Background

The nonstationarity of EEG/MEG signals is important for understanding the functioning of the human brain. From our previous research we know that short, 250–500-ms MEG signals are variance-nonstationary. The covariance of a stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time.

New method

We analyse data from 148-channel MEG, which represent rest state, unattended listening, and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain and for the dominant frequencies of 8–12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity, and gaussianity, and propose ARMA-modelling for their description.

Results

The analysed time series have weak-stationarity properties independently of the functional state of the brain and channel localization. Only a small percentage of them, mostly related to the cognitive task, reveal nonstationarity. The obtained mathematical models show that the spectral density of the analysed signals depends on only two to three previous trials.

Comparison with existing methods

The presented method has limitations related to FFT resolution and univariate models, but it is computationally simple and allows obtaining a low-complex stochastic model of the EEG/MEG spectrum variability.

Conclusions

Although physiological short-time MEG signals are in principle nonstationary in time, their power spectrum at the dominant (alpha) frequencies varies as a weakly stationary process. The proposed methodology has possible applications in prediction of EEG/MEG spectral properties in theoretical and clinical neuroscience.

中文翻译：

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静止状态、无人值守收听和调频音调分类期间 MEG 功率谱的试验间变异性的时间序列分析

背景

EEG/MEG 信号的非平稳性对于理解人脑的功能很重要。根据我们之前的研究，我们知道 250-500 毫秒的短 MEG 信号是方差非平稳的。随机过程的协方差在数学上与其谱密度相关，因此我们研究了这种非平稳信号的谱如何随时间变化。

新方法

我们分析来自 148 通道 MEG 的数据，这些数据代表静止状态、无人值守收听和调频音调分类。我们将短时 MEG 信号转换到频域，对于 8-12 Hz 的主要频率，我们准备了代表其​​试验间变异性的时间序列。然后，我们测试它们的水平和趋势平稳性、单位根、异方差性和高斯性，并提出 ARMA 建模来描述它们。

结果

分析的时间序列具有弱平稳性，与大脑的功能状态和通道定位无关。其中只有一小部分（主要与认知任务相关）显示出非平稳性。获得的数学模型表明，分析信号的频谱密度仅取决于两到三个先前的试验。

与现有方法的比较

所提出的方法具有与 FFT 分辨率和单变量模型相关的局限性，但它在计算上很简单，并且允许获得 EEG/MEG 频谱变异性的低复杂度随机模型。

结论

尽管生理短时 MEG 信号原则上在时间上是非平稳的，但它们在主要 (alpha) 频率下的功率谱作为一个弱平稳过程而变化。所提出的方法在理论和临床神经科学中脑电图/脑电图谱特性的预测中具有可能的应用。