© 1998 American Heart Association, Inc.
Original Contributions |
Activation of Cardiac Tissue by Extracellular Electrical Shocks
Formation of `Secondary Sources' at Intercellular Clefts in Monolayers of Cultured Myocytes
From the Department of Physiology, University of Berne, Berne, Switzerland.
Correspondence to Vladimir G. Fast, PhD, Cardiac Rhythm Management Laboratory, University of Alabama at Birmingham, B149 Volker Hall, 1670 University Blvd, Birmingham, AL 35294. E-mail fast{at}crml.uab.edu
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Abstract |
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Abstract—This study investigated the activation of cardiac tissue by "secondary sources," which are localized changes of the transmembrane potential (Vm) during the application of strong extracellular electrical shocks far from the shock electrodes, in cultures of neonatal rat myocytes. Cell monolayers with small intercellular clefts (length, 45 to 270 µm; width, 20 to 70 µm [mean±SD, 54±13 µm]; n=46) were produced using a technique of directed cell growth. Changes in Vm relative to the action potential amplitude (
Vm/APA) were measured using a fluorescent
voltage-sensitive dye and a 10x10 photodiode array. Shocks with
voltage gradients of 4 to 18 V/cm were applied across the clefts during
either the action potential (AP) plateau or diastole.
During the AP plateau, shocks induced secondary sources in the form of
localized hyperpolarizations and depolarizations in
the regions immediately adjacent to opposite sides of the clefts. The
strength of the secondary sources, defined as the difference of
Vm/APA across a cleft, increased with increasing cleft
length or increasing electrical field gradient. For shocks with a
gradient of 8.5 V/cm, the estimated critical cleft length necessary to
reach a Vm level corresponding to the diastolic
threshold of excitation was 171±7 µm. Accordingly, shocks with
average strength of 8.2 V/cm applied during diastole
produced secondary sources that directly excited cells adjacent to the
clefts when the cleft length was 196±53 µm (n=14) and that
failed when the cleft length was 84±23 µm (n=9,
P<001). The area of earliest excitation in such cases
coincided with the area of maximal depolarization induced during the
plateau phase. These data suggest that small inexcitable obstacles may
contribute to the Vm changes during the application of
strong extracellular electrical shocks in vivo.
Key Words: stimulation • defibrillation • optical mapping • voltage-sensitive dye • cell cultures
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Although strong electrical shocks are commonly used to terminate atrial and ventricular fibrillation, the mechanisms by which the extracellular electrical field affects Vm in a large mass of cardiac tissue and terminates fibrillation are not fully understood. Linear cable theory predicts that shock-induced changes in Vm will decay exponentially with distance from the stimulation sites.1 2 Between these regions of exponential decay, no transmembrane current is generated, and no changes in Vm occur.
To explain the defibrillatory effects of electrical shocks, the hypothesis of "secondary sources" was proposed.3 4 5 6 This hypothesis suggests that microscopic resistive nonuniformities in the tissue structure force the electrical current to be redistributed between extracellular and intracellular spaces and to produce changes in Vm, so-called secondary sources, far from the shock electrodes. If these secondary sources are sufficiently large in amplitude, they may excite or defibrillate a large mass of tissue.
Cardiac tissue contains resistive discontinuities at different spatial scales. On the smallest scale, barriers to electrical current flow are created by borders of individual cells and by high-resistance gap junctions. Resistive obstacles of larger dimensions are imposed by connective tissue sheets and the vasculature separating cell bundles and cell layers.7 8 The suggestion that boundaries of cardiac cells may induce secondary sources came from theoretical studies3 4 5 6 and from experiments on isolated ventricular myocytes in which the application of an extracellular electrical field produced large hyperpolarizations and depolarizations at opposite cell ends.9 10 However, this hypothesis was not confirmed by experiments carried out in two-dimensional networks of electrically coupled cells. In densely packed strands of cultured myocytes, no secondary sources were found at cell borders.11 At the same time, large changes in Vm were observed at boundaries of cell strands and at inexcitable obstacles produced by intercellular clefts.
The purpose of the present study was to systematically investigate the formation of secondary sources at inexcitable obstacles in cultures of heart cells. First, we analyzed the relationship between the obstacle dimensions and the magnitude of the shock-induced changes of Vm during the plateau phase of the AP. Second, we tested the prediction of the "secondary sources" hypothesis that during application of extracellular shocks in diastole, small obstacles can lead to the direct excitation of cardiac tissue at sites distant from the shock electrodes.
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Directed Cell Growth
Cell monolayers with desired growth patterns were produced on glass coverslips according to a previously published procedure,12 with some modifications (S. Rohr and R. Flückiger, unpublished data, 1997) that allowed localized coating of glass coverslips with collagen (type IV, Sigma).13 The growth pattern that is schematically shown in Fig 1A
consisted
of a rectangular cell monolayer (black) incorporating small
intercellular clefts (white) of variable dimensions. The length of
the clefts varied between 45 and 270 µm; the width was
54±13 µm (mean±SD, n=46), varying from 20 to 70 µm. The
separation between clefts was 0.93 and 0.5 mm in the horizontal
and vertical directions, respectively. In the direction parallel to the
extracellular field gradient (see below), the distance between the
clefts was significantly larger than the electrotonic space constant
(350 µm14 ), ensuring that changes in
Vm caused by individual clefts were not
interfering with each other.
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Fig 1B
shows a phase-contrast image of a small portion of a cell
monolayer, including an individual cleft. In the immediate vicinity of
the cleft, cells were oriented parallel to the cleft border, similar to
the cell alignment at borders of cultured cell strands described
previously.12 The region of partial cell
alignment extended for <60 µm, encompassing fewer than four
cells. Beyond this region, cells were polymorphic and oriented
randomly, similar to the isotropic cell cultures described
previously.12 13 Since the dimension of the
region with partial cell alignment was much smaller than the
electrotonic space constant (see above), the effect of such cell
alignment on changes in Vm was likely to be
minor.
Measurements were performed between the third and the seventh day in
culture. During measurements, cells were superfused with a Hanks'
balanced salt solution (GIBCO) with a composition of (mmol/L) NaCl 137,
KCl 5.4, KH2PO4 0.4,
NaH2PO4 0.4,
MgSO4 0.8, CaCl2 1.3,
NaHCO3 4.2, HEPES 5.0, and glucose 5.1. The pH of
the solution was 7.4, and the temperature was kept constant at 35°C.
The depth of the solution in the perfusion bath was 
3 mm.
Optical Recordings of Vm
Vms were measured from the change in
fluorescence of the voltage-sensitive dye RH-237 (Molecular
Probes). The dye was stored in a 2 mmol/L stock solution of
dimethyl sulfoxide and diluted to yield a final dye concentration of 2
to 3 µmol/L in the superfusion solution. Cell cultures were
superfused with the dye solution for 3 to 4 minutes.
The experimental setup for multisite optical recording has been described elsewhere in detail.15 16 17 Briefly, fluorescence measurements were made using an inverted microscope (Axiovert 35M, Zeiss) with objectives of x40 (numerical aperture, 1.3; Plan-Neofluar) and x20 (numerical aperture, 0.75; Fluar, Zeiss) and a 10x10 photodiode array (Centronic). Cells were exposed to excitation light for 80 ms. An area of 28x28 µm2 (x20 magnification) or 14x14 µm2 (x40 magnification) of cell culture corresponded to each photodiode, with a center-to-center distance of 30 and 15 µm, respectively. The photocurrents from the 96 diodes were converted to voltages, amplified, multiplexed, and digitized at a 12-bit resolution and a sampling rate of 25 kHz for each of the 96 channels.
Stimulation and Application of Electrical Shocks
Electrical stimulation of cells was performed at a cycle length
of 500 ms via a bipolar electrode composed of a glass pipette (tip
diameter, 80 to 120 µm) filled with Hanks' solution and a
silver wire coiled around the pipette tip. The pacing electrode was
positioned at a distance of >1 mm from the recording
site.
Extracellular electrical shocks were applied via two platinum plate
electrodes positioned at opposite ends of the perfusing bath (Fig 1A).
The bath measured 2.2x2.2 cm2, and the electrode
dimensions were 2x0.2 cm2. Monophasic truncated
exponential shocks with a duration of 10 to 12 ms were delivered using
one of two custom-built shock generators. The first shock generator was
built with a discharge capacitor of 122 µF. Pulses delivered from
this generator had time constants of voltage decay of 35 to 38 ms
independent of the shock strengths. The second generator was built with
a capacitor of 220 µF and had a stabilization circuit to ensure
slower decay of shock voltages. In this case, time constants of the
voltage decay varied with the shock strength. At shock strengths of 5
and 20 V/cm, the average time constants were 318 and 76 ms,
respectively. With both shock generators, the distribution of
shock-induced changes in membrane voltage were similar at equal shock
strengths. The generators were triggered by the stimulus and could
produce shocks at preselected times during the cardiac cycle. In most
of the measurements, the extracellular voltage gradient produced by the
shock in the bath was measured simultaneously with the
optical recordings of Vm by two silver
electrodes with diameters of 0.2 mm and interelectrode distances
of 3.5 mm. The electrodes were positioned near the mapping area
and aligned with the direction of electrical field.
Shocks of variable strength were delivered 20 ms after a
stimulation pulse that initiated an AP (plateau phase, Fig 1C) or 450
ms after the previous excitation (diastole). Shocks of
opposite polarities were examined at the same locations. In total, the
effects of electrical shocks on Vm and patterns
of activation spread were measured at 46 intercellular clefts in seven
cell dishes obtained from four cultures.
Data Analysis
Fig 1C shows an example of an AP recorded during application
of an electrical shock. The APA was taken as the difference in
fluorescence intensity measured before the onset of the AP and
immediately after the AP reached the plateau. The change in
fluorescence induced by the shocks,
Vm, was determined as the difference between
light intensities measured 1 ms before and 3 ms after the onset of the
shock. Shock-induced changes in the membrane potential were expressed
as a change (percentage) in fluorescence intensity relative to
the APA, ie, Vm/APA. In such a way, the
spatial variability in fluorescence intensity due to
inhomogeneous dye staining and nonuniformity of
illumination was corrected for. When an average APA of 100 mV is
assumed,12 15 the relative
Vm/APA values directly translate into changes
of Vm in millivolts. To calculate local
activation times, signals were digitally filtered using a gaussian
low-pass filter (cutoff frequency, 1.5 to 2
kHz).15 16 The activation times were determined
at 50% of the APA using linear interpolation between the nearest
sampling points.16 Activation maps and
isopotential maps of Vm/APA distribution were
constructed using linear interpolation and triangulation
algorithms.
Data were expressed as mean±SD. Differences were compared using the two-tailed nonpaired t test. They were considered statistically significant at P<.05.
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Spatial Distribution of Shock-Induced Changes of Vm at Inexcitable Obstacles
The effect of an electrical shock on the distribution of
Vm/APA near an intercellular cleft is
demonstrated in Fig 2. Panel A shows an
image of the cell monolayer and the grid indicating the position of the
photodiodes. The intercellular cleft is delineated with a dashed line.
The length and the width of the cleft were 240 and 60 µm,
respectively. The stimulation electrode was located above the mapping
area, and the shock electrodes were located on the left and the right
sides. Panel B shows the isochronal map of activation spread
initiated by the stimulus. The activation wave was split by the cleft
into two parts. Around the cleft, the activation spread was
homogeneous, suggesting no significant discontinuities in
intercellular electrical coupling11 in the
immediate vicinity of the cleft. The whole mapping area was
activated within 900 µs, which corresponded to a
conduction velocity of 30 cm/s.
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In Fig 2, panels C and D depict isopotential maps of the relative
changes in Vm, Vm/APA,
caused by electrical shocks of opposite polarities. Shocks with a
duration of 11 ms were applied 5 ms after the onset of APs. The
shock strength was 7.5 V/cm (panel C) and 8.5 V/cm (panel D). In panel
C, cells were depolarized on the right side and hyperpolarized on the
left side of the cleft. The isopotential map contained two localized
regions of maximal depolarization (blue) and maximal
hyperpolarization (red) adjacent to the obstacle,
corresponding to current sources and current sinks, respectively. The
polarity of the shock-induced changes in Vm
reversed across the obstacle. The changes in Vm
on opposite sides of the obstacle were only slightly asymmetrical, with
maximal values of hyperpolarization and
depolarization being -42% and 39%, respectively. With the reversed
shock polarity (panel D), the regions of depolarization and
hyperpolarization were interchanged. In this case,
the distribution of Vm became more
asymmetrical: maximal hyperpolarization was
considerably larger than maximal depolarization (-60% versus 34%).
Such levels of asymmetry were smaller than in our previous study
carried out in cultured strands,11 which was
likely due to relatively small values of Vm
changes in Fig 2. The reasons for the difference between effects of
shocks of opposite polarities is less clear. It could be due to
presence of discontinuities outside the mapping area (see
"Discussion").
Individual recordings illustrating changes in
Vm across the obstacle from the same experiment
are shown in Fig 3A and 3B for opposite
shock polarities. The shape of Vm traces in
most cases corresponded to the truncated exponential field pulse in
both depolarized and hyperpolarized areas. In a few cases, signals
deviated from this shape, which is exemplified by trace 5 in panel B,
which was likely to correspond to a motion artifact. Panels C and D
illustrate profiles of Vm/APA along the
horizontal axis (corresponding to the row of diodes from 1 to 8 in Fig 2) for the two shock polarities. In the first case (Fig 3C), the
profile was symmetrical, with depolarization and
hyperpolarization decaying within a short distance
from the obstacle. On both sides, the Vm changes
decreased from 40% to almost zero over a distance of 90 µm.
Such a voltage change is much larger than the voltage drop predicted
from the exponential decay, assuming a value for the one-dimensional
electrotonic space constant of 350 µm.14
It can be attributed to two factors. First, the secondary current
source produced by the obstacle was localized within a small cell area,
and current was dispersed in many directions, whereas in a
one-dimensional structure, current flows in only one direction. Second,
the voltage drop near the current source was further augmented by the
proximity to the current sink on the opposite side of the obstacle. A
very steep voltage decay was also observed when shock polarity was
reversed (Figs 3B and 3D).
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The effects of shocks on Vm/APA distribution
during the plateau phase of AP was assessed at 20 clefts in four cell
dishes obtained from two cell cultures. In 14 of 20 cases, the
Vm/APA distribution pattern exhibited an
abrupt transition from hyperpolarization to
depolarization across an obstacle at both shock polarities,
corresponding to the pattern shown in Figs 2 and 3. The location of the
maximal voltages was usually symmetrical, near the middle portion of
obstacles. Sometimes, however, one or both of the
Vm/APA extrema were moderately shifted from
the central position. This suggests that the voltage distributions in
these cases were affected by discontinuities in the monolayer structure
other than a given intercellular cleft. This effect was prominent in 6
of 20 cases where the sign of the Vm/APA did
not change across an obstacle with one or both shock polarities. An
example of this type of isopotential map is shown in Fig 4 (shock strength, 18 V/cm). With one
shock polarity (panels A and B), changes of Vm
near the obstacle (length, 100 µm) were predominantly
negative. Large negative changes of Vm were
recorded on the right side of the obstacle facing the cathode. On
the left side of the obstacle, small positive voltage deflections were
transiently recorded after the shock onset (traces 5, 6, and 7);
these deflections were then followed by negative changes. Across the
obstacle, there was an abrupt change of the
Vm/APA value from -88% to -16% (voltage
gradient of 72%). With the opposite shock polarity (panels C and D),
Vm/APA values on the right side became
positive, and there were practically no shock-induced changes of
Vm on the left side. Nevertheless, across the
obstacle, the Vm/APA changed by 48% (from
41% to -7%).
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Strength of Secondary Sources Produced by Obstacles
Fig 5 demonstrates the dependence of
the magnitude of secondary sources produced by inexcitable obstacles as
a function of the obstacle length and shock strength. As shown
schematically in Fig 5A, the magnitude of a secondary source was
defined as (Vm/APA)diff.
This procedure permitted exclusion of the contributions of remote
secondary sources (eg, see Fig 4) to the local Vm
changes. For a given obstacle, the average of two
(Vm/APA)diff values,
which were measured in response to shocks of opposite polarities, was
taken. Two shock strengths were evaluated. In the first group, the
average shock strength was 8.5±0.6 V/cm (range, 7.5 to 9.4 V/cm;
n=14). In the second group, the average shock strength was 18.0±1.0
V/cm (range, 16.1 to 19.3 V/cm; n=16). To compare the data within one
group, the individual measurements of
(Vm/APA)diff were scaled
by a factor equal to the ratio of the individual shock strength and the
average shock strength of the corresponding group, either 8.5 or 18.0
V/cm.
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) and 18 V/cm (
); R indicates the
correlation coefficient of the linear regression.
The (Vm/APA)diff values
measured across 20 clefts are plotted in Fig 5B. The cleft lengths were
in the range of 45 to 270 µm. Within this range of cleft
lengths, the relation between the obstacle length and the magnitude of
the secondary sources could be closely approximated by a linear fit.
The correlation factor was .91 and .88 for shock strengths of 8.5
and 18 V/cm, respectively. The slopes of the linear dependencies were
0.33±0.04%/µm (8.5-V/cm group) and 0.61±0.09%/µm (18-V/cm
group). The ratio between the two slope values was 1.85, and the ratio
between average shock strengths was 2.12. This nonlinear increase of
(Vm/APA)diff relative to
increasing shock strength is likely due to nonlinear membrane
properties. The cleft length was the primary geometrical determinant of
shock-induced changes in Vm in these experiments:
when (Vm/APA)diff values
were plotted as function of the cleft width (not shown), it would seem
that there was no correlation (correlation factors of .24 and .34 for
shock strengths of 8.5 and 18 V/cm, respectively).
From these data, an estimate of the critical obstacle length necessary
for direct activation of cells can be predicted. If it is assumed that
a shock produces symmetric changes in Vm and that
cells are excited in the area of maximal depolarization if
Vm is depolarized by 25% APA above the resting
level (corresponding to a depolarization of 25
mV18 ), cells will be directly activated
when the (Vm/APA)diff
value is >50%. From the linear functions in Fig 5B, this estimated
critical obstacle length is 85±8 µm for a shock strength of
18.0 V/cm and 171±7 µm for a shock strength of 8.5 V/cm.
Direct Stimulation of Cell Cultures by Secondary Sources
To test the prediction that resistive discontinuities cause direct
excitation of cardiac tissue during application of extracellular
shocks, shocks were delivered during diastole, and the
isochronal maps of activation spread initiated by shocks were
analyzed. Three shock strengths were tested in these
experiments with average values of 4.7 V/cm (n=8), 8.2 V/cm (n=28), and
18 V/cm (n=4). In all three groups, shocks produced one of the
following effects: (1) shocks of both polarities caused direct
excitation of cells adjacent to intercellular clefts; (2) shock of one
polarity resulted in direct excitation, whereas the shock of the
opposite polarity failed to excite cells; and (3) shocks of both
polarities failed to excite cells near clefts.
Fig 6 illustrates direct activation of
myocytes by a secondary source created by an inexcitable obstacle (same
experiment as shown in Fig 2). Panels A and C show isochronal maps
of activation spread initiated by shocks of opposite polarities, and
panels B and D show the corresponding recordings of
Vm from the sites surrounding the obstacle. Shock
strengths were 8.3 V/cm (panels A and B) and 8.2 V/cm (panels C and D).
With one shock polarity (panel A), a small cell region adjacent to the
obstacle on the left side was directly activated by the shock.
This was evident from the fact that the cells in this region had the
earliest activation times and that AP upstrokes (panel B, traces 1 and
2) exhibited biphasic shapes: the shock caused initial rapid membrane
depolarization (shown by arrows), which was followed by excitation.
This area of earliest activation could be superimposed on the region of
maximal depolarization produced by shock during the plateau phase of AP
(Fig 2D). Away from this area, the amplitude of initial depolarization
decreased (Fig 6D, traces 3 through 6). Cells on the right side of the
obstacle were transiently hyperpolarized by the shock, with
hyperpolarization gradually increasing toward the
center (traces 7 through 10). The initial membrane
hyperpolarization was followed by depolarization,
which resulted from the propagating wave initiated on the left side of
the obstacle. An almost symmetrically reversed activation pattern was
observed when the shock polarity was reversed (Fig 6C and 6D). The site
of the earliest activation in this case was located on the right side,
superimposed on the area of maximal depolarization during application
of shock in the plateau phase (Fig 2C). Since multiple clefts of
similar size were present in the cell monolayer, such clefts should
simultaneously activate cells at multiple
locations, resulting in a multicentric overall pattern of activation
spread.
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Fig 7 demonstrates an example of
asymmetric excitation when a shock of only one polarity was able to
directly excite cells near an obstacle (the same experiment as in Fig 4). With one polarity (Fig 7A and 7B; shock strength, 18 V/cm), shock
induced an initial depolarization of 20% of APA on the left side of
the obstacle (Fig 7B, arrows at traces 4 and 5). Despite this
depolarization, cells were not activated for 2 ms. After
that, activation appeared at two sites almost
simultaneously. The earliest activation was registered at
diode 1, which was likely caused by an excitation wave originating
outside of the mapping area and propagating from left to right. The
delay between the beginning of the shock and the appearance of the
excitation wave in the mapping area was 2.5 ms (Fig 7B, traces 1 and
2). If a velocity of 30 cm/s was assumed, this indicated that the
origin of this wave was located at a distance of 0.75 mm from the
obstacle. The mechanism of initiation of this wave excitation is not
known (see "Discussion"). At the time of arrival of the excitation
wave at the obstacle, a spatially isolated area of depolarization was
registered at a second site (diodes 3 and 4). Because of this temporal
coincidence with the arrival of the propagating wave, the activation at
this site was likely a result of two factors: (1) arrival of the
excitation wave initiated at the distant source and (2) facilitation by
local shock-induced membrane depolarization.
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With shock of reversed polarity (Fig 7C and 7D), a large initial
depolarization (shown by arrows in Fig 7D) was induced on the bottom
right side of the cleft, and cells were directly activated at
the shock onset. In addition, a second smaller source of excitation was
registered at the top right part of the mapping area. The larger area
of earliest activation corresponded to the area of maximal
depolarization produced by shock during the AP plateau (Fig 4C and 4D).
The stimulating efficacy of secondary sources depended on both shock
strength and obstacle length. With an average strength of 8.2 V/cm
(number of obstacles, n=28), shocks of both polarities directly excited
cells when the obstacle length was 196±53 µm (n=14). Shocks of
only one polarity resulted in direct activation when the obstacle
length was 134±49 µm (n=5, P<.05). No activation by
shocks of both polarities was observed at obstacles with lengths of
84±23 µm (n=9, P<.001). Thus, the critical obstacle
length necessary for the direct cell activation with shocks of 8.2 V/cm
was between 84 and 196 µm. The estimate of critical length of
171±7 µm obtained from shock-induced changes of
Vm during the plateau phase of AP (Fig 5) falls
within this range.
With an average shock strength of 4.7 V/cm (n=8), shocks of both polarities excited cells at obstacles with a length of 210±42 µm (n=2); shocks of only one polarity directly excited cells at obstacles with a length of 202±53 µm (n=2); and shocks of both polarities failed to produce excitation at obstacles with a length of 114±65 µm (n=4). At an average shock strength of 18 V/cm (n=4), shocks of both polarities excited cells in two cases (obstacle length, 98±53 µm); shocks of only one polarity excited cells in one case (obstacle length, 100 µm); and shocks of both polarities failed in another case (obstacle length, 45 µm).
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Discussion |
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In the present study, we investigated the formation of secondary sources of excitation at small inexcitable obstacles during the application of extracellular electrical shocks with a strength of 4 to 18 V/cm, which is similar to shocks used for defibrillation in patients.19 Two main results were obtained: (1) Extracellular shocks induced secondary sources at inexcitable obstacles, which were characterized by abrupt transition from hyperpolarization to depolarization on the opposite sides of the obstacles. The magnitude of the secondary sources increased with increasing the obstacle dimensions or increasing the shock strength. The estimated critical obstacle length for excitation was 171±7 µm for shocks with a strength of 8.5 V/cm. (2) These secondary sources were able to directly excite localized cell areas adjacent to the obstacles far from the shock electrodes. The critical obstacle length necessary for direct activation was between 84 and 196 µm for a shock strength of 8.2 V/cm.
Cell Culture as a Model for Studies of Defibrillation
Mechanism
The mechanism of defibrillation has two important aspects that are
not fully understood. First, it has not been clarified how an
extracellular field shock changes the Vm of the
cells located between the shock electrodes. Second, it is not clear how
shock-induced changes of Vm interact with
irregular electrical activity and interrupt fibrillation. Several
hypotheses have been proposed to explain this
process.20 21 22 23 24 25 26 27
Regarding the first aspect, it has been proposed that microscopic discontinuities in tissue structure play a crucial role in defibrillation by inducing secondary sources of excitation far from the shock electrodes.3 4 Until recently, the effects of the microscopic discontinuities on shock-induced changes of Vm could be investigated only by using computer models.3 4 5 6 28 29 Experimental studies in whole cardiac tissue are extremely difficult because of the three-dimensional structure of cardiac muscle, which prevents precise correlation of voltage changes with tissue structure at the microscopic level. To overcome this difficulty, we used two-dimensional cultures of neonatal rat myocytes, where shock-induced changes in Vm can be monitored with a very high spatiotemporal resolution and correlated to the microscopic structure. Another advantage of cell cultures is that their geometry can be modified using techniques for directed cell growth. By use of these techniques, many types of structures encountered in whole tissue can be created in cell cultures, including cell strands of variable widths,12 15 tissue expansions,16 30 anisotropic arrangement of myocytes,13 17 and monolayers with intercellular clefts of predefined dimensions.
There are several differences between cell cultures and intact cardiac tissue. Some of them, including the anisotropic bidomain properties of cardiac tissue,31 were discussed in a previous study.11 Another difference relates to the distribution of gap junctions. Gap junctions are distributed regularly within the cell perimeter in cultured neonatal cells,17 32 whereas gap junctions are more concentrated at cell ends in adult myocardium.33 34 In this respect, cultured cells more closely resemble neonatal heart tissue34 35 and remodeled cardiac tissue found in the infarction border zone.34 36 The nonuniformity of gap junction distribution found in the adult myocardium might affect the distribution of shock-induced changes of Vm at the subcellular scale. However, changes of Vm on a larger scale, which were investigated in the present work, are not likely to be significantly modified by this type of resistive nonuniformity.
Secondary Sources Produced by Inexcitable Obstacles
Electrical shocks applied to cell cultures produced localized
changes of Vm at the inexcitable obstacles far
from the primary stimulating electrodes. Typically, regions of
hyperpolarization and depolarization were observed
at the obstacles. As expected from secondary sources, there was an
abrupt transition from maximal hyperpolarization to
maximal depolarization across obstacles and a more gradual voltage
change with distance away from the obstacles (Fig 2). In several cases,
no change of Vm polarity across obstacles was
observed; ie, voltage changes were either all positive or all negative
(Fig 4). Such a voltage profile may be the result of the summation of
voltage changes produced by two secondary sources: one that was created
by the cleft located within the mapping area and one or more additional
sources located outside the mapping region. The mechanism for these
additional sources, which were also observed
previously,11 is not known. One possibility is
that they might be due to discontinuities in intracellular resistance
resulting from nonuniform expression of gap
junctions.17
The strength of the secondary sources, which was defined as the
difference of Vm/APA across an obstacle (Fig 5), was dependent on obstacle dimensions and on shock strength. Within
the range of cleft length investigated in the present study (45 to
270 µm), the source strength was linearly related to the cleft
length (Fig 5). With increasing cleft length, this dependence is
expected to become nonlinear, and then the
(Vm/APA)diff values are
expected to reach a steady level. In addition to the cleft length, the
source strength is expected to be dependent also on the cleft width,
because changing cleft width changes the total circumference of the
resistive boundary and, therefore, modulates the electrotonic
interaction between regions of current source and current sink on the
opposite sides of a cleft. However, our data indicated no significant
correlation with the cleft width. This finding does not necessarily
mean that such a dependence is absent. More likely, it was masked in
the present experiments by stronger dependence of the source
strength on the cleft length and by the fact that cleft width showed
relatively minor variations.
The dependence of
(Vm/APA)diff on cleft
length shown in Fig 5 was used to estimate the critical cleft length
that is necessary for direct cell excitation during
diastole. The parameter
(Vm/APA)diff was used
rather than the maximal level of depolarization for the following
reason: As it was shown previously in cultured cell strands,
shock-induced changes of Vm could be asymmetric
during the plateau phase and symmetric during
diastole.11 However, the sum of
hyperpolarization and depolarization in strands,
which corresponds to
(Vm/APA)diff measured in
the present experiments, was the same during both phases of the AP.
Thus, the depolarization level to be expected during
diastole is better represented by half of
(Vm/APA)diff measured
during the plateau phase than by the maximal level of depolarization in
this phase. The diastolic threshold of activation in adult
guinea pig myocytes is 25 mV more positive than the resting
potential.18 By using the same excitation
threshold for cultured neonatal rat myocytes, sufficiently large
changes of Vm were obtained during the
application of shocks with a strength of 8.5 V/cm at clefts that were
171±7 µm in length. We would like to point out that this
estimate is approximate. Based on knowledge of the exact value of the
threshold potential for activation of sodium channels in neonatal rat
myocytes and on inclusion into consideration of the concept of
"liminal length," which postulates that a certain amount of tissue
has to be activated in order to get a propagated response, a
more precise analysis could be
performed.37 38 39 40 However, the fact that the
estimate provided above is quite consistent with the results
obtained from the direct evaluation of the obstacle length critical for
excitation (see below) suggests that this simplified analysis
takes into account the major factors determining the activation
process.
Stimulation by Secondary Sources
Depending on the shock strength and cleft dimensions, shocks
applied during the diastolic phase directly excited cells
near the clefts. The direct cell excitation was initiated on the
leading edge of shock pulses ("make" response) in regions that
coincided with areas of maximal depolarization recorded during the
application of shocks in the plateau phase of the AP. It was not
possible to test the effects of the falling edge of the shock pulses
("break" response), because even with weaker shocks, the cells were
always excited before the end of the pulses, apparently by the
"make" excitation at distant locations.
The critical cleft length necessary for direct cell excitation during
the application of shocks with a mean gradient of 8.2 V/cm was in the
range of 84 to 196 µm, which includes the estimate obtained from
the Vm/APA measurements in the plateau phase.
It is interesting how these estimates extrapolate to the intact adult
tissue. To make such an extrapolation, differences in passive
properties and fiber orientation between cell cultures and intact
cardiac tissue have to be taken into account. By assuming continuous
representation of cardiac tissue and considering a case with a
cleft oriented longitudinally and an extracellular field gradient
applied in the transverse direction, the critical cleft length can be
predicted by scaling the longitudinal electrotonic space constant. In
arterially perfused papillary muscle, the longitudinal
space constant was 357 or 528 µm, depending on the presence of
superfusion solution.2 Scaling from a space
constant of 350 µm in cell cultures,14 the
critical length value for longitudinally oriented clefts in
ventricular myocardium is predicted to be <200
or 300 µm, depending on the experimental conditions.
Discontinuities with dimensions of several hundred
micrometers and larger are common in
ventricular myocardium. In human pectinate
muscle, connective tissue septa with such dimensions were found in
ventricular tissue from young individuals, and much larger
(up to 1 mm) septa were found in the aging
myocardium.41 Our data suggest that
such inexcitable obstacles may contribute to tissue excitation and
defibrillation during the application of extracellular electrical
shocks in the whole heart. The definitive answer to the question about
the role of such discontinuities in the whole heart will require taking
into account the three-dimensional tissue structure as well as the
specific geometrical arrangement of clefts. In particular, clefts in
the whole tissue might be closely spaced, allowing for strong
interaction between areas of hyperpolarization and
depolarization at neighboring clefts. Also, extracellular fields can be
oriented at different angles relative to the cleft axis during shock
application in the whole tissue. Future studies are necessary to
elucidate how these factors affect the formation of secondary sources
in the whole heart.
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Selected Abbreviations and Acronyms |
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Acknowledgments |
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This study was supported by the Swiss National Science Foundation and the Swiss Heart Foundation. Dr A.M. Gillis is a Scholar of the Alberta Heritage Foundation for Medical Research and was the recipient of the NASPE Bigelow Travelling Fellowship. We thank Regula Flückiger for help with preparation of cell cultures.
Received May 28, 1997; accepted November 17, 1997.
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