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.

Primary somatosensory contextual modulation is encoded by oscillation frequency change.

OBJECTIVE: This study characterized thalamo-cortical communication by assessing the effect of context-dependent modulation on the very early somatosensory evoked high-frequency oscillations (HF oscillations). METHODS: We applied electrical stimuli to the median nerve together with an auditory oddball paradigm, presenting standard and deviant target tones representing differential cognitive contexts to the constantly repeated electrical stimulation. Median nerve stimulation without auditory stimulation served as unimodal control. RESULTS: A model consisting of one subcortical (near thalamus) and two cortical (Brodmann areas 1 and 3b) dipolar sources explained the measured HF oscillations. Both at subcortical and the cortical levels HF oscillations were significantly smaller during bimodal (somatosensory plus auditory) than unimodal (somatosensory only) stimulation. A delay differential equation model was developed to investigate interactions within the 3-node thalamo-cortical network. Importantly, a significant change in the eigenfrequency of Brodmann area 3b was related to the context-dependent modulation, while there was no change in the network coupling. CONCLUSION: This model strongly suggests cortico-thalamic feedback from both cortical Brodmann areas 1 and 3b to the thalamus. With the 3-node network model, thalamo-cortical feedback could be described. SIGNIFICANCE: Frequency encoding plays an important role in contextual modulation in the somatosensory thalamo-cortical network.

Time-variant partial directed coherence for analysing connectivity: a methodological study.

For the past decade, the detection and quantification of interactions within and between physiological networks has become a priority-in-common between the fields of biomedicine and computer science. Prominent examples are the interaction analysis of brain networks and of the cardiovascular-respiratory system. The aim of the study is to show how and to what extent results from time-variant partial directed coherence analysis are influenced by some basic estimator and data parameters. The impacts of the Kalman filter settings, the order of the autoregressive (AR) model, signal-to-noise ratios, filter procedures and volume conduction were investigated. These systematic investigations are based on data derived from simulated connectivity networks and were performed using a Kalman filter approach for the estimation of the time-variant multivariate AR model. Additionally, the influence of electrooculogram artefact rejection on the significance and dynamics of interactions in 29 channel electroencephalography recordings, derived from a photic driving experiment, is demonstrated. For artefact rejection, independent component analysis was used. The study provides rules to correctly apply particular methods that will aid users to achieve more reliable interpretations of the results.

Towards the time varying estimation of complex brain connectivity networks by means of a General Linear Kalman Filter approach.

One of the main limitations of the brain functional connectivity estimation methods based on Autoregressive Modeling, like the Granger Causality family of estimators, is the hypothesis that only stationary signals can be included in the estimation process. This hypothesis precludes the analysis of transients which often contain important information about the neural processes of interest. On the other hand, previous techniques developed for overcoming this limitation are affected by problems linked to the dimension of the multivariate autoregressive model (MVAR), which prevents from analysing complex networks like those at the basis of most cognitive functions in the brain. The General Linear Kalman Filter (GLKF) approach to the estimation of adaptive MVARs was recently introduced to deal with a high number of time series (up to 60) in a full multivariate analysis. In this work we evaluated the performances of this new method in terms of estimation quality and adaptation speed, by means of a simulation study in which specific factors of interest were systematically varied in the signal generation to investigate their effect on the method performances. The method was then applied to high density EEG data related to an imaginative task. The results confirmed the possibility to use this approach to study complex connectivity networks in a full multivariate and adaptive fashion, thus opening the way to an effective estimation of complex brain connectivity networks.

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.

Connectivity analysis of somatosensory evoked potentials in patients with major depression. Analysis of connectivity.

OBJECTIVES: Connectivity analysis was used to investigate the processing of intracutaneous stimuli and directed interactions within the pain matrix in patients with major depression (MD) and healthy controls (HCs), by means of frequency selective generalized partial directed coherence (gPDC). METHODS: Eighteen patients with MD and 18 HCs underwent stimulations consisting of moderately painful intracutaneous electrical stimuli to the right and left middle fingers. Connectivity analysis was based on nine selected EEG electrodes. RESULTS: Stimulus-induced changes of the gPDC in a pre/post stimulus comparison and changes in the connectivity pattern in the post-stimulus condition were found. We could identify network changes correlating to the side stimulated, as well as differences between HCs and MD patients. CONCLUSIONS: These data support the suggestion that pain processing in response to noxious stimulation in MD patients is different compared to healthy controls, suggesting aberrant functional connectivity. Generalized partial directed coherence is shown to be a promising method to detect changes in connectivity in both within- and between-subject designs.

Modelling and analysis of time-variant directed interrelations between brain regions based on BOLD-signals.

Time-variant Granger Causality Index (tvGCI) was applied to simulated and measured BOLD signals to investigate the reliability of time-variant analysis approaches for the identification of directed interrelations between brain areas on the basis of fMRI data. Single-shot fMRI data of a single image slice with short repetition times (200 ms, 16000 frames/subject, 64x64 voxels) were acquired from 5 healthy subjects during an externally-driven, self-paced finger-tapping paradigm (57-59 single taps for each subject). BOLD signals were derived from the pre-supplementary motor area (preSMA), the supplementary motor area (SMA), and the primary motor cortex (M1). The simulations were carried out by means of a Dynamic Causal Modelling (DCM) approach. The tvGCI as well as time-variant Partial Directed Coherence (tvPDC) were used to identify the modelled connectivity network (connectivity structure - CS - of the DCM). Different CSs were applied by using dynamic systems (Generalized Dynamic Neural Network - GDNN) and trivariate autoregressive (AR) processes. The influence of the low-pass characteristics of the simulated hemodynamic response (Balloon model) and of the measuring noise was tested. Additionally, our modelling strategy considered "spontaneous" BOLD fluctuations before, during, and after the appearance of the event-related BOLD component. Couplings which were extracted from the simulated signals were statistically evaluated (tvGCI for shuffled data, confidence tubes for tvGCI courses). We demonstrate that connections of our CS models can be correctly identified during the event-related BOLD component and with signal-to-noise-ratios corresponding to those of the measured data. The results based on simulations can be used to examine the reliability of connectivity identification based on BOLD signals by means of time-variant as well as time-invariant connectivity measures and enable a better interpretation of the analysis results using fMRI data. A readiness-BOLD response was only detected in one subject. However, in two subjects a strong time-variant connection (tvGCI) from preSMA to SMA was observed 3 s before the tapping was executed. This connection was accompanied by a weaker rise of the tvGCI from preSMA to M1. These preceding interrelations were confirmed in the other subjects by the dynamics of tvGCI courses. Based on the results of tvGCI analysis, the time-evolution of an individual connectivity network is shown for each subject.

Signal informatics as an advanced integrative concept in the framework of medical informatics. New trends demonstrated by examples derived from neuroscience.

OBJECTIVES: The main objective is to show current topics and future trends in the field of medical signal processing which are derived from current research concepts. Signal processing as an integrative concept within the scope of medical informatics is demonstrated. METHODS: For all examples time-variant multivariate autoregressive models were used. Based on this modeling, the concept of Granger causality in terms of the time-variant Granger causality index and the time-variant partial directed coherence was realized to investigate directed information transfer between different brain regions. RESULTS: Signal informatics encompasses several diverse domains including: processing steps, methodologies, levels and subject fields, and applications. Five trends can be recognized and in order to illustrate these trends, three analysis strategies derived from current neuroscientific studies are presented. These examples comprise high-dimensional fMRI and EEG data. In the first example, the quantification of time-variant-directed information transfer between activated brain regions on the basis of fast-fMRI data is introduced and discussed. The second example deals with the investigation of differences in word processing between dyslexic and normal reading children. Different dynamic neural networks of the directed information transfer are identified on the basis of event-related potentials. The third example shows time-variant cortical connectivity networks derived from a source model. CONCLUSIONS: These examples strongly emphasize the integrative nature of signal informatics, encompassing processing steps, methodologies, levels and subject fields, and applications.

Time-variant analysis of fast-fMRI and dynamic contrast agent MRI sequences as examples of 4-dimensional image analysis.

OBJECTIVES: Image sequences with time-varying information content need appropriate analysis strategies. The exploration of directed information transfer (interactions) between neuronal assemblies is one of the most important aims of current functional MRI (fMRI) analysis. Additionally, we examined perfusion maps in dynamic contrast agent MRI sequences of stroke patients. In this investigation, the focus centers on distinguishing between brain areas with normal and reduced perfusion on the basis of the dynamics of contrast agent inflow and washout. METHODS: Fast fMRI sequences were analyzed with time-variant Granger causality (tvGC). The tvGC is based on a time-variant autoregressive model and is used for the quantification of the directed information transfer between activated brain areas. Generalized Dynamic Neural Networks (GDNN) with time-variant weights were applied on dynamic contrast agent MRI sequences as a nonlinear operator in order to enhance differences in the signal courses of pixels of normal and injured tissues. RESULTS: A simple motor task (self-paced finger tapping) is used in an fMRI design to investigate directed interactions between defined brain areas. A significant information transfer can be determined for the direction primary motor cortex to supplementary motor area during a short time period of about five seconds after stimulus. The analysis of dynamic contrast agent MRI sequences demonstrates that the trained GDNN enables a reliable tissue classification. Three classes are of interest: normal tissue, tissue at risk for death, and dead tissue. CONCLUSIONS: The time-variant multivariate analysis of directed information transfer derived from fMRI sequences and the computation of perfusion maps by GDNN demonstrate that dynamic analysis methods are essential tools for 4D image analysis.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

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).

[Fundus spectrometry in age-related maculopathy]. / Fundusspektrometrie bei altersbezogener Makulopathie.

BACKGROUND: Spectroscopic methods permit the non-invasive detection of fundus pigments by the wavelength-dependent absorption of fluorescence as well as by the fluorescence lifetime. From the relative concentrations of haemoglobin and oxyhaemoglobin, the oxygen saturation can be calculated. The onset of age-related maculopathy might be delayed by a high optical density of xanthophyll. The detection of alterations in fundus autofluorescence points to age-related pathomechanisms (accumulation of lipofuscin, formation of connective tissue). The detection of autofluorescence of redox-pairs of coenzymes results in information about metabolic states at the cellular level, and might make possible an early detection of age-related changes when they are still reversible. METHOD: The evaluation of reflectance spectra, detected by imaging ophthalmo-spectrometry, results in the calculation of oxygen saturation or in the optical density of xanthophyll or of melanin. Fluorescence spectra can be measured also by this technique. For the 2-dimensional determination of the distribution of xanthophyll, a very simple method was developed, requiring fundus illumination by one wavelength only. In the detection of time-resolved autofluorescence, the fluorescence lifetime is used for the determination of endogenous fluorophores. RESULTS: As result of comparing studies between ARM patients and healthy subjects, the consumption of retinal oxygen was increased already in the children of ARM patients. An increasing optical density of xanthophyll was determined after lutein supplementation. Differences in fluorescence lifetime were determined between ARM patients and healthy subjects, but their interpretation requires investigations of cell or of organ model cultures. CONCLUSIONS: The described methods permit in vivo basic investigations of ARM and can be considered as impulses for the development of diagnostic devices.

[Determination of the concentration distribution of macular pigment from reflection and fluorescence images]. / Bestimmung der Konzentrationsverteilung des Makulapigmentes aus Reflexions- und Fluoreszenzaufnahmen.

OBJECTIVE: The macular pigment xanthophyll protects the macula in two ways: firstly, it absorbs hazardous blue light and secondly, it acts as a radical scavenger. A low concentration of xanthophyll may be regarded as a risk factor for age-related macular degeneration (AMD). Therefore, we investigated a simple method to determine the xanthophyll concentration at the fundus which is suitable for patient screening. METHOD: The local distribution of xanthophyll density was determined from monochromatic blue reflection images and autofluorescence images of the fundus in 18 healthy volunteers (mean age: 23.9 years). The significance of the parameters maximal, global, and mean concentration were compared. RESULTS: The maximal optical density of xanthophyll determined from reflection images was found to be 0.29+/-0.08 (mean for all test persons) which is in good agreement with literature data. The total xanthophyll concentration which is proportional to the maximal density, appeared to be appropriate to describe a person's overall xanthophyll status. Because of the low intensity of autofluorescence images, these are less useful for the determination of the xanthophyll concentration. CONCLUSIONS: Because of it's simplicity, the determination of xanthophyll concentration as described here can be performed by every ophthalmologist using a fundus camera and is, therefore, suitable as a screening method.

Prediction of movement following noxious stimulation during 1 minimum alveolar anesthetic concentration isoflurane/nitrous oxide anesthesia by means of middle latency auditory evoked responses.

This paper investigates the applicability of generalized dynamic neural networks for the design of a two-valued anesthetic depth indicator during isoflurane/nitrous oxide anesthesia. The indicator construction is based on the processing of middle latency auditory evoked responses (MLAER) in combination with the observation of the patient's movement reaction to skin incision. The framework of generalized dynamic neural networks does not require any data preprocessing, visual data inspection or subjective feature extraction. The study is based on a data set of 106 patients scheduled for elective surgery under isoflurane/nitrous oxide anesthesia. The processing of the measured MLAER is performed by a recurrent neural network that transforms the MLAER signals into signals having a very uncomplex structure. The evaluation of these signals is self-evident, and yields to a simple threshold classifier. Using only evoked potentials before the pain stimulus, the patient's reaction could be predicted with a probability of 81.5%. The MLAER is closely associated to the patient's reaction to skin incision following noxious stimulation during 1 minimum alveolar anesthetic concentration isoflurane/nitrous oxide anesthesia. In combination with other parameters, MLAER could contribute to an objective and trustworthy movement prediction to noxious stimulation.

Training trajectories by continuous recurrent multilayer networks.

This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagin's maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.

Light paths in retinal vessel oxymetry.

The oxygen utilization and, therefore, the metabolic state, of a distinctive area of the retina may be calculated from the diameter of the supplying artery and vein, the haemoglobin oxygenation, and the velocity of the blood. The first two parameters can be determined by imaging spectrometry at the patients ocular fundus. However, the reflected light emerging from a vessel followed different pathways through the ocular fundus layers and the vessel embedded in the retina. The contribution of the single pathways to the vessel reflection profile is investigated by a Monte Carlo simulation. Considering retinal vessels with diameters of 25-200 microm we found the reflection from a thin vessel to be determined by the single and double transmission of light at 560 nm. The backscattering from the blood column determines the reflectance in the case of a thick vessel. However, both components are in the same order of magnitude. This has to be considered in the calculation of the oxygen saturation of blood in retinal vessels from their reflection spectra.

Identification of the stimulated hemiretina in primary school children and adults based on left and right hemifield pattern reversal visual evoked potentials--a comparative study.

OBJECTIVES: The analysis of left and right hemifield pattern-reversal visual evoked potentials (PVEPs) in children and the identification of the stimulated hemiretina testing different identification procedures previously applied to adults. METHODS: Lateral hemifield PVEPs were recorded in 40 children (6-11 years) and 27 adults (25-40 years) from, at least, 19 standard electrodes. Two procedures were tested for the determination of the stimulated hemifield: firstly, the evaluation of the values of instantaneous frequency at the occipital electrodes at P100 latency (determined by the global field power), and secondly, the application of a generalised dynamic neural network (GDNN) using the PVEP time course at selected electrode positions as the external input. RESULTS: P100 latency as well as P100 amplitude over the contralateral occiput in children were significantly greater than in adults. Contrary to the behaviour in adults, instantaneous frequency is not a robust identifier of left and right hemiretina stimulation in children. The best identification performances were achieved when using group trained GDNNs with the bipolar difference signals of electrodes P3/P4 or T5/T6 as the external input. CONCLUSIONS: The PVEPs at electrodes P3/P4 and T5/T6 contain essential information for the determination of the stimulated hemifield. This should be further considered during the development of on-line procedures for automatic PVEP detection in future studies.

Initial state training procedure improves dynamic recurrent networks with time-dependent weights.

The problem of learning multiple continuous trajectories by means of recurrent neural networks with (in general) time-varying weights is addressed. The learning process is transformed into an optimal control framework where both the weights and the initial network state to be found are treated as controls. For such a task, a learning algorithm is proposed which is based on a variational formulation of Pontryagin's maximum principle. The convergence of this algorithm, under reasonable assumptions, is also investigated. Numerical examples of learning nontrivial two-class problems are presented which demonstrate the efficiency of the approach proposed.

Identification of hemifield single trial PVEP on the basis of generalized dynamic neural network classifiers.

This paper is concerned with the application of generalized dynamic neural networks for the identification of hemifield pattern-reversal visual evoked potentials. The identification process is performed by different networks with time-varying weights using signals from different electrode positions as external inputs. Since dynamic neural networks are able to process time-varying signals, the identification of the stimulated hemiretinae is performed without feature extraction. The performance of the method presented is compared with a reference method based on the values of instantaneous frequency at the occipital electrode positions at P100 latency.