Bettermann H, Van Leeuwen P
Department of Clinical Research, Gemeinschaftskrankenhaus Herdecke, Germany.
Biol Cybern. 1998 Jan;78(1):63-70. doi: 10.1007/s004220050413.
Complexity measures of non-linear dynamics are a useful tool for quantifying observed stretching, folding, scaling and mixing processes in the Takens-reconstructed state space of heart period dynamics. Although such measures are not suited to provide evidence of deterministic chaos or to estimate true fractal dimensions and Lyapunov spectra in heart period time series, they allow the classification of RR dynamics and the identification of changes in RR complexity (RRC). The aim of this study was to develop appropriate measures and examine their utility in identifying the physiological effect of changes between the sleeping and waking state. Twenty-four hour electrocardiography (EEG) recordings and diaries noting their waking/sleeping period were obtained from 78 healthy subjects, aged 20 to 55 years. The approximate information dimension (ApD1) and the approximate Kolmogorov entropy (ApEn), introduced by Pincus, Kaplan and others, were modified in order to allow the calculation of strictly local values. That is, the local or pointwise dimensions and entropies were calculated for each reference vector with respect to its symmetric neighbourhood in time. For each subject the values for the local measures were averaged for 10-min periods, resulting in 144 global values over 24 h. Similarly, low- and high-frequency spectral parameters were calculated. All measures were examined and compared for the waking and the sleeping periods. All complexity measures as well as to a lesser degree high-frequency power showed a linear dependency on mean RR interval with a large individual variation. For the RRC measures this linear correlation was separated into two different clusters corresponding to the sleeping and waking periods. In almost all cases the correlation was greater in the waking period. In particular, in many cases no correlation was observed in the sleeping period. However, the r values for LF were appreciably lower and indicated solely a weak relationship to the RR interval in the waking period. Analysis of variance combining mean RR interval with RRC or spectral parameters singly and in couples revealed that the best separation with respect to physiological state could be achieved with the complexity measures, in particular with ApEn. The results show evidence of at least two dynamical regimes (phases) of heart period dynamics and a close but different functional relationship within the phases between RR interval and RR complexity. The separation between these regimes and the relatively sudden shift from one regime to the other suggest the existence of a phase transition with respect to waking and sleeping periods in terms of synergetics.
非线性动力学的复杂性度量是一种有用的工具，可用于量化在心脏周期动力学的Takens重构状态空间中观察到的拉伸、折叠、缩放和混合过程。尽管这些度量不适合提供确定性混沌的证据，也不适合估计心脏周期时间序列中的真实分形维数和Lyapunov谱，但它们可以对RR动力学进行分类，并识别RR复杂性（RRC）的变化。本研究的目的是开发合适的度量，并检验它们在识别睡眠和清醒状态之间变化的生理效应方面的效用。从78名年龄在20至55岁的健康受试者中获取了24小时心电图（EEG）记录以及记录其清醒/睡眠时段的日记。对Pincus、Kaplan等人提出的近似信息维数（ApD1）和近似Kolmogorov熵（ApEn）进行了修改，以便能够计算严格的局部值。也就是说，针对每个参考向量，相对于其在时间上的对称邻域计算局部或逐点维数和熵。对于每个受试者，将局部度量的值按10分钟时段进行平均，从而在24小时内得到144个全局值。同样，计算了低频和高频频谱参数。对清醒和睡眠时段的所有度量进行了检验和比较。所有复杂性度量以及在较小程度上的高频功率均显示出与平均RR间期呈线性相关，且个体差异较大。对于RRC度量，这种线性相关性被分为对应于睡眠和清醒时段的两个不同聚类。在几乎所有情况下，清醒时段的相关性更强。特别是，在许多情况下，睡眠时段未观察到相关性。然而，LF的r值明显更低，仅表明在清醒时段与RR间期的关系较弱。将平均RR间期与RRC或频谱参数单独及成对进行方差分析表明，使用复杂性度量，特别是ApEn，能够实现关于生理状态的最佳区分。结果显示了心脏周期动力学至少存在两种动态模式（阶段）的证据，以及在这些阶段中RR间期与RR复杂性之间紧密但不同的功能关系。这些模式之间的区分以及从一种模式到另一种模式的相对突然转变表明，从协同论的角度来看，在清醒和睡眠时段存在相变。
