Stein K M, Walden J, Lippman N, Lerman B B
Division of Cardiology, Department of Medicine, New York Hospital-Cornell Medical Center, New York, New York 10021, USA.
Am J Physiol. 1999 Aug;277(2):H452-8. doi: 10.1152/ajpheart.1999.277.2.H452.
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.
心房颤动时的心室反应常被描述为“混乱的”，但从严格的数学意义上来说，这一点尚未得到证实。混沌系统的一个决定性特征是对初始条件的敏感依赖性：相似的序列在短期内会以相似的方式演化，但随后会呈指数级发散。我们开发了一种非线性预测算法，以寻找心房颤动时心室反应中的可预测性以及对初始条件的敏感依赖性。该算法针对来自带有和不带有叠加白噪声的线性振荡器的模拟R-R间期、带有和不带有叠加白噪声的混沌信号（逻辑斯谛映射）以及伪随机信号进行了测试，然后应用于16例慢性心房颤动患者的R-R间期。线性振荡器表现出短期可预测性，且在更长远的未来不会丧失预测能力。混沌系统表现出较高的短期可预测性，但在更长远的未来会迅速下降。伪随机信号不可预测。心房颤动时的心室反应具有较弱的可预测性（16例患者中有8例具有统计学意义的可预测性），且对初始条件不具有敏感依赖性。虽然R-R间期序列并非完全不可预测，但低维混沌吸引子并不支配心房颤动期间不规则的心室反应。
