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Chaos 18 4 : , Pacemaker and network mechanisms of rhythm generation: cooperation and competition. J Theor Biol. Neuronal synchrony: peculiarity and generality. Chaos 18 3 , Artificial synaptic modification reveals a dynamical invariant in the pyloric CPG. Eur J Appl Physiol. Nowotny T, Rabinovich MI. Dynamical origin of independent spiking and bursting activity in neural microcircuits. Phys Rev Lett. Dynamical Principles in Neuroscience. Reviews of Modern Physics 78 4 : , Generation and reshaping of sequences in neural systems.

Biological Cybernetics 95 6 : , Dynamics of Sequential Decision Making. Rev Lett.

Scientists Discover Exotic New Patterns of Synchronization

Heteroclinic synchronization: ultrasubharmonic locking. Dynamics of sequential decision making. The role of sensory network dynamics in generating a motor program. Thursday, 16 May Friday, 17 May The study of nonlinear systems continues to yield new and fascinating phenomena.

Ozge Canli. Bogdan Penkovskyi.


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Xingang Wang. Alexander Dmitriev. Nefeli Tsigkri. Sergey Kashchenko.

Original Research ARTICLE

Markus Patzauer. Arkady Pikovsky Potsdam University.

Karl Pelka. Igor Franovic. Camille Poignard. Nataliya Stankevich. Giulia Ruzzene. Each EEG epoch was visually inspected for quality by a certified electrophysiologist G. Short contamination intervals were removed from the epochs after visual inspection, and these appeared to be under ms. Next, we calculated linear spectral and wavelet and nonlinear features for EEG epochs, separately for each channel. The frontal polar channels Fp1 and Fp2 were excluded from the analysis, as these were highly contaminated with motion-, muscle- and eye-related artifacts; as a result, 30 channels were retained.

HFD was calculated for the 2—10 Hz band and alpha band within 10—12 Hz. HFD for alpha was calculated across a narrower frequency band 10—12 Hz than for PSD and WT 8—12 Hz , based on previous findings of age-related variability in the alpha rhythm and its HFD for young adults aged between 20 and 30 years Portnova and Atanov, Envelopes were constructed using the Hilbert transform.

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Fractal dimension was assessed using the Higuchi method Higuchi, All initial values were separately averaged over all channels, different electrode pools and across the frequency band of interest. Only three bands were selected for calculation of the regressors: delta 2—4 Hz , alpha 8—12 Hz , and beta 16—20 Hz. We did not include theta rhythm patterns in the analysis because these were highly contaminated by artifacts caused by MRI gradient switching.

The theta band frequency of 4—8 Hz was also filtered out from the 2—20 Hz range used to calculate HFD. EEG features were calculated as the mean values from all electrodes except Fp1 and Fp2 for all frequency bands under investigation. Additionally, we measured the parameters of alpha-rhythm gradient from frontal to occipital areas and PSD of alpha, beta and delta bands, as well as HFD localized in different areas frontal, temporal, occipital, parietal, and central.

At the first level of analysis, the resulting sequences of EEG values each of the values were convolved with the canonical HRF. Following convolution, the obtained vectors of EEG pattern changes were used as regressors, along with 6 motion parameters for calculation of a multiple linear regression of the fMRI data in GLM separately for each EEG regressor.


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At the second level of analysis, first-level contrast images were subjected to a one-sample t -test for each regressor. Using FWE, we found no significantly correlated voxels for any of the given regressors with a cluster size of more than 3 voxels; at the uncorrected level, we frequently observed sparse activation with a voxel size of less than 10 voxels. We focused first on the spectral features of the alpha band as the most reliable index of resting state wakefulness with closed eyes during EEG.

The alpha-rhythm gradient showed no significant correlation with BOLD signal as alpha PSD averaged across frontal, temporal, occipital, parietal and central areas. We found positive correlations of BOLD fluctuations in resting state only with alpha PSD averaged across all electrodes for two brain regions: the right precuneus and the left culmen of the cerebellum Table 1 ; Figure 1A. However, these positive correlations of BOLD changes were at uncorrected level with cluster size more than 50 voxel and alpha band PSD measured in frontal, temporal, occipital, parietal and central areas.

We assumed that positive correlation of BOLD changes with increasing alpha PSD indicates areas of the brain in which activation coincides with alpha synchronization while negative correlation is associated with alpha desynchronization. However, we observed no negative correlations with alpha PSD.

Next, we looked specifically at correlations between BOLD signal and fluctuations of magnitude and frequency of the alpha peak mALP and fALP, respectively , which might also provide information about the synchronization-desynchronization process in EEG. Remarkably, instead of PSD, we observed only significant and positive correlations of BOLD changes with fALP in the following areas: right-hemispheric activation of the middle frontal gyrus, rolandic operculum, pars triangularis of the inferior frontal gyrus Broca area, BA 47 , middle temporal gyrus, insula BA 13 , fusiform gyrus BA 37 , culmen in the cerebellum, hippocampus, precentral gyrus BA 4 and middle orbitofrontal gyrus.

Table 1. Figure 1. Spatial brain maps with brain areas highlighted in which the BOLD signal increase showed a positive relation with the following EEG regressors: A frequency of alpha peak and B alpha band power. The figure shows the three most informative orthogonal slices for the EEG regressor. The areas, where activation was found to depend on the values of delta PSD, included the bilateral parahippocampal gyri, middle frontal gyri BA 9 and 10 , caudate nuclei, precuneus and anterior cingulate gyri BA Activation of the rolandic operculum, superior orbitofrontal cortex BA 10 and middle cingulate gyrus was observed only in the right hemisphere,; the inferior orbitofrontal cortex, precentral and postcentral gyri BA 1, 4, and 6 , cerebellum, thalamus and insula BA 13 and 45 were active in the left hemisphere.

Table 2.


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  • Figure 2. For the beta range of 16—20 Hz, only stdWT exhibited both positive and negative correlations with the BOLD signal in bilateral activation of the thalamus more prominent in the right hemisphere , right insula, parahippocampal gyrus and olfactory cortex, left medial frontal gyrus, supplementary motor area BA 6 , caudate nuclei, and putamen Table S1A; Figure S1A. However, these results did not survive FDR correction.

    The HFD of the studied frequency bands, as averaged across selected electrodes for the different areas, exhibited no significant association with brain activation as measured by fMRI. However, HFD for the whole EEG band in question 2—20 Hz was positively correlated with bilateral activation of the paracentral lobules and middle temporal gyri, which was more prominent in the right hemisphere.

    Other regions correlated with HFD also presented unequally in the hemispheres, including the inferior frontal, superior frontal and parahippocampal gyri, precuneus, insula and middle cingulate cortex and the rolandic operculum, which were more correlated with HFD changes in the right hemisphere. Activation of the superior occipital gyrus, inferior occipital gyrus and supramarginal gyrus was observed in the left hemisphere Table 3 ; Figures 3A,B. Table 3.

    Nonlinear Waves and Pattern Dynamics

    Figure 3. We compared the results of fMRI statistical mapping according to the mean spectral power of distinct frequency EEG bands, variability of alpha band peak frequency, temporal changes in EEG band power by wavelet analysis and complexity of the EEG signal as reflected in HFD changes. Our findings indicate that the spectral features of EEG frequency bands, variability of alpha peak and changes in HFD correlate significantly with local BOLD fluctuations in the brain during resting state.

    However, electrophysiological research suggests that a single cerebral rhythm more probably arises from synchronized activity of different neuronal populations than from one specific cerebral network Buzsaki and Draguhn, Although some adjacent frequency bands especially higher frequency rhythms such as beta and gamma may indicate the oscillatory activity of more local neuronal networks although for relatively short time intervals Sherman et al. Functional networks, which are typically associated with different cognitive functions, exhibit oscillations at several rhythmic frequencies coexisting in the same brain areas Varela et al.

    As a result, an EEG signal derived from neuronal activity is characterized by higher variability or nonstationarity in the time domain.

    The instability of rhythms, as well as temporal changes and EEG entropy, might therefore provide additional information about switches in the synchronization of neuronal activity related to different brain networks during the resting state condition. The present study supports the latter assumption, as we observed a clear association between EEG complexity changes and resting state BOLD signal fluctuations.

    Notably, we found a significant correlation of BOLD signal with mean EEG patterns averaged across all electrodes, but we found no reliable dependency of BOLD signal on topographically distinct EEG patterns from the frontal, temporal, parietal and occipital recording sites.