Computerized mapping of fibrillation in normal ventricular myocardium

Dynamical mechanism of atrial fibrillation: A topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets' hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead, this complexity is maintained as a dynamical balance between wave coalescence-a unique, previously unidentified, topological process that increases the number of wavelets-and wave collapse-a different topological process that decreases their number.

Twisted vortex filaments in the three-dimensional complex Ginzburg-Landau equation

The structure and dynamics of vortex filaments that form the cores of scroll waves in three-dimensional oscillatory media described by the complex Ginzburg-Landau equation are investigated. The study focuses on the role that twist plays in determining the bifurcation structure in various regions of the (alpha,beta) parameter space of this equation. As the degree of twist increases, initially straight filaments first undergo a Hopf bifurcation to helical filaments; further increase in the twist leads to a secondary Hopf bifurcation that results in supercoiled helices. In addition, localized states composed of superhelical segments interspersed with helical segments are found. If the twist is zero, zigzag filaments are found in certain regions of the parameter space. In very large systems disordered states comprising zigzag and helical segments with positive and negative senses exist. The behavior of vortex filaments in different regions of the parameter space is explored in some detail. In particular, an instability for nonzero twist near the alpha=beta line suggests the existence of a nonsaturating state that reduces the stability domain of straight filaments. The results are obtained through extensive simulations of the complex Ginzburg-Landau equation on large domains for long times, in conjunction with simulations on equivalent two-dimensional reductions of this equation and analytical considerations based on topological concepts.

Dynamics of spiral pairs induced by unidirectional propagating pulses

The dynamics of unidirectionally propagating pulses in a two-dimensional uniform excitable reaction-diffusion medium is investigated. It is shown that under weak diffusion coupling between medium points such a pulse can evolve into a pair of counter-rotating spirals (spiral pair). We analyze the drift of such a pair and examine the collisions between several drifting pairs. It is demonstrated that collisions can result in a special type of reflection or, alternatively, in new types of complex stationary spiral structures. A possible application of these findings for the diagnosis of cardiac arrhythmias is suggested.

Spatiotemporal correlation between phase singularities and wavebreaks during ventricular fibrillation

Phase Singularity and Wavebreak.

INTRODUCTION

Phase maps and the detection of phase singularities (PSs) have become a well-developed method for characterizing the organization of ventricular fibrillation (VF). How precisely PS colocalizes with wavebreak (WB) during VF, however, is unknown.

METHODS AND RESULTS

We performed optical mapping of 27 episodes of VF in nine Langendorff-perfused rabbit hearts. A WB is a point where the activation wavefront and the repolarization waveback meet. A PS is a site where its phase is ambiguous and its neighboring pixels exhibit a continuous phase progression from -pi to +pi. The correlation coefficient between the number of WBs and PSs was 0.78 +/- 0.09 for each heart and 0.81 for all VF episodes (P < 0.001), indicating a significant temporal correlation. We then superimposed the WBs and PSs for every 100 frames of each episode. These maps showed a high degree of spatial colocalization. To quantify spatial colocalization, the spatial shifts between the cumulative maps of WBs and PSs in corresponding frames were calculated by automatic alignment to obtain maximum overlap between these two maps. The spatial shifts were 0.04 +/- 0.31 mm on the x-axis and 0.06 +/- 0.27 mm on the y-axis over a 20 x 20 mm2 mapped field, indicating highly significant spatial correlation.

CONCLUSION

Phase mapping provides a convenient and robust approach to quantitatively describe wave propagation and organization during VF. The close spatiotemporal correlation between PSs and WBs establishes that PSs are a valid alternate representation of WB during VF and further validated the use of phase mapping in the study of VF dynamics.

Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model

Heterogeneity of cardiac tissue is an important factor determining the initiation and dynamics of cardiac arrhythmias. In this paper, we studied the effects of gradients of electrophysiological heterogeneity on reentrant excitation patterns using computer simulations. We investigated the dynamics of spiral waves in a two-dimensional sheet of cardiac tissue described by the Luo-Rudy phase 1 (LR1) ventricular action potential model. A gradient of action potential duration (APD) was imposed by gradually varying the local current density of K(+) current or inward rectifying K(+) current along one axis of the tissue sheet. We show that a gradient of APD resulted in spiral wave drift. This drift consisted of two components. The longitudinal (along the gradient) component was always directed toward regions of longer spiral wave period. The transverse (perpendicular to the gradient) component had a direction dependent on the direction of rotation of the spiral wave. We estimated the velocity of the drift as a function of the magnitude of the gradient and discuss its implications.

Filament instability and rotational tissue anisotropy: A numerical study using detailed cardiac models

The role of cardiac tissue anisotropy in the breakup of vortex filaments is studied using two detailed cardiac models. In the Beeler-Reuter model, modified to produce stable spiral waves in two dimensions, we find that anisotropy can destabilize a vortex filament in a parallelepipedal slab of tissue. The mechanisms of the instability are similar to the ones reported in previous work on a simplified cardiac model by Fenton and Karma [Chaos 8, 20 (1998)]. In the Luo-Rudy model, also modified to produce stable spiral waves in two dimensions, we find that anisotropy does not destabilize filaments. A possible explanation for this model-dependent behavior based on spiral tip trajectories is offered. (c) 2001 American Institute of Physics.

Ventricular fibrillation: mechanisms of initiation and maintenance

Ventricular fibrillation (VF) is the major immediate cause of sudden cardiac death. Traditionally, VF has been defined as turbulent cardiac electrical activity, which implies a large amount of irregularity in the electrical waves that underlie ventricular excitation. During VF, the heart rate is too high (> 550 excitations/minute) to allow adequate pumping of blood. In the electrocardiogram (ECG), ventricular complexes that are ever-changing in frequency, contour, and amplitude characterize VF. This article reviews prevailing theories for the initiation and maintenance of VF, as well as its spatio-temporal organization. Particular attention is given to recent experiments and computer simulations suggesting that VF may be explained in terms of highly periodic three-dimensional rotors that activate the ventricles at exceedingly high frequency. Such rotors may show at least two different behaviors: (a) At one extreme, they may drift throughout the heart at high speeds producing beat-to-beat changes in the activation sequence. (b) At the other extreme, rotors may be relatively stationary, activating the ventricles at such high frequencies that the wave fronts emanating from them breakup at varying distances, resulting in complex spatio-temporal patterns of fibrillatory conduction. In either case, the recorded ECG patterns are indistinguishable from VF. The data discussed have paved the way for a better understanding of the mechanisms of VF in the normal, as well as the diseased, human heart.

From local to global spatiotemporal chaos in a cardiac tissue model

Two kinds of chaos can occur in cardiac tissue, chaotic meander of a single intact spiral wave and chaotic spiral wave breakup. We studied these behaviors in a model of two-dimensional cardiac tissue based on the Luo-Rudy I action potential model. In the chaotic meander regime, chaos is spatially localized to the core of the spiral wave. When persistent spiral wave breakup occurs, there is a transition from local to global spatiotemporal chaos.

Coherence between body surface ECG leads and intracardiac signals increases during the first 10 s of ventricular fibrillation in the human heart

Ventricular fibrillation (VF) in the human heart is not well understood. The aim of this study was to measure changes in the phase relationship between the body surface ECG and intracardiac electrograms recorded during the first 10 s of human VF. We studied 11 episodes of VF and measured the coherence of (a) ECG lead I and ECG lead V1, (b) ECG lead V1 and the right ventricular apex (RVA) electrogram, and (c) ECG lead V1 and the smoothed RVA electrogram. Each coherence measurement was the average of the magnitude squared coherence function in the range 0-60 Hz, and measurements were made 1, 3, 5, 7 and 9 s after the onset of VF. Overall, the mean (SD) coherence was 31(6)% between ECG leads I and V1, 17(3)% between ECG lead V1 and the RVA electrogram, and 20(4)% between ECG lead V1 and the smoothed RVA electrogram. All three measurements of coherence increased significantly between 1 and 9 s with mean (SD) rates of 0.97(1.01)% s(-1), 0.8(1.18)% s(-1) and 0.82(1.19)% s(-1) respectively. These results show that propagation in human VF becomes more organized during the first 10 s of VF. This may be an optimal window for defibrillation.

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.

Evolving perspectives during 12 years of electrical turbulence

This Focus issue describes a problem in electrical dynamics which has fascinated generations of physiologists. There are today so many views of fibrillation that only the rarest generalization can embrace all of them. Fifty-two prominent investigators collaborate here to present aspects of the problem in these eighteen articles (including this introduction) tailored for readers whose principal expertise lies elsewhere. In "The High One's Lay" (Norse Runes, ca. 800) Odin remarks, "Much too early I came to many places: the beer was not yet ready, or was already drunk em leader " but to this one we come at very nearly the right time in 1998. This introduction attempts to guide newcomers by noting the changed or multiple meanings of novel technical terms while sorting the key facts and ideas into an order that facilitates comparison and contrast with those of a dozen years ago. This Focus issue is authored by some of the foremost innovators of both theory and experiment in this area. By assimilating their presentations the readers of Chaos can become well poised to appreciate and evaluate the definitive evidence expected in the next few years. (c) 1998 American Institute of Physics.

Two forms of spiral-wave reentry in an ionic model of ischemic ventricular myocardium

It is well known that there is considerable spatial inhomogeneity in the electrical properties of heart muscle, and that the many interventions that increase this initial degree of inhomogeneity all make it easier to induce certain cardiac arrhythmias. We consider here the specific example of myocardial ischemia, which greatly increases the electrical heterogeneity of ventricular tissue, and often triggers life-threatening cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. There is growing evidence that spiral-wave activity underlies these reentrant arrhythmias. We thus investigate whether spiral waves might be induced in a realistic model of inhomogeneous ventricular myocardium. We first modify the Luo and Rudy [Circ. Res. 68, 1501-1526 (1991)] ionic model of cardiac ventricular muscle so as to obtain maintained spiral-wave activity in a two-dimensional homogeneous sheet of ventricular muscle. Regional ischemia is simulated by raising the external potassium concentration ([K(+)](o)) from its nominal value of 5.4 mM in a subsection of the sheet, thus creating a localized inhomogeneity. Spiral-wave activity is induced using a pacing protocol in which the pacing frequency is gradually increased. When [K(+)](o) is sufficiently high in the abnormal area (e.g., 20 mM), there is complete block of propagation of the action potential into that area, resulting in a free end or wave break as the activation wave front encounters the abnormal area. As pacing continues, the free end of the activation wave front traveling in the normal area increasingly separates or detaches from the border between normal and abnormal tissue, eventually resulting in the formation of a maintained spiral wave, whose core lies entirely within an area of normal tissue lying outside of the abnormal area ("type I" spiral wave). At lower [K(+)](o) (e.g., 10.5 mM) in the abnormal area, there is no longer complete block of propagation into the abnormal area; instead, there is partial entrance block into the abnormal area, as well as exit block out of that area. In this case, a different kind of spiral wave (transient "type II" spiral wave) can be evoked, whose induction involves retrograde propagation of the action potential through the abnormal area. The number of turns made by the type II spiral wave depends on several factors, including the level of [K(+)](o) within the abnormal area and its physical size. If the pacing protocol is changed by adding two additional stimuli, a type I spiral wave is instead produced at [K(+)](o)=10.5 mM. When pacing is continued beyond this point, apparently aperiodic multiple spiral-wave activity is seen during pacing. We discuss the relevance of our results for arrythmogenesis in both the ischemic and nonischemic heart. (c) 1998 American Institute of Physics.

Electrical turbulence as a result of the critical curvature for propagation in cardiac tissue

In cardiac tissue, the propagation of electrical excitation waves is dependent on the active properties of the cell membrane (ionic channels) and the passive electrical properties of cardiac tissue (passive membrane properties, distribution of gap junctions, and cell shapes). Initiation of cardiac arrhythmias is usually associated with heterogeneities in the active and/or passive properties of cardiac tissue. However, as a result of the effect of wave front geometry (curvature) on propagation of cardiac waves, inexcitable anatomical obstacles, like veins and arteries, may cause the formation of self-sustained vortices and uncontrolled high-frequency excitation in normal homogeneous myocardium. (c) 1998 American Institute of Physics.