Julián J. González

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.

Assessment of changing interdependencies between human electroencephalograms using nonlinear methods

We investigate the problems that might arise when two recently developed methods for detecting interdependencies between time series using state space embedding are applied to signals of different complexity. With this aim, these methods were used to assess the interdependencies between two electroencephalographic channels from 10 adult human subjects during different vigilance states. The significance and nature of the measured interdependencies were checked by comparing the results of the original data with those of different types of surrogates. We found that even with proper reconstructions of the dynamics of the time series, both methods may give wrong statistical evidence of decreasing interdependencies during deep sleep due to changes in the complexity of each individual channel. The main factor responsible for this result was the use of an insufficient number of neighbors in the calculations. Once this problem was surmounted, both methods showed the existence of a significant relationship between the channels which was mostly of linear type and increased from awake to slow wave sleep. We conclude that the significance of the qualitative results provided for both methods must be carefully tested before drawing any conclusion about the implications of such results.

Why we sleep: the evolutionary pathway to the mammalian sleep

The cause of sleep is a complex question, which needs first, a clear distinction amongst the different meanings of a causal relationship in the study of a given behavior, second, the requisites to be met by a suggested cause, and third, a precise definition of sleep to distinguish behavioral from polygraphic sleep. This review aims at clarifying the meaning of the question and at showing the phylogenetic origin of the mammalian and avian sleep. The phylogenetic appearance of sleep can be approached through a study of the evolution of the vertebrate brain. This began as an undifferentiated dorsal nerve, which was followed by the development of an anterior simplified brain and ended with the formation of the multilayered mammalian neocortex or the avian neostriate. The successive stages in the differentiation of the vertebrate brain produced, at least, two different waking types. The oldest one is the diurnal activity, bound to the light phase of the circadian cycle. Poikilotherms control the waking from the whole brainstem, where their main sensorymotor areas lie. Mammals developed the thalamocortical lines, which displaced the waking up to the cortex after acquiring homeothermy and nocturnal lifestyle. In order to avoid competence between duplicate systems, the early waking type, controlled from the brainstem, was suppressed, and by necessity was turned into inactivity, probably slow wave sleep. On the other hand, the nocturnal rest of poikilotherms most probably resulted in rapid eye movement sleep. The complex structure of the mammalian sleep should thus be considered an evolutionary remnant; the true acquisition of mammals is the cortical waking and not the sleep.

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.

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.

Comparing generalized and phase synchronization in cardiovascular and cardiorespiratory signals

We made use of multivariate nonlinear analysis methods to study the interdependence between the cardiac interval variability and both the respiratory activity and the systolic pressure in rats. The study was carried out in basal conditions and after the application of different drugs affecting the cardiovascular system. The results showed that there are changes both in the extent and in the directionality of such interdependences because of the drugs. The inhibition of the NO and the parasympathetic blockade changed the cardiovascular coordination, with the latter one also modifying the interdependence between the cardiac interval and the respiratory signal. This suggests that the nonlinear approach might be very helpful to explore the interaction between subsystems of the cardiovascular control system.

Topography of EEG complexity in human neonates: effect of the postmenstrual age and the sleep state.

The topography of the EEG of human neonates is studied in terms of its power spectral density and its estimated complexity as a function of both the postmenstrual age (PMA) and the sleep state. The monopolar EEGs of three groups of seven neonates (preterm, term and older term) were recorded during active (AS) and quiet sleep (QS) from electrodes Fp1, Fp2, T3, T4, C3, C4, O1 and O2. The existence of changes between groups and sleep states in the power of delta, theta, alpha and beta bands and in the dimensional complexity of these electrodes was tested. Additionally, the nonlinearity of the EEG in each electrode and situation was analyzed. The results of the spectral measures show an increment of the power in the low frequency bands from AS to QS and with the PMA, which can be mainly traced on central and temporal electrodes. This change is shown as well by the dimensional complexity, which also presents the greatest differences in the central derivations. Moreover, the signals show evidence of nonlinearity in almost all the groups and situations, although a dynamic change from nonlinear to linear character is apparent in the central electrodes with increased PMA. As a result, it is concluded that nonlinear analysis methods provide a clear portrait of the integrated brain activity that complements the information of spectral analysis in the characterization of the brain development and the sleep states in neonates.

Non-linear asymmetric interdependencies in the electroencephalogram of healthy term neonates during sleep.

The multichannel electroencephalograph (EEG) of six healthy term neonates was recorded during awake as well as during active and quiet sleep. The existence and nature of the interdependencies among the different brain areas were studied by means of a multivariate variant of the surrogate data method. Such interdependencies were then quantified by using the coherence function and a newly developed non-linear index. The results showed that during quiet sleep these interdependencies were mostly non-linear, asymmetric and greater than those found during both awake and active sleep. We conclude that the index might be useful to define patterns of EEG interdependencies in healthy neonates, thereby allowing the early detection of brain dysfunctions.

ELECTROENCEPHALOGRAM FUNCTIONAL CONNECTIVITY BETWEEN RAT HIPPOCAMPUS AND CORTEX AFTER PILOCARPINE TREATMENT

The muscarinic agonist pilocarpine has been shown to increase the duration and total number of episodes presenting theta rhythm-simultaneously in hippocampus and cortex-in rats during the waking states. Theta waves are suggested to be involved in the flow of information between hippocampus and cortex during memory processes. This work investigates this functional interdependence using the spectral and phase synchronization analysis of the electroencephalogram (EEG) theta band recorded in these brain structures of rats after pilocarpine treatment. Pilocarpine was used at doses devoid of epilepticus-like seizures effects in conscious freely moving rats. The results showed that pilocarpine administration significantly increased the relative theta power during the waking states in the cortex, but not in the hippocampus of rats. Additionally, the EEG coherence between the hippocampal EEG theta band and that arising at the frontal cortex increased after pilocarpine treatment but only during the waking states. This result reveals an increase of the linear correlation between the theta waves of these two brain structures after pilocarpine treatment during the waking states. Moreover, phase synchronization results showed an effective phase locking with non-zero phase difference between hippocampus and frontal cortex theta waves that remained after pilocarpine treatment. Therefore, pilocarpine seems to reinforce the neural transmission waves from the hippocampus toward the cortex during waking. In conclusion, the present EEG study could suggest an effect of the muscarinic cholinergic agonist pilocarpine on the hippocampal-cortical functional connectivity.

Performance analysis of univariate and multivariate EEG measurements in the diagnosis of ADHD

OBJECTIVE To investigate the performance of univariate and multivariate EEG measurements in diagnosing ADHD subjects in a broad age range. METHODS EEG from eight cortical regions were recorded at rest during eyes open and eyes closed in 22 male ADHD subjects of combined type and 21 healthy male controls (age range 4-15 years). Univariate and interdependence measurements calculated from the frequency domain and from the reconstructed state spaces of EEG signals were computed, and their performance in discriminating ADHD from healthy subjects was analyzed. RESULTS Significant between-group differences in univariate measures were age-dependent. However, certain interdependence inter-hemispheric measures during eyes closed showed significant, age-independent between-groups differences. Among them, coherence in the beta band between inter-occipital regions and between left/occipital-right/central regions provided an overall accuracy classification rate of 74.4%. Even greater accuracy (86.7%) was obtained by an interdependence index of generalized synchronization between left/occipital-right/central regions and left/central-right/temporal regions. CONCLUSIONS EEG beta coherence and especially the degree of generalized synchronization between a few inter-hemispheric regions during resting state with eyes closed allow a high accuracy classification rate of ADHD subjects. SIGNIFICANCE Changes in inter-hemispheric EEG functional brain connectivity at rest are useful for ADHD diagnosis in a broad age range.