Thayer J F, Moulden S A
University of Missouri-Columbia 65211, USA.
Biomed Sci Instrum. 1997;33:491-6.
Researchers have recently applied nonlinear dynamical systems theory to physiological time series data. However, the direct implementation of the deterministic equations used to estimate the correlation dimension is problematic for physiological data. Importantly, the distinction between a nonlinear process and noise is particularly difficult for experimental data. One technique that has been developed to help with this distinction is the use of surrogate data. These data preserve many of the properties of the original time series but in fact are a randomization of the original data. Whereas in a sufficiently high embedding space the estimates of the correlation dimension of a nonlinear process will plateau, such estimates for a noise process will continue to rise with increases in the embedding dimension. In the present experiment two data sets were examined. Heart period time series were collected from a female subject during spontaneous breathing and breathing paced at 15 breaths per minute. Both data sets consisted of approximately 3000 interbeat intervals and embedding dimensions of m = 2 through m = 6 were examined. Results indicate that the correlation dimension estimate for the spontaneous breathing data reached a plateau around 4, whereas the surrogate data for this series showed no such plateau. For the paced breathing data, both the original and the surrogate data failed to show evidence of a plateau in the estimates of the correlation dimension. These results suggest that caution must be used in interpreting finite values of correlation dimension as evidence of a chaotic attractor in experimental data if no test for determinism is performed.
研究人员最近将非线性动力系统理论应用于生理时间序列数据。然而，用于估计关联维数的确定性方程的直接应用对于生理数据来说存在问题。重要的是，对于实验数据而言，区分非线性过程和噪声尤为困难。为帮助进行这种区分而开发的一种技术是使用替代数据。这些数据保留了原始时间序列的许多特性，但实际上是原始数据的随机化。在足够高的嵌入空间中，非线性过程的关联维数估计将趋于平稳，而噪声过程的此类估计将随着嵌入维数的增加而继续上升。在本实验中，研究了两个数据集。在自发呼吸和每分钟15次呼吸的呼吸起搏过程中，从一名女性受试者收集了心跳周期时间序列。两个数据集均由大约3000个心跳间期组成，并检查了从m = 2到m = 6的嵌入维数。结果表明，自发呼吸数据的关联维数估计在4左右达到平稳，而该序列的替代数据则未显示出这样的平稳状态。对于起搏呼吸数据，原始数据和替代数据在关联维数估计中均未显示出平稳的证据。这些结果表明，如果不进行确定性检验，在将关联维数的有限值解释为实验数据中混沌吸引子的证据时必须谨慎。
