Range entropy: A bridge between signal complexity and self-similarity

Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, ApEn and SampEn are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.Comment: This is the revised and published version in Entrop

Structural damage in early preterm brain changes the electric resting state networks

A robust functional bimodality is found in the long-range spatial correlations of newborn cortical activity, and it likely provides the developmentally crucial functional coordination during the initial growth of brain networks. This study searched for possible acute effects on this large scale cortical coordination after acute structural brain lesion in early preterm infants.EEG recordings were obtained from preterm infants without (n = 11) and with (n = 6) haemorrhagic brain lesion detected in their routine ultrasound exam. The spatial cortical correlations in band-specific amplitudes were examined within two amplitude regimes, high and low amplitude periods, respectively. Technical validation of our analytical approach showed that bimodality of this kind is a genuine physiological characteristic of each brain network. It was not observed in datasets created from uniform noise, neither is it found between randomly paired signals. Hence, the observed bimodality arises from specific interactions between cortical regions. We found that significant long-range amplitude correlations are found in most signal pairs in both groups at high amplitudes, but the correlations are generally weaker in newborns with brain lesions. The group difference is larger during high mode, however the difference did not have any statistically apparent topology. Graph theoretical analysis confirmed a significantly larger weight dispersion in the newborns with brain lesion. Comparison of graph measures to a child's performance at two years showed that lower clustering coefficient and weight dispersion were both correlated to better neurodevelopmental outcomes. Our findings suggest that the common preterm brain haemorrhage causes diffuse changes in the functional long-range cortical correlations. It has been recently recognized that the high mode network activity is crucial for early brain development. The present observations may hence offer a mechanistic link between early lesion and the later emergence of complex neurocognitive sequelae

Functional bimodality in the brain networks of preterm and term human newborns

The spontaneous brain activity exhibits long-range spatial correlations detected using functional magnetic resonance imaging (fMRI) signals in newborns when (1) long neuronal pathways are still developing, and (2) the electrical brain activity consists of developmentally unique, intermittent events believed to guide activity-dependent brain wiring. We studied this spontaneous electrical brain activity using multichannel electroencephalography (EEG) of premature and fullterm babies during sleep to assess the development of spatial integration during last months of gestation. Correlations of frequency-specific amplitudes were found to follow a robust bimodality: During low amplitudes (low mode), brain activity exhibited very weak spatial correlations. In contrast, the developmentally essential high-amplitude events (high mode) showed strong spatial correlations. There were no clear spatial patterns in the early preterm, but clear frontal and parieto-occipital modules at term age. A significant fronto-occipital gradient was also seen in the development of the graph measure clustering coefficient. Strikingly, no bimodality was found in the fMRI recordings of the fullterm babies, suggesting that early EEG activity and fMRI signal reflect different mechanisms of spatial coordination. The results are compatible with the idea that early developing human brain exhibits intermittent long-range spatial connections that likely provide the endogenous guidance for early activity-dependent development of brain networks

Generalised phase synchrony within multivariate signals: an emerging concept in time-frequency analysis

This paper introduces the notion of the instantaneous frequency (IF) based generalized phase synchrony in time-frequency analysis based on the concept of cointegration. This phase synchrony is then quantified by investigating the linear relationships between IF laws of nonstationary multivariate signals. The proposed approach is applied to a multichannel newborn EEG signal and the results are compared with that of a bivariate phase synchrony measure

Dynamic analysis of fMRI activation during epileptic spikes can help identify the seizure origin

Objective We use the dynamic electroencephalography-functional magnetic resonance imaging (EEG-fMRI) method to incorporate variability in the amplitude and field of the interictal epileptic discharges (IEDs) into the fMRI analysis. We ask whether IED variability analysis can (a) identify additional activated brain regions during the course of IEDs, not seen in standard analysis; and (b) demonstrate the origin and spread of epileptic activity. We explore whether these functional changes recapitulate the structural connections and propagation of epileptic activity during seizures. Methods Seventeen patients with focal epilepsy and at least 30 IEDs of a single type during simultaneous EEG-fMRI were studied. IED variability and EEG source imaging (ESI) analysis extracted time-varying dynamic changes. General linear modeling (GLM) generated static functional maps. Dynamic maps were compared to static functional maps. The dynamic sequence from IED variability was compared to the ESI results. In a subset of patients, we investigated structural connections between active brain regions using diffusion-based fiber tractography. Results IED variability distinguished the origin of epileptic activity from its propagation in 15 of 17 (88%) patients. This included two cases where no result was obtained from the standard GLM analysis. In both of these cases, IED variability revealed activation in line with the presumed epileptic focus. Two cases showed no result from either method. Both had very high spike rates associated with dysplasia in the postcentral gyrus. In all 15 cases with dynamic activation, the observed dynamics were concordant with ESI. Fiber tractography identified specific white matter pathways between brain regions that were active at IED onset and propagation. Significance Dynamic techniques involving IED variability can provide additional power for EEG-fMRI analysis, compared to standard analysis, revealing additional biologically plausible information in cases with no result from the standard analysis and gives insight into the origin and spread of IEDs

A novel multivariate phase synchrony measure: application to multichannel newborn EEG analysis

Phase synchrony assessment across non-stationary multivariate signals is a useful way to characterize the dynamical behavior of their underlying systems. Traditionally, phase synchrony of a multivariate signal has been quantified by first assessing all pair-wise phase relationships between different channels and then, averaging their phase coupling. This approach, however, may not necessarily provide a full picture of multiple phase ratios within non-stationary signals with time-varying statistical properties. Several attempts have been made to generalize pair-wise phase synchrony concept to multivariate signals. In this paper, we introduce a new measure of generalized phase synchrony based on the concept of circular statistics. The performance of the measure is evaluated with simulations using the Kuramoto and Rössler models and compared with that of three existing generalized phase synchrony measures based respectively on 1) the concept of co-integration, 2) S-estimator and 3) hyper-dimensional geometry. The simulation results represent the correct degree of synchronization between channels with negligible mean of squared error, i.e. below 4.2e. We then use the proposed measure to assess inter-hemispheric phase synchrony in two abnormal multichannel newborn EEG datasets with manually marked seizure/non-seizure and burst–suppression signatures. The EEG results suggest that the proposed measure is able to detect inter-hemispheric phase synchrony changes with higher accuracy than the other existing measures, i.e. 2% for seizure/non-seizure database and 11% for burst/suppression database than the best performing existing multivariate phase synchrony measure

Towards fast and reliable simultaneous EEG-fMRI analysis of epilepsy with automatic spike detection

Objective The process of manually marking up epileptic spikes for simultaneous electroencephalogram (EEG) and resting state functional MRI (rsfMRI) analysis in epilepsy studies is a tedious and subjective task for a human expert. The aim of this study was to evaluate whether automatic EEG spike detection can facilitate EEG-rsfMRI analysis, and to assess its potential as a clinical tool in epilepsy. Methods We implemented a fast algorithm for detection of uniform interictal epileptiform discharges (IEDs) in one-hour scalp EEG recordings of 19 refractory focal epilepsy datasets (from 16 patients) who underwent a simultaneous EEG-rsfMRI recording. Our method was based on matched filtering of an IED template (derived from human markup) used to automatically detect other ‘similar’ EEG events. We compared simultaneous EEG-rsfMRI results between automatic IED detection and standard analysis with human EEG markup only. Results In contrast to human markup, automatic IED detection takes a much shorter time to detect IEDs and export an output text file containing spike timings. In 13/19 focal epilepsy datasets, statistical EEG-rsfMRI maps based on automatic spike detection method were comparable with human markup, and in 6/19 focal epilepsy cases automatic spike detection revealed additional brain regions not seen with human EEG markup. Additional events detected by our automated method independently revealed similar patterns of activation to a human markup. Overall, automatic IED detection provides greater statistical power in EEG-rsfMRI analysis compared to human markup in a short timeframe. Conclusions Automatic spike detection is a simple and fast method that can reproduce comparable and, in some cases, even superior results compared to the common practice of manual EEG markup in EEG-rsfMRI analysis of epilepsy. Significance Our study shows that IED detection algorithms can be effectively used in epilepsy clinical settings. This work further helps in translating EEG-rsfMRI research into a fast, reliable and easy-to-use clinical tool for epileptologists