复杂系统间歇动力学的Koopman谱分析：阻塞性睡眠呼吸暂停病理生理过程的案例研究
Koopman Spectral Analysis of Intermittent Dynamics in Complex Systems: A Case Study in Pathophysiological Processes of Obstructive Sleep Apnea
摘要：
复杂系统，如病理生理过程，通常表现出混沌，非线性和间歇性的现象。Koopman算子理论和Hankel替代观点Koopman（HAVOK）模型已被广泛应用于将复杂系统动力学的混沌分解为间歇性受迫线性系统。虽然在HAVOK模式中，间歇强迫的统计量被用来描述非线性动力学的模式转换，但这些统计量不足以解释由高频爆发和罕见的间歇强迫引起的厚尾非高斯分布。本文提出了一种新的间歇动力学分析方法，利用谱分解和小波分析来表征各种间歇动力学模式的间歇相位、混沌爆发和局部谱时特性。为了验证我们的方法，阻塞性睡眠呼吸暂停障碍的呼吸暂停事件的不稳定性行为的情况下，心率变异性（HRV）特征提取。然后，利用HRV特征构造Hankel矩阵，通过奇异值分解得到最后一个特征时延坐标，并将其建模为间歇性强迫输入。OSA强迫的统计结果显示间歇强迫的厚尾分布，这与OSA病理生理过程的不稳定性相对应。OSA患者的爆发持续时间和爆发间持续时间的汇总平均值和标准差也计算为分钟和分钟。尺度图振幅和小波变换的频谱分解显示了与呼吸暂停事件相关的各种优势频率和动力学模式。
英文摘要：
Complex systems, such as pathophysiological processes, commonly exhibit chaotic, nonlinear, and intermittent phenomena. Koopman operator theory and Hankel alternative view of Koopman (HAVOK) model have been widely used to decompose the chaos of the complex system dynamics into an intermittent forced linear system. Although the statistics of the intermittent forcing have been proposed to characterize intermittencies in the HAVOK model, they were not adequate to attribute for the mode switching of nonlinear dynamics and the fat-tailed non-Gaussian distribution originated from high-frequency bursts and rarely-observed intermittent forcing. The paper proposed a new intermittency dynamics analysis approach to characterize the intermittent phases, chaotic bursts, and local spectral-temporal properties of various intermittent dynamics modes using spectral decomposition and wavelet analysis. To validate our methods, the intermittency behavior of apneic events in obstructive sleep apnea disorder was selected as the case, in which heart rate variability (HRV) features were extracted. Next, we constructed the Hankel matrix from the HRV features and obtained the last eigen time-delay coordinate by singular value decomposition of the Hankel matrix, which was modeled as an intermittent forcing input. The statistics of the forcing in OSA demonstrated the fat-tailed distribution of the intermittent forcing, which correspond to the intermittency of the underlying OSA pathophysiological process. The pooled means and standard deviations of the burst duration and the inter-burst duration across OSA patients were also calculated to be minutes and minutes. Scalogram amplitude and spectral decomposition of the wavelet transform exhibited various predominant frequencies and dynamics modes associated with apneic events.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
