© 1995 American Heart Association, Inc.
Articles |
Effects of Pacing on Stationary Reentrant Activity
Theoretical and Experimental Study
From the Department of Pharmacology, State University of New York Health Science Center at Syracuse.
Correspondence to Dr José Jalife, Department of Pharmacology, SUNY Health Science Center, 766 Irving Ave, Syracuse, NY 13210.
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Abstract It is well known that electrical pacing may either terminate or change the rate and/or ECG appearance of reentrant ventricular tachycardia. However, the dynamics of interaction of reentrant waves with waves initiated by external pacing are poorly understood. Prevailing concepts are based on simplistic models in which propagation occurs in one-dimensional rings of cardiac tissue. Since reentrant activation in the ventricles occurs in two or three dimensions, such concepts might be insufficient to explain the mechanisms of pacing-induced effects. We used numerical and biological models of cardiac excitation to explore the phenomena, which may take place as a result of electrical pacing during functionally determined reentry. Computer simulations of a two-dimensional array of electrically coupled FitzHugh-Nagumo cells were used to predict the response patterns expected from thin slices of sheep ventricular epicardial muscle, in which self-sustaining reentrant activity in the form of spiral waves was consistently initiated by premature stimulation and monitored by means of video mapping techniques. The results show that depending on their timing and shape, externally induced waves may collide with the self-sustaining spiral and result in one of three possible outcomes: (1) direct annihilation of the spiral, (2) multiplication of the spiral, or (3) shift of the spiral center (ie, core). Multiplication and shift of the spiral core were attended by changes in rate and morphology of the arrhythmia as seen by "pseudo-ECGs." Furthermore, delayed termination (ie, termination of the activity one to three cycles after the stimulus) occurred after both multiplication and shift of the spiral center. Both numerical predictions and experimental results support the hypothesis that whether a pacing stimulus will terminate a reentrant arrhythmia or modify its ECG appearance depends on whether the interactions between the externally induced wave and the spiral wave result in the de novo formation of one or more "wavebreaks." The final outcome depends on the stimulus parameters (ie, position and size of the electrodes and timing of the stimulus) as well as on the position of the newly formed wavebreak(s) in relation to that of the original wave.
Key Words: ventricular tachycardia • ventricular pacing • reentrant activity • spiral waves
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Electrical pacing is currently used as a diagnostic tool to determine the mechanism of ventricular tachycardia1 2 3 and as a method for prevention and termination of the arrhythmia.4 5 6 7 8 9 10 11 12 Although electrical stimulation may often terminate reentrant ventricular tachycardia, complications such as changes in the frequency and/or morphology of the tachycardia and induction of fibrillation have been reported previously.7 11 13 Mapping studies performed in a variety of animal models during functionally determined reentry have shown that external stimulation may result in (1) resetting of the activity with no changes, or only minor changes, in the activity; (2) changes in the shape and/or position of the rotation center or line of block; (3) changes in the "exit" pathway or in the direction of rotation; or (4) termination of the activity.14 15 16 17 18 To date, the mechanisms that have been proposed to explain the effects of pacing on reentrant arrhythmias have been based on the concept of one-dimensional reentry, in which activation may occur orthodromically or antidromically along preconceived paths in either one or two (figure-eight) hypothetical rings of cardiac tissue.1 2 3 19 Yet reentrant ventricular tachycardia is probably the result of wave propagation in two- or three-dimensional myocardium.20 In the present study, we have used concepts derived from the theory of wave propagation in excitable media21 22 23 24 to analyze the effects of pacing on functionally determined vortexlike (spiral-wave) reentrant excitation. Computer simulations carried out in a simple model of a generic excitable medium were used to predict the possible outcomes of the interaction between self-sustaining spiral waves and externally induced waves. Small pieces of sheep ventricular epicardial muscle undergoing self-sustaining spiral-wave activity were used to test such predictions and the hypothesis that termination of spiral waves by electrical pacing is mediated by the formation of a new wavebreak whose front collides with and annihilates the original vortex. In addition, the possible mechanisms underlying pacing-induced changes in the ECG appearance and rate of reentrant activity were studied, as were the effects of changes in the stimulation parameters.
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Materials and Methods |
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Mathematical Model
The computer model is similar to that used in a previous study.25 Briefly, a two-dimensional homogeneous and, unless otherwise indicated, isotropic matrix of 16x16 electrically coupled cells was devised in which the response of each cell depended on two variables, U for transmembrane potential and V for total slow current, according to the following formulation:
 | (1) |
 | (2) |
describes the dynamics of an electrical potential on
the membrane capacitance (C) due to transmembrane current
[F(U)-V], external current
(Iex), and current through intercellular spaces with
junctional conductance (G). Equation 2 describes the dynamics of slow
ionic currents where 
is the time constant. The condition
U/n=0, where n is the normal to the boundary,
("impermeability" condition) was set for the boundary.
We used a piecewise linear function [F(U)] and piecewise constant
function [(U)]. The introduction of the voltage dependence
of allowed us to decrease recovery time and thus to reduce
computational cost by minimizing both the spiral rotation period and
the necessary array size.25 In addition, a smaller array
was used in the present study compared with previous
studies.25 We have observed that the dynamics of spiral
waves were similar to those found with larger arrays.
Parameter values used in calculations were similar to those
described previously.25 To solve the differential
equations numerically we used a simple Euler method of integration. The
diffusion terms were evaluated by finite differences using the
following five-point formula:
 | (3) |
We used parameters derived from experimental results to
scale our model. Accordingly, 
U=1.0 was related to 120 mV, a space
unit of 1 mm (ie, 1 element=1.2 mm), and a time unit of 8 ms (ie, time
step=0.8 ms). As such, the model reproduces all of the main features of
spiral-wave dynamics in isolated cardiac muscle.25
Stimulation Protocol
For all simulations, a stationary counterclockwise-rotating
spiral wave was initiated by using the cross-field stimulation
technique.26 27 28 A conditioning planar wave was initiated
by a stimulus S1 applied to the entire top border of the
array. A premature planar wave stimulus S2 was applied to
the right border (ie, perpendicular to S1) of the array. As
a result, a stationary counterclockwise spiral wave was induced with
its core located near the center of the array (Dcb,
9.6 mm). The size of the core, estimated as the area in which the
amplitude did not reach 50% of the absolute maximum amplitude, was
1 element (1.2x1.2 mm).
After stabilization of the activity (after the third rotation), single stimuli with a current intensity of three times the diastolic threshold (as measured before spiral-wave initiation) were introduced in steps of 8 ms throughout the spiral cycle (170 ms). The stimuli were applied at varying intervals in reference to the previous response. The electrode size and shape, as well as Dce, were varied systematically. The electrode size and shape were given by the number of elements that were directly stimulated. Four different electrodes were used: a "point" electrode consisting of 2x2 elements (2.4x2.4 mm) and a long electrode that occupied the whole height of the array (16 elements, or 19.2 mm) with varying widths (2, 3, and 4 elements, or 2.4, 3.6, and 4.8 mm, respectively). For a given set of simulations, each electrode was placed at four to six locations starting at the right border of the array (Dce, 9.6 mm) and ending at the center of the core (Dce, 0 mm).
Experimental Model
Preparation
Young sheep were anesthetized with sodium pentobarbital
(35 mg/kg IV). The hearts were rapidly removed and placed in warm,
oxygenated Tyrode's solution. Square pieces of epicardial
muscle (20x20x0.5 mm) were cut with a dermatome. Care was taken to
avoid the regions containing the main coronary arteries or any
large bands of connective tissue or fat. Suitable preparations were
immediately transferred to a Plexiglas chamber (40x40x6 mm) and
pinned to the wax floor of the chamber, which was mounted on an
antivibration table. The tissues were continuously superfused (20
mL/min) with Tyrode's solution containing (mmol/L) NaCl 130, KCl 4,
NaHCO3 24, NaH2PO4 1.2,
MgCl2 1, CaCl2 1.8, and glucose 5.6. Solutions
were bubbled with 95% O2/5% CO2 (pH
7.4; temperature, 37±0.5°C).
Optical Recording Techniques
The optical recording techniques have been described in
detail elsewhere.25 Briefly, the preparations were stained
with the voltage-sensitive dye di-4-ANEPPS (Molecular Probes, Inc).
The dye was applied 1 hour after tissue equilibration by continuous
superfusion of a recirculating volume (100 mL) of the
dye-containing Tyrode's solution. The dye was allowed to bind for
2- to 3-minute periods, with subsequent washout with dye-free
solution. To avoid mechanical artifacts induced by the contractions of
the preparations, diacetyl monoxime (15 mmol/L)25 was
added to the superfusate before the beginning of the
optical recordings. The light from a tungsten-halogen lamp
was collimated and made quasimonochromatic by using an interference
filter (520 nm) together with a KG-3 Schott heat filter and a heat
reflecting filter. The light was then reflected 90° from a dichroic
mirror (560 nm) and focused onto the preparation. A 50-mm objective
lens was used to collect the emitted light. The emitted light was
transmitted through the emission filter (645 nm) and projected onto
a CCD solid state video camera (Cohu series 6500). The video images
(typically, 400x200 pixels) were acquired with a 4-megabyte 8-bit A/D
frame grabber board (Epix Inc) in a noninterlace mode with a speed of
60 frames per second (16.66 ms per frame). The board was mounted in a
Zenith 486/33 computer and was used to digitize the analog signal from
the camera and to process the imaged data. To reveal the signal, the
background fluorescence was subtracted from each frame.
Low-pass spatial filtering was applied to improve the visualization
of signals. Individual frames were convolved with a cone-shaped
kernel. Although the spatial resolution provided by the video camera
was 0.05 mm, the effective spatial resolution after filtering was
0.5 mm. No temporal averaging was used. A red-green-blue
(RGB) color monitor (model PVM 13420, Sony) was used to display the
images. To facilitate the description of the figures, all pictures are
presented as white and black images in which white and black
represent all values of membrane potential above and below 30%
maximum depolarization, respectively. Transmembrane potentials were
continuously recorded by using a glass microelectrode filled with 3
mol/L KCl and connected to a WPI dual microprobe system (model 700,
World Precision Instruments).
Stimulation Protocol
Basic and premature stimuli were delivered through one of four
pairs of Ag/AgCl lateral electrodes embedded onto the wax bottom of the
chamber. A pair of Pulsar 6i stimulators (Frederick Haer Co) was used
as the stimulation source. For lateral stimulation, each pair of
electrodes was long enough (20 mm) to stimulate almost the entire
length of one edge of the preparation. The cross-field stimulation
technique was used for the induction of the reentrant
arrhythmia in the experimental preparation.20 21 22 23 24
Briefly, the basic stimulus (S1) was applied through one of
the lateral electrodes (basic cycle length, 300 ms; pulse duration, 5
ms; pulse amplitude, 1.5 to 3 times threshold). Premature stimulation
(S2) was subsequently applied perpendicularly through a
different lateral electrode (S2 duration, 5 to 10 ms;
intensity, two to five times threshold). The presence of stationary
spiral-wave activity was confirmed by obtaining two video
recordings of 1.5 to 3.5 s in duration during the first 5
minutes after the onset of the activity. In addition, the stability of
the activity was continuously monitored by means of the intracellular
electrode. Once stationary spiral-wave activity was established,
one of the pairs of long electrodes was used to deliver single stimuli
(10 ms in duration and three times diastolic threshold, as
measured before spiral-wave initiation) at varying phases of the
rotation period. Unfortunately, because of the limitations of the
experimental design (see "Discussion"), it was not possible to
carry out in any given episode a systematic analysis of the
effects of changing variables such as timing, electrode size, or
position on the spiral-wave activity. Thus, we opted for providing
qualitative rather than quantitative tests to our model
predictions.
Definitions
Wavebreak
According to the theory of nonlinear wave propagation in
excitable media,23 a wavebreak is different from a planar
wave or a circular wave in that the wave front is discontinuous so that
at a given point in space, there is a contact between the wave front
and its own repolarizing tail. In general, a pronounced curvature that
promotes slow conduction is developed at the broken end of the wave. As
a result, the broken end of the wave tends to rotate, giving rise to a
spiral wave. For the purposes of the present study, the formation
of a new wavebreak is considered analogous to the formation of a new
spiral wave, whether it completes a full rotation or not.
Spiral Wave
A spiral wave is a rotating wavebreak. The broken end of the
wavebreak (ie, the inner tip of the spiral) rotates by following a
trajectory that defines the center or core of the spiral wave.
Spiral-wave concepts may be used to describe functionally
determined reentry in general, including leading circle, anisotropic
reentry, and figure-eight reentry.
Core
The core is the area circumscribed by the trajectory of the
wavebreak. The transmembrane activity is significantly reduced within
the core. We measure the core as the region in which the maximum
transmembrane voltage change (ie, amplitude) is <30% of the absolute
maximum amplitude recorded in the periphery of the preparation
during spiral-wave activity.28 In each experiment, the
location and size of the core were estimated by analyzing the video
frames after background subtraction. A frame-stack display
technique25 28 allowed us to plot the spatial distribution
of the activity as a function of time and was used off-line to
determine the size and the exact position of the core before, during,
and after the interaction with the externally applied stimuli. Although
in most cases the core shape was irregular, to simplify the
analysis we used the area of the smallest rectangle that
enclosed the core. Three additional variables were measured by
using the frame-stack plot: Dcb, defined as the
distance between the center of the core and the nearest border;
Dce, defined as the distance between the center of
the core and the center of the stimulating electrode; and in cases of a
pair of spirals (ie, figure-eight reentry), Dic,
defined as the distance between the centers of the cores. In cases of
figure-eight reentry, Dcb was measured only for the
core that was closer to one of the boundaries of the preparation.
Simulated ECG
Pseudo-ECGs25 29 were recorded in both
biological and numerical experiments. For the experiments, the ECG was
calculated as follows: (1) Each video frame was divided into two halves
(ie, left and right). (2) At each point in time (ie, one video frame),
the average transmembrane voltage activity (ie, the change in
fluorescence intensity) obtained from all pixels in one half of
the frame was calculated. (3) The same value was calculated from the
opposite half. (4) These two values were then subtracted from each
other according to the following expression: Dx=
El-Er,
where El and Er represent the sum of the pixel values
from the left and right halves of the frame, respectively. The same
procedure was used for computer simulations in which the transmembrane
potential was represented by the variable U.
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Interaction Between Waves: Collision, Fusion, and Wavebreak
According to the theory of nonlinear waves, three major types of phenomena may take place in any given excitable medium as a result of the interaction of two propagating waves: collision, fusion, and wavebreak. Furthermore, such phenomena underlie the dynamic response of functional reentry in two-dimensional sheets of excitable media to external stimulation. As illustrated schematically in Fig 1
, the final result of the interaction between
two waves depends on the shape of the individual waves, as well as on
the region of the wave that is affected by such an interaction (ie, the
wave front or the wave tail). The interaction between two planar wave
fronts propagating toward each other is shown in panels A and B. In
this case, head-on collision (C in panel B) results in mutual
annihilation of the waves. In panels C and D, the interaction between a
planar wave front and a wave front with positive curvature leads to
fusion (F in panel D) at each end of the collision line. The two newly
formed wave fronts have a pronounced negative curvature (ie, the wave
front is concave), which results in faster conduction velocity in the
upward and downward directions. Panels E and F illustrate the kind of
interaction that occurs between two orthogonally propagating waves with
one initiated shortly after the other by the method of cross-field
stimulation.25 28 In panel E, a planar wave front
(S1), initiated by simultaneous stimulation of
the leftmost column of cells, was propagated toward the right border of
the matrix. Note that the wave front of this wave is no longer
present in the array. Shortly thereafter, a second planar wave
(S2) was initiated by simultaneous stimulation
of all the cells in the top row. The S2 wave intersected
the repolarizing tail of S1. As a result, a wavebreak (B in
panel E) took place at the intersection point. The broken wave front
then developed a pronounced curvature, with decreasing conduction
velocities toward the broken end, which forced the wave to rotate
(panel F). Hence, a broken wave front develops into a rotor, which is
the sine qua non condition for the formation of spiral-wave
activity,23 although its persistence as such depends on
the presence (or lack thereof) of other waves, as well as on its
interaction with the borders of the medium. Collision, fusion, and
wavebreaks may also occur during the interaction between
self-sustaining spiral waves and waves initiated by external
stimulation. As predicted by the numerical experiments below, depending
on the initial position of the wavebreaks, the end result of the
stimulation may be termination, multiplication, or shift in the core
position.
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Model Predictions
In all simulations, single self-sustaining counterclockwise
vortices were initiated by cross-field stimulation. After
stabilization (three full rotations) of the spiral, single stimuli were
applied at varying times corresponding to 20 different phases within
the spiral cycle. Stimuli were applied with electrodes of four
different sizes and from four to six different locations (see
"Materials and Methods"). In every case, the initial event was
the formation of a new wavebreak. In some cases, the broken wave
collided with the rotating spiral, resulting in mutual annihilation and
termination of all activity. In other cases, the new wavebreak
developed into a spiral that coexisted with the original spiral, giving
rise to a figure-eight type of reentry. When the formation of the
new wavebreak was accompanied by annihilation of the original spiral,
the final result was observed as a shift in the position of the core.
Finally, in other cases, there was no formation of a new wavebreak, so
that external stimulation was not followed by any apparent change in
the dynamics of the original activity. Thus, the final effect of an
externally applied stimulus on spiral wave activity may be summarized
as follows: (1) termination of the activity, (2) multiplication with
establishment of figure-eight reentry, (3) change in the position
of the core, and (4) no effect. The occurrence of each response
depended on the stimulus timing as well as on the electrode size and
position as illustrated in the pie charts of Fig 2. Note
that although simulations were performed by using all combinations of
electrode sizes and positions, only six representative
examples are shown. Each pie chart represents the spiral cycle.
When a relatively small square electrode was used (upper pie charts),
stimulation was followed by a shift in the core position or no apparent
change in the activity. The closer the stimulating electrode to the
core, the higher the probability for shift to occur. With the larger
electrode (lower pie charts) the probability for shift dramatically
decreased as the distance from the core increased. Also, lack of effect
was more likely to occur when stimuli were applied at larger distances
from the core. In addition, with larger electrodes a time window of
annihilation was observed at all distances. Finally, at the farthest
distance, multiplication of the spiral occurred for stimulation applied
over 25% of the spiral cycle. It is important to note that although
termination of the spiral was observed at all three distances, the
mechanism of termination was different in each case (see below). In the
following sections, we illustrate the underlying mechanisms of each of
the responses described above.
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Termination
A single stimulus applied during spiral-wave activity may
result in termination of the activity. In some cases, the termination
is delayed for one to four rotations, during which there are changes in
the morphology and/or rate of the arrhythmia. In other cases,
termination occurs immediately after the stimulus. In the former cases,
termination is preceded either by multiplication of the spiral or by a
shift in the core position. Fig 3A presents the ECG
obtained from example of delayed termination. As shown by the ECG, a
single stimulus (ST in panel A) led to a change in the morphology and
rate of the tachycardia and, after two complexes,
termination of the activity. Panel B shows the sequence of events that
took place before, during, and after the stimulus. In this and the
following figures, each frame corresponds in time to the letter
indicated under the ECG in panel A. In each snapshot (panel B, frames a
through h), white represents activity, black indicates
repolarized cells, and the arrows indicate the direction of local
propagation. The asterisks indicate the position of the wavebreaks. The
bars above and below frame b indicate the position and width of the
cell matrix that was depolarized directly by the stimulus (ie, size and
position of the stimulating electrode). Frame a shows a
counterclockwise-rotating spiral immediately before the stimulus
was applied. The position of its core (ie, original wavebreak) is
indicated as 1*. Frame b was obtained at the moment of stimulus
delivery near the right border of the array. The "electrode" size
was 3.6x19.2 mm, and Dce was 3.6 mm. The externally
initiated wave front intersected the repolarizing tail of the spiral
wave, giving rise to a new wavebreak (2*), which developed into a new
clockwise-rotating spiral wave (frame d). Despite the fact that
there was fusion of the two wave fronts toward the bottom of the array,
the new spiral coexisted with the original one, thus giving rise to a
figure-eight reentry (frames e through g). However, after one full
cycle, the tips of both spirals collided with each other (frame g),
thus terminating the activity. Indeed, as shown in frames g and h,
head-on collision of the wave fronts led to mutual annihilation in
the upward direction and fusion toward the bottom left corner.
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The simulation shown in Fig 4 is an example of delayed
termination (panel A) preceded by a shift in the core position. The
stimulus was delivered to the center of the spiral (ie,
Dce, 0 mm) by using the same electrode size as in
Fig 3. The timing of the stimulus was different from
that used in Fig 3, as shown by the position of the
spiral immediately before the stimulus (panel A). Under these
conditions, the upper part of the externally induced wave intersected
the repolarizing tail of the spiral wave at two points, giving rise to
the formation of two new wavebreaks (2* and 3* in frame b). The bottom
part collided with the wave front of the spiral (arrows). Soon after
its formation, wavebreak 2* collided with wavebreak 1*, leading to
mutual annihilation. Wavebreak 3*, on the other hand, succeeded in
developing into a counterclockwise-rotating spiral (frames d
through g) similar to the original one but at a different position.
However, because of the short distance between 3* and the upper border
of the array, the activity stopped after one full rotation (frame
h).
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Fig 5 shows an example of termination of the
spiral-wave activity immediately after the stimulation (panel A).
The test stimulus parameters were similar to those used in
Fig 3, but Dce was 2.4 mm, and the stimulus
was delivered at an earlier phase within the rotation period. As a
result, a new wavebreak 2* was created (frame b), which rotated in the
opposite direction of 1*. Because 2* was in proximity to 1*, a
collision occurred that terminated the activity immediately (frames c
through h). This simulation demonstrates that even in the case in which
termination occurs almost immediately after the application of the test
stimulus, the process is mediated by the formation of a new wavebreak
(2*).
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As shown in Fig 2, termination was observed only when
large electrodes were used. Although the length of the time window
during which termination occurred was similar at various stimulation
sites, the mechanism underlying termination varied with the stimulation
site. Thus, termination was preceded by core shift at Dce=0
and by multiplication at Dce=7.2 and occurred immediately
after the stimulus at Dce=3.6.
Multiplication
Fig 6 shows an example in which the test stimulus
failed to interrupt the arrhythmia. Instead, the stimulus was
followed by changes in rate and morphology of the
tachycardia. In panel A, a stimulus (ST) applied at the end
of the third QRS complex led to permanent abbreviation of the cycle
length by 6%. The underlying mechanism of such changes is
illustrated in panel B. The stimulus parameters were as
follows: electrode size, 3.6x19.2 mm; Dce, 3.6 mm. Frame a
shows the counterclockwise-rotating spiral and the position of its
core (1*). Frame b, obtained at the moment of stimulation, shows a
wavebreak formation (2*) at the intersection of the new wave front with
the repolarizing tail of the spiral. Thus, a new clockwise-rotating
spiral emerged (note that 2* is relatively far from 1* in contrast to
the case shown above in Fig 3). In frame c, the
collision of the center of the new wave front with the spiral wave
front resulted in fusion. However, collision did not prevent the wave
from rotating around both cores. The final result was a stable pattern
of figure-eight reentry (frames d through h). Note that the
interaction between counterrotating spirals resulted in a decrease in
the cycle length. As shown in Fig 2, single stimuli led
to brief time windows of multiplication only when large electrodes were
used and the stimuli were applied relatively far from the core. In
fact, multiplication was never observed at Dce of
<3.6 mm.
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Shift of the Core Position
The model predicts that a shift in the position of the spiral core
may result in termination of the activity when the core is shifted to a
site near one of the boundaries of the medium (Fig 4).
The model also predicts that when the newly formed wavebreak is distant
from the boundaries, the result should be a change in the rate and ECG
morphology of the rhythm. The ECG of Fig 7A demonstrates
that in this case the test stimulus leads to a permanent abbreviation
of the cycle length of 6% and to a change in the morphology of the
arrhythmia. The main difference between the present example
and that shown in Fig 4 is that because of an early
stimulus, wavebreak 3* occurred at a larger distance from the upper
border of the array. Consequently, the newly formed spiral had
sufficient room all around its core to continue its rotation, which
enabled it to become stationary at a faster rate and with a new
morphology in the pseudo-ECG. The decrease in the rotation period was
secondary to an increased interaction between the core and the
boundary, which in turn determined the acceleration of the activity
(see "Discussion"). Shift of the core position was observed with
all electrode sites and was most prominent when the stimulus was
applied at relatively short distances from the core (Fig 2).
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Ineffective Stimulus
An example in which the spiral-wave activity remained
unperturbed after stimulation is presented in Fig 8. The stimulation parameters were the same
as those used in Fig 7, except for the fact that in Fig 8 the test stimulus was applied at a later phase in the
spiral period. As shown by the ECG in panel A of Fig 8,
the rate and the morphology of the QRS remained unchanged after the
stimulus (ST). In panel B, the stimulus (frame b) activated the
region just behind the tip of the spiral. The intersection between the
spiral wave and the externally induced wave occurred only at the spiral
wave front. Accordingly, in this case there was no formation of new
wavebreaks. In addition, the position of the spiral core (1*) remained
unchanged (frames e through h). As shown in Fig 2, the
likelihood of this type of response should increase with the
Dec and should not be greatly affected by the size of the
stimulating electrode.
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Experimental Results
Acceleration, Deceleration, and Termination
The numerical predictions were tested in 17 spiral-wave
episodes obtained in 10 thin sheets of sheep epicardial muscle.
Termination of the activity by a single stimulus was demonstrated in 7
episodes (Table). Termination was preceded by
multiplication in 1 case (episode 2) and by shift of the core position
in 3 cases (episodes 13 to 15) and occurred immediately after the
stimulus in three other cases (episodes 3 to 5). In the other 10
episodes, external stimuli resulted in acceleration (episodes 1 and 6
to 9), deceleration (episodes 10 to 12), or no effect (episodes 16 and
17).
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Fig 9 illustrates the series of events that led first to
acceleration and then to termination of the spiral-wave activity
following the introduction of a single pulse. Panel A shows the
pseudo-ECG obtained during that episode. The first three complexes on
the left correspond to the last three rotations of a stationary spiral,
which had been maintained for >10 minutes. A single stimulus (ST in
panel A) applied at the arrow led initially to a change in the QRS
morphology, with abbreviation of the cycle length from 133 to 121 ms
and then to 117 ms and, finally, termination of the activity. The
mechanism of such phenomena was studied frame by frame in the video
images presented in panel B. The arrows indicate the direction
of propagation. Before stimulation (time, 0 ms), the spiral wave
rotated in a counterclockwise manner. At 16 ms, a planar wave was
initiated from the right border of the preparation at Dce
of 12 mm. The externally induced wave collided with the repolarizing
tail of the spiral, thus creating a new wavebreak, which became
apparent a few milliseconds later (time, 32 ms) as a
clockwise-rotating spiral. Because both spirals coexisted, a
figure-eight–type reentry was established. Both spirals
underwent two complete rotations (from 32 to 224 ms). However, the core
of the new spiral was not stable, such that Dic decreased
from 5 to 4 mm during the first and second rotations
to <2 mm at 224 ms. Finally, the tips of the spirals collided with
each other and fused into a single wave front (240 to 304 ms), which
propagated toward the lower left corner of the preparation, and then
all activity stopped. Thus, in this example, delayed termination was
mediated by the initiation of a new counterrotating spiral. Yet, a
progressive reduction in Dic resulted in collision that was
followed by mutual annihilation. Note that figure-eight reentry
resulted in transient abbreviation of the rotation cycle. The sequence
of events observed in these experiments was accurately predicted by our
computer simulations (see Fig 3).
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In three cases, termination of the spiral occurred immediately after
the stimulus. In those cases, we failed to identify the formation of
any new spiral-wave activity. However, our computer simulations
(see above) predicted that in cases of immediate termination a new
wavebreak is still formed but collides with the original spiral and
disappears before a full rotation is completed. Fig 10
shows one example in which the application of a single stimulus
resulted in immediate termination of the activity (see the ECG in panel
A). Panel B shows a series of video frames obtained during the same
episode. A counterclockwise-rotating spiral wave was observed
before stimulation (time, 0 ms). A stimulus was applied to the right
border of the preparation (time, 64 ms). The upper part of the new wave
front encountered the refractory tail of the spiral wave, which
resulted in the formation of a new wavebreak. Because of the short
distance (<3 mm) between the new wavebreak and the spiral core (time,
80 ms), there was a collision between the two waves, which led to the
termination of the rotating activity (time, 160 ms). A similar
situation was observed in the other two cases.
|
Multiplication into two stable counterrotating spirals (ie,
figure-eight reentry) after stimulation was observed in one case.
In Fig 11, panel A demonstrates that this effect was
accompanied by a change in the ECG morphology of the
tachycardia following the application of the stimulus. In
addition, the cycle length was abbreviated from 167 to 133 ms. Panel B
shows snapshots obtained before (left) and after (right) stimulation.
On the left, a single counterclockwise-rotating spiral was
observed. The core was 4.5x3 mm in size (Dcb, 3
mm). A single stimulus delivered to the left border
(Dce, 7 mm; not shown) resulted in the formation of
two counterrotating spirals (figure-eight reentry). The sizes of
the new cores were 1.4x2.5 mm (left, counterclockwise) and 4x2.7 mm
(right, clockwise). The main difference between the stimulus effects in
example of Fig 11 and those shown previously in the
experiment shown in Fig 9 is that in the former, a
relative small Dic set the stage for collision of the two
spiral wave tips and subsequent termination of the activity. On the
other hand, in Fig 11, a relatively long
Dic (9.5 mm) allowed for the maintenance of the
reentrant pattern. In fact, the activity was stationary and lasted for
>10 minutes (not shown). Note that as predicted by our computer
simulations, the presence of figure-eight reentry was associated
with acceleration and change in the ECG morphology.
|
In 10 cases, a single stimulus was followed by either acceleration
(n=4), deceleration (n=3), or termination (n=3) of the activity as a
result of a shift in the position of the core (see Table). The
mechanism by which a single stimulus leads to a displacement of the
spiral core has been discussed on the basis of the computer predictions
(see above). In all these cases, the modification of the spiral cycle
was attributed to either a different size of the new core or a
different distance between the new core and the boundaries of the
preparation (Dcb). Fig 12 depicts an
example in which a single stimulus was followed by deceleration of the
activity. Panel A shows the ECG patterns obtained before (left) and
after (right) the application of the stimulus. The cycle length
increased from 108 to 133 ms, and there was a clear change in the
"QRS" morphology. Panel B shows single video frames obtained
before (left) and several seconds after (right) the application of the
stimulus. Before stimulation, the spiral wave rotated in a
counterclockwise manner around a very elongated core (7.3x0.8 mm),
which was close to the right edge of the preparation. Stimulation from
the right border (Dce, 2 mm; not shown) resulted in
a displacement of the core downward and to the left. The distance
between the center of the core and the right border of the preparation
increased from 3.6 to 9.4 mm. Yet the distance between the new core and
the left border remained relatively large. Accordingly, the resulting
change in cycle length in this case can be attributed to a different
Dcb. In addition, the presence of a fixed discontinuity (an
area of slower propagation) in the area of the new core led to a clear
change in the shape and size of the new core, which may have
contributed to the slowing of the activity (panel C). The mechanism
responsible for deceleration following a shift in the core position
could not be determined in two other cases in which the new core was
located out of the limits of the recording area.
|
As shown in the Table, acceleration of the activity following a shift
in the core position was attended by reduction in the core size (n=4)
with reduction in Dcb (n=3) and increase in Dcb
(n=1). In three episodes, the shift in the core position resulted in
termination of the activity following a brief period of instability,
during which the position of the core changed on a beat-to-beat
basis. In all three cases, Dcb was slightly reduced. It is
possible, however, that just before termination, the actual values of
Dcb were much smaller than those indicated in the
Table.
As shown also in the Table, in two cases, single or even multiple
stimuli failed to induce changes in the spiral-wave activity. In
both, rate-dependent block was apparent in the region between the
core and the stimulation source. Accordingly, externally induced waves
failed to reach the area of the core. In one such case, however,
repetitive stimulation led to the formation of a new spiral in the area
between the core and the stimulating electrodes. Such a spiral was
nonstationary, since it disappeared before the interruption of the
stimulation. In either episode, both the rotation period and QRS
morphology of the tachycardia were the same before and
after stimulation despite repetitive pulse application at high
frequency. Thus, in both experimental preparations and computer
simulations there were conditions in which single or repetitive stimuli
were unable to effect any changes in the properties of the stationary
spirals. Yet the reason for the negative results in each case seems to
be unrelated to that in the other (see "Discussion").
Stimulation Parameters: Electrode Size and Location and
Stimulus Timing
As shown in the Table, the effects of externally applied stimuli
on spiral-wave activity depended on the electrode location as well
as on the stimulus timing. This is not surprising, since as previously
indicated, the main factor in determining the ultimate effect of
stimulation is the initial position of the wavebreak with respect to
both the original core and the borders of the medium. The overall
results show that the likelihood for annihilation, multiplication, and
absence of effect increased while the likelihood for shift decreased
with the increase in Dec. Furthermore, the larger the
electrode size, the larger the time window for both annihilation and
multiplication. Unfortunately, we could not carry out a systematic
study of the effects of changes of stimulation parameters
in our experiments (see "Limitations of the Experimental Model"),
which makes it difficult to compare the experimental results with those
obtained from the simulations. However, as shown in the Table, there
are some aspects that seem to be in agreement with the numerical
results. For example, although shift of the core position occurred in
10 cases with a wide variety of Dce, significant
displacement of the core (>10 mm) occurred when Dce was
relatively small (3.8±1.5 mm). On the other hand, Dce was
relatively large in cases of multiplication and direct termination
(7.4±2.4 mm).
|
Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Numerous mapping studies14 15 16 17 18 have shown that in most cases, external stimulation applied during functionally determined reentry may affect the rotating activity, thus indicating the presence of a fully excitable gap. Stimulated waves may indeed terminate the activity or lead to changes in the morphology or rate of the arrhythmia. In some cases, no significant changes were observed after effective resetting or entrainment of the arrhythmia. The mechanisms proposed to explain the interaction between functionally determined reentrant activity and stimulated waves are based on the concept of one-dimensional reentry. In such models, the interruption of reentrant excitation by external stimulation occurs as a result of block of the paced wave in the anterograde direction (ie, interaction with the refractory tail of the reentrant wave) and collision with the oncoming reentrant wave front in the retrograde direction. Regional heterogeneities such as areas of slow conduction within the circuit or nonuniform anisotropic propagation are thought to play a major role in determining the effect of stimulated waves.14 In addition, the presence of more than one region with a sufficiently high anisotropic ratio is thought to be a prerequisite in cases in which stimulated waves resulted in shift of the position of the rotating center.15 In the present study, we have used concepts derived from the theory of nonlinear wave propagation in two-dimensional media20 21 22 23 24 30 31 32 33 34 to test the hypothesis that termination of self-sustaining vortices by externally applied stimuli is mediated by the initiation of a new vortex.24 In addition, depending on the timing of the stimulus as well as on the electrode position and size, the formation of a new spiral may result in either multiplication or shift in the position of the original core. These phenomena may occur even in the absence of areas of slow conduction or high anisotropic ratios. Thus, on the basis of our computer simulations and experimental results, we propose a new mechanism for the interaction between self-sustaining reentrant waves and externally induced waves.
The Concept of Wavebreak
A major contribution of the theory of spiral waves to the
understanding of the mechanisms of reentrant arrhythmias is the
concept of wavebreak.23 25 During the propagation of a
wave initiated by a point source (ie, a circular or elliptical wave) or
by a linear source (ie, a planar wave), the wave front is always
followed by a recovery band of finite dimensions. Such a band
corresponds to the action potential duration. The distance between the
front and its tail of repolarization is the wavelength of excitation.
Obviously, the velocity of propagation of planar and circular waves is
relatively constant at all points along the entire wave front. Under
these conditions, the edge of the wave front and the edge of the wave
tail never meet each other. In contrast, reentrant spiral waves show a
unique phenomenon, whereby wave front and wave tail of the same wave
actually touch each other at a specific point or
wavebreak.23 25 When a wavebreak is formed, propagation of
the wave front abruptly stops at that point while proceeding at
progressively higher velocity as the distance from the wavebreak
increases. Consequently, the wave front develops a convex curvature
that reaches maximum at the wavebreak point. In fact, at this point,
the curvature is so steep that activation of the tissue ahead fails.
Instead, the wave begins to rotate around a small region (ie, the core)
of excitable but unexcited tissue. Thus, the wavebreak acts effectively
as the pivoting point, which forces the wave to rotate around the core
and leads to the formation of a vortex. In other words, a
self-sustained spiral wave may be initiated simply by inducing a
wavebreak.25
As demonstrated in the present study, the concept of wavebreak is important not only for the understanding of spiral-wave initiation but also for the understanding of the effects of externally induced waves on stationary spiral-wave activity. In fact, when the externally initiated wave front intersects the repolarizing tail of the spiral wave, a wavebreak occurs, and a new spiral wave may emerge. The newly formed spiral wave may evolve in one of three different ways, thus determining the response to the stimulus: (1) It may collide head on with the original spiral, which results in mutual annihilation before the new wavebreak completes a full rotation. In this case, the activity would be immediately terminated. (2) It may stabilize and coexist with the original spiral, leading to changes in the rate and morphology of the arrhythmia as a result of figure-eight reentry. In this case, the newly formed wavebreak may become stationary, or the two waves may terminate after a few rotations as a result of mutual annihilation (ie, delayed termination). (3) The new spiral wave may persist as such after the original spiral has been annihilated; this spiral wave will appear as a shift in the core position. In this case, the end result may be either a new stationary arrhythmia with a different rate and/or QRS morphology or termination of the activity if the new core is too close to the boundaries of the excitable medium (ie, delayed termination). Hence, in all types of responses observed here, the initiation of a wavebreak seems to be the basic mechanism whose dynamics determine the final outcome of the perturbation.
Acceleration and Deceleration of the Activity
Mapping studies in the infarcted canine heart have shown
acceleration of functional reentry following stimulated waves as a
result of the occurrence a new arc of block that is shorter than the
original one.15 In those cases, the length of the line of
block is attributed to the anisotropic properties of the tissue.
Acceleration of reentrant activity was also observed in cases of
anatomically determined reentry in which two waves travel around the
same circuit.32 Theoretical studies33 34 35 have
predicted that even in homogeneous and continuous media
when Dcb is less than or equal to twice the core diameter,
the rotation period of the spiral should be abbreviated. The reason for
such an abbreviation is that the border zone is a region of high
resistance that lowers the electrical load acting on the spiral wave
front. Accordingly, in the vicinity of the borders, the wave front
becomes more efficient in activating the cells ahead on its path and
may propagate at a faster speed. In our simulations, the original
spiral was located in the center of the array, such that any shift in
the position of the core led to a decrease in Dcb. Hence,
it was not surprising that shifts in the core position were always
attended by acceleration of the activity. Although shortening in
Dcb may explain the acceleration observed in the
experimental episodes, a different mechanism for acceleration should
also be considered. Indeed, in all experimental cases, the shift of the
core was also attended by changes in the core shape and size. Such
changes are attributed to the presence of small heterogeneities in our
preparations, which may affect propagation. Pertsov et
al25 have shown that spiral waves that are attached to
small inexcitable regions rotate at a slower rate compared with those
in which the core is formed by totally normal tissue. In our
preparations, a shift of the core from a region of uniformly
anisotropic tissue to a region containing such discontinuities led to
an increase in the core size, which may have contributed to the slowing
of the activity (Fig 12). The same line of thought
applies to those cases in which the arrhythmia was accelerated.
Both decrease in Dcb and in core size should be considered
as possible underlying mechanisms.
Our computer simulations indicate that acceleration should also be
expected to occur as a result of multiplication (ie, figure-eight
reentry), especially when Dic is relatively short but
larger than a critical value. One explanation for the acceleration in
these cases is related to that used in the case of interaction with the
borders.33 34 35 In figure-eight reentry, when the
individual wave fronts propagate over the region that lies between the
cores (ie, common pathway), each constitutes an inexcitable barrier for
the other. In this case, fusion of both wave fronts results in the
formation of a new wave front with negative (ie, concave) curvature
(see Fig 1D). Accordingly, propagation over the central common pathway
should be accelerated.
Termination of the Activity
The mechanisms proposed to explain termination of functionally
determined reentry by external stimulation are based on the presence of
an area of slow conduction in the circuit. The stimulated wave would
block retrogradely with the rotating wave and anterogradely
in the region of slow conduction or, in the case of figure-eight
reentry, at the central common pathway.14 18 In the
present study, we present an alternative mechanism in which
termination of spiral-wave activity by external stimulation is
mediated by the formation of a new counterrotating spiral wave. Our
numerical simulations predict that even in the cases in which a new
spiral is formed, termination may fail to occur. According to
theoretical studies, mutual annihilation of two counterrotating spirals
occurs only when Dic is less than a critical distance
(CDic) whose value is approximately twice the core
diameter.33 Two counterrotating spirals are expected to
rotate without interfering with each other when
Dic>CDic. In two of our experiments, single
stimuli applied during spiral-wave activity resulted in
multiplication. In one of them, Dic was 9.5 mm, ie, larger
than twice the diameter of the largest core, and the activity remained
stable for a long period of time as a figure-eight reentry. In the
other case, external stimulation resulted in the formation of two
unstable rotors, which stopped spontaneously after only two rotations.
Dic in this case was only 2 mm, which was smaller than
twice the diameter of any of the cores.
Termination of the activity immediately following the stimulus occurred in three of our experiments. The computer simulations predict that in cases of direct termination, the stimulus should still give rise to a new wavebreak. However, because of the central location of the wavebreak, collision with the original spiral and mutual annihilation occurs before the completion of a full rotation of the new spiral. Recently, a similar mechanism of termination of anatomically determined reentry was described in the context of antiarrhythmic drug effects.36 In that study, a new functional loop, rotating in a direction opposite to that of the circulating wave, was observed as a result of the addition of agents known to slow conduction. Termination resulted from the subsequent head-on collision of both waves.
Finally, in cases in which the new spiral persists after the annihilation of the original spiral (ie, shift of the core position), termination may occur as a result of collision of the new spiral with the boundaries of the medium. According to numerical experiments,34 the critical distance between the core and the border is also approximately twice the diameter of the core.
Absence of Effect
Functionally determined reentry may remain unmodified after
external stimulation in cases in which there is no excitable
gap14 or even after resetting or entrainment of the
activity.16 In the latter case, stimulated waves are
thought to be forced into the reentry circuit by preferential pathways
determined by the anisotropic characteristics of the tissue. An
alternative explanation for the continuation of unchanged reentrant
activity following effective resetting or entrainment is that
stimulated waves must follow the wake of recovery of excitation left by
the rotating activity.15
Our computer simulations predicted that within a given range of stimulation parameters, an externally induced wave may invade the core and result in a new wavebreak near the original core. In those cases, the changes in morphology and rate following stimulation may be negligible. We could not observe this mechanism in our experiments. In two of our experimental episodes, the spiral-wave activity remained unperturbed after external stimulation. In both cases, the occurrence of conduction block in the region between the electrode and the core prevented the external waves from activating the core area. Thus, the position and the course of the original core remained unchanged after stimulation. In another experiment (not included in the present study), the rotating activity remained unchanged after effective entrainment. In this case, however, the core was attached to a small discontinuity (ie, a small branch of a coronary artery), which made the activity "anatomically" determined. Thus, the absence of effects following effective entrainment may be more likely in cases in which the activity is rotating around an anatomic obstacle.
Limitations of the Computer Model
Various types of models have been used to study propagation of
excitation in heart tissue. These range from very simple cellular
automata models21 37 38 to highly complex ionic models
that rely on partial differential equations of the Hodgkin and Huxley
type.39 40 The model we have used in the present study
is based on the FHN equations,25 40 41 which have an
intermediate level of complexity. The FHN model is not an ionic model
in the common sense, since all slow ionic currents are combined into
one variable that is responsible for repolarization and recovery of
excitability. Thus, as such, the model cannot be used to study ionic
mechanisms responsible for the system's behavior but rather to provide
analytic and qualitative representations of that system's
dynamic properties.41 In addition, in the present
study, we have used a very simple version of FHN equations with
piecewise linear approximation of all nonlinear
functions.25 33 In selecting the model
parameters, we have attempted to approximate as much as
possible the electrophysiological
characteristics of the myocardial tissue. However, its
representation of the action potential shape is less accurate
than that provided, for example, by the model of van Capelle and
Durrer.30 Yet our version requires much less computational
resources and at the same time provides reasonable qualitative results.
We adjusted the parameters in our model in such a way as to
obtain the same rotation period/refractory period ratio as observed in
our experiments (Ts/Tr1.4; see
"Results"). Because of the discreteness of the model (the size of
the single element is 0.6 mm), it may not account for all phenomena
associated with anisotropic propagation in cardiac muscle at the
microscopic scale.42 Yet, as confirmed by our previous
studies, the model is sufficient to explain many global features of
spiral-wave reentrant activity, including the shape of the wave
front and, more important, the properties of the core. In fact, the
addition of uniform anisotropy has been shown to modify the shape of
the spiral without significantly altering the dynamics.25
The presence of uniform anisotropy is expected to change our results
only quantitatively in terms of the distance between the stimulating
electrode and core. For instance, a given response to a stimulus
delivered in the longitudinal direction will be observed at a shorter
distance if the same stimulus is delivered in the transverse
direction.
Finally, the model used in the present study is that of a continuous excitable medium, which is obviously not the case for isolated cardiac muscle. Indeed, much emphasis has recently been placed by a number of investigators on the fact that cardiac muscle is a highly discontinuous anisotropic medium.42 This is not only the result of the cell orientation but, more important, the discrete nature of cell-to-cell connections as well as the presence of bands of connective tissue, arteries, and other obstacles acting to interfere with the propagating wave. Perhaps some of the discrepancies encountered between the model predictions and the experimental results in those cases in which the externally produced waves had no effect on the self-sustaining spiral-wave activity emerged as a result of this important limitation of the computer model.
Limitations of the Experimental Model
The main limitation of our experimental study is that although in
any given experiment, several consecutive spiral-wave episodes
could be initiated, the characteristics of the individual spiral wave
could not be exactly reproduced from one episode to the next. Indeed,
although repetitive activity was initiated in all of our experiments,
once a change was induced by the external stimulation, or after
annihilation, it was nearly impossible to initiate a new spiral wave
whose core size and location were identical to those of the previous
episode. Accordingly, we could not study the influence of a given
variable by systematically changing parameters (ie,
electrode size, electrode location, and timing of the stimulus) under
the unaltered initial conditions.
Another limitation relates to the fact that the experiments were carried out in very thin pieces of ventricular epicardial muscle, which were cut in such a way as to confine the propagation of electrical waves to two-dimensional space. It is expected that in both computer and experimental results, the borders of the medium contributed significantly either to change the rate of the activity or to terminate the rotation. Although inexcitable borders such as coronary arteries, bands of connective tissue, or even scar tissue indeed exist in the intact heart, those borders are probably not well represented by the four boundaries of our square numerical model.
Finally, it is important to note that the spiral waves studied here rotated around a center that was composed predominantly of normal excitable tissue.25 28 The reentrant activity that occurs around relatively large areas of depressed conductivity in the damaged myocardium need not exhibit the dynamic behavior observed in the present experiments. Thus, it is premature to draw any conclusions about the applicability of these results to the understanding of arrhythmic behavior in the heart and its control by programmed electrical stimulation.
Conclusions
Simple experimental and mathematical models are valuable tools for
the study of reentrant arrhythmias in a two-dimensional
medium. Our results indicate that vortexlike reentry is a process
susceptible to manipulation with external electrical stimuli. Such
manipulation may lead to dynamic changes of the activity, including
spatial displacement and multiplication, which would be difficult to
conceive if the reentrant activity were restricted to a fixed
one-dimensional ring of tissue. On the basis of our numerical and
experimental results, we propose that the effects of external stimuli
on vortexlike reentry may be the result of the formation of new
vortices and that the size and location of the stimulating electrode,
as well as the timing of the stimulus, play an important role in
determining the final outcome and side effects external pacing.
|
Selected Abbreviations and Acronyms |
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Acknowledgments |
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This study was supported by grants PO1-HL-39707 and RO1-HL-29439 from the National Heart, Lung, and Blood Institute, National Institutes of Health and by grants from Interuniversitair Cardiologisch Instituut Nederland and from De Hart-Long Instituut van het Academisch Ziekenhuis te Utrecht, The Netherlands. Dr Davidenko is an Established Investigator of the American Heart Association.
Received February 22, 1995; accepted August 28, 1995.
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