Biomedical subjects

Andreas Galka

Publications and source records attributed to Andreas Galka.

6 recordsLinked to original sources

PubMed2006

Localized short-range correlations in the spectrum of the equal-time correlation matrix.

We suggest a procedure to identify those parts of the spectrum of the equal-time correlation matrix C where relevant information about correlations of a multivariate time series is induced. Using an ensemble average over each of the distances between eigenvalues, all nearest-neighbor distributions can be calculated individually. We present numerical examples, where (a) information about cross correlations is found in the so-called "bulk" of eigenvalues (which generally is thought to contain only random correlations) and where (b) the information extracted from the lower edge of the spectrum of C is statistically more significant than that extracted from the upper edge. We apply the analysis to electroencephalographic recordings with epileptic events.

Journal Article↗

PubMed2005

Modelling non-stationary variance in EEG time series by state space GARCH model.

We present a new approach to modelling non-stationarity in EEG time series by a generalized state space approach. A given time series can be decomposed into a set of noise-driven processes, each corresponding to a different frequency band. Non-stationarity is modelled by allowing the variances of the driving noises to change with time, depending on the state prediction error within the state space model. The method is illustrated by an application to EEG data recorded during the onset of anaesthesia.

Anesthesia↗

PubMed2005

Detection and characterization of changes of the correlation structure in multivariate time series.

We propose a method based on the equal-time correlation matrix as a sensitive detector for phase-shape correlations in multivariate data sets. The key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix. Consequently, detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors. The performance of the technique is demonstrated by application to N(f)-tori, autoregressive models, and coupled chaotic systems. The high sensitivity, the comparatively small computational effort, and the excellent time resolution of the method recommend it for application to the analysis of complex, spatially extended, nonstationary systems.

Journal Article↗

PubMed2004

Recursive penalized least squares solution for dynamical inverse problems of EEG generation.

In the dynamical inverse problem of electroencephalogram (EEG) generation where a specific dynamics for the electrical current distribution is assumed, we can impose general spatiotemporal constraints onto the solution by casting the problem into a state space representation and assuming a specific class of parametric models for the dynamics. The Akaike Bayesian Information Criterion (ABIC), which is based on the Type II likelihood, was used to estimate the parameters and evaluate the model. In addition, dynamic low-resolution brain electromagnetic tomography (LORETA), a new approach for estimating the current distribution is introduced. A recursive penalized least squares (RPLS) step forms the main element of our implementation. To obtain improved inverse solutions, dynamic LORETA exploits both spatial and temporal information, whereas LORETA uses only spatial information. A considerable improvement in performance compared to LORETA was found when dynamic LORETA was applied to simulated EEG data, and the new method was applied also to clinical EEG data.

Brain↗

PubMed2004

A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering.

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal evolution of the distributed generators of the EEG can be reconstructed at each voxel of a discretisation of the gray matter of brain. By fitting linear autoregressive models with neighbourhood interactions to EEG time series, new classes of inverse solutions with improved resolution and localisation ability can be explored. For the purposes of model comparison and parameter estimation from given data, we employ a likelihood maximisation approach. Both for instantaneous and dynamical inverse solutions, we derive estimators of the time-dependent estimation error at each voxel. The performance of the algorithm is demonstrated by application to simulated and clinical EEG recordings. It is shown that by choosing appropriate dynamical models, it becomes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions.

Algorithms↗

PubMedDate not supplied

Impulse response function based on multivariate AR model can differentiate focal hemisphere in temporal lobe epilepsy.

The purpose of this study is to propose and investigate a new approach for discriminating between focal and non-focal hemispheres in intractable temporal lobe epilepsy, based on applying multivariate time series analysis to the discharge-free background brain activity observed in nocturnal electrocorticogram (ECoG) time series. Five unilateral focal patients and one bilateral focal patient were studied. In order to detect the location of epileptic foci, linear multivariate autoregressive (MAR) models were fitted to the ECoG data; as a new approach for the purpose of summarizing these models in a single relevant parameter, the behavior of the corresponding impulse response functions was studied and described by an attenuation coefficient. In the majority of unilateral focal patients, the averaged attenuation coefficient was found to be almost always significantly larger in the focal hemisphere, as compared to the non-focal hemisphere. Also the amplitude of the fluctuations of the attenuation coefficient was significantly larger in the focal hemisphere. Moreover, in one patient showing a typical regular sleep cycle, the attenuation coefficient in the focal hemisphere tended to be larger during REM sleep and smaller during Non-REM sleep. In the bilateral focal patient, no statistically significant distinction between the hemispheres was found. This study provides encouraging results for new investigations of brain dynamics by multivariate parametric modeling. It opens up the possibility of relating diseases like epilepsy to the properties of inconspicuous background brain dynamics, without the need to record and analyze epileptic seizures or other evidently pathological waveforms.

Adult↗