Pavel Sovka

Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping

This paper suggests an approximation to the statistical distribution of a magnitude squared coherence (MSC) function estimated with segment overlapping. So far, the statistical distribution is known for an MSC computed without segment overlapping only. However, as the overlapped segmentation provides a more accurate MSC estimate, its statistical distribution is desired to allow its evaluation. This paper provides an approximation of the cumulative density function, probability density function, confidence limit formula, confidence interval computation and a procedure for the comparison of two MSC estimates, all for an MSC accurately estimated with the segment overlapping. Additionally, the benefits of the knowledge of the approximated statistics are illustrated on EEG-EMG (i.e. cortico-muscular) MSC estimates.

EEG-EMG coherence enhancement

The paper introduces a new approach to the estimation of the EEG-EMG coherence, which is used to examine the functional connection between a human brain and muscles. A typical EEG-EMG coherence estimation, with a magnitude squared coherence (MSC) barely exceeding 0.15, is enhanced so that MSC reaches or even goes above 0.5. The proposed method is mathematically analyzed, and its properties are discussed. Additionally, the paper includes several EEG-EMG coherence analysis results, with MSC exceeding 0.5.

Intra- and inter-hemispheric coupling of electroencephalographic 8-13 Hz rhythm in humans and force of static finger extension.

The coupling of electroencephalographic (EEG) 8-13 Hz oscillations during static right finger extension performed under four different force levels was analyzed in 12 right-handed subjects. Increases in force of static muscle contraction were accompanied by increases in the 8-13 Hz band coherence between the contralateral sensorimotor area (S1/M1) and the ipsilateral S1/M1, frontal and parietal cortex, between supplementary motor area and bilateral S1/M1, and between posterior parietal cortex and bilateral S1/M1. The results suggest increased functional coupling between primary and higher-order motor areas during increased motor effort.

High-resolution movement EEG classification

The aim of the contribution is to analyze possibilities of high-resolution movement classification using human EEG. For this purpose, a database of the EEG recorded during right-thumb and little-finger fast flexion movements of the experimental subjects was created. The statistical analysis of the EEG was done on the subjects basis instead of the commonly used grand averaging. Statistically significant differences between the EEG accompanying movements of both fingers were found, extending the results of other so far published works. The classifier based on hidden Markov models was able to distinguish between movement and resting states (classification score of 94–100%), but it was unable to recognize the type of the movement. This is caused by the large fraction of other (nonmovement related) EEG activities in the recorded signals. A classification method based on advanced EEG signal denoising is being currently developed to overcome this problem.

Effects of muscle contraction on somatosensory event-related EEG power and coherence changes.

Effects of isometric muscle contraction on amplitude and coherence changes of EEG rhythms during repetitive cutaneous electrical stimulation were analyzed in 10 right-handed subjects. Subjects received electrical stimuli at intensity above pain threshold to their right middle finger while either squeezing a rubber tube with the right index finger and thumb, or keeping their ipsilateral hand muscles relaxed. EEG was recorded using 111 closely spaced electrodes. Somatosensory stimuli were followed by reduction of the relative 8-12 and 16-24 Hz band power (at 0.2-0.4 s) in bilateral primary sensorimotor cortices (S1/M1) and medial frontal cortex, and by a subsequent increase in 16-24 Hz band power (at 0.9 s). Isometric muscle contraction strongly suppressed these band power changes. The 8-12 and 16-24 Hz mean coherence in a wide region surrounding the contralateral S1/M1 and in the medial frontal cortex showed an initial decrease, partially paralleling band power changes, and later an increase. Ipsilateral S1/M1 showed a decrease in 8-12 Hz coupling only with the central and frontal electrodes of the same hemisphere. Muscle contraction reduced all coherence changes, but enhanced the 8-12 Hz coherence between ipsilateral S1/M1 and posterior parietal cortex. Early post-stimulus decrease of oscillatory coupling between S1/M1 and premotor cortex and between S1/M1 and medial frontal cortex suggests that these cortical regions act rather independently during processing of somatosensory information, and synchronize only later when the band power in contralateral S1/M1 increases. Motor cortex activation associated with ipsilateral hand muscle contraction interferes with cortical processing of somatosensory stimuli in S1/M1 cortices.

Regularization Techniques in Realistic Laplacian Computation

This paper explores regularization options for the ill-posed spline coefficient equations in the realistic Laplacian computation. We investigate the use of the Tikhonov regularization, truncated singular value decomposition, and the so-called lambda-correction with the regularization parameter chosen by the L-curve, generalized cross-validation, quasi-optimality, and the discrepancy principle criteria. The provided range of regularization techniques is much wider than in the previous works. The improvement of the realistic Laplacian is investigated by simulations on the three-shell spherical head model. The conclusion is that the best performance is provided by the combination of the Tikhonov regularization and the generalized cross-validation criterion-a combination that has never been suggested for this task before.

Electroencephalographic correlates of paced breathing

Multichannel EEG, respiration, blood pressure and ECG were recorded during paced breathing at five frequencies in 18 subjects in order to elucidate the effects of paced breathing on power changes in alpha, beta and theta bands, and on rhythmical variability of these parameters. Mean power in the beta band and low-frequency beta power variability (0.12-0.04 Hz) increased during paced breathing at frequencies of 0.25 and 0.20 Hz. The total variability of alpha power in the right parietal and occipital electrodes decreased during paced breathing at 0.1 Hz compared with initial rest. The results point to increased cortical excitability during paced breathing at eupnoeic frequencies and to diminished cortical sensitivity to desynchronizing influences during paced breathing at 0.1 Hz.

Potential approximation in realistic Laplacian computation

OBJECTIVE This paper aims to improve the shortcomings of the extant methodologies for realistic Laplacian (RL) computation, and correct the erroneous claims published in the past. METHODS We implemented several variants of RL computation methods, using various potential approximation techniques and different regularization approaches. The individual variants of the RL computation were tested using simulations based on a realistic head model computed with the boundary element method (BEM). The results which disagreed with previously published works were further analyzed, and the reasons for the disagreement were identified. RESULTS We identified the best regularization techniques for the surface potential approximation, and we showed that once these techniques are used there is often little difference between various potential approximations, which is in contrast with previous claims that promoted the radial basis function (RBF) approximation. Further, our analysis shows that the RBF approximation suffers from Runge phenomenon, which cannot be mitigated simultaneously for both deep and shallow sources; therefore, its good performance is guarantied only if a priori knowledge about the source depth is available. CONCLUSIONS The previously published methodology for RL computation was not optimal. Improvements are possible if the newly suggested approach is used. SIGNIFICANCE The methodology presented in our paper allows more efficient utilization of the RL, providing a useful tool for processing of high density EEG recordings. Presented techniques allow to achieve high EEG spatial resolution, and avoid unnecessary spatial blurring caused by the problems in the previously published RL methodology.

Electrode Position Scaling in Realistic Laplacian Computation

This note discusses the effects of the electrode position scaling on the realistic Laplacian (RL) computation. It is shown that when the RL is estimated with the help of Tikhonov regularization and the generalized cross-validation (GCV) criterion, improper electrode position scaling may influence the GCV criterion, which results in the decrease of RL precision. We identify what the proper scaling should be, and we provide a closer examination of how the GCV criterion is affected by the electrode position scaling.

Fast Communication: Approximation of the null distribution of the multiple coherence estimated with segment overlapping

In this fast communication we suggest an approximation of the null distribution of the multiple coherence (MC) estimated with segment overlapping. The approximation is based on the formulas known for the non-overlapped segmentation, but the parameter corresponding to the number of segments is altered. The suggested approximation is statistically tested through a Monte Carlo simulation, and it is shown that its precision is quite high for a considerable range of MC parameters.