measured in control and the leakage resistance [r.sub.d] (Fig. 4b) is weak: the coefficient of determination ([R.sup.2]) is 0.1243, when [r.sub.o] = 0.5 [micro]m.

[FIGURE 4 OMITTED]

There are reports on the input resistance values ranging from tens of kOhms to ten megohms in the cardiac tissue [17-21]. The value range is very wide and depends on the measurement technique, the object of investigation, and the animal species. For example, when the input resistance was measured in the trabecular area of the rabbit's right atrium using the double-barreled microelectrode technique, the obtained values ranged from 180 to 500 kOhms [22], but when the single-barreled microelectrode was used the average value of [R.sub.in] was 320 kOhms [23]. The investigation of intercellular communication in the mouse right atrium by means of a double-barreled microelectrode yielded the input resistance values from 300 kOhms to 600 kOhms [24]. The input resistance, when measured at the same site using two microelectrodes, was found to be 35 kOhms [25]. Yet it is known that, in the rabbit's right atrium, deterioration of the electric communication induced by increasing the intracellular concentration of [Ca.sup.2+] ions markedly increases the input resistance, which is also true of the Purkinje fibers in the dog's heart [17]. An increase in the input resistance of the cardiac tissue may be also induced by ouabain [26]. An increase in the input resistance is also noted when the preparation of the rabbit's right atrium was placed in the hypertonic solution [27]. However, in none of the above cases the intracellular communication was completely blocked and therefore they cannot be used for the assessment of the influence of membrane damage on the measurement results. Furthermore, all measurements have been performed by using different techniques, and the causes of the deterioration of the intercellular electric communication are very different. However, no data on measurement of the input resistance under influence of heptanol was found. In the ideal case, the measured input resistance consists of the resistance of the closest cellular myoplasm, the resistance of contact membrane and the resistance of cellular membrane connected in parallel (Fig. 1a). If the cellular membrane is damaged, the resistance of the damaged site is parallel to the resistance of the contact membrane (Fig. 1b).

As has been shown in the two-dimensional and three-dimensional models of syncytial media, the input resistance is but slightly dependent on the resistance of the electrogenic membrane [28]. Besides, heptanol blocks the intercellular electric communication almost without exerting any effect on the resistance of the electrogenic membrane [6]. Therefore, it may be assumed that during the experiment the resistance of the electrogenic membrane remains the same both under normal conditions and under heptanol-induced intercellular decoupling. The input resistance of the tissue which consists of tightly packed cells slightly depends on the resistance of the membrane and is mainly defined by the resistance of intercellular contacts [22], and therefore it is possible that upon the total blockade of the intercellular electric communication, input resistance would increase a few dozens of times. For a cylindrical cell, 50 [micro]m long and 15 [micro]m in diameter, whose membrane resistivity is 3 to 4 kOhm-[cm.sup.2] and is equal to the resistivity in the trabecular cells of the rabbit's right atrium [23], the input resistance should increase by about 100 times. Our results show that, with heptanol-induced blockade of the intercellular electric communication, the input resistance increases only by 1.52 to 4.51 times. Since the heptanol of 3.5 mM concentration blocks intercellular contacts and have no marked influence on the resistance of cellular membrane this inadequacy between theoretical calculation and experimental data can be explained by the emerging of the leakage current through the damaged site where the microelectrode is inserted and therefore an increment of the input resistance is significantly less than is predicted by the model. So the leakage resistance [r.sub.d] should be added to the equivalent diagram for the input resistance (Fig. 1b).

After making such an assumption, the damage resulting from the insertion of a double microelectrode may be assessed. It may be concluded that the leakage via the damaged area has a large effect on the results of input resistance measurement. Besides, as the resistance of the damaged site is connected in parallel to the membrane and the intercellular contacts resistances, the bigger the value of input resistance measured during the experiment, the larger the effect of the damaged site resistance on the accuracy of measurements.

Conclusions

The double-barreled electrode is difficult to insert into the cell due to a relative large diameter of the tip. New technologies should provide for decreasing the later, thereby facilitating the microelectrode insertion and decreasing the membrane damage. Such an improved microelectrode would make it possible to reduce the dependency of the input resistance values measured on inhomogeneities of the membrane. On the other hand, due to the increased value of the measured input resistance, the resistance of the damaged site would have a bigger effect on the accuracy of measurements. Therefore, the double-barreled microelectrode technique should only be used for a qualitative assessment of intercellular communication.

Received 2009 02 13

References

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A. Grigaliunas, R. Veteikis

Institute for Biomedical Research, Kaunas University of Medicine

Eiveniu st. 4, LT-50161 Kaunas, Lithuania, phone: +370 3 7 302966, e-mail: romualdas.veteikis@kmu.lt

K. Lukosevicius, K. Muckus

Kaunas Academy of Physical Education

Sporto st. 6, LT-44221 Kaunas, Lithuania, phone: +370 37 302648, e-mail: lukaskaz@yahoo.com
Table 1. Experimentally obtained values of the input
resistance (MOhm) in the rabbit's right atrium.
[R.sub.im]--input resistance under normal conditions
(averages of all measurements in individual experiments),
RH--input resistance measured in the presence of heptanol
(averages of all measurements in individual experiments);
Av--average of all experiments

Expt No       1      2      3      4      5

[R.sub.im]   0.85   0.71   0.47   0.51   0.65
[R.sub.h]    1.29   1.17   1.69   2.24   1.63

Expt No       6      7      8      9      10

[R.sub.im]   0.74   0.55   0.73   0.59   0.68
[R.sub.h]    2.41   1.51   2.07   1.71   2.12

Expt No       11     12     13     14     15    Av.

[R.sub.im]   0.44   0.8    0.95   0.85   0.83   0.69
[R.sub.h]    1.33   1.51   2.5    2.59   1.85   1.84
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Title Annotation:MEDICINE TECHNOLOGY/MEDICINOS TECHNOLOGIJA
Author:Grigaliunas, A.; Veteikis, R.; Lukosevicius, K.; Muckus, K.
Publication:Elektronika ir Elektrotechnika
Article Type:Report
Geographic Code:4EXLT
Date:Aug 1, 2009
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