Spiral waves of spreading depression in the isolated chicken retina

Existence of the theoretically predicted spiral waves of excitation in intact two-dimensional networks of excitable elements has been experimentally confirmed in the isolated chicken retina. The preparation supports the waves of Leão's spreading depression (SD) the concentric propagation of which from the point of origin can be directly observed as a change of the optical properties of the retinal tissue. The propagation rate of 3.7 mm/min (35°C) decreased to 1.5 mm/min for SD waves elicited during relative refractory period. When a several-mm long segment of the SD wave had been blocked by anodal polarization, the laterally opened ends of the wavefront started to spread after termination of polarization into the previously blocked tissue, gradually turning around and penetrating into the region recovering from the original SD. One or two simultaneously generated spiral waves of SD continued to rotate for several cycles. Spiral SD could also be elicited by punctiform cathodal polarization (1 mA) applied to the SD wave-rear. Since the new SD wave could only spread into the recovering tissue it formed a laterally open wavefront, the free ends of which eventually turned around and started spiral SD. With continued reverberation the nucleus of the spiral SD wave gradually migrated across the retina until it approached an obstacle (e.g., pecten) which stopped further spiral propagation. Spiral SD waves were elicited in 31 retinal preparations and lasted for 4.5 cycles on the average. Average cycle duration was 4.7 min. Spontaneous spiral SD waves were observed in preparations incubated in Mg²⁺-free media. The spiral SD waves in retina are compared with mathematical models of analogous phenomena. It is argued that spiral SD waves probably exist in the cerebral cortex of rats and account for generation of repetitive SD waves sometimes elicited by overlapping stimulation of two cortical regions.     

Unidirectional block of propagation of a single autowave in a narrow gap and emergence of a two-dimensional reentry depends on geometry of the obstacle and on excitability of the media

Using mathematical simulation we show that the occurrence of excitation wave circulation (reentry) around an unexcitable obstacle depends on both the geometry of the obstacle and the excitation threshold. The reentry formation is shown to take place in a wide range of model parameters.     

Wavelet formation in excitable cardiac tissue: the role of wavefront-obstacle interactions in initiating high-frequency fibrillatory-like arrhythmias.

High-frequency arrhythmias leading to fibrillation are often associated with the presence of inhomogeneities (obstacles) in cardiac tissue and reduced excitability of cardiac cells. Studies of antiarrhythmic drugs in patients surviving myocardial infarction revealed an increased rate of sudden cardiac death compared with untreated patients. These drugs block the cardiac sodium channel, thereby reducing excitability, which may alter wavefront-obstacle interactions. In diseased atrial tissue, excitability is reduced by diminished sodium channel availability secondary to depolarized rest potentials and cellular decoupling secondary to intercellular fibrosis. Excitability can also be reduced by incomplete recovery between successive excitations. In all of these cases, wavefront-obstacle interactions in a poorly excitable medium may reflect an arrhythmogenic process that permits formation of reentrant wavelets leading to flutter, fibrillation, and sudden cardiac death. To probe the relationship between excitability and arrhythmogenesis, we explored conditions for new wavelet formation after collision of a plane wave with an obstacle in an otherwise homogeneous excitable medium. Formulating our approach in terms of the balance between charge available in the wavefront and the excitation charge requirements of adjacent medium, we found analytically the critical medium parameters that defined conditions for wavefront-obstacle separation. Under these conditions, when a parent wavefront collided with a primitive obstacle, the resultant fragments separated from the obstacle boundaries, subsequently curled, and spawned new "daughter" wavelets. We identified spatial arrangements of obstacles such that wavefront-obstacle collisions leading to spawning of new wavelets could produce high-frequency wavelet trains similar to fibrillation-like arrhythmias.     

Electric field perturbations of spiral waves attached to millimeter-size obstacles

Reentrant spiral waves can become pinned to small anatomical obstacles in the heart and lead to monomorphic ventricular tachycardia that can degenerate into polymorphic tachycardia and ventricular fibrillation. Electric field-induced secondary source stimulation can excite directly at the obstacle, and may provide a means to terminate the pinned wave or inhibit the transition to more complex arrhythmia. We used confluent monolayers of neonatal rat ventricular myocytes to investigate the use of low intensity electric field stimulation to perturb the spiral wave. A hole 2-4 mm in diameter was created in the center to pin the spiral wave. Monolayers were stained with voltage-sensitive dye di-4-ANEPPS and mapped at 253 sites. Spiral waves were initiated that attached to the hole (n = 10 monolayers). Electric field pulses 1-s in duration were delivered with increasing strength (0.5-5 V/cm) until the wave terminated after detaching from the hole. At subdetachment intensities, cycle length increased with field strength, was sustained for the duration of the pulse, and returned to its original value after termination of the pulse. Mechanistically, conduction velocity near the wave tip decreased with field strength in the region of depolarization at the obstacle. In summary, electric fields cause strength-dependent slowing or detachment of pinned spiral waves. Our results suggest a means to decelerate tachycardia that may help to prevent wave degeneration.     

Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core.

Previous experimental studies have clearly demonstrated the existence of drifting and stationary electrical spiral waves in cardiac muscle and their involvement in cardiac arrhythmias. Here we present results of a study of reentrant excitation in computer simulations based on a membrane model of the ventricular cell. We have explored in detail the parameter space of the model, using tools derived from previous numerical studies in excitation-dynamics models. We have found appropriate parametric conditions for sustained stable spiral wave dynamics (1 s of activity or approximately 10 rotations) in simulations of an anisotropic (ratio in velocity 4:1) cardiac sheet of 2 cm x 2 cm. Initially, we used a model that reproduced well the characteristics of planar electrical waves exhibited by thin sheets of sheep ventricular epicardial muscle during rapid pacing at a cycle length of 300 ms. Under these conditions, the refractory period was 147 ms; the action potential duration (APD) was 120 ms; the propagation velocity along fibers was 33 cm/s; and the wavelength along fibers was 4.85 cm. Using cross-field stimulation in this model, we obtained a stable self-sustaining spiral wave rotating around an unexcited core of 1.75 mm x 7 mm at a period of 115 ms, which reproduced well the experimental results. Thus the data demonstrate that stable spiral wave activity can occur in small cardiac sheets whose wavelength during planar wave excitation in the longitudinal direction is larger than the size of the sheet. Analysis of the mechanism of this observation demonstrates that, during rotating activity, the core exerts a strong electrotonic influence that effectively abbreviates APD (and thus wavelength) in its immediate surroundings and is responsible for the stabilization and perpetuation of the activity. We conclude that appropriate adjustments in the kinetics of the activation front (i.e., threshold for activation and upstroke velocity of the initiating beat) of currently available models of the cardiac cell allow accurate reproduction of experimentally observed self-sustaining spiral wave activity. As such, the results set the stage for an understanding of functional reentry in terms of ionic mechanisms.     

Art Winfree and the bidomain model of cardiac tissue

This paper reviews Art Winfree's contributions to the bidomain model of cardiac tissue. Specifically, he first predicted quatrefoil reentry, he showed that an S1 refractory gradient is not required for an S2 stimulus to induce reentry, and his work on spiral wave meandering led to studies on how the path of the tip of a spiral wave is influenced by tissue anisotropy.     

Mechanisms of destabilization and early termination of spiral wave reentry in the ventricle by a class III antiarrhythmic agent, nifekalant

Nifekalant (NF) is a novel class III antiarrhythmic agent that is effective in preventing life-threatening ventricular tachycardia/fibrillation (VT/VF). We investigated mechanisms of destabilization and early termination of spiral-type reentrant VT by NF in a two-dimensional subepicardial myocardial layer of Langendorff-perfused rabbit hearts (n = 21) using a high-resolution optical action potential mapping system. During basic stimulation, NF (0.1 microM) caused uniform prolongation of action potential duration (APD) without affecting conduction velocity and an increase of APD restitution slope. VTs induced by direct current stimulation in the presence of NF were of shorter duration (VTs > 30 s: 2/54 NF vs. 19/93 control). During VTs in control (with visible rotors), the wave front chased its own tail with a certain distance (repolarized zone), and they seldom met each other. The average number of phase singularity (PS) points was 1.31 +/- 0.14 per 665 ms (n = 7). In the presence of NF, the wave front frequently encountered its own tail, causing a transient breakup of the spiral wave or sudden movement of the rotation center (spatial jump of PS). The average number of PS was increased to 1.63 +/- 0.22 per 665 ms (n = 7, P < 0.05) after NF. The mode of spontaneous termination of rotors in control was in most cases (9/10, 90.0%) the result of mutual annihilation of counterrotating wave fronts. With NF, rotors frequently terminated by wave front collision with the atrioventricular groove (12/19, 63.2%) or by trapping the spiral tip in a refractory zone (7/19, 36.8%). Destabilization and early termination of spiral wave reentry induced by NF are the result of a limited proportion of excitable tissue after modulation of repolarization.     

In silico optimization of atrial fibrillation-selective sodium channel blocker pharmacodynamics

Atrial fibrillation (AF) is the most common type of clinical arrhythmia. Currently available anti-AF drugs are limited by only moderate efficacy and an unfavorable safety profile. Thus, there is a recognized need for improved antiarrhythmic agents with actions that are selective for the fibrillating atrium. State-dependent Na(+)-channel blockade potentially allows for the development of drugs with maximal actions on fibrillating atrial tissue and minimal actions on ventricular tissue at resting heart rates. In this study, we applied a mathematical model of state-dependent Na(+)-channel blocking (class I antiarrhythmic drug) action, along with mathematical models of canine atrial and ventricular cardiomyocyte action potentials, AF, and ventricular proarrhythmia, to determine the relationship between their pharmacodynamic properties and atrial-selectivity, AF-selectivity (atrial Na(+)-channel block at AF rates versus ventricular block at resting rates), AF-termination effectiveness, and ventricular proarrhythmic properties. We found that drugs that target inactivated channels are AF-selective, whereas drugs that target activated channels are not. The most AF-selective drugs were associated with minimal ventricular proarrhythmic potential and terminated AF in 33% of simulations; slightly fewer AF-selective agents achieved termination rates of 100% with low ventricular proarrhythmic potential. Our results define properties associated with AF-selective actions of class-I antiarrhythmic drugs and support the idea that it may be possible to develop class I antiarrhythmic agents with optimized pharmacodynamic properties for AF treatment.     

Region [corrected] of slowed conduction acts as core for spiral wave reentry in cardiac cell monolayers

Pathophysiological heterogeneity in cardiac tissue is related to the occurrence of arrhythmias. Of importance are regions of slowed conduction, which have been implicated in the formation of conduction block and reentry. Experimentally, it has been a challenge to produce local heterogeneity in a manner that is both reversible and well controlled. Consequently, we developed a dual-zone superfusion chamber that can dynamically create a small (5 mm) central island of heterogeneity in cultured cardiac cell monolayers. Three different conditions were studied to explore the effect of regionally slowed conduction on wave propagation and reentry: depolarization by elevated extracellular potassium, sodium channel inhibition with lidocaine, and cell-cell decoupling with palmitoleic acid. Using optical mapping of transmembrane voltage, we found that the central region of slowed conduction always served as the core region around which a spiral wave formed and then revolved following a period of rapid pacing. Because of the localized slowing in the core region, we observed experimentally for the first time an S shape of the spiral wave front near its tip. These results indicate that a small region of slowed conduction can play a crucial role in the formation, anchoring, and modulation of reentrant spiral waves.     

Theoretical Study of Cardiac Transient Conduction Blocks on Reentries Induction. Applications to Antiarrhythmic Drugs

Limitations of antiarrhythmic drugs on cardiac sudden death prevention appeared since the early 80's. The "Cardiac Arrhythmia Suppression Trial"(CAST) showed more recently that mortality was significantly higher inpatients treated with some particular antiarrhythmic drugs than in non-treated patients. In this field, our group recently demonstrated that a bolus of a Class 1B antiarrhythmic drug was able to trigger a ventricular fibrillation due to transient blocks induction. The aim of the present work was to systematically study, by use of the van Capelle and Durrer (VCD) model which allows to simulate ventricular activation wave propagation, the link between arrhythmogenic effects and the ability of transient blocks to possibly degenerate in severe arrhythmias. A fragment of the ventricular wall is represented by an array of 16384elements electrically coupled. Effects of induction of one or several transient blocks, as the effects of their size and duration on possible induction of reentries have been studied. Results obtained show that various combinations between these different parameters may trigger reentries, ventricular tachycardia and/or more complex patterns assimilable to ventricular fibrillation. These results clearly evidence the fact that possible induction of transient blocks may directly be related to risk factor associated to arrhythmogenic effects of antiarrhythmic drugs. This revised version was published online in June 2006 with corrections to the Cover Date.     

Resonant Drift of Spiral Waves in the Complex Ginzburg-Landau Equation

Weak periodic external perturbations of an autowave medium can cause large-distance directed motion of the spiral wave. This happens when the period of the perturbation coincides with, or is close to the rotation period of a spiral wave, or its multiple. Such motion is called resonant or parametric drift. It may be used for low-voltage defibrillation of heart tissue. Theory of the resonant drift exists, but so far was used only qualitatively. In this paper, we show good quantitative agreement of the theory with direct numerical simulations. This is done for Complex Ginzburg-Landau Equation, one of the simplest autowave models.     

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.     

Effects of Na(+) and K(+) channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue

Na(+) and K(+) channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na(+) and K(+) channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na(+) channel blockade decreased, whereas K(+) channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na(+) channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na(+) channel blockade first increased and then decreased the average duration or transient time () of fibrillation. In mother rotor fibrillation, Na(+) channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K(+) channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.     

Antiarrhythmic drugs impair hepatic uptake and secretory function by different mechanisms in the isolated perfused rat liver

In the present study the effect of various antiarrhythmic drugs on hepatic perfusion parameters, uptake capacity of organic anions and biliary secretion using the isolated perfused rat liver was examined. Infusion of verapamil (VP), diltiazem, N-propyl-ajmaline (NPAB), and quinidine at pharmacological doses induced consistently a 1.4-1.6-fold increase in portal pressure accompanied by a approximately 60% decrease in bile flow and a approximately 65% inhibition of biliary taurocholate (TC) excretion. Furthermore, hepatic uptake of oxygen, bromosulphthalein (BSP), and TC was significantly reduced. All these effects were dose-dependent and reversible upon withdrawal of the drugs. Studies of the hepatic circulation using a Trypan blue staining technique demonstrated a patchy perfusion pattern during infusion of the antiarrhythmic drugs as compared to the homogenously stained control organ. The hemodynamic alterations and the impairment of the hepatic initial uptake function could be entirely prevented by concomitant administration of the vasodilator papaverine. Bile flow and biliary TC excretion, however, were still inhibited under these conditions. The present results indicate that antiarrhythmic drugs produce cholestasis in the isolated perfused rat liver independently of their adverse effect on hepatic hemodynamics.     

Signal emission and signal propagation during early aggregation in Dictyostelium discoideum.

Waves of chemotactic movement during the early phase of aggregation in Dictyostelium discoideum are of 2 kinds, concentric waves produced by cells that emit cyclic AMP signals spontaneously, and spirals generated by excitations relayed continuously around loops of excitable cells. The period of a spiral wave is the time taken for the excitation to make one complete circuit of the pacemaker loop. We have compared signal emission from the 2 types of source in time-lapse films made at a variety of temperatures. Our results show that spiral waves have a characteristic period length throughout most if not all of the early phase of aggregation, and that the period of concentric waves is generally longer and more variable. Temperature has a pronounced effect on period length and a lesser effect on propagation velocity. We find that each individual wave is propagated at constant velocity over distances of 1-2 cm but that the velocity of successive waves declines. This decline probably reflects some cumulative effect of the chemotactic excitations on the excitable properties of the aggregating cells.     

Effect of the form and anisotropy of the left ventricle on the drift of spiral waves

Three-dimensional spiral waves of electrical excitation in the myocardium are sources of dangerous cardiac arrhythmias. In this work, the dynamics of spiral waves of electrical excitation were studied in a symmetric anatomical model of the human heart left ventricle and a realistic ionic cell model of the human ventricular myocardium. Three factors that affect the drift waves in the heart were compared for the first time: the geometry of the heart wall, myocardial anisotropy, and wave chirality. Cardiac anisotropy was identified as a main factor in determining the drift of spiral waves. In the isotropic case, the dynamics were determined by the wall thickness, but did not depend on the wave chirality. In the anisotropic case, chirality was found to play a crucial role.

     

Selection of Multiarmed Spiral Waves in a Regular Network of Neurons

Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.     

Action of etmozin and ethacizin on dopaminergic adenylate cyclase of the striate system of the brain

The authors studied the effect of phenothiazine and butyrophenone neuroleptics and that of the antiarrhythmic drugs etmozine and etacizine on the dopamine--activated adenylate cyclase of the rabbit brain striatum. It was shown that all the neuroleptics under study prevented the development of the activating effect of dopamine, whereas the antiarrhythmic drugs administered at the same concentrations did not influence adenylate cyclase stimulation with dopamine. The affinity of etmozine and etacizine for dopamine receptors was 15-20 times less than the affinity of the typical neuroleptic trifluoroperazine. It is concluded that application of etmozine and etacizine to the treatment of arrhythmias is not complicated by neuroleptic or other dopaminergic effects of these drugs.