Time-series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattended listening, and frequency-modulated tones classification.

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.

Averaging auditory evoked magnetoencephalographic and electroencephalographic responses: a critical discussion.

In the analysis of data from magnetoencephalography (MEG) and electroencephalography (EEG), it is common practice to arithmetically average event-related magnetic fields (ERFs) or event-related electric potentials (ERPs) across single trials and subsequently across subjects to obtain the so-called grand mean. Comparisons of grand means, e.g. between conditions, are then often performed by subtraction. These operations, and their statistical evaluation with parametric tests such as ANOVA, tacitly rely on the assumption that the data follow the additive model, have a normal distribution, and have a homogeneous variance. This may be true for single trials, but these conditions are rarely met when ERFs/ERPs are compared between subjects, meaning that the additive model is seldom the correct model for computing grand mean waveforms. Here, we summarize some of our recent work and present new evidence, from auditory-evoked MEG and EEG results, that the non-normal distributions and the heteroscedasticity observed instead result because ERFs/ERPs follow a mixed model with additive and multiplicative components. For peak amplitudes, such as the auditory M100 and N100, the multiplicative component dominates. These findings emphasize that the common practice of simply subtracting arithmetic means of auditory-evoked ERFs or ERPs is problematic without prior adequate transformation of the data. Application of the area sinus hyperbolicus (asinh) transform to data following the mixed model transforms them into the requested additive model with its normal distribution and homogeneous variance. We therefore advise checking the data for compliance with the additive model and using the asinh transform if required.

Variance stabilization for computing and comparing grand mean waveforms in MEG and EEG.

Grand means of time-varying signals (waveforms) across subjects in magnetoencephalography (MEG) and electroencephalography (EEG) are commonly computed as arithmetic averages and compared between conditions, for example, by subtraction. However, the prerequisite for these operations, homogeneity of the variance of the waveforms in time, and for most common parametric statistical tests also between conditions, is rarely met. We suggest that the heteroscedasticity observed instead results because waveforms may differ by factors and additive terms and follow a mixed model. We propose to apply the asinh-transformation to stabilize the variance in such cases. We demonstrate the homogeneous variance and the normal distributions of data achieved by this transformation using simulated waveforms, and we apply it to real MEG data and show its benefits. The asinh-transformation is thus an essential and useful processing step prior to computing and comparing grand mean waveforms in MEG and EEG.

Application of modern tests for stationarity to single-trial MEG data: transferring powerful statistical tools from econometrics to neuroscience.

Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto- (MEG) or electroencephalography (EEG). One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are only indirectly inferred either from the Gaussianity (e.g. the Shapiro-Wilk test or Kolmogorov-Smirnov test) or the randomness of the time series and the absence of trend using very simple time-series models (e.g. the sign and trend tests by Bendat and Piersol). We present a novel approach to the analysis of the stationarity of MEG and EEG time series by applying modern statistical methods which were specifically developed in econometrics to verify the hypothesis that a time series is stationary. We report our findings of the application of three different tests of stationarity--the Kwiatkowski-Phillips-Schmidt-Schin (KPSS) test for trend or mean stationarity, the Phillips-Perron (PP) test for the presence of a unit root and the White test for homoscedasticity--on an illustrative set of MEG data. For five stimulation sessions, we found already for short epochs of duration of 250 and 500 ms that, although the majority of the studied epochs of single MEG trials were usually mean-stationary (KPSS test and PP test), they were classified as nonstationary due to their heteroscedasticity (White test). We also observed that the presence of external auditory stimulation did not significantly affect the findings regarding the stationarity of the data. We conclude that the combination of these tests allows a refined analysis of the stationarity of MEG and EEG time series.

The M100 component of evoked magnetic fields differs by scaling factors: implications for signal averaging.

MEG and EEG studies of event-related responses often involve comparisons of grand averages, requiring homogeneity of the variances. Here, we examine the possibility, implied by the nature of neural sources and the measuring principles involved, that the M100 component of auditory-evoked magnetic fields of different subjects, hemispheres, to different stimuli, and at different sensors differs by scaling factors. Such a multiplicative model predicts a linear increase in the standard deviation with the mean, and thus would have important implications for averaging and comparing such data. Our analyses, at the sensor and the source level, clearly show that the multiplicative model applies. We therefore propose geometric, rather than arithmetic, averaging of the M100 component across subjects and suggest a novel and superior normalization procedure. Our results question the justification of the common practice of subtracting arithmetic grand averages.