AHEART August 46/2

Stein, Kenneth M., Jeff Walden, Neal Lippman, and Bruce B. Lerman. Ventricular response in atrial fibrillation: random or deterministic? Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H452–H458, 1999.—The ventricular response in atrial fibrillation is often described as ‘‘chaotic,’’ but this has not been demonstrated in the strict mathematical sense. A defining feature of chaotic systems is sensitive dependence on initial conditions: similar sequences evolve similarly in the short term but then diverge exponentially. We developed a nonlinear predictive forecasting algorithm to search for predictability and sensitive dependence on initial conditions in the ventricular response during atrial fibrillation. The algorithm was tested for simulated R-R intervals from a linear oscillator with and without superimposed white noise, a chaotic signal (the logistic map) with and without superimposed white noise, and a pseudorandom signal and was then applied to R-R intervals from 16 chronic atrial fibrillation patients. Short-term predictability was demonstrated for the linear oscillators, without loss of predictive ability farther into the future. The chaotic system demonstrated high shortterm predictability that declined rapidly further into the future. The pseudorandom signal was unpredictable. The ventricular response in atrial fibrillation was weakly predictable (statistically significant predictability in 8 of 16 patients), without sensitive dependence on initial conditions. Although the R-R interval sequence is not completely unpredictable, a low-dimensional chaotic attractor does not govern the irregular ventricular response during atrial fibrillation.