Arkady M. Pertsov

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.

Distribution of Excitation Frequencies on the Epicardial and Endocardial Surfaces of Fibrillating Ventricular Wall of the Sheep Heart

Tissue heterogeneities may play an important role in the mechanism of ventricular tachycardia (VT) and fibrillation (VF) and can lead to a complex spatial distribution of excitation frequencies. Here we used optical mapping and Fourier analysis to determine the distribution of excitation frequencies in >20 000 sites of fibrillating ventricular tissue. Our objective was to use such a distribution as a tool to quantify the degree of organization during VF. Fourteen episodes of VT/VF were induced via rapid pacing in 9 isolated, coronary perfused, and superfused sheep ventricular slabs (3x3 cm(2)). A dual-camera video-imaging system was used for simultaneous optical recordings from the entire epi- and endocardial surfaces. The local frequencies of excitation were determined at each pixel and displayed as dominant frequency (DF) maps. A typical DF map consisted of several (8.2+/-3.6) discrete areas (domains) with a uniform DF within each domain. The DFs in adjacent domains were often in 1:2, 3:4, or 4:5 ratios, which was shown to be a result of an intermittent Wenckebach-like conduction block at the domain boundaries. The domain patterns were relatively stable and could persist from several seconds to several minutes. The complexity in the organization of the domains, the number of domains, and the dispersion of frequencies increased with the rate of the arrhythmia. Domain patterns on the epicardial and endocardial surfaces were not correlated. Sustained epicardial or endocardial reentry was observed in only 3 episodes. Observed frequency patterns during VT/VF suggest that the underlying mechanism may be a sustained intramural reentrant source interacting with tissue heterogeneities.

Frequency-Dependent Breakdown of Wave Propagation Into Fibrillatory Conduction Across the Pectinate Muscle Network in the Isolated Sheep Right Atrium

Atrial fibrillation (AF) may result from stationary reentry in the left atrium (LA), with fibrillatory conduction toward the right atrium (RA). We hypothesize that periodic input to the RA at an exceedingly high frequency results in disorganized wave propagation, compatible with fibrillatory conduction. Simultaneous endocardial and epicardial optical mapping (di-4-ANEPPS) was performed in isolated, coronary-perfused sheep RA. Rhythmic pacing of Bachmann’s bundle allowed well-controlled and realistic conditions for LA-driven RA. Pacing at increasingly higher frequencies (2.0 to 6.0 Hz) led to increasing delays in activation distal to major branching sites of the crista terminalis and pectinate bundles, culminating in spatially distributed intermittent blockade at or above ≈6.5 Hz. At this “breakdown frequency,” the direction of RA propagation became completely variable from beat to beat and thus transformed into fibrillatory conduction. Such frequency-dependent changes were independent of action potential duration. Rather, the spatial boundaries between proximal and distal frequencies correlated well with branch sites of the pectinate musculature. Thus, there exists a breakdown frequency in the sheep RA below which activity is periodic throughout the atrium and above which it is fibrillation-like. The data are consistent with the ideas that during AF, high-frequency activation initiated in the LA undergoes fibrillatory conduction toward the RA, and that sink-to-source effect at branch points of the crista terminalis and pectinate muscles is important in determining the complexity of the arrhythmia.

Incomplete Reentry and Epicardial Breakthrough Patterns During Atrial Fibrillation in the Sheep Heart

BACKGROUND The mechanisms underlying atrial fibrillation and its initiation are not fully understood. Our hypothesis is that atrial fibrillation results from complex activation involving the subendocardial muscle network. METHODS AND RESULTS We have used video imaging to study the sequence of activation on the surface of the right atrium of the Langendorff-perfused sheep heart during pacing, atrial fibrillation, and its initiation. We recorded transmembrane potentials simultaneously from over 20,000 sites. We observed two types of patterns of wave propagation during the initiation of atrial fibrillation. The first type resulted from heterogeneties of refractoriness and transmural propagation near the stimulating electrode. The second type involved heterogeneity in conduction away from the pacing site. During atrial fibrillation, the average period of activation was 138 +/- 25 ms (n = 6), and complete reentrant pathways were never observed. Propagation patterns were characterized by a combination of incomplete reentry, breakthrough patterns, and wave collisions. Incomplete reentry occurred when waves propagated around thin lines of block and then terminated. Breakthrough patterns were frequent and occurred every 215 ms on average. The location of these breakthrough sites and the lines of block during incomplete reentry were not randomly distributed but appeared to be related to preferential propagation in the underlying subendocardial muscle structures. A computer model of atrial free wall connected to a pectinate muscle suggested that subendocardial muscles lead to epicardial breakthrough patterns that act to destabilize reentry. CONCLUSIONS These results suggest that the complex three-dimensional structure of the atria plays a major role in the activation sequences during atrial fibrillation and its initiation.

Visualizing Excitation Waves inside Cardiac Muscle Using Transillumination

Voltage-sensitive fluorescent dyes have become powerful tools for the visualization of excitation propagation in the heart. However, until recently they were used exclusively for surface recordings. Here we demonstrate the possibility of visualizing the electrical activity from inside cardiac muscle via fluorescence measurements in the transillumination mode (in which the light source and photodetector are on opposite sides of the preparation). This mode enables the detection of light escaping from layers deep within the tissue. Experiments were conducted in perfused (8 mm thick) slabs of sheep right ventricular wall stained with the voltage-sensitive dye di-4-ANEPPS. Although the amplitude and signal-to-noise ratio recorded in the transillumination mode were significantly smaller than those recorded in the epi-illumination mode, they were sufficient to reliably determine the activation sequence. Penetration depths (spatial decay constants) derived from measurements of light attenuation in cardiac muscle were 0.8 mm for excitation (520 +/- 30 nm) and 1.3 mm for emission wavelengths (640 +/- 50 nm). Estimates of emitted fluorescence based on these attenuation values in 8-mm-thick tissue suggest that 90% of the transillumination signal originates from a 4-mm-thick layer near the illuminated surface. A 69% fraction of the recorded signal originates from > or =1 mm below the surface. Transillumination recordings may be combined with endocardial and epicardial surface recordings to obtain information about three-dimensional propagation in the thickness of the myocardial wall. We show an example in which transillumination reveals an intramural reentry, undetectable in surface recordings.

Wavebreak Formation During Ventricular Fibrillation in the Isolated, Regionally Ischemic Pig Heart

Abstract— Both fixed and dynamic heterogeneities were implicated in the mechanism of wavebreak (WB) generation during ventricular fibrillation (VF). However, their relative roles remain unclear. We hypothesized that during ischemic VF, the WBs are produced primarily because of a fixed heterogeneity; namely, the gradient of refractoriness across the ischemic border zone (BZ). Ischemia was induced in 15 isolated blood-perfused hearts by occluding the left anterior descending coronary artery. Simultaneous video imaging (≈32×32 mm2) of Di-4-ANEPPS fluorescence in the ischemic zone (IZ), the BZ, and the nonischemic zone (NIZ) was performed. Dominant-frequency maps were constructed to assess gradients of refractoriness during VF. We used singularity points analysis to quantify the incidence of WBs per square centimeter per second. During preischemic VF, the distribution of WBs was relatively uniform. Ischemia caused an increase of WBs in the BZ (from 6.2±2.8 to 10.8±4.0) and a decrease of WBs in the IZ (from 5.8±2.8 to 2.8±1.4), without a significant change in NIZ (from 6.4±2.3 to 4.1±1.7). This finding is fully consistent with the dominant-frequency distribution during ischemic VF: the average dominant frequency was significantly slower in IZ than in NIZ (7.8±0.7 versus 10.1±1.0 Hz), suggesting a large gradient in refractory periods across the BZ. We concluded that acute regional ischemia plays a dual role in the maintenance of VF, decreasing the incidence of WB in the IZ while increasing it in the BZ. This suggests a predominant role of fixed heterogeneities in the formation of WB during VF in acute regional ischemia.

Synthesis of voltage-sensitive fluorescence signals from three-dimensional myocardial activation patterns.

Voltage-sensitive fluorescent dyes are commonly used to measure cardiac electrical activity. Recent studies indicate, however, that optical action potentials (OAPs) recorded from the myocardial surface originate from a widely distributed volume beneath the surface and may contain useful information regarding intramural activation. The first step toward obtaining this information is to predict OAPs from known patterns of three-dimensional (3-D) electrical activity. To achieve this goal, we developed a two-stage model in which the output of a 3-D ionic model of electrical excitation serves as the input to an optical model of light scattering and absorption inside heart tissue. The two-stage model permits unique optical signatures to be obtained for given 3-D patterns of electrical activity for direct comparison with experimental data, thus yielding information about intramural electrical activity. To illustrate applications of the model, we simulated surface fluorescence signals produced by 3-D electrical activity during epicardial and endocardial pacing. We discovered that OAP upstroke morphology was highly sensitive to the transmural component of wave front velocity and could be used to predict wave front orientation with respect to the surface. These findings demonstrate the potential of the model for obtaining useful 3-D information about intramural propagation.

Depth-resolved optical imaging of transmural electrical propagation in perfused heart

We present a study of the 3-dimensional (3D) propagation of electrical waves in the heart wall using Laminar Optical Tomography (LOT). Optical imaging contrast is provided by a voltage sensitive dye whose fluorescence reports changes in membrane potential. We examined the transmural propagation dynamics of electrical waves in the right ventricle of Langendorf perfused rat hearts, initiated either by endo-cardial or epi-cardial pacing. 3D images were acquired at an effective frame rate of 667Hz. We compare our experimental results to a mathematical model of electrical transmural propagation. We demonstrate that LOT can clearly resolve the direction of propagation of electrical waves within the cardiac wall, and that the dynamics observed agree well with the model of electrical propagation in rat ventricular tissue.

Optical Action Potential Upstroke Morphology Reveals Near-Surface Transmural Propagation Direction

The analysis of surface-activation patterns and measurements of conduction velocity in ventricular myocardium is complicated by the fact that the electrical wavefront has a complex 3D shape and can approach the heart surface at various angles. Recent theoretical studies suggest that the optical upstroke is sensitive to the subsurface orientation of the wavefront. Our goal here was to (1) establish the quantitative relationship between optical upstroke morphology and subsurface wavefront orientation using computer modeling and (2) test theoretical predictions experimentally in isolated coronary-perfused swine right ventricular preparations. We show in numerical simulations that by suitable placement of linear epicardial stimulating electrodes, the angle &phgr; of wavefronts with respect to the heart surface can be controlled. Using this method, we developed theoretical predictions of the optical upstroke shape dependence on &phgr;. We determined that the level VF* at which the rate of rise of the optical upstroke reaches the maximum linearly depends on &phgr;. A similar relationship was found in simulations with epicardial point stimulation. The optical mapping data were in good agreement with theory. Plane waves propagating parallel to myocardial fibers produced upstrokes with VF*<0.5, consistent with theoretical predictions for &phgr;>0. Similarly, we obtained good agreement with theory for plane waves propagating in a direction perpendicular to fibers (VF*>0.5 when &phgr;<0). Finally, during epicardial point stimulation, we discovered characteristic saddle-shaped VF* maps that were in excellent agreement with theoretically predicted changes in &phgr; during wavefront expansion. Our findings should allow for improved interpretation of the results of optical mapping of intact heart preparations.

Rotating spiral waves in a modified Fitz-Hugh-Nagumo model

Abstract A modified Fitz-Hugh-Nagumo model (a two-variable reaction-diffusion system with an excitable kinetics and a diffusing fast variable) was used to study numerically the rotating waves in a circular domain and in a two-dimensional ring. Large deviations from a Wiener type of behaviour of rotating spiral waves were revealed. We have shown that there are conditions under which: (i) vortices can appear in a medium with a hole but do not exist in a disk; (ii) two kinds of vortices with considerably differing periods can occur in the same ring; (iii) there is a non-monotonic dependence of vortex period on the hole size. These phenomena are believed to take place in myocardial tissue and in chemical active media. The conditions under which they could be observed experimentally are discussed.