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(Circulation. 1996;94:1962-1973.)
© 1996 American Heart Association, Inc.

Articles

Mechanism of Spontaneous Termination of Functional Reentry in Isolated Canine Right Atrium

Evidence for the Presence of an Excitable but Nonexcited Core

Takanori Ikeda, MD; Takumi Uchida, MD; Dustan Hough, BS; John J. Lee, MD; Michael C. Fishbein, MD; William J. Mandel, MD; Peng-Sheng Chen, MD; Hrayr S. Karagueuzian, PhD

the Division of Cardiology, Department of Medicine, and Department of Pathology (M.C.F.), Cedars-Sinai Medical Center, 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 D-6066, Los Angeles, CA 90048.

	Abstract

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Background According to the spiral wave hypothesis of reentry, the core of functional reentry remains excitable but not excited. We sought to determine whether the core remains excitable and whether excitation of the core by an outside wave front leads to termination of the reentry in the atrium.

Methods and Results In nine isolated canine right endocardial atrial tissues (3.8 by 3.2 cm wide), reentry was induced by a premature point stimulus (S₂). The isochronal activation maps and dynamics of the activation patterns were visualized with the use of 509 bipolar electrodes (1.6-mm resolution). The S₂ applied after 8 regular beats induced reentry with a mean cycle length of 162±20 ms (15 episodes). Reentry had a large excitable gap (93±26 ms) as determined by early capture with twice the level of threshold stimuli. The central area (core) around which the wave fronts rotated had a mean surface area of 12±3 mm². The electrograms located in the core of the reentry registered no or very low amplitude potentials. In 13 of 15 episodes, reentry terminated when an outside new wave front merged with the original wave front and excited the core. Core excitation caused disruption of the original wave front, and the newly formed wave front(s) vanished at the tissue border within 77±18 ms. In 2 episodes, reentry terminated abruptly when an outside new wave front propagating in a direction opposite to the reentrant wave front collided with the leading edge of the reentrant wave front.

Conclusions Functional reentry in the atrium is compatible with a spiral wave of excitation with an excitable but nonexcited core and a large excitable gap. Reentry may be terminated either by direct excitation of the core that displaces the wave front to the tissue border or by collision with an outside new wave front.

Key Words: excitation • reentry • mapping • atrium • waves

	Introduction

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Atrial fibrillation is thought to result from multiple reentrant wave fronts that sustain rapid and irregular activity.^{1 2} These reentrant wave fronts often are functionally based, as shown in both animal³ and human atrial fibrillation studies.⁴ The most commonly accepted explanation of the mechanism of functional reentry is offered by the leading-circle hypothesis,⁵ which maintains that once reentry is initiated, the center (core) of the reentrant wave front is continuously invaded by multiple centripetal wavelets and is therefore refractory. In contrast, the spiral wave hypothesis of reentry states that the core remains excitable but nonexcited during reentry.⁶ The reason the core remains nonexcited is that propagation of the wave front is governed by the source-sink relationship, ie, the safety factor.^{7 8} The safety factor of the tip of spiral wave reentry near the core is very low because of the pronounced wave front curvature.^{6 9} Block occurs because the wave front near the core cannot propagate beyond a certain critical curvature even though the cells downstream are fully excitable.^{6 9 10} Therefore, it is anticipated that the core of a spiral wave reentry might be excited by an outside wave front with an appropriate safety factor for propagation.¹⁰ If, in fact, this is the case, then excitation of the core might be possible in the case of reentry by spiral wave and not possible in the case of reentry caused by the leading-circle mechanism.

The purpose of the present study was to analyze the events that follow the interaction of an outside wave front with the central core of a functionally determined reentry in isolated atrial tissues. Specifically, we sought to determine whether the core of functional reentry in the atrium remains excitable during reentry and whether excitation of the core by an outside wave front may disrupt the reentrant wave front, leading to its termination.

	Methods

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Isolated Atrial Tissue Preparations
Nine mongrel dogs of either sex weighing 22 to 26 kg were anesthetized with sodium pentobarbital (35 to 40 mg/kg IV). Arterial blood pressure was monitored continuously via the left femoral artery. A thoracotomy was performed by the midsternal approach, and 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 and mounted in the tissue bath with the endocardial surface up. The isolated atrial tissues were 3.8 x 3.2 cm wide and 0.5 to 2 mm thick and had no anatomic obstacles. Thus, the size of the isolated atrial tissues was the same as the size of the mapping electrode plaque. The tissue bath was superfused continuously with Tyrode's solution at a rate of 10 mL/min and maintained at 36.5°C and pH 7.4. The Tyrode's solution had the following ionic composition in mmol/L: NaCl 125, KCl 4.5, NaH₂PO₄ 1.8, CaCl₂ 2.7, MgCl₂ 0.5, NaHCO₃ 24, and dextrose 5.5, in triple-distilled deionized water. Both the bath and the stock Tyrode's solutions were gassed continuously with 95% O₂/5% CO₂.¹¹

Electrophysiological Studies
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 stimuli (S₁) with double the diastolic current threshold at cycle lengths of 300 to 400 ms were applied either at the left edge or the bottom of the tissue. Premature stimuli (S₂) with current strengths of 4 to 8 times the diastolic current threshold (1 to 5 mA) were applied 1.5 cm distal to the S₁ site near the center of the tissue. In each tissue, the refractory period was measured at the middle left edge of the tissue by the extrastimulus method. After 8 regularly driven beats at 400-ms cycle length, a premature stimulus with twice the diastolic threshold current was applied with the use of the same S₁ stimulating electrode. To determine the excitable gap duration of a reentrant wave front, single stimuli (at twice the diastolic current threshold) were applied from the left edge of the tissue during reentry at progressively longer coupling intervals beginning immediately after the atrial depolarization. The ability of these single premature stimuli to prematurely depolarize (capture) the atrium during reentry indicates the presence of an excitable gap. The difference between the reentrant cycle length and the shortest atrial captured interval was used to estimate the duration of the excitable gap.

Computerized Mapping System
A custom-made, 509-channel, computerized mapping system, EMAP (Uniservices), was used to construct isochronal activation maps.^{12 13} The data were acquired continuously for 8 seconds at 1000 samples/s with 18-bit accuracy. The signals were filtered with a high-pass filter of 0.5 Hz.^{12 13}

Recording Electrode
A plaque electrode array of 3.8 x 3.2 cm (Fig 1) composed of 509 bipolar electrodes in 21 columns and 25 rows was used in the present study. 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 electrode plaque was gently placed on the endocardial surface to map activation. In three of the nine right atrial preparations, a different mapping plaque electrode was used. In this protocol, the same 509 bipolar electrode configuration was constructed on the floor of the tissue bath. Each bipolar electrode protruded 3 mm from the bottom of the tissue bath. The endocardial surface of each of the three atrial tissues was placed face down on the electrode array. In this way, endocardial activation maps were constructed during freely flowing Tyrode's solution between the electrode array and the atrial tissue.

View larger version (42K): [in this window] [in a new window]   Figure 1. Configuration of the recording electrode array composed of 21 columns and 25 rows with a total of 509 bipolar electrodes. The smaller square is an enlarged view (circle in the electrode array) that shows four pairs of neighboring bipolar electrodes.

Method of Construction of Isochronal Activation Map
The times of activation were determined by the computer according to our previously described algorithm.^{12 13} Briefly, the maximal 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. The investigators then had the option to select the threshold dV/dt value (a percentage of the dV/dt value) and the interval (in milliseconds). In the example shown in Fig 2A, the threshold values were 20% and 100 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 selected threshold interval. 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. For multiphasic waveforms, the maximal slope of the activation complex was selected by the computer to be the time of activation, and only one activation was assigned for the entire 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 maximum deflection.^{12 13} 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 activation on the other channels, thus generating the isochronal map.

View larger version (121K): [in this window] [in a new window]   Figure 2. Color-coded isochronal activation map (A) and selected bipolar electrograms (B) during regular pacing in an isolated canine right atrial endocardial tissue. Regular pacing was applied at the bottom of the tissue. Note the presence of nonuniform conduction velocity during regular pacing (A). The average propagation was slower in the bottom, faster in the middle, and slower in the upper portion of the figure. The average conduction velocity from one edge of the tissue to the other was 44 cm/s. The absence of conduction block indicates the absence of anatomic obstacles in these isolated atrial muscles. The numbers on the map show the locations of individual recording electrodes and give the time of activation, with the onset of the regular stimuli (S1) as time zero. In the dark-blue areas, the + symbols indicate electrode locations and the numbers are the activation times. Times of activation and isochronal lines are color-coded according to the color bar at the top of map. S1 is the site of regular stimulation with a bipolar electrode at a cycle length of 400 ms. B, Selected bipolar electrograms recorded from sites a to i during S1 pacing shown in A. The long, arrow-headed line indicates the direction of the wave front propagation. The vertical bar at the beginning of each recording shows voltage calibration.

Method of Dynamic Display of Activation Wave Fronts
After activation times were edited manually, the pattern of activation was visualized on a computer screen on which each electrode site was illuminated when an activation was registered.¹³ For the purpose of dynamic display, if two deflections (double potentials) were observed, both deflections were selected as activation regardless of the duration of the isoelectric interval. During each activation when an electrode site was illuminated, the computer directed the corresponding site to be illuminated initially red, then yellow, green, light blue, and finally dark blue before it faded away. Each illumination was selected to persist for 6 to 10 ms. Selected color snapshots were obtained on a hard copy (Hewlett Packard Paint Jet XL300) at different times during reentry.

Size of the Central Region (Core) of the Reentrant Wave Front
During dynamic display of the reentrant wave front, when the central core of the reentry remained stationary, its contour was traced by use of a mouse and custom-written software. We traced the contour of the core on the computer screen by freezing the motion and then advancing it in 10- to 20-ms steps for one full revolution.¹³

Histological Analysis
After conclusion of the electrophysiological studies, the isolated atrial tissues were fixed in 10% neutral buffered formalin. The positions of the stimulating electrodes and the mapping electrode array were marked with dyes of different colors. Five-micrometer sections parallel to the endocardial surface were taken, and myocardial fiber orientation and the presence, if any, of tissue abnormalities were determined in the hematoxylin-eosin–stained sections. Five to eight sections were taken in each tissue sample. In addition, in each tissue, two to four cross sections in the epicardial-endocardial direction were also taken and stained with hematoxylin and eosin to determine tissue thickness.

Statistical Analysis
Differences between the means were tested by use of paired and unpaired t tests. Linear regression analysis was performed to correlate excitable gap with cycle lengths by use of StatView software (Macintosh). A value of P<.05 was considered significant. Data are presented as mean±SD.

	Results

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The activation maps obtained by the two different mapping electrode configurations were essentially similar. We therefore pooled their results.

Activation Pattern During Regular Pacing
Fig 2A shows a color-coded isochronal activation map during regular pacing in a representative isolated canine right atrial tissue. Selected electrograms are shown in Fig 2B. In this and in all atrial tissues studied, the presence of sequential activation of the entire atrial tissue during regular pacing with no conduction block indicates the absence of anatomic obstacles in our isolated atrial muscle. The mean total activation time was 85±4 ms. However, the conduction velocity was not uniform during regular pacing (Fig 2A). The nonuniformity of the conduction velocity is due to the presence of gross endocardial structural discontinuities and nonuniformities (Fig 3A). Histological analysis verified the complex pattern of atrial fiber orientation (Fig 3B) caused by the complex pectinate muscle geometry (Fig 3A). The mean refractory period at the pacing site during pacing at a cycle length of 400 ms was 99±14 ms.

View larger version (288K): [in this window] [in a new window]   Figure 3. A, Gross anatomic structure of a representative isolated canine right atrial endocardial appendage. Note the absence of uniform atrial fiber tracts and the complex pectinate atrial muscle structure. Each numbered scale corresponds to 1 cm. B, Histology of an isolated canine right endocardial atrial tissue. Note the absence of uniform atrial fiber orientation. The nonuniformity of atrial fiber orientation makes the atrium behave in a more or less isotropic manner. Magnification x25.

Characteristics of Induced Functional Reentry
Reentrant wave fronts were induced with an S₂ at a mean S₁-S₂ coupling interval of 138±26 ms. In a total of nine isolated right atrial tissues, 15 episodes of spontaneous termination of single reentrant wave fronts were studied. Six episodes of clockwise and 9 episodes of counterclockwise rotations had a mean cycle length of 162±20 ms (range, 130 to 220 ms). The direction of the rotation had no significant effect on the cycle length of reentry.

Fig 4A shows a color-coded isochronal activation map of an S₂-induced reentry rotating in a counterclockwise direction (same tissue as in Fig 2). In this and in all tissues studied, the induced reentrant wave front encompassed the entire isolated atrial tissue. We did not observe a reentrant wave front that was confined to a selected portion of the isolated atrium. Selected electrograms around the core of reentry are shown in Fig 4B. Rotation occurred around an area of apparent functional conduction block (area of bunched isochrones) near the center of the tissue. Note that this region showed no conduction block during regular pacing (compare with Fig 2A). Fig 5A shows electrograms that were recorded from the center of the region of block (sites k, l, q, and r), the locations of which are shown in Fig 4A. Note that these sites remained electrically silent during reentry. The maximum voltage deflections at these central sites were always <10% of the voltage deflections recorded at the periphery. Therefore, these small-voltage deflections were not considered local activation. Electrodes located at the periphery of the site of block showed greater-amplitude slowly rising electrical activity, ie, sites j, m, p, and s (Fig 5A), the locations of which are shown in Fig 4A. These distinct deflections were considered to reflect local activation and were included in the construction of the isochronal activation map. However, they may represent far-field effects that may result from electrotonic interaction with neighboring active sites. Electrodes located further away from the center registered high-amplitude electrograms with faster rise times, indicating local activation, ie, sites i, n, o, and t (Fig 5A). The locations of these activation sites adjacent to the central quiescent region are shown in Fig 4A. All sites that remained electrically silent during reentry (ie, sites k, l, q, and r) underwent full activation during regular pacing (compare Fig 5A and 5B). This indicates that during reentry, the electrically silent area was confined to 2 rows of electrodes covering an area of 3 to 4 mm. In 5 of 15 episodes, the central core was stationary, and the electrograms located in the core registered no electrical activity. During reentry with a stationary core, the cycle length of the reentry remained stable and the morphology of consecutive electrograms did not change (see Fig 4B).

View larger version (132K): [in this window] [in a new window]   Figure 4. Color-coded isochronal activation maps (A) and selected bipolar electrograms (B) of an induced reentry. Selected electrograms recorded around the core of the reentry (sites a to h) are shown on the activation maps. Same tissue as shown in Fig 3. Reentry occurs in a stable counterclockwise manner with a period of 158 ms. The long, arrow-headed line (activation times 3 to 139 ms in B) indicates the activation sequence analyzed for construction of the activation map. Note the bunching of the isochronal lines in the middle of A, indicating an area of apparent conduction block or an area of very slow conduction that was absent during regular pacing (see Fig 2A). Electrode locations and color codes as in Fig 2.

View larger version (35K): [in this window] [in a new window]   Figure 5. Bipolar electrograms recorded from sites specified in the isochronal maps shown in Fig 4A. A, During reentry. Note the presence of electrical quiescence (arrows) near the core of the reentry (sites k, i, q, and r) and small-amplitude deflections (circles) registered by the electrodes located just adjacent to the electrically silent electrodes (sites j, m, p, and s). In contrast, during regular pacing (B) at 400 ms cycle length, all the electrodes shown in A (including the ones that remained electrically silent during reentry) registered high-amplitude deflections indicating local activation.

In 10 episodes, the central core of the single reentrant wave front drifted slightly (3.2 to 6.4 mm) while reentrant excitation continued (Fig 6). Fig 6A shows an isochronal activation map of a reentrant wave front with a counterclockwise rotation during a slightly drifting central core. The drift of the core was associated with beat-to-beat variation of the cycle length of the reentry and changes in the configuration of electrogram morphology (Fig 6B). In all episodes of drifting cores, the electrograms located in the core registered low-amplitude potentials that varied on a beat-to-beat basis, alternating between double potentials, electrical quiescence, and high-amplitude potentials. These variations resulted from the drift of the core. For example, when the core drifted to a new location, these electrograms were no longer located within the core, and as a result, larger-amplitude potentials, indicative of local activation, were recorded (Fig 6B, sites f, g, i, and j). Return of the core to these same sites caused diminution of the electrogram amplitude and even complete electrical quiescence (Fig 6B, site h). The amplitude of these low-amplitude potentials was <0.4 mV as opposed to 0.5 to 8 mV in areas located >5 mm from the center of the core.

View larger version (136K): [in this window] [in a new window]   Figure 6. Isochronal activation map (A) and selected bipolar electrograms (B) of an induced atrial reentry that showed slight drifting of its core during the dynamic display. The position of the core of the reentrant wave front is shown with f through j. B, Electrograms recorded from the periphery of the reentrant wave fronts, ie, sites a through e, and from within the drifting core, ie, sites f through j, shown on the isochronal map. The morphology of the electrograms at the periphery of the reentrant wave front remained constant (arrow-headed lines, 6 to 123 ms) and high-amplitude deflections were seen. However, during drifting of the core, fluctuations of 26 ms in the cycle length of the reentry (150 to 176 ms) could be observed. The electrograms in the core did not show regular activation on a beat-to-beat basis. Rather, double potentials (arrows), electrical quiescence, and low-amplitude (<0.4 mV) deflections characterized the electrical profile of the drifting core (compare with Fig 4B). Electrode locations and color codes as in Fig 2.

Estimation of the Central Core Area
In five episodes, the central core of the reentrant wave front remained stationary. The stationary nature of the core enabled us to trace its contour during one complete revolution from consecutive snapshots during the animated display (see Fig 7). In all episodes, the shape of the reentrant atrial wave front appeared circular, similar to our previous simulation studies in which an isotropic excitable medium was used.¹⁴ The mean diameter of the core was 3.9±0.8 mm with a mean surface area of 12±3 mm².

View larger version (96K): [in this window] [in a new window]   Figure 7. Core-size estimation from consecutive snapshots taken during one complete rotation of a stationary reentrant atrial wave front. Time was arbitrarily chosen as zero when the leading edge of the reentry (arrows) was in the middle of the tissue (A). Starting with the wave front in the center (A), the edge of the reentrant wave front near the tip was traced. The process of making continuous tracings of the leading edge of reentry was continued until one full counterclockwise rotation (160 ms) was completed (A through G). The resultant circular area had a diameter of 3 to 4 mm and an area of 11 mm2. This represents the electrically silent core of the reentry. H, Composite diagram made by tracing the leading edge of the wave fronts of the snapshots shown in A through G. The persistence of each colored dot is 10 ms.

Excitable Gap During Reentrant Activity
The presence of an excitable gap was demonstrated by prematurely depolarizing the atrium during reentry with an applied stimulus of twice the diastolic current threshold. Fig 8A illustrates the ability of applied single stimuli to capture prematurely during reentrant activity with a cycle length of 160 ms. In this example, the shortest captured coupling interval during reentry was 80 ms (Fig 8A, electrogram d). This suggests the presence of an excitable gap of 50% of the cycle length. The mean duration of the excitable gap was 93±26 ms (six episodes), which corresponds to a mean of 54% of the cycle length of the reentry. A significant (P<.005) positive linear correlation (r=.94) was found between the cycle length of the reentry and the duration of the excitable gap (Fig 8B).

View larger version (23K): [in this window] [in a new window]   Figure 8. Determination of the excitable gap interval. A, Bipolar electrograms (recorded from the middle top of the tissue) during a reentrant activity that lasted for 22 seconds in an isolated canine right atrial endocardium. The cycle length of the induced reentry was 160 ms. Single stimuli (arrows) were applied at the left middle edge of the tissue at progressively longer recovery intervals after atrial activation (electrograms a through f). The earliest captured interval was 80 ms (asterisk in electrogram d). Stimuli with longer coupling intervals were also associated with capture (asterisks in electrograms e and f). The estimated excitable gap of the reentry was 80 ms (160-80=80 ms). B, Regression of pooled data of six episodes of reentry in a total of six tissues. The abscissa represents the cycle length of the reentry, and the ordinate represents the excitable gap interval. A significant positive linear correlation was found between the excitable gap and the cycle length of the reentry.

New Activation Wave Fronts
During all episodes of induced reentry, new activation wave fronts that were unrelated to the reentrant activity suddenly emerged. These wave fronts arose at the tail of the reentrant wave front a mean of 86±10 ms (13 episodes) after the passage of the reentrant wave front. The early excitation of the tail of the reentrant wave front by a mean of 76 ms (162-86=76 ms) before the arrival of the next expected reentrant excitation provided additional confirmation of the presence of an excitable gap that amounted to 47% of the cycle length of the reentry. The presence of an excitable gap was thus confirmed with both an intrinsically initiated premature wave front and an externally applied single premature point stimulus.

Spontaneous Termination of the Reentry
Fifteen episodes of spontaneous termination of atrial reentry were analyzed. The mean duration of these reentrant wave fronts that terminated spontaneously without applied electrical stimuli was 3.2±2.8 seconds. Thirteen of the 15 episodes terminated when the leading edge of the reentrant wave front and an outside new wave front merged together and excited the core of the reentry. Fig 9 illustrates an example of the events leading to termination of reentry after excitation of the core. The central core area remained electrically silent (Fig 9A through 9H). However, during the second rotation, which starts with Fig 9E, a new wave front emerged at the right middle edge of the tissue at 312 ms (Fig 9H), when the leading edge of the reentrant wave front was in the left middle edge of the tissue. These two wave fronts merged together near the middle of the tissue at 348 ms (Fig 9I). The new wave front formed by the merger of the two wave fronts suddenly penetrated the core and excited it at 376 ms (Fig 9J). The wave front then propagated toward the upper edge of the tissue (Fig 9K), and reentry terminated 75 ms after core excitation. All wave fronts then vanished, and the tissue became quiescent (Fig 9L). Fig 10 shows the electrograms recorded during the termination of reentry shown in Fig 9. Electrograms a to f in Fig 10A were recorded distal to the core, electrograms g to i were recorded within the core, and electrogram j was recorded adjacent to the core, as shown diagrammatically in Fig 10B. During reentry, electrograms a to f in Fig 10A activated sequentially from a to f at a cycle length of 152 ms, whereas the electrodes located in the central core (sites g, h, and i) recorded no electrical activity. Electrode j, located adjacent to the core, showed a relatively low–amplitude potential. During the last cycle of reentry, which began at electrode site a (time, 152 ms) and ended when the wave front reached site e at 272 ms, a new wave front emerged at site a (time, 282 ms), which was 22 ms earlier than the next expected reentrant beat at site a (two periods of 152 ms=304-282=22 ms). This new wave front that originated at site a merged with the incoming reentrant wave front at site f at 296 ms and activated the core electrodes at sites g, h, and i at 300 to 302 ms. After activation of the core, the resulting disrupted wave front propagated toward the top border of the tissue, causing termination of the reentry 75 ms after excitation of the core (see Fig 9J through 9L). Excitation of the core provided evidence that the core of the reentry, while excitable, remained nonexcited during reentry. During regular pacing, the electrodes at sites g, h, and j, which remained electrically silent during reentry, showed full activation (Fig 10C). Similar patterns of events leading to reentry termination were observed in the remaining 12 episodes. The mean time interval between excitation of the core and termination of reentry was 77±18 ms (13 episodes).

View larger version (153K): [in this window] [in a new window]   Figure 9. Termination of reentry during core excitation by wave interference. A through L, Color snapshots (as in Fig 7) taken at different moments (times indicated by numbers under each frame). A through E show one full counterclockwise rotation (arrows) at a period of 152 ms before termination. The white outline in the middle of the tissue represents the core of the reentry, which remained electrically silent during the reentrant activity. During the second rotation, a new wave front emerged from the middle right side of the tissue (H; time, 312 ms; arrows pointing west). This new wave front merged with the incoming front during its second rotation toward the middle of the tissue (I; time, 348 ms) and penetrated the core and excited it (J; time, 376 ms). The wave front then reached the top of the tissue (K) and died out (L). The white outline of the core in K represents the initial location of the core of the reentry.

View larger version (31K): [in this window] [in a new window]   Figure 10. Electrogram characteristics during reentry and during termination. A, Selected electrograms from the periphery (sites a through f) and the core (sites g through j) recorded immediately before and during the termination of reentry shown in Fig 9. B, Diagram showing all the recording sites (a through j) relative to the core position: sites a through f (outside the core), sites g through i (inside the core), and site j (adjacent to the core). The first arrow-headed line in A (times, 0 to 124 ms) shows the electrograms during the first rotation shown in Fig 9. Note the absence of electrical activity in the core during reentry (sites g through i). During the second rotation (A; times, 152 to 296 ms; middle arrow-headed line), a new wave front emerged at 282 ms near site a, as shown in Fig 9H (arrows pointing west). The merger of the two wave fronts was then followed by excitation of the core at 300 to 302 ms, as indicated by the sudden appearance of high-amplitude electrograms in the core at sites g, h, and i. The electrode at site j (302 ms) located at the border of the core also showed a gain in its amplitude during core excitation. C, Activation of the same tissue during regular pacing at a cycle length of 400 ms from the bottom of the tissue. Note that electrograms g through j shown in A and B had high-amplitude deflections during regular pacing, indicating the absence of conduction block at these sites.

In two episodes, termination of reentry occurred when an outside new wave front collided with the leading edge of the reentrant wave front, causing abrupt extinction of the wave fronts and immediate termination of the reentry. Fig 11 illustrates one example of termination caused by collision of the reentrant wave front with a new wave front propagating in a direction opposite to the reentrant wave front and away from the core of the reentry.

View larger version (123K): [in this window] [in a new window]   Figure 11. Termination of reentry caused by the collision between an outside wave front and the reentrant atrial wave front. The snapshots were taken at the times indicated at the bottom of each frame, as in Figs 7 and 9. A through D, One complete clockwise rotation at a cycle length of 153 ms. During the second rotation, a new wave front emerged at the upper left corner of the tissue at 238 ms (F). This new wave front propagated counterclockwise (arrows in F) because tissue refractoriness at the immediate tail of the reentrant wave front prevented clockwise rotation. Collision of the two wave fronts (indicated by two pairs of opposing arrows) occurred at 254 ms (G) and caused immediate termination of reentry. The tissue then became quiescent (I).

Histological Analysis
Histological sections of the right atrial appendage showed normal-looking atrial fibers and a complete absence of anatomic obstacles in all tissues studied. Atrial fiber orientation showed complex distributions where longitudinally oriented fibers encountered fiber tracts that were oblique and/or perpendicular to the main fiber tract (Fig 3B). We could not find a specific relationship between atrial fiber orientation and the site of conduction block. In a given tissue, conduction slowing and conduction block could occur either along or across the fiber orientation.

	Discussion

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In the present study, we demonstrated that functionally based reentrant wave fronts in the isolated right atrium have an excitable gap and a central core that remains excitable but not excited. Excitation of the core leads to termination of reentry as the wave front vanishes at the border of the tissue.

Mechanism of Functional Reentry in the Atrium
Two major characteristics of functional reentry were found in the present study. First, there is an excitable but nonexcited central core, and second, excitation of the core of the functional reentry leads to termination of reentry. It may be argued that block at the core of the reentry may be caused by centripetally conducting waves, and the electrograms at the center will have small amplitudes or display only electrotonic deflections.⁵ It could also be argued that such a block might occur before the exact center of the core is reached, thus leaving the core in a nonexcited state. If this were the case, some of the electrodes in the core might be expected to remain electrically silent after core excitation because of prolonged refractoriness, whereas other electrodes would manifest activation. However, this was not the case. All the electrodes located in the core manifested large-amplitude deflections on excitation of the core. This suggests the absence of block caused by prolonged refractoriness. Therefore, a different mechanism is required to explain the observed block near the core. The spiral wave hypothesis of reentry might provide an insight into the nature of such a block that is independent of refractoriness. According to the spiral wave theory of reentry, the core remains nonexcited because the safety factor for propagation of the wave front near the core (wave front tip) is very low; as a result, it undergoes block even though the cells downstream are fully excitable.^{6 9 10} The safety factor for propagation is governed by the source-sink relationship,^{7 8 9} which may cause block when the curvature of the wave front tip exceeds a certain limit known as the "critical curvature."^{6 9} Core excitation and shortcutting of the reentrant "circuit" are therefore prevented because the leading edge of the reentrant wave front cannot overcome the critical curvature to excite the core. However, the core might be excited when a new wave front merges with the leading edge of the reentry and causes an increase in the intensity of the depolarizing current (source) that overcomes the critical curvature. When such an increase in the intensity of the source occurs, the core might be excited. Therefore, it appears that the mechanism of functional reentry in the atrium is compatible with the spiral model of reentry. The presence of a large excitable gap provides additional indirect evidence; such a gap is shown to be present in the spiral model of reentry^{6 10 15} and absent in the originally proposed leading-circle concept.⁵

Our findings are also incompatible with the mechanisms of anisotropic reentry demonstrated in the ventricular epicardial border zone after myocardial infarction.^{16 17} We did not find a relationship between the areas of slow conduction or block and the underlying atrial fiber orientation. The lack of a specific relationship between fiber orientation and the site of conduction block during reentry is incompatible with anisotropic reentry, because tissue anisotropy is a major cause of reentry in the model of anisotropic reentry.^{16 17}

An Excitable Gap Is Present in the Reentrant Wave Front
An excitable gap was reported to exist in functional reentrant wave fronts in in situ normal ventricles during ventricular fibrillation^{18 19} and during functional reentry at the epicardial border zone, causing ventricular tachycardia.²⁰ An excitable gap was also found in isolated ventricular epicardial slices^{6 15} and in an early study in isolated rabbit atria by Allessie et al.²¹ Therefore, the presence of an excitable gap appears to be compatible with diverse models of functional reentry.

New Activation Wave Fronts: Their Origin and Mechanism
Our ability to trace the complete reentrant circuit, with an area of late activation from the previous cycle spatially adjacent to the earliest activation of the next cycle, indicates that reentry was located on the endocardial surface. However, new wave fronts, independent of the rotating wave front, often emerged at discrete endocardial sites, a finding consistent with previous reports by Schuessler et al.^{22 23} Those authors dismissed automaticity because of the presence of high concentrations of acetylcholine and suggested that the mechanism of these new wave fronts was microreentry,²⁴ ie, <1 mm size scale, which is above the present spatial resolution. These new wave fronts, however, provided a unique opportunity to evaluate their interaction with the central core of reentry.

Excitation of the Core Terminates Reentry
The merger of a new wave front with the leading edge of the reentrant wave front leading to excitation of the core constitutes a major mechanism of termination of functional reentry in the atrium. Direct excitation of the core provides compelling evidence that the core of the reentry remains excitable during reentry.^{6 10} Termination of functional reentry by excitation of the core by an outside wave front has recently been shown in situ in ventricles during fibrillation,¹⁸ in simulation studies,²⁵ and in isolated epicardial ventricular tissues in sheep.¹⁰ Fig 12 illustrates the characteristics of the reentrant wave front in our model. The presence of an excitable gap (Fig 12A) allows the new wave front to merge with the leading edge of the reentrant wave front and excite the core, leading to its termination (Fig 12B). The stimulating efficacy of the leading edge of a functional reentrant wave front is not strong enough (subthreshold) to excite the core because of its pronounced curvature.^{6 9} However, when the curved wave front merges with another wave front, the new activation wave front created by the phenomenon of summation assumes threshold value²⁶ and successfully excites the core. When the core becomes excited, wave front rotation ceases, the newly formed front propagates toward the border of the tissue, and activity is terminated. In two previous studies,^{10 25} it was suggested that excitation of the core shifted the core to the tissue border, causing termination of the reentrant wave front activity.

View larger version (38K): [in this window] [in a new window]   Figure 12. Interaction of a new wave front with the core of the reentry. A, The positions of the interacting outside wave front and the core of the reentrant wave front. The thick black line on the left represents the reentrant wave front rotating in a counterclockwise direction (curved arrow), the gray area indicates the absolute refractory region, and the white dotted area indicates the partial refractory region. The white area, 50% of the circle, represents the excitable tissue. B, The result of the interaction between the two waves. Core excitation by the new wave front disrupted the reentrant wave front and obliterated the core, as it could no longer be defined. The resultant newly formed wave fronts propagated toward the edges of the tissue, leading to termination of the reentry.

Study Limitations
The exact nature of the core excitability (partially or fully excitable) remains undefined because no transmembrane cellular recordings were made from the core. Extracellular electrograms cannot define the cellular nature of the observed electrical silence at the core of reentry. Although we exclusively mapped the endocardial surface without simultaneous epicardial mapping, the full accounting of the reentry (juxtaposition of latest next to earliest activation) indicates that endocardial mapping was adequate. Furthermore, the relatively thin (0.5 to 2 mm) atrial wall could not accommodate intramurally the larger-sized spiral wave core.

Conclusions
The mechanism of functional reentry in the atrium is consistent with a spiral wave of excitation that has an excitable but nonexcited core. Excitation of the core by an outside wave front disrupts the reentrant wave front and leads to termination of reentry as the newly formed wave front migrates toward the border of the tissue. Termination of reentry may also occur when the reentrant wave front collides with an outside wave front.

	Acknowledgments

 
This study was supported in part by an NIH SCOR grant (HL-52319); an NIH FIRST Award (HL-50259); the Cedars-Sinai ECHO Foundation; the Ralph M. Parsons Foundation, Los Angeles Calif; an American Heart Association National Center Grant-in-Aid (92009820) and an AHA Wyeth-Ayerst Established Investigatorship Award (Dr Chen); and a Cedars-Sinai Research Institute Fellowship Award (Dr Ikeda). We thank Prediman K. Shah, MD, for his support of our work, Avile McCullen and Meiling Yuan for their technical assistance, and Elaine Lebowitz for her secretarial assistance.

Received December 19, 1995; revision received April 15, 1996; accepted May 6, 1996.

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