From the Division of Cardiovascular Disease, Departments of Medicine,
Biomedical Engineering, and Physiology and Biophysics, University of Alabama
at Birmingham.
Correspondence to Raymond E. Ideker, MD, PhD, Cardiac Rhythm Management Laboratory, B140 Volker Hall, 1670 University Blvd, Birmingham, AL 35294-0019. E-mail rei{at}crml.uab.edu
Abstract
Background—Theoretical models
suggest that an electrical stimulus causes regions of depolarization
and hyperpolarization on either side of a
myocardial discontinuity. This study determined experimentally whether
an artificial discontinuity gives rise to an activation front in
response to an electrical stimulus, consistent with the
creation of such polarized regions.
Methods and Results—After a thoracotomy in six dogs, a
504-unipolar-electrode plaque was sutured to the right
ventricular epicardium to map activations. From a line
electrode parallel to one side of the plaque, 10 S1 stimuli
were delivered, followed by S2 and S3 stimuli
(S1S1, S1S2,
S2S3 interval=300 ms). S1 and
S3 stimuli were 25 mA; 5-ms S2 stimuli of both
polarities were initially 25 mA and increased in 25 mA increments. The
plaque was removed, and a transmural incision was made through the
ventricular wall in the middle of the mapped region and
sutured closed. The plaque was replaced and the stimulation protocol
repeated. Before the incision, S2 stimuli directly
activated tissue only near the stimulation site. An activation
front arose at the border of the directly activated region and
propagated across the plaque. As the S2 stimulus strength
was increased, the size of the directly activated region
increased. After the incision, sufficiently large S2
stimuli caused direct activation of tissue adjacent to the transmural
incision as well as at the stimulation site. Activation fronts that
arose adjacent to the transmural incision either propagated proximally
toward the stimulation site and collided with the activation front
originating from the stimulation wire or propagated distally away from
the incision. Minimum S2 stimulus strengths activating
areas adjacent to the incision were only 45±14% (cathode) and
39±18% (anode) of the strengths required to directly activate
the same area before the incision was formed
(P<.05).
Conclusions—Myocardial discontinuities can give rise to
activation fronts after a stimulus, suggesting the presence of
polarized regions adjacent to the discontinuity.
An electrical shock
is thought to defibrillate by directly exciting tissue to cause new
cardiac action potentials or extension of action
potentials.1 2 3 4 5 One of several factors that may
contribute to the mechanisms by which the shock directly excites
myocardium to cause a new action potential in tissue
distant from the defibrillation electrodes is discontinuities between
myofibers or between bundles of myofibers.6 7
These discontinuities can be normal, such as interstitial
connective tissue and blood vessels, or abnormal, such as myocardial
infarct scars and surgical incisions. By interrupting the closely
coupled syncytium of myocytes, these discontinuities interrupt the
intracellular space, requiring current that crosses the discontinuity
caused by the shock to exit the intracellular space on one side and
reenter the intracellular space on the other side of the discontinuity
(Figure 1
This study determined whether the magnitude of these secondary sources
can be sufficient to directly activate tissue adjacent to the
discontinuity. This was done by use of a series of electrical stimuli
of increasing strength given before and after a large discontinuity was
created by a transmural incision made through the right ventricle of
the canine heart. Activation sequence maps were examined to see whether
activation fronts arose from either side of the surgical incision,
which would indicate that the discontinuity formed by the incision
created a virtual electrode.
Methods
Six dogs (18 to 22.5 kg) were anesthetized with
pentobarbital (30 mg/kg), intubated and mechanically ventilated with
supplemental oxygen, and given maintenance
intravenous fluids. The ECG and arterial blood
pressure were continuously monitored. Core body temperature,
arterial blood gas values, and electrolyte levels were
maintained within normal limits. Succinylcholine (0.3 mg/kg) was
administered as needed to minimize skeletal muscle stimulation by the
shocks. The chest was opened through a right thoracotomy, and a
pericardial cradle was created to expose the right ventricle. A plaque
containing 504 unipolar epicardial recording electrodes
arranged in a 24x21 pattern was sutured onto the right ventricle
(Figure 2
All stimuli were 5-ms, square, constant-current pulses of the same
polarity, with the S1S1,
S1S2, and
S2S3 intervals equal to 300
ms. The S1 and S3 stimuli
were 25 mA. After 10 S1 stimuli, the
S2 stimulus initially was 25 mA and then was
increased in 25-mA increments until all tissue under the plaque was
directly excited as determined by analysis of results during
the study. Cathodal pulses were delivered first, followed by anodal
pulses.
After all stimuli were delivered, the plaque was removed, with the
sutures left in place. With umbilical tape, the superior and
inferior venae cavae were constricted, and a transmural
incision averaging 3.6±0.3 cm in length was formed by a cut through
the right ventricle in the middle of the mapped area (Figure 2
After the experiment, a lethal dose of KCl was given, and the heart was
removed. The region under the plaque was excised, and the tissue was
fixed in formalin and sectioned parallel to the epicardial surface at
0.5-mm increments. Fiber orientation was determined from the
histological sections. All animals were treated and
cared for in accordance with the National Institutes of Health
Guide for the Care and Use of Laboratory Animals.
Data Acquisition
Data Analysis
For each polarity, the minimum current required to directly
activate the areas adjacent to the transmural incision after
the incision was compared with the current required to directly
activate the same areas before the incision. Also, the current
required to directly activate all columns of the mapped region
both before and after the incision was determined for each polarity.
Direct activation of the mapped area was determined by viewing of
animation sequences and by electrogram analysis. Tissue under
electrodes that did not record an activation after
S2 stimulation was considered to be directly
excited by the stimulus as described
previously.14 15 To quantify the effect of the
incision on the activation sequence, the time interval was determined
from the beginning of the S1 stimulus to
activation at electrode 254 in the center of the plaque distal to the
incision (Figure 2
Data are expressed as mean±SD unless otherwise specified. ANOVA with
repeated measures and Student's t test for paired samples
were used to determine statistical significance. A value of
P
Results
Cathodal Stimuli
Increasing S2 strength increased the area
of tissue directly activated. Figures 3B
After Incision Formation
As the S2 stimulus strength increased, areas of
direct activation were observed on both sides of the incision as well
as at the stimulation site. Activations originating on the proximal
side of the incision propagated toward the stimulating electrode,
colliding with the wave front arising near the stimulating electrode
(Figures 3E
Activation Times
Anodal Stimuli
After Incision Formation
When the anodal S2 strength was increased to 50
mA for all animals (Table 2
Activation Times
Cathodal Stimuli Versus Anodal Stimuli
Visual analysis of the computer animation of activation as well
as statistical comparison of the activation times after
S1 and S2 stimuli in the
two sham-treated animals in which no incision was sham-treated
indicated no significant differences in the activation patterns
observed before and after the sham procedure, suggesting that the
changes in the other six animals were caused by the incision.
Comparison and statistical analysis of the ST segments measured
from electrode 254 before and after the incision indicated a
significant change from before (0.58±0.72 mV) to after (6.96±2.68 mV)
the incision. As the study progressed, the degree of ST-segment change
decreased from 6.96±2.68 to 3.82±3.51 mV (P=.11).
Fiber Orientation
Discussion
Our major finding is that surgical incisions can create secondary
sources during electrical stimulation. Evidence for this finding is
that an electrical stimulus given from an electrode >2 cm away from
the incision causes activation fronts to arise and propagate away from
the incision at a stimulus strength that does not give rise to
activation fronts in this area before the incision. In addition to
visual examination of the animation sequences and isochronal maps
(Figure 3
A likely reason that activation arose near the incision was that
the incision altered the transmembrane potential response in the
adjacent myocardium caused by the S2
stimulus. Such transmembrane potential changes were observed in a
simulation using the bidomain formulation by Street and
Plonsey.16 The surgical incision is thought to
interrupt the intracellular space but, because the
myocardium is sutured back together, not to interrupt the
extracellular space. Because the intracellular space is interrupted,
any intracellular current that would normally flow during the
S2 stimulus is forced to exit the intracellular
space, cross the incision in the extracellular space, and then reenter
the intracellular space on the other side of the incision (Figure 1
Injury potentials caused by the incision may have influenced
these findings. To explore this possibility, computer simulations were
performed that are presented in the "Appendix." These
simulations suggest that changes in the transmembrane potential caused
by the incision can lower the stimulus strength required to directly
excite tissue at the incision (Figure 7D
The S2 stimulus was delivered in
diastole, when activation is thought to occur in tissue
that is sufficiently depolarized, but not in regions of
hyperpolarization.17 18
Depolarization should occur on the distal side of the incision when the
stimulus electrode is a cathode and on the proximal side of the
incision when the stimulus electrode is an anode (Figures 1
The reason for these observations is unclear, but it may be related to
the "dog bone" phenomenon reported by Wikswo and
others,19 20 21 who found that along myofibers only
1 to 2 mm away from an anode, the change in transmembrane
potential reversed from hyperpolarization to
depolarization. Conversely, a few millimeters along fibers away from a
cathode, depolarization changed to
hyperpolarization. Similar findings have recently
been observed for a wire stimulating electrode as used in our
study.22 These changes in transmembrane potential
are not seen in the simulation discussed in the "Appendix," because
they are one-dimensional. If the same changes occur just outside the
secondary sources formed by the incision, a depolarized region should
exist just proximal to the hyperpolarized region on the proximal side
of the incision during a cathodal stimulus. Similarly, a depolarized
region should exist just distal to the hyperpolarized region on the
distal side of the incision during an anodal S2
stimulus. The areas of depolarization may give rise to the activation
fronts seen in these regions after the S2
stimulus. Because the field strength of the S2
stimulus decreases with distance away from the electrode, it is
probably smaller on the distal side of the incision than on the
proximal side. If so, the depolarized region on the distal side of the
incision during an anodal S2 stimulus may be
weaker than the depolarized region on the proximal side during a
cathodal stimulus. This may explain why a larger
S2 stimulus is necessary to create an activation
front on the distal side of the incision for an anodal stimulus than on
the proximal side for a cathodal stimulus.
Another possible reason for this poststimulus activation behavior is
the injury currents created by the incision (see "Appendix").
Experimentally, injury currents were detected adjacent to the incision
in all animals. As the stimulation protocol progressed, the ST-segment
changes tended to decrease with time, although they never completely
disappeared. This suggests that the tissue surrounding the incision
never had ample time to heal and as such may have continually produced
an elevation in the transmembrane potential, which in turn may have
altered tissue excitability after the incision. A third possible
explanation for these findings is that break excitation occurred in
areas hyperpolarized during the stimulus. For cathodal stimuli, break
excitation may occur in the hyperpolarized region on the proximal side
of the incision, resulting in subsequent propagation toward the
stimulation wire. For an anodal shock of the same strength,
hyperpolarization distal to the incision may be
smaller than on the proximal side of the incision for a cathodal shock
as a result of the smaller electrical field on the distal side of the
incision, because it is farther from the stimulating electrode than the
proximal side. Consequently, a larger stimulus strength would be
required to directly activate the distal side of the incision
by means of break excitation for anodal stimuli. On the basis of the
results generated from the simulations, however, break excitation is
not the likely means of stimulation observed in this set of
experiments, even in the presence of injury currents (see
"Appendix").
These results have several implications for defibrillation. It is
likely that secondary sources are not specific for surgical incisions
but rather can form at any site in which the intracellular space is
interrupted. Such interruptions occur naturally between bundles of
myocardial fibers and where blood vessels and nerves traverse the
myocardium. Thus, these results support the findings of
Gillis et al6 and suggest that secondary sources
can be an important mechanism for defibrillation. The magnitude of the
secondary source probably depends on many factors, including size of
the discontinuity, strength of the shock field, fiber orientation, and
degree of anisotropy. This study indicates that when the discontinuity
is transmural and several centimeters long, the secondary source can
significantly affect the response to a shock. Such an interruption
directly activated the tissue on at least one side of the
incision with a stimulus strength that was only 39% of that required
to directly activate this tissue when the interruption was
absent (Table 2
Scars caused by infarction, cardiomyopathy, or
surgical incisions may also serve as secondary sources. This phenomenon
may explain why defibrillation thresholds are typically not increased
by infarction,23 24 even though current shunting
may occur through the scar, because its conductivity is higher than
that of myocardium.25 Current
shunting may be offset by secondary sources at the infarct border.
Surgical or ablation lesions may alter the defibrillation
threshold. If the incisions are not transmural and do not extend to a
boundary, they may be arrhythmogenic by allowing reentry to form around
the anatomic barrier formed by the incision. If they are transmural and
reach a boundary, however, they may lower the defibrillation threshold
by creating barriers to conduction that decrease the incidence of
reentrant pathways immediately after the shock, just as the maze
surgical procedure decreases the incidence of spontaneous reentry
leading to atrial fibrillation.26 Our study
raises the possibility that surgical or ablation lesions also may lower
the defibrillation threshold by a second mechanism: creation of
secondary sources. These secondary sources may lower the shock strength
needed to directly activate tissue, thus lowering the
defibrillation threshold.
Appendix 1
We performed computer simulations to examine the effects
of elevated [K+]e, one
factor responsible for injury potentials associated with acute injury
near the incision. Electrical activity was modeled by use of a
one-dimensional bidomain representation of tissue
structure,27
The numerical solution scheme was similar to that reported
previously.28 Ordinary differential equations
defining the gating variables for the individual ionic currents of
Iion in Equation 2
To represent configurations similar to the experiments,
we performed simulations using models that included (1) no incision and
nominal [K+]e (5.4
mmol/L, resting membrane potential [RMP]= -82.3 mV); (2) an
incision, represented as a complete interruption in
intracellular coupling between adjacent nodes located 2.5 cm from the
left edge, combined with nominal
[K+]e; (3) no incision
and elevated [K+]e at
nodes 2 to 3 cm from the left edge; and (4) an incision combined with
elevated [K+]e. In each
simulation, the cathode was located on the left edge of the model and
the anode on the right edge. In models 1 and 2, shock strengths were
increased until the diastolic threshold for stimulation
(DTS) current was found. In models 3 and 4,
[K+]e current was
increased until a shock of strength 0.96xDTS initiated a
depolarization wave front from the elevated
[K+]e region.
No Incision, Nominal [K+]e
Incision, Nominal [K+]e
No Incision, Elevated [K+]e
Incision, Elevated [K+]e
Acknowledgments
This study was supported by a National Institutes of Health
research grant (HL-42760), a special opportunity award from the
Whitaker Foundation, a grant-in-aid of research from Sigma Xi, a
National Science Foundation/National Young Investigator Award
(BES-9457212), and a grant from the National Institutes of Health
(R29-HL-54024). The authors wish to thank Dr William M. Smith and
Catherine M. Sreenan for their statistical analyses and helpful
editorial comments. We are also grateful to Sharon B. Melnick and
Anthony L. Sims for their expert technical assistance.
Footnotes
Presented in part at the North American Society of Pacing and Electrophysiology Young Investigators Award Competition at the 18th Annual Scientific Sessions, New Orleans, La, May 7–10, 1997.
Received August 7, 1997;
revision received November 12, 1997;
accepted November 23, 1997.
References
© 1998 American Heart Association, Inc.
Basic Science reports
Myocardial Discontinuities
A Substrate for Producing Virtual Electrodes That Directly Excite the Myocardium by Shocks
Key Words: defibrillation • excitation • mapping • electrical stimulation
). This transmembrane current
should alter the transmembrane potential near the discontinuity,
causing depolarization on one side and
hyperpolarization on the other. Thus, secondary
sources can be created with a virtual cathode in the depolarized region
and a virtual anode in the hyperpolarized region.
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Figure 1. Effect of an intracellular discontinuity on
current flow. Top, As current (indicated by arrows) crosses from
extracellular compartment to intracellular, a change in transmembrane
potential is observed. Near an extracellular anode, transmembrane
potential (Vm) is hyperpolarized as shown below. Near
cathode, current exits intracellular compartment and depolarizes
transmembrane potential. Bottom, When an intracellular discontinuity is
present (hatched region), current is forced from intracellular to
extracellular compartment and reenters cell on other side of
discontinuity. On side of discontinuity closer to anode, a virtual
cathode is formed as current leaves cell while a virtual anode is
formed on opposite side of discontinuity as current reenters
cell. ). The interelectrode distance
was 2 mm, resulting in a mapped area of 18.4
cm2 . The return electrode was sutured to the
aortic root. A silver wire 4 cm long was sutured along one side of the
plaque (Figure 2) for application of a series of stimuli, called
S1, S2, and
S3. A titanium mesh electrode sutured on the left
ventricle was used as the return electrode for stimulation.
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Figure 2. Mapped area and incision on right ventricle. Each
small circle represents a recording site on mapping
plaque. Location of electrode 254 is indicated. 
). The
incision was sutured closed, and venous inflow was reinstituted. After
the animal stabilized, as determined from ECG, blood-pressure, and
blood-gas measurements, the plaque was resutured to the same location,
and the stimulation protocol as described above was then repeated. In
addition to the six experimental animals, two sham-treated animals were
also studied. These animals underwent the same protocol as described
above minus the creation of the incision.
Simultaneous recordings were made from
the plaque with a 528-channel mapping system8
with AC-coupled amplifiers with a 0.5-Hz high-pass filter and a 500-Hz
low-pass filter. During the S2 stimulus, the
attenuators were switched on, amplifiers were DC-coupled, and the gain
of each channel was decreased. The signals were digitized at 2000
samples per second per channel and stored on a Sun workstation (Sun
Microsystems Inc) for analysis during and after the
experiment.
The direction of wave fronts and the presence of collision
or block were observed on a computer screen showing animated maps of
the first derivative of the electrograms (dV/dt)9
determined by a parabola fitted to five data
points.10 Electrodes were displayed as
recording an activation when dV/dt was more negative than -0.5
V/s.11 In some cases, activation times were
manually assigned to the fastest downslope12 of
the electrograms to construct isochronal maps by use of discrete
smooth interpolation.13 Electrodes with signals
that were saturated or too noisy to allow identification of activations
were not analyzed. ). The time interval from the beginning of the
S2 stimulus at the minimum strength required to
directly activate tissue adjacent to the incision until the
activation time at electrode 254 was also determined. These times were
recorded both before and after the incision was created. Activation
after the S3 stimulus was examined to determine
whether the large S2 stimulus altered the
activation sequence in response to a 25-mA stimulus. To assess the
presence of injury currents as a result of the incision, ST segments
were measured in all six animals at electrode 254 and compared at three
times: the beginning of the study, immediately after the incision, and
the end of the study. 
.05 was considered significant.
Before Incision Formation
Before the incision, activation after cathodal
S1 stimuli originated near the stimulating
electrode and propagated across the recorded area (Figures 3A and 4A).
Activation times for the S3 stimuli were similar
to those for the S1 stimuli. The isochronal
activation contours for five of the six animals were approximately
linear and parallel to the stimulating electrode.
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Figure 3. Isochronal activation maps after cathodal
stimuli for one animal. Isochrones are drawn at 5-ms intervals
timed from onset of S1 or S2 stimulus. Arrows
represent direction of activation. Darkened regions
represent areas directly activated by stimulus. Black
vertical bars represent approximate location of transmural
incision. A, S1 stimulus delivered before incision; B,
75-mA S2 stimulus delivered before incision; C, 250-mA
S2 stimulus delivered before incision; D, S1
stimulus delivered after incision; E, 75-mA S2 stimulus
delivered after incision; F, orientation of long axis of myocardial
fibers. *Most proximal electrode in row 6, from which
recordings are shown in Figure 4 .
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Figure 4. Electrograms recorded from row 6 of
electrodes during activation sequences in Figure 3 . Electrode most
proximal to stimulating electrode is at top and most distal electrode
of row is at bottom of each panel. Vertical daggers represent
activation times; arrows, direction of propagation. Each electrogram
tracing begins with 5-ms stimulus. A, S1 stimulus delivered
before incision; B, 75-mA S2 stimulus delivered before
incision; C, 250-mA S2 stimulus delivered before incision;
D, S1 stimulus delivered after incision; E, 75-mA
S2 stimulus delivered after incision. and 4B show an example
for a 75-mA S2 stimulus that was sufficient only
to directly activate a few electrodes in the first two columns
of the plaque. At the border of the directly activated area, a
wave front arose and propagated across the mapped area. As the
S2 stimulus strength was increased, more tissue
was directly activated. For a 250-mA S2
stimulus (Figures 3C and 4C), almost the entire proximal half of the
plaque was directly activated. In Figure 4C, the top seven
traces appear to be directly activated by the
S2 stimulus, which corresponds to the direct
activation of the first seven columns of electrodes in this region
shown in Figure 3C. Eventually, the S2 stimulus
strength was increased enough (400 to 600 mA, Table 1) to directly activate all
columns of the mapped region.
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Table 1. Minimum Current Required to Activate All
Columns of the Mapped Area, mA
For cathodal S1 stimuli after the incision,
wave fronts propagated away from the stimulating electrode, blocked
near the proximal border of the incision, and wrapped around the ends
of the incision to collide on the distal side of the incision (Figures 3D and 4D). The activation patterns after S3
stimuli were similar to those after S1
stimuli. and 4E). Activations originating on the distal side of the
incision propagated distally off the mapped region. The minimum
S2 strength required to directly activate
areas adjacent to the incision averaged 104±37 mA (Table 2). This strength differs significantly
from the strength required to directly activate the same tissue
before the incision (229±49 mA). The area directly activated
by a 75-mA S2 stimulus before the incision
(Figure 3B) was smaller than that directly activated after the
incision (Figure 3E). Before the incision was made, an
S2 strength of 250 mA was necessary to directly
activate the tissue at the site of the incision (Figure 3C).
The S2 strength required to activate all
of the mapped region after the incision was also significantly
different from that required before the incision (Table 1).
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Table 2. Minimum Current Required to Activate Area
Adjacent to Transmural Incision, mA
The time interval from the S1 stimulus to
activation at electrode 254 was significantly shorter before the
incision than after (Table 3),
consistent with the incision's creating a barrier that
increased the conduction path from the stimulus site to the electrode
(Figure 3A versus 3D). At the minimum S2 stimulus
strength that caused activations adjacent to the incision (104±37 mA),
the time from the S2 stimulus to activation at
electrode 254 was longer than for this same S2
stimulus strength before the incision (Table 4), consistent with direct
activation at the incision's creating a shorter conduction path
(Figure 3B versus 3E).
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Table 3. Interval From Beginning of S1 Stimulus
to Activation at Electrode 254, ms
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Table 4. Interval From Beginning of S2 Stimulus
to Activation at Electrode 254, ms
Before Incision Formation
As for cathodal S1 stimuli, activation after
anodal S1 stimuli originated from the proximal
portion of the plaque (Figures 5A and 6A). For anodal pulses, however, the line
of propagation was approximately parallel with the stimulation wire in
only two animals, although this was observed in five animals with
cathodal S1 pulses. The S3
stimulus activation patterns were again similar to those of
S1 stimuli. As for cathodal
S2 stimuli, increasing anodal
S2 strength increased the area of tissue directly
activated (Figures 5B and 6B). The average anodal
S2 stimulus strength required to activate
all columns of the mapped region was 517±75 mA (Table 1).
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Figure 5. Isochronal activation maps after anodal
stimuli for one animal. Isochrones are drawn at 5-ms intervals
timed from onset of S1 or S2 stimulus. Arrows
represent direction of activation. Darkened regions
represent areas directly activated. Black vertical
lines represent approximate location of transmural incision. A,
S1 stimulus delivered before incision; B, 75-mA
S2 stimulus delivered before incision; C, S1
stimulus delivered after incision; D, 75-mA S2 stimulus
delivered after incision; E, 250-mA stimulus delivered after incision;
F, orientation of long axis of myocardial fibers.
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Figure 6. Electrograms recorded from row 15 of
electrodes during activation sequences in Figure 5 . Electrode most
proximal to stimulating electrode is at top and most distal electrode
is at bottom of each panel. Vertical daggers represent
activation times. Arrows represent direction of propagation.
Each electrogram tracing begins with 5-ms stimulus. A, S1
stimulus delivered before incision; B, 75-mA S2 stimulus
delivered before incision; C, S1 stimulus delivered after
incision; D, 75-mA S2 stimulus delivered after incision; E,
250-mA S2 stimulus delivered after incision.
After the incision, wave fronts originated near the anodal
S1 stimulation site, propagated until they
blocked at the incision, and then wrapped around the ends of the
incision to propagate and collide on the distal side of the incision
(Figures 5C and 6C), similar to the activation sequence after cathodal
S1 stimulation. ), areas of direct activation were observed
adjacent to the incision, as with cathodal S2
stimulation. Unlike with cathodal S2 stimuli,
however, activation originated only on the proximal side of the
incision at this anodal S2 strength (Figures 5D and 6D). The wave fronts that arose from the proximal side of the
incision wrapped around to collide on the distal side of the incision.
The anodal S2 strength that directly
activated the area proximal to the incision was significantly
smaller than that required to activate the same tissue before
the incision was formed (Table 2). When the S2
stimulus strength increased to 163±65 mA (Table 2), activation began
to originate directly from the tissue on the distal side of the
incision. This S2 stimulus strength was so large
that it directly activated all of the tissue proximal to the
incision (Figures 5E and 6E).
As with the cathodal S1 stimuli, the
time from anodal S1 stimulation to activation at
electrode 254 was shorter before than after the incision (Table 3),
consistent with creation of a conduction barrier by the
incision. For the minimum anodal S2 strength that
caused direct activation at the incision (50 mA), no significant
difference was observed for activation times at electrode 254 before
and after the incision (Table 4), consistent with the
observation that, at this minimum S2 stimulus
strength, direct activation occurred only on the proximal side of the
incision.
Before and after the incision, anodal stimuli directly
activated tissue just proximal to the incision site at a
significantly lower S2 strength than did cathodal
stimuli (Table 2). No significant differences were observed for the two
polarities in the stimulus strength required to activate the
entire mapped region both before and after the incision (Table 1).
Activation times at electrode 254 (Table 3) were significantly shorter
for anodal than cathodal S1 stimuli before the
incision, whereas no significant differences for the two polarities
were observed after the incision. Conversely, the activation times at
electrode 254 were significantly shorter for cathodal than anodal
S2 stimuli after but not before the incision
(Table 4).
Fiber orientation for five animals ranged from 48° to 103°
with respect to the parallel stimulation wire and incision (Figures 3F and 5F). For the sixth animal, the average fiber angle was 8°, nearly
parallel to the stimulation wire and incision. The five hearts with a
similar fiber orientation ranged in weight from 155 to 183 g,
whereas the sixth heart had a large interatrial defect and weighed
344 g. ), this finding was verified by quantification of the changes
in activation time at a recording electrode near the incision
(electrode 254, Figure 2). Before the incision, the time for activation
to reach this electrode after a cathodal S2
stimulus of 104±37 mA was 23±7 ms, whereas after the incision, this
electrode recorded activation significantly earlier, 8±4 ms, in
response to the same S2 stimulus (Table 4). ).
As current crosses the cell membrane, it alters the transmembrane
potential. In this way, the incision serves as a boundary to current
flow, causing depolarization on one side of the incision and
hyperpolarization on the
other.6 7 ). Elevation of the resting membrane
potential to just below the threshold for activation of the sodium
channels can cause the electrical stimulus to activate the
tissue in this region even in the absence of an incision (Figure 7C).
However, the alteration to cause this effect is extreme (ie, 17
mmol/L extracellular potassium concentration) and may not be
present 30 minutes after the incision is created.
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Figure 7. Top, Fiber represents bidomain tissue
structure 10 cm long. Field stimulation is at fiber's ends. Incision
is 2.5 cm from left end. For some simulations,
[K+]e was altered in a 1-cm area around
incision. Bottom, Four panels representing model results
for each scenario described in "Appendix." For each panel, two
times are shown: 5 ms (left) and 10 ms (right) after onset of
stimulation. A, Changes in transmembrane potential (Vm) in
absence of incision and with normal [K+]e; B,
changes in Vm in presence of incision and with normal
[K+]e; C, changes in Vm in
absence of incision but elevated [K+]e; D,
changes in Vm in presence of both incision and elevated
[K+]e. P indicates proximal; D, distal.
Dotted lines represent 0 mV. A and B, Solid line
represents change in Vm at diastolic
threshold for stimulation (DTS), and dashed line represents
change in Vm at 96% DTS. C and D, Lines represent
changes in Vm at different potassium concentrations with a
96% DTS stimulus. and 7).
Activation propagated away from both sides of the incision, not just
the side that was thought to be depolarized. For a cathodal
S2 stimulus, activation propagated away from both
sides of the incision with the smallest S2
stimulus strength that caused activation to originate near the incision
(Figure 3E). For an anodal S2 stimulus,
activation first appeared only at the proximal side of the incision as
the S2 strength was increased (Figure 5D). As the
anodal stimulus strength was increased still further, activation fronts
also originated from the distal side of the incision (Figure 5E). ). The interruption had a smaller but still significant
effect on direct activation by the shock 1 to 2 cm distal to the
incision; the mean shock strength needed to directly activate
tissue beneath all columns of the plaque was reduced 34% by the
incision (Table 1).
View this table:
[in a new window]
Table 5. Modeling Parameters
where
(1) 
i is intracellular conductivity,
e is interstitial conductivity,
i is intracellular potential,
e is interstitial potential, and
Im is transmem-brane current density.
Im was further specified in terms of
membrane sources:
where Cm is specific membrane capacitance,
Vm=(
(2) i-e)
is transmembrane potential, Iion is ionic
current source density, and Am is ratio of
membrane surface to intracellular volume. Substituting
i=Vm+e
into Equation 1, Equation 2 is rewritten as
where
Gix=(gil/Am)
is a coupling coefficient expressed in terms of the specific
intracellular conductivity along the fiber axis
(gil) and
Giy=(git/Am)
is expressed in terms of the specific intracellular conductivity across
the fiber axis (git). In solving Equation 3
(3) , we
assumed sealed end boundary conditions at the edges of the tissue and
the interstitium. The model was 10 cm long and 50 µm wide,
resulting in 2002 nodes (Table 5). We
determined the interstitial potential distributions from
the transmembrane potential distribution using a rewritten form of
Equation 2,
where
Gex=(gel/Am)
is a coupling coefficient expressed in terms of the specific
interstitial conductivity along the fiber axis
(gel) and
Gey=(get/Am)
is expressed in terms of the specific interstitial
conductivity across the fiber axis (get).
(4) were integrated
numerically in time by an analytic method with Luo-Rudy membrane
equations at all tissue nodes.29 30 Equations 3, and 4 were discretized in space with a five-point finite-difference
stencil. Discretization in time used a semi-implicit averaging scheme
analogous to the Crank-Nicholson method in one space dimension. Because
the matrix for the linear system was sparse, efficient solutions for
Vm were achieved with a preconditioned conjugate
gradient scheme (DITSOL_PCG from the Digital Equipment Corp Digital
Extended Math Library, dxml). A 5-ms monophasic "shock" was applied
by modification of the difference equations for nodes on the left and
right edges of the model to fix the interstitial potentials
on each edge. Calculations were then continued for 5 ms after the
shock. The resulting sparse linear system for
e was solved with the same preconditioned
conjugate gradient method as in solutions for
Vm.
At the end of the stimulus, depolarization occurred at the
cathode at DTS and 0.96xDTS (Figure 7A). At 10 ms, an action potential
arose from the site of depolarization for the DTS stimulus and
propagated toward the anode (Figure 7, right). Because the 0.96xDTS
stimulus did not reach threshold, no action potential occurred.
With the incision, an area of depolarization occurred with both
stimulus strengths at the cathode (Figure 7A). For both stimulus
strengths, areas of hyperpolarization and
depolarization occurred adjacent to the proximal and distal sides of
the incision, respectively (Figure 7B, left). At 10 ms after the
stimulus (Figure 7B, right), a depolarization wave front arose at the
stimulation site for the DTS stimulus. A wave front also arose from the
distal side of the incision where depolarization was created by the
stimulus. No wave front arose at either site after the 0.96xDTS
stimulus.
In the absence of an incision, when extracellular
potassium was increased to 16 and 17 mmol/L, resting membrane
potential was elevated to -55.1 and -53.6 mV, respectively (Figure 7C, left). At 10 ms after the stimulus, the 0.96xDTS stimulus elicited
an action potential at a potassium concentration of 17 mmol/L but
not 16 mmol/L. This action potential propagated in both directions
away from the site of elevated potassium but not from the cathodal end
of the tissue, because the stimulus was slightly less than the DTS
(Figure 7C, right).
With the incision present, 5 ms after the onset of the
0.96xDTS stimulus, an area of depolarization occurred at the cathode
for both concentrations of potassium (Figure 7B). At the incision,
hyperpolarization and depolarization were observed
on the proximal and distal sides of the incision, respectively (Figure 7D, left). The degree of polarization was slightly larger for 7
mmol/L [K+]e (RMP= -75.8
mV) than for 6 mmol/L
[K+]e (RMP= -79.6 mV).
At 10 ms after the onset of the 0.96xDTS stimulus, a wave front arose
on the distal side of the incision for 7 mmol/L but not 6
mmol/L potassium concentration (Figure 7D, right).
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