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(Circulation Research. 1997;81:753-764.)
© 1997 American Heart Association, Inc.

Articles

Attachment of Meandering Reentrant Wave Fronts to Anatomic Obstacles in the Atrium

Role of the Obstacle Size

Takanori Ikeda, Masaaki Yashima, Takumi Uchida, Dustan Hough, Michael C. Fishbein, William J. Mandel, Peng-Sheng Chen, , Hrayr S. Karagueuzian

From the Division of Cardiology (T.I., M.Y., T.U., D.H., W.J.M., P.-S.C., H.S.K.), Department of Medicine, and the Department of Pathology (M.C.F.), Cedars-Sinai Medical Center, Burns and Allen Research Institute, and UCLA School of Medicine, Los Angeles, Calif.

Correspondence to Hrayr S. Karagueuzian, PhD, Division of Cardiology, Cedars-Sinai Research Institute, 8700 Beverly Blvd, Room 6066, Los Angeles, CA 90048. E-mail Karagueuzian{at}csmc.edu

	Abstract

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Abstract Acetylcholine chloride (ACh) induces nonstationary meandering reentrant wave fronts in the atrium. We hypothesized that an anatomic obstacle of a suitable size prevents meandering by causing attachment of the reentrant wave front tip to the obstacle. Eight isolated canine right atrial tissues (area, 3.8x3.2 cm) were mounted in a tissue bath and superfused with Tyrode's solution containing 10 to 15 µmol/L ACh. Holes with 2- to 10-mm diameters were sequentially created in the center of the tissue with biopsy punches. Reentry was induced by a premature stimulus after eight regular stimuli at 400-ms cycle length. The endocardial activation maps and the motion of the induced reentry were visualized dynamically before and after each test lesion using 509 bipolar electrodes. In the absence of a lesion (n=8), the induced single reentrant wave front, in the form of a spiral wave, meandered irregularly from one site to another before terminating at the tissue border. Holes with 2- to 4-mm diameters (n=6) had no effect on meandering. However, when the hole diameters were increased to 6 mm (n=8), 8 mm (n=8), and 10 mm (n=6), the tip of the spiral wave attached to the holes, and reentry became stationary. Transition from meandering to an attached state converted the irregular and polymorphic electrogram to a periodic and monomorphic activity with longer cycle lengths (101±11 versus 131±9 ms for no hole versus 10-mm hole, respectively; P<.001). Regression analysis showed a significant positive linear correlation between the cycle length of the reentry and the hole diameter (r=.89, P<.01) and between the cycle length of the reentry and the excitable gap (r=.89, P<.05). We conclude that a critically sized anatomic obstacle converts a nonstationary meandering reentrant wave front to a stationary one. This transition converts an irregular "fibrillation-like" activity into regular monomorphic activity.

Key Words: reentry • mapping • atrium • source-sink relationship • acetylcholine

	Introduction

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The core of a functionally based reentrant wave front does not always remain stationary but meanders from one site to another. Meandering of reentrant wave fronts¹ is shown to exist in experimental^{2 3} and human⁴ AF. Studies in ventricular tissues have shown that the motion of the core stops when it encounters an unexcitable obstacle.^{5 6} Arrest of meandering occurs because the tip of the reentrant wave front attaches to an obstacle and continuously rotates around it in a stable manner.^{5 6 7} When the "tip" of the reentry, defined as the innermost edge of the reentrant wave front that encircles the central core, attaches itself to the core, the irregular (polymorphic) electrical activity, characteristic of meandering, terminates, and a periodic (monomorphic) activity emerges.^{5 6 7} We define "attachment" as a mode of reentrant activation when the tip of the reentry follows a fixed path in the boundary of the anatomic obstacle during consecutive reentrant cycles. If the tip trajectories are superimposed on consecutive reentrant cycles, then there is attachment. Otherwise, there is tip separation or detachment from the obstacle.^{8 9} In the atria, many naturally occurring anatomic obstacles are present. These obstacles, such as the coronary sinus orifice and the orifice of the pulmonary veins, can serve as anatomic obstacles for attachment of the reentrant wave front. Clinically, this could result in the transition from fibrillatory to "flutter-like" activity during the same episode of an atrial tachyarrhythmia.^{10 11} However, at present, it is not known whether an anatomic obstacle can serve as an attachment site for a nonstationary reentrant wave front in the atrium and, if so, what size obstacle is needed for a successful attachment. We have recently shown that functional reentry in the atrium is compatible with the mechanism of the spiral wave of excitation,¹² in which the tip of the spiral wave meanders irregularly when exposed to ACh.³ The purpose of the present study was to test the following two hypotheses. First, an anatomic obstacle of a critical size prevents meandering of the atrial reentrant wave front by attaching its tip to the obstacle. Second, attachment of a meandering reentrant wave front converts the "fibrillation-like" activity to a regular periodic rhythm resembling atrial flutter.

	Materials and Methods

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Experimental Preparation
Eight mongrel dogs of either sex weighing between 22 and 27 kg were anesthetized with 35 to 40 mg/kg IV sodium pentobarbital. Arterial blood pressure was continuously monitored via the left femoral artery. A thoracotomy was performed by the midsternal approach. The hearts were rapidly removed and placed in cold oxygenated Tyrode's solution. After separation of the atria from the ventricles, the right atrial appendage and part of its adjacent atrial chamber were isolated with sharp scissors. The isolated atrial tissues were 3.8x3.2 cm in area and 0.5- to 2-mm thick (Fig 1). Anatomic obstacles (holes) with diameters of 2, 4, 6, 8, and 10 mm were created sequentially in the center of the tissue (Fig 1) using sharp skin biopsy punches (Acu-Punch, Acuderm Inc). At the end of each study with a given hole size, a larger concentric hole was made, and the dynamics of the induced reentry were reevaluated with the new lesion. In two tissues, the effects of 6- to 10-mm-diameter holes were tested directly without the prior testings of the effects of 2- and 4-mm-diameter holes. The contour of the cut region was identified by the locations of the exposed electrodes, and it was transferred to the computer template used for direct visualization of the reentrant activity. The error in transferring the graphed diameter was <1.6 mm. All electrodes located within the cut region remained electrically silent during either pacing or reentry (see "Results"). The tissue bath was continuously superfused with Tyrode's solution containing 10 to 15x10^-6 mmol/L ACh (Sigma Chemical Co) at a rate of 10 mL/min and maintained at 36.5°C and at pH 7.4. The Tyrode's solution had the following ionic composition (mmol/L): NaCl 125, KCl 4.5, NaH₂PO₄ 1.8, CaC1₂ 2.7, MgCl₂ 0.5, NaHCO₃ 24, and dextrose 5.5, in distilled deionized water.^{12 13} ACh was present in all tissues studied before and after the creation of central holes. Both the bath and the stock Tyrode's solutions were continuously gassed with 95% O₂/5% CO₂.

View larger version (146K): [in this window] [in a new window]   Figure 1. Gross structure of a representative isolated canine right atrial endocardial appendage with its adjacent atrial chamber. A 10-mm-diameter hole was created in the center of the tissue. Initially, the diameter of the hole was 2 mm. The diameter was then progressively increased to 4, 6, 8, and finally 10 mm. The tissue size (see scale in cm) was the same as the plaque electrode array. S indicates superior; A, appendage; I, inferior; and P, pectinate.

Recording Electrodes
A rectangular plaque electrode array (3.8x3.2 cm) containing 509 bipolar electrodes in 25 rows and 21 columns was constructed on the floor of the tissue bath (Fig 2). Sixteen channels in the uppermost row were not functional, leaving a total of 509 functional channels. The interelectrode distance was 1.6 mm, and the interpolar distance was 0.5 mm. The electrodes were made of stainless steel wires of 0.4-mm diameter that were insulated, except at the tip. The isolated tissue was gently placed, endocardial side down, on the plaque electrode array (Fig 2). The upper nonfunctional electrode row did not touch the tissue. Each bipolar electrode protruded 3 mm from the bottom of the tissue bath, allowing free flow of the oxygenated Tyrode's solution that maintained tissue viability for the entire 2-hour study period.¹² The presence of sharp electrogram deflections on the entire endocardial mapped surface indicated the absence of injury potentials. The electrograms were filtered between 0.5 and 500 Hz and were acquired continuously for 8 seconds at 1000 samples/s with 18-bit accuracy.^{12 14 15} Tissue stability was confirmed by the presence of constant endocardial and epicardial diastolic excitability thresholds on repeat measurements (every 20 to 30 minutes) during the entire 2-hour study period. Tissue stability was further confirmed by the presence of similar isochronal activation maps at the beginning and at the end of the experiment of regularly driven beats.

View larger version (34K): [in this window] [in a new window]   Figure 2. Schematic representation of the electrode plaque mounted on the floor of the tissue bath. The plaque has 509 (out of 525) functional bipolar electrodes (0.5-mm interpolar distance) in 21 columns and 25 rows. The interelectrode distance (center to center of the bipole) is 1.6 mm. The endocardial side of the atrium was mounted on the plaque and superfused with oxygenated Tyrode's solution containing ACh.

Transmembrane AP Recordings
In order to determine cellular electrical viability of cells near the hole, we used conventional glass microelectrodes^{13 16 17} to record transmembrane APs from three additional endocardial atrial tissues. Digitized data (10-kHz sampling rate) were stored using Axoscope 1.1 (Axon Instrument, Inc). dV/dt_max of the phase-zero AP was determined from the digitized signal (Axoscope). Simultaneous two-cell AP recordings were made from cells within 1 mm of the boundary of the hole and from cells 10 to 15 mm away from the hole near the periphery of the tissue. In each tissue, we recorded from 4 cells near the hole and from 4 cells at the periphery for a total of 12 cells in all three tissues. The AP recordings were made during regular pacing at 300-ms cycle length and during induced reentrant activity in the presence of 10x10^-6 mmol/L ACh. During endocardial transmembrane AP recordings, a simultaneous epicardial activation map was obtained during regular pacing and during induced atrial activity by our in vitro mapping system (Fig 2).

Induction of Reentrant Wave Fronts
The isolated atrial tissues were paced with polytetrafluoroethylene-coated (except at the tip) bipolar silver wires (0.1-mm tip diameter) with a 2-mm interpolar distance. Regular (S₁) stimuli with twice the diastolic threshold current and 5-ms pulse widths at cycle lengths of 300 to 400 ms were applied either at the middle left or at the middle lower edge of the tissue. A premature (S₂) stimulus, with increasing current strengths (1 to 20 mA) and decreasing coupling intervals was applied at 0.5 to 1.5 cm distal to the S₁ site near the central hole of the tissue. Premature stimuli were applied until reentry or tissue refractoriness was reached. When reentry was not induced, higher S₂ current strengths were tested. The configuration of the electrode for the S₂ stimulus was the same as the electrode for the S₁ stimulus.

Determination of the Refractory Period and the Excitable Gap
Refractoriness
The refractory period at selected endocardial sites was determined by the S₁-S₂ extrastimulus method. After eight S₁ stimuli at 400-ms cycle length, an S₂ stimulus with twice the diastolic threshold current was applied at progressively shorter coupling intervals until loss of capture. The longest S₁-S₂ interval associated with noncapture was the effective refractory period. S₂ was applied at the same site as the S₁ stimulus. In five tissues we determined the refractory period at 25 endocardial sites (five rows and five columns) 5 mm apart, for a total of 125 sites. The refractory period at the boundary of the central hole was also determined at 30° to 40° increments (eight sites) along the perimeter of an 8-mm hole.

Excitable Gap
To determine the duration of the excitable gap during stationary (attached) reentry, single stimuli at twice the diastolic threshold current were applied between the top middle edge of the tissue and the middle upper perimeter of the hole. A monitoring bipolar silver electrode (polytetrafluoroethylene-coated, except at the tip) with 0.1-mm diameter and 1-mm interpolar distance was positioned within 2 mm of the stimulating electrode. The stimuli were applied at progressively longer coupling intervals, as determined by the local bipolar electrogram. The shortest captured interval after the start of the depolarization near the pacing site was taken as the recovery time. The difference between the cycle length of the reentry and the shortest captured interval (recovery time) was taken as the duration of the excitable gap.¹² During detached (meandering) reentrant wave fronts (see "Results"), excitable gap duration could not be determined by timed stimulation because of the nonstationary nature of the reentrant wave front.

Construction of Activation Pattern
A custom-made multichannel computerized mapping system (EMAP, Uniservices) was used to construct activation patterns. The times of activation were determined by the computer according to our previously described algorithm.^{3 12 14 15} Briefly, the maximum dV/dt of the range for data analysis was first determined by the computer. The S₂ artifact, which had an artificially large dV/dt, was excluded. Because it is unlikely that the computer would be 100% specific and sensitive in selecting activations, manual editing was performed for each activation on each channel. After activation times were edited manually, the patterns of activation were visualized dynamically on a computer screen on which each electrode site was illuminated when an activation was registered.^{3 12 15} During each activation when an electrode site was illuminated, the computer directed the corresponding site to be illuminated initially red, then yellow, then green, then light blue, and then finally dark blue before the original background dark color reemerged.^{3 12 15} Each illumination was selected to persist for 6 to 10 ms. The total duration of illumination of each dot by one activation could thus be preset at 30 to 50 ms. These times were chosen because they were shorter than the refractory periods of the atrial tissue and the fastest cycle length of the induced reentry. The total duration of the illumination does not reflect true tissue refractoriness but was used to monitor conveniently the wave-front dynamics. In cases of very rapid and irregular activity, shorter durations were used. Both 6- and 10-ms durations were used in most episodes to ensure correct delineation of the wave-front dynamics. Selected color snapshots were obtained on a hard copy (Hewlett-Packard Paint Jet XL300) at different moments during reentry.^{3 12 15}

Trajectory of a Reentrant Wave Front
During dynamic display of activation, the approximate location of the tip of a reentrant wave front was first identified from a still frame. The trajectory of the reentry tip was then traced using a mouse and custom-written software by advancing the still frames in 10- to 20-ms intervals for several consecutive reentrant cycles.^{3 12 15} Typically, when meandering occurred, the tip of the reentry did not return to the same point from which it originated. In cases of stationary reentry, tip trajectories of consecutive reentrant cycles were superimposed on each other.

Statistical Analysis
Differences between the means of the cycle lengths and conduction velocities in tissues with no hole and in tissues with different hole sizes were tested using ANOVA (Bonferroni/Dunn test). Linear regression analysis was performed to correlate hole size with conduction velocity and with cycle length and to correlate cycle length with excitable gap duration using StatView 4.5 (Macintosh) and GB-STAT statistical software.¹⁸ A value of P=.05 was considered significant. Data are presented as mean±SD.

	Results

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Activation Patterns During Regular Pacing
Fig 3 illustrates, in a representative atrial tissue, the lack of effect of a central hole (8-mm diameter) on the sequence and the total atrial activation time during regular pacing. In all eight isolated atrial tissues studied at baseline (without a central hole), the presence of sequential activation during S₁ pacing without conduction slowing and/or block indicated the absence of anatomic obstacles (Fig 3A and 3B). When a central hole was created, activation proceeded around the hole with no detectable evidence of conduction alteration (Fig 3D and 3E). The mean total activation time during S₁ pacing was 78±3 ms in the absence of a central hole (Fig 3A and 3B) and was not significantly different when holes of 2-, 4-, 6-, and 8-mm diameters were created (77±4, 78±3, 80±4, and 80±2 ms, respectively). A slight but significant (P<.05) increase in the total activation time (84±4 ms) was observed when the hole diameter size was increased to 10 mm. Although we could not detect any particular site in which the small additional conduction delay occurred, it is plausible that the additional delay might be caused by a diminished source-to-sink ratio. A 10-mm hole shortens the length of the two independent fronts propagating along the two lateral sides of the hole that decrease the number of the depolarized cells ("source"). A decrease in the source along and past the hole (here sink is not decreased) may cause an overall 3- to 4-ms conduction delay. Repeat construction of activation maps at the end of the study reproduced the isochrones constructed during the beginning of the experiment in all tissues studied (Fig 3). The mean endocardial diastolic excitability threshold measured with bipolar stainless steel hook electrodes, at the beginning and at the end of the experiments, was 0.35±0.2 and 0.45±0.2 mA, respectively (P=NS). Similarly, the epicardial diastolic excitability threshold was 0.54±0.2 and 0.48±0.2 mA (P=NS), respectively, at the beginning and at the end of the experiment.

View larger version (72K): [in this window] [in a new window]   Figure 3. Consecutive color-coded snapshots during regular pacing before (A and B) and after the creation of a 6-mm-diameter central hole in the same tissue (D and E). Each snapshot was taken at the time indicated under each frame, with the onset of S1 as time 0. The white dot at the bottom of the tissue is the site of S1 pacing at 400-ms cycle length. The letters a to e in panels A and D correspond to the locations of bipolar recordings shown in panels C and F, respectively. The persistence of each colored dot was 8 ms, with each frame representing a 40-ms activation isochrone. Note the absence of conduction block, presence of identical activation sequence, and bipolar electrogram morphology at the beginning (A, B, and C) and at the end (D, E, and F) of the experiment.

Transmembrane Potential Properties of Cells Near the Hole
Fig 4A shows simultaneous APs from two cells, one within 1 mm from an 8-mm-diameter hole (top recordings) and the second 1 cm from the edge of the tissue near the S₁ pacing site. The AP properties (measured during pacing at 300-ms cycle length and in the presence of 15x10^-6 mmol/L ACh) of the cells at these two sites were not significantly different from each other. In a total of 12 cell pairs recorded in three tissue samples (4 cell pairs from each tissue), the resting membrane potential, AP amplitude, 90% repolarization time, and dV/dt_max were as follows: 76±7 versus 74±9 mV, 108±9 versus 105±12 mV, 84±11 versus 87±13 ms, and 65±11 versus 58±14 V/s in the cells distant versus cells close to the hole (8-mm diameter), respectively. The effective refractory period and the diastolic threshold current near the hole were not significantly different from cells located 10 to 15 mm away from the hole (66.9±18 versus 72±16 ms and 0.32±0.12 versus 0.30±01.5 mA, respectively) (P=NS). During S₂-induced reentry, cells near the obstacle and at the periphery became activated during each cycle of the reentry (Fig 4A and 4B).

View larger version (41K): [in this window] [in a new window]   Figure 4. Transmembrane AP recordings from isolated canine endocardial right atrial tissues. A, Simultaneous recordings from two cells. Cell 1 is from within 1 mm of the boundary of an 8-mm-diameter hole (near the S1 pacing site), and cell 2 is 1 cm away from the hole opposite the S1 pacing site. Beg indicates a bipolar electrogram between the S1 site and cell 1. Three regularly (cycle length, 300 ms) driven beats (S1) are shown, followed by a premature stimulus (S2). The S2 induces rapid reentry that remains attached to the hole, as indicated by simultaneous epicardial mapping (data not shown). Both cells show regular 1:1 capture during each reentrant cycle with a monomorphic Beg. B, Transmembrane AP recording from a cell within 1 mm of a 4-mm-diameter hole (top) and a bipolar electrogram (bottom). Three regularly driven beats (cycle length, 300 ms; S1) were followed by a premature (S2-induced) meandering reentrant wave front (epicardial mapping, data not shown) with irregular bipolar morphology. One-to-one regular capture by the cell near the obstacle during phase-3 repolarization (arrows pointing upward) indicates that meandering is unrelated to prolonged refractoriness of cells at the boundary. Recordings in panels A and B were made in the presence of 15x10-6 mmol/L ACh.

Characteristics of the S₂ Stimulus for the Induction of Reentry
The creation of central holes of 2- to 10-mm diameters had no effect on the mean duration of the S₁-S₂ coupling intervals (78±10 ms) and the mean S₂ current strength (8±5 mA) that induced reentry. The mean refractory period at the S₂ site remained unchanged (69±9 ms) after the creation of holes with progressively larger diameters (2 to 10 mm).

Reentrant Wave Fronts in the Absence of a Central Hole
Thirteen episodes of reentry (mean cycle length, 101±11 ms ) were induced before creating central holes in a total of eight tissues (Table). Reentry was clockwise in 7 episodes and counterclockwise in the remaining 6 episodes. In all of these episodes, reentry was nonstationary as the central core of the reentry meandered from one site to another. Meandering prevented measurement of the "natural core size" because of a complex and irregular contour inscribed by the irregularly meandering core. Fig 5 illustrates a representative example of a meandering reentrant wave front rotating in a clockwise direction. In all 13 episodes, new wave fronts emerged at the tail of the meandering reentrant wave front 60 to 100 ms after a previous activation. Fig 5H shows the emergence of a new wave front at the tail of the reentrant wave front 60 ms after a previous activation. These new wave fronts interacted with the meandering reentrant wave front but failed to terminate reentry. In 5 of 13 episodes, reentry lasted for >10 minutes. In these episodes, reentry was terminated by pacing. In the remaining 8 episodes, reentry terminated spontaneously at the tissue border within 1 to 3 minutes. Meandering of the reentrant wave fronts was associated with irregular bipolar electrogram morphology and constantly changing cycle lengths. Fig 6 shows selected bipolar electrograms during the reentry shown in Fig 5. These wave-front dynamics, including the patterns of spontaneous termination and bipolar polymorphism, are consistent with our previous results.^{3 12}

View this table: [in this window] [in a new window]   Table 1. Relation Between Hole Diameter, Reentry Cycle, Cycle Length, and Conduction Velocity

View larger version (111K): [in this window] [in a new window]   Figure 5. Consecutive color-coded snapshots of a single meandering reentrant wave front in a clockwise direction with a cycle length of 100 ms (panels A through G) and the emergence of a new wave front (panel H). Time was arbitrarily chosen as 0 when the innermost of the leading edge of the wave front (asterisk) was in the right middle edge of the tissue (panel A). In all subsequent panels (panels B through K), the location of the tip is indicated by an asterisk. The persistence of each illuminated dot was 6 ms, with each snapshot representing a 30-ms activation isochrone. The composite trajectory of the meandering tip of the reentrant wave front (panels A through G) is shown in panel L by first plotting the locations of the asterisk in panels A through K and then consecutively connecting them by lines. When the wave tip was at the upper edge of the tissue rotating in a clockwise direction (top double arrows in panel H), a new wave front emerged at the lower right edge of the tissue (panel H). This new wave front propagated in both antidromic (two small arrows pointing upward in bottom of panel H) as well as in orthodromic manner (two small arrows pointing downward in the bottom of panel H). The antidromic front collided with the leading edge of the original reentrant wave front at the right middle edge of the tissue (double bars in panel I), which eventually becomes annihilated (panels I through K). However, the orthodromic front continued to rotate in a clockwise direction like the original reentrant wave front (panels J and K). Panel L shows the composite trajectory of the meandering tip obtained with 10-ms increments. X in panel L denotes the site of the emergence of the new wave front, and the double horizontal bars denote the site of the collision of the two wave fronts shown in panel I. The letters a through d mark the sites of bipolar recordings shown in Fig 6.

View larger version (25K): [in this window] [in a new window]   Figure 6. Selected bipolar electrograms recorded during reentry from sites indicated by the letters a through d in Fig 5L. The two dotted horizontal lines indicate the time interval (0 to 272 ms) shown in Fig 5A through 5K. Note the presence of irregular and nonuniform bipolar electrogram morphology during the meandering reentrant wave front. Note beat-to-beat variations of the rate with a mean cycle length of 98 ms.

Reentrant Wave Fronts in the Presence of a Central Hole
Fig 7 shows the effect of a central hole with a 4-mm diameter on an induced reentrant wave front. The induced reentry propagated in the counterclockwise direction and was nonstationary as the core meandered from one site to another. The tip of the meandering reentrant wave front did not attach to the hole, because it could variably get closer to (Fig 7B) and further away from (Fig 7D through 7G) the hole. In Fig 7G, for example, the electrodes at the southern border of the hole were not activated by the leading edge of the reentrant wave front. However, this same area of the tissue was activated later (Fig 7H), indicating that the tissue in that area was excitable and not refractory, consistent with transmembrane AP recordings near the obstacle shown in Fig 7B. We had seen similar meandering of reentry in six tissues with holes of 4-mm diameter in a total of 9 episodes. Similar results were also obtained in six tissues with 2-mm-diameter holes in a total of 9 episodes (Table). In all tissues with 2- and 4-mm-diameter holes, the tip of the reentrant wave front did not consistently attach itself to the hole. Rather, the tip of the reentrant wave front variably approached and departed from the boundary of the obstacle during reentry, resulting in irregular transmembrane AP amplitude and activation intervals near the obstacle (Fig 4B). The creation of 2- and 4-mm-diameter holes had no significant effect on the mean cycle length of the reentry (99±10 and 103±8 ms, respectively) (Table). During meandering of the reentrant wave front in tissues with 2-and 4-mm-diameter holes, new wave fronts emerged, as was the case in the intact tissues before the induction of the lesions (Fig 5). The bipolar electrograms recorded during meandering of reentry in tissues with 2- and 4-mm-diameter holes showed polymorphism characterized with nonuniform electrogram morphology and variable cycle lengths (Figs 4B and 8).

View larger version (136K): [in this window] [in a new window]   Figure 7. Color snapshots showing an induced single meandering reentrant wave front in an isolated atrial tissue with a 4-mm-diameter central hole. Time was arbitrarily chosen as 0 when the innermost of the leading edge (asterisk) of the wave front was in the upper middle edge of the tissue (panel A). The reentrant wave front rotated in a counterclockwise direction (double arrows in panels A through H) at a cycle length of 102 ms. During a given rotation, the tip of the reentry variably drifted toward and away from the central hole (panels A through H) without consistently attaching to it. For example, in panel E the tip of the reentry (asterisk) did not depolarize the middle upper boundary region of the hole, despite the availability of ample time for full recovery (>98 ms) but did depolarize it some 78 ms later (panel H). Panel I is the composite trajectory of the meandering tip of the reentry, as described in Fig 5. The persistence of each colored dot was 6 ms; thus, each frame represents a 30-ms activation isochrone. The letters a through d show the sites of selected electrograms shown in Fig 8.

View larger version (25K): [in this window] [in a new window]   Figure 8. Selected bipolar electrograms recorded during meandering reentry from sites indicated by the letters a through d in Fig 7I. The two dotted horizontal lines indicate the time interval (0 to 174 ms) shown in Fig 6A through 6H. Note the presence of irregular and nonuniform bipolar electrogram morphology during meandering of the reentrant wave front with a central hole of 4-mm diameter. Note beat-to-beat variations of the rate with a mean cycle length of 103 ms.

In contrast to the smaller-sized holes, holes with 6-, 8-, and 10-mm diameters caused a continuous attachment of the tip of the reentrant wave front to the obstacle during consecutive reentrant rotations. The attachment of the tip of the reentry to the obstacle converted the nonstationary to a stationary reentrant wave front. Fig 9 illustrates an example of tip attachment in a tissue with a 10-mm-diameter hole. Reentry with a clockwise direction (double arrows in Fig 9A through 9H) at a cycle length of 134 ms is shown in this example. Effective attachment of the tip of the reentry to the hole is evident as the tip of the reentry remains attached to the hole throughout the entire interval of the rotation. The rotating front returns to the same point from which it originated during one rotation period (Fig 9A and 9E). Attachment was seen in all eight tissues with 6- and 8-mm-diameter holes (10 episodes) and in six tissues with 10-mm-diameter holes (10 episodes) (Fig 9). The bipolar electrograms during a tip-attached stationary reentry had a uniform morphology and a constant cycle length (Figs 4A and 10). In addition, during induced stationary reentry in all tissues studied with 6- to 10-mm-diameter holes, no new wave front ever emerged during up to 10 minutes of monitoring.

View larger version (152K): [in this window] [in a new window]   Figure 9. Color snapshots of an induced single rotating reentrant wave front in a tissue with a 10-mm-diameter central hole. Time was arbitrarily chosen as 0 ms, when the tip (asterisk) of the reentrant wave front was in the right middle edge of the tissue (panel A). The persistence of each colored dot was 8 ms; thus, each frame represents a 40-ms activation isochrone. The induced reentrant wave front rotated in a clockwise direction (two small arrows in panels A through H) at a cycle length of 134 ms. The tip of the reentry (white asterisks in panels A through I) remained constantly attached to the central hole, as shown by two consecutive rotations around the hole (panels A through H). Panel I is a composite diagram that shows the trajectory of the tip of the reentry during two consecutive rotations. The trajectories are superimposable (panel I). The letters a through d show the locations (yellow asterisks) of the selected bipolar electrograms shown in Fig 10.

View larger version (24K): [in this window] [in a new window]   Figure 10. Selected bipolar electrograms recorded during anchored reentry from sites a through d shown in Fig 9I. The two dotted horizontal lines indicate the time interval (0 to 232 ms) shown in Fig 9A through 9H. Note the uniform morphology of the electrograms and the constant cycle length of 134 ms during the reentry.

Relationship Between Hole Size and Cycle Length of the Reentry
The mean cycle length of the reentry was significantly (P<.001, Bonferroni/Dunn test) longer in tissues with 6-, 8-, and 10-mm-diameter holes (121±11, 125±10, and 131±9 ms, respectively) than those in tissues with no holes or 2- and 4-mm-diameter holes (Table). No significant differences in reentry cycle length were found in tissues with 6-, 8-, and 10-mm-diameter holes (Table) (Bonferroni/Dunn test). Fig 11A is a regression line of the cycle length versus hole diameter for attached reentry in all eight tissues studied. A positive linear correlation (correlation coefficient, .86) was found between the hole diameter (mm) and the cycle length (ms) of the anchored reentrant wave front: y (cycle length in ms)=106+2.5x (hole diameter in mm).

View larger version (16K): [in this window] [in a new window]   Figure 11. Regression lines of the hole diameter vs the mean cycle length (CL) (A) and vs the mean conduction velocity (CV) (B) of the induced reentry. The dashed line in panels A and B represents the extrapolated values to zero hole diameter (natural core) of the mean CL (A) and mean CV (B). (See the Table and text for more details.)

Relationship Between Conduction Velocity Around the Hole and the Hole Size
Constant attachment of the tip of the reentry to the fixed border of the circular holes with 6- to 10-mm diameters allowed us to estimate the velocity of conduction with reasonable degree of accuracy. Since the traveled path of the circular hole-attached tip of the reentry is 2xradius of the hole (ie, perimeter of the circle) and the conduction time over this path is identical to the cycle length of the reentry, conduction velocity could be calculated by dividing the perimeter of the hole (distance) by the cycle length (time) of the reentry. With such calculations, a significant (P<.05) positive linear correlation was found between the hole diameter (x axis) and the conduction velocity (y axis), with a correlation coefficient of .99 (Fig 11B): y (cm/s)=3.1+2.1x (mm). Conduction velocity significantly (P<.001, Bonferroni/Dunn test) increased at each step increase in the hole diameter from 6 to 8 to 10 mm (15.5±1.4, 20.2±1.6, and 24±1.5 cm/s, respectively) (Table, Fig 11B).

Excitable Gap During Reentry Around a Hole
The ability of the reentry to remain attached and stationary to the holes with 6- to 10-mm-diameter holes allowed us to determine the duration of the excitable gap. We applied premature stimuli at twice the diastolic current threshold at the middle top of the tissue during attached reentrant wave fronts of excitations. Fig 12A shows the shortest coupling interval (82 ms) that an applied stimulus captures in the atrium after a reentrant beat (tracing 4). Since the cycle length of the reentry was 120 ms (top recording), the estimated excitable gap was 38 ms. Fig 12B shows pooled results in three tissues with 6-, 8-, and 10-mm-diameter holes (three episodes with each hole size for a total of nine episodes). A significant (P<.005) positive linear correlation (r=.89) was detected between the excitable gap duration and the cycle length of the anchored reentry (Fig 12B).

View larger version (19K): [in this window] [in a new window]   Figure 12. Regression line of the cycle length vs the excitable gap of the induced reentry. The top recording of panel A shows sustained monomorphic reentry at a cycle length of 120 ms. The recordings labeled 1 to 6 in panel A show the application of a single electrical stimulus at progressively longer coupling intervals (from 1 to 6). Earliest capture occurs at a coupling interval of 82 ms (recording 4). This value is shown with an arrow in panel B. In panel B, the results of three tissues with 6-, 8-, and 10-mm-diameter holes (total of nine data points) are plotted vs the cycle length and the regression line drawn. A significant positive linear correlation was found between the cycle length of the reentry and the excitable gap.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

 
Attachment of a meandering reentrant atrial wave front to a critically sized anatomic obstacle constitutes the major finding of the present study. Attachment converts polymorphic fibrillation-like electrograms, characteristic of a meandering reentrant atrial wave front,³ to a monomorphic flutter-like activity. Atrial fibrillation and atrial flutter need not always be the result of different mechanisms.¹¹ Rather, they can reflect two different dynamic behaviors of a single reentrant wave front. Clinically, a change from AF to atrial flutter was recognized by Lewis more than 70 years ago¹⁰ and more recently confirmed by experimental¹⁹ and clinical^{20 21} studies. Conversion from atrial flutter to AF in the canine sterile pericarditis model was shown to be associated with the destabilization of a single reentrant wave front into meandering and multiple wave fronts.¹¹

Attachment and the Size of the Anatomic Obstacle
The safety factor for propagation is determined by the relationship between the current source of the wave front and the need of adjacent cells of depolarizing current to reach threshold for excitation (sink).^{22 23} Not all segments of a reentrant wave front have the same intrinsic stimulating efficacy (source). For example, the tip of the reentrant wave front, by virtue of its high curvature, has lower safety margin (source) for propagation than the less curved periphery of the wave front.²² In addition, not all regions of a propagating wave front confront the same current load (sink). The presence of local variations in the source-to-sink ratio causes a discontinuous wave front. In our case, the discontinuity results in separation of the reentry tip from the obstacle boundary and detachment from the hole. Detachment results from a low source-to-sink ratio rather than from prolonged cellular refractoriness near the obstacle, because the cells near the hole are excited during phase-3 repolarization during rapid reentrant activity (Fig 4B). If refractoriness had been the mechanism of wave front detachment, then the cells near the hole would still be refractory during the next reentry cycle.

An obstacle of relatively larger size lowers the sink of a rotating wave front with a resultant increase in the source-to-sink ratio (safety factor). The increase in the safety factor leads to the depolarization of all the cells at the boundary of the obstacle. Depolarization of all the cells at the boundary of the obstacle results in attachment. Although earlier simulation studies²⁴ stressed the importance of hole size relative to the spiral wave period and stability, it was only recently that a precise quantitative description of the source-sink balance at the boundary of the obstacle was provided.^{8 25 26} The results of simulation studies in Dr Starmer's laboratory⁸ support our proposed mechanistic speculation. When the ratio of the source at the tip of the wave front is higher than the charge requirement (load or sink) of the cells at the boundary of the obstacle, the front successfully depolarizes all the cells at the boundary (perimeter) of the obstacle causing attachment. However, when the source-to-sink ratio of the tip of the front diminishes (as in cases of acute turns around smaller holes), the cells at the boundary of the obstacle can no longer be depolarized. This results in separation of the front from the boundary of the hole. Spach et al²⁷ in studies of isolated superfused canine right atria have shown that conduction block at branch sites requires abrupt acute turns (larger sink) but that absence of block at the same site of wave front propagation does not require making an acute turn (smaller sink). Optical mapping studies of Girouard et al²⁸ involving the rabbit ventricle confirmed that an abrupt change in current load (sink) during wave-front pivoting around a linear obstacle rather than refractoriness and/or fiber structure was a major determinant for reentrant wave-front stability. The results of our transmembrane AP recordings near the obstacle are compatible with the source-to-sink mismatch hypothesis of separation rather than with the prolonged local cellular refractoriness hypothesis. Fig 13 illustrates our hypothesis. This figure shows two holes, one large and one small. A reentrant wave front is rotating around the hole in a counterclockwise direction. When the hole is large, the sink (ie, number of cells at rest) is relatively small. This leads to successful depolarization of all the cells at the boundary of the hole, resulting in attachment. However, when the hole is small, the same reentrant wave front (source) must excite additional cells at rest, resulting in source-to-sink mismatch and wave-front detachment.

View larger version (19K): [in this window] [in a new window]   Figure 13. Hole diameter and the source-sink relationship. A reentrant wave front propagating in a counterclockwise direction is shown (three upright arrows). The source is the tip of the reentrant wave front; the sink (cells at rest) is the area between the tip of the reentry and the boundary of the hole. The two circles represent the perimeters of the two holes with different diameters. The shaded circle represents the smaller hole; the open circle, the larger hole. The sinks associated with these two holes relative to the approaching wave front are different. When reentry rotates around the smaller hole, a larger number of cells at rest must be depolarized to the threshold by the approaching front. The added number of cells, represented by additional sink (labeled A), decreases the source-to-sink ratio and the safety factor for propagation. A decreased source-to-sink ratio cannot depolarize the "added" number of cells because of dissipation of the depolarizing current into a larger area. In this case, the wave front detaches from the obstacle. With the larger hole, however, the approaching depolarizing wave front engages itself into a smaller sink. As a result, it depolarizes all the cells at the boundary of the hole. In this, case the wave front remains attached to the hole.

Hole Size Versus Cycle Length of Reentry
Larger holes significantly increased the conduction velocity around the hole while causing a slight but not significant prolongation of the reentry period, consistent with simulation studies.^{24 29 30} Faster speeds of propagation may result from a higher safety factor for propagation in tissues with larger holes because of the higher source-to-sink ratios (Fig 13). However, since the traveled path around the perimeter of a larger holes also increased, the net effect was no increase or only a small increase in the reentry period (Table, Fig 11A). Assuming that a linear relationship between conduction velocity around the hole and the hole diameter exists even for smaller diameter holes (<6 mm), extrapolation of the regression line of velocity (y axis) versus diameter (x axis) to zero hole diameter yields a conduction velocity of 3.1 cm/s (Fig 11B). This extrapolated conduction velocity to zero hole diameter (ie, functional reentry) corresponds to the velocity of the leading edge of the reentry around its natural core during functional reentry. Since the mean cycle length of reentry in the absence of a hole is 106 ms (extrapolated value in Fig 11A) and is very close to the actual experimental value of 101 ms (Table), then the distance traveled during one period around the circular perimeter of the natural core¹² should correspond to 3.28 mm. This perimeter corresponds to a radius of 0.52 mm (1-mm diameter) and reflects the radius of the natural core of atrial reentry in the presence of ACh. The extrapolated value of the radius of the natural core in the presence of ACh is smaller than the core radius measured directly during stationary reentry in the absence of ACh, ie, 2 mm.¹² The decrease in the core radius from 2 to 0.5 mm could explain the mechanism by which ACh accelerates reentry rate. This speculation is compatible with the results obtained in isolated normal ventricular tissue^{31 32} and at the epicardial border zone of healing infarcts in in situ canine hearts.³³ Acceleration of functional reentry in these studies was shown to be associated with a reduction of the central core size around which rotation occurred.^{31 32 33} In addition, ACh-induced reduction of the natural core size suggests that ACh increases the critical wave-front curvature²² (ie, the curvature at which propagation fails). The increase in the critical curvature explains the ability of very small reentrant wave front to sustain activity for longer duration, a phenomenon that does not occur in the absence of ACh.^{2 12} Our experimentally extrapolated value of critical curvature is compatible with simulation studies.³⁴

Polymorphic Versus Monomorphic Electrograms
Meandering of a single reentrant atrial wave front caused fibrillation-like activity as in ventricular tissue^{7 35} and in simulation studies.³⁶ It would therefore appear that in addition to the multiple-wavelet hypothesis of AF,^{2 37 38} a single meandering reentrant wave front may also cause fibrillation in the atrium. Prevention of meandering by attachment to an obstacle may convert AF to atrial flutter, a phenomenon recognized a long time ago.¹⁰ The ability of flutter to convert to fibrillation may also depend on the cellular electrophysiological properties of the atrial tissue and on the rate of the flutter. For example, if the atria are diseased (fibrosis), relatively slower flutters may undergo fibrillatory conduction (wave-front breakups), leading to AF. In normal atria on the other hand, faster atrial flutter rates may be needed for conversion to AF. Slower flutters may remain stable in normal atria. Conversion from fibrillation to flutter is compatible with the observation made in ventricular tissue^{7 35} and in simulation studies,^{1 36 39} where attachment of a single meandering reentry converts polymorphic activity into a regular monomorphic activity.

New Wave Fronts
Meandering was always associated with the emergence of new wave fronts that appeared to have no direct relationship to the original reentrant wave front. Emergence of new wave fronts was also described by Allessie et al,³⁷ Schuessler and colleagues,^{2 40} and Gray et al⁴¹ and by us.³ It is possible that rapid meandering of the wave front in the complex right atrial structure alters the sequence of activation and recovery, promoting wave break³¹ and initiation of new reentrant or nonreentrant wave fronts. Consistent with this suggestion is the absence of new wave fronts in all tissues and in all episodes in which meandering was eliminated by wave-front attachment at the boundary of the hole.

Excitable Gap and Anatomic Obstacle
The ability to electrically capture the ACh-treated atrium during attached reentry and the emergence of new wave fronts at the tail of a meandering reentry indicates that an excitable gap is present. The presence of a positive linear correlation between the cycle length and the duration of the excitable gap holds true regardless of the presence of ACh¹² or a central obstacle. These findings are compatible with the results obtained in ventricular tissue⁴² and in atrial tissue with no ACh present.¹²

Limitations of the Study
The origin of the new wave fronts that emerged during meandering reentrant wave front could not be defined in the present study. The fact that ACh is always present argues against an automatic mechanism.^{2 40 43 44} It is possible that the new wave fronts originate from either epicardial or intramural sites that could not be detected by our mapping technique. Alternatively, it may be argued that the new wave fronts originate from an "ischemic core" of the superfused tissue. However, the complete absence of such new wave fronts during attached reentry (tissues with 6- to 10-mm-diameter holes) argues against this hypothesis. Although not proven, it is likely that the irregular activation-recovery patterns during a single meandering reentrant wave front promote wave breaks and the generation of new wave fronts.

It is possible that the excitable gap interval could be underestimated. This underestimation, 15 ms may result as follows: The site of the stimulation and the site of the recording bipolar electrode used to measure the earliest captured interval are 2 to 3 mm apart. This may cause an underestimation of, at most, 5 ms (spatial component). In addition, it is possible that the earliest captured stimulus (electrical stimuli applied randomly) may not reflect the true earliest captured interval. For example, we do not know whether a stimulus applied 1 ms before the "earliest" captured beat would result in block. Our results show that the latest noncaptured interval just immediately before the earliest captured beat (Fig 12) ranged between 6 and 18 ms, causing an average of 12 ms of underestimation (temporal component). Although we do not know the exact amount, the error in underestimating the excitable gap is 17 ms.

Conclusion
We conclude that a critically sized obstacle prevents meandering of a reentrant atrial wave front by causing it to attach to the obstacle. Arrest of meandering of a single reentrant wave front converts polymorphic fibrillation-like activity to a monomorphic flutter-like activity.

	Selected Abbreviations and Acronyms

 

ACh = acetylcholine chloride AF = atrial fibrillation AP = action potential S (with subscript) = stimulus

	Acknowledgments

 
This study was supported in part by a National Institutes of Health SCOR grant (HL-52319) and FIRST award (HL-50259) and by the Ralph M. Parsons Foundation, Los Angeles, Calif, and was done during the tenure of a Cedars-Sinai ECHO Foundation award (Dr Karagueuzian), an American Heart Association Wyeth-Ayerst Established Investigator award (Dr Chen), and a Cedars-Sinai Burns and Allen Research Institute fellowship award (Dr Ikeda). We are grateful to Prediman K. Shah, MD, for his support of our research, and we wish to thank Drs Peter Hunter, David Bulllivant, Sylvain Martel, and Serge LaFontaine for constructing the mapping system, Avile McCullen and Meiling Yuan for their technical assistance, and Elaine Lebowitz for her secretarial assistance.

Received April 21, 1997; accepted July 22, 1997.

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