Vol. 279, Issue 3, H1055-H1070, September 2000
Virtual electrode polarization in the far field: implications
for external defibrillation
Igor R.
Efimov1,
Felipe
Aguel2,
Yuanna
Cheng1,
Brian
Wollenzier1, and
Natalia
Trayanova2
1 Department of Cardiology, Cleveland Clinic Foundation,
Cleveland, Ohio 44195; and 2 Department of Biomedical
Engineering, Tulane University, New Orleans, Louisiana 70112
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ABSTRACT |
We recently suggested that failure of
implantable defibrillation therapy may be explained by the virtual
electrode-induced phase singularity mechanism. The goal of this study
was to identify possible mechanisms of vulnerability and defibrillation
by externally applied shocks in vitro. We used bidomain simulations of
realistic rabbit heart fibrous geometry to predict the passive
polarization throughout the heart induced by external shocks. We also
used optical mapping to assess anterior epicardium electrical activity during shocks in Langendorff-perfused rabbit hearts (n = 7). Monophasic shocks of either polarity (10-260 V, 8 ms, 150 µF) were applied during the T wave from a pair of mesh electrodes.
Postshock epicardial virtual electrode polarization was observed after
all 162 applied shocks, with positive polarization facing the cathode
and negative polarization facing the anode, as predicted by the
bidomain simulations. During arrhythmogenesis, a new wave front was
induced at the boundary between the two regions near the apex but not
at the base. It spread across the negatively polarized area toward the
base of the heart and reentered on the other side while simultaneously spreading into the depth of the wall. Thus a scroll wave with a
ribbon-shaped filament was formed during external shock-induced arrhythmia. Fluorescent imaging and passive bidomain simulations demonstrated that virtual electrode polarization-induced scroll waves
underlie mechanisms of shock-induced vulnerability and failure of
external defibrillation.
sudden cardiac death; ventricular fibrillation; external shock; optical mapping; bidomain simulations
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INTRODUCTION |
THE ABILITY OF ELECTRIC
STIMULI to induce cardiac arrest presumably due to ventricular
fibrillation was established by Hoffa and Ludwig (19) 150 years ago. On the other hand, Prevost and Battelli (23)
demonstrated that ventricular fibrillation can be terminated by an
electric discharge delivered directly into the heart. Further
development of this idea carried out by Mirowski et al.
(21) and Schuder et al. (27) resulted in a
new therapy, implantable cardioverter defibrillator (ICD), which has
been recognized as one of the most effective means against sudden
cardiac death (1). Unfortunately, the cost of the ICD
therapy remains a limiting factor of its wider application.
Alternatively, external defibrillation (17, 37) has become
a common therapy in literally every emergency room in the developed
world. Recent development of semiautomatic external defibrillators,
which do not require the presence of a trained health professional, may
significantly extend the area of application of the therapy, including
public places and private homes. This potential wider application
raises additional concerns regarding the safety and optimization of
external defibrillation therapy. However, these issues cannot be
addressed without a better understanding of the mechanisms of external defibrillation.
We recently suggested a mechanism that might be responsible for the
failure of implantable defibrillation therapy (6). Our
hypothesis is based on the finding that ICD shocks produce areas of
positive and negative polarization of various amplitudes next to each
other, known as virtual electrode polarizations (VEP) (28,
30). A new wave front may be formed in a region where strong
positive and negative polarizations meet. Such wave fronts have been
shown to rapidly excite negatively polarized areas after the shock
withdrawal, thus eliminating all shock-induced excitable regions and,
ultimately, completing successful defibrillation (2). On
the other hand, areas where both strong polarizations are adjacent to
an area of no polarization meet the criteria of a phase singularity
(6) and are responsible for the formation of reentrant
circuits. Thus the virtual electrode-induced phase singularity may
result in a new arrhythmia and, consequently, in failure of
defibrillation therapy.
In this report we suggest that VEP is a common mechanism by which the
shock affects cardiac tissue and thus may also be responsible for the
success and failure of external defibrillation therapy. We chose two
complementary research approaches to elucidate the mechanisms of
vulnerability to external shocks. We used a bidomain simulation
approach, which has been critically important in predicting the VEP
effect during shocks (24, 25, 32). It has the ability to
provide insights into the shock-induced transmembrane polarization in
the myocardium. Because of issues of computational tractability, only
the passive version of the bidomain model can be used in a
three-dimensional geometry. It, however, lacks the power to predict the
postshock response and requires experimental confirmation. Fluorescent
imaging of defibrillation has proven to be the only technique capable
of faithfully recording the electrical activity during defibrillation
shocks (4, 7). However, this method lacks the ability to
map voltage in three dimensions. Thus the combination of the two
methodologies provides a unique array of tools capable of predicting
the three-dimensional voltage distribution and the postshock active response.
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METHODS |
Computational methods.
The finite-element method was employed to model external
defibrillation. A uniform field shock was delivered via a conductive bath to an anatomically precise representation of the rabbit
ventricles, including the fibrous structure. The myocardium was modeled
as a bidomain, and the transmembrane potential
(Vm) distribution induced by the shock was
calculated. The combination of realistic fiber architecture, realistic
geometry, and the bidomain model make possible the accurate prediction
of the location and shape of virtual electrodes induced by electric
field shocks.
Bidomain model.
The bidomain model is commonly used (18, 33) to accurately
reproduce the electrical activity of excitable tissue. It is a system
of two reaction-diffusion equations, one for the extracellular space
and the other for the intracellular space, coupled by the transmembrane
current. For computational tractability and because the initial
response of myocardial tissue to external shocks is predominantly the
formation of shock-induced virtual electrodes, assuming a passive
membrane behavior is a good approximation (18, 32). Thus
the membrane is modeled as a parallel combination of a conductance and
a capacitance. Furthermore, because we are interested in the
Vm distribution induced by a uniform electric field shock and not in the evolution of such a distribution, the time
dependence of the transmembrane current was eliminated, resulting in a
significant computational acceleration. The model was thus simplified
to a system of two differential equations coupled by a
constant-resistance membrane
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(1)
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(2)
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(3)
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where 
i, e, and
Vm are the intracellular, extracellular, and
transmembrane potentials, respectively. The fiber architecture is
incorporated into the model via the global intracellular and extracellular conductivity tensors, 
i and
e (3)
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(4)
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where 
· T is
the outer product of the unit vector parallel to the local fiber
direction with itself, I is the 3 × 3 identity matrix,
and 
i,e represents the longitudinal (l) or transverse
(t) component of the local intracellular and extracellular
conductivities of a cardiac fiber.
The bath inside the ventricular cavities and outside the heart
satisfies Laplace's equation. At the interface between myocardium and
bath, the intracellular current satisfies a no-flux condition and the
extracellular current satisfies a conservation-of-flux condition.
All parameters used in the simulations and their values are listed in
Table 1.
Geometry and finite-element grid.
Because the shape of virtual electrodes is greatly affected by tissue
geometry and fibrous architecture, it was critical to use anatomically
accurate geometry and measured fibrous architecture. The rabbit
ventricle geometry and fiber structure were provided by Vetter and
McCulloch (34) as a regularly sampled set of data. A
regular mesh was constructed using these data. Model dimensions, space
constants, and finite-element mesh statistics are listed in Table 1.
The finite-element mesh discretization was smaller than the smallest
length constant. Simulated shock was applied from a pair of flat
electrodes, which reproduced the conditions in the rabbit experiments.
Figure 1 shows the anterior and posterior view of the model.
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Fig. 1.
Model of the rabbit heart that incorporates realistic fiber
geometry. Anterior and posterior views of the computer-simulated heart
are shown together with 2 flat electrodes that reproduce the
experimental configuration (see Fig. 2). Landmarks refer to the right
ventricle (RV) and the left ventricle (LV).
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Experimental methods.
Experiments were performed in vitro on Langendorff-perfused rabbit
hearts (n = 7; Fig.
2A). Detailed protocols have
been published (5, 7). Isolated rabbit hearts were removed
and placed onto a Langendorff apparatus, where the hearts were perfused
with modified Tyrode solution containing 15 mM 2,3-butanedione monoxime
(BDM; Sigma Chemical), the excitation-contraction uncoupler. In two experiments, shocks were applied without and with BDM. The temperature and pH were maintained at 36 ± 0.5°C and 7.35 ± 0.05, respectively.
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Fig. 2.
Experimental preparation and optical mapping setup.
A: Langendorff-perfused rabbit heart was paced at the apex
or base (not shown) with a bipolar electrode made of a twisted pair of
Teflon-coated silver wires. Shocks were applied during the T wave from
a pair of mesh electrodes located on both sides of the heart. The heart
was stained with di-4-ANEPPS. Electrical activity was measured from the
anterior epicardium. The area enclosed in the rectangle is field of
view. B: fluorescence was excited with quasi-monochromatic
light (520 ± 45 nm) from a constant-current light source.
Emission was collected at >610 nm with a 16 × 16 photodiode
array. Each signal was individually amplified and digitized by a
computer for the off-line analysis.
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The heart was positioned in a temperature-controlled water-jacketed
glass chamber with the anterior right ventricular (RV) wall facing the
optical apparatus. The chamber was filled with Tyrode solution. The
solution level was adjusted to cover the heart and the shocking
electrodes positioned at both sides of the chamber. The heart was
gently held by three pistons (placed on posterior and left and right
lateral sides of the heart) that could be adjusted from outside the
chamber. Figure 2A shows the heart as seen by the optical
apparatus. The field of view is selected with a box. A peristaltic pump
maintained a rate of flow of 25 ml/min. A pacing bipolar Ag-AgCl
electrode with 1-mm interelectrode distance was placed at the apex or
base of the heart. In addition, three 12-mm Ag-AgCl pellets (WPI)
located on the right and left sides and at the bottom of the chamber
were used to monitor the electrocardiogram. A pair of custom-made
10-mm-long 2-mm-diameter titanium defibrillation electrodes were used
to deliver rescue shocks if needed. One electrode was inserted into the
RV cavity through the right pulmonary artery. The other was kept in the bath 2-3 cm behind and 1-2 cm above the heart.
Experimental protocol and data analysis.
A previously described (6, 7) optical mapping system
schematically shown in Fig. 2B was used in our experiments.
The heart was stained with the voltage-sensitive dye di-4-ANEPPS, as
previously described (7). Fluorescence was excited at
520 ± 45 nm and collected at >610 nm by the 16 × 16 photodiode array (model C4675, Hamamatsu). The magnification was
adjusted to focus on an area from 0.5 × 0.5 to 1.0 × 1.0 mm
per diode. The entire field of view varied between 8 × 8 and
16 × 16 mm. After amplification, the signals were sampled at
1,894 frames/s. Each frame included 256 optical channels and 8 instrumentation channels.
The heart was continuously paced at a cycle length of 300 ms. The
pacing stimulus strength was adjusted to twice the diastolic threshold
of excitation. Shocks (150 µF, 8 ms) were applied during the T wave
from a clinical defibrillator (model VHS-02, Ventritex). A total of 162 shocks was delivered with an average of 23.1 ± 16.2 shocks/heart.
The stimulator was paused for 2 s after the shock. Each scan
contained 1.5-2 s of data, including the last basic beat action
potential, the action potential altered by a shock, and two or more
subsequent action potentials (see Fig. 5D).
The signal analysis software used in this study was described
previously (6, 7). This program automatically calculated the maps of activation (26), repolarization
(9), action potential duration (9), and
calibrated Vm (11). Maps of
activation and repolarization were built using
(dVm/dt)max and
(d2Vm/dt2)max
methods, respectively. Maps of Vm were
calculated assuming a normal resting potential of 
85 mV, and an
action potential amplitude of 100 mV was present at all recording
sites. This approach is similar to a technique used in the atrium
(16). Contour maps were automatically built using Origin
5.0 (Microcal Software).
We estimated the upper and lower limits of vulnerability (ULV and LLV)
in five hearts. Accurate measurements of these two parameters were not
conducted to reduce the number of shocks applied to the same heart.
Estimation was done by identifying arrhythmic responses to shocks of
various strengths. A response was considered arrhythmic if at least one
extra beat was induced. The lowest shock voltage at which the
arrhythmia was induced was considered to be the LLV; the highest shock
voltage was the ULV. The two parameters were averaged for both
polarities. We recognize that such an estimate is likely to
overestimate ULV and underestimate LLV. Despite this limitation, we
could correlate the two parameters with observed VEP and postshock
response, allowing us to address vulnerability to arrhythmias.
Values are means ± SD. Comparison between variables was analyzed
by Student's two-tailed t-test for paired and unpaired
samples. Differences were considered significant if P < 0.05.
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RESULTS |
Epicardial VEP in the bidomain model.
Figure 3 shows a steady-state epicardial
distribution of shock-induced Vm in the passive
bidomain model. Preshock Vm was set at 0 mV.
Figure 3 shows that the RV epicardium was depolarized by the shock,
whereas the left ventricular (LV) epicardium was hyperpolarized by the
shock. As seen from the width of white and lightly colored areas, the
Vm gradient between the two polarizations was
not uniform throughout the epicardium. The apical view reveals that the
gradient between positive and negative polarization is the steepest at
the apex and decreases toward the base. We recently showed that the
amplitude of the VEP gradient is the main predictor of sites of origin
of a VEP-induced wave front (2). This observation suggests
that the wave front is more likely to originate at the apex than at the
base. Therefore, conditions for virtual electrode-induced phase
singularity might be met and reentry might ensue (6).
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Fig. 3.
Epicardial transmembrane polarization in the passive
bidomain model of the rabbit heart induced by the uniform applied
electric field. Anterior, posterior, and apical views are shown.
Positive and negative polarizations are shown in red and blue,
respectively. Polarization in the heart was set to 0 mV before the
shock. Color bar is saturated; i.e., transmembrane potentials
(Vm) above +100 or below 100 mV are clipped to
±100 mV.
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Epicardial VEP in the rabbit heart.
Figure 4 shows transmembrane polarization
measured in one experiment. Subsequent Figures (5-10) show
similar observations from three more experiments.
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Fig. 4.
Monophasic shock-induced epicardial polarization in the
rabbit heart. A: photograph of the heart. The area enclosed
in the red rectangle is the 16 × 16 mm field of view mapped by
the optical system. B: representative simultaneous
recordings from regions of positive and negative polarization
superimposed with normal action potentials recorded at the same sites
during a normal heartbeat. Shock-induced polarizations
( Vm) in C and D were
calculated by subtracting the normal response from the shock-induced
response. Voltage was calibrated on the basis of the assumption that
normal action potential amplitude is 100 mV. C:
shock-induced polarization profiles recorded along the middle
horizontal row of recording sites at the last sample (528 µs) of the
shock. Different colors represent data recorded during shocks of
different intensity (±50 to ±250 V). D: maps of
polarization produced by shocks of different polarity and intensity.
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Shock-induced polarization was measured from the 16 × 16 mm field
of view shown in Fig. 4A. Simultaneous positive and negative polarizations shown in Fig. 4B were observed during all 162 shocks of any polarity and either strength without exceptions. Figure 4D demonstrates patterns of VEP resulting from 10 shocks of
different polarities and intensities. Positive polarization was always
produced near the cathode and negative polarization near the anode.
Figure 4, C and D, shows that the polarizations
were dependent on the strength of the shock. However, in two hearts, we
observed a seemingly paradoxical lack of strength dependence in the
area of negative polarization. One such example is illustrated in Fig.
4C, left. These observations can be explained by the
three-dimensional nature of VEP (see below).
Interestingly, these polarization patterns confirm a minor twist, in
the shape of a zigzag, of the border between the oppositely polarized
virtual electrodes at the basal part of the anterior epicardium
predicted by the bidomain simulation (Fig. 3, anterior view). Indeed,
the polarization pattern shown in Fig. 4D, bottom left,
shows clear protrusion of negative polarization and no polarization into the right part of the epicardium near the base, similar to that
observed in Fig. 3. This zigzag is due to a slight epicardial surface
invagination in this area and, perhaps, to an irregular fiber
orientation at this site (34).
Thus fluorescent imaging revealed polarization patterns in all seven
studied hearts, which are in qualitative agreement with the
pattern predicted theoretically. What are the consequences of these
polarizations? We examine postshock electrical activity and present its
analysis below.
Virtual electrode-induced phase singularity.
We estimated LLV and ULV in five hearts, which were 22.0 ± 21.7 V
and 161.0 ± 25.1 V, respectively. Table
2 summarizes these estimates. To identify
the mechanisms of shock-induced arrhythmia, we analyzed only responses
to shocks within the vulnerability limits.
Figure 5 shows an example of
shock-induced arrhythmogenesis. Figure 5A is a photograph of
the heart as seen by the photodiode array. The field of view included
the anterior RV and LV epicardium, with the left anterior descending
artery in the middle. The heart was paced at the apex with a bipolar
electrode. The shocking anode and cathode were placed at a distance of
~1 cm from the LV and RV, respectively. The recorded data shown in
Fig. 5D included a normal action potential and an onset of
arrhythmia produced by a 100-V, 8-ms shock. The map of
Vm measured during the last 528 µs of the
shock is presented in Fig. 5B. This map is in qualitative agreement with that shown in Fig. 4D. The
Vm distribution indicates strong VEP: the RV
epicardium is positively polarized, while the left is negatively
polarized. The boundary between the two areas is located approximately
at the left anterior descending artery. The gradient between
the two polarized regions is unevenly distributed between the
apical and basal part of the field of view. The basal gradient is
significantly weaker than that near the apex.
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Fig. 5.
Virtual electrode-induced phase singularity during
externally applied shocks. A: monophasic shock (100 V, 8 ms)
was applied between the 2 mesh electrodes marked as an anode and a
cathode. The shock was applied during the T wave. The heart was paced
at the apex. The area enclosed in the rectangle is the field of view
mapped with the optical imaging system. B: pattern of
Vm at the end of the shock. Isopotential contour
lines are drawn 5 mV apart on the basis of the assumption that the
normal resting potential is 85 mV and action potential amplitude is
100 mV. C: map of postshock activation. Isochrone contour
lines are drawn 10 ms apart relative to the end of shock (0 ms). A wave
front originates near the apex at the boundary between the positively
and negatively polarized regions. The resulting vortex spreads
counterclockwise. D: a data trace from a recording channel
with coordinates x = 10, y = 5 (blue
circle in A). Three time bars indicate the 300-ms scale, the
time frame analyzed in C, and the time frame shown in Fig.
6. Arrow, the end of the shock corresponding to the voltage map in
B. Data demonstrate low-amplitude electrotonic oscillations
of Vm in the core of the reentry (first 2 beats
during arrhythmia onset) followed by full-amplitude action potentials
recorded when the core of the vortex left this area (last 2 beats).
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The postshock activation map (Fig. 5C) shows an onset of
reentrant arrhythmia. Figure 6
illustrates signals recorded from all 256 channels during the first 1.5 rotations of reentry. Specifically, the time bar shown in Fig.
5D indicates the time frame illustrated in Fig. 6. A new
wave front was generated near the apical part of the field of view at
the boundary between positively and negatively polarized regions. This
wave front was produced only in the lower part of the field of view,
where strong negative polarization completely restored excitability.
Because of incomplete recovery of excitability, the upper basal
myocardium was not able to sustain such activation until tens of
milliseconds after the shock, a time interval needed for the wave front
to propagate and for these areas to repolarize.
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Fig. 6.
Raw data recorded during arrhythmogenesis associated with
the virtual electrode-induced phase singularity. Data illustrate 256 records 200 ms in duration recorded before, during, and after the shock
illustrated in Fig. 5. The records start 10 ms before the shock. An
isochronal map shows only the first rotation of the vortex.
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Such a difference in wave front generation can be explained by the
difference in the shock-induced polarization gradient between base and
apex (Fig. 5B). In addition, negative polarization at the
apex was also stronger than that at the base. That resulted in complete
deexcitation and recovery of excitability at the apex and only partial
deexcitation at the base. Resulting reentry was counterclockwise. Thus
the virtual electrode-induced phase singularity phenomenon was observed
during externally applied shock, similar to ICD shocks
(6).
Reversal of shock polarity resulted in reversal of the VEP pattern and
the direction of reentry rotation. Figure
7A shows the pattern of
Vm recorded from the same field of view as in
Fig. 4. Now the RV epicardium was negatively polarized, and the LV epicardium was positively polarized. As in the previous case, a wave
front was formed at the boundary between the positive and negative
polarization near the apex and spread across the negatively polarized
region at the RV epicardium. Then the wave front followed the wave of
repolarization and invaded the basal part of the RV and then the LV
epicardium. A reentrant circuit was created, and a sustained arrhythmia
resulted from it.
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Fig. 7.
Polarity dependence of the virtual electrode-induced
phase singularity mechanism. Conditions are the same as in Figs. 5 and
6, except for the reversed polarity of the shock. A: pattern
of Vm at the end of the shock. Isopotential
lines are drawn 5 mV apart. B: map of postshock activation.
Isochrone contour lines are drawn 10 ms apart starting from the end of
the shock (0 ms). A wave front originates near the apex at the boundary
between the positively and negatively polarized regions. The vortex
spreads clockwise. C: representative recording showing the
onset of sustained arrhythmia. Arrow, time frame in B.
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These virtual electrode-induced phase singularities were induced in all
seven studied hearts. The reversal of shock polarities also resulted in
reversal of direction of reentry in all seven hearts. When a wave of
reexcitation was observed immediately after the shock withdrawal, it
always originated in the negatively polarized area near the apex.
However, in a few cases, a delay was observed between the shock
withdrawal and the wave of reexcitation detected in our epicardial
field of view. Furthermore, some of the observed wave fronts did not
result in arrhythmia.
Site of origin of the wave front of reexcitation.
On the basis of our observation that the wave fronts originated from
the apical part of the field of view, we hypothesized that the earliest
activation can be seen directly at the apex. To prove this hypothesis,
we mapped the electrical activity directly at the apex by 1)
moving our field of view down and mapping anterior apical epicardium
and 2) turning the heart to a horizontal position with the
apex facing our mapping system while keeping the same heart orientation
with respect to the shocking electrodes.
Figure 8 shows an example of mapping at
the apex of the anterior epicardium. The heart is different from that
used in Fig. 4. A monophasic shock (100 V, 8 ms) was delivered
by the cathode facing the RV and the anode facing the LV (Fig.
8A). As seen in the raw traces shown in Fig. 8C,
the shock depolarized the RV epicardium and negatively polarized the LV
epicardium. Figure 8B shows a 10-ms isochrone map of
activation. The wave front of excitation originated at the apex of the
LV and spread toward the base, then turned around a pivoting point and
invaded the RV epicardium. Thus a sustained ventricular tachycardia was
induced.
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Fig. 8.
Onset of arrhythmia at the anterior apex of the heart.
A: digital image of the preparation, the pacing electrode,
and the shocking electrodes. Data were collected from an 18 × 18-mm area of anterior epicardium including the apex. B:
isochronal map of activation. Lines are drawn 10 ms apart. The time
scale starts at the end of the shock. C: optical recordings
collected before, during, and after the monophasic shock (100 V, 8 ms).
Records start 10 ms before the shock. Data were used to plot the map of
activation in B.
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Reversal of shock polarity resulted in reversal of the direction of
vortex rotation from counterclockwise to clockwise (Fig. 9). In this case, the anode was on the RV
side while the cathode faced the LV. However, reversal of shock
polarity did not change the apical origin of the wave of excitation; it
was elicited at the apex of the RV epicardium. Figure 9C
illustrates traces taken around the core of the vortex during its first
rotation. The bold trace was recorded at the pivoting point and shows
slow-rising low-amplitude responses.
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Fig. 9.
Reversal of shock polarity reversed the vortex rotation
but not the apical site of origin. The field of view and other
conditions are the same as in Fig. 8. A: map of optical
signals collected before, during, and after the shock. The thick traces
are shown again in C. B: 10-ms isochrone map of
activation. The time scale starts at the end of the shock.
C: representative traces around the core of the vortex. The
bold trace shows slow-rising responses observed at pivoting points.
Arrow, direction of conduction.
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To complete verification of our hypothesis, we turned the heart
horizontally and imaged the tip of the apex. The heart was positioned
in such a way that the anterior epicardium was up, the posterior
epicardium was down, and the RV was on the left side and the LV on the
right side of the field of view. This orientation presumably did not
alter the electric field distribution near the apex. As described
previously, the apex was bathed by the perfusate and did not touch the
glass wall of the chamber. Figure 10
shows a representative example of these measurements from another heart. Figure 10A shows a 200-ms segment of data starting
from the onset of a normal action potential and then a 200-V
shock-induced onset of sustained arrhythmia. However, a complete
reentrant circuit was not observed in this field of view, because it
was presumably located at the anterior and posterior epicardium at some
distance from the apex beyond the field of view of our imaging system. Figure 10B shows a 50-ms interval of the data shown in Fig.
10A, starting 10 ms before the shock application. Cells on
the left side of the field of view were rapidly depolarized during the shock, whereas cells on the right were negatively polarized by the
shock and then depolarized after shock withdrawal. Average activation
time in these channels was 5.6 ± 3.2 ms (n = 24 channels) after shock withdrawal. Figure 10C presents the
distribution of Vm at the end of the shock (the
last 528 µs of the shock). Finally, Fig. 10D shows
representative traces from six recording sites selected with the box in
Fig. 10A. These sites are located at the border of the
virtual electrodes, with strong positive polarization at one side and
negative polarization at the other. The same measurements were
conducted in one more heart, in which the average activation time was
6.2 ± 2.8 ms (n = 31) after withdrawal of the
200-V shock. These activation times were the earliest detected in our
experiments. Thus the origin of the wave front was indeed at the apex
in these two hearts.
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Fig. 10.
Origin of the wave front of reexcitation at the apex.
The map of Vm was acquired at the tip of the
apex. The field of view was 16.5 × 16.5 mm and included the RV on
the left and the LV on the right of the field of
view. Because of the high curvature of the apical epicardium, only the
middle photodiodes were able to record signals. The monophasic shock
was 200 V in amplitude and 8 ms in duration. It was applied 100 ms
after the upstroke. A: map of action potentials altered by
the shock. Record duration is 200 ms. Vertical scale is in arbitrary
units. B: map of shock-induced changes in
Vm. Record duration is 50 ms, including 10 ms
before the shock, 8 ms during the shock, and 32 ms after the shock.
Note the immediate depolarization produced by the shock on the
left and the negative polarization with subsequent
reexcitation on the right. Vertical scale is in arbitrary
units. C: gray-scale map of Vm
measured during the last 528 µs of the shock. Note the negative
polarization on the right and the positive polarization on
the left in the field of view. D: representative
traces from the area enclosed in the rectangle in A
illustrating the genesis of the wave front after the shock
withdrawal.
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Three-dimensional pattern of VEP predicted by the bidomain model.
Because of the absorption of the excitation and emission light,
fluorescent imaging is limited in its ability to assess midmyocardial electrical activity. Therefore, we used the bidomain model to predict
the polarization throughout the entire heart, including the right and
left midmyocardium, the endocardium, and the septum. Figure
11 shows the results. As evident from
the ventricular cross sections presented in Fig. 11, VEP was produced
throughout the entire heart in a complex fashion. The exact pattern is
strongly influenced by the orientation of the heart with respect to
electrodes (not shown). Yet, several features of VEP are common to any
external stimulation with homogeneous electric field. Every surface of the myocardium is positively polarized if it faces the cathode and
negatively polarized if it faces the anode. The surface polarizations are stronger in amplitude than any bulk polarization. As previously shown by Wiedmann (35) and Trayanova (31),
such surface polarization decays exponentially with distance from the
surface. In some areas, the polarization extends deeper than the
surface myocardial layers because of the fiber curvature effect
(29). Furthermore, the gradient between the positive and
the negative polarizations is distributed unevenly, with strong
gradient in some areas (e.g., RV free wall in slice 4) and
weak gradients in others (e.g., LV free wall in slice 4).
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Fig. 11.
Virtual electrode polarization throughout the rabbit
ventricles predicted by a bidomain model. Left: anterior
view of the computer model geometry; right: 9 horizontal
cross-section planes (1-9). Vm
polarization was produced by a 5.8 V/cm electric field delivered via a
pair of electrodes shown in blue and red at top. Positive
and negative polarizations are shown in red and blue, respectively.
Color bar is saturated; i.e., Vm above +100 or
below 100 mV are clipped to ±100 mV.
|
|
This observation suggests that the sites of origin of the shock-induced
wave fronts may occur not only at the apex, as illustrated in Figs.
5-10. Such wave fronts can also originate at the
endocardium, where strong positive polarization meets strong negative
polarization (e.g., points of connection between the septum and the RV
endocardium). In addition, such wave fronts may originate within the
bulk of the myocardium. In this case, the wave fronts would propagate toward the epicardium or the endocardium depending on which of the two
surfaces is negatively polarized. Slice 6 exemplifies another complexity of the VEP within the myocardium. Septal
polarization in this slice indicates that several small and isolated
wave fronts might originate within the septum. Such fragments of wave
fronts may result in O- or U-shaped scroll waves sustained within the septum if the size of the heart and the wavelength permit.
Unfortunately, verification of this hypothesis is beyond the
capabilities of our mapping system.
One effect, however, can be verified. As we recently showed during ICD
shocks, a scroll wave with ribbon-shaped filament (11) can
be observed by optical mapping that is consistent with these bidomain
simulations. Indeed, let us assume that the polarization shown in Fig.
11 was produced in refractory myocardium, which is in its plateau phase
of electrical activity. Slice 4 shows that the strong
negative polarization at the LV is confined near the epicardium only.
Thus a complete deexcitation and recovery of excitability may also be
confined to a layer of tissue near the epicardium. In contrast, the
adjacent midmyocardium is only partially deexcited and remains
refractory. Thus a postshock wave front in the LV could initially
propagate only in the thin intense-blue surface region seen on the
right in slice 4 in Fig. 11. This fact has a direct impact
on the pathway the activation will take after the external shock.
Indeed, after the shock, a wave front of excitation would originate
near the left anterior descending coronary artery at the epicardium and
then would spread along the epicardial layer, as shown in Figs. 5 and
8. Consistent with the polarization shown in Fig. 11, the wave front
will remain confined to the surface layers of the strong shock-induced
negative polarization. After the recovery of the epicardial regions
that were only weakly negatively or positively polarized, this wave may
reenter and form an arrhythmia, as shown above. However, at the same
time, deeper layers would also recover and become excitable, as for
instance the midmyocardial layer in slice 4 of Fig. 11. Thus
the wave front would dive inside the myocardium and simultaneously
invade the recovered RV. Therefore, a scroll wave would be formed,
which would have a ribbon-shaped filament. Such a filament will
traverse the epicardium along the line where epicardial polarization
gradient exists, turn 90° toward the LV spanning the entire LV
midmyocardium, and reenter the epicardium at the posterior side.
Similar scroll waves may be induced in the septum and the RV. However,
the RV scroll will not be observed at the surface, because the
deexcited region in this case is hidden at the endocardium. Shock
reversal will expose the RV scroll but hide the LV scroll. However, the
difference in thickness between the RV and the LV may result in
different outcome of the scroll-wave induction and maintenance in the
two ventricles and the septum.
Evidence of a three-dimensional scroll wave produced by VEP.
As shown in Figs. 5-9, the line of steep gradient between the
positive and negative polarizations at the epicardium is the line of
block of the induced vortex. Similarly, there is a theoretically predicted surface between the opposite-in-sign epicardial and bulk
polarizations that may serve as a filament of a scroll wave in three
dimensions. However, such a surface may or may not be visible to direct
epicardial mapping, depending on its depth. If such a filament is
located within 1-2 mm from the epicardium, it may be detected by
the optical system as "dual-humped" signals (8, 10,
11).
The data already presented here support such a hypothesis. Indeed,
careful examination of Fig. 6 reveals that nearly all signals in the
upper right corner show typical "dual-humped" morphology carrying
the signature of a deeper wave front (8, 10). Similar dual-humped signals are evident in Fig. 8C.
Figure 12 provides yet another example
of dual-humped signals. In this case, we chose a reentry produced by a
120-V shock in the same heart as in Figs. 5 and 6. Signals shown in
Fig. 12C demonstrate a strong dual-humped morphology. The
epicardial activation map (Fig. 12A) was reconstructed using
only the largest peaks of (dV/dt)max. It shows that a wave of excitation was generated at the apex within the
first 10 ms after shock withdrawal, which occurred at 520 ms. As
illustrated in Fig. 12C, this wave front propagated upward. After reaching the upper boundary of the field of view, the wave turned
around in a fashion similar to that in Fig. 5C but at a higher vertical location in the field of view, invaded the already recovered RV epicardium, and spread toward the apex (Fig. 12,
A and B). At the same time, the LV signals show
second components (Fig. 12C), which were ignored during the
construction of the upper map. These were used to construct the map of
activation at the endocardium or midmyocardium. After its arrival at
the top boundary of the field of view, the wave front made a turn to
the left. Figure 12B shows that the recording sites were
sequentially activated. Simultaneously, another wave front originated
there and spread backward toward the apex along the right side of the
field of view (Fig. 12C). As evident from the endocardial or
midmyocardial recordings, there was an uninterrupted wave front
propagating from the base to the apex. Such a peculiar activation
pattern cannot be explained within the two-dimensional paradigm.
Indeed, how is it possible that the same sites in the upper right
corner of Fig. 12A were reactivated within 30-40 ms if
normal action potential duration in this area was 175 ms? Only a
three-dimensional scroll wave of the type described above can easily
explain such propagation. Figure 12A illustrates our
reconstruction of the scroll wave and its ribbon-shaped filament. At
first, the wave shown with red isochrones propagated within the space
limited by the epicardial surface and the filament. After recovery of
the adjacent tissue, the scroll wave invaded it below and to the left
of the filament.
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Fig. 12.
Qualitative reconstruction of a scroll wave with
ribbon-shaped filament resulting from a monophasic external shock (120 V, 8 ms). Conditions are identical to those in Fig. 5, except for the
stronger shock intensity (120 vs. 100 V). A: isochrone map
of activation (10 ms) constructed on the basis of the largest postshock
(dV/dt)max peaks only (epicardial
spread of activation) or (dV/dt)max
peaks detected after 580 ms (midmyocardial or endocardial map). Thick
black line traces the boundaries of the ribbon-shaped filament. Arrows,
spread of activation in the epicardial and transmural directions. The
shock ended at 520 ms. B and C select the 2 columns of signals illustrated in B and C. B: left column of recording sites. Only 1 wave of excitation
was observed after the shock withdrawal. C: right column of
recording sites. Two waves of excitation propagated through the area.
|
|
Similar analysis revealed activation sequences supporting scroll waves
in two more hearts. In the remaining four hearts, the dual-humped
signals were present but were not easily interpretable. Perhaps the
complexity of midmyocardial VEP contributed to the more complex
dynamics of the scroll waves.
| |
DISCUSSION |
This study presents theoretical and in vitro experimental data
obtained during externally applied electric shocks. The data show that,
similar to internally applied shocks investigated in our previous
studies (2, 6, 7, 11), external shocks evoke a VEP
pattern. It provides the basis for a virtual electrode-induced phase
singularity and the resulting reentrant scroll wave, which underlie
shock-induced arrhythmogenesis. Yet there are important differences
between these two cases. The pattern of epicardial polarization
produced by externally applied shocks is different from that induced by
internal shocks. Only two areas of opposite polarization are present on
the epicardium: negative facing the cathode and positive facing the
anode. As a result, only one wave front is induced; it begins at the
epicardium and ends at the endocardium while propagating through the
apex of the heart. This wave front has two wave breaks, which could
result in two reentrant circuits: one at the anterior and another at
the posterior epicardium. This is different from the effect of internal
shocks, which could potentially induce four reentrant circuits
(quatrefoil reentry) (20).
Recent progress in theoretical and experimental approaches to
defibrillation research has resulted in formulation of the VEP theory
(32). A growing body of evidence suggests that VEP is perhaps the most important component of the interaction between externally applied electric field and heterogeneous myocardium. A
number of structural heterogeneities of different spatial scales have
been considered as a substrate of shock-induced stimulation and
defibrillation. These heterogeneities include, in order of increasing
spatial scale, cell-to-cell junctions (22), syncitial heterogeneities (14, 15), unequal anisotropy between
intra- and extracellular domains (28), tissue-bath
interface (12, 31, 35), and fiber curvature
(29). In addition, heterogeneity of the external field
itself may contribute to VEP (28). The larger the spatial
heterogeneity in the external field, the stronger the shock-induced
polarization (32). VEP described by Sepulveda et al.
(28) arise around small-sized electrodes that generate strongly nonuniform fields. Such VEP has been observed during ICD
shocks and may play an important role in internal defibrillation (6, 12). However, external defibrillation is clearly
driven by different VEP mechanism(s). It is possible that fiber
curvature and tissue-bath interface play the major role in this type of defibrillation mostly because of their spatial scale. Our data provide
the first experimental and theoretical evidence supporting this
prediction (13, 32).
An earlier study by Zhou et al. (36) did not present any
evidence of VEP during externally applied shocks. Only a single transmembrane polarization polarity along the line connecting the two
opposite electrodes was observed during any given shock polarity. This
observation contradicts our experimental and theoretical findings,
according to which positive and negative polarizations are present
during shocks of any polarity. Comparison of our results with those of
Zhou et al. is difficult because of the differences in recording
methodology. Zhou et al. recorded electrical activity from only nine
posterior epicardium spots near the base, whereas we imaged nearly the
entire anterior epicardium. Most importantly, Zhou et al. used a
bipolar electrode to estimate extracellular voltage gradient
"immediately adjacent to each laser recording spot as shocks were
given" (36). Such an electrode pair and a piece of
silicone rubber that held it may have altered the transmembrane polarization because of tissue-bath interface or secondary sources near
the recording stainless steel electrodes. As in our previous experiments (12), we verified such a possibility by
mapping when the heart was touching the glass window and when it was
placed at a distance from it. Contact with the glass window somewhat reduced but did not eliminate the opposite polarization observed without the contact.
Our data show that the steep gradients between oppositely polarized
areas are sites of wave front origination. Careful three-dimensional mapping of such regions may help identify these sites and, most importantly, the locations of the phase singularities. As is evident from the fluorescent imaging data, the bidomain simulation provided accurate prediction of such sites at the epicardium. Indirect evidence
of scroll waves developed after the shock supports the endocardial and
midmyocardial distribution of shock-induced Vm, as predicted by the bidomain model. Thus it appears feasible in the
future to be able to theoretically predict the areas of potential phase
singularities on the basis of the specific ventricular geometry and
defibrillation lead configuration. Yet, careful mapping of three-dimensional VEP is required to fully support the theory. This is
especially important in hearts with structural disease. Areas of
infarct, fibroses, or ischemia would change VEP and might provide
additional substrate for wave front initiation and phase singularities.
Limitations.
Our study is limited because of the inability to experimentally assess
electrical activity in the three-dimensional myocardium. Furthermore,
stand-alone passive bidomain simulations have limited predictive power
because of the lack of representation of the ionic currents in the
computer model. Yet, the combination of optical imaging of the
epicardial surface of the ventricles with three-dimensional passive
bidomain model simulations provides guidance as to what the deep
myocardial activity could be, as well as an assurance of the correct
interpretation of our experimental findings.
The passive bidomain simulations predict only the shock-induced
Vm changes throughout the three-dimensional
myocardium and not the postshock activity. Although highly desirable,
inclusion of ionic membrane kinetics in the rabbit heart model remains
an insurmountable task. First, the ionic model would increase the memory requirement by over an order of magnitude. In addition, we
estimate that to obtain 200-ms of data, the CPU time requirements would
increase four to seven orders of magnitude. Before we are able to
approach a problem of such magnitude, more efficient numerical algorithms need to be implemented.
Our study is also limited because of the use of BDM as
excitation-contraction uncoupler. Such treatment may have an effect on
ionic channel conductance and arrhythmogenesis. We verified the extent
of this limitation by mapping Vm during external
shocks in two hearts with and without BDM. These measurements showed that positive and negative polarizations are present in both cases. Unfortunately, strong movement artifacts did not allow reconstructing the pattern of activation during arrhythmogenesis.
| |
ACKNOWLEDGEMENTS |
The authors thank Dr. McCulloch (University of California, San
Diego) and his group for providing the rabbit heart fiber orientation and geometry and Dr. Eason (University of Vermont) for invaluable help
with the simulations.
| |
FOOTNOTES |
This study was supported by National Heart, Lung, and Blood Institute
Grants R01-HL-58808 (I. R. Efimov), R01-HL-59464 (I. R. Efimov), and R01-HL-63195 (N. Trayanova), National Science Foundation
Grants DMF-9709754 (N. Trayanova) and BES-9809132 (N. Trayanova), and
American Heart Association Ohio Valley Affiliate Grant-in-Aid 9806201 (I. R. Efimov).
Address for reprint requests and other correspondence: I. R. Efimov, Biomedical Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106 (E-mail: ire{at}po.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.
Received 22 December 1999; accepted in final form 6 March 2000.
| |
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TOP
ABSTRACT
INTRODUCTION
