Effects of Pacing on Stationary Reentrant Activity
Theoretical and Experimental Study
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.
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.
Materials and Methods
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 16×16 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: Equation 1 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 τ 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 [τ(U)]. The introduction of the voltage dependence of τ 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: where Ui,j is the value of U at grid point (i,j). The size of each grid element was hx=hy=h=1.2, and the time step was ht=0.1. Programs were written in Pascal, and analysis was performed on a Zenith 486/33 computer using an EPIX video imaging board (computation time for 10 spiral rotations, 42 s). Video images of potential distribution in space U(x,y) were displayed (white, maximum excitation; black, rest).
We used parameters derived from experimental results to scale our model. Accordingly, ΔU=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
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 (1.2×1.2 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 2×2 elements (2.4×2.4 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).
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 (≈20×20×0.5 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 (40×40×6 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, 400×200 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).
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.
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.
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.
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.
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=ΣEl−ΣEr, where ΣEl and ΣEr 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.
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.
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.
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 3.6×19.2 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.
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).
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*).
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.
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, 3.6×19.2 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.
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⇑).
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.
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).
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⇑).
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 4.5×3 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 1.4×2.5 mm (left, counterclockwise) and 4×2.7 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 (7.3×0.8 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).
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/Tr≈1.4; 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.
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
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.
- © 1995 American Heart Association, Inc.
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