利用时频分析研究非相位锁定脑电活动

doi:10.3724/SP.J.1042.2018.1349

摘要/Abstract

摘要：

时频分析技术自20世纪80年代被引入到心理学脑电数据分析领域以来, 克服了传统的时域ERP方法只能分析相位锁定成分的缺陷, 可以帮助研究者挖掘到脑电信号中非相位锁定的成分。在心理学领域, 应用最多的时频分析方法是小波变换和Hilbert变换, 而能量、相位一致性和耦合是三个最常用的分析指标。研究者利用不同的分析指标来揭示不同的心智过程。不同频段的能量被认为体现了不同的认知过程, 如α能量被发现与注意选择性有关, 而γ能量则与特征整合相关。相位一致性常被用于讨论ERP产生的机制。耦合则通常说明了长距离脑区之间的信息交流以及高级脑区对低级脑区的认知控制, 在完成各种复杂认知任务的时候会表现出不同的耦合模式。

关键词: 时频分析, 小波变换, Hilbert变换, 能量, 相位一致性, 耦合

Abstract:

Since the introduction of the time-frequency analysis technique into the field of EEG data in the 1980’s, researchers can excavate non-phase locked components in EEG signals, overcoming the previous shortcomings of traditional ERP methods. In the field of psychology, the two most commonly used time-frequency analysis methods are wavelet transform and Hilbert transform. Power, phase locking index (PLI), and coherence are three important indices of time-frequency analysis. Power in different frequency band is typically considered to reflect different mental processes. For example, α power is frequently related to selective attention, while γ energy is often associated with feature binding. Researchers use PLI to investigate the mechanism generated by an ERP component. Coherence indicates the exchange of information between long-distance brain regions and cognitive control of higher-level brain regions in the low-level brain regions, which show different patterns in various complex cognitive tasks.

Key words: time-frequency analysis, wavelet transform, Hilbert transform, power, PLI, coherence

中图分类号:

B845

武侠, 钟楚鹏, 丁玉珑, 曲折. (2018). 利用时频分析研究非相位锁定脑电活动. 心理科学进展 , 26(8), 1349-1364.

WU Xia, ZHONG Chupeng, DING Yulong, QU Zhe. (2018). Application of time-frequency analysis in investigating non-phase locked components of EEG. Advances in Psychological Science, 26(8), 1349-1364.

图/表 9

图1 事件发生后可能的脑电活动变化。A, 频率反应(frequency response), 事件发生后原本脑电自发活动的振荡频率发生了变化; B, 振幅反应(amplitude response), 事件发生后, 原本脑电自发活动的能量发生了变化; C, 相位重置(phase resetting), 事件发生后, 原本脑电自发活动的相位发生了扰动, 相位在试次之间变得一致; D, 新增成分(additive response), 事件发生后, 出现了一种与自发脑电活动无关的新成分, 各试次之间新成分相似。(图摘自维基百科, "Neural oscillation," 2018)

图2 时变信号的傅立叶变换示意图。A、B为信号示意图, 其中A为前半段为振幅为1的10 Hz正弦振荡, 后半段为振幅为1.5的20 Hz余弦振荡; B为前半段为振幅为1.5的20 Hz余弦振荡, 后半段为振幅为1的10 Hz正弦振荡。C、D分别为A、B信号的傅立叶变换结果。

图3 对图2中的两个时变信号的时频分析示意图。A、B、C分别给出了窗口傅立叶变换、小波变换、Hilbert变换的分析结果。第一列、第二列分别为对图2A和图2B信号的分析结果。彩图见电子版, 下同。

图4 复Morlet小波示意图, 实线是小波的实部, 虚线是小波的虚部。复Morlet小波的实部和虚部相位相差90度, 都可以看做是正余弦信号加了高斯窗口构成的向两端急剧衰减的振荡信号。

图5 窗口傅立叶变换和小波变换小波族(wavelet family)子小波对比。A, 窗口傅立叶变换的时间窗口长度固定, 对于高低频信号都有同样的时域和频域分辨率; B, 小波变换高低频的子小波有相同的周期数, 时间窗口长度并不相等。对于低频信号, 时间窗口更长, 时域分辨率更差, 频域分辨率更好; 高频信号则时间窗口短, 时域分辨率好, 频域分辨率差。

图6 计算evoked能量和induced能量示意图, A, 每个试次的γ振荡示意图, 蓝框内为evoked活动, 绿框内为induced活动; B, 波形叠加平均后的平均振荡波形, 只剩下了evoked活动; C, 每个试次的时频能量示意图, 可以看到每个试次的induced能量; D, 左侧evoked能量是平均波形时频分析的结果, 右侧induced能量是单个试次时频能量平均结果减去evoked能量的差异值。

图7 PLI计算原理示意图, A, 单个试次某时刻某频率的能量和相位用复平面内向量表示, 圆代表单位圆, 向量在单位圆上的投影为只表示相位大小的单位向量; B, 若干试次的单位向量(黑色的点为单位向量的末端, 省去了箭头), 这些单位向量集中在第一象限, 平均向量(绿色)的大小(PLI)接近于1; C, 若干试次的单位向量平均分散在4个象限, 平均向量的大小(PLI)接近于0。

图8 不同电极相位同步性计算原理示意图。A,上, 两个不同电极某试次某时刻各自的相位示意图, 下, 两个电极某试次某时刻的相位差; B,上, 两个不同电极另外一个试次某时刻(与A时刻相同)各自相位, 下, 两个电极该时刻相位差; C,左, 两电极不同试次某时刻相位差的分布靠近第一象限, 平均向量的模接近1, 右, 两电极不同试次某时刻相位差均匀分布, 平均向量的模接近于0。

图9 低频相位和高频能量耦合以及计算方法示意图。A为耦合示意图, 表现为高频能量以一定的低频周期振荡变化。B、C、D为耦合计算原理示意图, B为某个时刻高频能量和低频相位组成的复数在复平面上对应一个点; C为许多时刻点的分布, 偏向第一象限, 平均复向量指向第一象限; D为许多时刻点的分布, 在四个象限均匀分布, 平均向量长度很小, 几乎为0。

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