Mechanism of spontaneous termination of functional reentry in isolated canine right atrium. Evidence for the presence of an excitable but nonexcited core

Percolation theory as a conceptual framework to explain spontaneous atrial fibrillation termination: a pilot study

Atrial fibrillation (AF) strikingly possesses the ability to abruptly transition into more organized electrical activity and spontaneously terminate, even after persisting for long periods. Despite being central to the clinical behavior and treatment of AF, these phenomena remain incompletely understood. In this paper, we hypothesized that the spontaneous termination of AF may represent a type of percolation phase transition, which is more likely to occur when a domain spanning cluster of refractory sites in the atrium are connected (called a 'percolation cluster'). This was assessed in n=50 computational simulations of AF developed using the Aliev-Panfilov (APV) 2-dimensional cell model. In self-terminating simulations of AF, it was found that the average refractory cluster size, χ(p) (median: 647.7), and the largest refractory cluster size, M1 (median: 1702.3), abruptly increased just prior to AF spontaneously terminating, indicating the onset of the formation of a domain spanning percolation cluster. In contrast, simulations of sustained AF did not demonstrate an increase in χ(p) (median: 463.0) and M1 (median: 1448.2). Self-terminating AF simulations also demonstrated hallmark properties characteristic of a percolation phase transition, such as an abrupt increase in χ(p) at the critical occupation probability pc. The cluster size distribution was also shown to obey a power law for various occupation probabilities p, also indicative of a percolation phase transition. Collectively, these properties suggests that the spontaneous termination of AF could be a form of percolation phase transition, which could provide new insights for AF treatment.

Predictors and impact of postoperative atrial fibrillation following thoracic surgery: a state-of-the-art review

This review of 19 studies (39,783 patients) of atrial fibrillation after thoracic surgery addresses the pathophysiology, incidence, and consequences of atrial fibrillation in this population, as well as its prevention and management. Interestingly, atrial fibrillation was most often identified in patients not previously known to have the disease. Rhythm control with amiodarone was the most commonly used treatment and nearly all patients were discharged in sinus rhythm. Major predictors were age; male sex; history of atrial fibrillation; congestive heart failure; left atrial enlargement; elevated brain natriuretic peptide level; and the invasiveness of procedures. Overall, patients with atrial fibrillation stayed 3 days longer in hospital. We also discuss the importance of standardising research on this subject and provide recommendations that might mitigate the impact postoperative atrial fibrillation on hospital resources.

Calcium Handling Defects and Cardiac Arrhythmia Syndromes

Calcium ions (Ca²⁺) play a major role in the cardiac excitation-contraction coupling. Intracellular Ca²⁺ concentration increases during systole and falls in diastole thereby determining cardiac contraction and relaxation. Normal cardiac function also requires perfect organization of the ion currents at the cellular level to drive action potentials and to maintain action potential propagation and electrical homogeneity at the tissue level. Any imbalance in Ca²⁺ homeostasis of a cardiac myocyte can lead to electrical disturbances. This review aims to discuss cardiac physiology and pathophysiology from the elementary membrane processes that can cause the electrical instability of the ventricular myocytes through intracellular Ca²⁺ handling maladies to inherited and acquired arrhythmias. Finally, the paper will discuss the current therapeutic approaches targeting cardiac arrhythmias.

Dynamics of Pivoting Electrical Waves in a Cardiac Tissue Model

Through a detailed mathematical analysis we seek to advance our understanding of how cardiac tissue conductances govern pivoting (spiral, scroll, rotor, functional reentry) wave dynamics. This is an important problem in cardiology since pivoting waves likely underlie most reentrant tachycardias. The problem is complex, and to advance our methods of analysis we introduce two new tools: a ray tracing method and a moving-interface model. When used in combination with an ionic model, they permit us to elucidate the role played by tissue conductances on pivoting wave dynamics. Specifically we simulate traveling electrical waves with an ionic model that can reproduce the characteristics of plane and pivoting waves in small patches of cardiac tissue. Then ray tracing is applied to the simulated pivoting waves in a manner to expose their real displacement. In this exercise we find loci with special characteristics, as well as zones where a part of a pivoting wave quickly transitions from a regenerative to a non-regenerative propagation mode. The loci themselves and the monitoring of the ionic model state variables in this zone permit to elucidate several aspects of pivoting wave dynamics. We then formulate the moving-interface model based on the information gathered with the above-mentioned analysis. Equipped with a velocity profile v(s), s: distance along of the pivoting wave contour and the steady- state action potential duration (APD) of a plane wave during entrainment, APDss(T), at period T, this simple model can predict: shape, orbit of revolution, rotation period, whether a pivoting wave will break up or not, and whether the tissue will admit pivoting waves or not. Because v(s) and APDss(T) are linked to the ionic model, dynamical analysis with the moving-interface model conveys information on the role played by tissue conductances on pivoting wave dynamics. The analysis conducted here enables us to better understand previous results on the termination of pivoting waves. We surmise the method put forth here could become a means to discover how to alter tissue conductances in a manner to terminate pivoting waves at the origin of reentrant tachycardias.

Electrophysiological Mechanisms of Gastrointestinal Arrhythmogenesis: Lessons from the Heart

Disruptions in the orderly activation and recovery of electrical excitation traveling through the heart and the gastrointestinal (GI) tract can lead to arrhythmogenesis. For example, cardiac arrhythmias predispose to thromboembolic events resulting in cerebrovascular accidents and myocardial infarction, and to sudden cardiac death. By contrast, arrhythmias in the GI tract are usually not life-threatening and much less well characterized. However, they have been implicated in the pathogenesis of a number of GI motility disorders, including gastroparesis, dyspepsia, irritable bowel syndrome, mesenteric ischaemia, Hirschsprung disease, slow transit constipation, all of which are associated with significant morbidity. Both cardiac and gastrointestinal arrhythmias can broadly be divided into non-reentrant and reentrant activity. The aim of this paper is to compare and contrast the mechanisms underlying arrhythmogenesis in both systems to provide insight into the pathogenesis of GI motility disorders and potential molecular targets for future therapy.

Mechanisms of cardiac arrhythmias

Blood circulation is the result of the beating of the heart, which provides the mechanical force to pump oxygenated blood to, and deoxygenated blood away from, the peripheral tissues. This depends critically on the preceding electrical activation. Disruptions in the orderly pattern of this propagating cardiac excitation wave can lead to arrhythmias. Understanding of the mechanisms underlying their generation and maintenance requires knowledge of the ionic contributions to the cardiac action potential, which is discussed in the first part of this review. A brief outline of the different classification systems for arrhythmogenesis is then provided, followed by a detailed discussion for each mechanism in turn, highlighting recent advances in this area.

Dynamics of atrial arrhythmias modulated by time-dependent acetylcholine concentration: a simulation study

AIM

The autonomic nervous system modulates atrial activity, notably through acetylcholine (ACh) release. This time-dependent action may alter the dynamics of atrial arrhythmia. Our aim is to investigate in a computer model the changes induced by ACh release and degradation on the dynamical regime of a reentry.

METHODS AND RESULTS

A functional reentry was simulated in a 10 × 5 cm(2) two-dimensional tissue with canine atrial membrane kinetics including an ACh-dependent K(+) current. The local ACh concentration was altered over time in a circular region following a predefined spatiotemporal profile (ACh release and degradation) characterized by its maximum ACh level, time constant of release/degradation, and diameter of the region. Phase singularities were tracked to monitor the complexity of the dynamics. Four scenarios were identified: (i) the original reentry remained stable; (ii) repolarization gradients induced by ACh release caused wavebreaks, resulting in a transient complex dynamics that spontaneously converted to a single stable reentry; (iii) the reentry self-terminated through wavebreaks and wavefront interactions; (4) wavebreaks led to a complex dynamics that converted to two or three reentries that remained stable after ACh degradation. Higher ACh level, short ACh release time constant, larger heterogeneous region, and short distance between the heterogeneous region and the spiral tip were associated with higher occurrence of ACh-induced wavebreaks.

CONCLUSION

Variation of ACh concentration over time may modulate the complexity of atrial arrhythmias.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Light-induced termination of spiral wave arrhythmias by optogenetic engineering of atrial cardiomyocytes

AIMS

Atrial fibrillation (AF) is the most common cardiac arrhythmia and often involves reentrant electrical activation (e.g. spiral waves). Drug therapy for AF can have serious side effects including proarrhythmia, while electrical shock therapy is associated with discomfort and tissue damage. Hypothetically, forced expression and subsequent activation of light-gated cation channels in cardiomyocytes might deliver a depolarizing force sufficient for defibrillation, thereby circumventing the aforementioned drawbacks. We therefore investigated the feasibility of light-induced spiral wave termination through cardiac optogenetics.

METHODS AND RESULTS

Neonatal rat atrial cardiomyocyte monolayers were transduced with lentiviral vectors encoding light-activated Ca(2+)-translocating channelrhodopsin (CatCh; LV.CatCh∼eYFP↑) or eYFP (LV.eYFP↑) as control, and burst-paced to induce spiral waves rotating around functional cores. Effects of CatCh activation on reentry were investigated by optical and multi-electrode array (MEA) mapping. Western blot analyses and immunocytology confirmed transgene expression. Brief blue light pulses (10 ms/470 nm) triggered action potentials only in LV.CatCh∼eYFP↑-transduced cultures, confirming functional CatCh-mediated current. Prolonged light pulses (500 ms) resulted in reentry termination in 100% of LV.CatCh∼eYFP↑-transduced cultures (n = 31) vs. 0% of LV.eYFP↑-transduced cultures (n = 11). Here, CatCh activation caused uniform depolarization, thereby decreasing overall excitability (MEA peak-to-peak amplitude decreased 251.3 ± 217.1 vs. 9.2 ± 9.5 μV in controls). Consequently, functional coresize increased and phase singularities (PSs) drifted, leading to reentry termination by PS-PS or PS-boundary collisions.

CONCLUSION

This study shows that spiral waves in atrial cardiomyocyte monolayers can be terminated effectively by a light-induced depolarizing current, produced by the arrhythmogenic substrate itself, upon optogenetic engineering. These results provide proof-of-concept for shockless defibrillation.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Cardiac potassium channel subtypes: new roles in repolarization and arrhythmia

About 10 distinct potassium channels in the heart are involved in shaping the action potential. Some of the K+ channels are primarily responsible for early repolarization, whereas others drive late repolarization and still others are open throughout the cardiac cycle. Three main K+ channels drive the late repolarization of the ventricle with some redundancy, and in atria this repolarization reserve is supplemented by the fairly atrial-specific KV1.5, Kir3, KCa, and K2P channels. The role of the latter two subtypes in atria is currently being clarified, and several findings indicate that they could constitute targets for new pharmacological treatment of atrial fibrillation. The interplay between the different K+ channel subtypes in both atria and ventricle is dynamic, and a significant up- and downregulation occurs in disease states such as atrial fibrillation or heart failure. The underlying posttranscriptional and posttranslational remodeling of the individual K+ channels changes their activity and significance relative to each other, and they must be viewed together to understand their role in keeping a stable heart rhythm, also under menacing conditions like attacks of reentry arrhythmia.

Modeling atrial arrhythmias: impact on clinical diagnosis and therapies

Atrial arrhythmias are the most frequent sustained rhythm disorders in humans and often lead to severe complications such as heart failure and stroke. Despite the important insights provided by animal models into the mechanisms of atrial arrhythmias, direct translation of experimental findings to new therapies in patients has not been straightforward. With the advances in computer technology, large-scale electroanatomical computer models of the atria that integrate information from the molecular to organ scale have reached a level of sophistication that they can be used to interpret the outcome of experimental and clinical studies and aid in the rational design of therapies. This paper reviews the state-of-the-art of computer models of the electrical dynamics of the atria and discusses the evolving role of simulation in assisting the clinical diagnosis and treatment of atrial arrhythmias.

Inwardly rotating spirals in nonuniform excitable media

Inwardly rotating spirals (IRSs) have attracted great attention since their observation in an oscillatory reaction-diffusion system. However, IRSs have not yet been reported in planar excitable media. In the present work we investigate rotating waves in a nonuniform excitable medium, consisting of an inner disk part surrounded by an outer ring part with different excitabilities, by numerical simulations of a simple FitzHugh-Nagumo model. Depending on the excitability of the medium as well as the inhomogeneity, we find the occurrence of IRSs, of which the excitation propagates inwardly to the geometrical spiral tip.

Collision-based spiral acceleration in cardiac media: roles of wavefront curvature and excitable gap

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.

Spontaneous suppression of spiral turbulence based on feedback strategy

Control of defect-mediated turbulence or spiral turbulence has been a subject of pattern dynamics study in the last two decades. As a result, many control strategies has been proposed in theory and tested in computer simulation. Here we propose a self-regulation system that can spontaneously eliminate topological defects in the reaction-diffusion system that suffers from the Doppler instability. The core of the self-regulation scheme is a feedback introduction of local inhomogeneities around spiral tips. We used modified FitzHugh-Nagumo model in computer simulations and light-sensitive Belousov-Zhabotinsky reaction in experiments to test the functionality of the proposed system. We found that if the inhomogeneities were induced on the spiral tips once they were identified, the spiral can be exterminated thus the spiral turbulence can be controlled. Compared with the studies on anatomic obstacles in heart, this self-regulation model may provide a possible mechanism for spontaneous termination of cardiac fibrillation.

Annihilation and reflection of spiral waves at a boundary for the Beeler-Reuter model

We employ a reaction diffusion equation with local dynamics specified by the Beeler-Reuter model to study the meandering of spiral waves. With the appropriate choice for the conductances of sodium and calcium channels, the trajectory of the tip of a spiral wave lies on a straight line. The phenomenon of annihilation or reflection of a spiral at the boundaries of the domain is studied. This phenomenon is analyzed in terms of the variable j , which controls the reactivation of the sodium channel in the Beeler-Reuter model. The results presented can have potential applications in the study of cardiac arrhythmias by providing insight on the interaction between spiral waves and obstacles in the heart.

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.

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.

Substrate size as a determinant of fibrillatory activity maintenance in a mathematical model of canine atrium

Tissue size has been considered an important determinant of atrial fibrillation (AF), but recent work has questioned the critical size hypothesis. Here, we use a previously developed mathematical model of the two-dimensional canine atrium with realistic action potential, ionic, and conduction properties to address substrate size effects on the maintenance of fibrillatory activity. Cholinergic AF was simulated at different acetylcholine (ACh) concentrations ([ACh]) and distributions, with substrate area varied 11.1-fold. Automated phase singularity detection was used to facilitate the analysis of arrhythmic activity. The duration of activity induced by a single extrastimulus increased with increasing substrate dimensions. Two general mechanisms underlying activity were observed and were differentially affected by substrate size. For large mean [ACh], single primary rotors anchored in low-[ACh] zones maintained activity and substrate dimensions were not critical. At lower mean [ACh], extensive spiral wave meander prevented the emergence of single stable rotors. Prolonged activity was favored when substrate size permitted a sufficiently large number of simultaneous longer-lasting rotors that extinction of all was unlikely. Thus either single dominant rotor or multiple reentrant spiral generator mechanisms could maintain fibrillatory activity in this model and were differentially dependent on substrate size. These results speak to recent debates about the role in AF of single driver rotors versus multiple reentrant circuit mechanisms by suggesting that either may maintain fibrillatory atrial activity depending on atrial size and electrophysiological properties.

Critical mass hypothesis revisited: role of dynamical wave stability in spontaneous termination of cardiac fibrillation

The tendency of atrial or ventricular fibrillation to terminate spontaneously in finite-sized tissue is known as the critical mass hypothesis. Previous studies have shown that dynamical instabilities play an important role in creating new wave breaks that maintain cardiac fibrillation, but its role in self-termination, in relation to tissue size and geometry, is not well understood. This study used computer simulations of two- and three-dimensional tissue models to investigate qualitatively how, in relation to tissue size and geometry, dynamical instability affects the spontaneous termination of cardiac fibrillation. The major findings are as follows: 1) Dynamical instability promotes wave breaks, maintaining fibrillation, but it also causes the waves to extinguish, facilitating spontaneous termination of fibrillation. The latter effect predominates as dynamical instability increases, so that fibrillation is more likely to self-terminate in a finite-sized tissue. 2) In two-dimensional tissue, the average duration of fibrillation increases exponentially as tissue area increases. In three-dimensional tissue, the average duration of fibrillation decreases initially as tissue thickness increases as a result of thickness-induced instability but then increases after a critical thickness is reached. Therefore, in addition to tissue mass and geometry, dynamical instability is an important factor influencing the maintenance of cardiac fibrillation.

Mechanisms of Atrial Fibrillation: Lessons From Animal Models

Studies in animal models have provided extremely important insights about atrial fibrillation (AF). The classic mechanisms that still form the framework for our understanding of AF (focal activity, single-circuit or "mother wave" reentry, and multiple circuit reentry) were established based on animal studies almost 100 years ago. The past 10 years have witnessed a tremendous acceleration of animal work in this area, including the development of a range of AF models in clinically relevant pathological substrates (eg, atrial tachycardia remodeling, congestive heart failure, pericarditis, ischemic heart disease, mitral valve disease, volume overload states, respiratory failure) and the establishment of an increasing number of genetically defined transgenic mouse models. This article reviews the contribution of animal models to our knowledge about AF mechanisms and to clinical management, dealing with such issues as the theory of reentry; the specific applications of various animal models and their contribution to our understanding of electrophysiologic, ionic, and molecular mechanisms; the role of the autonomic nervous system and regional factors; and the development of novel therapeutic approaches. The complementary nature of animal research and clinical investigation is emphasized and the clinical relevance of findings in experimental models is highlighted.

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.

Progressive action potential duration shortening and the conversion from atrial flutter to atrial fibrillation in the isolated canine right atrium

OBJECTIVES

We sought to evaluate the effects of progressive shortening of the action potential duration (APD) on atrial wave front stability.

BACKGROUND

The mechanisms of conversion from atrial flutter to atrial fibrillation (AF) are unclear.

METHODS

Isolated canine right atria were perfused with 1 to 5 micromol/l of acetylcholine (ACh). We mapped the endocardium by using 477 bipolar electrodes and simultaneously recorded transmembrane potentials from the epicardium. The APD(90) was measured during regular pacing (S(1)) with cycle lengths of 300 ms. Atrial arrhythmia was induced by a premature stimulus (S(2)).

RESULTS

At baseline, only short runs of repetitive beats (<10 cycles) were induced. After shortening the APD(90) from 124 +/- 15 ms to 72 +/- 9 ms (p < 0.01) with 1 to 2.5 micromol/l of ACh, S(2) pacing induced single, stable and stationary re-entrant wave fronts (307 +/- 277 cycles). They either anchored to pectinate muscles (5 tissues) or used pectinate muscles as part of the re-entry (4 tissues). When ACh was raised to 2.5 to 5 micromol/l, the APD(90) was further shortened to 40 +/- 12 ms (p < 0.01); S(2) pacing induced in vitro AF by two different mechanisms. In most episodes (n = 13), AF was characterized by rapid, nonstationary re-entry and multiple wave breaks. In three episodes with APD(90) <30 ms, AF was characterized by rapid, multiple, asynchronous, but stationary wave fronts.

CONCLUSIONS

Progressive APD shortening modulates atrial wave front stability and converts atrial flutter to AF by two mechanisms: 1) detachment of stationary re-entry from the pectinate muscle and the generation of multiple wave breaks; and 2) formation of multiple, isolated, stationary wave fronts with different activation cycle lengths.

Monophasic action potentials of the right atrium in patients with paroxysmal atrial fibrillation

To investigate the mechanism of atrial fibrillation (AF), monophasic action potentials (MAPs) from the atrial myocardium were studied in 7 patients with paroxysmal AF (PAF) and in 7 control individuals. The MAPs were recorded using a contact catheter during sinus rhythm and continuous pacing at the high right atrium (HRA) with pacing cycle lengths of 600, 500 and 400 ms. MAPs were obtained from 6 sites in each participant. The MAPD90 was measured from onset to 90% of MAP repolarization. Average, maximal and minimal MAPD90 (avMAPD90, maxMAPD90 and minMAPD90) were obtained from all participants. The dispersion of MAPD90 (dispMAPD90) was defined as the difference between maxMAPD90 and minMAPD90. The width of each atrial potential (WAP) and the wavelength index (WLI=MAPD90/WAP) were determined. Average, maximal and minimal WLI (avWLI, maxWLI and minWLI) were obtained from all participants. The avMAPD90 and maxMAPD90 did not significantly differ between the 2 groups. The minMAPD90 in the PAF group was significantly smaller than that in the control group at HRA pacing with cycle lengths of 500 and 400 ms (210+/-18ms vs 245+/-14 ms, p<0.05; 207+/-23 ms vs 238+/-20 ms, p<0.05; respectively). The dispMAPD90 was significantly longer in the PAF group than in the control group during sinus and HRA pacing. The WAP value did not differ between the 2 groups. The minWLI in the PAF group was significantly smaller than that in the control group at HRA pacing with cycle lengths of 500 and 400 ms (3.3+/-0.5 vs 3.8+/-0.3, p<0.05; 3.2+/-0.4 vs 3.7+/-0.3, p<0.02). A shortened and widened dispersion of atrial refractoriness may play an important role in the genesis of AF. Furthermore, smaller wavelengths may form in the atrium of patients with PAF.

Basic mechanisms of atrial fibrillation--very new insights into very old ideas

Atrial fibrillation (AF) was recognized and studied extensively in the early twentieth century, but many fundamental aspects of the arrhythmia were poorly understood until quite recently. It is now recognized that AF can be initiated by a variety of mechanisms that share the ability to cause extremely rapid, irregular atrial electrical activity. Once initiated, AF causes alterations in atrial electrical properties (electrical remodeling), including both rapid functional changes and slower alterations in ion channel gene expression, which promote the maintenance of AF and facilitate reinitiation of the arrhythmia should it terminate. Electrical remodeling decreases the atrial refractory period in a heterogeneous way, thus decreasing the size and stability of potential functional atrial reentry waves and promoting multiple-circuit reentry. Whatever the initial cause of AF, electrical remodeling is likely to be a final common pathway that ultimately supervenes. Recent advances in understanding ion channel function, regulation, and remodeling at the molecular level have allowed for a much more detailed appreciation of the basic determinants of AF. Improvements in the clinical management of AF will inevitably follow the recent advances in our understanding of its detailed pathophysiology.

Influence of wavefront dynamics on transmembrane potential characteristics during atrial fibrillation

INTRODUCTION

Although computerized mapping studies have demonstrated the presence of multiple wavelets during atrial fibrillation (AF) and that action potential amplitude and duration in AF vary significantly from beat to beat, no study has correlated the single cell action potential changes with the patterns of activation during AF.

METHODS AND RESULTS

We studied wavefront dynamics and single cell transmembrane potential (TMP) characteristics in 12 isolated perfused canine right atria. The endocardial surface was mapped using 477 bipolar electrodes while TMP was recorded with a standard glass microelectrode from an epicardial cell. AF was induced in the presence of acetylcholine. Successful simultaneous TMP recordings and activation maps were made during six episodes of AF and for a total of 141 activations. Large variations of TMP amplitude and duration were observed frequently; 34% of them have a low amplitude (<50% of the amplitude recorded during pacing). Low-amplitude potentials were recorded when the impaled cell was (1) in an area of random reentry (67%, n = 36); (2) within 3.2 mm of the core of organized functional reentry (22%, n = 12); (3) in the middle of two merging wavefronts (9%, n = 5); and (4) at the point of spontaneous wavebreak (2%, n = 1).

CONCLUSION

Large variations of TMP are observed frequently during in vitro AF. Low-amplitude TMPs are associated with specific patterns of AF activation wavefronts.

Nicotine increases ventricular vulnerability to fibrillation in hearts with healed myocardial infarction

The vulnerability of the infarcted hearts to ventricular fibrillation (VF) was tested in in situ canine hearts during nicotine infusion. The activation pattern was mapped with 477 bipolar electrodes in open-chest anesthetized dogs (n = 8) 5-6 wk after permanent occlusion of the left anterior descending coronary artery. Nicotine (129 +/- 76 ng/ml) lengthened (P < 0.01) the pacing cycle length at which VF was induced from 171 +/- 8.9 to 210 +/- 14. 7 ms. Nicotine selectively amplified the magnitude of conduction time and monophasic action potential (MAP) amplitude and duration (MAPA and MAPD, respectively) alternans in the epicardial border zone (EBZ) but not in the normal zone. With critical reduction of the MAPA and MAPD in the EBZ, conduction block occurred across the long axis of the EBZ cells. Block led immediately to reentry formation in the EBZ with a mean period of 105 +/- 10 ms, which, after one to two rotations, degenerated to VF. Nicotine widened the range of diastolic intervals over which the dynamic MAPD restitution curve had a slope >1. We conclude that nicotine facilitates conduction block, reentry, and VF in hearts with healed myocardial infarction by increasing the magnitude of depolarization and repolarization alternans consistent with the restitution hypothesis of vulnerability to VF.

Preferential depression of conduction around a pivot point in rabbit ventricular myocardium by potassium and flecainide

INTRODUCTION

During reentrant arrhythmias, the circulating wavefront often makes a sharp turn around a functional or anatomic barrier. We tested the hypothesis that lowering the safety factor for conduction by high K+ or flecainide preferentially depresses conduction of sharply turning wavefronts.

METHODS AND RESULTS

In 16 Langendorff-perfused rabbit hearts, a thin layer of anisotropic ventricular myocardium was made using a cryoprocedure. In this layer, a linear radiofrequency lesion was made parallel to the fiber orientation. The tip of the lesion was extended by a short incision. U-turning wavefronts were initiated by pacing at one side of the lesion. A mapping electrode (240 electrodes, resolution 350 to 700 microm) was used to measure conduction times and velocity of planar waves (longitudinal and transverse) and U-turning wavefronts. The safety factor for conduction was lowered by high potassium (8, 10, and 12 mmol/L) and flecainide (1 and 2 mg/L). On average, high potassium and flecainide increased the conduction times of U-turning wavefronts 1.6 times more than longitudinal or transverse planar wavefronts (P < 0.01). At a critical lowering of the excitatory current, functional conduction block occurred at the pivot point, which forced the wavefront to make a longer U-turn. In these cases, the total U-turn conduction time increased from 27+/-9 msec to 75+/-37 msec. About 40% of this delay was caused by a shift of the pivot point and consequent lengthening of the returning pathway.

CONCLUSION

Lowering the amount of excitatory current by potassium or flecainide preferentially impairs U-turn conduction. The occurrence of long delays and conduction block at pivot points may explain the mode of action of Class I drugs.

Mechanisms of atrial fibrillation and flutter and implications for management

Both electrophysiologic and anatomical substrates are important in the generation and maintenance of atrial fibrillation. This review discusses the nature of re-entrant wavefronts in atrial fibrillation and the importance of anatomical structures, such as the pectinate muscles, in the generation and maintenance of re-entry. The involvement of the pectinate muscle structure on intra-atrial re-entry may have significant implications for both ablation and pharmacologic management of patients with atrial fibrillation.

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.

Nicotine Increases Spatiotemporal Complexity of Ventricular Fibrillation Wavefront on the Epicardial Border Zone of Healed Canine Infarcts

BACKGROUND: The influence of a pharmacologic agent on wavefront dynamics during ventricular fibrillation (VF) in a setting of remodeled and healed myocardial infarction (MI) remains poor explored. We hypothesized that nicotine, by virtue of its complex direct and indirect cardiovascular effects, increases wavefront complexity during VF. Specifically, we sought to determine whether nicotine increases the number and complexity (approximate entropy) of wavelets during stage II VF in hearts with healed MI. METHODS AND RESULTS: The left anterior descending coronary artery was permanently occluded in five mongrel dogs and wavefront dynamics during VF studied 5 to 6 weeks after occlusion in the open-chest anesthetized state. VF was induced by rapid pacing and the activation pattern mapped on the surviving epicardial border zone (EBZ) of the left ventricle with a plaque (3.2 x 3.8 cm) having 477 bipolar electrodes 1.6 mm apart. VF was mapped before and 20 minutes after 5 µg/kg/min nicotine infusion. Nicotine with a mean arterial plasma concentration of 127 +/- 76 ng/mL (range 57 to 240 ng/mL) significantly (P <.01) increased the number of wavelents from 3.8 +/- 0.4 to 5 +/- 0.41. The increased number of wavelets was caused by an increase (P <.01) in the spontaneous breakup of wavefronts from 4.1 +/- 0.9 times/s to 6.9 +/- 1.1 times/s. Wavebreak over the EBZ was functional in nature as no breakup occurred during normal sinus rhythm. Approximate entropy, a measure of complexity, significantly (P <.01) increased after nicotine administration from 0.23 +/- 0.02 to 0.28 +/- 0.01. CONCLUSIONS: Nicotine increases the number of wavelets and their complexity during VF by promoting spontaneous wavebreak over the EBZ of healed MI.

Properties of spiral waves in a piece of isotropic myocardium

Tachyarrhythmias of the heart can be due to the presence of one or more spiral waves of electrical activity. Spiral waves were simulated using a previously described ionic model of cardiac action potentials in a 75 x 75 network of compartments. The compartments were connected by means of resistors and made isotropic in order to catch basic properties of spiral waves. The cross-field stimulation technique was used to generate single or double spiral waves. The analysis showed that a spiral wave was created when the second excitation front became critically curved, in the wake of the preceding wave, so that decremental propagation occurred. A spiral wave could also be generated from a wave circulating around an obstacle when the obstacle size was suddenly reduced. The spiral waves steadily circled around an area with excitable but unexcited cells. An undisturbed spiral wave in the isotropic medium circled around in a stable pathway, but drifted along the borders of cells made non-excitable. An excitation within an existing spiral wave could generate new spiral waves that interacted with each other and formed complex excitation patterns. A sudden prolongation of the refractory period reduced the central area with unexcited cells in the spiral pathway but only slightly prolonged the revolution time. A further prolongation of the refractory period extinguished the spiral wave when the tip of the spiral wave invaded refractory areas. The described ionic compartment model could accurately produce spiral waves with properties in line with experimental results reported by others.

Uncommon atrial flutter: characteristics, mechanisms, and results of ablative therapy

Thirty-seven patients with atrial flutter were studied with catheter mapping and radiofrequency ablation. Uncommon atrial flutter occurred in 20 out of 37 (54%) patients. Atrial endocardial mapping showed two types of uncommon atrial flutter. In 15 patients (group I) it was characterized by a single clockwise circuit whereas in 5 patients (Group II) it was characterized by the presence of more than one circuit and/or localized atrial fibrillation. RFA ablation was acutely successful in 14 out of 15 patients (93%) in Group I and in 2 out of 5 (40%) patients in Group II. On long-term follow-up a significantly larger number of patients in Group I versus Group II (86% vs 20%) remained free of atrial flutter recurrence. We conclude that uncommon atrial flutter is a heterogeneous entity involving one or more reentrant circuits. Uncommon atrial flutter with multiple circuits may not be suitable for RFA.

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.

Characteristics of wave fronts during ventricular fibrillation in human hearts with dilated cardiomyopathy: role of increased fibrosis in the generation of reentry

OBJECTIVES

We sought to evaluate the characteristics of wave fronts during ventricular fibrillation (VF) in human hearts with dilated cardiomyopathy (DCM) and to determine the role of increased fibrosis in the generation of reentry during VF.

BACKGROUND

The role of increased fibrosis in reentry formation during human VF is unclear.

METHODS

Five hearts from transplant recipients with DCM were supported by Langendorff perfusion and were mapped during VF. A plaque electrode array with 477 bipolar electrodes (1.6-mm resolution) was used for epicardial mapping. In heart no. 5, we also used 440 transmural bipolar recordings. Each mapped area was analyzed histologically.

RESULTS

Fifteen runs of VF (8 s/run) recorded from the epicardium were analyzed, and 55 episodes of reentry were observed. The life span of reentry was short (one to four cycles), and the mean cycle length was 172 +/- 24 ms. In heart no. 5, transmural scroll waves were demonstrated. The most common mode of initiation of reentry was epicardial breakthrough, followed by a line of conduction block parallel to the epicardial fiber orientation (34 [62%] of 55 episodes). In the areas with lines of block, histologic examination showed significant fibrosis separating the epicardial muscle fibers and bundles along the longitudinal axis of fiber orientation. The mean percent fibrous tissue in these areas (n = 20) was significantly higher than that in the areas without block (n = 28) (24 +/- 7.5% vs. 10 +/- 3.8%, p < 0.0001).

CONCLUSIONS

In human hearts with DCM, epicardial reentrant wave fronts and transmural scroll waves were present during VF. Increased fibrosis provides a site for conduction block, leading to the continuous generation of reentry.

Spatial and temporal organization during cardiac fibrillation

Cardiac fibrillation (spontaneous, asynchronous contractions of cardiac muscle fibres) is the leading cause of death in the industrialized world, yet it is not clear how it occurs. It has been debated whether or not fibrillation is a random phenomenon. There is some determinism during fibrillation, perhaps resulting from rotating waves of electrical activity. Here we present a new algorithm that markedly reduces the amount of data required to depict the complex spatiotemporal patterns of fibrillation. We use a potentiometric dye and video imaging to record the dynamics of transmembrane potentials at many sites during fibrillation. Transmembrane signals at each site exhibit a strong periodic component centred near 8 Hz. This periodicity is seen as an attractor in two-dimensional-phase space and each site can be represented by its phase around the attractor. Spatial phase maps at each instant reveal the 'sources' of fibrillation in the form of topological defects, or phase singularities, at a few sites. Using our method of identifying phase singularities, we can elucidate the mechanisms for the formation and termination of these singularities, and represent an episode of fibrillation by locating singularities. Our results indicate an unprecedented amount of temporal and spatial organization during cardiac fibrillation.

Patterns of spiral tip motion in cardiac tissues

In support of the spiral wave theory of reentry, simulation studies and animal models have been utilized to show various patterns of spiral wave tip motion such as meandering and drifting. However, the demonstration of these or any other patterns in cardiac tissues have been limited. Whether such patterns of spiral tip motion are commonly observed in fibrillating cardiac tissues is unknown, and whether such patterns form the basis of ventricular tachycardia or fibrillation remain debatable. Using a computerized dynamic activation display, 108 episodes of atrial and ventricular tachycardia and fibrillation in isolated and intact canine cardiac tissues, as well as in vitro swine and myopathic human cardiac tissues, were analyzed for patterns of nonstationary, spiral wave tip motion. Among them, 46 episodes were from normal animal myocardium without pharmacological perturbations, 50 samples were from normal animal myocardium, either treated with drugs or had chemical ablation of the subendocardium, and 12 samples were from diseased human hearts. Among the total episodes, 11 of them had obvious nonstationary spiral tip motion with a life span of >2 cycles and with consecutive reentrant paths distinct from each other. Four patterns were observed: (1) meandering with an inward petal flower in 2; (2) meandering with outward petals in 5; (3) irregularly concentric in 3 (core moving about a common center); and (4) drift in 1 (linear core movement). The life span of a single nonstationary spiral wave lasted no more than 7 complete cycles with a mean of 4.6+/-4.3, and a median of 4.5 cycles in our samples. Conclusion: (1) Patently evident nonstationary spiral waves with long life spans were uncommon in our sample of mostly normal cardiac tissues, thus making a single meandering spiral wave an unlikely major mechanism of fibrillation in normal ventricular myocardium. (2) A tendency toward four patterns of nonstationary spiral tip motion was observed. (c) 1998 American Institute of Physics.

Spatiotemporal complexity of ventricular fibrillation revealed by tissue mass reduction in isolated swine right ventricle. Further evidence for the quasiperiodic route to chaos hypothesis

We have presented evidence that ventricular fibrillation is deterministic chaos arising from quasiperiodicity. The purpose of this study was to determine whether the transition from chaos (ventricular fibrillation, VF) to periodicity (ventricular tachycardia) through quasiperiodicity could be produced by the progressive reduction of tissue mass. In isolated and perfused swine right ventricular free wall, recording of single cell transmembrane potentials and simultaneous mapping (477 bipolar electrodes, 1.6 mm resolution) were performed. The tissue mass was then progressively reduced by sequential cutting. All isolated tissues fibrillated spontaneously. The critical mass to sustain VF was 19.9 +/- 4.2 g. As tissue mass was decreased, the number of wave fronts decreased, the life-span of reentrant wave fronts increased, and the cycle length, the diastolic interval, and the duration of action potential lengthened. There was a parallel decrease in the dynamical complexity of VF as measured by Kolmogorov entropy and Poincaré plots. A period of quasiperiodicity became more evident before the conversion from VF (chaos) to a more regular arrhythmia (periodicity). In conclusion, a decrease in the number of wave fronts in ventricular fibrillation by tissue mass reduction causes a transition from chaotic to periodic dynamics via the quasiperiodic route.

Spirals, chaos, and new mechanisms of wave propagation

The chaos theory is based on the idea that phenomena that appear disordered and random may actually be produced by relatively simple deterministic mechanisms. The disordered (aperiodic) activation that characterizes a chaotic motion is reached through one of a few well-defined paths that are characteristic of nonlinear dynamical systems. Our group has been studying VF using computerized mapping techniques. We found that in electrically induced VF, reentrant wavefronts (spiral waves) are present both in the initial tachysystolic stage (resembling VT) and the later tremulous incoordination stage (true VF). The electrophysiological characteristics associated with the transition from VT to VF is compatible with the quasiperiodic route to chaos as described in the Ruelle-Takens theorem. We propose that specific restitution of action potential duration (APD) and conduction velocity properties can cause a spiral wave (the primary oscillator) to develop additional oscillatory modes that lead to spiral meander and breakup. When spiral waves begin to meander and are modulated by other oscillatory processes, the periodic activity is replaced by unstable quasiperiodic oscillation, which then undergoes transition to chaos, signaling the onset of VF. We conclude that VF is a form of deterministic chaos. The development of VF is compatible with quasiperiodic transition to chaos. These results indicate that both the prediction and the control of fibrillation are possible based on the chaos theory and with the advent of chaos control algorithms.