Wavefront Dynamics Research Articles

Widening of the Excitable Gap and Enlargement of the Core of Reentry During Atrial Fibrillation With a Pure Sodium Channel Blocker in Canine Atria

This study aimed to assess the effects of pilsicainide, a pure sodium channel blocker, on electrophysiological action and wavefront dynamics during atrial fibrillation (AF). In a newly developed model of isolated, perfused, and superfused canine atria (n=12), the right and left endocardia were mapped simultaneously by use of a computerized mapping system. AF was induced with 1 to 5 micromol/L acetylcholine. The antifibrillatory actions of pilsicainide on AF cycle length (AFCL), refractory period (RP), conduction velocity (CV), excitable gap (EG), and the core of the mother rotor were studied. The RP was defined as the shortest coupling interval that could capture the fibrillating atrium. The EG was estimated as the difference between the AFCL and RP. At baseline, multiple wavefronts were observed. After 2.5 microg/mL infusion of pilsicainide, all preparations showed irregular activity, and AF was terminated in 2 preparations. The AFCL and RP were prolonged, and CV was decreased significantly. The EG was widened (147%; P<0.01), and the core perimeter was increased (100%; P<0.01). Increasing the dosage either terminated AF (6 preparations) or converted to organized activity (ie, atypical atrial flutter) (4 preparations). On the maps, all "unorganized" AFs were terminated with the excitation of the core of the mother rotor by an outside wavefront, whereas in preparations with atrial flutter, pilsicainide did not terminate its activity. Widening of the EG by pilsicainide facilitates the excitation of the core of the mother rotor, leading to the termination of AF. In some experiments, pilsicainide converts AF to persistent atrial flutter.

Two types of ventricular fibrillation in isolated rabbit hearts: importance of excitability and action potential duration restitution.

The combined effects of excitability and action potential duration (APD) restitution on wavefront dynamics remain unclear. We used optical mapping techniques to study Langendorff-perfused rabbit hearts. In protocol IA (n=10), D600 at increasing concentrations was infused during ventricular fibrillation (VF). With concentration increased to 0.5 mg/L, fast VF (dominant frequency, 19.1+/-1.8 Hz) was consistently converted to ventricular tachycardia (VT). However, increasing D600 further to 2.5 or 5.0 mg/L converted VT to slow VF (11.9+/-2.3 Hz, P=0.0011). In an additional 4 hearts (protocol IB), tetrodotoxin converted a preexisting VT to slow VF (11.0+/-1.4 Hz). Optical maps show wandering wavelets in fast VF, organized reentry in VT, and spatiotemporal periodicity in slow VF. In protocol II, we determined APD and conduction time(-1) (CT(-1)) restitutions during D600 infusion. CT(-1) was used as an estimate of excitability. At 0.1 mg/L, APD and CT(-1) restitutions were steep and flat, respectively. APD restitution became flattened when D600 increased to 0.5 mg/L, converting fast VF to VT. Further increasing D600 to 2.5 or 5.0 mg/L steepened CT(-1) restitution and widened the range of S(1) pacing cycle lengths over which CT(-1) decreased, converting VT to slow VF. Two types of VF exist in isolated rabbit hearts. Fast (type I) VF is associated with a steep APD restitution, a flat CT(-1) restitution, and wandering wavelets. Slow (type II) VF is associated with a flat APD restitution, a steep CT(-1) restitution, and spatiotemporal periodicity. Both excitability and APD restitution are important in VF maintenance.

Effects of amiodarone on wave front dynamics during ventricular fibrillation in isolated swine right ventricle.

The effects of acute amiodarone infusion on dynamics of ventricular fibrillation (VF) are unclear. Six isolated swine right ventricles (RVs) were studied in vitro. Activation patterns during VF were mapped optically, whereas action potentials were recorded with a glass microelectrode. At baseline, VF was associated with frequent spontaneous wave breaks. Amiodarone (2.5 microg/ml) reduced spontaneous wave breaks and increased the cycle length (CL) of VF from 83.3 +/- 17.8 ms at baseline to 118.4 +/- 25.8 ms during infusion (P < 0.05). Amiodarone increased the reentrant wave front CL (114.4 +/- 15.5 vs. 78.2 +/- 19.0 ms, P < 0.05) and central core area (4.1 +/- 3.8 vs. 0.9 +/- 0.3 mm2, P < 0.05). Within 30 min of infusion, VF terminated (n = 1), converted to ventricular tachycardia (VT) (n = 1) or continued at a slower rate (n = 4). Amiodarone flattened the APD restitution curves. We conclude that amiodarone reduced spontaneous wave breaks. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased core size of reentrant wave fronts.

DYNAMIC SYSTEMS ADMITTING THE NORMAL SHIFT AND WAVE EQUATIONS

We consider wave equations on Riemannian manifolds and investigate wave front dynamics in the semiclassical approximation. The problem of finding wave equations whose wave front dynamics is described by Newtonian dynamic systems admitting the normal shift is solved. A subclass of these dynamic systems that can be defined by modified Lagrange and Hamilton equations is described explicitly.

Turbulence experiments in the swash zone

Turbulence and water surface elevation measurements were carried out in the swash zone which was induced by plunging and collapsing breakers in a wave flume. Three different period regular waves were generated on a 1/10 smooth impermeable concrete beach and the water surface elevations were collected by a number of wave gauges and a run-up meter lying on the bottom. Velocity measurements were carried out by a Laser Doppler velocimeter system, at spatial steps of 1 mm from the bottom, along three vertical sections in the swash zone. The data have been used to describe the wave front dynamics, to derive the length and velocity macro and micro scales and the Eulerian frequency spectrum. In some points, it shows a double structure. The results add to and expand on similar results obtained by other researchers in the surf zone.

Effects of amiodarone on wavefront dynamics during ventricular fibrillation in isolated swine right ventricle Chikaya Omichi, Shengmei Zhou, Moon-Hyoung Lee, Che-Ming Chang, Alan Garfinkel, James N. Weiss, Shien-Fong Lin, Hrayr S. Karagueuzian, Peng-Sheng Chen. Cedars Sinai Medical Center, Division of Cardiology, Los Angeles, CA, UCLA School of Medicine, Los Angeles, CA

Effects of amiodarone on wavefront dynamics during ventricular fibrillation in isolated swine right ventricle Chikaya Omichi, Shengmei Zhou, Moon-Hyoung Lee, Che-Ming Chang, Alan Garfinkel, James N. Weiss, Shien-Fong Lin, Hrayr S. Karagueuzian, Peng-Sheng Chen. Cedars Sinai Medical Center, Division of Cardiology, Los Angeles, CA, UCLA School of Medicine, Los Angeles, CA

Influence of wavefront dynamics on transmembrane potential characteristics during atrial fibrillation.

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

Three-dimensional surface reconstruction and fluorescent visualization of cardiac activation.

Optical imaging of transmembrane potentials in cardiac tissue is a rapidly growing technique in cardiac electrophysiology. Traditional studies typically use a monocular imaging setup, thus limiting investigation to a restricted region of tissue. However, studies of large-scale wavefront dynamics, especially those during fibrillation and defibrillation, would benefit from visualization of the entire epicardial surface. To solve this problem, a panoramic cardiac visualization algorithm was developed which performs the two tasks of reconstruction of the surface geometry of the heart, and representation of the panoramic fluorescence information as a texture mapping onto the geometry that was previously created. This system permits measurement of epicardial electrodynamics over a geometrically realistic representation of the actual heart being studied. To verify the accuracy of the algorithm, the procedure was applied to synthetic images of a patterned ball; further verification was provided by application of the algorithm to a model heart placed in the experimental setup. Both sets of images produced mean registration image errors on the order of 2 pixels, corresponding to roughly 3 mm on the geometry. We demonstrate the algorithm by visualizing epicardial wavefronts on an isolated, perfused rabbit heart.

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.

The dynamics of vortex-like reentry wave filaments in three-dimensional computer models

Recent studies using computer simulation and biological studies in 2-dimensional excitable media have suggested that spiral wave reentrant activation and its core dynamics are important elements in the mechanism of functional reentrant tachyarrhythmias, such as atrial and ventricular fibrillation. However, vortex-like reentry has been observed in homogeneous 3-dimensional excitable media, and the dynamics of the related “filaments,” which have 3-dimensionally connected “cores” in 2 dimensions, have not been clarified. In order to determine whether the filaments of vortex-like reentry waves can be observed in 3-dimensional media using a mathematical ionic current heart model and whether the abnormal ionic currents in myocardium affect the complexity of the filaments, we studied the qualitative features of vortex-like reentry dynamics using mathematical models in computer simulations. We employed the Luo-Rudy Phase I and the FitzHugh-Nagumo models for our heart media, which were cubic and ventricular shaped, and consisted of 8,000,000 and 5,636,654 myocardial units, respectively. Functional reentry, in the form of vortex waves, was induced in the media by the S1–S2 method. The vortex-like reentry waves and their filaments were displayed by computer graphics. Computations were performed on an NEC SX-4 supercomputer (NEC, Tokyo, Japan) using programs written in C language. Computer simulation studies have shown that the filament dynamics of vortex-like reentry in the original Luo-Rudy model is considerably more complex than that in the FitzHugh-Nagumo model. However, when we mathematically modified the L-type calcium current and shortened the action potential duration, just as occurs with sustained rapid ventricular pacing, the dynamics of the vortex-like reentrant wave fronts and the filaments were similar in both models. Our results suggested that the original character of myocardium causes drastic changes in filament shape and location, resulting in intricate functional reentrant waves, and that if the L-type calcium current is depressed, the complexity of the dynamics of the filaments are decreased to some degree.

Wavefronts in bistable hyperbolic reaction–diffusion systems

We study the dynamics of wavefronts that arise in bistable systems with correlated diffusion in time. For the piecewise linear reaction term the speed of propagation of these fronts is obtained analytically. The shape and the width of the front are analyzed by means of two different methods usually employed for parabolic diffusion. It is shown that for hyperbolic reaction–diffusion equations the wavefront presents a discontinuity in the slope.

Effects of procainamide on wave-front dynamics during ventricular fibrillation in open-chest dogs.

There is increasing evidence that both functional reentrant wave fronts and multiple wavelets are present during ventricular fibrillation (VF). However, the effects of procainamide on the characteristics of activation waves during VF are poorly understood. Seven dogs were studied; six underwent subendocardial chemical ablation procedures. A plaque with 317 to 480 bipolar electrodes was sutured to the right ventricular free wall, and the patterns of activation were registered with a computerized mapping system. VF was electrically induced, and the patterns of activation were registered at baseline and during procainamide infusion (serum concentration, 9.3+/-1.9 microg/mL). Among the six dogs that had their subendocardium ablated, reentrant wave fronts were present in 6 of the 108 runs of VF at baseline and in 6 of the 100 runs of VF during procainamide infusion. By analyzing the wave fronts, we found that the cycle length, refractory period, conduction velocity, and wavelength at baseline were 101+/-9 ms, 54+/-5 ms, 0.93+/-0.21 mm/ms, and 51+/-16 mm, respectively, and during procainamide infusion, values became 125+/-11 ms (P<.001), 119+/-7 ms (P<.001), 0.42+/-0.02 mm/ms (P<.001), and 50+/-4 mm (P=.8), respectively. The vast majority of the activation waves do not form organized reentry. These activation waves broke up more frequently at baseline than during procainamide administration. The number of activation waves was 7.25+/-1.39 s(-1) x cm(-2) at baseline and 4.45+/-1.80 s(-1) x cm(-2) during procainamide administration (P<.001). The dog without subendocardial ablation had similar results. Procainamide decreases the number of wavelets during VF by preventing spontaneous wave breaks. This represents a novel mechanism of antiarrhythmic drug action.

Early-time dynamics of wave fronts in disordered triangular lattices

Early-time dynamics of wave fronts in disordered triangular lattices

Meandering and unstable reentrant wave fronts induced by acetylcholine in isolated canine right atrium.

The mechanism(s) by which acetylcholine (ACh) increases atrial vulnerability to reentry and maintains its activity for longer durations remains poorly defined. In the present study we used high-resolution activation maps to test the hypothesis that ACh promotes meandering of atrial reentrant wave fronts, resulting in breakup and the generation of new wave fronts that sustain the activity. Reentry was induced in 11 isolated canine right atrial tissues (3.8 x 3.2 cm) by a premature point stimulus (S2) before and after superfusion with ACh (15 x 10(-6) M). Endocardial isochronal activation maps were constructed with the use of 509 bipolar electrodes (1.6-mm spatial resolution), and the dynamics of the activation wave fronts were visualized with animation. A vulnerable period was found during which an S2 current strength > 4.4 +/- 2.5 mA [lower limit of vulnerability (LLV)] and < 26 +/- 13 mA [upper limit of vulnerability (ULV)] induced a single stationary reentrant wave front that lasted 3 +/- 2.5 s with a period of 159 +/- 17 ms (16 episodes). AC shortened the refractory period from 100 +/- 12 to 59 +/- 9 ms (P < 0.001) and increased vulnerability to reentry induction by simultaneous decrease in the LLV (0.7 +/- 0.2 mA, P < 0.001) and an increase in the ULV (82 +/- 24 mA, P < 0.01). ACh accelerated the rate (period of 110 +/- 16 ms, P < 0.001) and converted the stationary reentrant wave front to a nonstationary (meandering) reentrant wave front showing polymorphic electrograms, i.e., "fibrillation-like" activity (22 episodes). Rapid meandering of the reentry tip led to wave front breakup (18 episodes) and the generation of new wave fronts (19 episodes). These wave front dynamics also led to sustained (76 +/- 224 s, P < 0.001) fibrillation-like electrograms. We conclude that ACh increases the ULV and promotes meandering of a single reentrant wave front, leading to breakup and the generation of new wave fronts. Single meandering and complex wave front dynamics cause fibrillation-like activity and sustain the activity for longer duration.

Refraction of active waves in reaction—diffusion media

The refraction of active waves is analyzed for a stable—metastable reaction—diffusion system consisting of two regions with different diffusion coefficients. The equations governing the evolution of wavefronts are derived by means of an asymptotic perturbation method for boundary layers. These equations describe non-stationary refraction near the steady state regime. It is shown that the dynamics of wavefronts separates into that in the region near the boundary and that far from the boundary.

SPATIAL DISORDER AND WAVE FRONTS IN A CHAIN OF COUPLED CHUA'S CIRCUITS

Dynamics of a chain of coupled Chua's circuits is investigated. Existence of spatial disorder is revealed. Dynamics of wave fronts in the limiting case of a continuous medium is studied.

Dynamics of wave fronts in excitable media

The dynamics of wave fronts in two dimensional excitable media is analytically studied. By means of the asymptotic perturbation method for wave fronts in reaction-diffusion systems, we derive a space-derivative Burgers' equation which governs the shape of boundary layers and their propagation. Application of Lie group analysis of differential equations yields group-invariant solutions of this equation and their classification. Some classes of the group-invariant solutions determine the remarkable patterns; expanding circle waves, rotating spiral waves. Initial value problems for the Burgers' equation are also studied, and a spiral wave is shown to be asymptotically realized under some proper boundary conditions.