Cardiac fibrillation (spontaneous, asynchronous contractions of cardiac muscle fibres) is the leading cause of death in the industrialized world, yet it is not clear how it occurs. It has been debated whether or not fibrillation is a random phenomenon. There is some determinism during fibrillation, perhaps resulting from rotating waves of electrical activity. Here we present a new algorithm that markedly reduces the amount of data required to depict the complex spatiotemporal patterns of fibrillation. We use a potentiometric dye and video imaging to record the dynamics of transmembrane potentials at many sites during fibrillation. Transmembrane signals at each site exhibit a strong periodic component centred near 8 Hz. This periodicity is seen as an attractor in two-dimensional-phase space and each site can be represented by its phase around the attractor. Spatial phase maps at each instant reveal the 'sources' of fibrillation in the form of topological defects, or phase singularities, at a few sites. Using our method of identifying phase singularities, we can elucidate the mechanisms for the formation and termination of these singularities, and represent an episode of fibrillation by locating singularities. Our results indicate an unprecedented amount of temporal and spatial organization during cardiac fibrillation.

The mechanism of reentrant ventricular tachycardia was studied in computer simulations and in thin (z20x20x0.5-mm) slices of dog and sheep ventricular epicardial muscle. A two-dimensional matrix consisting of 96x96 electrically coupled cells modeled by the FitzHugh-Nagumo equations was used to analyze the dynamics of self-sustaining reentrant activity in the form of elliptical spiral waves induced by premature stimulation. In homogeneous anisotropic media, spirals are stationary and may last indefinitely. However, the presence of small parameter gradients may lead to drifting and eventual termination of the spiral at the boundary of the medium. On the other hand, spirals may anchor and rotate around small discontinuities within the matrix. Similar results were obtained experimentally in 10 preparations whose electrical activity was monitored by means of a potentiometric dye and high-resolution optical mapping techniques; premature stimulation triggered reproducible episodes of sustained or nonsustained reentrant tachycardia in the form of spiral waves. As a rule, the spirals were elongated, with the major hemiaxis parallel to the longitudinal axis of the cells. The period of rotation (183+±68 msec [mean± SD]) was longer than the refractory period (131±38 msec) and appeared to be determined by the size of the spiral's core, which was measured using a newly devised "frame-stack" plot. Drifting of spiral waves was also observed experimentally. Drift velocity was 9.8% of the velocity of wave propagation. In some cases, the core became stationary by anchoring to small arteries or other heterogeneities, and the spiral rotated rhythmically for prolonged periods of time. Yet, when drift occurred, spatiotemporal variations in the excitation period were manifested as a result of a Doppler effect, with the excitation period ahead of the core being 20±6% shorter than the excitation period behind the core. As a result of these coexisting frequencies, a pseudoelectrocardiogram of the activity in the presence of a drifting spiral wave exhibited "QRS complexes" with an undulating axis, which resembled those observed in patients with torsade de pointes. The overall results show that spiral wave activity is a property of cardiac muscle and suggest that such activity may be the common mechanism of a number of monomorphic and polymorphic tachycardias. (Circulation Research 1993;72:631-650) KEY WORDS * reentry * ventricular tachycardia spirals R] eentrant excitation may lead to exceedingly rapid, self-sustaining, regular or irregular activity throughout the heart, which is the hallmark of life-threatening arrhythmias such as ventricular tachycardia and ventricular fibrillation.12 Recent experimental studies3-7 support the hypothesis8-11 that reentrant excitation in ventricular muscle may be the result of spiral wave activity. This * torsade de pointes * Doppler effect * drifting in the cytosol of Xenopus oocytes.16 In the case of the heart, the spiral wave concept may be complementary to more traditional ideas that are based on ...

MItL to the following relationship: 11 3. 5. Dibbs et a)., AIDS Res. Hum. Retrovir. 10, 607 and 2BD1 A135533 02, DAMD grant 1 7 94-J-4431 (1994) Fig. 1 A, the frequency of lence in 3Ds only, then we will find no breakrotation of the rotor (f s = 7.5 Hz) was calculated

Tissue heterogeneities may play an important role in the mechanism of ventricular tachycardia (VT) and fibrillation (VF) and can lead to a complex spatial distribution of excitation frequencies. Here we used optical mapping and Fourier analysis to determine the distribution of excitation frequencies in >20 000 sites of fibrillating ventricular tissue. Our objective was to use such a distribution as a tool to quantify the degree of organization during VF. Fourteen episodes of VT/VF were induced via rapid pacing in 9 isolated, coronary perfused, and superfused sheep ventricular slabs (3x3 cm(2)). A dual-camera video-imaging system was used for simultaneous optical recordings from the entire epi- and endocardial surfaces. The local frequencies of excitation were determined at each pixel and displayed as dominant frequency (DF) maps. A typical DF map consisted of several (8.2+/-3.6) discrete areas (domains) with a uniform DF within each domain. The DFs in adjacent domains were often in 1:2, 3:4, or 4:5 ratios, which was shown to be a result of an intermittent Wenckebach-like conduction block at the domain boundaries. The domain patterns were relatively stable and could persist from several seconds to several minutes. The complexity in the organization of the domains, the number of domains, and the dispersion of frequencies increased with the rate of the arrhythmia. Domain patterns on the epicardial and endocardial surfaces were not correlated. Sustained epicardial or endocardial reentry was observed in only 3 episodes. Observed frequency patterns during VT/VF suggest that the underlying mechanism may be a sustained intramural reentrant source interacting with tissue heterogeneities.

We have investigated the role of wave-front curvature on propagation by following the wave front that was diffracted through a narrow isthmus created in a two-dimensional ionic model (Luo-Rudy) of ventricular muscle and in a thin (0.5-mm) sheet of sheep ventricular epicardial muscle. The electrical activity in the experimental preparations was imaged by using a high-resolution video camera that monitored the changes in fluorescence of the potentiometric dye di-4-ANEPPS on the surface of the tissue. Isthmuses were created both parallel and perpendicular to the fiber orientation. In both numerical and biological experiments, when a planar wave front reached the isthmus, it was diffracted to an elliptical wave front whose pronounced curvature was very similar to that of a wave front initiated by point stimulation. In addition, the velocity of propagation was reduced in relation to that of the original planar wave. Furthermore, as shown by the numerical results, wave-front curvature changed as a function of the distance from the isthmus. Such changes in local curvature were accompanied by corresponding changes in velocity of propagation. In the model, the critical isthmus width was 200 ,um for longitudinal propagation and 600 gm for I n a cable of electrically coupled cells, slow conduction and block often result from a decreased transmembrane inward current and/or uncoupling between cells. In each case, the "safety factor," defined as the ratio between the current available to excite cells downstream (the "source") and the current needed to excite those cells (the "sink"), determines whether there will be conduction or block. If there is conduction, the safety factor determines the velocity of propagation.1 The sink-to-source relation is contemplated by the concept of liminal length, which establishes that there is a minimal length of a one-dimensional fiber that needs to be excited simultaneously for propagation to proceed.1-3 However, in normal cardiac muscle, certain structural factors may lead to an "impedance mismatch" between the sink and the source, with a consequent alteration of the propagation process. Such factors have been well studied in a number of experimental Received February 25, 1994; accepted August 29, 1994 transverse propagation of a single planar wave initiated proximal to the isthmus. In the experiments, propagation depended on the width of the isthmus for a fixed stimulation frequency. Propagation through an isthmus of fixed width was rate dependent both along and across fibers. Thus, the critical isthmus width for propagation was estimated in both directions for different frequencies of stimulation. In the longitudinal direction, for cycle lengths between 200 and 500 milliseconds, the critical width was <1 mm; for 150 milliseconds, it was estimated to be between 1.3 and 2 mm; and for the maximum frequency of stimulation (117±15 milliseconds), it was >2.5 mm. In the transverse direction, critical width was between 1.78 and 2.32 mm for a basic cycle length of 200 milliseconds. It inc...