Vol. 282, Issue 2, H565-H575, February 2002
Mechanisms of make and break excitation revisited:
paradoxical break excitation during diastolic stimulation
Vladimir P.
Nikolski,
Aleksandre T.
Sambelashvili, and
Igor R.
Efimov
Department of Biomedical Engineering, Case Western Reserve
University, Cleveland, Ohio 44106-7207
 |
ABSTRACT |
10.1152/ajpheart.00544.2001. Onset and termination of electric
stimulation may result in "make" and "break" excitation of the
heart tissue. Wikswo et al. (30) explained both types of
stimulations by virtual electrode polarization. Make excitation
propagates from depolarized regions (virtual cathodes). Break
excitation propagates from hyperpolarized regions (virtual anodes).
However, these studies were limited to strong stimulus intensities. We examined excitation during weak near-threshold diastolic stimulation. We optically mapped electrical activity from a 4 × 4-mm area of epicardium of Langendorff-perfused rabbit hearts (n = 12) around the pacing electrode in the presence (n = 12) and absence (n = 2) of 15 mM 2,3-butanedione
monoxime. Anodal and cathodal 2-ms stimuli of various intensities were
applied. We imaged an excitation wavefront with 528-µs resolution. We
found that strong stimuli (×5 threshold) result in make excitation,
starting from the virtual cathodes. In contrast, near-threshold
stimulation resulted in break excitation, originating from the virtual
anodes. Characteristic biphasic upstrokes in the virtual cathode area
were observed. Break and make excitation represent two extreme cases of
near-threshold and far-above-threshold stimulations, respectively. Both
mechanisms are likely to contribute during intermediate clinically
relevant strengths.
optical mapping; virtual electrode; pacing
| |
INTRODUCTION |
THE ABILITY OF ELECTRIC
POINT STIMULATION to produce a response in excitable tissues
(11, 28) and induce (12) or terminate (17) arrhythmia in the heart is well known. However, the
exact mechanisms of electric stimulation have been obscure until the recent discovery of virtual electrode polarization (VEP) produced by
point stimulation (13, 15, 24, 30, 31). It results in a
characteristic "dogbone" pattern of positive and negative polarizations. These polarizations of opposite sign are thought to be
induced by a so-called virtual cathode and virtual anode. These virtual
electrodes represent the driving force, which can be mathematically
expressed as an activating function (19, 27), which is
also referred to as secondary sources (10). The activating function is governed by two major parameters: the gradient of extracellular electric field and structural heterogeneity of the heart,
contributing to the polarization of the cellular membrane during
stimulus. Active ionic properties of the heart, particularly calcium
channels, modulate these polarizations (2, 18, 20, 22).
Dekker (4) demonstrated that both the onset (make) and
termination (break) of stimulation of appropriate intensity and duration could produce a propagated response. Roth (20)
and Wikswo et al. (30) provided the first mechanistic
explanation of the "make" and "break" stimulation based on the
VEP phenomenon.
According to their theory, clinically relevant make stimulation
produces initial depolarization at sites of positive polarization or
virtual cathodes. Such stimulus-induced depolarization results in the
opening of activation, or the m gates of sodium channels. Sodium
entering the cell through the opened channels completes the
depolarization. Adjacent areas of hyperpolarization (virtual anode) are
subsequently driven to depolarization by the diffusion of transmembrane
potential (Vm) through electrotonic coupling. Thus, during make stimulation, the heartbeat originates at the virtual
cathode and is delayed at the virtual anode.
Break stimulation represents an entirely different mechanism. Break
excitation usually is induced by a termination (break) of a very long
pulse, usually lasting >100 ms. Such duration is required to avoid or
separate make stimulation. For example, Wikswo et al. (30)
used 150- and 180-ms pulses, which started during the refractory period
to avoid make stimulation and then terminated after the recovery of
excitability, producing break excitation. In this case,
stimulus-induced positive polarization does not evoke an active
response, because sodium channels in this area of virtual cathode
remain inactivated. In contrast, virtual anode forces accelerated the
recovery from inactivation (opening of h gates) of sodium channels,
providing an excitable substrate for the depolarization propagation at
the cessation of the stimulus. Subsequently, this break excitation of
hyperpolarized areas of virtual anode spreads to the rest of the
tissue, which is completely recovered by that time. Thus, during break
stimulation, the heartbeat originates at virtual anode and is delayed
at the virtual cathode. Alternatively, it is possible to induce break
excitation by a stimulus as short as 5 ms applied during a relative
refractory period (6, 7, 14, 21); however, this type of
stimulation was not considered in our study.
The goal of our study was to investigate mechanisms of stimulation with
clinically relevant short stimuli of near-threshold intensities
delivered from unipolar and bipolar electrodes during diastole.
| |
METHODS |
Experimental preparation.
This study conformed to the guidelines of the American Heart
Association. The experiments were performed on perfused cardiac preparations obtained from New Zealand White rabbits (n = 12). The heart was placed horizontally onto a Langendorff apparatus, where it was retrogradely perfused with oxygenated modified Tyrode solution (Fig. 1) as previously described
(6). The saline level above the heart was 5-7 mm.
View larger version (116K):
[in this window]
[in a new window]
|
Fig. 1.
Experimental preparation. A photograph of an isolated
Langendorff-perfused rabbit heart is shown. We used three electrodes.
The first electrode was used for basic pacing outside the field of
view. The second electrode was used for test stimulation, and the third
electrode was used for recording electrical activity. A separate
electrode for basic stimulation was used to reduce tissue damage at the
studied stimulation site.
|
|
The heart was stained with 0.5 µM of the voltage-sensitive dye
pyridinium,
4-[2-{6-(dibutylamino)-2-naphthalenyl}-ethenyl]- 1-(3-sulfopropyl)-,
hydroxide, inner salt (di-4-ANEPPS). Motion artifacts in
optical recordings were suppressed by the excitation-contraction uncoupler 2,3-butanedione monoxime (BDM; 15 mM). In two preparations, we conducted optical recordings with and without BDM.
The heart was paced at a steady-state cycle length of 400 ms at the
base of left ventricle with a basic pacing electrode (Fig. 1). Test
stimuli were applied with a test stimulus electrode in the middle of
the field of view (yellow box in Fig. 1) at a coupling interval of 350 ms with an amplitude of 0.2-60 mA and a duration of 2 ms from a
constant current source (A385, WPI). A recording electrode was used to
detect a propagated response to confirm suprathreshold pacing. The
basic pacing stimulus strength was adjusted to twice the diastolic
threshold of excitation.
Optical mapping techniques.
Figure 2 illustrates the high-resolution
epifluorescence optical mapping setup used in our experiments. The
light produced by a 250-W quartz tungsten halogen direct current power
source passed through a 520 ± 45-nm excitation filter, was
reflected by a 585-nm dichroic mirror, passed through a 50-mm lens, and illuminated the field of view at the anterior epicardium of the rabbit
heart. The fluorescence emitted from the heart was collected by the
same lens, passed through the dichroic mirror (>585 nm), and was
additionally filtered by a long-pass filter (>610 nm). It was then
focused on the sensing area of a l6 × 16 photodiode array (C4675,
Hamamatsu). The magnification was adjusted to 250 × 250 µm per
diode, such that the entire array covered a field of view of 4 × 4 mm. The current produced by each of the 256 photodiodes passed
through a separate current-to-voltage converter integrated within the
same head stage (C4675, Hamamatsu). The outputs of the first-stage
amplifiers were connected to 256 second-stage amplifiers, alternating
current coupled with a time constant of 30 s (32).
Resetting of the second-stage amplifiers before data acquisition was
used to remove the direct current offset of the optical signals.
Sampling was performed at a rate of 2,900 frames/s. Each frame included
256 optical channels and 8 instrumentation channels and was stored for
off-line analysis. Instrumentation channels recorded
electrocardiograms, stimulation and defibrillation triggers, and
perfusion pressure. Custom-developed data acquisition and analysis
software was used as previously described (5).
View larger version (23K):
[in this window]
[in a new window]
|
Fig. 2.
Experimental setup. Fluorescence was excited by light produced by a
250-W quartz tungsten halogen direct current (DC) power light source.
The excitation light passed through a 520 ± 45-nm excitation
filter and was then reflected by a 585-nm dichroic mirror to the
surface of the preparation. The fluorescence emitted from the heart was
collected by a 50-mm lens, passed through a long-pass filter (>610
nm), and was focused on the sensing area of the l6 × 16 photodiode array. The 256 signals were amplified, filtered, and then
digitized for off-line analysis.
|
|
Data analysis and signal calibration.
Photodiode fluorescence signals recorded from the 4 × 4-mm area
around the test stimulus electrode were normalized on changes during
the last basic beat, assuming the resting potential and action
potential amplitude were 
85 and 100 mV, respectively (Fig. 3, left) (3). Our
normalization was based on the optical signal collected during the last
basic beat propagating from the basic pacing electrode (see Fig. 1 for
location of the electrode) because 1) basic beat provides a
nearly linear wavefront moving across the field of view, and
2) normalization on the signals obtained during clearly
nonuniform propagation after a test stimulus, which was applied in the
center of the field of view, could be dependent from the test stimulus
strength. The intensity graphs (Fig. 3, right), representing
the surface distribution of VEP, were plotted from the data collected
in the middle of a 2-ms stimulus (VEP maps in Fig. 3). We resampled the
initial 16 × 16 data array to a 256 × 256 matrix by cubic
spline interpolation. The color scale (Fig. 3) reflects the change of
the fluorescence caused by the voltage-sensitive dye di-4-ANEPPS,
which corresponds to the changes in Vm from 95
to 75 mV. The circles in Fig. 3 mark the electrode positions, and
the + and symbols show the stimulus polarities. The
orientation of the myocardial fibers is indicated by the arrow.
View larger version (47K):
[in this window]
[in a new window]
|
Fig. 3.
Data analysis. This figure illustrates the technique used for
calibrating virtual electrode (VE) patterns during epicardial
stimulation. The traces on the left show the
fluorescence signals from 4 different areas located near the electrode
tips (circles with + and symbols) 10 ms before and 60 ms
after stimulus. The signals shown were recorded by 4 photodiodes from
250 × 250-mm areas each. Similar traces were obtained from all
256 photodiodes. We assumed that 1) the changes in
fluorescence are proportional to the changes in transmembrane
potential, 2) the baseline fluorescence before the test
stimulus corresponds to 85 mV, and 3) the fluorescence
during the full depolarization corresponds to +15 mV. After such
recalibration, we plotted the values from all traces in the middle of a
2-ms DC diastolic stimulus as an intensity graph (right)
with a 95-mV (red) to 75-mV (blue) color scale. For the purpose of
display, a 16 × 16 matrix was interpolated to a 256 × 256 element grid by the cubic spline method. Top and
bottom areas show the calibration technique for different
bipolar electrode orientations.
|
|
Numerical model.
We guided our experiments with theoretical predictions derived
from the bidomain model. It is based on the representation of the
tissue as two interpenetrating extra- and intracellular domains, each
having different conductivities along and across the direction of the
fibers (24, 26). The state variables describing the system
are intracellular (
i) and extracellular potentials
(e) defined everywhere in the domain of interest (
). The variable of physiological importance is Vm,
defined as the difference (Vm = i e). The following coupled
reaction-diffusion equations constitute the bidomain model
|
(1)
|
|
(2)
|
where 
i and e are
intra- and extracellular conductivity tensors, respectively;
Im is the volume density of the transmembrane current; and I0 is the volume density of the
stimulation (shock) current.
The stimulus current density from the point-size electrode placed at a
point (x1,y1) can be
described in terms of 
-function as i0
(x x1) (y y1).
The transmembrane current (Im) is
generally represented as the sum of capacitive, ionic, and
electroporation currents (26)
|
(3)
|
where 
is the surface-to-volume ratio (total membrane area
divided by total tissue volume), t is time,
Cm is the specific membrane capacitance,
Iion(Vm,t) is
the ionic current, and
G(Vm,t) is the
electroporation conductance.
The last is described by empirical equations (26), e.g.
|
(4)
|
where 
, , and 
are electroporative coefficients and
Vrest is the resting Vm.
The values of all the parameters are given in Tables
1 and 2.
For the case of the passive bidomain model, which does not consider
active ion channel kinetics, when the main point of interest is the
steady-state Vm distribution, the expression
for Im simplifies to Ohm's law
|
(5)
|
where Rm is the membrane resistance times
unit area.
For the case of the active bidomain as a model of cardiac myocytes, we
used the Drouhard-Roberge version of the Beuler-Reuter model
(1), modified by Skoubine et al. (26), to
extend the model for strong electric fields.
We used the following boundary conditions
|
(6)
|
For numerical solution of the bidomain system, we used a square
8 × 8-mm grid with the space step hx = hy = 0.2 mm, and the time step was 
t = 0.005 ms. To invert the sparse matrix, we employed the generalized
minimum residual method (16, 23) as the most robust and
fast for our case. We used diagonal preconditioning for this method.
Calculations were performed on a Dell Pentium III PC.
| |
RESULTS |
Virtual electrode polarization pattern.
Numerical simulations predicted that during unipolar anodal stimulus
the VEP pattern represents a "dogbone"-shaped hyperpolarized area
with two positive polarization zones at both sides (Fig. 4A), as previously shown by
Sepulveda et al. (24). Simulated cathodal stimulus
produced the same VEP but with inverted polarities. Modeling of the
bipolar pacing revealed a more complex pattern of VEP, dependent on the
location of the stimulating dipole with respect to the fibers (Fig. 4,
B and C), as was previously reported by Trayanova
and Pilkington (29) and Sepulveda and Wikswo
(25).
View larger version (16K):
[in this window]
[in a new window]
|
Fig. 4.
Numerically simulated virtual electrode patterns for an
interelectrode distance of 0.8 mm. Results were obtained from the
passive two-dimensional bidomain model with unequal anisotropy ratios.
A: 40 mA/cm anodal current applied to the center of the
8 × 8-mm square sheet; B: bipolar stimulation with the
two electrodes located perpendicular to the direction of the fibers;
C: bipolar stimulation with the electrodes located along the
direction of the fibers. Zero level corresponds to the resting
transmembrane potential (white).
|
|
Experimental data for the virtual electrode polarization patterns
during unipolar anodal and cathodal stimuli (Fig.
5, A and D) are in
excellent agreement with the results of Sepulveda et al.
(24) and our own numerical simulations. Results of
the bipolar stimulation of either polarity are shown in Fig. 5,
B, C, E, and F. The bipolar
electrode was oriented perpendicularly and along the epicardial fibers.
The interelectrode distance was 0.8 mm. One can see how dramatically
the VEP is affected by the pacing dipole orientation as it was
predicted by theory (25, 29). Figures
6 and 7
show how the VEP changes in response to the increase in the
interelectrode distance from 0.5 to 1.5 mm. The VEP observed during
unipolar stimulation using one of two of the same bipolar electrode
leads with different polarity are also presented for comparison. As it is shown, the greater the electrode dipole
separation, the more closer the VEP pattern corresponds to simple
superimposition of individual VEP from single electrode leads. Closer
placement of the two electrodes leads to distortion due to the
electrotonic interaction between the two patterns produced by
individual electrodes.
View larger version (60K):
[in this window]
[in a new window]
|
Fig. 5.
Virtual electrode patterns optically recorded from a
4 × 4-mm area of the rabbit anterior epicardium during unipolar
and bipolar stimulation. A and D: conventional
"dogbone"-shaped virtual electrode polarizations (VEP) during
unipolar cathodal and anodal stimulation. B and
E: VEP during bipolar stimulation with a pacing dipole
placed perpendicular to myocardial fibers. C and
F: results of bipolar stimulation with electrodes along the
fibers. The interelectrode distance was 0.8 mm. Images were collected
in the middle of a 2-ms diastolic stimulus.
|
|
View larger version (89K):
[in this window]
[in a new window]
|
Fig. 6.
Virtual electrode patterns for an interelectrode distance of 0.5 mm. A and B: VEP during bipolar stimulation. For
comparison, C and D show VEP during unipolar
anodal (+) and cathodal () stimulation. Data were optically recorded
from a 4 × 4-mm area of anterior epicardium of the rabbit heart
in the middle of a 2-ms diastolic stimulus.
|
|
View larger version (75K):
[in this window]
[in a new window]
|
Fig. 7.
Virtual electrode patterns for an interelectrode distance
of 1.5 mm. Data were optically recorded from a 4 × 4-mm area of
anterior epicardium of the rabbit heart in the middle of a 2-ms
diastolic stimulus. A and D show the VEP during
bipolar stimulation with the different polarity. B,
C, E, and F show the VEP when only one
of the lead (+ or ) was used for the unipolar
stimulation.
|
|
Origin of wavefront of activation during unipolar stimulation.
To visualize how excitation originates, we low-pass filtered the
data in each optical trace at 250 Hz, differentiated [change in
fluorescence over time (dF/dt)] by subtraction two
sequential frames (31), and normalized to the last basic
beat recorded from the same channel
[(dF/dt)/(dF/dt)max] for all of the
256 optical channels. When we suppressed the motion artifacts with BDM,
the derivative normalization gave an analogous result to raw signal
normalization because the action potential shapes in all channels were
similar during the last basic beat. Without BDM the derivative
normalization method was the only one possible. The two-dimensional
intensity graphs of normalized derivative values
[(dF/dt)/(dF/dt)max] for each time
frame were used to construct an animation of a wavefront. We set
"0" at +20% of (dF/dt)max during basic beat
action potential and "1" at 100% of the same value.
Figure 8 shows patterns of VEP and
snapshots of wavefronts of excitation for different electrode
configurations and pacing current strengths. Maps of VEP were recorded
in the middle of a 2-ms stimulus. The first frames in each row (0 ms)
in Fig. 8 correspond to the middle of the stimulus and resemble the
stimulus-induced VEP, because the positive dF/dt corresponds
to depolarization, whereas the negative dF/dt corresponds to
hyperpolarization. The rest of the frames in Fig. 8 show how the wave
of activation spreads from the pacing site.
View larger version (77K):
[in this window]
[in a new window]
|
Fig. 8.
Activation wavefront propagation during near- and
far-from-threshold pacing stimuli. The orange-black intensity plots of
normalized optical signal derivatives {change in fluoresence over
time [(dF/dt)]/maximum change in fluorescence over time
[(dF/dt)max]} at different time frames visualize the
propagation of the excitation wavefront resulting from unipolar and
bipolar pacing. The black color corresponds to the resting potential
and the white color corresponds to the wavefront of excitation, which
is defined as the maximum rate of rise of the transmembrane potential.
Left: corresponding VEP patterns (red-blue plots) at 0 ms
(in the middle of a 2-ms stimulus).
|
|
Figure 8, A and B, illustrates the case of anodal
excitation by strong far-from-threshold (×3) +15-mA and threshold
+5-mA stimuli. Threshold was determined with a 1-mA step. These results appear to agree with the results of Wikswo et al. (30).
Comparison of maps of VEP shows a predictable difference in the
amplitude of positive and negative polarizations. As previously
described by Wikswo et al. (30), make excitation in both
cases started at areas of positive polarization (virtual cathode; Fig.
8A, 0 ms) and spread outward in all directions. As seen from
the comparison of Fig. 8B at 0 and 5 ms, the near-threshold
stimulus initially failed to produce a wavefront of excitation from one
of two virtual cathodes, which was located in the lower right corner.
Therefore, the heartbeat originated only from the upper left virtual
cathode. As a result of this failure, a prominent delay in the
formation of the wavefront of excitation was observed compared with the +15-mA stimulus, which was able to produce wavefronts from both virtual cathodes.
Cathodal stimulation resulted in a different pattern of activation for
far-from-threshold (Fig. 8C, 15 mA) versus near-threshold (Fig. 8D, 5 mA) stimuli. Maps of VEP appeared similar with
an expected difference in the amplitude of both positive and negative polarizations, produced by the virtual cathode and virtual anode, respectively. The far-from-threshold (Fig. 8C) stimulus
induced a wavefront via the make excitation mechanism. Indeed, at 0 ms, the area of virtual cathode produced a prominent wavefront of excitation in the shape of a dogbone. This wavefront spread outward, initially forming a square (Fig. 8C, 5 ms) due to some delay
at areas of hyperpolarization (virtual anode). Later, the wavefront took an elliptical shape with the center coinciding with the
stimulation site (not shown). In contrast, near-threshold stimulation
(Fig. 8D) resulted in activation via the break excitation
mechanism. Indeed, the dogbone-shaped wavefront of excitation (Fig.
8D, 0 ms) formed by the virtual cathode failed to excite all
surrounding tissue. Only the hyperpolarized area of virtual anode was
excited (Fig. 8D, 5 ms). Furthermore, the two areas of
virtual cathodes were excited unequally, such that only the upper left
virtual anode area produced a propagated response (asterisk in Fig.
8D, 5 ms). The resulting elliptical pattern was centered on
this virtual anode instead of the stimulation electrode.
We observed breaklike excitation during cathodal stimulation at
intensities of ×1 through ×2 threshold of excitation in all 12 experiments. In each experiment, we made 60-80 measurements to
scan the different current strengths. Those of them
(5-8) that were in the mentioned range induced a
breaklike activation pattern. In these cases, the locations of the
excitation corresponded to the virtual anode areas, which in rabbit
hearts are 0.8-1.4 mm from the electrode tip in the longitudinal
to cell fiber direction. We did not observe such phenomenon during
anodal stimulation at any strength.
Origin of wavefront of activation during bipolar stimulation.
Similar break excitation was observed during bipolar near-threshold
stimulation. Figure 8E illustrates this case. A bipolar stimulation electrode was oriented perpendicular to the fibers. Initial
activation (Fig. 8E, 0 ms) again corresponded to the virtual cathode (compare with VEP map). However, this activation failed to
produce a propagated response in all directions except the one area of
virtual anode in the left lower corner of the field of view. A
wavefront of excitation formed in this area at 5 ms (Fig.
8E, 5 ms) and spread outward in all directions. An ellipse was centered on this virtual anode rather than the site of stimulation.
Control measurements in the absence of BDM.
The observed difference in a wavefront formation between near-threshold
and far-above-threshold stimulation was preserved in the absence of BDM
(Fig. 9). The pacing threshold was
significantly smaller when the heart was perfused without BDM (0.3 ± 0.2 vs. 2.7 ± 0.8 mA). Therefore, it was difficult to resolve
the VEP pattern for the near-threshold stimulus (Fig. 9B, 0 ms). Nevertheless, the comparison of the initial positions of
wavefronts of excitation (Fig. 9, A, 2.4 ms, and
B, 2.5 ms) clearly shows that during the near-threshold
cathodal stimulation the wavefront also starts from the hyperpolarized
areas of VEP (asterisks in Fig. 9B, 2.5 ms) as it did in the
BDM experiment (Fig. 8D). Furthermore, the left virtual
anode produced a stronger wavelet compared with the right wavelet.
View larger version (42K):
[in this window]
[in a new window]
|
Fig. 9.
Activation wavefront propagation during near- and
far-from-threshold cathodal pacing stimuli without 2,3-butanedione
monoxime (BDM). The orange-black intensity plots of normalized optical
signal derivatives
[(dF/dt)/(dF/dt)max] at different
time frames visualize the propagation of the excitation wavefront
resulting from unipolar cathodal pacing of the heart without BDM. The
black color corresponds to the resting potential and white color
corresponds to the wavefront of excitation, which is defined as the
maximum rate of rise of the transmembrane potential.
|
|
Biphasic action potential upstroke.
Figure 10A shows VEP and the
optical traces from the virtual anode (blue) and cathode (red) regions
during cathodal stimulus of a near-threshold strength. The traces
demonstrate that the virtual cathode produces an initial depolarization
of transmembrane potential. However, this depolarization does not
succeed in depolarizing neighboring regions. This is perhaps due to
source-sink mismatch. As a result, this region is partially repolarized
upon stimulus withdrawal due to the diffusion of
Vm into neighboring hyperpolarized regions. This
biphasic morphology of the upstroke of the response (Fig.
10A, right, red trace) corresponds to the decay
of the wavefront at the virtual cathode area shown in Fig.
8D. Simultaneously, the virtual anode produces transient
hyperpolarization, which rapidly reverses upon stimulus withdrawal.
This reversal overshoots the resting potential and produces an active
response, which initiates the heartbeat, driving areas of virtual
cathode (Fig. 10A, left, blue trace) after a
delay. Optical recordings often are distorted due to depth averaging.
Therefore, the observed phenomenon could be explained by averaging of
superficial regions of virtual cathode and a slightly deeper region of
virtual anode, which could come close in the z-direction due
to the rotation of fiber orientation (9). To rule
out this hypothesis, we conducted numerical simulations in an active
two-dimensional bidomain model.
View larger version (35K):
[in this window]
[in a new window]
|
Fig. 10.
Biphasic upstrokes of action potentials produced by
near-threshold stimulation. VEP (left) and optical signal
traces (right) from hyperpolarized and depolarized areas for
near-threshold cathodal stimulus are shown. A: experimental
data; B: data from the two-dimensional active numerical
model.
|
|
Computer simulations confirmed our experimental observations (Fig.
10B). Near-threshold stimulus applied to the center of the square sheet of the bidomain model resulted in VEP, which is shown at
the end of a 2-ms pulse. After termination of the stimulus, the
wavefront started at the virtual anode areas (hyperpolarized regions),
driving the areas of virtual cathode (depolarized regions).
| |
DISCUSSION |
Break excitation is believed to occur when areas depolarized by
the external field cannot develop an active potential due to sodium
channel inactivation (30). In this case, their
depolarization diffuses to the adjacent hyperpolarized regions, which
start the break excitation wavefront. A similar mechanism plays a role
on a spatially larger scale in shock-induced vulnerability and
defibrillation failure (8).
We present evidence suggesting that similar effects take place
during near-threshold cathodal stimulation, when the pacing current
strength is insufficient to start an active potential in the
depolarized area of VEP. Then, as in the case of classic break
excitation, the depolarization electrotonically diffuses into initially
hyperpolarized regions, where it is able to initiate an active
potential. But the initially depolarized tissue remains excitable
compared with the classic break excitation because the pacing stimulus
is short and the state of inactivation is not reached.
Our data suggest that both make and break excitation mechanisms play
roles during clinically relevant short diastolic cathodal stimuli. Make
excitation is the predominant mechanism for strong stimuli with
strength far-above-threshold of excitation. In contrast, weak
near-threshold stimuli appear to be driven by a break excitation mechanism. A future careful experimental and theoretical examination of
the transition from the break mechanism to the make mechanism with an
increasing stimulus strength may have important implications because it
takes place at clinically relevant intensities.
Limitations.
The major part of our study was accomplished with the
excitation-contraction uncoupler BDM, which is known to affect ionic channel conductivities. This can amplify the observed effect of break
excitation by enhancing the role of initial hyperpolarization, which
can decrease the number of blocked sodium channels and promote an
active response to depolarization from adjacent VEP regions. Yet, as
demonstrated by our control study, a similar break excitation phenomenon is observed during near-threshold stimuli in hearts perfused
without BDM.
Our numerical model and experimental interpretations ignored the
three-dimensional nature of stimulus-induced VEP. The data recorded
from the heart surface may represent an average from cellular layers at
different depths with different polarizations. This can explain the
quantitative discrepancy between the numerical simulation and
experimental data. However, qualitatively these two approaches do
demonstrate the break excitation at near-threshold stimuli with
characteristic biphasic morphology of the upstroke.
| |
ACKNOWLEDGEMENTS |
This study was supported by the Whitaker Foundation, by National
Heart, Lung, and Blood Institute Grant R01 HL-67322, and by the Elmer
L. Lindseth endowment.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: I. R. Efimov, Dept. of Biomedical Engineering, Case Western Reserve Univ.,
10900 Euclid Ave., Cleveland, OH 44106-7207 (E-mail:
ire{at}cwru.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
10.1152/ajpheart.00544.2001
Received 25 June 2001; accepted in final form 1 October 2001.
| |
REFERENCES |
1.
Beeler, GW,
and
Reuter H.
Reconstruction of the action potential of ventricular myocardial fibres.
J Physiol (Lond)
268:
177-210,
1977[Abstract/Free Full Text].
2.
Cheek, ER,
Ideker RE,
and
Fast VG.
Nonlinear changes of transmembrane potential during defibrillation shocks: role of Ca(2+) current.
Circ Res
87:
453-459,
2000[Abstract/Free Full Text].
3.
Cheng, Y,
Mowrey KA,
Van Wagoner DR,
Tchou PJ,
and
Efimov IR.
Virtual electrode induced re-excitation: a basic mechanism of defibrillation.
Circ Res
85:
1056-1066,
1999[Abstract/Free Full Text].
4.
Dekker, E.
Direct current make and break thresholds for pacemaker electrodes on the canine ventricle.
Circ Res
27:
811-823,
1970[Abstract/Free Full Text].
5.
Efimov, IR,
Aguel F,
Cheng Y,
Wollenzier B,
and
Trayanova N.
Virtual electrode polarization in the far field: implications for external defibrillation.
Am J Physiol Heart Circ Physiol
279:
H1055-H1070,
2000[Abstract/Free Full Text].
6.
Efimov, IR,
Cheng Y,
Van Wagoner DR,
Mazgalev T,
and
Tchou PJ.
Virtual electrode-induced phase singularity: a basic mechanism of failure to defibrillate.
Circ Res
82:
918-925,
1998[Abstract/Free Full Text].
7.
Efimov, IR,
Cheng YN,
Biermann M,
Van Wagoner DR,
Mazgalev T,
and
Tchou PJ.
Transmembrane voltage changes produced by real and virtual electrodes during monophasic defibrillation shock delivered by an implantable electrode.
J Cardiovasc Electrophysiol
8:
1031-1045,
1997[Web of Science][Medline].
8.
Efimov, IR,
Gray RA,
and
Roth BJ.
Virtual electrodes and de-excitation: new insights into fibrillation induction and defibrillation.
J Cardiovasc Electrophysiol
11:
339-353,
2000[Web of Science][Medline].
9.
Entcheva, E,
Eason J,
Efimov IR,
Cheng Y,
Malkin RA,
and
Claydon F.
Virtual electrode effects in transvenous defibrillation-modulation by structure and interface: evidence from bidomain simulations and optical mapping.
J Cardiovasc Electrophysiol
9:
949-961,
1998[Web of Science][Medline].
10.
Fast, VG,
Rohr S,
Gillis AM,
and
Kleber AG.
Activation of cardiac tissue by extracellular electrical shocks: formation of "secondary sources" at intercellular clefts in monolayers of cultured myocytes.
Circ Res
82:
375-385,
1998[Abstract/Free Full Text].
11.
Galvani, L.
De vibribus electricitatis in motu musculari.
Commentarius De Bononiesi Scientarium et Ertium Instituto atque Academia Commentarii
7:
363-416,
1791.
12.
Hoffa, M,
and
Ludwig C.
Einige neue Versuche uber Herzbewegung.
Zeitschrift Rationelle Medizin
9:
107-144,
1850.
13.
Knisley, SB,
Hill BC,
and
Ideker RE.
Virtual electrode effects in myocardial fibers.
Biophys J
66:
719-728,
1994[Web of Science][Medline].
14.
Lin, FC,
Roth BJ,
and
Wikswo JP.
Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism.
J Cardiovasc Electrophysiol
10:
574-586,
1999[Web of Science][Medline].
15.
Neunlist, M,
and
Tung L.
Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation.
Biophys J
68:
2310-2322,
1995[Web of Science][Medline].
16.
Press, WH,
Teukolsky SA,
Vetterling WT,
and
Flannery BP.
Numerical Recipies in C. Cambridge, UK: Cambridge University Press, 1997.
17.
Prevost, JL,
and
Battelli F.
Sur quel ques effets des dechanges electriques sur le coer mammifres.
Comptes Rendus Seances Acad Sci
129:
1267,
1899.
18.
Ranjan, R,
Chiamvimonvat N,
Thakor NV,
Tomaselli GF,
and
Marban E.
Mechanism of anode break stimulation in the heart.
Biophys J
74:
1850-1863,
1998[Web of Science][Medline].
19.
Rattay, F.
Ways to approximate current-distance relations for electrically stimulated fibers [Erratum. J Theor Biol 128: Oct. 21, 1987, p. 527].
J Theor Biol
125:
339-349,
1987[Web of Science][Medline].
20.
Roth, BJ.
A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode.
IEEE Trans Biomed Eng
42:
1174-1184,
1995[Web of Science][Medline].
21.
Roth, BJ.
Nonsustained reentry following successive stimulation of cardiac tissue through a unipolar electrode.
J Cardiovasc Electrophysiol
8:
768-78,
1997[Web of Science][Medline].
22.
Roth, BJ,
and
Chen J.
Mechanism of anode break excitation in the heart: the relative influence of membrane and electrotonic factors.
Journal of Biological Systems
7:
541-552,
1999.
23.
Saad, Y,
and
Schultz MH.
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems.
SIAM J Sci Statist Comput
7:
856,
1986.
24.
Sepulveda, NG,
Roth BJ,
and
Wikswo JP.
Current injection into a two-dimensional anisotropic bidomain.
Biophys J
55:
987-999,
1989[Web of Science][Medline].
25.
Sepulveda, NG,
and
Wikswo JP.
Bipolar stimulation of cardiac tissue using an anisotropic bidomain model.
J Cardiovasc Electrophysiol
5:
258-267,
1994[Web of Science][Medline].
26.
Skouibine, K,
Trayanova N,
and
Moore P.
A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium.
Math Biosci
166:
85-100,
2000[Web of Science][Medline].
27.
Sobie, EA,
Susil RC,
and
Tung L.
A generalized activating function for predicting virtual electrodes in cardiac tissue.
Biophys J
73:
1410-1423,
1997[Web of Science][Medline].
28.
Swammerdam, J.
Biblia Naturae. Leyden, Germany: Boerhaave, 1738.
29.
Trayanova, NA,
and
Pilkington TC.
The use of spectral methods in bidomain studies.
In: High-Performance Computing in Biomedical Research, edited by Pilkington TC.. Boca Raton, FL: CRC, 1993, p. 403-425.
30.
Wikswo, JP,
Lin S-F,
and
Abbas RA.
Virtual electrodes in cardiac tissue: a common mechanism for anodal and cathodal stimulation.
Biophys J
69:
2195-2210,
1995[Web of Science][Medline].
31.
Wikswo, JP, Jr,
Wisialowski TA,
Altemeier WA,
Balser JR,
Kopelman HA,
and
Roden DM.
Virtual cathode effects during stimulation of cardiac muscle. Two-dimensional in vivo experiments.
Circ Res
68:
513-530,
1991[Abstract/Free Full Text].
32.
Wu, JY,
and
Cohen LB.
Fast multisite optical measurement of membrane potential.
In: Fluorescent and Luminiscent Probes for Biological Activity: A Practical Guide to Technology for Quantitative Real-Time Analysis, edited by Mason WT.. San Diego, CA: Academic, 1993, p. 389-404.
Am J Physiol Heart Circ Physiol 282(2):H565-H575
0363-6135/02 $5.00
Copyright © 2002 the American Physiological Society
TOP
ABSTRACT
INTRODUCTION
![<FR><NU>d<IT>G</IT></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><IT>&agr; </IT>exp[<IT>&bgr;</IT>(<IT>V</IT><SUB>m</SUB><IT>−V</IT><SUB>rest</SUB>)<SUP>2</SUP>]{1<IT>−</IT>exp[−<IT>&ggr;</IT>(<IT>V</IT><SUB>m</SUB><IT>−V</IT><SUB>rest</SUB>)<SUP>2</SUP>]}](/content/vol282/issue2/fulltext/H565/img005.gif)
