Controlling cardiac chaos.

The extreme sensitivity to initial conditions that chaotic systems display makes them unstable and unpredictable. Yet that same sensitivity also makes them highly susceptible to control, provided that the developing chaos can be analyzed in real time and that analysis is then used to make small control interventions. This strategy has been used here to stabilize cardiac arrhythmias induced by the drug ouabain in rabbit ventricle. By administering electrical stimuli to the heart at irregular times determined by chaos theory, the arrhythmia was converted to periodic beating.

Chaos control of cardiac arrhythmias.

Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity.

Surrogate for nonlinear time series analysis.

We present a surrogate for use in nonlinear time series analysis. This surrogate algorithm has significant advantages over the most commonly used surrogates, in that it provides a more robust statistical test by producing an entire population of surrogates that are consistent with the null hypothesis. We will show that for the currently used surrogate algorithms, although individual surrogate files are consistent with the null hypothesis the population of surrogates generated is not. The surrogate is tested on a linear stochastic process and a continuous nonlinear system.

The fundamentals of controlling chaos.

The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. A detailed exposition of the mathematics of chaos control is presented, with an eye toward implementation in computer-controlled experiments.

Surrogates for finding unstable periodic orbits in noisy data sets.

Recently, searches for unstable periodic orbits in biological and medical applications have become of interest. The motivations for this research range, in order of ascending complexity, from efforts to understand the dynamics of simple sensory neurons, through speculations regarding neural coding, to the hopeful development of new diagnostic and/or control techniques for cardiac and epileptic pathologies. Biological and medical data are, however, noisy and nonstationary. Findings of unstable periodic orbits in such data thus require convincing assessments of their statistical significance. Such tests are accomplished by comparison with surrogate data files designed to test an appropriate null hypothesis. In this paper we test surrogates generated by three different algorithms against correlated noise as well as stable periodic orbits. One of the surrogates is new, and has been specifically designed to preserve the shape of the attractor. We discuss the suitability of these surrogates and argue that the simple shuffled one correctly tests the appropriate null hypothesis.

Controlling chaos in the brain.

In a spontaneously bursting neuronal network in vitro, chaos can be demonstrated by the presence of unstable fixed-point behaviour. Chaos control techniques can increase the periodicity of such neuronal population bursting behaviour. Periodic pacing is also effective in entraining such systems, although in a qualitatively different fashion. Using a strategy of anticontrol such systems can be made less periodic. These techniques may be applicable to in vivo epileptic foci.

Electric field suppression of epileptiform activity in hippocampal slices.

1. The effects of relatively small external DC electric fields on synchronous activity in CA1 and CA3 from transverse and longitudinal type hippocampal slices were studied. 2. To record neuronal activity during significant field changes, differential DC amplification was employed with a reference electrode aligned along an isopotential with the recording electrode. 3. Suppression of epileptiform activity was observed in 31 of 33 slices independent of region studied and type of slice but was highly dependent on field orientation with respect to the apical dendritic-somatic axis. 4. Modulation of neuronal activity in these experiments was readily observed at field strengths < or = 5-10 mV/mm. Suppression was seen with the field oriented (positive to negative potential) from the soma to the apical dentrites. 5. In vivo application of these results may be feasible.

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.