Coupled oscillators for modeling and analysis of EEG/MEG oscillations.

This study presents three EEG/MEG applications in which the modeling of oscillatory signal components offers complementary analysis and an improved explanation of the underlying generator structures. Coupled oscillator networks were used for modeling. Parameters of the corresponding ordinary coupled differential equation (ODE) system are identified using EEG/MEG data and the resulting solution yields the modeled signals. This model-related analysis strategy provides information about the coupling quantity and quality between signal components (example 1, neonatal EEG during quiet sleep), allows identification of the possible contribution of hidden generator structures (example 2, 600-Hz MEG oscillations in somatosensory evoked magnetic fields), and can explain complex signal characteristics such as amplitude-frequency coupling and frequency entrainment (example 3, EEG burst patterns in sedated patients).

On the rhythmicity of quadratic phase coupling in the tracé alternant EEG in healthy neonates.

The time-variant quadratic phase coupling (QPC) in trace alternant (TA) EEG patterns in healthy full-term neonates (quiet sleep) was investigated by means of time-variant bispectral analysis. The frequency plain 1-1.5 Hz <=> 3.5-4.5 Hz was used as the region-of-interest. QPC rhythms with a frequency of approximately 0.1 Hz were found in all neonates (n = 6). It can be demonstrated that the QPC rhythm of the TA is generated by a pattern-spanning time-variant phase-locking process characterising early functional interactions in the immature brain.

A processing scheme for time-variant phase analysis in EEG burst activity of premature and full-term newborns in quiet sleep: a methodological study.

A processing scheme for the investigation of neonatal electroencephalographic burst oscillations that is composed of time-variant methods for linear and nonlinear phase analysis is introduced. Starting from a time-frequency analysis of oscillations' amplitudes, time-variant approaches for quantification of phase locking, n:m phase synchronization, and quadratic phase coupling are applied. Tracé discontinue patterns from premature newborns and tracé alternant patterns from full-term newborns were investigated using bipolar EEG recordings. Maturation-related differences between the burst generation mechanisms can be shown, which are reflected in group-specific patterns of augmentation, timing, and grouping of time-varying phase characteristics of the EEG burst oscillations. We demonstrate for both groups (premature and full-term newborns) that phase-locked low-frequency oscillations are pronounced in the frequency range of 0.5-1.5 Hz. Phase-locked oscillations also occur in a frequency range of >3 Hz. The amplitude of a phase-locked 2-Hz oscillation is higher in full-term than in premature newborns. After onset, n:m synchronization and an increase in bicoherence occur earlier in the premature group (between 0.5-1.5 Hz and 3.0-6.0 Hz). It can be suggested that during the maturation process, the driving force of thalamic structures decreases and that cortical activity plays an increasingly important role in the process of burst generation.

Phase synchronisation of the three leg joints in quiet human stance.

Quiet human stance is a dynamic multi-segment phenomenon. In literature, coupled ankle and hip actions are in the focus and examinations are usually restricted to frequency contributions below 4 Hz. Very few studies point to the knee playing an active role, and just one study gives evidence of higher frequency contributions. In order to investigate the dynamic coupling of all three leg joints in more depth, we revisited an experimental data set on quiet human stance. Since phase synchronisation is a strong indicator of non-linear coupling behind, we used the phase synchronisation index (PSI) to quantify the degree of leg joint coupling as a function of frequency. One main result is that we did not find any synchronisation between ankle and hip across the whole frequency range examined up to 8 Hz. In contrast, there is significant synchronisation between ankle and knee at a couple of frequencies between 1.25 Hz and 8 Hz when looking at the kinematics. Their joint torques rather synchronise below 2 Hz. There is also synchronisation between knee and hip kinematics above 6 Hz, however, only significant at one frequency bin in our data set. From this, we would infer that the multiple mechanical degrees of freedom contributing to quiet human stance should be chosen according to, thus map, physiology. Thereby, the knee is indispensable and bi-articular muscles play a central role in organising quiet human stance. Examining the non-stationarity of phase synchronisations will probably advance the understanding of self-organisation of quiet human stance.

A time-variant processing approach for the analysis of alpha and gamma MEG oscillations during flicker stimulus generated entrainment.

Repetitive flicker stimulation (photic driving) offers the possibility to study the properties and coupling characteristics of stimulation-sensitive neuronal oscillators by means of the MEG/EEG analysis. With flicker frequencies in the region of the individual alpha band frequency, the dynamics of the entrainment process of the alpha oscillation, as well as the dynamics of the accompanying gamma oscillations and the coupling between the oscillations, are investigated by means of an appropriate combination of time-variant analysis methods. The Hilbert and the Gabor transformation reveal time-variant properties (frequency entrainment, phase locking, and n:m synchronization) of the entrainment process in the whole frequency range. Additionally, time-variant partial directed coherence is applied to identify ocular saccadic interferences and to study the directed information transfer between the recording sites of the simultaneously derived MEG/EEG data during the entrainment. The MEG data is the focus of this methodological study as the entrainment effects of the alpha oscillation are stronger in MEG than in the EEG. The occipital brain region (visual cortex) was mainly investigated and the dynamics of the alpha entrainment quantified. It can be shown that at the beginning of this entrainment, a transient, strongly phase-locked "40-Hz" gamma oscillation occurs.

Time-variant analysis of linear and non-linear phase couplings of and between frequency components of EEG burst patterns in full-term newborns.

Time-variant (tv) phase-locking and synchronization characteristics of and between low-frequency (≤ 1.5 Hz) and high-frequency EEG oscillations (≥ 3.5 Hz) of the tracé alternant (TA) pattern in full-term newborns have been quantified to explore the origin of quadratic phase coupling (QPC, as non-linear phase coupling measure) between the frequency ranges 1 - 1.5 Hz ⇔ 3.5 - 4.5 Hz, which characterize the specific interactions of oscillations during the TA's burst activity. Using the Gabor transformation two measures of linear phase coupling, the phase-locking index (PLI) and the n:m phase synchronization index (PSI) have been determined. Phase-locking within the frequency ranges 1 -1.5 Hz and 3.5 - 4.5 Hz, and synchronization between both frequency ranges exists. These phase characteristics are significant 2 sec after burst onset and are associated with the maximum-values of the QPC(1 - 1.5 Hz ⇔ 3.5 - 4.5 Hz) which demonstrates that a specific neuronal coordination between the dynamics of phases and of amplitude-frequency dependencies must be underlying.

Analysis and modeling of time-variant amplitude-frequency couplings of and between oscillations of EEG bursts.

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.