Objectives: Empirical mode decomposition (EMD) is a frequently used signal processing approach which adaptively decomposes a signal into a set of narrow-band components known as intrinsic mode functions (IMFs). For multi-trial, multivariate (multiple simultaneous recordings), and multi-subject analyses the number and signal properties of the IMFs can deviate from each other between trials, channels and subjects. A further processing of IMFs, e.g. a simple ensemble averaging, should determine which IMFs of one signal correspond to IMFs from another signal. When the signal properties have similar characteristics, the IMFs are assigned to each other. This problem is known as correspondence problem. Methods: From the mathematical point of view, in some cases the correspondence problem can be transformed into an assignment problem which can be solved e.g. by the Kuhn-Munkres algorithm (KMA) by which a minimal cost matching can be found. We use the KMA for solving classic assignment problems, i.e. the pairwise correspondence between two sets of IMFs of equal cardinalities, and for pairwise correspondences between two sets of IMFs with different cardinalities representing an unbalanced assignment problem which is a special case of the k-cardinality assignment problem. Results:A KMA-based approach to solve the correspondence problem was tested by using simulated, heart rate variability (HRV), and EEG data. The KMA-based results of HRV decomposition are compared with those obtained from a hierarchical cluster analysis (state-of-the-art). The major difference between the two approaches is that there is a more consistent assignment pattern using KMA. Integrating KMA into complex analysis concepts enables a comprehensive exploitation of the key advantages of the EMD. This can be demonstrated by non-linear analysis of HRV-related IMFs and by an EMD-based cross-frequency coupling analysis of the EEG data. Conclusions: The successful application to HRV and EEG analysis demonstrates that our solutions can be used for automated EMD-based processing concepts for biomedical signals.

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.

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.

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. 2010 Elsevier B.V. All rights reserved.

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.

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.

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.

An automatic EEG pattern detection unit was developed and tested for the recognition of burst-suppression periods and for the separation of burst from suppression patterns. The median, standard deviation and the 95% edge frequency were computed from single channels of the EEG within a moving window and completed by the continuous computation of frequency band power via an adapted Hilbert resonance filter. These parameters were given to the inputs of two hierarchically arranged artificial neural networks (NNs). The output signals of NNs indicate the suppression and burst phases. The burst recognition was focused on the precise recognition of the burst onset. In subsequent processing steps the time course of percentages of burst patterns within their corresponding burst-suppression-phases was calculated and the time locations of burst onsets can be used to trigger an averaging for a burst-related analysis. The data for our investigations were derived from the routine EEG derivations of 12 patients with various neurosurgical diseases. A group-related training of the NNs was realized. For the group-related trained NNs EEG data for 6 patients were used for training and the data of 6 other patients for testing the classification performance of the pattern recognition units. Additionally, the reliability of the detection algorithm was tested with data of two patients with convulsive state, resistant to treatment, and burst-suppression like pattern EEG.