Ventricular response in atrial fibrillation: random or deterministic?
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 short-term 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.
Stein
K M
KM
Division of Cardiology, Department of Medicine, New York Hospital-Cornell Medical Center, New York, New York 10021, USA. kstein@mail.med.cornell.edu
Walden
J
J
Lippman
N
N
Lerman
B B
BB
D000368:Aged; D000465:Algorithms; D001281:Atrial Fibrillation / Q000503:physiopathology*; D002908:Chronic Disease; D003198:Computer Simulation; D004562:Electrocardiography; D005260:Female; D005544:Forecasting; D006339:Heart Rate; D006801:Humans; D008297:Male; D008875:Middle Aged; D008955:Models, Cardiovascular; D016276:Ventricular Function