Incomplete Reentry and Epicardial Breakthrough Patterns During Atrial Fibrillation in the Sheep Heart
Background The mechanisms underlying atrial fibrillation and its initiation are not fully understood. Our hypothesis is that atrial fibrillation results from complex activation involving the subendocardial muscle network.
Methods and Results We have used video imaging to study the sequence of activation on the surface of the right atrium of the Langendorff-perfused sheep heart during pacing, atrial fibrillation, and its initiation. We recorded transmembrane potentials simultaneously from over 20 000 sites. We observed two types of patterns of wave propagation during the initiation of atrial fibrillation. The first type resulted from heterogeneities of refractoriness and transmural propagation near the stimulating electrode. The second type involved heterogeneity in conduction away from the pacing site. During atrial fibrillation, the average period of activation was 138±25 ms (n=6), and complete reentrant pathways were never observed. Propagation patterns were characterized by a combination of incomplete reentry, breakthrough patterns, and wave collisions. Incomplete reentry occurred when waves propagated around thin lines of block and then terminated. Breakthrough patterns were frequent and occurred every 215 ms on average. The location of these breakthrough sites and the lines of block during incomplete reentry were not randomly distributed but appeared to be related to preferential propagation in the underlying subendocardial muscle structures. A computer model of atrial free wall connected to a pectinate muscle suggested that subendocardial muscles lead to epicardial breakthrough patterns that act to destabilize reentry.
Conclusions These results suggest that the complex three-dimensional structure of the atria plays a major role in the activation sequences during atrial fibrillation and its initiation.
The cellular mechanisms of AF continue to be a difficult and fascinating problem in the field of cardiac electrophysiology. Indeed, although there is general agreement that AF is most likely a reentrant rhythm disturbance, the precise pathophysiological bases of its initiation and maintenance have not been resolved. In addition, as newer and more sophisticated high-resolution mapping studies have appeared in recent years,1 2 the old controversy of whether AF results from the activity of a simple but irregular “mother wave” (a rotor) cycling at a high frequency in a self-sustaining manner3 4 5 or from actual fractionation of the mother wave into multiple daughter wavelets that become independent offspring6 7 seems to have reemerged.2 8 Thus, it would seem that there is still ample need to revisit the problem of AF.
Moe et al9 10 suggested that the stability of fibrillation was a function of several factors, including a nonuniform distribution of refractory periods, a sufficiently large area of tissue, and a relatively brief refractory period and/or relatively slow conduction velocity of the impulse. Under such conditions, the persistence of the arrhythmia was a matter of statistical probability and depended on the number of independent wavelets. If that number was large, the chance of coalescence into a single wave front was small; if the conduction velocity was large, then coalescence was highly probable; if the refractory period was long, then the number of wavelets would diminish and result in a transition into atrial flutter or sinus rhythm. The above considerations were consistent with the fact that vagal stimulation, which leads to an inhomogeneous abbreviation and thus dispersion of refractory periods, increases the probability of sustained fibrillation.11 12
In 1985, Allessie et al7 were able to map the spread of excitation in the atria of a dog heart during acetylcholine-induced AF and provided the first demonstration in vivo of multiple propagating wavelets giving rise to turbulent atrial activity. Moreover, these investigators estimated that sustaining fibrillation in the canine atrium required a critical number of four to six wavelets, which was supported by the pharmacological experiments of Wang et al13 in which termination of AF by class 1C antiarrhythmic drugs was preceded by a decrease in the mean number of wavelets.
Subsequent experiments in dogs2 14 as well as more recent intraoperative mapping studies in humans15 16 have provided important insight into the characteristics of wave front propagation during fibrillation and have given support to Moe's idea9 10 that multiple wavelets of propagation give rise to the seemingly chaotic activation patterns observed in the ECGs of patients with AF. However, they have not answered many critical questions about the origin of the turbulent activity giving rise to the multiple wavelets. For example, is spontaneously occurring fibrillation the result of a “mother rotor” that breaks and fractionates into multiple independent offspring? What are the fundamental characteristics of the waves and of the tissue that sustains them that enable their coexistence and perpetuation in the form of “fine fibrillation”? In the model by Moe et al,9 a random distribution of refractory periods was essential for the establishment of fibrillation, in such a way that closely apposed cardiac cells could have widely different refractory periods. However, our present knowledge about the electrophysiological characteristics of cardiac tissues indicates that such a random distribution of refractory periods is not possible because the strong electric connections that exist between neighboring cardiac cells tend to greatly diminish any differences that might exist in the duration of their action potentials17 and thus refractory periods. Therefore, it seems that if any dispersion of refractoriness exists in the myocardial mass, such a dispersion occurs as macroscopic spatial gradients18 19 of refractoriness rather than microscopic, randomly distributed temporal dispersion of refractoriness.9 20
Another important question that remains unanswered is what role, if any, the three-dimensional structure and the complex geometry of the atrial myocardium play in the formation and maintenance of multiple wavelet propagation during fibrillation. Spach et al21 showed that repolarization inhomogeneities exist in the right atrium of the dog, with the sinoatrial region displaying the longest repolarization times. It was shown that these repolarization inhomogeneities can provide either a proarrhythmic or antiarrhythmic effect.22 Premature impulses originating in the sinus node region propagated without conduction disturbances, whereas premature beats from sites distal to the sinus node resulted in conduction block at multiple sites. In a recent study, Schuessler et al2 demonstrated that there are specific regions in which the activation of the epicardium and endocardium are discordant, particularly in those areas in which the wall thickness is >0.5 mm. Moreover, such a discordance increases with increases in the excitation frequency, which suggests that during AF, discordant epicardial versus endocardial activation may become critical and lead to functional block, particularly in those regions in which the three-dimensional anatomy of the atrium is most complex.
In the present study, we use high-resolution video imaging to record electric wave propagation on the surface of the right atrium of the sheep during pacing, AF, and its initiation. In addition, we have performed computer simulations in an effort to predict the patterns of wave propagation that might occur in a spatially complex structure such as the right atrium. Overall, these data reveal that atrial activation is not a two-dimensional phenomenon as commonly believed. Particularly during AF, the complex atrial structure and transmural activation play a major role in the atrial excitation patterns.
Langendorff-Perfused Sheep Heart Preparation
Young sheep of either sex (weight, 18 to 40 kg) were anesthetized with sodium pentobarbital (35 mg/kg IV). The heart was rapidly removed through a sternectomy, then connected to the Langendorff apparatus. The coronary arteries were perfused continuously via a cannula in the aortic root with warm Tyrode's solution buffered to a pH of 7.4 under a pressure head of 50 to 60 mm Hg at a rate of 200 to 300 mL/min. The solution consisted of the following (in mmol/L): NaCl, 148; KCl, 5.4; CaCl2, 1.8; MgCl2, 1.0; NaHCO3, 5.8; NaH2PO4, 0.4; glucose, 5.5. The solution was bubbled constantly with 95% oxygen and 5% CO2; the temperature (36°C to 38°C) was monitored by a probe (YSI model 520) inserted into the right or left atrium and connected to a telethermometer. The effluent was discarded for the initial 20 minutes, after which we recirculated the Tyrode's solution. We ensured that the heart was in sinus rhythm and contracting forcefully and rhythmically. To stop the contraction of the heart and thus record the fluorescence associated with the electric activity in the absence of mechanical artifacts, we added DAM to the Tyrode's solution at a final concentration of 10 mmol/L. After this, a bolus injection of 15 mL of the voltage-sensitive dye di-4-ANEPPS (4-[2-[6-(dibutylamino)-2-naphthalenyl]ethenyl)-1-(3-sulfopropyl) pyridinium hydroxide (10 μg/mL) dissolved in DMSO was injected into the coronary arteries. Voltage-sensitive dyes respond linearly to true changes in transmembrane potential and have been used to record transmembrane signals from heart tissue.23 A bipolar EG was recorded by taking the difference of two extracellular electrodes (separation >1 cm) placed on the atrial surface.
High-Resolution Optical Mapping
A diagram of the experimental setup for the Langendorff system is presented in Fig 1A⇓. The video imaging procedure is the same as described earlier for the rabbit heart.24 Briefly, the light from a tungsten-halogen lamp was collimated and made quasimonochromatic by the use of an interference filter (520 nm) together with a heat filter. The light was then reflected 90° from a dichroic mirror (560 nm) so that the light shone on the epicardial surface of the right atrium of the vertically hanging heart. A 50-mm objective lens was used to collect the emitted light with a depth of field of ≈12 mm. The emitted light was transmitted through the emission filter (645 nm) and projected onto a CCD video camera (Cohu 6500). Our video camera may be set to run in an asynchronous reset mode, permitting acquisitions at 120 or even 240 frames/s (sampling at 8.33- and 4.166- ms, respectively; hereafter referred to as 8- and 4-ms sampling intervals). Although the amount of light gathered at the sensors is proportionately reduced because of the reduced integration time, experiments at each sampling rate have shown that there is an adequate signal to reliably measure and analyze the electric activity of our preparations at these rates (see “Results”). The video images (typically 200×100 pixels) of the epicardium of the right atrium were acquired with an A/D frame grabber (Epix) in a noninterlace mode. The frame-grabber board was mounted on a Gateway Pentium computer that was used to process the imaged data. To reveal the signal, the background fluorescence was subtracted from each frame. Low-pass spatial filtering (weighted average of 3×5 or 7×15 neighboring pixels) was applied to improve the signals. The spatial resolution varied with the magnification and spatial filtering but was ≈0.5 mm. A diagram of the right atrial epicardial surface as viewed by the video camera is shown in Fig 1B⇓. The recording area of the video camera was a rectangular region that encompassed most of the free wall of the right atrium.
Ensemble averaging was performed on-line in most pacing experiments to improve the SNR. During paced recordings, the stimulator sent a pulse to the frame grabber to begin acquiring a sequence of video images (a movie) for each beat. The number of acquired frames was set so that the length of each movie was less than the cycle length of stimulation (BCL). Each paced beat was saved in the frame grabber and then the movies were averaged together to achieve one ensemble averaged beat. Because the signal (electric activity) was the same from beat to beat but the noise was different, the SNR improved by √N, where N was the number of beats averaged. The number of beats averaged varied with the size of the image and the pacing rate but ranged from 20 to 50, resulting in a 4× to 7× improvement in the SNR. Ensemble averaging was also performed for sinus rhythm by triggering the movie acquisition from a recording electrode placed near the sinus node.
During our preliminary experiments, we discovered that the green light we have been using for fluorescence excitation penetrates through myocardial tissue and thus may excite the potential dependent fluorescence inside the myocardial wall. This means that changes in membrane potential within the wall contribute to the fluorescence signal and therefore can be detected. This observation may have important practical implications leading to noninvasive optical recording of electric activity within the myocardium.
We achieved optical recording through the atrial wall (transillumination) by transmitting the filtered excitation light via a fiber-optic light guide introduced into the right atrium through the inferior vena cava.25 A single CCD camera was used to record the fluorescence excited by the light source from inside the right atrial cavity and projected through the right atrial free wall. The rest of the experimental setup was identical to that shown in Fig 1A⇑.
Viability and Integrity of the Heart
To determine whether the presence of tissue necrosis affected the recorded excitation patterns, the atria were isolated at the end of each experiment and immediately thereafter incubated for 15 to 30 minutes in phosphate-buffered (pH 7.4) TTC (14 g/L). TTC stains the viable cells of the exposed surfaces of the myocardium red.26 Infarcted myocardium that is depleted of dehydrogenases remains unstained. Thus, areas of tissue necrosis and their borders could be clearly delineated in each piece of tissue.
Image and Signal Processing
Isochrone maps were generated from the sequence of video image of electric activity on the heart surface by analysis of the value of each pixel over time.24 A point in the time plot was labeled as part of a wave front if it was the fastest part of the upstroke, ie, the maximum first derivative. Thresholds helped to eliminate maxima due to noise in the experimental recordings. Because of motion-induced smearing, a set of pixels perpendicular to the motion of the wave front activated in a single frame. Thus, the resulting wave fronts seen in the image data were not lines but bands. Isochrone bands derived from video images required no interpolation of data. Isochrone lines were determined from the borders of the isochrone bands. In some cases, the low SNR made the generation of isochrone lines difficult. In these cases, we determined the activation times on the basis of the point at which the signal from each site became greater than a cutoff fluorescence intensity. The high spatial resolution of the video imaging system allowed localization of the wave front at the sampling times with a high degree of accuracy (W.T. Baxter, MS, unpublished results, 1996).
The determination of conduction velocity is not straightforward, and knowledge of the direction of the propagating wave is necessary to calculate anisotropy and local conduction values. To calculate a global measure of conduction velocity, we computed “activation times” by determining the location and time that the first and last activations occurred on the right atrium. The difference of these two activation times was then divided by the distance between the locations of the corresponding sites to give a global measure of conduction velocity. We called this measure CVavg. In addition, because of the high spatial resolution of our system, we were able to determine the direction of wave propagation with a high degree of accuracy. Therefore, we could use isochrone maps (which required no interpolation between points; see above) to compute the apparent local conduction velocity by calculating the distance between the wave front in successive frames. In this way, apparent conduction velocity could be calculated for various regions and directions. Conduction velocity was calculated in this manner only for recordings at sampling intervals of 4 ms and for which three to four parallel wave fronts were identified.
The APD was measured as the duration of the action potential from the upstroke to the point in time when the voltage had returned to a given proportion of the resting value. This value may be measured from optical recordings in a manner similar to electrode recordings. For optical data, a level of 70% has been chosen to keep the estimates of APD well above the baseline noise.19 For a given pixel during a trial at a fixed stimulating frequency, there may be several complete action potentials. The average of all these APDs was used as the APD for that pixel at that frequency. In some experiments, ensemble averaging was accomplished such that each recorded action potential represented an average of many beats (see above). In this way, APD maps were computed for the entire visible surface (≈20 000 sites) of the preparation, in which the APD was represented by color or gray level. The mean value of each APD map was used as a measure of APD, and the SD of the map was used to study the dispersion of APD. Therefore, for each animal at each frequency, ≈20 000 sites and 3 to 50 beats were averaged to obtain a robust measure of APD.
Data are presented as mean±SD. Comparisons were performed by use of individual or paired Student's t tests where appropriate as well as the nonparametric Wilcoxon test.
Serial sectioning was performed on a 2×4-cm rectangular piece of the sheep right atrium that consisted of a thin free wall and a branching network of pectinate muscles. The specimen was fixed in 10% buffered neutral formalin and washed and embedded in paraffin by use of standard histological techniques. Slices were cut transmurally perpendicular to the crista terminalis and stained by use of Masson's trichrome method, which provided differential staining for muscle bundles and connective tissue.26 The specimen was sliced transmurally on a large microtome to a thickness of 5 μm, and pictures were taken of these slices. Digital images of the slices were acquired by use of the CCD video camera and frame grabber (see above).
For the studies of activation processes in the three-dimensional atrial wall, we have relied on numerical predictions derived from computer models.19 24 27 We have used the simple qualitative approximation given by the FitzHugh-Nagumo–type equations (see Reference 25 for a full description of model equations, advantages, and limitations). This enabled us to perform simulations of wave propagation in generic excitable media and to provide testable predictions about atrial propagation dynamics at a relatively low computational cost. The atrial model incorporates a representation of a segment of the right atrial free wall.\mathit|<|C|<|\cdot|>||>||<|\partial|>|\mathit|<|U|>|/|<|\partial|>|\mathit|<|t|>||<|=|>|\mathit|<|F|>|(\mathit|<|U|>|)|<|-|>|\mathit|<|V|>||<|+|>|\mathit|<|div|>|(\mathit|<|G|>||<|\bigtriangledown|>|\mathit|<|U|>|)|<|+|>|\mathit|<|Ie|>||<|\partial|>|\mathit|<|V|>|/|<|\partial|>|\mathit|<|t|>||<|=|>|(\mathit|<|U|>||<|-|>|\mathit|<|V|>|)/\mathit|<||<|\tau|>||>|(\mathit|<|U|>|)Equation 1 describes the dynamics of an electric potential on the membrane capacitance C due to transmembrane current F(U)−V, external current Ie, and current through intercellular spaces described by the diffusion term div(G▿U); here, G is a conductivity tensor. Equation 2 describes the dynamics of slow ionic current. We have used a piecewise linear function, F(U), and piecewise constant function, τ(U):\mathit|<|F|>|(\mathit|<|U|>|)|<|=|>||<|-|>|\mathit|<|c_|<|1|>|U|>| at \mathit|<|U|>||<|<|>|\mathit|<|e_|<|1|>||>||<|\tau|>|(\mathit|<|U|>|)|<|=|>||<|\tau|>|\mathit|<|_|<|1|>||>| at \mathit|<|U|>||<|<|>|\mathit|<|b_|<|1|>||>|The introduction of the voltage dependence of τ allowed us to decrease recovery time and thus reduce computational cost by minimizing both the rotation period of reentrant waves and the necessary array size. A similar model has been used elsewhere19 27 and has been shown to reproduce all of the main features of reentrant wave dynamics. Parameter values used in calculations of Equations 3 and 4 were similar to those that have been described previously,27 namely, c1=4, c2=0.8, c3=15, and e1=0.018. The parameters a and e2 are found from the continuity condition for F(U): a=1+c1/c2; e2=[(c1+c2)e1+c3]/(c3+c2); τ1=0.5; τ2=16.66; τ3=3.5; b1=0.01; b2=0.95.
Video imaging of atrial activity was recorded in 12 isolated Langendorff-perfused sheep hearts. We carried out initial optical mapping experiments (n=5) to study the electrophysiological characteristics of the right atrial free wall and to gain some insight into the patterns of wave propagation on the atrial epicardial surface. We then studied the patterns of wave propagation on the right atrial epicardium during AF and its initiation (n=7). Different groups of animals were used for pacing and AF studies because the pacing trials and the determination of defibrillation thresholds that usually preceded the AF episodes were time-consuming and could not be accomplished in the same animal. After each experiment, the atria were stained with TTC and visually analyzed for evidence of necrosis. Any atria that showed evidence of necrosis were excluded from the analysis.
Optical Mapping Experiments During Sinus Rhythm and Pacing
Video imaging of wave propagation during sinus rhythm and during pacing at various rates was performed to characterize our preparation and is presented below. The average cycle length during sinus rhythm was 603±50 ms in control and 680±120 ms after the addition of the DAM and dye (n=5; P=NS).
Isochrone Maps and Spatial Patterns of Wave Propagation
Spatial patterns of wave propagation in the right atrium are illustrated as isochrone bands shown in Fig 2⇓ for sinus rhythm (A) and pacing at BCL=500 ms (B) and BCL=150 ms (C) in the same heart. During sinus rhythm at a cycle length of 550 ms, there was nonuniform conduction with a breakthrough site of activity (red) in the RAA. The first activation on the epicardial surface occurred at the sulcus terminalis near its junction with the vena cava. The impulse then rapidly activated the majority of the right atrium in 20.5 ms. The local conduction velocity was uniform except at the RAA, where apparent conduction velocity was more rapid. Pacing from the epicardium at the sulcus terminalis at a rate similar to the sinus rate exhibited a much different pattern of propagation. The conduction velocity was slower and more uniform (Fig 2B⇓). The wave of excitation propagated from the stimulating electrode in an elliptical pattern, with uniform local conduction and no evidence of breakthrough activity. Pacing at a faster rate (BCL=150 ms) showed slower and more heterogeneous conduction patterns (Fig 2C⇓). The vertical conduction velocity exhibited a greater reduction at fast pacing rates than did the horizontal velocity. The fact that a breakthrough pattern was observed during sinus rhythm but a uniform pattern of propagation during pacing was observed on the epicardial surface indicates the possibility that preferential propagation was occurring through the subepicardial pathways.
The right atrium was paced by use of pulses of 1.5 to 2.0× the threshold amplitude with a duration of 10 ms (threshold was determined at a pacing cycle length of 500 ms). The average APD was calculated for BCLs from 500 to 150 ms (see “Methods”). The cycle length dependence of APD is illustrated in Fig 3A⇓. Recall that each APD value from each animal is an average of 10 000 to 20 000 sites from 3 to 50 beats. The APD decreased from 134 to 95 ms as BCL was decreased from 500 to 150 ms and displayed a steady-state APD versus BCL relationship similar to that in the dog.28 The inset of Fig 3A⇓ shows an action potential from the center of the free wall at BCLs of 500 and 150 ms. For these experiments, the limit of 1:1 wave propagation was ≈150 ms. Alternans and Wenckebach-like patterns were observed only for BCLs close to the limit of 1:1 propagation. The shortest cycle length at which we observed changes on a beat-to-beat basis was 160 ms.
APD Dispersion and BCL
Our original hypothesis was that the initiation of reentry that occurred when the right atrium was paced at fast rates was due to an increase in the spatial heterogeneity of refractoriness.20 We attempted to show this by calculating the dispersion of APD (coefficient of variation of APD) as a function of cycle length. This relationship is shown in Fig 3B⇑. Surprisingly, the dispersion of APD did not increase at faster rates, which indicates that another mechanism was responsible for the induction of reentry. It is important to note, however, that although no gradients in APD were observed on the epicardial surface of the atrium during pacing at twice the diastolic threshold, we cannot rule out the possibility that transmural gradients in APD developed at fast rates.
Conduction Velocity and Anisotropy
As illustrated in Fig 4A⇓, the CVavg on the epicardial surface of the atrial free wall decreased as BCL was decreased. The CVavg ranged from 51.7±7.9 cm/s at BCL=500 ms to 34.7±4.1 cm/s at BCL=150 ms. The CVavg during sinus rhythm was 55.3±4.6 cm/s and was not statistically different from that at BCL=500 ms. The isochrone maps from the pacing sequences recorded by use of the 4-ms sampling interval (see Fig 2⇑) were used to calculate apparent conduction velocity in the horizontal and vertical directions of the isolated free hanging heart (n=4). The horizontal direction was always the direction of fastest propagation and roughly corresponded to the direction of the sulcus terminalis along the roof of the right atrium. The local apparent conduction velocity data are shown in Fig 4B⇓. Both horizontal and vertical conduction velocities decreased as BCL was lowered. A nonparametric Wilcoxon test indicated the velocity was greater in the horizontal direction (P<.05). The greatest difference was at BCL=160 ms, at which level the horizontal conduction velocity was 50.8±9.7 cm/s and the vertical velocity was 32.3±4.5 cm/s. Therefore, the anisotropic ratio was different from 1 and was 1.6 at BCL=160 ms. In one preparation, the stimulus was applied at three sites: (1) the roof of the right atrium on the sulcus terminalis, (2) the RAA, and (3) near the inferior vena cava. No statistical differences were observed between sites.
Because wavelength is the product of refractory period and conductance velocity (CV), the wavelength could only be determined at the shortest BCLs, at which the APD was similar to the refractory period. The wavelength at BCL=160 ms was calculated as CV×APD70/0.7 to account for the fact that the APD was calculated at 70% repolarization. The wavelength at BCL=160 ms was 4.9±0.8 cm in the vertical direction and 7.1±1.5 cm in the horizontal direction.
Optical Mapping of Reentry Initiation
We observed two types of patterns of wave propagation during the initiation of atrial arrhythmias induced by point stimulation on the epicardial surface. The first type was the result of heterogeneities of refractoriness and transmural propagation near the stimulating electrode (type I). The second type involved heterogeneity in conduction away from the pacing site (type II).
Type I: Heterogeneities of Refractoriness and Transmural Propagation
Transillumination versus epifluorescence
Previous experiments in the isolated dog right atrium2 have indicated that propagation in the epicardium and the endocardium may be discordant, particularly at fast rates. To determine what role such a discordant propagation may have in the initiation of reentry, rapid pacing (BCL=140 ms) from the epicardial surface by use of 10-ms pulses of 5× the diastolic threshold was performed in two sequential episodes in the same experiment, with the first paced beat triggering the beginning of the optical and EG recording acquisition. The first episode was recorded by use of epifluorescence, whereas the second recording used transillumination. Fig 5⇓ shows the 8-ms color isochrone maps (red=0 to 8 ms) from beat numbers one and three for epifluorescence (left) and transillumination (right) recorded during pacing at a rate of 140 ms on the epicardial surface of the right atrium. Beat one is shown at the top, beat three is shown at the bottom, and the EG is shown in the middle. Notice that the EGs were almost identical for both epifluorescence and transillumination, suggesting that the underlying electric activity was very similar in the two experiments. The first beat initiated by the pacing protocol spread uniformly away from the stimulating electrode, and the majority of the atrium was depolarized within 33 ms (Fig 5⇓, top). The subsequent beats arrived before full repolarization. These beats exhibited slow conduction and a Wenckebach-like pattern at the site of the EG, as demonstrated by the beat-to-beat increase in the interval between the stimulus artifact and the excitation complex. During beat three, the wave failed to propagate downward from the stimulation site. It propagated in the upward direction but was not observed as continuous conduction on the epicardium (Fig 5⇓, bottom left). Breakthrough sites (green) were evident ≈4 mm above the stimulating electrode. The wave front then proceeded to the left and to the right with a slower conduction velocity. We hypothesized that the breakthrough was the result of transmural activation at the site of stimulation with continuous activation in the subendocardium and subsequent propagation upward and in the epicardial direction. To test this hypothesis, we positioned a fiber-optic cable within the right atrium to record the transillumination signal for the same stimulation protocol. The isochrone map for beat three that used transillumination is shown in Fig 5⇓ (bottom right). Notice that a continuous pattern of wave propagation was observed, which indicates that our hypothesis was correct. By recording the signal through the atrial wall, we could observe the continuous activity upward from the site of stimulation. The remaining pattern of activity that resulted from beat three is similar to the epifluorescence experiment, indicating transmural activation throughout.
As was shown by the data presented in Fig 3B⇑, during stimulation with pulses of 1.5 to 2.0× the threshold amplitude, the global measure of APD dispersion (coefficient of variation) did not exhibit frequency dependence as expected. However, at higher stimulus strengths, APD increased near the stimulating electrode, which led to large spatial gradients in APD. Such gradients were manifested at high rates of stimulation, as in the case of Fig 5⇑, which shows that rapid pacing (BCL=140 ms) with pulses of 5× the diastolic threshold led to conduction block near the stimulation site during beat 3. In this experiment, pacing was continued for a total of 10 beats (not shown), after which nonsustained repetitive activity was observed, which indicated that the pacing protocol initiated an arrhythmia. During beat 5, the wave front circumventing the stimulus site to the left side of the preparation blocked, allowing reentry to develop in the clockwise direction.
APD gradients and unidirectional block
The area of unidirectional block in the experiment shown in Fig 5⇑ corresponds to the region of long APD when stimulating at fast rates. To study the effect of APD gradients on the initiation of this arrhythmia, we paced the same preparation at BCLs of 400 and 200 ms and constructed APD maps. The high spatial resolution of the video camera permits the construction of such maps and enables the direct visualization and quantification of spatial dispersion (nonuniformity) of APD. APD maps were generated for a large area of the anterior free wall of the right atrium for both BCLs, and the same rectangular region of 22 500 pixels was selected for analysis at the two pacing rates. A rectangular region was chosen to eliminate the errors that occur near the edge of the image (W.T. Baxter, MS, et al, unpublished results, 1995). The APDs for the two BCLs ranged from 90 to 165 ms and are color coded (red to purple) in the APD maps shown in Fig 6⇓ (Fig 6A⇓: BCL=400 ms; Fig 6B⇓: BCL=200 ms). The histograms of the APD maps are shown at the bottom of Fig 6⇓. The mean APD was shorter for the faster pacing rate (122 versus 147 ms). In addition, in this experiment, the dispersion of APD as measured by the normalized SD (SD/mean) was greater for BCL=200 than for BCL=400 ms (11% versus 5%, respectively). Furthermore, for both pacing rates, the area near the tip of the stimulating electrode showed the longest APD. This caused a pronounced gradient in APD at BCL=200 ms (Fig 6B⇓). The increased APD near the stimulating electrode provided a substrate for conduction abnormalities that led to wave breaks and arrhythmogenesis.
Type II: Heterogeneities of Conduction Distal to the Pacing Site
Reentry could also be initiated as a result of heterogeneity in conduction away from the pacing site. Fig 7⇓ shows an isochrone map of beat eight in an episode in which reentry was initiated by burst pacing using a sequence of 10 pulses (BCL=220 ms). In this case, pacing caused the wave to block below and to the left of the stimulating electrode, leading to a wave propagating counterclockwise that collided with the next paced beat. When the stimulator was turned off, the counterclockwise wave continued rotating unimpeded, leading to a reentrant arrhythmia. This is illustrated in Fig 7B⇓, which shows individual pixel recordings from five different sites on the surface of the right atrium (see Fig 7A⇓) during 1200 ms of activity.
Although reentrant patterns were observed transiently on the epicardial surface during the initiation of AF, we never observed more than one rotation of a reentrant circuit exhibiting continuous propagation. Fig 8⇓ shows two sequential isochrone maps (Fig 8A and 8B⇓⇓) calculated from video recordings obtained during the transition to AF. The recordings from 5 sites are shown in Fig 8C⇓. In the beat shown in Fig 8A⇓, these 5 sites were located around the line of block, and electrotonic effects were observed in sites 2 and 4, which were located on opposite sides of the line of block. In the beat shown in Fig 8B⇓, however, the line of block moved, and then sites 2 and 4 activated within 8 ms of each other. These maps display complete reentrant loops; however, activation was not continuous along the reentrant circuit. There were long intervals during which the wave front was not observed on the epicardial surface. For example, the interval between the last activation shown in Fig 8A⇓ and the first activation of the next beat (Fig 8B⇓) was 75 ms. The average value for this interval was 78±5 ms (n=7). It should be noted that only rarely did two sequential beats exhibit similar reentrant patterns as shown in Fig 8⇓.
The isochrone maps displayed in Fig 8⇑ show reentrant waves propagating around very narrow lines of block in the right atrium free wall. These lines of block were oriented mainly along the horizontal direction, although they usually exhibited slight curvature (see Fig 8⇑). We estimated the length of these lines of block by drawing a series of straight lines on the isochrone maps. The average length of these lines of block was 1.8±0.3 cm (n=7). The average difference between latest and earliest activations within one beat was 168±60 ms (this interval was shorter than the arrhythmia period owing to noncontinuous wave propagation). The conduction velocity around these lines of block was calculated from the difference of the earliest and latest activations and 2× the length of the functional circuit (24.4±8.8 cm/s). This value is the time it takes the tip of the wave to traverse the circuit divided by twice the length of the line of block. This value of conduction velocity is different from the horizontal conduction velocity (P<.005) and the vertical velocity (P<.05) at BCL=160 ms. The arrhythmia period during these beats was 246±55 ms; therefore, the slow conduction was not due to the rate of the arrhythmia but most likely was due to the steep curvature (isochrones are oblique, not perpendicular to the line of block, in Fig 8⇑) at the edge of the wave front propagating around these thin lines of block.24 27 29
Optical Mapping of AF
We analyzed 15 episodes of AF from six animals. We studied the patterns of activation from the epicardial surface of the right atrial free wall of the Langendorff-perfused sheep heart. In the Langendorff-perfused heart, the patterns of wave propagation during AF were complex. During AF, the average period of activation was 138±25 ms, and complete reentrant pathways were never observed on the epicardium. The propagation patterns were characterized by a combination of incomplete reentry, breakthrough patterns, and collisions of waves.
In Fig 9⇓, we show 4-ms isochrone maps from a 600-ms interval (Fig 9A through 9E⇓) of an episode of AF recorded from the epicardium. A horizontal pseudo EG, obtained by integrating the transmembrane signal both on the right and left sides of the image and taking the difference,24 27 is shown in Fig 9G⇓, with a horizontal bar indicating the time interval used to create the isochrone maps. Fig 9A⇓ shows the first wave, which propagated from the left side of the preparation at t=29 ms (red) and blocked in the middle, then propagated at the top and bottom but later blocked. These conduction block patterns were the result of late activation in the previous sequence. At t=117 ms, a breakthrough (light blue) occurred at the right side; the wave front propagated to the left and then curled down and back to the right but blocked at t=158 ms (purple). Fig 9B⇓ shows the next wave, which entered the top left of the preparation at t=167 ms (red) and collided with a wave that entered from the top at t=175 ms (yellow) and then stopped because of refractoriness on the right side of the right atrial free wall (black). Another wave entered the bottom left at t=192 ms (green) but blocked immediately. Later, at t=204 ms and t=208 ms, two new waves, one entering from the lower left (blue) and the other from the bottom (blue), collided and blocked. Fig 9C⇓ shows a wave that entered from the right at t=246 ms (red), blocked near the top, but propagated to the left and then curled upward and back to the right, displaying conduction block at t=313 ms. This wave collided with another wave (blue) that entered from the top right at t=292 ms and then blocked shortly thereafter (t=308 ms). In Fig 9D⇓, two waves (red) are shown that appeared during the next beat, one at t=371 ms that started in the RAA (top right) and then conducted downward and subsequently curled toward the left and collided with the other wave beginning at the lower left of the preparation (t=375 ms). The wave that came from the lower left propagated upward, then to the right, and then blocked at t=463 ms. Fig 9E⇓ shows a wave (red) that conducted from the upper right at t=521 ms and fused with a breakthrough site near the center of the right atrial free wall (t=525 ms) and then curled upward and back to the right, blocking in a similar manner to that in the previous beat at t=579 ms.
We attempted to determine the relationship between cycle length and conduction block from epicardial recordings during AF. However, the sites that exhibited conduction block at a certain instant were not correlated with the previous cycle length at that point. That is, there was no statistical difference between the cycle lengths for propagated beats and for blocked beats. For example, in Fig 9C⇑, the wave blocked at the upper right of the image, although there was no heterogeneity in refractoriness in this region. Fig 9F⇑ shows the signals from two neighboring sites (separated by 2.8 mm) near the region of block shown in Fig 9C⇑ (the asterisk in Fig 9C⇑ indicates the location of these sites). The sites exhibited similar patterns of activity from the beginning of the recording (Fig 9A⇑), and both sites activated at t=125 ms. When the next wave propagated into this region (Fig 9B⇑), site 1 activated at t=271 ms, but site 2 blocked. The wave then circumvented a line of block, propagating to the left, then curling upward and back to the right, activating site 2 at t=304 ms. Therefore, the wave propagated through site 1 154 ms after the previous activation but blocked at site 2. The reason conduction block occurred in this region is not clear, but it appears that the block was not due to heterogeneity in refractoriness.
We analyzed >5 seconds of epicardial activation patterns in two right atria during sustained AF to study breakthrough patterns and incomplete reentry. Breakthrough sites were identified as the center of regions in which activation initiated and propagated in all directions. Furthermore, breakthrough sites were restricted to regions in which epicardial activation in the surrounding sites did not activate 40 ms before the breakthrough in all directions. Breakthrough patterns were very frequent and occurred every 215 ms on average. However, ≈20% of these breakthrough sites occurred as pairs. The locations of the breakthrough sites are shown for two animals in Fig 10A⇓. The locations of the breakthrough sites were not randomly distributed but were located approximately along the horizontal direction in the middle of the right atrium and the RAA.
To calculate lines of block during AF, we defined incomplete reentry as waves that propagated completely (360°) around thin lines of block and then terminated as described above. Only waves that rotated completely around thin lines of block were analyzed; however, rotating waves were often interrupted by collisions with outside waves. The lines of block during incomplete reentry are shown for the two atria in Fig 10B⇑. The length of these lines of block ranged from 0.92 to 3.4 cm (mean±SD, 2.1±0.7 cm). The locations of the lines of block during incomplete reentry were concentrated in the middle to lower right atrium and the RAA, where there is a dense endocardial network of pectinate muscles. Furthermore, these sites of block qualitatively corresponded to the breakthrough sites.
To correlate the breakthrough sites and the lines of block to the subendocardial structure, we sectioned a portion of a sheep right atrium (see “Methods”). Fig 11⇓ shows a diagram of the intact right atrium and three thin (5-μm) sections cut transmurally. The three sections shown in Fig 11⇓ were taken from the tissue 5 mm apart and approximately at the locations of the gray vertical bars. The crista terminalis separates the smooth portion of the excitable tissue of the vena cava from the pectinate muscle structure of the right atrial subendocardium. The right atrium comprises of a thin sheet attached to pectinate muscle bundles. Three main muscle bundles as well as the crista terminalis are oriented horizontally in the right atrial free wall. The direction of these bundles corresponds to the lines of block and the location of breakthrough sites shown in Fig 10⇑. In addition, the pectinate muscle bundles are thickest and most complicated in the RAA.
Destabilization of Reentry in Computer Model
To provide additional insight into the effects of the subendocardial atrial structure on reentrant arrhythmias, we investigated the excitation patterns associated with reentrant activation in a “pectinate muscle bridge” model. As described above, we did not observe well-organized reentrant activity on the epicardial surface of the right atrium for more than one beat. In addition, epicardial breakthrough wave fronts occurred frequently during AF, and their location was related to the atrial structure. Taken together, the above data suggest that propagation through a pectinate muscle into the underlying atrial free wall may act to destabilize functional reentry by the interaction of such wave fronts with any reentrant activation front that may form in the atrial free wall. We tested this hypothesis in computer simulations using an oversimplified model in which a single pectinate muscle bundle was attached to a two-dimensional epicardial sheet. Simulations using such a “handle” model demonstrated that even a simple bridge connecting two sites on a sheet acts to destabilize reentrant vortices. We first used a two-dimensional sheet (80×80 matrix) incorporating simple Fitzhugh kinetics (see “Methods”). We initiated a spiral wave with S1-S2 cross-field stimulation that induced a spiral wave that rotated around a circular core and whose location was determined by the timing of the premature S2 wave.27 For these parameters, the spiral wave was stationary and gave rise to repetitive activation sequences. A snapshot of activity and the horizontal pseudo EG,24 27 which exhibited a stable monomorphic pattern, are shown in Fig 12A⇓. The potential distribution in space U(x,y) is displayed as gray levels, with white being maximum excitation and black complete rest.
After 13 rotations, the geometry of the matrix was changed by connection of a thin handle (6 cells wide, 3 cells thick) to the top of the two-dimensional grid as shown in Fig 12B⇑. Only the ends of the handle were attached to the grid. The diffusion coefficient (see “Methods”) in the handle was 2× greater than in the sheet. The right end of the handle was placed within the core region of the stationary spiral. The length of the handle was varied, and therefore the left end of the handle was placed at various horizontal locations at the same vertical location (row) as the right end. The right end of the handle is shown in Fig 12C through 12E⇑ as an asterisk, and the left end is labeled as a circle. As the spiral rotated, waves propagated up through the left end of the handle, traveled along its length, and finally invaded the silent core region as a breakthrough, which destabilized the core and led to spiral drift. The direction of drift was determined by the phase of the spiral when the breakthroughs occurred, which was further governed by the length of the handle. For long (>36 cells) and short (<32 cells) handle lengths, the spiral was eventually pushed to one of the edges of the matrix. For handles of intermediate lengths (32 to 36 cells), however, the spiral drifted over to the left side of the handle, where it then interacted with the left junction. The data in Fig 12C through 12E⇑ correspond to a simulation for a handle length of 36 cells. Fig 12C⇑ shows the initial position of the rotor. Because the right end of the handle was located within the silent core region, initially no activity propagated through this end. As the spiral wave rotated, however, a wave front entered the handle from its left end and then invaded the core region as a breakthrough (Fig 12D⇑). This acted to push the spiral wave core toward the left. This pattern of activity continued, with breakthrough patterns emerging from the right end of the handle and forcing the spiral to move toward the other end. After 9 rotations, the core reached the left end of the handle and interrupted the left-to-right sequence of propagation in the handle (Fig 12E⇑). This resulted in a transient pause in activity along the handle. After one period, however, the spiral wave front activated the right end of the handle, causing waves to propagate along the handle from right to left. The horizontal pseudo EG shown in the bottom panel of Fig 12⇑ exhibits a complex pattern similar to AF. The resulting dynamics were strongly influenced by the size of the junctions. For junctions comparable to the size of the core, the spiral core remained in the vicinity of the left junction, but for junction sizes smaller than the core, the position of the core oscillated between the two junctions. These results show that even a single pectinate muscle bundle can have profound effects on the dynamics of reentry and that the pseudo EGs from these simulations exhibited complex patterns similar to those in AF.
Are the Atria Functionally Three-dimensional Structures?
It has generally been accepted that the atria behave electrophysiologically as two-dimensional sheets. The right and left atria, however, are composed of a thin epicardial sheet attached to a complex pectinate muscle structure. In fact, there is much evidence supporting the notion that the complex anisotropic structure plays a role in wave propagation.2 21 22 To study wave propagation in the epicardium, we first stimulated the epicardial surface and observed an elliptical spread of activation that was slightly modified at high rates. The anisotropic ratio was nearly 1 except at high rates, at which it changed to 1.6. This ratio is much smaller than the ratio of 10 observed along the pectinate muscles on the endocardium.30 Our data suggest that the interaction between the thin epicardial sheet and the pectinate muscle is complex and requires further investigation. In addition, transillumination revealed that activation sequences exhibiting breakthrough patterns could result from continuous activation in heart cells beneath the epicardium (Fig 5⇑). Furthermore, the activation patterns during AF and its initiation give strong support to the idea that AF is a three-dimensional phenomenon. During AF and its initiation, we observed incomplete reentry in which activation was not continuous along the reentrant circuit. Histological analysis suggested that these thin lines of block corresponded to anatomic heterogeneities (eg, major pectinate muscle bundles) on the endocardium. There was a long interval (78 ms) during which no epicardial activation occurred (Fig 8⇑), which suggests that part of the reentrant pathway involved transmural propagation. During sustained AF, we observed frequent breakthrough patterns of activity at sites that were probably related to the pectinate muscle network. Although we cannot rule out ectopic foci, the fact that 20% of these breakthrough sites occurred as pairs strongly suggests that they resulted from transmural activation. Our modeling studies also suggest that these breakthrough patterns resulted from transmural activation through pectinate muscle bundles.
Initiation of Atrial Arrhythmias
We observed two types of activation sequences during the initiation of atrial arrhythmias induced by point stimulation on the epicardial surface. At low stimulation strengths (2× threshold at BCL=500 ms), heterogeneous conduction occurred away from the pacing site. APD maps showed no relationship between the spatial pattern of APD and heterogeneous conduction patterns. Furthermore, the dispersion of APD did not increase at fast rates (Fig 3B⇑), which suggests that dispersion of refractoriness was not the mechanism for the induction of arrhythmias in our preparations. However, at high stimulation strengths (5× threshold), APD was prolonged near the pacing site (Fig 6⇑) and subepicardial propagation was observed near the stimulation site (Fig 5⇑). These sites of prolonged APD resulted in transient lines of block that led to the initiation of reentry. APD maps revealed that gradients in APD were related to the induction of reentrant arrhythmias only at very high unphysiological stimulation strengths. The spatial dispersion of APD was only measured on the epicardial surface; therefore, we cannot rule out the possibility of transmural APD gradients developed at fast rates.
Atrial Reentry and Fibrillation
The length of the incomplete reentrant circuits calculated from isochrone maps was 1.8 cm during the initiation of AF and 2.1 cm during sustained AF. All together, the length of these lines of block was 2.0±0.6 cm. Two times the length of these lines of block (ie, the length of the reentrant pathway: 4.0 cm) was shorter than the wavelength in the horizontal direction (7.1 cm; P<.05) and in the vertical direction (4.9 cm; P=NS). Depending on the orientation of the line of block, the length of the reentrant pathway for continuous propagation to occur would range from 4.9 to 7.1 cm (vertical and horizontal wavelengths at BCL=160 ms). If the head of a reentrant wave followed a path length less than this wavelength, the wave would block because the wave front would collide with tissue that was refractory. The lines of block were oriented mostly along the horizontal direction (see Figs 8 and 10⇑⇑) and were shorter than the horizontal wavelength; therefore, this mechanism may explain the phenomenon of incomplete reentry that we observed. Furthermore, we never observed a reentrant wave propagating continuously on the epicardial surface for more than one rotation. The values of wavelength that we observed (5 to 7 cm) for the 20-kg sheep compare favorably with data reported by Rensma et al,31 who estimated the atrial wavelength of the 30-kg dog to be ≈6 to 7 cm.
Our recordings of AF in the sheep heart are consistent with those observed in both intact canine and human atria.7 32 The sequences of activation on the right atrial free wall during AF in canines and humans show incomplete reentry and breakthrough patterns similar to our recordings.7 32 In fact, in the study by Allessie et al,7 only exceptional cases showed that an impulse followed the same circular route more than once. In addition, the lifetime of the individual AF wavelets was short, and rotating waves rarely survived for more than a few hundred milliseconds. In the intact heart, we saw multiple breakthrough sites that were not randomly distributed. Furthermore, the sites of incomplete reentry were oriented horizontally and appeared to correspond to the breakthrough sites. Thus, it seems likely that the observations by us and others of apparently short-lived and often incomplete vortices of reentrant activity as well as breakthrough patterns during AF are the result of the complex, highly dimensional structure of the atria, which enables discordant epicardial and endocardial activation and the appearance of multiple sites of block and breakthrough sites. Hence, our results support the idea that traditional concepts that view the mechanisms of AF in the light of two-dimensional multiple wavelet propagation need to be revisited. It should be noted that we concentrated on the activation patterns and underlying geometry in the right atrium. However, the left atrium also has a complex subendocardial structure, and previous studies7 have suggested that interaction between the right and left atria plays an important role during AF.
Atrial Versus Ventricular Arrhythmias
The complexity of the atrial arrhythmias observed in our experiments seems much greater than the complexity of ventricular arrhythmias that we have observed previously in our laboratory. In the ventricles, reentrant spiral waves were observed.24 The organizing centers of these spiral waves were elliptical and could drift over much of the ventricular surface.24 33 In the intact atrium, however, we have never seen a reentrant wave on the epicardium for more than one beat. Furthermore, these reentrant waves rotated around very thin lines of conduction block (Fig 8⇑). Moreover, in our atrial experiments, there was no relationship between refractory period and conduction block as was shown for intact ventricles.34 In fact, nearby regions exhibited heterogeneous conduction despite being in a similar phase of repolarization (Fig 9F⇑). Therefore, an excitable gap could not be determined as was done for intact ventricles.34 However, the large variability in cycle length in our experiments is consistent with the findings of Kirchhof et al14 that an excitable gap exists in the atrium during fibrillation. Our results strongly suggest that the complexity of the atrial structure, particularly in regard to the highly heterogeneous macroscopic branching and irregular networking of pectinate muscles, plays a major role in the mechanism of fibrillation. Our modeling results show that simply adding a “pectinate muscle bridge” to a two-dimensional sheet of tissue acts to destabilize reentry. Furthermore, our simulations revealed breakthrough patterns at the site of the sheet pectinate muscle junction and irregular activation patterns characteristic of AF. Our results suggest that bringing together our knowledge of atrial structure with our understanding of the dynamics of nonlinear wave propagation in excitable media may lead to accurate, quantitative models of AF. Such models may be useful in providing testable predictions about complex propagation in the atrium and about the manner in which fibrillation is initiated and perpetuated.
Advantages of Our Technique
This article presents the first recordings of activation sequences of the intact atria made by use of video imaging. Several unique advantages are offered by this technique. First, video imaging provides high spatial resolution, with simultaneous recordings from 10 000 to 30 000 sites. This is two orders of magnitude greater than typical extracellular recordings. Even after spatial filtering, the spatial resolution was always <1 mm. Second, the fluorescent signal recorded is directly proportional to the transmembrane potential, which allows repolarization to be studied. Third, the activation pattern can be related to the underlying anatomy with a high degree of accuracy (0.01 mm2). Finally, video imaging allowed us to study transmural activation by inserting a fiber-optic cable inside the right atrium and recording a signal representing all levels of myocardium.25
Limitations of Our Technique
Many of our recordings were from the epicardial surface of the atria. It has been calculated that the signal recorded during epifluorescence recordings is from a layer of cells 0.3 mm thick.35 This thickness is certainly thinner than the portion of myocardium connected via pectinate muscles. Therefore, the epicardial recordings reveal mostly surface phenomena. This may be an important limitation, because there is considerable evidence from our data that transmural activation played a large role in the activation sequences in the atria. However, the technique of transillumination allows us to gain significant insight into the degree of discordance between epicardial and endocardial activation and into the specific pathways followed by the wave fronts responsible for transmural activation. Another limitation of our study is that we used DAM to remove the electric-mechanical interaction in the cardiac cells. DAM has minor effects including a shortening of APD in sheep ventricular muscle,36 but its effects on atrial tissue have been less studied. Because the mechanical contractions of heart cells are delayed ≈100 ms from the electric activity, we could use video imaging to track the wave fronts of individual beats without DAM. In three Langendorff preparations, we calculated the total activation time and CVavg of the right atrium during sinus rhythm in the absence of DAM, and these values were not different from those obtained in the presence of DAM.
Selected Abbreviations and Acronyms
|APD||=||action potential duration|
|BCL||=||basic cycle length|
|CVavg||=||average (mean) conduction velocity|
|RAA||=||right atrial appendage|
This study was supported by grants P01-HL39707 and RO1-HL29439 from the National Heart, Lung, and Blood Institute, National Institutes of Health, grant No. 94016950 from the American Heart Association, and an educational grant from InControl, Inc. This work was completed during the Michael Bilitch NASPE fellowship awarded to Dr Gray. We would like to thank Jiang Jiang, LaVerne Gilbert, Jianping Chen, Evan Foster, and JoAnne Getchonis for technical assistance. A CL+ ink jet color printer (SUN Microsystems Inc) was used in the preparation of the color figures.
- Received January 8, 1996.
- Revision received May 31, 1996.
- Accepted June 12, 1996.
- Copyright © 1996 by American Heart Association
Schuessler RB, Kawamoto T, Hand DE, Mitsuno M, Bromberg BI, Cox JL, Boineau JP. Simultaneous epicardial and endocardial activation sequence mapping in the isolated canine right atrium. Circulation. 1993;88:250-263.
Mines GR. On circulating excitations in heart muscle and their possible relation to tachycardia and fibrillation. Trans R Soc Can. 1914;8:43-52.
Garrey W. The nature of fibrillary contraction of the heart: its relation to tissue mass and form. Am J Physiol. 1914;33:397-414.
Lewis T. The Mechanism and Graphic Registration of the Heart Beat. 3rd ed. London, England: Shaw & Sons; 1925:319-374.
Allessie MA, Lammers WEJEP, Bonke FIM, Hollen J. Experimental evaluation of Moe's multiple wavelet hypothesis of atrial fibrillation. In: Zipes DP, Jalife J, eds. Cardiac Electrophysiology and Arrhythmias. Orlando, Fla: Grune & Stratton; 1985:265-275.
Ortiz J, Niwano S, Abe H, Rudy Y, Johnson NJ, Waldo AL. Mapping the conversion of atrial flutter to atrial fibrillation and atrial fibrillation to atrial flutter: insights into mechanisms. Circ Res. 1994;74:882-894.
Moe GK. Computer simulation of cardiac arrhythmias. In: Manning GW, Ahuja SP, eds. Electrical Activity of the Heart. Springfield, Ill: Charles C. Thomas; 1969.
Wang J, Bourne GW, Wang Z, Villemaire C, Talajic M, Nattel S. Comparative mechanism of antiarrhythmic drug action in experimental atrial fibrillation: importance of use-dependent effects on refractoriness. Circulation. 1993;88:1030-1044.
Kirchhof CJHJ, Chorro F, Scheffer GJ, Brugada J, Konings K, Zetelaki Z, Allessie M. Regional entrainment of atrial fibrillation studied by high-resolution mapping in open-chest dogs. Circulation. 1993;88:736-749.
Cox JL, Canavan TE, Schuessler RB, Cain ME, Lindsay BD, Stone C, Smith PK, Corr PB, Boineau JP. The surgical treatment of atrial fibrillation, II: intraoperative electrophysiologic mapping and description of the electrophysiologic basis of atrial flutter and atrial fibrillation. J Thorac Cardiovasc Surg. 1991;101:406-426.
Koninigs KTS, Kirchhof CJHJ, Smeets JRLM, Wellens HJJ, Penn OC, Allessie MA. High density mapping of electrically induced atrial fibrillation in man. Circulation. 1994;89:1665-1680.
Mendez C, Mueller WJ, Merideth J, Moe GK. Interactions of transmembrane potentials in canine Purkinje fibers and at Purkinje fiber-muscle junctions. Circ Res. 1969;24:361-372.
Rosenbaum DS, Kaplan DT, Kanay A, Jackson L, Garan H, Cohen RJ, Salama G. Repolarization inhomogeneities in ventricular myocardium change dynamically with abrupt cycle length shortening. Circulation. 1991;84:1333-1345.
Davidenko JM, Pertsov AM, Baxter WT, Salomonsz R, Cabo C, Jalife J. High resolution mapping of action potential duration gradients in isolated sheep epicardial muscle. Circulation. 1993;88(suppl I):I-327. Abstract.
Han J, Moe GK. Nonuniform recovery of excitability in ventricular muscle. Circ Res. 1964;14:44-60.
Spach MS, Dolber PC, Anderson PAW. Multiple regional differences in cellular properties that regulate repolarization and contraction in the right atrium of adult and newborn dogs. Circ Res. 1989;65:1594-1611.
Spach MS, Dolber PC, Heidlage JF. Interaction of inhomogeneities of repolarization with anisotropic propagation in dog atria. Circ Res. 1989;65:1612-1631.
Salama G, Morad M. Merocyanine 540 as an optical probe of transmembrane activity in the heart. Science. 1976;48:485-487.
Gray RA, Jalife J, Panfilov AV, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Nonstationary vortex-like reentry as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation. 1995;91:2454-2469.
Gray RA, Jalife J, Mudamgha A, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Spatio-temporal activation patterns leading to reentry in the right atrium of the sheep. PACE. 1995;18(4II):831. Abstract.
Pertsov AM, Davidenko JM, Salomonsz R, Baxter WT, Jalife J. Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circ Res. 1993;72:631-650.
Elharrar V, Surawicz B. Cycle length effect on restitution of action potential duration in dog cardiac fibers. Am J Physiol. 1983;244:H782-H792.
Cabo C, Pertsov AM, Baxter WT, Davidenko JM, Gray RA, Jalife J. Wavefront curvature as a cause of slow conduction and block in isolated cardiac muscle. Circ Res. 1994;75:1014-1028.
Spach MS, Miller WT, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. The discontinuous nature of propagation in normal canine cardiac muscle. Circ Res. 1981;48:39-54.
Rensma PL, Allessie MA, Lammers W, Bonke FIM, Schalij MJ. Length of excitation wave and susceptibility to reentrant atrial arrhythmias in normal conscious dogs. Circ Res. 1988;62:395-410.
Schuessler RB, Boineau JP, Bromberg BI, Hand DE, Yamauchi S, Cox JL. Normal and abnormal activation of the atrium. In: Zipes DP, Jalife J, eds. Cardiac Electrophysiology: From Cell to Bedside. Philadelphia, Pa: WB Saunders; 1995:543-562.
Gray RA, Jalife J, Panfilov AV, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. Mechanisms of cardiac fibrillation: drifting rotors as a mechanism of cardiac fibrillation. Science. 1995;270:1222-1223.
Cha YM, Birgersdotter-Green U, Wolf PD, Peters BB, Chen PS. The mechanism of termination of reentrant activity in ventricular fibrillation. Circ Res. 1994;74:495-506.
Knisley SB. Transmembrane voltage changes during unipolar stimulation of rabbit ventricle. Circ Res. 1995;77:1229-1239.
Liu Y, Cabo C, Salomonsz R, Delmar M, Davidenko J, Jalife J. Effects of diacetyl monoxime on the electrical properties of sheep and guinea pig ventricular muscle. Cardiovasc Res. 1993;27:1991-1997.