Interaction Between Strong Electrical Stimulation and Reentrant Wavefronts in Canine Ventricular Fibrillation
Abstract This study was designed to test the hypothesis that the effects of a strong electrical stimulus on reentrant wavefronts in ventricular fibrillation (VF) are dependent on the timing of the stimulus. We studied six open-chest dogs by computerized mapping techniques. A plaque electrode array with up to 509 bipolar electrodes was placed on the right ventricular epicardium. The interelectrode distance was 1.6 mm, and the interpolar distance was 0.5 mm. After eight baseline pacing stimuli (S1) with cycle lengths of 300 ms, a strong premature stimulus (S2) (73±10 mA) was given to induce VF. In subsequent episodes, a second strong premature stimulus (S3) was given at progressively longer S2-S3 intervals in 20-ms increments. The results showed that, at baseline, the S2 consistently induced figure-eight reentry and VF. The VF cycle length immediately after the S2 averaged 108±17 ms. The S3 resulted in one of the following responses: (1) termination of reentry and VF; (2) induction of different reentrant wavefronts or a focal pattern of repetitive activation; or (3) persistence of the same figure-eight reentry. The intervals between the S3 and the immediately preceding activation at the site of the S3 (the recovery intervals) were 39±12 ms (range, 20 to 60 ms) and 61±20 ms (range, 30 to 90 ms) for response patterns 1 and 2, respectively. The recovery intervals associated with response pattern 3 were either ≤30 ms (22±8 ms) or ≥80 ms (94±15 ms). The differences among these four intervals were significant (P<.001). We conclude that the effects of strong electrical stimulation on the reentrant wavefronts in VF are dependent on the recovery interval since the previous local activation. A protective zone occurred between 20 and 60 ms, during which time a strong electrical stimulus could terminate reentry and abort VF. This zone was followed by a vulnerable period during which new activation wavefronts could be induced. If a strong electrical stimulus was given shortly after or sufficiently long after the previous local activation, the same figure-eight reentrant pattern continued.
A protective zone is known to be present at the early stage of ventricular fibrillation (VF), during which a critically timed second stimulus (S3) or a train of stimuli can prevent the induction of VF by an earlier stimulus (S2) or by a train of stimuli delivered during the vulnerable period of normal rhythm.1 2 It has been hypothesized that the S3 exerts its protective effects by terminating local reentrant activity induced by the S2.3 On the basis of theoretical considerations, the efficacy of the S3 in terminating reentry is critically dependent on the time of the stimulus.4 5 A stimulus that is too early fails to terminate reentry because of refractoriness, and a stimulus that has been applied too late may result in new wavefronts that recommence (reinitiate) reentry. Because the patterns of activation during VF are complex and variable, it is difficult to deliver a stimulus at a predetermined time in the reentrant pathway and to thus test its effects. One exception is that, at the onset of electrically induced VF, activation patterns may be more predictable. A previous study6 demonstrated that reentry was the mechanism by which an S2 can induce VF. This reentrant pattern forms a figure eight when the line connecting the baseline stimulus (S1) and the S2 is roughly parallel to the myocardial fiber orientation.6 7 Although the efficacy of the S2 in inducing VF is a probability function, if the S2 stimulus strength is increased to 40 mA above the fibrillation threshold, the S2 can induce VF at nearly 100% efficacy.8 Therefore, this model is ideally suited for testing the mechanisms of the protective zone, not only because the path and the cycle length of reentrant excitation are predictable but also because there is a high probability of VF induction by the S2 at baseline. An S3 can be delivered during the reentrant activations at predetermined intervals. Because of the high probability of VF induction by the S2, the efficacy of the S3 in terminating reentry and in protecting the heart from VF can be reliably determined. In the present study, we used this model together with computerized mapping techniques to determine the effects of timed S3 stimulation on reentrant activation induced by the S2. The results were used to test the following hypotheses: (1) that an S3 can result in termination, reinitiation, or no change in reentrant activations and VF and (2) that these effects are dependent on the time at which the stimulus is delivered during the reentrant activation.
Materials and Methods
Recording and Pacing Electrode Array
The first dog was studied with two electrode arrays placed next to each other. The first plaque electrode array consisted of 96 channels, forming 10 columns and 10 rows (14.4×14.4 mm). Each electrode was made of insulated stainless steel wires with a diameter of 0.4 mm. The interelectrode spacing was 1.6 mm, and the interpolar distance was 0.5 mm. The S1 was given at the edge. Both the S2 and the S3 were given at the same site at the center of this electrode array. The upper edge of the electrode array was within 2 cm of the pulmonic valve. The second electrode array also had 96 channels, forming 11 columns and 9 rows (30×24 mm). These electrodes were made of the same stainless steel electrodes but with silver balls 2 mm in diameter soldered to the tip of each wire. The interpolar distance was 1 mm, and the interelectrode distance was 3 mm.
After the data were analyzed for dog 1, we found that the interelectrode distance of the electrodes with the silver ball at the end was too large to record discrete activations during VF. Therefore, the remaining five dogs were studied with an electrode array that was made of the same material and had the same interelectrode and interpolar spacing as the first electrode array used in dog 1. This electrode array consisted of 317 electrodes forming 21 columns and 16 rows when dog 2 was studied. The same electrode array was then expanded to 509 channels, with 21 columns and 25 rows, and this version was used to study the last four dogs. The upper edge of the electrode array was within 2 cm of the pulmonic valve. Therefore, the mapped region included both the right ventricular outflow tract and the right ventricular free wall. Fig 1⇓ shows the electrode location and the patterns of activation after the S1.
Adult mongrel dogs of either sex were studied. The dogs were anesthetized by intravenous administration of 25 to 35 mg/kg of sodium pentobarbital,9 intubated with a cuffed endotracheal tube, and ventilated via a Harvard respirator (Harvard Apparatus). The depth of anesthesia was monitored by eyelid and pedal reflexes. A venous line was inserted through a femoral vein to infuse pentobarbital at a rate of 0.05 mg · kg−1 · min−1 throughout the experiment. Additional doses of pentobarbital were given when needed.
An arterial line was inserted into the femoral artery to continuously monitor blood pressure. Blood was periodically sampled to determine the pH, Po2, Pco2, base excess, and bicarbonate concentrations. Rectal temperature was monitored continuously and maintained at 35°C to 37°C by heating the table with warm circulating water. The chest was opened through a median sternotomy, and the heart was suspended in a pericardial cradle. A plaque electrode array was sutured to the right ventricular epicardium to record activations and to deliver electrical stimuli. To ensure that a figure-eight pattern of reentrant activation was observed after the S2 stimulus, the line connecting the S1 and the S2 was roughly parallel to the myocardial fiber orientation.7
An S1 stimulus at twice bipolar diastolic pacing threshold was given at the right edge of the electrode array (Fig 1⇑). After eight S1 stimuli, an S2 stimulus of 10-mA strength and 10-ms duration was given to scan the T wave. The S1-S2 interval started at 90 ms. If VF was not induced, the S1-S2 interval was increased at 10-ms increments until 240 ms was reached. If VF was not induced, the S2 strength was increased in 5-mA steps until VF was induced. This last S2 strength was used as the conventional VF threshold.
To ensure a high probability of VF induction, the S2 and S3 strengths used in the subsequent study protocol were 40 mA higher than the conventional VF threshold.8 The S1-S2 interval was fixed at the interval that first induced VF. Five consecutive episodes of VF were then induced with this S2 strength and coupling interval to ensure inducibility. An S3 of the same current strength as the S2 but with half the duration (5 ms) was then added to the stimulation protocol with an initial S2-S3 interval of either 15 or 20 ms. The S2-S3 intervals were increased at 20-ms intervals until 500 ms was reached. The S3 was then turned off, and several episodes of VF were induced by the S2 alone to demonstrate that the S2 was still effective in inducing VF at the end of the study. A defibrillation shock was given immediately after 8 seconds of data was acquired by the mapping system. There were 5-minute intervals between each fibrillation-defibrillation episode.
At the end of the study, the tissue was excised and fixed in formalin for at least 48 hours. The upper, lower, right, and left edges were stained with black, green, blue, and yellow dyes, respectively. The tissue was then embedded in paraffin. A section was taken parallel to the epicardium and was stained with hematoxylin and eosin for light-microscopic examination to determine the myocardial fiber orientation.
One or two episodes of baseline VF were analyzed for each dog to document the consistent induction of figure-eight reentry. To determine whether or not the S3 terminated the reentrant wavefronts, we selectively analyzed a consecutive set of five to seven episodes per dog. These episodes were 20 ms apart so as to cover an interval of at least 100 ms. This coverage is necessary because the average cycle length of VF in this model approximates 100 ms.6 The times of activation were determined by computer according to the following algorithm (Fig 2⇓): The maximal dv/dt of the range for data analysis was first determined by the computer. In Fig 2⇓, the range for data analysis included the entire tracing after the end of the S2 artifact. The S2 artifact, which had an artificially large dv/dt, was excluded. The investigators then had the option to choose a threshold dv/dt value (a percentage of the maximal dv/dt) and a threshold interval (in ms). In the example shown in Fig 2⇓, the threshold values were 20% and 50 ms, respectively. The computer selected a time as the time of local activation if the dv/dt at that time exceeded the threshold value and if the interval between that time and the time of previous activation exceeded the threshold interval. Because each channel has a different signal-to-noise ratio, the threshold value could vary from channel to channel at the investigator’s discretion. A threshold interval of roughly 50 ms was usually used as a starting interval, but any interval could be used at the discretion of the investigator. The vertical line in Fig 2⇓ indicates the times of selected activations. The number at the top of each line indicates the interval between that activation and the onset of the S2 stimulation artifact. The unfilled arrows point to the tick marks on the 0-mV baseline. These tick marks were separated by 200 ms.
Because it was unlikely that the computers would be 100% specific and sensitive in selecting activations, as was the case for channel I6 in Fig 2⇑, manual editing was always performed for each activation. If two deflections (double potentials) were observed, both deflections were selected as activations regardless of the duration of this isoelectric interval. Therefore, some activations selected may represent an electrotonic activation rather than a true local activation. The solid arrows in Fig 2⇑ point to the deflections that would be manually selected as activations. A dynamic display of activation patterns was then visualized on a computer screen in which each electrode site was illuminated when an activation was registered.
The advantage of selecting all deflections as activations is that the investigators did not have to apply artificial criteria to reject or accept a deflection as a local activation. The disadvantage is that it is difficult to illustrate the dynamic display with a limited number of still-frame pictures. For purposes of illustration, it was necessary to also construct conventional isochronal activation maps.6 10 The criteria for selecting local activations for conventional isochronal map generation have been reported elsewhere.7 11 Briefly, for the biphasic and the multiphasic wave forms, the maximal slope of the activation complex was selected by the computer to be the time of activation, and only one activation time was assigned to the entire complex if no isoelectric period was present within the complex. If the activation complexes were monophasic with a single maximum or minimum, the time of activation was assigned to be at the peak of the maximal deflection. Only one activation was selected on the channel with multiple activations to represent the time of these multiple complexes. The activation that we selected was the one that was the largest and had the steepest slope among all the neighboring activations. This activation time was then used to match the activations on the other channels, thus generating the isochronal map. For channel I6, shown in Fig 2⇑, the deflections marked by the solid arrow B were selected to match the activations in channel I19 for the isochronal map generation. The deflections marked by arrows A, C, and D were not selected for the purpose of generating isochronal maps. The isochronal maps were then compared with the dynamic display to ensure that the isochronal maps adequately represented the direction of the wavefront propagation shown in the display.
To determine whether or not the effects of the S3 were influenced by the recovery interval preceding the S3, we determined the times of activation recorded by the electrodes near the S2 and the S3 sites. Instead of selecting a single channel to represent the times of activation in that region, we used a group of channels near the S2. The reentrant wavefronts were displayed dynamically on the screen. The time was advanced in 10-ms steps. The site near the S2 and the S3 was deemed activated if more than three channels around the stimulation site were activated within that 10-ms window. The interval between the S3 and the immediately preceding activation at the site of the S3 was defined as the recovery interval for the S3. This recovery interval was an estimate of the status of repolarization of the cells near the S3. A short recovery interval implies that the cells had only a short time to recover from a previous activation and therefore were most likely still refractory at the time of S3 stimulus. On the other hand, a long recovery interval implies that the cells had a long time to recover, allowing S3 to elicit a full response. An intermediate recovery interval implies that the cells were relatively refractory. A strong stimulus given during this time might induce graded responses12 and not full action potentials. These graded responses may prolong the duration of refractoriness and contribute to the induction of new reentrant wavefronts and VF.6 7
All statistical analysis was performed by use of systat.13 Analysis of variance was used to compare the recovery intervals for the S3 associated with different responses: S3 that aborted reentry, S3 that changed patterns of reentry, and S3 that did not change the baseline figure-eight reentrant pattern. A value of P≤.05 was considered significant.
The dogs weighed 23±2 kg. In each dog, the patterns of activation after S1 stimulation (Fig 1⇑) showed no evidence of functional conduction block. Activation after S2 stimulation showed figure-eight reentry leading to the onset of VF (Fig 3⇓). There was juxtaposition of early and late sites in consecutive activations. The ECG at the onset of VF shows that the first two beats were more compatible with ventricular tachycardia, whereas the later parts of the tracing were more compatible with true VF. These findings are compatible with Wiggers’ stages I and II VF,14 respectively. The actual activations recorded by the same episode are shown in Fig 4⇓. The cycle lengths of VF at baseline were 108±17, 122±20, and 102±10 ms for the first, second, and third reentrant cycles, respectively.
A total of 40 episodes were analyzed. Among them, 7 episodes were baseline VF and 6 episodes had S2-S3 intervals that were too short to allow the reentrant wavefront to complete one rotation. In the remaining 27 episodes, the S3 was followed by sinus rhythm in 9 episodes and followed by VF in 18 episodes.
S3 Did Not Terminate VF
Among the 18 episodes in which the S3 was followed by VF, 10 episodes were associated with continuation patterns of figure-eight reentry. Fig 5⇓ shows one example, when the S3 was given 155 ms after the S2. The patterns of activation after the S3 were similar to those before the S3, with persistence of the figure-eight reentry. There was juxtaposition of early and late sites in consecutive activations. Fig 6⇓ shows the actual activations recorded. The recovery interval for the S3 in this example was 37 ms measured at site I8. This short recovery interval implies that the S3 occurred at the early stages of repolarization. Among the 10 episodes with continuation of figure-eight reentry and VF, 5 episodes had short recovery intervals (≤30 ms). The average recovery interval of these 5 episodes was 22±8 ms. In the remaining 5 episodes, the recovery intervals were long (≥80 ms), with an average of 94±15 ms.
When the S3 was given with an S3 recovery interval of 61±20 ms, the patterns of activation changed from a figure-eight reentry into a focal pattern (n=2), single loop of reentry (n=2), or complex activation patterns showing neither a clear focus nor a reentrant wavefront (n=4). In all 8 episodes, VF continued despite the loss of the figure-eight reentrant pattern on the epicardium. Figs 7⇓ and 8⇓ show an example of the S3 changing the pattern of activation from a figure-eight into a focal pattern. Fig 7A⇓ shows a figure-eight pattern with the latest activation occurring roughly 155 ms after the S2 stimulation. Fig 7B⇓ shows the second activation after the S2. The S3 was given at 195 ms, which interrupted the figure-eight reentrant pattern. Fig 7C⇓ shows that the wavefront shown in B continued to activate the remaining parts of the mapped region after the time of the S3. Fig 7D⇓ shows that a new pattern of activation occurred 70 ms after the S3 (arrow). Fig 7E⇓ shows subsequent activation, which differs from the previous activation because a large area was activated by stimulations within 10 ms of each other (red). Although the early site in E and the late site in D (the blue area above the arrow in D) were spatially close to each other, they were temporally quite separated. The earliest site in E occurred 390 ms after the S2, which was 70 ms after the activation wavefront last visited this area. These patterns of activation in Fig 7D⇓ and 7E⇓ are most compatible with epicardial breakthrough from a focus or intramural reentrant pathway inside the myocardium. Fig 8⇓ shows the actual activations recorded. The recovery interval for the S3 as measured at electrode sites I8 and I9 in this episode was ≈80 ms, which was associated with a significant alteration of the figure-eight reentrant pattern.
S3 Terminates Reentry and Protects the Heart From VF
When the S3 was given slightly earlier (n=9), both reentry and VF were abruptly terminated. Figs 9⇓ and 10⇓ show an example. The S2-S3 interval was 155 ms. Fig 9A⇓ shows a figure-eight reentrant pattern induced by an S2. The reentrant excitation was interrupted by the S3 stimulus (Fig 9B⇓). Fig 9C⇓ shows the wavefront propagation after the S3. This wavefront was a continuation of that shown in B. Reentry did not continue, and VF was prevented. Fig 10⇓ shows actual activations recorded from the same episode. Channel M9 shows that reentrant excitation occurred after the S2. However, the S3 terminated reentry between O13 and M13. Among the nine episodes in which an S3 aborted reentry and protected the heart from VF, the recovery interval for the S3 averaged 39±12 ms.
Relation Between Recovery Interval and the Effects of S3
Fig 11⇓ shows the distribution of the recovery intervals. The protective zone was distributed from 20 to 60 ms, and the vulnerable zone (new patterns of activation) was distributed from 30 to 90 ms. The recovery intervals associated with no change of activation were distributed at the two ends of the spectrum. The differences among the recovery intervals for these four groups of recovery intervals were statistically significant (P<.001 by analysis of variance).
Histological sections showed normal canine ventricular myocardium (Fig 12⇓). There was no evidence of tissue necrosis or scar formation that could form anatomic barriers to prevent electrical activation. If the lower edge of the mapping plaque was used as 0° reference, with the angles taken counterclockwise, the angle of the fiber orientation averaged 35±21°. The angle between the fiber orientation and the line connecting the S1 and the S2 averaged 22±27°.
Effects of S3 on Ventricular Vulnerability to Single Strong Premature Stimulation
Both a previous study8 and the present study showed that a single strong electrical stimulus (S2) at 40 mA above the fibrillation threshold can reliably induce VF in the vulnerable period of the cardiac cycle. In the present study, we found that a second premature stimulus (S3), delivered to the site of the S2, can modify ventricular vulnerability to the S2. Fig 13⇓ shows a hypothesis regarding the operation of the mechanisms by which the S3 modifies ventricular vulnerability. This figure depicts only one of the two reentrant wavefronts of the figure-eight reentry. The total duration of the effective refractory period and the relative refractory period was based on a previous study,11 which showed that the refractory period of fibrillating ventricular muscle ranges from 48 to 77 ms. This refractory period is also consistent with that estimated by computer simulation studies.15 We hypothesize that the first 50 ms was the effective refractory period, which was followed by 20 to 30 ms of relative refractory period. The remaining part of the cycle was an excitable gap. When the S3 was given roughly 39 ms after the preceding activation, the reentrant wavefront was terminated and VF was aborted. When the S3 was given 61 ms after the preceding activation, a new activation pattern was induced and VF continued. When the S3 was given 22 ms after the preceding activation, at a time when the reentrant activation wavefront would have just revisited that site, no change of activation pattern was observed. When the S3 was given 94 ms after the preceding activation, when the cells near the S3 were fully recovered, the patterns of activation were also not changed. These findings support the hypothesis that, depending on the time of the electrical stimulation relative to the reentrant activation, a stimulus may result in termination, reinitiation, or no change of the reentrant wavefronts or VF.
A “protective zone” is known to be present in the cardiac cycle, during which a stimulus can prevent the induction of VF by an earlier stimulus (S2) delivered during the vulnerable period.1 2 It has been hypothesized that the stimulus exerts its protective effects by terminating local reentrant activity induced by an earlier stimulus.3 The results of this study confirmed this hypothesis. However, we also demonstrated that the stimulus can prevent the continuation of reentry and VF only when it falls within a specific period during reentrant excitation. This specific period occurred 39 ms after the previous activation, an interval insufficiently long for the ventricular cells to fully recover from previous activation.11 A strong stimulus occurring before complete recovery may induce graded responses12 16 and hence prolong the action potential duration and refractoriness.17 18 When the leading edge of the reentrant wavefront revisited this area, it could not reenter. This circumstance thus resulted in bidirectional conduction block and the termination of reentry.
Shortly after the protective zone, an S3 changed the patterns of activation but did not terminate VF. The changes were not subtle. In some parts of the mapped region, the wavefronts traveled in opposite directions before and after the S3. This finding indicates that the S3 initiated new patterns of activation, while the reentrant wavefronts preceding the S3 were terminated. The recovery interval associated with new patterns of activation averaged 61 ms. This interval roughly corresponded to the relative refractory period that exists in fibrillating ventricular cells.11
No Change of Activation
When the recovery interval (94±15 ms) was almost as long as the VF cycle length, the S3 occurred at a time when the cells would have been activated by the reentrant wavefront. The S3 therefore did not significantly change the patterns of activation. On the other hand, if the recovery interval was 22±8 ms, the S3 had occurred in the early stages of repolarization. Because a stimulus occurring in the very early stages of repolarization may not result in significant alteration of the action potential,12 the S3 did not significantly change the patterns of activation. In either case, the figure-eight reentrant pattern was allowed to continue undisturbed.
Although the figure-eight reentry was unchanged, the patterns of activation shown in Fig 5⇑ indicate that the S3 nevertheless had some influence on the reentrant wavefronts. One evidence is that the frame line of Fig 5C⇑ moved closer to the S1 site than the frame line shown in Fig 5A⇑. These findings indicate that the S3 might have activated cells that would not have been activated by the original reentrant wavefronts. Depending on the strength and the timing of the S3, the number of the cells activated may also change. Therefore, even when figure-eight reentry was maintained, the S3 may still influence the patterns of the reentrant activation.
Implications Regarding the Mechanisms of Defibrillation
It is well known that successful defibrillation depends on the strength of the electric shock; the higher the shock strength, the greater the probability of successful defibrillation.19 However, the importance of the timing of the shock on the results of defibrillation has not been fully appreciated. In this study, we demonstrated that a second premature stimulus (S3) could either terminate reentry or perpetuate reentry induced by an earlier premature stimulus (S2), depending on the time in the activation cycle at which the stimulus occurs. A vulnerable period (61±20 ms after the preceding activation) was identified. The timing of this vulnerable period was similar to the timing of the preshock intervals at the early sites after an unsuccessful defibrillation shock (64±11 ms).10 This relationship supports the hypothesis10 20 21 22 23 that an unsuccessful shock terminates all activation wavefronts but fails to halt VF because it initiates new activation wavefronts by falling into the vulnerable period. Successful defibrillation occurs if the shock strength is above the upper limit of vulnerability so that it cannot reinitiate VF. Alternatively, if the shock strength is below the upper limit of vulnerability in only a small area of the ventricles but the timing of activation in that area happens to be in the protective zone, then the shock can also successfully defibrillate. Because the activation patterns during VF are complex, whether a shock will occur during the protective or the vulnerable zone is determined by chance. Furthermore, because the upper limit of vulnerability is also a probability function,24 25 whether or not a shock delivered during the vulnerable period will reinduce VF is also determined partially by chance. Therefore, defibrillation threshold testing is a probability function,19 and the probability-of-success curve for defibrillation threshold testing may be shallower than the probability-of-success curve for the upper limit of vulnerability testing.26
Limitation of the Study
One limitation of this study is in the methods used for the measurement of the recovery interval near the site of the S3. The activations near this site often had small amplitudes and a slow rate of rise (channel I8 in Fig 6⇑). These deflections may represent electrotonic responses and not true local activation. To partially circumvent this uncertainty, we measured the times of activation recorded by the activation of a group of three or more electrodes near the site of the S3, rather than by any single arbitrarily selected electrode. If three or more electrodes near the S3 were activated within 10 ms of each other, that 10-ms window was used as the time of activation. The difference between this 10-ms window and the 10-ms window that included the S3 was the recovery interval for that episode. In the example shown in Fig 6⇑, the recovery interval of channel I8 was 37 ms, whereas the recovery interval entered into statistical analysis and Fig 11⇑ was 30 ms.
For future clinical applications, these small and low-amplitude electrograms near the site of the S3 may not be detectable by the implanted devices. We also analyzed the recovery intervals based on the large-amplitude electrograms near the earliest site of the reentrant circuit. In this model, the earliest sites were between the sites of the S1 and the S2. The results showed that the recovery intervals for the protective, vulnerable, and no-change zones were also statistically different. Whether this latter method will prove to be more clinically useful is unknown.
This work was done during the tenure of an American College of Cardiology/Merck fellowship and an American Heart Association (AHA), Greater Los Angeles Affiliate, Clinician Scientist Award to Dr Hwang and an AHA/Wyeth-Ayerst Established Investigatorship Award to Dr Chen. It was supported in part by a FIRST award (HL-50259) and a Specialized Center of Research grant (HL-52319) from the National Institutes of Health, an AHA National Center Grant-in-Aid (92009820), the Electrocardiographic Heartbeat Organization, and the Ralph M. Parsons Foundation. The authors wish to thank James Forrester, MD, for his support; Peter Hunter, PhD, David Bullivant, PhD, Sylvain Martel, and Serge LaFontaine for constructing the mapping system; Avile McCullen, Meiling Yuan, and Tamiko Davis for technical assistance; Arthur T. Winfree, PhD, for reviewing this manuscript; and Elaine Lebowitz for secretarial assistance.
Reprint requests to Peng-Sheng Chen, MD, Room 5342, Cedars-Sinai Medical Center, 8700 Beverly Blvd, Los Angeles, CA 90048. E-mail firstname.lastname@example.org.
- Received October 26, 1994.
- Accepted April 14, 1995.
- © 1995 American Heart Association, Inc.
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