Assignment of Empirical Mode Decomposition Components and Its Application to Biomedical Signals.

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.

Dynamics of directed interactions between brain regions during interburst-burst EEG patterns in quiet sleep of full-term neonates.

The study investigates time-variant directed interactions between brain regions during the interburst-burst EEG pattern (tracé alternant) characteristic of quiet sleep in healthy neonates. The transition from interburst to burst is of particular interest as the generation of the EEG characteristics at burst onset reflects timing and time-variant interplay between the cortical and the thalamo-cortical brain structures. To study the dynamics of the interactions, time-variant partial directed coherence (PDC), a measure of effective connectivity, was used which allows analysis in the time-frequency range. The main results of the grand mean PDC analysis are: (1) PDC time-frequency patterns are frequently associated with phase-locked oscillations. (2) Interhemispheric interactions are dominant between frontal, central and occipital electrodes and intrahemispheric interactions are much less substantial. (3) An interaction breakdown for the frequency ranges 1-4 Hz (Fp(1) ⇒ Fp(2)) and 0.5-3 Hz (Fp(2) ⇒ Fp(1)) exists which lasts about 2.5s and which is located at about burst onset. (4) Strong interactions in the high-frequency range 3.5-4.5 Hz between the frontal electrodes can be observed for both directions at the burst onset. It can be concluded that the evolution of strong interactions in the high-frequency range, which starts shortly before or at the burst onset from frontal regions to anteroposterior directions as well as the frontal interhemispheric interactions, are associated with the burst onset generation. Additionally, the collapsing of the interactions before burst onset and after the burst are indicative of neuronal reorganisation processes.

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

OBJECTIVE: Burst activity of the 'trace alternant' (TA) EEG pattern in the quiet sleep of full-term newborns is investigated to explore the timing and the time-variant coupling characteristics of and between a burst's oscillatory components. The working hypothesis is that signal properties provide information about the neuronal initiation processes of the burst, and about the coupling and interrelation dynamics between cortical low-frequency oscillations and high-frequency spindles in thalamic structures which substantially contribute to the burst pattern. METHODS: For time-variant phase-locking index (PLI), phase-synchronization index (PSI), quadratic phase coupling (QPC) measures, and amplitude-frequency dependency analyses the Gabor and the Hilbert transformation, both implemented as fast Fourier transformation-based approaches, were used. Additionally, models of mutually coupled Duffing oscillators were adapted to the burst data derived from the neonates ('measured bursts'), and the corresponding 'modeled burst' simulations were analyzed in comparison to the measured bursts. RESULTS: A strong phase-locking of the high-frequency oscillations and synchronization between low- and high-frequency oscillatory activity at burst onset can be observed. The QPC courses and the amplitude of all oscillations rise slightly before or at the burst onset and reach their maximum within the following 1-3 s after onset. Additionally, correlative envelope-envelope and envelope-frequency couplings within and between the burst oscillations can be demonstrated. All theses time-variant signal properties can be simulated by the model. CONCLUSIONS: The amplitude-independent phase measures point to a phase stabilization of high-frequency oscillatory activity which occurs before the initiation of the low-frequency oscillation. This finding points to a trigger process in which the thalamus is initially involved. After burst onset the cortical low-frequency oscillation modulates the high-frequency oscillatory activities, where modulation and additional coupling effects can be explained by three mutually coupled oscillators. SIGNIFICANCE: The model-based analysis strategy offers an up-to-date methodological guideline and sets a new standard of analysis for the investigation of EEG patterns and event-related potentials.

Time-variant parametric estimation of transient quadratic phase couplings between heart rate components in healthy neonates.

The heart rate variability (HRV) can be taken as an indicator of the coordination of the cardio-respiratory rhythms. Bispectral analysis using a direct (fast Fourier transform based) and time-invariant approach has shown the occurrence of a quadratic phase coupling (QPC) between a low-frequency (LF: 0.1 Hz) and a high-frequency (HF: 0.4-0.6 Hz) component of the HRV during quiet sleep in healthy neonates. The low-frequency component corresponds to the Mayer-Traube-Hering waves in blood pressure and the high-frequency component to the respiratory sinus arrhythmia (RSA). Time-variant, parametric estimation of the bispectrum provides the possibility of quantifying QPC in the time course. Therefore, the aim of this work was a parametric, time-variant bispectral analysis of the neonatal HRV in the same neonates used in the direct, time-invariant approach. For the first time rhythms in the time course of QPC between the HF component and the LF component could be shown in the neonatal HRV.

Model-related analysis of EEG burst patterns in sedated patients.

A model-related analysis approach was introduced to study amplitude-frequency dependencies within and between EEG frequency components. An oscillator network was used to model EEG burst patterns of sedated patients during encephalographic burst-suppression periods (BSP). The parameter set of the oscillator network was determined for a set of bursts during BSP. In this way, these burst-related parameter sets were used to investigate (i) the dynamics of interrelation of the amplitude and frequency within and between the frequency components during the occurrence of burst patterns and (ii) changes of signal properties (burst-by-burst) during the BSP. Representative results are demonstrated for one patient (group of 7 patients).

On the spatio-temporal organisation of quadratic phase-couplings in 'tracé alternant' EEG pattern in full-term newborns.

OBJECTIVE: The time courses of quadratic phase-coupling (QPC) of electroencephalographic burst and interburst patterns of the 'trace alternant' (TA) in full-term newborns have been quantified. METHODS: Using the Gabor expansion, a fast Fourier transformation based method, biamplitude, bicoherence and phase-bicoherence time courses of both burst and interburst patterns have been determined (common average reference EEG recordings). With a frequency resolution of 0.25 Hz and a frequency grid of 1-1.5 <==> 3.5-4.5 Hz (region-of-interest), a number of 15 frequency pairs result. These pairs have been investigated. RESULTS: The burst and the interburst patterns are characterized by temporally and topographically different QPC profiles. All differences are dominant at the electrode Fp1 followed by Fp2. There is a significant difference (combined multiple and global test strategy) in the QPC characteristics between both patterns within the time period from 0.75 to 1.5 s after the pattern onset at electrode Fp1. The maximal QPC in burst patterns (especially at Fp1) can be observed during this time period. In contrast to this finding, maximal QPC in interburst patterns (at Fp1) are reached immediately after the onset and at 3 s. Summarising all findings, a QPC-rhythm of 0.1 Hz during TA can be assumed. CONCLUSIONS: It can be assumed that the QPC rhythm of the TA is generated by a pattern-spanning time-variant phase-locking process and there are indications for a possible correspondence between the QPC rhythm and vegetative rhythms. SIGNIFICANCE: This study showed that advanced, time-variant analysis methods quantifying QPC rhythms are able to add new scientific information to the understanding of nature, characteristics and significance of TA in the neonatal EEG.

Technique for the quantification of transient quadratic phase couplings between heart rate components.

A technique for the time-variant analysis of quadratic phase coupling (QPC) in heart rate data is introduced and tested in 6 human neonates during quiet sleep. The set up of the approach is based up on the assumption that QPCs in the heart rate variability (HRV) are related to amplitude modulation effects. The application of the biamplitude deals with the detection of the coupling pattern and the bicoherence is used for the statistical quantification of coupling. By means of the results of bispectral analysis the time-variant processing has been adapted. The frequency-selective complex demodulation of the HRV leads to the envelope of the respiratory sinus arrhythmia (RSA), this has been used as one input for a time-variant coherence analysis. The other input is the low-pass filtered 10-second-rhythm of the HRV. A time-continuous quantification of the QPC, caused by amplitude modulation (10-second-rhythm modulates the RSA), is possible using this approach. According to our observed results in neonatal HRV both a phase co-ordination between the 10-second-rhythm and RSA as well as a non-linear coupling (amplitude modulation) between these HRV components can be seen.

Quantification of transient quadratic phase couplings within EEG burst patterns in sedated patients during electroencephalic burst-suppression period.

The time dynamics of the quadratic phase coupling within burst patterns during electroencephalic burst-suppression has been quantified. It can be shown that a transient quadratic phase coupling (QPC) exists between the frequency ranges 0 to 2.5 and 3 to 7.5 Hz and between the frequency ranges 0 to 2.5 and 8 to 12 Hz. The QPC can be explained by an amplitude modulation, where the slow rhythm modulates the rhythmic activities with a higher frequency. By means of time-variant bicoherence analysis, a strong phase-locking between the modulating and the modulated component can be identified. The phase-locking is demonstrable within the first 250 ms after the burst onset and comes up to the maximum between 750 and 1250 ms. The effect is maintained over the whole first part of the burst (2 s) with a decreasing tendency after 1250 ms. All these effects cannot be found in the EEG before entering the burst suppression period (BSP). The transient coupling phenomena in the EEG bursts during BSP can be regarded as indicators for short-term interrelations between the underlying electrophysiologic processes.

Interrelations between EEG frequency components in sedated intensive care patients during burst-suppression period.

The EEG during basic sedation and burst patterns during electroencephalic burst-suppression patterns (BSP) were analyzed. The aim of EEG analysis was the characterization and quantification of the interrelations between distinct frequency components in both states of sedation. The data for the investigations were derived from the routine EEG derivations of 12 patients with various neurosurgical diseases. It can be demonstrated that the degree of interrelation (amplitude modulation) between a low-frequency component (0-2.5 Hz) and oscillations with higher frequency (3-7.5 and 8-12 Hz) is increased in burst patterns during BSP compared with the EEG during basic sedation. It can be concluded that the degree of interrelations depends on the sedation depth induced by hypnotic drugs.

New approaches for the detection and analysis of electroencephalographic burst-suppression patterns in patients under sedation.

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 EEC.

Multimodal time-variant signal analysis of neonatal EEG burst patterns.

It can be shown that dominant rhythmic signal components of neonatal EEG burst patterns (discontinuous EEG in quiet sleep) are characterized by a quadratic phase coupling (bispectral analysis), i.e. a multiplicative interaction (connection) between the underlying electrophysiological processes can be assumed. By means of pattern recognition algorithms as well as time-variant spectral and coherence analysis, a so-called "initial wave" (narrow band rhythm within a frequency range of 3-12 Hz) can be demonstrated within the first part of the burst pattern. The detection of this signal component and of the quadratic phase coupling is more successful in the frontal region. By means of amplitude demodulation of the "initial wave" the phase coupling can be attributed to an amplitude modulation. The results were derived from 6 neonates (20 burst patterns for each neonate; 8-channel recordings). A 16-channel EEG-recording was analyzed for one neonate.

Analysis of the interrelations between a low-frequency and a high-frequency signal component in human neonatal EEG during quiet sleep.

It can be shown that dominant rhythmic signal components of neonatal EEG burst patterns (discontinuous EEG in quiet sleep) are characterised by a quadratic phase coupling (bispectral analysis). A so-called 'initial wave' (narrow band rhythm within a frequency range of 3-12 Hz) can be demonstrated within the first part of the burst pattern. The detection of this signal component and of the phase coupling is more successful in the frontal region. By means of amplitude demodulation of the 'initial wave' and a subsequent coherence analysis the phase coupling can be attributed to an amplitude modulation, i.e. the envelope curve of the 'initial wave' shows for a distinct period of time the same qualitative course as the signal trace of a 'lower' frequency component (0.75-3 Hz). The results were derived from six neonates (20 burst patterns for each neonate; 8 channel recordings).

[An experimental study on the use of the Hilbert operator as a method of signal preprocessing for the determination of oxygen saturation in retinal vessels]. / Experimentelle Studie zur Anwendung des Hilbertoperators als Methode zur Signalvorverarbeitung für die Bestimmung der Sauerstoffsättigung in retinalen Gefässen.

For the non-invasive measurement of the oxygen saturation in human retinal vessels, the light reflected by a vessel and its surroundings is evaluated. Differences in the absorption and scattering properties of the optical media provide so-called vessel profiles, but the central vessel section is often disturbed by a regular reflex. In order to eliminate this reflex, a method based on the Hilbert transform is presented, which can be used for the determination of logarithmic differences between the reflected light on and that beside the vessel. The data for our investigations were produced by simulation of the radiation transport in multi-layered tissue. A linear regression between expected and measured values based on 40 pairs was used for the evaluation of the proposed method. A linear relationship was shown to exist.

A new approach for detecting the position of retinal vessels and calculating their diameter on the basis of dynamic spectral analysis.

Fast adaptive algorithms were used for the detection of retinal vessels and for pre-processing the signals. By using different methods of dynamic spectral analysis, the local frequency of the vessels was determined. On this basis a method of calculating the diameters of the vessels was constructed; it is robust in relation to disturbances in the domain of the edges.

Dynamic description of stochastic signal by adaptive momentary power and momentary frequency estimation and its application in analysis of biological signals.

The importance of dynamic spectral analysis of time-varying signals in medicine, biology and technology is increasing rapidly. The basic spectral parameters are momentary power and momentary frequency. The paper presents adaptive recursive estimation methods for these spectral parameters. Their specific properties are investigated, and the possibilities of applications in computer-assisted analysis of biological and technical signals are demonstrated, even satisfying real-time requirements.