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.

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

Alternans and arrhythmia dynamics are affected by the spatial dispersion of APD restitution as well as CV restitution, not simply the slope of APD restitution. Therefore, a direct link of the APD restitution slope to alternans and arrhythmia dynamics in rabbit heart does not exist. Designing antiarrhythmic drugs to alter only the restitution slope may not be appropriate.

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...