Spatial organization, predictability, and determinism in ventricular fibrillation.
ABSTRACT The degree of spatial organization of ventricular fibrillation (VF) is a fundamental dynamical property of the arrhythmia and may determine the success of proposed therapeutic approaches. Spatial organization is closely related to the dimension of VF, and hence to its predictability and controllability. We have explored several techniques to quantify spatial organization during VF, to predict patterns of activity, and to see how spatial organization and predictability change as the arrhythmia progresses. Epicardial electrograms recorded from pig hearts using rectangular arrays of unipolar extracellular electrodes (1 mm spacing) were analyzed. The correlation length of VF, the number of Karhunen-Loeve modes required to approximate data during VF, the number, size and recurrence of wavefronts, and the mean square error of epicardial potential fields predicted 0.256 seconds into the future were all estimated. The ability of regularly-timed pacing stimuli to capture areas of fibrillating myocardium during VF was confirmed by a significant increase in local spatial organization. Results indicate that VF is neither "low-dimensional chaos" (dimension <5) nor "random" behavior (dimension= infinity ), but is a high-dimensional response with a degree of spatial coherence that changes as the arrhythmia progresses. (c) 1998 American Institute of Physics.
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ABSTRACT: A well-defined order-disorder transition occurs in the capillary waves on a fluid layer driven by vertical oscillation. The transition is characterized by a sharp decline in both the translational correlation length and the long-range orientational order of the pattern, and an onset in the characteristic frequency f* of chaotic fluctuations varying approximately as (A-Ad)1/2, for driving amplitudes above a threshold Ad. The transition is geometry dependent even when the container size is 50-100 times the wavelength.Physical Review Letters 02/1989; 62(4):422-425. · 7.94 Impact Factor
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ABSTRACT: A mathematical model of impulse propagation in a nonuniform two-dimensional system was prepared as a program for a digital computer. The model exhibited self-sustained turbulent activity having many similarities to atrial fibrillation. The activity was not the result of fixed impulse generators or circuits, but was sustained by irregular drifting eddies which varied in position, number, and size. Increasing the refractory periods while retaining nonuniformity resulted in arrest of activity. Restoration of absolute uniformity resulted in periodic activity characterized by fixed re-entrant circuits without obstacles. Reduction of the area of the model altered the self-sustained activity in the direction of arrest, and the creation of internal obstacles resulted in a periodic circus movement flutter. The behavior of the model suggests the formulation of a “fibrillation” number, similar in concept to the Reynolds number related to turbulence in fluid flow.American Heart Journal 03/1964; 67:200-20. · 4.50 Impact Factor
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ABSTRACT: Ventricular fibrillation (VF) is a fatal cardiac arrhythmia, characterized by uncoordinated propagation of activation wavefronts in the ventricular myocardium. Short-term predictions of epicardial potential fields during VF in pigs were attempted using linear techniques, and prediction accuracy was measured at various stages during sustained episodes. VF was induced in five pigs via premature electrical stimulation. Unipolar electrograms were recorded from an epicardial array of 506 electrodes in a 22 x 23 array with 1-mm spacing. Optimal spatial basis functions (modes) and time-varying weighting coefficients were found using the Karhunen-Loeve decomposition. Linear autoregressive (AR) models incorporating the dynamics of only a few spatial modes led to predicted patterns that were qualitatively similar to observed patterns. Predictions were made 0.256 s into the future, based on 0.768 s of past data, over an area of approximately 5 cm2 on the ventricular epicardium. The mean squared error of predictions varied from as much as 1.23 to as little as 0.14, normalized to the variance of the actual data. Inconsistency in long-term forcasts is partly due to the limitations of linear AR models. Changes in predictability, however, were consistent. Predictability varied inversely with spatial complexity, as measured by the mean squared error of a five-mode approximation. Predictability also increased significantly during the first minute of VF.IEEE Transactions on Biomedical Engineering 10/1995; 42(9):898-907. · 2.35 Impact Factor