Lo Men-Tzung, Novak Vera, Peng C-K, Liu Yanhui, Hu Kun
Division of Gerontology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 1):061924. doi: 10.1103/PhysRevE.79.061924. Epub 2009 Jun 29.
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.
物理和生理系统信号之间的相位相互作用可以提供有关系统潜在控制机制的有用信息。物理和生物记录通常存在噪声，并表现出非平稳性，这可能会影响相位相互作用的估计。我们系统地研究了非平稳性对两种相位分析的影响，包括：（i）基于傅里叶分解的广泛使用的传递函数分析（TFA），以及（ii）最近提出的基于希尔伯特 - 黄变换（HHT）——一种先进的非线性分解算法的多模态压力流（MMPF）分析。我们考虑了在物理和生理信号中经常出现的三种非平稳性类型：（i）数据段缺失，（ii）数据中嵌入的线性和阶跃函数趋势，以及（iii）数据中不同频率的多个混沌振荡成分。通过生成具有指定相位偏移的两个耦合振荡信号，我们量化了在将人工非平稳性引入振荡信号后估计相位偏移的变化。我们发现，所有三种类型的非平稳性都会影响基于傅里叶和基于HHT的相位分析的性能，在估计两个振荡信号之间的相位偏移时引入偏差和随机误差。我们还提供了真实生理数据（脑血流和血压）中的非平稳性示例，并展示了非平稳性如何使结果解释复杂化。此外，我们提出了某些可以在TFA和MMPF方法中实施的策略，以减少非平稳性的影响，从而提高这两种方法的性能。
