Topologic charge densities can be calculated easily and efficiently to reveal phase singularity behavior. However, the differences between theoretical and experimental observations of singularity separation distances indicate the need for more sophisticated numerical models.

Cardiac reentrant arrhythmias may be examined by using time-series analysis, where a state variable is plotted against the same variable with an embedded time delay tau to form a phase portrait. The success of this procedure is contingent upon the resultant phase-space trajectories encircling a fixed origin. However, errors in interpreting the dynamics of phase singularities associated with reentry may arise due to the trajectories not encircling the origin or due to a poor choice of tau. We demonstrate an algorithm which is capable of establishing proper orbits without the need to specify tau. We find that phase singularities could be localized closer to the point of initial formation than was possible previously, which is important for the purposes of singularity tracking and investigating electrodynamic interactions.

The unique time course of an excitable element in cardiac tissue can be represented as the phase of its trajectory in state space. A phase singularity is defined as a spatial point where the surrounding phase values changes by a total of 2 pi, thereby forming the organizing center for a reentrant excitatory wave, a phenomenon which occurs in cardiac fibrillation. In this paper, we describe a methodology to detect the singular filament in numeric simulations of three-dimensional (3-D) scroll waves by using the concept of topological charge. Here, we use simple two-variable models of cardiac activity to construct the state space, generate the phase field, and calculate the topological charge as a summation of 3-D convolution operations. We illustrate the usage of the algorithm on the basic dynamics of vortex ring filament behavior as well as the more complex spatiotemporal behavior observed in fibrillation. We also compare the motion of filament wavetips as determined by the phase field produced by two-variable state space and single-variable, time-delay embedded state space. Finally, we examine the state spaces produced by a more complex three-variable model. We conclude that the use of state-space analysis, along with the unique properties of topological charge, allows for a novel means of filament localization.

Optical mapping with voltage-sensitive dyes provides a high-resolution technique to observe cardiac electrodynamic behavior. Although most studies assume that the fluorescent signal is emitted from the surface layer of cells, the effects of signal attenuation with depth on signal interpretation are still unclear. This simulation study examines the effects of a depth-weighted signal on epicardial activation patterns and filament localization. We simulated filament behavior using a detailed cardiac model, and compared the signal obtained from the top (epicardial) layer of the spatial domain with the calculated weighted signal. General observations included a prolongation of the action upstroke duration, early upstroke initiation, and reduction in signal amplitude in the weighted signal. A shallow filament was found to produce a dual-humped action potential morphology consistent with previously reported observations. Simulated scroll wave breakup exhibited effects such as the false appearance of graded potentials, apparent supramaximal conduction velocities, and a spatially blurred signal with the local amplitude dependent upon the immediate subepicardial activity; the combination of these effects produced a corresponding change in the accuracy of filament localization. Our results indicate that the depth-dependent optical signal has significant consequences on the interpretation of epicardial activation dynamics.

Optical imaging of transmembrane potentials in cardiac tissue is a rapidly growing technique in cardiac electrophysiology. Traditional studies typically use a monocular imaging setup, thus limiting investigation to a restricted region of tissue. However, studies of large-scale wavefront dynamics, especially those during fibrillation and defibrillation, would benefit from visualization of the entire epicardial surface. To solve this problem, a panoramic cardiac visualization algorithm was developed which performs the two tasks of reconstruction of the surface geometry of the heart, and representation of the panoramic fluorescence information as a texture mapping onto the geometry that was previously created. This system permits measurement of epicardial electrodynamics over a geometrically realistic representation of the actual heart being studied. To verify the accuracy of the algorithm, the procedure was applied to synthetic images of a patterned ball; further verification was provided by application of the algorithm to a model heart placed in the experimental setup. Both sets of images produced mean registration image errors on the order of 2 pixels, corresponding to roughly 3 mm on the geometry. We demonstrate the algorithm by visualizing epicardial wavefronts on an isolated, perfused rabbit heart.