L. Joshua Leon

Spatiotemporal evolution of ventricular fibrillation.

Sudden cardiac death is the leading cause of death in the industrialized world, with the majority of such tragedies being due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular disturbance of the heart rhythm that quickly renders the heart incapable of sustaining life. Rotors, electrophysiological structures that emit rotating spiral waves, occur in several systems that all share with the heart the functional properties of excitability and refractoriness. These re-entrant waves, seen in numerical solutions of simplified models of cardiac tissue, may occur during ventricular tachycardias,. It has been difficult to detect such forms of re-entry in fibrillating mammalian ventricles. Here we show that, in isolated perfused dog hearts, high spatial and temporal resolution mapping of optical transmembrane potentials can easily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross-correlation. During this early fibrillatory interval, frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism that lacks the epicardial manifestations of rotors despite continued myocardial perfusion.

Watershed-Based Segmentation and Region Merging

In recent years, the watershed line has emerged as the primary tool of mathematical morphology for image segmentation. Several very efficient algorithms have been devised for the determination of watersheds. Nevertheless, the application of watershed algorithms to an image is often disappointing: the image is oversegmented into a large number of tiny, shallow watersheds, where one wanted to obtain only a few deep ones. This paper presents a novel approach to watershed merging. Mainly, it addresses the following question: given an image, what is the closest image that has a simpler watershed structure? The basic idea is to replicate the process of watershed merging that takes place when rain falls over a real landscape: smaller watersheds progressively fill until an overflow occurs. The water then flows to a nearby, larger or deeper watershed, in which the overflown watersheds are merged. The methods presented in this paper apply the minimum extensive modifications possible to a given image to obtain a new one that has many fewer watersheds but is still “close” to the original. Their usefulness is demonstrated for several biomedical applications.

Cholinergic Atrial Fibrillation in a Computer Model of a Two-Dimensional Sheet of Canine Atrial Cells With Realistic Ionic Properties

Classical concepts of atrial fibrillation (AF) have been rooted in Moe’s multiple-wavelet hypothesis and simple cellular-automaton computer model. Recent experimental work has raised questions about the multiple-wavelet mechanism, suggesting a discrete “driver region” underlying AF. We reexplored the theoretical basis for AF with a 2-dimensional computer model of a 5×10-cm sheet of atrial cells with realistic ionic and coupling properties. Vagal actions were formulated based on patch-clamp studies of acetylcholine (ACh) effects. In control, a single extrastimulus resulted in a highly meandering unstable spiral wave. Simulated electrograms showed fibrillatory activity, with a dominant frequency (DF, 6.5 Hz) that correlated with the mean rate. Uniform ACh reduced core meander of the spiral wave by ≈70% (as measured by the standard deviation of spiral-wave tip position) and accelerated the DF to 17.0 Hz. Simulated vagally induced refractoriness heterogeneity caused wavefront breakup as accelerated reentrant activity in regions of short refractoriness impinged on regions unable to respond in a 1:1 fashion because of longer refractoriness. In 7 simulations spanning the range of conditions giving sustained AF, 5 were maintained by single dominant spiral waves. On average, 3.0±1.3 wavelets were present (range, 1 to 7). Most wavelets were short-lived and did not contribute to AF maintenance. In contrast to predictions of the multiple-wavelet hypothesis, but in agreement with recent experimental evidence, our model indicates that AF can result from relatively stable primary spiral-wave generators and is significantly organized. Our results suggest that vagal AF may arise from ACh-induced stabilization of the primary spiral-wave generator and disorganization of the heterogeneous tissue response. The full text of this article is available at http://www.circresaha.org.

Mechanisms of Atrial Fibrillation Termination by Pure Sodium Channel Blockade in an Ionically-Realistic Mathematical Model

The mechanisms by which Na+-channel blocking antiarrhythmic drugs terminate atrial fibrillation (AF) remain unclear. Classical “leading-circle” theory suggests that Na+-channel blockade should, if anything, promote re-entry. We used an ionically-based mathematical model of vagotonic AF to evaluate the effects of applying pure Na+-current (INa) inhibition during sustained arrhythmia. Under control conditions, AF was maintained by 1 or 2 dominant spiral waves, with fibrillatory propagation at critical levels of action potential duration (APD) dispersion. INa inhibition terminated AF increasingly with increasing block, terminating all AF at 65% block. During 1:1 conduction, INa inhibition reduced APD (by 13% at 4 Hz and 60% block), conduction velocity (by 37%), and re-entry wavelength (by 24%). During AF, INa inhibition increased the size of primary rotors and reduced re-entry rate (eg, dominant frequency decreased by 33% at 60% INa inhibition) while decreasing generation of secondary wavelets by wavebreak. Three mechanisms contributed to INa block–induced AF termination in the model: (1) enlargement of the center of rotation beyond the capacity of the computational substrate; (2) decreased anchoring to functional obstacles, increasing meander and extinction at boundaries; and (3) reduction in the number of secondary wavelets that could provide new primary rotors. Optical mapping in isolated sheep hearts confirmed that tetrodotoxin dose-dependently terminates AF while producing effects qualitatively like those of INa inhibition in the mathematical model. We conclude that pure INa inhibition terminates AF, producing activation changes consistent with previous clinical and experimental observations. These results provide insights into previously enigmatic mechanisms of class I antiarrhythmic drug-induced AF termination. The full text of this article is available online at http://circres.ahajournals.org

A method for visualization of ventricular fibrillation: Design of a cooled fiberoptically coupled image intensified CCD data acquisition system incorporating wavelet shrinkage based adaptive filtering.

The measurement of cardiac transmembrane potential changes with voltage sensitive dyes is in increasing use. Detection of these very small fluorescent alterations using large multiplexed arrays, such as charge coupled device (CCD) cameras at high sampling rates, has proven challenging and usually requires significant averaging to improve the signal-to-noise ratio. To minimize the damage of living tissue stained with voltage sensitive dyes, excitation photon exposure must be limited, with the inevitable consequence of diminishing the fluorescence that is generated. State-of-the-art high frame rate CCD cameras have read noise levels in the 5-10 e(-) rms range, which is at least two orders of magnitude above that required to detect voltage sensitive dye alterations at individual pixels corresponding to 1 mm(2) heart regions illuminated with levels of 100 mW/cm(2) at frame rates approaching 1000 frames/sec. Image intensification is thus required prior to photon quantification. We report here the development of such a data acquisition system using commercially available hardware. Additionally, in the past ten years, a mathematical theory of multiresolution has been developed, and new building blocks called wavelets, allow a signal to be observed at different resolutions. Wavelet analysis also makes possible a new method of extricating signals from noise. We have incorporated spatially adaptive filters based on wavelet denoising of individual pixels to significantly reduce the multiple noise sources present in the acquired data. (c) 1998 American Institute of Physics.

Calculation of Transmembrane Current From Extracellular Potential Recordings: A Model Study

Transmembrane Current Estimation. Introduction: A mathematical/computer model of cardiac tissue was used to study the estimation of transmembrane current (EIm) from extracellular potential recordings.

Propagation on a central fiber surrounded by inactive fibers in a multifibered bundle model

We studied uniform propagation on a central active fiber surrounded by inactive fibers in a multifibered bundle model lying in a large volume conductor. The behavior of a fully active bundle is considered in a companion paper. The bundle is formed by concentric layers of small cylindrical fibers (radius 5 μm), with a uniform minimum distance (d) between any two adjacent fibers, to yield a bundle radius of about 72μm. Individual vidual fibers are identical continuous cables of excitable membrane based on a modified Beeler-Reuter model. The intracellular volume fraction (fi) increases to a maximum of about 90% asd is reduced and remains unchanged ford<0.01 μm. In the range ofd<0.01 μm, the central fiber is effectively shielded from external effects by the first concentric layer of inactive fibers, and a large capacitive load current flows across the surrounding inactive membranes. In addition, the fiber proximity produces a circumferentially nonuniform, current density (proximity effect) that is equivalent to an increased average longitudinal interstitial resistance. The conduction velocity is reduced asd becomes smaller in the range ofd<0.1 μm, the interstitial potential becomes larger, and both the maximum rate of rise and time constant of the foot of the upstroke are increased. On the other hand, ford>0.1 μm, there are negligible changes in the shape of the upstroke, and the, behavior of the central fiber is close to that of a uniform cable in a restricted volume conductor. Ford larger than about 1.2 μm, the active fiber environment is close to an unbounded isotropic volume conductor.

Action potential propagation in a thin strand of cardiac fibers

Action potential propagation in a strand of cardiac fibers was studied using a model developed from potential theory which incorporates both microscopic structural details and realistic membrane dynamics. The conduction velocity and τfoot of the propagating transmembrane action potential were found to vary directly with the density of fibers within the bundle, whereas Vmax varied in the opposite direction.

Figure-of eight reentry in a model of cardiac tissue

A model of a thin sheet of myocardium was used to examine the role played by tissue anisotropy in the induction of reentry. We found that figure of eight reentry could be induced in the model using a properly timed premature stimulus, however if the anisotropy ratio was too low (conduction velocity ratios less than 4:1) the reentry was not sustained.