Maciej Kaminski

A new method of the description of the information flow in the brain structures

The paper describes the method of determining direction and frequency content of the brain activity flow. The method was formulated in the framework of the AR model. The transfer function matrix was found for multichannel EEG process. Elements of this matrix, properly normalized, appeared to be good estimators of the propagation direction and spectral properties of the investigated signals. Simulation experiments have shown that the estimator proposed by us unequivocally reveals the direction of the signal flow and is able to distinguish between direct and indirect transfer of information. The method was applied to the signals recorded in the brain structures of the experimental animals and also to the human normal and epileptic EEG. The sensitivity of the method and its usefulness in the neurological and clinical applications was demonstrated.

Determination of EEG activity propagation: pair-wise versus multichannel estimate

Performance of different estimators describing propagation of electroencephalogram (EEG) activity, namely: Granger causality, directed transfer function (DTF), direct DTF (dDTF), short-time DTF (SDTF), bivariate coherence, and partial directed coherence are compared by means of simulations and on the examples of experimental signals. In particular, the differences between pair-wise and multichannel estimates are studied. The results show unequivocally that in most cases, the pair-wise estimates are incorrect and a complete set of signals involved in a given process has to be used to obtain the correct pattern of EEG flows. Different performance of multivariate estimators of propagation depending on their normalization is discussed. Advantages of multivariate autoregressive model are pointed out.

Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method

A modification of directed transfer function-direct DTF-is proposed for the analysis of direct information transfer among brain structures on the basis of local field potentials (LFP). Comparison of results obtained by the analysis of simulated and experimental data with a new dDTF and DTF method is shown. A new measure to estimate direct causal relations between signals is defined. The present results demonstrate the effectiveness of the new dDTF method and indicate that the dDTF method can be used to obtain the reliable patterns of connections between various brain structures.

Topographic analysis of coherence and propagation of EEG activity during sleep and wakefulness

Overnight sleep EEG recorded from 21 derivations was studied in 8 healthy subjects. The vector autoregressive model was fitted to all 21 channels simultaneously. Ordinary, multiple and partial coherences and directed transfer functions were estimated for sleep stages and wakefulness. Ordinary coherences give rather trivial information that coherence decreases with distance. Partial coherences revealed specific structure that was well repeatable for the subjects studied. Differences in coherence patterns between sleep stages were found by means of statistical tests. An increase of coherence was found for sleep stages 2, 3 and 4. Directed transfer function made possible the identification of the main centers from which EEG activity is spreading during sleep and wakefulness. During sleep the influence of subcortical structures was manifested by propagation of activity from the fronto-central region. The range of this interaction was highest in sleep stages 3 and 4. An EEG analysis, based on the approach of treating time series as a realization of one process and on the simultaneous (not pair-wise) evaluation of signals offers new possibilities in the investigation of synchronization and functional relations in the brain.

Analysis of mesial temporal seizure onset and propagation using the directed transfer function method

The directed transfer function (DTF) method, a multichannel parametric method of analysis based on an autoregressive model, is a newly developed tool that permits determination of patterns of flow of activity. The DTF method of analysis was applied to seizures originating from mesial temporal lobe structures in 3 patients recorded by combined subdural grid and depth electrode arrays. These first applications to human intracranial recordings demonstrated that the DTF method can accurately determine patterns of seizure onset and propagation. In addition the DTF method can provide evidence regarding patterns of flow of seizure activity that are not readily apparent from visual inspection of the EEG recordings. Important considerations for appropriate application of the DTF method for the analysis of intracranial ictal recordings are discussed.

Information flow between hippocampus and related structures during various types of rat's behavior

The relationships among the CA1 field of hippocampus, the entorhinal-piriform area, the subiculum and the lateral septum were studied in various behavioral states in the rat. The EEG signals recorded simultaneously from chronically implanted electrodes were analyzed by means of a multichannel autoregressive (AR) model. Power spectra, ordinary, multiple and partial coherences, and directed transfer functions were calculated. The method of analysis which took into account all signals simultaneously, not pair-wise, made it possible to estimate the spectral characteristics and the directions of the EEG flow between structures. The pattern of the EEG activity propagation depended on the type of behavior, difficulty of the task performed by the animal, and the phase of the trial. Our results not only confirmed the existence of connections between analyzed structures, but also showed that these connections may have different strengths during various types of behavior.

Transmission of Brain Activity During Cognitive Task

The transmission of brain activity during constant attention test was estimated by means of the short-time directed transfer function (SDTF). SDTF is an estimator based on a multivariate autoregressive model. It determines the propagation as a function of time and frequency. For nine healthy subjects the transmission of EEG activity was determined for target and non-target conditions corresponding to pressing of a switch in case of appearance of two identical images or withholding the reaction in case of different images. The involvement of prefrontal and frontal cortex manifested by the propagation from these structures was observed, especially in the early stages of the task. For the target condition there was a burst of propagation from C3 after pressing the switch, which can be interpreted as beta rebound upon completion of motor action. In case of non-target condition the propagation from F8 or Fz to C3 was observed, which can be connected with the active inhibition of motor cortex by right inferior frontal cortex or presupplementary motor area.

Directed Transfer Function is not influenced by volume conduction—inexpedient pre-processing should be avoided

The problem of brain connectivity has been gaining more and more interest in the last years. Connectivity can be estimated by different techniques and at the different levels of the hierarchy of the nervous system. Here we shall consider functional connectivity at the level of the brain structures, in particular connectivity measures derived from scalp EEG measurements. A multitude of estimators are being used for connectivity estimation: linear, nonlinear, bivariate and multivariate. The disadvantage of bivariate estimators is connected with the fact, that in virtue of common feeding many spurious connections are found. This fact was demonstrated in works: (Blinowska et al., 2004; Kuś et al., 2004). Let us consider the common situation when a source is emitting activity measured at N electrodes. In case of bivariate measures beside N true connections also false connections between all electrodes will be find in virtue of common feeding and their number will be [N(N − 1)/2 − N], so they will outnumber the true connections. This fact directed the interest of the scientific community to the multivariate methods of connectivity estimation. In particular, multivariate estimators based on the Granger causality principle allow to estimate directed connectivity and does not produce spurious connections. Among these estimators widely applied are: Directed Transfer Function (Kaminski and Blinowska, 1991) and Partial Directed Coherence (Baccala and Sameshima, 2001) based on the Multivariate Autoregressive Model (MVAR). Currently DTF and PDC are commonly used and have became a part of various signal processing packages, e.g., eConnectome (http://econnectome.umn.edu), Octave-Forge (http://octave.sourceforge.net/tsa/function/mvfreqz.html), Epilab (http://www.epilepsiae.eu/project_outputs/epilab_software), SIFT (http://sccn.ucsd.edu/wiki/SIFT). Unfortunately we have noticed that quite often the application to DTF of inappropriate preprocessing routines produces misleading results. Moreover, the use of these routines is not necessary in virtue of the properties of DTF. As the authors of the DTF estimator, we are particularly concerned that the method is applied correctly. Among the pre-processing methods used before DTF application the most common approach is to project the signals into the source space in order to eliminate volume conduction effect. However, DTF for a pair of channels i and j is nonzero only, if there is a phase difference between channels i and j. The volume conduction is a propagation of the electromagnetic field, so it does not produce a phase difference at electrodes. Therefore, DTF is practically insensitive to volume conduction. The fact that the estimators of connectivity based on the phase difference between channels are not influenced by the volume conduction was also recognized in Stam et al. (2009). The influence of a signal of a constant phase on DTF was demonstrated by means of simulation. For the set of EEG signals we have added a sinusoid, with the same phase for each signal. The amplitude of that sinusoid (of 20 Hz) was similar to the amplitudes of EEG signals. The result is shown in Figure ​Figure1.1. We can observe a prominent peak at 20 Hz in the power spectra of the signals, but this peak is absent in DTF functions. Figure 1 The DTFs (as functions of frequency) estimated for a set of EEG signals. (A) The results for original dataset, (B) same data with 20 Hz sinusoid added with constant phase to each channel. On the diagonals of the panels power spectra are shown. The propagation ... The fact that DTF is not influenced by volume conduction effects is further supported by the excellent topographical agreement of DTF results with the evidence obtained from anatomical data, imaging studies and physiological experiments. Clear cut patterns of propagation emerged from these studies. As the examples may serve the studies of finger movement (Ginter et al., 2001; Kuś et al., 2006), localization of epileptic focus (Franaszczuk et al., 1994) results obtained for Constant Attention Test (Blinowska et al., 2010) and working memory paradigm (Brzezicka et al., 2010; Blinowska et al., 2013). More examples may be found in Blinowska (2011); Blinowska and Zygierewicz (2011). The animations illustrating dynamically changing patterns of connectivity obtained by the Short-time Directed Transfer Function (SDTF) in some of the above mentioned experiments are available at http://brain.fuw.edu.pl/~kjbli. Since DTF is immune to volume conduction the pre-processing procedures such as projections on the cortex surface or Laplace transform are not needed. Moreover, they destroy the original correlation structure of the set of signals. If we mix the information from different channels calculating for example Laplacian, we influence the correlation between signals and the information about the phase relations between channels is disturbed. As a result, information on causality or, in another words, on the propagation of activity from channel j to i is lost. The results of the works where the preprocessing involving projection on the cortex was applied show a disorganized structure of connectivity. The pre-processing of the data before the DTF application should be limited to subtraction of the mean, possibly division by the variance and digital filtering. However, the filtering must not influence phases of signals. These can be achieved by filtering forward and backward (e.g., Matlab procedure filtfilt). The signals should be referenced to the “neutral” derivation, e.g., linked ears, nose, or similar. No common average or bipolar reference may be used. There should be no preprocessing by means Hjorth or Laplace transform, Independent Components Analysis or projection of signals on the cortex. In the view of robustness of DTF in respect to volume conduction, these procedures are obsolete, furthermore, they are harmful and may produce misleading results. It is worth mentioning that in general methods of connectivity estimation based on phase differences are insensitive to volume conduction. For instance this property holds also for Partial Directed Coherence, but not for ordinary coherence, because it contains common component, which includes activity of no phase difference between electrodes. In conclusion we would like to underline that the preprocessing of the signals for estimation of connectivity should be based on the thorough understanding of the properties of the applied methods.

Vibrational Optical Activity of Cysteine in Aqueous Solution: A Comparison of Theoretical and Experimental Spectra

Raman, Raman optical activity (ROA), infrared (IR), and vibrational circular dichroism (VCD) spectra of cysteine in aqueous solution have been measured and calculated by means of density functional theory. The influence of aqueous environment on the spectra of cysteine has been simulated by means of implicit (polarizable continuum model) and explicit (molecular dynamics, solute-solvent clusters) methods. The results indicate that, while PCM reproduces some of the features of the spectra, the best description is rendered by the microsolvation model (solute-solvent clusters). The shape of the bands is in some cases more correctly reproduced by MD, but their intensities and positions are not, since these simulations are hampered by the standard force field being parametrized for conformations of peptides rather than isolated amino acids. The calculated ROA spectra have been used to extract conformational ratios from the experimental spectra, and again, the best results (as verified by simulations of other spectra) have been obtained when using the microsolvation model. This procedure renders three zwitterion conformers dominating the spectra of hydrated cysteine, of conformational ratios of 35, 33, and 24%, respectively.

Information Transfer During a Transitive Reasoning Task

For about two decades now, the localization of the brain regions involved in reasoning processes is being investigated through fMRI studies, and it is known that for a transitive form of reasoning the frontal and parietal regions are most active. In contrast, less is known about the information exchange during the performance of such complex tasks. In this study, the propagation of brain activity during a transitive reasoning task was investigated and compared to the propagation during a simple memory task. We studied EEG transmission patterns obtained for physiological indicators of brain activity and determined whether there are frequency bands specifically related to this type of cognitive operations. The analysis was performed by means of the directed transfer function. The transmission patterns were determined in the theta, alpha and gamma bands. The results show stronger transmissions in theta and alpha bands from frontal to parietal as well as within frontal regions in reasoning trials comparing to memory trials. The increase in theta and alpha transmissions was accompanied by flows in gamma band from right posterior to left posterior and anterior sites. These results are consistent with previous neuroimaging (fMRI) data concerning fronto-parietal regions involvement in reasoning and working memory processes and also provide new evidence for the executive role of frontal theta waves in organizing the cognition.