Mechanisms of vortices termination in the cardiac muscle.

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.

Wave emission from heterogeneities opens a way to controlling chaos in the heart.

The effectiveness of chaos control in large systems increases with the number of control sites. We find that electric field induced wave emission from heterogeneities (WEH) in the heart gives a unique opportunity to have as many control sites as needed. The number of pacing sites grows with the amplitude of the electric field. We demonstrate that WEH has important advantages over methods used in clinics, and opens a new way to manipulate vortices in experiments, and potentially to radically improve the clinical methods of chaos control in the heart.

Pinning force in active media.

Pinning of vortices by defects plays an important role in various physical (superconductivity, superfluidity, etc.) or biological (propagation in cardiac muscle) situations. Which defects act as pinning centers? We propose a way to study this general problem by using an advection field to quantify the attraction between an obstacle and a vortex. A full solution is obtained for the real Ginzburg-Landau equation (RGLE). Two pinning mechanisms are found in excitable media. Our results suggest strong analogies with the RGLE when the heterogeneity is excitable. Unpinning from an unexcitable obstacle is qualitatively harder, resulting in a stronger pinning force. We discuss the implications of our results to control vortices and propose experiments in a chemical active medium and in cardiac tissue.

A physical approach to remove anatomical reentries: a bidomain study.

Controlling cardiac chaos is often achieved by applying a large damaging electric shock-defibrillation. It removes all waves, without differentiating reentries and normal waves, anatomical and functional reentries. Anatomical reentries can be removed by anti-tachycardia pacing (ATP) as well. But ATP requires the knowledge of the position of the reentry, and an access to it with an invasive stimulating electrode. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of an anatomical reentry, without knowing its position and even to locations where access with a stimulating electrode is not possible. The energy needed is two orders of magnitude less than defibrillation energy. The results are insensitive to both a detailed ionic model and to the geometry of the fibers.

Unpinning and removal of a rotating wave in cardiac muscle.

Rotating waves in cardiac muscle may be pinned to a heterogeneity, as it happens in superconductors or in superfluids. We show that the physics of electric field distribution between cardiac cells permits one to deliver an electric pulse exactly to the core of a pinned wave, without knowing its position, and even to locations where a direct access is not possible. Thus, unpinning or removal of rotating waves can be achieved. The energy needed is 2 orders of magnitude less than defibrillation energy. This opens a way to new manipulations with pinned vortices both in experiments and in cardiac clinics.

Effects of electroporation on optically recorded transmembrane potential responses to high-intensity electrical shocks.

The outcome of defibrillation shocks is determined by the nonlinear transmembrane potential (DeltaVm) response induced by a strong external electrical field in cardiac cells. We investigated the contribution of electroporation to DeltaVm transients during high-intensity shocks using optical mapping. Rectangular and ramp stimuli (10-20 ms) of different polarities and intensities were applied to the rabbit heart epicardium during the plateau phase of the action potential (AP). DeltaVm were optically recorded under a custom 6-mm-diameter electrode using a voltage-sensitive dye. A gradual increase of cathodal and well as anodal stimulus strength was associated with 1) saturation and subsequent reduction of DeltaVm; 2) postshock diastolic resting potential (RP) elevation; and 3) postshock AP amplitude (APA) reduction. Weak stimuli induced a monotonic DeltaVm response and did not affect the RP level. Strong shocks produced a nonmonotonic DeltaVm response and caused RP elevation and a reduction of postshock APA. The maximum positive and maximum negative DeltaVm were recorded at 170 +/- 20 mA/cm2 for cathodal stimuli and at 240 +/- 30 mA/cm2 for anodal stimuli, respectively (means +/- SE, n = 8, P = 0.003). RP elevation reached 10% of APA at a stimulus strength of 320 +/- 40 mA/cm2 for both polarities. Strong ramp stimuli (20 ms, 600 mA/cm2) induced a nonmonotonic DeltaVm response, reaching the same largest positive and negative values as for rectangular shocks. The transition from monotonic to nonmonotonic morphology correlates with RP elevation and APA reduction, which is consistent with cell membrane electroporation. Strong shocks resulted in propidium iodide uptake, suggesting sarcolemma electroporation. In conclusion, electroporation is a likely explanation of the saturation and nonmonotonic nature of cellular responses reported for strong electric stimuli.

Head-on collisions of waves in an excitable FitzHugh-Nagumo system: a transition from wave annihilation to classical wave behavior.

For the particular case of an excitable FitzHugh-Nagumo system with diffusion, we investigate the transition from annihilation to crossing of the waves in the head-on collision. The analysis exploits the similarity between the local and the global phase portraits of the system. We find that the transition has features typical of the nucleation theory of first-order phase transitions, and may be understood through purely geometrical arguments. In the case of periodic boundary conditions, the transition is an infinite-dimensional analog of the creation and the vanishing of limit cycles via a homoclinic Andronov bifurcation. Both before and after the transition, the behavior of a single cell continues to be typical for excitable systems: a stable equilibrium state, and a threshold above which an excitation pulse can be induced. The generality and qualitative character of our argument shows that the phenomenon described can be observed in excitable systems well beyond the particular case presented here.

Unpinning of a rotating wave in cardiac muscle by an electric field.

The possibility of terminating cardiac arrhythmias with electric fields of moderate intensity is a challenging problem from a fundamental point of view and an important issue for clinical applications. In an effort to understand how anatomical re-entries are affected by electric fields, we found that a weak shock, with an amplitude of an order of magnitude less than the defibrillating shock, may unpin the vortices rotating around the defects (obstacles). The unpinning results from a depolarization of the tissue near the obstacle, induced by an external electric field within a distance of order lambda approximately 1 mm. Unpinning was observed both in the FitzHugh model of excitable tissue, and in a specific Beeler-Reuter model of cardiac tissue. This theoretical observation suggests that anatomical re-entries can be transformed into functional re-entries, an effect that can be tested in experiments with cardiac muscle.

Chirality dependent component of vortex advection in excitable media.

An advective field induces drift of a vortex in excitable media. The component of the drift velocity C( perpendicular ) perpendicular to the field is known to change its sign with the chirality of the vortex. In an experiment with vortices in an electric field in a chemical excitable medium, we have found unexpectedly that C( perpendicular ) changes its sign also independently of chirality with changing composition of the medium. We did not succeed to explain this phenomenon by using existing mathematical models of chemical excitable media. The experiment described calls for more realistic models.(c) 1999 American Institute of Physics.

Deexcitation of cardiac cells.

Excitation and deexcitation are fundamental phenomena in the electrophysiology of excitable cells. Both of them can be induced by stimulating a cell with intracellularly injected currents. With extracellular stimulation, deexcitation was never observed; only cell excitation was found. Why? A generic model with two variables (FitzHugh) predicts that an extracellular stimulus can both excite the cell and terminate the action potential (AP). Our experiments with single mouse myocytes have shown that short (2-5 ms) extracellular pulses never terminated the AP. This result agrees with our numerical experiments with the Beeler-Reuter model. To analyze the problem, we exploit the separation of time scales to derive simplified models with fewer equations. Our analysis has shown that the very specific form of the current-voltage (I-V) characteristics of the time-independent potassium current (almost no dependence on voltage for positive membrane potentials) is responsible here. When the shape of the I-V characteristics of potassium currents was modified to resemble that in ischemic tissues, or when the external potassium concentration (K0) is increased, the AP was terminated by extracellular pulses. These results may be important for understanding the mechanisms of defibrillation.

Models of defibrillation of cardiac tissue.

Heterogeneities, such as gap junctions, defects in periodical cellular lattices, intercellular clefts and fiber curvature allow one to understand the effect of an electric field in cardiac tissue. They induce membrane potential variations even in the bulk of the myocardium, with a characteristic sawtooth shape. The sawtooth potential, induced by heterogeneities at large scales (tissue strands) can be more easily observed, and lead to stronger effects than the one induced at the cellular level. In the generic model of propagation in cardiac tissue (FitzHugh), 4 mechanisms of defibrillation were found, two mechanisms based on excitation (E(A),E(M)), and two-on de-excitation (D(A),D(M)). The lowest electric field is required by an E(M) mechanism. In the Beeler-Reuter ionic model, mechanism D(M) is impossible. We critically review the experimental basis of the theory and propose new experiments. (c) 1998 American Institute of Physics.

Two biophysical mechanisms of defibrillation of cardiac tissue.

We have studied the mechanisms whereby a strong electric shock terminates chaotic wave propagation in cardiac tissue (defibrillation). In a generic model of cellular excitable tissue with two variables, we have found two mechanisms: one based on excitation (E), and another based on de-excitation (D) of cells by the small scale periodic component of transmembrane potential induced by the shock. Symmetry properties of the current-voltage characteristics describing the dynamics of the fast ionic currents, along with the strength of the electric field determine which of these mechanisms operates. A prediction of this work to be tested experimentally is that upon increasing the electric field one mechanism may switch to another, resulting in the following unusual sequence of events: defibrillation is first possible by mechanism E at moderate fields, then impossible, and finally possible by mechanism D, at higher fields.

Cardiac transient outward potassium current: a pulse chemistry model of frequency-dependent properties.

Recent voltage-clamp studies of isolated myocytes have demonstrated widespread occurrence of a transient outward current (I(to)) carried by potassium ions. In the canine ventricle, this current is well developed in epicardial cells but not in endocardial cells. The resultant spatial dispersion of refractoriness is potentially proarrhythmic and may be amplified by channel blockade. The inactivation and recovery time constants of this channel are in excess of several hundred milliseconds, and consequently channel availability is frequency dependent at physiological stimulation rates. When the time constants associated with transitions between different channel conformations are rapid relative to drug binding kinetics, the interactions between drugs and an ion channel can be approximated by a sequence of first-order reactions, in which binding occurs in pulses in response to pulse train stimulation (pulse chemistry). When channel conformation transition time constants do not meet this constraint, analytical characterizations of the drug-channel interaction must then be modified to reflect the channel time-dependent properties. Here we report that the rate and steady-state amount of frequency-dependent inactivation of I(to) are consistent with a generalization of the channel blockade model: channel availability is reduced in a pulsatile exponential pattern as the stimulation frequency is increased, and the rate of reduction is a linear function of the pulse train depolarizing and recovery intervals. I(to) was reduced in the presence of quinidine. After accounting for the use-dependent availability of I(to) channels, we found little evidence of an additional use-dependent component of block after exposure to quinidine, suggesting that quinidine reacts with both open and closed I(to) channels as though the binding site is continuously accessible. The model provides a useful tool for assessing drug-channel interactions when the reaction cannot be continuously monitored.

Proarrhythmic response to potassium channel blockade. Numerical studies of polymorphic tachyarrhythmias.

BACKGROUND: Prompted by the results of CAST results, attention has shifted from class I agents that primarily block sodium channels to class III agents that primarily block potassium channels for pharmacological management of certain cardiac arrhythmias. Recent studies demonstrated that sodium channel blockade, while antiarrhythmic at the cellular level, was inherently proarrhythmic in the setting of a propagating wave front as a result of prolongation of the vulnerable period during which premature stimulation can initiate reentrant activation. From a theoretical perspective, sodium (depolarizing) and potassium (repolarizing) currents are complementary so that if antiarrhythmic and proarrhythmic properties are coupled to modulation of sodium currents, then antiarrhythmic and proarrhythmic properties might similarly be coupled to modulation of potassium currents. The purpose of the present study was to explore the role of repolarization currents during reentrant excitation. METHODS AND RESULTS: To assess the generic role of repolarizing currents during reentry, we studied the responses of a two-dimensional array of identical excitable cells based on the FitzHugh-Nagumo model, consisting of a single excitation (sodium-like) current and a single recovery (potassium-like) current. Spiral wave reentry was initiated by use of S1S2 stimulation, with the delay timed to occur within the vulnerable period (VP). While holding the sodium conductance constant, the potassium conductance (gK) was reduced from 1.13 to 0.70 (arbitrary units), producing a prolongation of the action potential duration (APD). When gK was 1.13, the tip of the spiral wave rotated around a small, stationary, unexcited region and the computed ECG was monomorphic. As gK was reduced, the APD was prolonged and the unexcited region became mobile (nonstationary), such that the tip of the spiral wave inscribed an outline similar to a multipetaled flower; concomitantly, the computed ECG became progressively more polymorphic. The degree of polymorphism was related to the APD and the configuration of the nonstationary spiral core. CONCLUSIONS: Torsadelike (polymorphic) ECGs can be derived from spiral wave reentry in a medium of identical cells. Under normal conditions, the spiral core around which a reentrant wave front rotates is stationary. As the balance of repolarizing currents becomes less outward (eg, secondary to potassium channel blockade), the APD is prolonged. When the wavelength (APD.velocity) exceeds the perimeter of the stationary unexcited core, the core will become unstable, causing spiral core drift. Large repolarizing currents shorten the APD and result in a monomorphic reentrant process (stationary core), whereas smaller currents prolong the APD and amplify spiral core instability, resulting in a polymorphic process. We conclude that, similar to sodium channel blockade, the proarrhythmic potential of potassium channel blockade in the setting of propagation may be directly linked to its cellular antiarrhythmic potential, ie, arrhythmia suppression resulting from a prolonged APD may, on initiation of a reentrant wave front, destabilize the core of a rotating spiral, resulting in complex motion (precession) of the spiral tip around a nonstationary region of unexcited cells. In tissue with inhomogeneities, core instability alters the activation sequence from one reentry cycle to the next and can lead to spiral wave fractination as the wave front collides with inhomogeneous regions. Depending on the nature of the inhomogeneities, wave front fragments may annihilate one another, producing a nonsustained arrhythmia, or may spawn new spirals (multiple wavelets), producing fibrillation and sudden cardiac death.

Control of rotating waves in cardiac muscle: analysis of the effect of an electric field.

The effect of an electric field on rotating waves in cardiac muscle is considered from a theoretical point of view. A model of excitation propagation taking into account the cellular structure of the heart is presented and studied. The application of a direct current electric field along the cardiac tissue is known to induce changes in membrane potential which decay exponentially with distance. Investigation of the model shows that the electric field induces a gradient of potential inside a cell which does not decay with distance, and results in modification of excitation propagation which extends a considerable distance from the electrodes. In two dimensions, it induces a drift of rotating waves. The effect of the electric field on propagation velocity and on rotating waves cannot be obtained in any arbitrary models of cardiac muscle. For an electric field of about 1 V cm-1 and junctional resistances of about 20 M omega, the change in velocity of propagation can be up to several percent, resulting in a drift velocity of rotating waves of the order of 1 cm s-1. To test these predictions, experiments with cardiac preparations are proposed.

Vulnerability in an excitable medium: analytical and numerical studies of initiating unidirectional propagation.

Cardiac tissue can display unusual responses to certain stimulation protocols. In the wake of a conditioning wave of excitation, spiral waves can be initiated by applying stimuli timed to occur during a period of vulnerability (VP). Although vulnerability is well known in cardiac and chemical media, the determinants of the VP and its boundaries have received little theoretical and analytical study. From numerical and analytical studies of reaction-diffusion equations, we have found that 1) vulnerability is an inherent property of Beeler-Reuter and FitzHugh-Nagumo models of excitable media; 2) the duration of the vulnerable window (VW) the one-dimensional analog of the VP, is sensitive to the medium properties and the size of the stimulus field; and 3) the amplitudes of the excitatory and recovery processes modulate the duration of the VW. The analytical results reveal macroscopic behavior (vulnerability) derived from the diffusion of excitation that is not observable at the level of isolated cells or single reaction units.

Wave mechanisms of pattern formation in microbial populations.

The occurrence of spatially ordered structures plays an important role in biology (examples: morphogenesis, ecosystems, dynamics of populations, etc.). Turing proposed a reaction-diffusion process that is the basis for most theoretical studies of stationary biological pattern formation. Now, when Turing structures are obtained in experiments (40 years after Turing's publication), it is interesting to discover whether Turing structures are the only mechanism used by nature in biological pattern formation. In microbial growth, we have found experimental evidence of an alternative to the Turing model that is based on waves displayed in excitable media. In studies of Escherichia coli populations, we observed that interacting taxis waves create motionless patterns. Taxis waves consuming two different substrates (serine and aspartic acid) were involved. Taxis waves consuming serine stop when they collide. However, those supported by consumption of aspartic were initiated at the collision line. Colliding and annihilating in turn, the waves give rise to stationary pattern formation, and wave theory provides an alternative to the classical Turing mechanism.

Vagally induced depression of impulse propagation as a cause of atrial tachycardia.

It is known that parasympathetic influence favors induction of re-entrant atrial tachycardias (ATs). This effect is usually interpreted as a result of inhomogeneous shortening of atrial refractoriness leading to increased probability of circus movement following a premature impulse. However, early microelectrode studies showed that in spontaneously beating isolated frog atria, intensive vagal stimulation (VS) induced paroxysms of rapid AT in the absence of myocardial extrastimulation. This AT was found to correlate with inexcitability of some of the impaled fibers of the atria. It was supposed that temporary, vagally induced, inexcitable areas of the atria could lead to re-entry, serving as a site of unidirectional conduction. This hypothesis was recently evaluated by direct multielectrode mapping of excitation sequence during vagally induced AT in frog atria. Recording from 32 sites with a spatial resolution of 1-2 mm clearly showed that the AT was due to re-entry. The ATs were always preceded by vagally induced depression of conduction, with some areas of the atria being completely blocked. As the vagal influence decreased, the blocked areas recovered in an inhomogeneous manner. The re-entrant AT was initiated when a sinus impulse arrived during a certain phase of the recovery. Unlike the well-known mechanism of re-entry, which is based on inhomogeneous refractoriness and extrabeat(s), the re-entrant AT in our model depended on vagally induced conduction block and could be launched by a single sinus impulse.