Bullock T H, Achimowicz J Z, Duckrow R B, Spencer S S, Iragui-Madoz V J
Department of Neurosciences, University of California, San Diego, La Jolla 92093-0201, USA.
Electroencephalogr Clin Neurophysiol. 1997 Dec;103(6):661-78. doi: 10.1016/s0013-4694(97)00087-4.
The hypothesis that the intracranial EEG has local structure and short-term non-stationarity is tested with a little-studied measure of non-linear phase coupling, the bicoherence in human subdural and deep temporal lobe probe data from 11 subjects during sleeping, waking and seizure states. This measure of cooperativity estimates the proportion of energy in every possible pair of frequency components, F1, F2 (from 1 to 50 Hz in this study), that satisfies the definition of quadratic phase coupling (phase of component at F3, which is F1 + F2, equals phase of F1 + phase of F2). Derived from the bispectrum, which segregates the non-Gaussian energy, auto-bicoherence uses the frequency components in one channel; cross-bicoherence uses one channel for F1 and F2 and another for F3. These higher order spectra are used in physical systems for detection of episodes of non-linearity and transients, for pattern recognition and robust classification, relatively immune to Gaussian components and low signal to noise ratios. Bicoherence is found not to be a fixed character of the EEG but quite local and unstable, in agreement with the hypothesis. Bicoherence can be quite different in adjacent segments as brief as 1.6 s as well as adjacent intracranial electrodes as close as 6.5 mm, even when the EEG looks similar. It can rise or fall steeply within millimeters. It is virtually absent in many analysis epochs of 17s duration. Other epochs show significant bicoherence with diverse form and distribution over the bifrequency plane. Isolated peaks, periodic peaks or rounded mountain ranges are either widely scattered or confined to one or a few parts of the plane. Bicoherence is generally an invisible feature: one cannot usually recognize the responsible form of non-linearity or any obvious correlate in the raw EEG. During stage II/III sleep overall mean bicoherence is generally higher than in the waking state. During seizures the diverse EEG patterns average a significant elevation in bicoherence but have a wide variance. Maximum bispectrum, maximum power spectrum, maximum and mean bicoherence, skewness and asymmetry all vary independently of each other. Cross-bicoherence is often intermediate between the two auto-bicoherence spectra but commonly resembles one of the two. Of the known factors that contribute to bicoherence, transient as distinct from ongoing wave forms can be more important in our data sets. This measure of non-linear higher moments is very sensitive to weak quadratic phase coupling; this can come from several kinds of waveforms. New methods are needed to evaluate their respective contributions. Utility of this descriptor cannot be claimed before more carefully defined and repeatable brain states are studied.
采用一种研究较少的非线性相位耦合测量方法——双相干性，对颅内脑电图具有局部结构和短期非平稳性这一假设进行了检验。该测量方法针对11名受试者在睡眠、清醒和癫痫发作状态下的人类硬膜下和颞叶深部探针数据中的双相干性进行分析。这种协同性测量方法估计了每一对可能的频率成分F1、F2（本研究中为1至50赫兹）中满足二次相位耦合定义（F3处成分的相位，即F1 + F2，等于F1的相位加上F2的相位）的能量比例。双相干性源自双谱，双谱可分离非高斯能量，自双相干性使用一个通道中的频率成分；交叉双相干性则使用一个通道获取F1和F2，另一个通道获取F3。这些高阶谱用于物理系统中检测非线性事件和瞬变、模式识别以及稳健分类，相对不受高斯成分和低信噪比的影响。研究发现，双相干性并非脑电图的固定特征，而是具有相当的局部性和不稳定性，这与假设相符。即使脑电图看起来相似，双相干性在短至1.6秒的相邻段以及相距仅6.5毫米的相邻颅内电极之间也可能有很大差异；它可能在几毫米范围内急剧上升或下降。在许多持续17秒的分析时段中，双相干性实际上并不存在；而在其他时段，双相干性在双频平面上呈现出显著的不同形式和分布，孤立的峰值、周期性峰值或圆形山脉状分布要么广泛分散，要么局限于平面的一个或几个部分。双相干性通常是一个不可见的特征：人们通常无法在原始脑电图中识别出导致其产生的非线性形式或任何明显的相关因素。在II/III期睡眠期间，总体平均双相干性通常高于清醒状态。癫痫发作期间，各种脑电图模式的双相干性平均显著升高，但变化范围很大。最大双谱、最大功率谱、最大和平均双相干性、偏度和不对称性均相互独立变化。交叉双相干性通常介于两个自双相干性谱之间，但通常类似于两者之一。在已知影响双相干性的因素中，与持续波形不同的瞬态在我们的数据集中可能更为重要。这种非线性高阶矩测量方法对弱二次相位耦合非常敏感，而这种耦合可能来自多种波形。需要新的方法来评估它们各自的贡献。在研究更精确界定且可重复的脑状态之前，无法断言该描述符的实用性。
