Low-energy control of electrical turbulence in the heart.

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ E(α). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Bistable reaction-diffusion systems can have robust zero-velocity fronts.

We show that for a class of bistable reaction-diffusion systems, zero-velocity fronts can be robust in the singular limit where one of the diffusion coefficients vanishes. In this case, stationary fronts can persist along variations of the system parameters. This property contrasts with the standard result that the front velocity v(&mgr;), expressed as a function of a control parameter &mgr;, is zero only at some isolated values &mgr;(0), and thus not giving robustness to zero-velocity fronts when &mgr; is varied. (c) 2000 American Institute of Physics.

Effect of an externally applied electric field on excitation propagation in the cardiac muscle.

Classical theory of potential distribution in cardiac muscle (cable theory) postulates that all effects of electric field (internally or externally applied) should decay exponentially with a space constant of the order of the tissue space constant ( approximately 1 mm). Classical theory does not take into account the cellular structure of the heart. Here, we formulate a mathematical model of excitation propagation taking into account cellular gap junctions. Investigation of the model has shown that the classical description is correct on the macroscopic scale only. At microscopic scale, electric field is modulated with a spatial period equal to the cell size (Plonsey and Barr), with the zero average. A very important new feature found here is that this effect of electric field does not decay at arbitrary big distances from the electrode. It opens the new way to control the excitation propagation in the cardiac muscle. In particular, we show that electric field can modify the velocity of propagation of an impulse in cardiac tissue at arbitrary big distances from electrode. In 2-dimensions, it can make rotating waves drift. To test these predictions, experiments with cardiac preparations are proposed.

Persistence of zero velocity fronts in reaction diffusion systems.

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.

Mechanisms of unpinning and termination of ventricular tachycardia.

High-energy defibrillation shock is the only therapy for ventricular tachyarrhythmias. However, because of adverse side effects, lowering defibrillation energy is desirable. We investigated mechanisms of unpinning, destabilization, and termination of ventricular tachycardia (VT) by low-energy shocks in isolated rabbit right ventricular preparations (n = 22). Stable VT was initiated with burst pacing and was optically mapped. Monophasic "unpinning" shocks (10 ms) of different strengths were applied at various phases throughout the reentry cycle. In 8 of 22 preparations, antitachycardia pacing (ATP: 8-20 pulses, 50-105% of period, 0.8-10 mA) was also applied. Termination of reentry by ATP was achieved in only 5 of 8 preparations. Termination by unpinning occurred in all 22 preparations. Rayleigh's test showed a statistically significant unpinning phase window, during which reentry could be unpinned and subsequently terminated with E80 (magnitude at which 80% of reentries were unpinned) = 1.2 V/cm. All reentries were unpinned with field strengths < or = 2.4 V/cm. Unpinning was achieved by inducing virtual electrode polarization and secondary sources of excitation at the core of reentry. Optical mapping revealed the mechanisms of phase-dependent unpinning of reentry. These results suggest that a 20-fold reduction in energy could be achieved compared with conventional high-energy defibrillation and that the unpinning method may be more effective than ATP for terminating stable, pinned reentry in this experimental model.