Simulation of voltage-sensitive optical signals in three-dimensional slabs of cardiac tissue: application to transillumination and coaxial imaging methods.

Voltage-sensitive dyes are an important tool in visualizing electrical activity in cardiac tissue. Until today, they have mainly been applied in cardiac electrophysiology to subsurface imaging. In the present study, we assess different imaging methods used in optical tomography with respect to their effectiveness in visualizing 3D cardiac activity. To achieve this goal, we simulate optical signals produced by excitation fronts initiated at different depths inside the myocardial wall and compare their properties for various imaging modes. Specifically, we consider scanning and broad-field illumination, including trans- and epi-illumination. We focus on the lateral optical resolution and signal intensity, as a function of the source depth. Optical diffusion theory is applied to derive a computationally efficient approximation of the point-spread function and to predict voltage-sensitive signals. Computations were performed both for fluorescent and absorptive voltage-sensitive dyes. Among all the above-mentioned methods, fluorescent coaxial scanning yields the best resolution (<2.5 mm) and gives the most information about the intramural cardiac activity.

Intramural wave propagation in cardiac tissue: asymptotic solutions and cusp waves.

The cardiac muscle is well known to conduct electric impulses anisotropically, showing a larger conduction velocity along than across fibers. Fiber orientation is not uniform within the cardiac wall, but rotates by as much as 180 degrees throughout the wall thickness. Numerical simulations and experiments have indicated that this rotational anisotropy considerably affects the spread of excitation in cardiac tissue: the wave front shows a complex intramural shape with trailing cusps. The cusps can travel across layers and reach the epicardial and endocardial surfaces where they cause apparent accelerations of propagation. In the present study we provide an analytical description of the asymptotic wave front, as well as of cusp waves. We investigate the motion of cusp waves, based on the assumption that they occur at the intersection of asymptotic solutions, and we show that our theoretical analysis is in close agreement with numerical simulations. The asymptotic solutions are found to be determined purely by the fiber organization within the cardiac wall, independent of the excitable properties of cardiac tissue.

Rectification of the background potassium current: a determinant of rotor dynamics in ventricular fibrillation.

Ventricular fibrillation (VF) is the leading cause of sudden cardiac death. Yet, the mechanisms of VF remain elusive. Pixel-by-pixel spectral analysis of optical signals was carried out in video imaging experiments using a potentiometric dye in the Langendorff-perfused guinea pig heart. Dominant frequencies (peak with maximal power) were distributed throughout the ventricles in clearly demarcated domains. The fastest domain (25 to 32 Hz) was always on the anterior left ventricular (LV) wall and was shown to result from persistent rotor activity. Intermittent block and breakage of wavefronts at specific locations in the periphery of such rotors were responsible for the domain organization. Patch-clamping of ventricular myocytes from the LV and the right ventricle (RV) demonstrated an LV-to-RV drop in the amplitude of the outward component of the background rectifier current (I(B)). Computer simulations suggested that rotor stability in LV resulted from relatively small rectification of I(B) (presumably I(K1)), whereas instability, termination, and wavebreaks in RV were a consequence of strong rectification. This study provides new evidence in the isolated guinea pig heart that a persistent high-frequency rotor in the LV maintains VF, and that spatially distributed gradients in I(K1) density represent a robust ionic mechanism for rotor stabilization and wavefront fragmentation.

Standing excitation waves in the heart induced by strong alternating electric fields.

We studied the effect of sinusoidal electric fields on cardiac tissue both experimentally and numerically. We found that periodic forcing at 5-20 Hz using voltage applied in the bathing solution could stop the propagation of excitation waves by producing standing waves of membrane depolarization. These patterns were independent of the driving frequency in contrast to classical standing waves. The stimulus strength required for pattern formation was large compared to the excitation threshold. A novel tridomain representation of cardiac tissue was required to reproduce this behavior numerically.

Shaping of a scroll wave filament by cardiac fibers.

Scroll waves of electrical excitation in heart tissue are implicated in the development of lethal cardiac arrhythmias. Here we study the relation between the geometry of myocardial fibers and the equilibrium shape of a scroll wave filament. Our theory accommodates a wide class of myocardial models with spatially varying diffusivity tensor, adjusted to fit fiber geometry. We analytically predict the exact equilibrium shapes of the filaments. The major conclusion is that the filament shape is a compromise between a straight line and full alignment with the fibers. The degree of alignment increases with the anisotropy ratio. The results, being purely geometrical, are independent of details of ionic membrane mechanisms. Our theoretical predictions have been verified to excellent accuracy by numerically simulating the stable equilibration of a scroll filament in a model of the FitzHugh-Nagumo type.

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.

Topological constraint on scroll wave pinning.

Scroll waves in an excitable medium rotate about tubelike filaments, whose ends, when they exist, can lie on the external boundary of the medium or be pinned to an inclusion. We derive a topological rule that governs such pinning. It implies that some configurations cannot occur although they might otherwise have been expected. Heart tissue provides an application of these concepts. Computational illustrations based on a FitzHugh-Nagumo model are given.

Predicting filament drift in twisted anisotropy.

Excitable media with twisted anisotropy have recently been attracting significant interest because of their applicability to wave propagation in heart tissue. Here we consider the dynamics of an intramural scroll wave whose filament lies initially within an arbitrary layer of mutually parallel cardiac fibers, and drifts parallel to itself from layer to layer. Earlier simulations have demonstrated that such a filament stabilizes in a layer whose fiber direction is the same as its own. In the present paper we analytically derive the trajectory of the filament, and obtain good agreement with earlier numerical data. For sufficiently sparse scrolls, our analysis predicts an equilibrium alignment perpendicular rather than parallel to the fibers.

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.

Dynamics of intramural scroll waves in three-dimensional continuous myocardium with rotational anisotropy.

It has been suggested that reentrant activity in three-dimensional cardiac muscle may be organized as a scroll wave rotating around a singularity line called the filament. Experimental studies indicate that filaments are often concealed inside the ventricular wall and consequently, scroll waves do not manifest reentrant activity on the surface. Here we analyse how such concealed scroll waves are affected by a twisted anisotropy resulting from rotation of layers of muscle fibers inside the ventricular wall. We used a computer model of a ventricular slab (15x15x15 mm(3)) with a fiber twist of 120 degrees from endocardium to epicardium. The action potential was simulated using FitzHugh-Nagumo equations. Scroll waves with rectilinear filaments were initiated at various depths of the slab and at different angles with respect to fiber orientation. The analysis shows that independent of initial conditions, after a certain transitional period, the filament aligns with the local fiber orientation. The alignment of the filament is determined by the directional variations in cell coupling due to fiber rotation and by boundary conditions. Our findings provide a mechanistic explanation for the prevalence of intramural reentry over transmural reentry during polymorphic ventricular tachycardia and fibrillation.

Spiral drift and core properties.

We consider the drift of a stable, nonmeandering rotating spiral wave in a singly diffusive FitzHugh-Nagumo medium with generic reaction functions; the drift is assumed to be caused by a weak time-independent diffusivity gradient or convection term in the fast-variable equation. We address, to first order in the perturbation, the standard problem whose statement reads, "Given the unperturbed solution, as well as the model's parameters, predict the speed and direction of the drift in terms of the strength and direction of the perturbation." Our main results are as follows: First, we establish a mathematical equivalence between true gradients and convective perturbations; second, a variety of numerical examples, taken from computer simulations, are presented as a reference base for testing drift theories; and third, we propose a semiempirical solution to the drift problem, requiring only two quantities to be measured off the unperturbed spiral, namely, its period of rotation and the value of the fast variable at its center; good agreement with numerical simulations is found for moderately sparse spirals.

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.

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.

Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle.

In cardiac tissue, during partial blockade of the membrane sodium channels, or at high frequencies of excitation, inexcitable obstacles with sharp edges may destabilize the propagation of electrical excitation waves, causing the formation of self-sustained vortices and turbulent cardiac electrical activity. The formation of such vortices, which visually resembles vortex shedding in hydrodynamic turbulent flows, was observed in sheep epicardial tissue using voltage-sensitive dyes in combination with video-imaging techniques. Vortex shedding is a potential mechanism leading to the spontaneous initiation of uncontrolled high-frequency excitation of the heart.

Effects of pacing on stationary reentrant activity. Theoretical and experimental study.

It is well known that electrical pacing may either terminate or change the rate and/or ECG appearance of reentrant ventricular tachycardia. However, the dynamics of interaction of reentrant waves with waves initiated by external pacing are poorly understood. Prevailing concepts are based on simplistic models in which propagation occurs in one-dimensional rings of cardiac tissue. Since reentrant activation in the ventricles occurs in two or three dimensions, such concepts might be insufficient to explain the mechanisms of pacing-induced effects. We used numerical and biological models of cardiac excitation to explore the phenomena, which may take place as a result of electrical pacing during functionally determined reentry. Computer simulations of a two-dimensional array of electrically coupled FitzHugh-Nagumo cells were used to predict the response patterns expected from thin slices of sheep ventricular epicardial muscle, in which self-sustaining reentrant activity in the form of spiral waves was consistently initiated by premature stimulation and monitored by means of video mapping techniques. The results show that depending on their timing and shape, externally induced waves may collide with the self-sustaining spiral and result in one of three possible outcomes: (1) direct annihilation of the spiral, (2) multiplication of the spiral, or (3) shift of the spiral center (ie, core). Multiplication and shift of the spiral core were attended by changes in rate and morphology of the arrhythmia as seen by "pseudo-ECGs." Furthermore, delayed termination (ie, termination of the activity one to three cycles after the stimulus) occurred after both multiplication and shift of the spiral center. Both numerical predictions and experimental results support the hypothesis that whether a pacing stimulus will terminate a reentrant arrhythmia or modify its ECG appearance depends on whether the interactions between the externally induced wave and the spiral wave result in the de novo formation of one or more "wavebreaks." The final outcome depends on the stimulus parameters (ie, position and size of the electrodes and timing of the stimulus) as well as on the position of the newly formed wavebreak(s) in relation to that of the original wave.

Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart.

BACKGROUND: Ventricular tachycardia may result from vortexlike reentrant excitation of the myocardium. Our general hypothesis is that in the structurally normal heart, these arrhythmias are the result of one or two nonstationary three-dimensional electrical scroll waves activating the heart muscle at very high frequencies. METHODS AND RESULTS: We used a combination of high-resolution video imaging, electrocardiography, and image processing in the isolated rabbit heart, together with mathematical modeling. We characterized the dynamics of changes in transmembrane potential patterns on the epicardial surface of the ventricles using optical mapping. Image processing techniques were used to identify the surface manifestation of the reentrant organizing centers, and the location of these centers was used to determine the movement of the reentrant pathway. We also used numerical simulations incorporating Fitzhugh-Nagumo kinetics and realistic heart geometry to study how stationary and nonstationary scroll waves are manifest on the epicardial surface and in the simulated ECG. We present epicardial surface manifestations (reentrant spiral waves) and ECG patterns of nonstationary reentrant activity that are consistent with those generated by scroll waves established at the right and left ventricles. We identified the organizing centers of the reentrant circuits on the epicardial surface during polymorphic tachycardia, and these centers moved during the episodes. In addition, the arrhythmias that showed the greatest movement of the reentrant centers displayed the largest changes in QRS morphology. The numerical simulations showed that stationary scroll waves give rise to monomorphic ECG signals, but nonstationary meandering scroll waves give rise to undulating ECGs characteristic of torsade de pointes. CONCLUSIONS: Polymorphic ventricular tachycardia in the healthy, isolated rabbit heart is the result of either a single or paired ("figure-of-eight") nonstationary scroll waves. The extent of the scroll wave movement corresponds to the degree of polymorphism in the ECG. These results are consistent with our numerical simulations that showed monomorphic ECG patterns of activity for stationary scroll waves but polymorphic patterns for scroll waves that were nonstationary.

Wave-front curvature as a cause of slow conduction and block in isolated cardiac muscle.

We have investigated the role of wave-front curvature on propagation by following the wave front that was diffracted through a narrow isthmus created in a two-dimensional ionic model (Luo-Rudy) of ventricular muscle and in a thin (0.5-mm) sheet of sheep ventricular epicardial muscle. The electrical activity in the experimental preparations was imaged by using a high-resolution video camera that monitored the changes in fluorescence of the potentiometric dye di-4-ANEPPS on the surface of the tissue. Isthmuses were created both parallel and perpendicular to the fiber orientation. In both numerical and biological experiments, when a planar wave front reached the isthmus, it was diffracted to an elliptical wave front whose pronounced curvature was very similar to that of a wave front initiated by point stimulation. In addition, the velocity of propagation was reduced in relation to that of the original planar wave. Furthermore, as shown by the numerical results, wave-front curvature changed as a function of the distance from the isthmus. Such changes in local curvature were accompanied by corresponding changes in velocity of propagation. In the model, the critical isthmus width was 200 microns for longitudinal propagation and 600 microns for transverse propagation of a single planar wave initiated proximal to the isthmus. In the experiments, propagation depended on the width of the isthmus for a fixed stimulation frequency. Propagation through an isthmus of fixed width was rate dependent both along and across fibers. Thus, the critical isthmus width for propagation was estimated in both directions for different frequencies of stimulation. In the longitudinal direction, for cycle lengths between 200 and 500 milliseconds, the critical width was < 1 mm; for 150 milliseconds, it was estimated to be between 1.3 and 2 mm; and for the maximum frequency of stimulation (117 +/- 15 milliseconds), it was > 2.5 mm. In the transverse direction, critical width was between 1.78 and 2.32 mm for a basic cycle length of 200 milliseconds. It increased to values between 2.46 and 3.53 mm for a basic cycle length of 150 milliseconds. The overall results demonstrate that the curvature of the wave front plays an important role in propagation in two-dimensional cardiac muscle and that changes in curvature may cause slow conduction or block.