Ernesto Pereda

Nonlinear multivariate analysis of neurophysiological signals

Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependence between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.

Non-linear behaviour of human EEG : fractal exponent versus correlation dimension in awake and sleep stages

The question of whether the finite values of the correlation dimension (D2), used as an index of EEG complexity are due to its chaotic nature or they reflect its behaviour as linearly-correlated noise, remains open. This report aims at clarifying this by measuring D2 and analysing the non-linear nature of EEG through the method of surrogate data as well as by calculating the fractal exponent (beta) via coarse graining spectral analysis (CGSA) in nine adult subjects during waking and sleep states. The results show that even if it is possible to get an estimation of D2 in all states, non-linear structure appears to be present only during slow wave sleep (SWS). EEG exhibits random fractal structure with 1/f(-beta) spectrum (1 < beta < 3) and a negative linear correlation between D2 and beta in all states except during SWS. In consequence, in those states, finite D2 values could be attributed to the fractal nature of EEG and not to the presence of low-dimensional chaos, and therefore, it the use of beta would be more appropriate to describe the complexity of EEG, due to its lower computational cost.

HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality.This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox.Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

Functional Connectivity in Mild Cognitive Impairment During a Memory Task: Implications for the Disconnection Hypothesis

Mild cognitive impairment (MCI) has been considered an intermediate state between healthy aging and dementia. The early damage in anatomical connectivity and progressive loss of synapses that characterize early Alzheimers disease suggest that MCI could also be a disconnection syndrome. Here, we compare the degree of synchronization of brain signals recorded with magnetoencephalography from patients (22) with MCI with that of healthy controls (19) during a memory task. Synchronization Likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. During the memory task patients showed higher interhemispheric synchronization than healthy controls between left and right -anterior temporo-frontal regions (in all studied frequency bands) and in posterior regions in the γ band. On the other hand, the connectivity pattern from healthy controls indicated two clusters of higher synchronization, one among left temporal sensors and another one among central channels. Both of them were found in all frequency bands. In the γ band, controls showed higher Synchronization Likelihood values than MCI patients between central-posterior and frontal-posterior channels and a high synchronization in posterior regions. The inter-hemispheric increased synchronization values could reflect a compensatory mechanism for the lack of efficiency of the memory networks in MCI patients. Therefore, these connectivity profiles support only partially the idea of MCI as a disconnection syndrome, as patients showed increased long distance inter-hemispheric connections but a decrease in antero-posterior functional connectivity.

Interdependencies in the spontaneous EEG while listening to music

We studied the patterns of interdependency between different brain regions during the performance of higher cognitive functions. Our goal was to check the existence in these patterns of both task-related differences (e.g. listening to music vs. rest) and training-related differences (musicians vs. non-musicians). For this purpose, a non-linear measure, called similarity index (S.I.), was used to detect asymmetric interdependencies between different brain regions by means of EEG signals. Relatively active and passive regions of the brain were found where the degree of activity was represented by excited degrees of freedom. The S.I. obtained during listening to different kinds of music was compared statistically with the S.I. with eyes closed, and significant changes (P< or = 0.05) were entered into schematic brain maps. A topographical representation of the S.I. yielded differences in the interdependency while performing different cognitive tasks. The results demonstrate the occurrence of task-related differences in both groups of subjects. Furthermore, subjects with musical training possessed significantly higher degrees of interdependencies than such without musical training while listening to music but not to text. We conclude that the new measure can be successfully applied for studying the dynamical co-operation between cortical areas during higher cognitive functioning.

Interhemispheric differences in awake and sleep human EEG : a comparison between non-linear and spectral measures

Interhemispheric differences in the EEG of nine healthy right-handed human subjects (C3 vs. C4 derivations) were investigated during resting wake with closed eyes (CE) and sleep stages I, II, III, IV and REM. The harmonic power spectral density within the EEG main spectral bands, the fractal (Dr) and the correlation (D2) dimension as well as the largest Lyapunov exponent (lambda1) of both hemispheres were compared. In addition, the relationships between non-linear and spectral measures were analyzed. Dr, D2, lambda1 and the power in alpha band exhibited interhemispheric differences during waking, the values from the right hemisphere (RH) being higher than those of the left (LH) except for lambda1. During slow wave sleep (SWS), non-linear parameters detected opposite EEG asymmetries (D2 in stage III and lambda1 in stage IV) to those found in the other behavioural stages. In addition, both D2 and lambda1 were correlated (negatively) with the power in the delta band, but lambda1 was also correlated (positively) with the power in the alpha and beta bands. In conclusion, RH appears to be more complex though more predictable than the LH during CE and sleep stages I and II, these characteristics changing to the LH during SWS.

Best of both worlds: promise of combining brain stimulation and brain connectome

Transcranial current brain stimulation (tCS) is becoming increasingly popular as a non-pharmacological non-invasive neuromodulatory method that alters cortical excitability by applying weak electrical currents to the scalp via a pair of electrodes. Most applications of this technique have focused on enhancing motor and learning skills, as well as a therapeutic agent in neurological and psychiatric disorders. In these applications, similarly to lesion studies, tCS was used to provide a causal link between a function or behavior and a specific brain region (e.g., primary motor cortex). Nonetheless, complex cognitive functions are known to rely on functionally connected multitude of brain regions with dynamically changing patterns of information flow rather than on isolated areas, which are most commonly targeted in typical tCS experiments. In this review article, we argue in favor of combining tCS method with other neuroimaging techniques (e.g., fMRI, EEG) and by employing state-of-the-art connectivity data analysis techniques (e.g., graph theory) to obtain a deeper understanding of the underlying spatiotemporal dynamics of functional connectivity patterns and cognitive performance. Finally, we discuss the possibilities of using these combined techniques to investigate the neural correlates of human creativity and to enhance creativity.

Effective detection of coupling in short and noisy bivariate data

In the study of complex systems, one of the primary concerns is the characterization and quantification of interdependencies between different subsystems. In real-life systems, the nature of dependencies or coupling can be nonlinear and asymmetric, rendering the classical linear methods unsuitable for this purpose. Furthermore, experimental signals are noisy and short, which pose additional constraints for the measurement of underlying coupling. We discuss an index based on nonlinear dynamical system theory to measure the degree of coupling which can be asymmetric. The usefulness of this index has been demonstrated by several examples including simulated and real-life signals. This index is found to effectively disclose the nature and the degree of interactions even when the coupling is very weak and data are noisy and of limited length; by this way, new insight into the functioning of the underlying complex system is possible.

Assessment of electroencephalographic functional connectivity in term and preterm neonates

OBJECTIVE To study how functional connectivity of neonate EEG during sleep is assessed by different interdependence indices and to analyze its dependence on conceptional (CA), gestational (GA) and/or chronological age (CRA). METHODS EEG data from eight cortical regions were recorded during active (AS) and quiet sleep (QS) in three groups of seven neonates each: preterm (PT; GA: 33-34 weeks; CA: 39-40 weeks), junior-term (JT; GA: 38-39 weeks; CA: 39-40 weeks) and senior-term neonates (ST; GA: 38-39 weeks; CA: 44-45 weeks). EEG functional connectivity was assessed by means of the coherence function (its magnitude (MSC) and its imaginary part (IMC)) and a measure of phase synchronization called phase lag index (PLI). RESULTS Inter-hemispheric connectivity: (a) during AS in the beta band, the MSC of the ST group was greater than that of the PT group for the temporal region; (b) during QS in the delta band, both PLI and IMC of the ST group were different to those of the PT group for the frontopolar and central regions, whereas ST-JT differences were only found for PLI. Intra-hemispheric connectivity: (a) during AS in the beta band the MSC of the ST group was greater than that of the PT group for the left frontopolar-centrotemporal and right occipital-centrotemporal regions; (b) during QS in the beta band, both IMC and PLI were different for the JT group than for the PT and the ST groups for the right and left occipital-centrotemporal regions. CONCLUSIONS EEG inter- and intra-hemispheric functional connectivity in neonates during sleep changes with the CA and CRA in delta and beta bands. SIGNIFICANCE The neonates brain development during the first weeks of life can be traced from changes in the characteristics of EEG functional connectivity.

Nonlinear, fractal, and spectral analysis of the EEG of lizard, Gallotia galloti

Electroencephalogram (EEG) from dorsal cortex of lizard Gallotia galloti was analyzed at different temperatures to test the presence of fractal or nonlinear structure during open (OE) and closed eyes (CE), with the aim of comparing these results with those reported for human slow-wave sleep (SWS). Two nonlinear parameters characterizing EEG complexity [correlation dimension (D2)] and predictability [largest Lyapunov exponent (λ1)] were calculated, and EEG spectrum and fractal exponent β were determined via coarse graining spectral analysis. At 25°C, evidence of nonlinear structure was obtained by the surrogate data test, with EEG phase space structure suggesting the presence of deterministic chaos (D2 ∼6, λ1 ∼1.5). Both nonlinear parameters were greater in OE than in CE and for the right hemisphere in both situations. At 35°C the evidence of nonlinearity was not conclusive and differences between states disappeared, whereas interhemispheric differences remained for λ1. Harmonic power always increased with temperature within the band 8-30 Hz, but only with OE within the band 0.3-7.5 Hz. Qualitative similarities found between lizard and human SWS EEG support the hypothesis that reptilian waking could evolve into mammalian SWS.