Aronis Konstantinos N, Berger Ronald D, Calkins Hugh, Chrispin Jonathan, Marine Joseph E, Spragg David D, Tao Susumu, Tandri Harikrishna, Ashikaga Hiroshi
Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287, USA.
Chaos. 2018 Jun;28(6):063130. doi: 10.1063/1.5023588.
The mechanism of atrial fibrillation (AF) maintenance in humans is yet to be determined. It remains controversial whether cardiac fibrillatory dynamics are the result of a deterministic or a stochastic process. Traditional methods to differentiate deterministic from stochastic processes have several limitations and are not reliably applied to short and noisy data obtained during clinical studies. The appearance of missing ordinal patterns (MOPs) using the Bandt-Pompe (BP) symbolization is indicative of deterministic dynamics and is robust to brief time series and experimental noise. Our aim was to evaluate whether human AF dynamics is the result of a stochastic or a deterministic process. We used 38 intracardiac atrial electrograms during AF from the coronary sinus of 10 patients undergoing catheter ablation of AF. We extracted the intervals between consecutive atrial depolarizations (AA interval) and converted the AA interval time series to their BP symbolic representation (embedding dimension 5, time delay 1). We generated 40 iterative amplitude-adjusted, Fourier-transform (IAAFT) surrogate data for each of the AA time series. IAAFT surrogates have the same frequency spectrum, autocorrelation, and probability distribution with the original time series. Using the BP symbolization, we compared the number of MOPs and the rate of MOP decay in the first 1000 timepoints of the original time series with that of the surrogate data. We calculated permutation entropy and permutation statistical complexity and represented each time series on the causal entropy-complexity plane. We demonstrated that (a) the number of MOPs in human AF is significantly higher compared to the surrogate data (2.7 ± 1.18 vs. 0.39 ± 0.28, p < 0.001); (b) the median rate of MOP decay in human AF was significantly lower compared with the surrogate data (6.58 × 10 vs. 7.79 × 10, p < 0.001); and (c) 81.6% of the individual recordings had a rate of decay lower than the 95% confidence intervals of their corresponding surrogates. On the causal entropy-complexity plane, human AF lay on the deterministic part of the plane that was located above the trajectory of fractional Brownian motion with different Hurst exponents on the plane. This analysis demonstrates that human AF dynamics does not arise from a rescaled linear stochastic process or a fractional noise, but either a deterministic or a nonlinear stochastic process. Our results justify the development and application of mathematical analysis and modeling tools to enable predictive control of human AF.
人类心房颤动（AF）维持的机制尚未确定。心脏颤动动力学是确定性过程还是随机过程的结果仍存在争议。区分确定性过程和随机过程的传统方法有几个局限性，不能可靠地应用于临床研究中获得的短时间且有噪声的数据。使用班特 - 庞贝（BP）符号化出现的缺失序数模式（MOPs）表明存在确定性动力学，并且对短时间序列和实验噪声具有鲁棒性。我们的目的是评估人类房颤动力学是随机过程还是确定性过程的结果。我们使用了10例接受房颤导管消融患者冠状窦在房颤期间的38份心内房电图。我们提取了连续心房去极化之间的间期（AA间期），并将AA间期时间序列转换为其BP符号表示（嵌入维数5，时间延迟1）。我们为每个AA时间序列生成了40个迭代幅度调整傅里叶变换（IAAFT）替代数据。IAAFT替代数据与原始时间序列具有相同的频谱、自相关和概率分布。使用BP符号化，我们比较了原始时间序列前1000个时间点与替代数据中MOPs的数量和MOP衰减率。我们计算了排列熵和排列统计复杂度，并在因果熵 - 复杂度平面上表示每个时间序列。我们证明：（a）与替代数据相比，人类房颤中MOPs的数量显著更高（2.7±1.18对0.39±0.28，p < 0.001）；（b）与替代数据相比，人类房颤中MOP衰减的中位数率显著更低（6.58×10对7.79×10，p < 0.001）；（c）81.6%的个体记录的衰减率低于其相应替代数据的95%置信区间。在因果熵 - 复杂度平面上，人类房颤位于该平面确定性部分，该部分位于具有不同赫斯特指数的分数布朗运动轨迹上方。该分析表明，人类房颤动力学并非源于重标度线性随机过程或分数噪声，而是源于确定性过程或非线性随机过程。我们的结果为开发和应用数学分析及建模工具以实现对人类房颤的预测控制提供了依据。
