.-The restitution kinetics of action potential duration (APD) were investigated in paced canine Purkinje fibers (P; n ϭ 9) and endocardial muscle (M; n ϭ 9), in isolated, perfused canine left ventricles during ventricular fibrillation (VF; n ϭ 4), and in endocardial muscle paced at VF cycle lengths (simulated VF; n ϭ 4). Restitution was assessed with the use of two protocols: delivery of a single extrastimulus after a train of stimuli at cycle length ϭ 300 ms (standard protocol), and fixed pacing at short cycle lengths (100-300 ms) that induced APD alternans (dynamic protocol). The dynamic protocol yielded a monotone increasing restitution function with a maximal slope of 1.13 Ϯ 0.13 in M and 1.14 Ϯ 0.17 in P. Iteration of this function reproduced the APD dynamics found experimentally, including persistent APD alternans. In contrast, the standard protocol yielded a restitution relation with a maximal slope of 0.57 Ϯ 0.18 in M and 0.84 Ϯ 0.20 in P, and iteration of this function did not reproduce the APD dynamics. During VF, the restitution kinetics at short diastolic interval were similar to those determined with the dynamic protocol (maximal slope: 1.72 Ϯ 0.47 in VF and 1.44 Ϯ 0.49 in simulated VF). Thus APD dynamics at short coupling intervals during fixed pacing and during VF were accounted for by the dynamic, but not the standard, restitution relation. These results provide further evidence for a strong relationship among the kinetics of electrical restitution, the occurrence of APD alternans, and complex APD dynamics during VF. restitution kinetics; complex dynamics; ventricular arrhythmias RATE-DEPENDENT ALTERATIONS of action potential duration (APD) and refractoriness are believed to be important determinants of ventricular arrhythmias (6,7,9,13,16,17,19,23,28,30). The changes in APD that accompany changes in rate reflect the dependence of APD on the preceding diastolic interval (DI), a relationship characterized by electrical restitution (2-4, 10-12). Several experimental and computer modeling studies (9, 15-17, 19, 20, 26) have suggested that the kinetics of electrical restitution have important implications for the development of ventricular arrhythmias. In particular, it has been proposed that a steep slope (Ն1) of the restitution relation may determine whether single spiral waves of electrical activity splinter into multiple smaller spirals, thereby creating a transition from ventricular tachycardia to ventricular fibrillation (5, 17, 31).The breakup of spiral waves is thought to be precipitated by oscillations of APD that are of sufficiently large amplitude to cause conduction block along the spiral wave front (17). This type of oscillation, also known as APD alternans, is a well-recognized phenomenon that occurs in ventricular tissue at rapid rates of stimulation and after abrupt shortening of the cycle length (21,25,26). During alternans, a short (long) DI sequence generates a short (long) APD sequence. This dynamic property is linked to the slope of the restitution relation in that, for persiste...

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult due to the nonlinear interaction of excitation waves within a heterogeneous anatomical substrate1–4. Lacking a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation5–7. Here, we establish the relation between the response of the tissue to an electric field and the spatial distribution of heterogeneities of 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 a power law τ∝Eα. 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 novel control strategy, we demonstrate, for the first time, 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 at the same time provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Despite recent advances in our understanding of the mechanism for ventricular fibrillation (VF), important electrophysiological aspects of the development of VF still are poorly defined. It has been suggested that the onset of VF involves the disintegration of a single spiral wave into many self-perpetuating waves. It has been further suggested that such a process requires that the slope of the electrical restitution relation be >/=1. The same theory anticipates that a single spiral wave will be stable (not disintegrate) if the maximum slope of the restitution relation is <1. We have shown previously that the slope of the restitution relation during rapid pacing and during VF is >/=1 in canine ventricle. We now show that drugs that reduce the slope of the restitution relation (diacetyl monoxime and verapamil) prevent the induction of VF and convert existing VF into a periodic rhythm. In contrast, a drug that does not reduce the slope of the restitution relation (procainamide) does not prevent the induction of VF, nor does it regularize VF. These results indicate that the kinetics of electrical restitution is a key determinant of VF. Moreover, they suggest novel approaches to preventing the induction or maintenance of VF.

Although alternans of action potential duration (APD) is a robust feature of the rapidly paced canine ventricle, currently available ionic models of cardiac myocytes do not recreate this phenomenon. To address this problem, we developed a new ionic model using formulations of currents based on previous models and recent experimental data. Compared with existing models, the inward rectifier K(+) current (I(K1)) was decreased at depolarized potentials, the maximum conductance and rectification of the rapid component of the delayed rectifier K(+) current (I(Kr)) were increased, and I(Kr) activation kinetics were slowed. The slow component of the delayed rectifier K(+) current (I(Ks)) was increased in magnitude and activation shifted to less positive voltages, and the L-type Ca(2+) current (I(Ca)) was modified to produce a smaller, more rapidly inactivating current. Finally, a simplified form of intracellular calcium dynamics was adopted. In this model, APD alternans occurred at cycle lengths = 150-210 ms, with a maximum alternans amplitude of 39 ms. APD alternans was suppressed by decreasing I(Ca) magnitude or calcium-induced inactivation and by increasing the magnitude of I(K1), I(Kr), or I(Ks). These results establish an ionic basis for APD alternans, which should facilitate the development of pharmacological approaches to eliminating alternans.

Background-Electrically based therapies for terminating atrial fibrillation (AF) currently fall into 2 categories:antitachycardia pacing and cardioversion. Antitachycardia pacing uses low-intensity pacing stimuli delivered via a single electrode and is effective for terminating slower tachycardias but is less effective for treating AF. In contrast, cardioversion uses a single high-voltage shock to terminate AF reliably, but the voltages required produce undesirable side effects, including tissue damage and pain. We propose a new method to terminate AF called far-field antifibrillation pacing, which delivers a short train of low-intensity electric pulses at the frequency of antitachycardia pacing but from field electrodes. Prior theoretical work has suggested that this approach can create a large number of activation sites ("virtual" electrodes) that emit propagating waves within the tissue without implanting physical electrodes and thereby may be more effective than point-source stimulation. Methods and Results-Using optical mapping in isolated perfused canine atrial preparations, we show that a series of pulses at low field strength (0.9 to 1.4 V/cm) is sufficient to entrain and subsequently extinguish AF with a success rate of 93% (69 of 74 trials in 8 preparations). We further demonstrate that the mechanism behind far-field antifibrillation pacing success is the generation of wave emission sites within the tissue by the applied electric field, which entrains the tissue as the field is pulsed. Conclusions-AF in our model can be terminated by far-field antifibrillation pacing with only 13% of the energy required for cardioversion. Further studies are needed to determine whether this marked reduction in energy can increase the effectiveness and safety of terminating atrial tachyarrhythmias clinically. Key Words: arrhythmia Ⅲ atrium Ⅲ cardioversion Ⅲ fibrillation Ⅲ mapping A trial fibrillation (AF) is the most common sustained cardiac arrhythmia worldwide, 1 affecting Ͼ2.2 million people in the United States alone. 2 Complications associated with chronic AF include increased risk for both thromboembolism and stroke. 2 Left untreated, paroxysmal AF often progresses to permanent AF, which is resistant to therapy. 3 Although underlying anatomic or pathophysiological factors may fuel this progression, 3 AF itself may lead to its own perpetuation through electric, structural, and metabolic remodeling of atrial tissue. The realization that AF begets AF 4 has led to management strategies that are designed to avoid the progression of AF by reducing the frequency and duration of AF episodes. Clinical Perspective on p 476One such strategy, cardioversion, attempts to reset all electric activity in the atria and requires the use of large (Ͼ5 V/cm) electric field gradients. 5-7 These high energies cause pain and trauma for the patient, damage the myocardium, and reduce battery life in implanted devices. 8 Another strategy, antitachycardia pacing (ATP), seeks to avoid the development of permanent AF by suppressing paroxysmal A...

Theoretical studies have indicated that alternans (period-doubling instability) of action potential duration is associated with a restitution relation with a slope >or=1. However, recent experimental findings suggest that the slope of the restitution relation is not necessarily predictive of alternans. Here, we compared a return map memory model to action potential data from an ionic model and found that the memory model reproduced dynamics that could not be explained by a unidimensional restitution relation. Using linear stability analysis, we determined the onset of the alternans in the memory model and confirmed that the slope of the restitution curve was not predictive.

Abstract-Interruption of periodic wave propagation by the nucleation and subsequent disintegration of spiral waves is thought to mediate the transition from normal sinus rhythm to ventricular fibrillation. This sequence of events may be precipitated by a period doubling bifurcation, manifest as a beat-to-beat alternation, or alternans, of cardiac action potential duration and conduction velocity. How alternans causes the local conduction block required for initiation of spiral wave reentry remains unclear, however. In the present study, a mechanism for conduction block was derived from experimental studies in linear strands of cardiac tissue and from computer simulations in ionic and coupled maps models of homogeneous one-dimensional fibers. In both the experiments and the computer models, rapid periodic pacing induced marked spatiotemporal heterogeneity of cellular electrical properties, culminating in paroxysmal conduction block. These behaviors resulted from a nonuniform distribution of action potential duration alternans, secondary to alternans of conduction velocity. This link between period doubling bifurcations of cellular electrical properties and conduction block may provide a generic mechanism for the onset of tachycardia and fibrillation. (Circ Res. 2002;90: 289-296.)Key Words: ventricular fibrillation Ⅲ alternans Ⅲ conduction block O ur current understanding of the mechanism for ventricular fibrillation is incomplete, as reflected by the statistic that sudden death continues to be the leading cause of mortality in the Western world. One candidate mechanism for fibrillation is the nucleation of a pair of counterrotating spiral waves, which subsequently disintegrate into multiple wavelets, 1,2 in association with a period doubling bifurcation of cellular electrical properties. 3-6 However, the mechanism by which a period doubling bifurcation may precipitate the local conduction block necessary for the initiation of spiral wave reentry is unknown.Previous studies have shown that the induction and propagation of period doubling bifurcations in cardiac tissue depend on the recovery properties for action potential duration (D) and conduction velocity (V), where D or V for a given action potential (D nϩ1 or V nϩ1 , respectively) is a function of the preceding interval (I n ) between action potentials. 7-10 If the function D nϩ1 ϭf(I n ) has a maximum slope Ն1, 1:1 stimulus:response locking during pacing at long cycle lengths is replaced by 2:2 locking at short cycle lengths, with 2:2 locking being characterized by beat-to-beat, long-short alternations of D and I.During 2:2 locking, alternation of I also causes an alternation of V, where V nϩ1 ϭc(I n ). Alternation of V influences action potential propagation and the spatial distribution of D along a cardiac fiber. 11,12 If the fiber is sufficiently long, the long-short D pattern at one end of the fiber reverses phase and becomes a short-long pattern at the other end. This phenomenon, known as discordant alternans, has been observed in computer simulations o...

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.