Induction of meandering functional reentrant wave front in isolated human atrial tissues

Not all rotors, effective ablation targets for nonparoxysmal atrial fibrillation, are included in areas suggested by conventional indirect indicators of atrial fibrillation drivers: ExTRa Mapping project

Background

Effects of nonparoxysmal atrial fibrillation (non-PAF) ablation targeting complex fractionated atrial electrogram (CFAE) areas and/or low voltage areas (LVAs) are still controversial.

Methods and Results

A recently developed online real-time phase mapping system (ExTRa Mapping) was used to conduct LVA mapping and simultaneous ExTRa and CFAE mapping in 28 non-PAF patients after pulmonary vein isolation (PVI). Nonpassively activated areas, in the form of meandering rotors and/or multiple wavelets assumed to contain non-PAF drivers, partly overlapped with CFAE/LVAs but not always coincided with them.

Conclusion

Real-time rotor imaging, rather than conventional indirect indicators only, might be very useful for detecting non-PAF drivers.

Rate Control Strategy Elevated To Primary Treatment For Atrial Fibrillation: Has The Last Word Already Been Spoken?

In the last decade, we were able to see the light shed by several trials and observational studies that dealt with the appropriate manner of treating patients with atrial fibrillation (AF). Recently the AF management by cardiologists has become more aggressive, in part because of an improved comprehension of this rhythm disturbance, as well as, the availability of new treatment strategies. Increasing awareness of AF as a disease rather than as an acceptable alternative to sinus rhythm has led to search for clear arguments to support a certain strategy as a gold standard. In this respect, the decision of whether to restore sinus rhythm, or to control the ventricular rate and allow AF to persist is of critical importance. The results of randomized, controlled trials addressing this matter shed some light on the proper way of treatment for these AF patients. The AFFIRM and RACE trials and their respective sub-studies showed surprising results. The vast majority of physicians were surprised to learn that the rate control strategy was elevated to the position of primary treatment for the AF management instead of the all-time recognized rhythm control approach to restoration and maintenance of sinus rhythm. The use of anticoagulants in the trials was different in the treatment strategies. There was a greater anticoagulant use in the rate control arm because of the belief that anticoagulation can be discontinued in the rhythm control arm when sinus rhythm was restored and maintained for one month. On the other hand, only pharmacological agents were used to maintain sinus rhythm in those trials, however, there is increasing evidence that AF ablation can restore and maintain sinus rhythm in a great proportion of patients. Indeed, there are some limitations and several interesting aspects of these trials and other studies that will be discussed. The last word has not been spoken yet.

Irregular excitation patterns in reaction-diffusion systems due to perturbation by secondary pacemakers

Spatiotemporal excitation patterns in the FitzHugh-Nagumo model are studied, which result from the disturbance of a primary pacemaker by a secondary pacemaker. The primary and secondary pacemakers generate regular waves with frequencies f(pace) and f(pert), respectively. The pacemakers are spatially separated, but waves emanating from them encounter each other via a small bridge. This leads to three different types I-III of irregular excitation patterns in disjunct domains of the f(pace)-f(pert) plane. Types I and II are caused by detachments of waves coming from the two pacemakers at corners of the bridge. Type III irregularities are confined to a boundary region of the system and originate from a partial penetration of the primary waves into a space, where circular wave fronts from the secondary pacemaker prevail. For this type, local frequencies can significantly exceed f(pace) and f(pert). The degree of irregularity found for the three different types is quantified by the entropy of the local frequency distribution and an order parameter for phase coherence.

Electrophysiological Changes of the Atrium in Patients with Lone Paroxysmal Atrial Fibrillation

Introduction: Paroxysmal atrial fibrillation (PAF) is a common arrhythmia, and it is associated with various cardiac conditions. On the other hand, lone PAF has no identifiable underlying cause, and can occur any time for no apparent reason. The underlying causes may modify the electrophysiological properties of the atrium in different ways and extent. However this setting may be different in patients with lone PAF. We sought to investigate the atrial electrophysiological properties in lone PAF. Material and Methods: This study included 62 control subjects (Control group) and 58 patients with lone PAF (LAF group). The following atrial vulnerability parameters induced by programmed atrial stimulation were assessed and quantitatively measured: 1) the atrial effective refractory period (ERP), 2) the atrial conduction delay (CD) zone, and 3) the maximum CD. Results: The mean atrial ERP of the Control group was 215±29 ms, and that of LAF group was 208±28 ms, p<0.05. The mean atrial CD zone of the LAF group was (50±28 ms) significantly greater than that of controls (34±22 ms) (p<0.01). The mean maximum CD of the LAF group (62±29 ms) was also significantly greater than that of controls (43±20 ms) (p<0.01). Conclusions : There is a greater conduction delay of the atrium and shorter refractoriness in patients with lone PAF. Patients without underlying causes for the development of PAF exhibit abnormalities in the electrophysiological properties of the atrium.

The role of connexin40 in atrial fibrillation

Connexin40 (Cx40) is a major gap-junction protein in the atrial myocardium. In the heart, gap junctions are responsible for cell-to-cell conduction of the action potential. In several cardiac diseases, the expression of connexins is changed and is associated with increased propensity for arrhythmias. Atrial fibrillation (AF) is the most common arrhythmia in man with a diverse clinical presentation, different underlying mechanisms, and difficult treatment. The vulnerability to arrhythmias of the heart is determined by the combined presence of an arrhythmogenic substrate and initiating triggers. The arrhythmogenic substrate is formed by reduced effective refractory period, enhanced spatial dispersion of refractoriness, or abnormal atrial impulse conduction. Initiating triggers of AF most frequently originate from firing foci in the pulmonary veins and/or superior caval vein. Prolonged episodes of AF result in electrical and structural remodelling that favours the reoccurrence or perpetuation of AF. This electrical remodelling embodies changes in Cx40 expression and distribution, both in the atrial myocardium itself and in the thoracic veins. In addition, Cx40 gene mutations or polymorphisms give an inherited predisposition to AF. This review focuses on the role of Cx40 in AF, showing that abnormal Cx40 expression is correlated with both trigger formation from the thoracic veins as well as enhanced vulnerability of the atrial myocardium to AF.

Surgical Treatment of Atrial Fibrillation

Atrial fibrillation (AF) is now commonly treated at the time of valvular heart surgery or coronary artery bypass grafting. Surgical ablation of AF, which is predicated upon the Maze procedure, includes creation of lines of conduction block and excision of the left atrial appendage. A full bi-atrial lesion set is associated with success in 80% to 95% of patients and virtually eliminates the risk of late stroke. A complex but safe operation, the classic cut-and-sew Maze procedure has been applied by relatively few surgeons. However, recent advances in understanding of the pathogenesis of AF and development of new ablation technologies enable surgeons to perform pulmonary vein isolation, create linear left and right atrial lesions, and remove the left atrial appendage rapidly and safely. Lesions are created under direct vision, minimizing the risk of damage to the pulmonary veins and adjacent mediastinal structures. Recently developed instrumentation now enables thoracoscopic and keyhole approaches, facilitating extension of epicardial AF ablation and excision of the left atrial appendage to patients with isolated AF and no other indication for cardiac surgery. In addition, novel devices designed specifically for minimally invasive epicardial exclusion of the left atrial appendage will broaden the range of treatment options for patients with AF, possibly eliminating the need for anticoagulation in selected patients.

Atrial fibrillation: a historical perspective

Atrial fibrillation (AF) undoubtedly has become one of the most well studied arrhythmias today in terms of pathophysiology and diagnostic and therapeutic (interventional) electrophysiology. Although it lends itself to an apparently easy diagnosis on a surface ECG, myriad electromechanical mechanisms underlie its origin. An era of technology has been reached that makes AF not only "treatable" but also potentially "curable." This article aims at walking through the historical corridors and maze that have led to the present-day understanding of this most common yet complex arrhythmia.

Identification of local myocardial repolarization time by bipolar electrode potential

PURPOSE

The aim of this study was to investigate whether bipolar electrode potentials (BEPs) reflect local myocardial repolarization dynamics, using computer simulation.

METHODS

Simulated action potential and BEP mapping of myocardial tissue during fibrillation was performed. The BEP was modified to make all the fluctuations have the same polarity. Then, the modified BEP (mBEP) was transformed to "dynamic relative amplitude" (DRA) designed to make all the fluctuations have the similar amplitude.

RESULTS

The repolarization end point corresponded to the end of the repolarization-related small fluctuation that clearly appeared in the DRA of mBEP. Using the DRA of mBEP, we could reproduce the repolarization dynamics in the myocardial tissue during fibrillation.

CONCLUSIONS

The BEP may facilitate identifying the repolarization time. Furthermore, BEP mapping has the possibility that it would be available for evaluating repolarization behavior in myocardial tissue even during fibrillation. The accuracy of activation-recovery interval was also reconfirmed.

Atrial natriuretic peptide (ANP) suppresses acute atrial electrical remodeling in the canine rapid atrial stimulation model

OBJECTIVES

Atrial electrical remodeling is considered to play an important role in the appearance of atrial fibrillation. The effect of atrial natriuretic peptide (ANP) on atrial electrical remodeling was evaluated in a canine atrial stimulation model.

METHODS

In 15 beagle dogs, electrodes for pacing and recording were fixed on the atrial surface. In 10/15 dogs, rapid atrial stimulation (400 bpm) was performed for 7 h at the right atrial appendage (RAA) and the remaining 5 were used as the sham without rapid pacing. In 5/10 dogs with rapid pacing, human atrial natriuretic peptide (ANP) was infused (1.0 microg/kg/min). The effective refractory period (ERP) and the monophasic action potential duration (MAP) were evaluated at 0, 3, and 7 h after rapid pacing. The expression levels of mRNAs of ion channels or transporters were evaluated from the atrial samples of sham and after a 7 hour pacing.

RESULTS

In the control group with rapid pacing (n=5), the atrial ERP and MAP duration were shortened at all atrial sites, e.g., ERP from 148+/-14 ms to 109+/-8 ms at RAA, P=0.006. In contrast in the ANP group, neither the ERP nor MAP duration showed a significant shortening and the effect of ANP on hemodynamic parameter was relatively small. Expression levels of the mRNA were not significantly different between the control and ANP groups.

CONCLUSIONS

Administration of ANP prevented the shortening of the ERP and MAP duration in the rapid atrial stimulation model. The effect of ANP on atrial electrical remodeling was considered to be due to its direct action on the myocardium.

Histopathological Features of the Resected Left Atrial Appendage as Predictors of Recurrence After Surgery for Atrial Fibrillation in Valvular Heart Disease

BACKGROUND

A histopathological assessment of left atrial appendages (LAA) resected during surgical treatment for atrial fibrillation (AF) was made, with the aim of improving the prediction of postoperative AF recurrence.

METHODS AND RESULTS

This clinicopathological study involved 57 surgical cases of valvular AF and 34 age- and sex-matched control autopsy cases with a history of sinus rhythm. LAA from the cases with valvular AF showed greater hypertrophy of cardiomyocytes (p<0.0001), greater nuclear enlargement (p<0.0001), more bizarre nuclei (BN; p<0.0001), and more intercellular fibrosis (ICF; p<0.001). Partial disarray of cardiomyocytes and fatty infiltration were recognized in both the AF and control groups. Thirty-seven cases had maintained sinus rhythm after surgery from 7 months to 10 years. AF recurred within a month of surgery in 17 and after a month in 3; there was no significant difference in histopathological features between them. These 20 cases had more cellular hypertrophy (p<0.025), nuclear enlargement (p<0.025), BN (p<0.01), and ICF (p<0.025) than those who maintained sinus rhythm after surgery.

CONCLUSIONS

The histopathological findings for LAA reflected the underlying valvular diseases; however, the most reliable predictors of postoperative AF recurrence were hypertrophy of cardiomyocytes, bizarre shaped nuclei, and extensive ICF.

Long-term follow-up of changes in fibrillation waves in patients with persistent atrial fibrillation: spectral analysis of surface ECG

BACKGROUND

Little is known about the shortening of atrial refractoriness as a result of electrical remodeling in atrial fibrillation (AF) in clinical cases, especially in terms of long-term follow-up, because of a lack of noninvasive testing methods.

METHODS AND RESULTS

The present study population comprised 38 consecutive patients with persistent AF (PAF, >1 month). Before and after the follow-up period of 1-14 months, surface ECGs were recorded for analysis. In each case, the fibrillation wave was purified by subtracting the QRS-T complex template and then power spectral analysis was performed. The mean fibrillation cycle length (FCL) and FCL coefficient of variation (FCL-CV) were determined from peak power frequency in 20 epochs in each recording. The change in FCL (FCL) was calculated by subtracting the baseline FCL from the FCL after the follow-up period. To correct for the difference in the follow-up period, DeltaFCL was divided by the follow-up period in each case. In 38 cases, mean FCL decreased from 160+/-20 ms to 151+/-19 ms (p<0.05), and the FCL-CV also decreased from 15+/-9% to 12+/-5% (p<0.05). The corrected DeltaFCL was -2.4+/-7.6 (ms/month) and there was a significant negative correlation between corrected DeltaFCL and baseline FCL (p<0.01).

CONCLUSION

Shortening of the FCL during a relatively long-term follow-up period was observed in patients with PAF.

Of circles and spirals: Bridging the gap between the leading circle and spiral wave concepts of cardiac reentry

The “leading circle model” was the first detailed attempt at understanding the mechanisms of functional reentry, and remains a widely-used notion in cardiac electrophysiology. The “spiral wave” concept was developed more recently as a result of modern theoretical analysis and is the basis for consideration of reentry mechanisms in present biophysical theory. The goal of this paper is to present these models in a way that is comprehensible to both the biophysical and electrophysiology communities, with the idea of helping clinical and experimental electrophysiologists to understand better the spiral wave concept and of helping biophysicists to understand why the leading circle concept is so attractive and widely used by electrophysiologists. To this end, the main properties of the leading circle and spiral wave models of reentry are presented. Their basic assumptions and determinants are discussed and the predictions of the two concepts with respect to pharmacological responses of arrhythmias are reviewed. A major difference between them lies in the predicted responses to Na+-channel blockade, for which the spiral wave paradigm appears more closely to correspond to the results of clinical and experimental observations. The basis of this difference is explored in the context of the fundamental properties of the models.

Characterization of fibrillatory rhythms by ensemble vector directional analysis

Recent studies have demonstrated that fibrillatory rhythms are not random phenomena but have definable patterns. However, standard mapping techniques may have limitations in their ability to identify the organization of fibrillation. The purpose of this study was to develop and apply a method, "ensemble vector mapping," for characterizing the spatiotemporal organization of fibrillation. Ventricular fibrillation was induced by burst pacing in normal mongrel dogs. In a separate protocol, atrial fibrillation was induced by epicardial aconitine application. Epicardial electrograms were recorded from a 112-electrode plaque array using a computerized mapping system. Vectors were created by summing orthogonal bipolar electrograms. The magnitude of the vectors was transformed using a logarithmic function, integrated over time, and normalized for local electrogram amplitude to produce an "ensemble vector" index whose magnitude is high when beat-to-beat activation direction is consistent and low when activation direction is variable. The mean index was 137 +/- 36 mV/s during ventricular pacing at a cycle length of 300 ms but only 39 +/- 23 mV/s during ventricular fibrillation (P < 0.001). The ensemble vector index was also lower during atrial fibrillation (60 +/- 54 mV/s) than during atrial pacing (115 +/- 27 mV/s, P < 0.01 vs. atrial fibrillation) but not as low as during ventricular fibrillation (P < 0.05, atrial vs. ventricular fibrillation). The index was also capable of distinguishing atrial tachycardia from atrial fibrillation. Ensemble vector mapping produces an objective assessment of the consistency of myocardial activation during fibrillation. The consistency of activation direction differs in different models of fibrillation and is higher during atrial than ventricular fibrillation. This technique has the potential to rapidly characterize repetitive activation patterns in fibrillatory rhythms and may help distinguish among different characteristics of fibrillatory rhythms.

Bepridil prevents paroxysmal atrial fibrillation by a class III antiarrhythmic drug effect

BACKGROUND

[corrected] Bepridil, a multiple ion-channel blocker, has been reported to prevent paroxysmal atrial fibrillation (PAF). The f-f interval of PAF during treatment with bepridil versus class Ic antiarrhythmic drugs was compared.

METHODS

Fifty-two patients with PAF were randomized to bepridil, 200 mg/day (n = 14) versus flecainide, 100 to 200 mg/day (n = 15) or pilsicainide, 75 to 150 mg/day (n = 23). The drug was considered effective when symptomatic episodes of PAF were decreased to < 50% during a follow-up of 2 to 6 months. The f-f interval was measured in 12-lead ECGs of initial PAF episodes.

RESULTS

Bepridil and Ic were effective in 10 of 14 (71.4%) and 24 of 38 patients (63.2%), respectively (ns). In the Ic group, the f-f interval was longer in successfully (114 +/- 48 ms) than in unsuccessfully (68 +/- 25 ms) treated patients (P = 0.002). In the bepridil group, the f-f interval was shorter in successfully (84 +/- 27 ms) than unsuccessfully (155 +/- 68 ms) treated patients (P = 0.015). When comparing unsuccessfully treated patients, the f-f interval in the bepridil group was significantly longer than in the Ic group (P = 0.007).

CONCLUSIONS

Bepridil was as effective as Ic drugs in the prevention of PAF. Because it was more effective in smaller (functional) than larger (anatomical) reentrant circuits, the effect of bepridil was considered to be mainly attributable to a class III antiarrhythmic action.

Evaluation of the effect of bepridil on paroxysmal atrial fibrillation: relationship between efficacy and the f-f interval in surface ECG recordings

Bepridil, a multi-ion channel blocker, is effective for some types of cardiac arrhythmias, and so its effect on the paroxysmal atrial fibrillation (PAF) was evaluated in the present study, comparing it with class Ic antiarrhythmic drugs. The relationship between efficacy and the f-f interval in the surface ECG recording was also analyzed. Sixty-one symptomatic PAF patients were randomized to a bepridil group (200 mg/day, n=23) or class Ic drug group (flecainide 100-200 mg/day or pilsicainide 75-150 mg/day, n=38). The drug was considered effective for PAF prevention when symptomatic episodes of PAF were decreased to less than 50% during the follow-up period of 2-6 months. The f-f interval in the surface 12-lead ECG trace was evaluated during a PAF episode. Both bepridil and the class Ic drugs were effectively prevented PAF (15/23 (65.2%) vs 24/38 (63.1%) patients, NS). In the class Ic drug group, the f-f interval was longer in the effective cases (114+/-48 ms) than in the non-effective cases (68+/-26 ms, p=0.0002). In contrast, in the bepridil group the f-f interval was shorter in the effective cases (85+/-26 ms) than in the non-effective ones (152+/-45 ms, p=0.0005). When comparing the non-effective cases in the 2 groups, the bepridil group showed a significantly longer f-f interval than the class Ic drug group (p=0.0003). As a result of drug administration, the class Ic drugs prolonged the f-f interval from 78+/-33 ms to 128+/-46 ms (p=0.0004) whereas bepridil showed no change (109+/-39 ms vs 135+/-47 ms). For clinical PAF prevention, the effect of bepridil matched that of class Ic antiarrhythmic drugs. Because bepridil was effective in PAF patients with relatively shorter f-f intervals without prolonging the f-f interval, bepridil is considered to work mainly as a class III antiarrhythmic drug.

Effect of fibre rotation on the initiation of re-entry in cardiac tissue

Transmural rotation of cardiac fibres can have a big influence on the initiation of re-entry in the heart. However, owing to computational demands, this has not been fully explored in a three-dimensional model of cardiac tissue that has a microscopic description of membrane currents, such as the Luo-Rudy model. Using a previously described model that is computationally fast, re-entry in three-dimensional blocks of cardiac tissue is induced by a cross-shock protocol, and the activity is examined. In the study, the effect of the transmural fibre rotation is ascertained by examining differences between a tissue block with no rotation and ones with 1, 2 and 3 degrees of rotation per fibre layer. The direction of the re-entry is significant in establishing whether or not re-entry can be induced, with clockwise re-entry being easier to initiate. Owing to the rotating anisotropy that results in preferential propagation along the fibre axis, the timing of the second stimulus in the cross-shock protocol has to be changed for different rates of fibre rotation. The fibre rotation either increases or decreases the window of opportunity for re-entry, depending on whether the activation front is perpendicular or parallel to the fibre direction. By varying the transmural extent of the S2, it is found that a deeper stimulus has to be applied to the blocks with fibre rotation to create re-entry. Increasing the transmural resistance also tends to reduce the extent of the S2 required to induce re-entry. Results suggest that increasing fibre rotation reduces the susceptibility of the tissue to re-entry, but that more complex spatiotemporal patterns are possible, e.g. stable figure-of-eight re-entries and transient rotors. Three mechanisms of re-entry annihilation are identified: front catchup, filling of the excitable gap and core wander.

Relation between cellular repolarization characteristics and critical mass for human ventricular fibrillation

INTRODUCTION

The critical mass for human ventricular fibrillation (VF) and its electrical determinants are unclear. The goal of this study was to evaluate the relationship between repolarization characteristics and critical mass for VF in diseased human cardiac tissues.

METHODS AND RESULTS

Eight native hearts from transplant recipients were studied. The right ventricle was immediately excised, then perfused (n = 6) or superfused (n = 2) with Tyrode's solution at 36 degrees C. The action potential duration (APD) restitution curve was determined by an S1-S2 method. Programmed stimulation and burst pacing were used to induce VF. In 3 of 8 tissues, 10 microM cromakalim, an ATP-sensitive potassium channel opener, was added to the perfusate and the stimulation protocol repeated. Results show that, at baseline, VF did not occur either spontaneously or during rewarming, and it could not be induced by aggressive electrical stimulation in any tissue. The mean APD at 90% depolarization (APD90) at a cycle length of 600 msec was 227+/-49 msec, and the mean slope of the APD restitution curve was 0.22+/-0.08. Among the six tissues perfused, five were not treated with any antiarrhythmic agent. The weight of these five heart samples averaged 111+/-23 g (range 85 to 138). However, after cromakalim infusion, sustained VF (> 30 min in duration) was consistently induced. As compared with baseline in the same tissues, cromakalim shortened the APD90 from 243+/-32 msec to 55+/-18 msec (P < 0.001) and increased the maximum slope of the APD restitution curve from 0.24+/-0.11 to 1.43+/-0.10 (P < 0.01).

CONCLUSION

At baseline, the critical mass for VF in diseased human hearts in vitro is > 111 g. However, the critical mass for VF can vary, as it can be reduced by shortening APD and increasing the slope of the APD restitution curve.

[The activation patterns during atrial fibrillation in an experimental model]

INTRODUCTION AND OBJECTIVES

In atrial fibrillation, along with the mechanisms of complete reentry and random activation focal activation patterns have been described which have been attributed both to propagation from the endocardium and to the existence of zones with automatic activity. The objectives of present study are to analyze and quantify the atrial activation patterns in an experimental model of atrial fibrillation.

MATERIAL AND METHODS

In 11 Langendorff-perfused rabbit hearts atrial fibrillation was induced by atrial burst pacing after right atrial dilatation with an intra-atrial balloon. A multiple electrode consisting of 121 electrodes and positioned in the right atrial free wall was used to construct the activation maps corresponding to 10 segments of 100 ms in 11 different episodes of sustained atrial fibrillation (one per experiment).

RESULTS

Of the 110 segments analyzed, 44 (40%) corresponded to random activation patterns. Fifteen segments (14%) corresponded to complete reentry, and in these cases the number of consecutive rotations ranged from 1 to 2.25 (mean 1.4 +/- 0.4). In 49 segments (44%) a single activation front was seen to pass through the recording area without block; alternatively, two simultaneous fronts were recorded that did not re-excite the zone activated by the other. In two segments (2%) there was a focal activation pattern without evidence of propagation from the epicardium surrounding the activated zone.

CONCLUSIONS

a) in the experimental atrial fibrillation model used, random activation patterns are more frequent than complete reentry patterns; b) complete reentry can occur in areas smaller than 1 cm2, and c) focal activation during atrial fibrillation is rare.

Transmembrane potential properties of atrial cells at different sites of a spiral wave reentry: cellular evidence for an excitable but nonexcited core

Transmembrane action potentials (TAPs) were recorded during simultaneous mapping of a reentrant wavefront induced in canine isolated atria. The activation pattern was visualized dynamically using a high resolution electrode catheter mapping system. During functional reentry (spiral wave), cells in the core of the spiral wave remained quiescent near their resting membrane potential. Cells away from the core progressively gained TAP amplitude and duration, and at the periphery of the spiral wave the cells generated TAPs with full height and duration. During anatomical reentry, when the tip of the wavefront remained attached to the obstacle (a condition of high source-to-sink ratio), the TAP near the obstacle had normal amplitude and duration. However, when the tip of the wavefront detached from the obstacle (condition of lowered source-to-sink ratio) the TAP lost amplitude and duration. These results are consistent with the theory that the source-to-sink ratio determines the safety factor for wave propagation and wave block near the core. With decreasing source-to-sink ratio, TAP progressively decreases in amplitude and duration. In the center of the core, the cells, while excitable, remain quiescent near their resting potential. This decrease reflects a progressive decrease in the source-to-sink ratio. TAP vanishes in the core where cells remain quiescent near their resting potential. Functional and meandering reentrant wavefronts are compatible with the spiral mechanism of reentry where block at the rotating point is provided by the steep curvature of the wave tip.