Alejandra Figliola

Wavelet entropy: a new tool for analysis of short duration brain electrical signals.

Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order/disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order/disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials.

EEG analysis using wavelet-based information tools

Wavelet-based informational tools for quantitative electroencephalogram (EEG) record analysis are reviewed. Relative wavelet energies, wavelet entropies and wavelet statistical complexities are used in the characterization of scalp EEG records corresponding to secondary generalized tonic-clonic epileptic seizures. In particular, we show that the epileptic recruitment rhythm observed during seizure development is well described in terms of the relative wavelet energies. In addition, during the concomitant time-period the entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus, for this kind of seizures, triggers a self-organized brain state characterized by both order and maximal complexity.

Analysis of wavelet-filtered tonic-clonic electroencephalogram recordings.

EEG signals obtained during tonic-clonic epileptic seizures can be severely contaminated by muscle and physiological noise. Heavily contaminated EEG signals are hard to analyse quantitatively and also are usually rejected for visual inspection by physicians, resulting in a considerable loss of collected information. The aim of this work was to develop a computer-based method of time series analysis for such EEGs. A method is presented for filtering those frequencies associated with muscle activity using a wavelet transform. One of the advantages of this method over traditional filtering is that wavelet filtering of some frequency bands does not modify the pattern of the remaining ones. In consequence, the dynamics associated with them do not change. After generation of a ‘noise free’ signal by removal of the muscle artifacts using wavelets, a dynamic analysis was performed using non-linear dynamics metric tools. The characteristic parameters evaluated (correlation dimension D2 and largest Lyapunov exponent λ1) were compatible with those obtained in previous works. The average values obtained were: D2=4.25 and λ1=3.27 for the pre-ictal stage; D2=4.03 and λ1=2.68 for the tonic seizure stage; D2=4.11 and λ1=2.46 for the clonic seizure stage.

Using nonlinear dynamic metric tools for characterizing brain structures

The collective dynamic behavior of the neural mass of different brain structures can be assessed from electroencephalographic recordings with depth electrodes measurements at regular time intervals (EEG time series). In recent years, the cheery of nonlinear dynamics has developed methods for quantitative analysis of experimental time series. The aim of this article is to report a new attempt to characterize global brain dynamics through electrical activity using these nonlinear dynamical metric tools. In addition, the authors study the dependence of the metric magnitudes on brain structure. The methods employed in this work are independent of any modeling of brain activity. They rely solely on the analysis of data obtained from a single variable time series. The authors analyze the EEG signals from depth electrodes that intersect different brain anatomical structures in a patient with refractory epilepsy prone to surgical treatment. The electrical signal provided by this type of electrode guarantees a low noise signal.

Study of EEG Brain Maturation Signals with Multifractal Detrended Fluctuation Analysis

In this work, we have study the EEG signals of birds during the first 6 weeks of life. The aim of the article is to perform a quantitative analysis of the dynamical changes observed in these signals due to the brain maturation effects. The signals’ long scaling behaviour is study by Multifractal Detrended Fluctuation Analysis (MFDFA). This method allows the multifractal characterization of these EEG nonstationary time series and characterize the different stage of bird brain maturation.

ABOUT THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE ESTIMATION OF THE MULTIFRACTAL SPECTRUM OF NATURAL SERIES

Complex natural systems present characteristics of scalar invariance. This behavior has been experimentally verified and a large related bibliography has been reported. Multifractal Formalism is a ...

Detection of delay time between the alterations of cardiac rhythm and periodic breathing

Analysis of time-series multichannel physiological data were performed using wavelets. Wavelet provides a time-scale description and lead us to decompose any signal into frequency bands. A better precision in the frequency domain is often necessary to detect stationary phenomena or characterize time–frequency structures. A natural idea is to combine wavelet analysis with local Fourier analysis using an appropriate strategy: the wave packets. In this paper, we apply trigonometric wave packets to determine the time lag between the start of the apneas in the breathing and the consistent disorder in the cardiac rhythm. We show that breathing dynamic drives the evolution of the cardiac rhythm.

A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients

The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the statistical complexity evaluated with different sets of multiresolution wavelet coefficients are considered. Both methodologies are applied to the quantitative EEG time series analysis of a tonic-clonic epileptic seizure, and comparative results are presented. In particular, even when both methods describe the dynamical changes of the EEG time series, the one based on wavelet leaders presents a better time resolution.

Chapter 65 Time-frequency analysis of sensorial brain activity

Publisher Summary Electroencephalogram (EEG) reflects the activities of neuronal ensembles producing oscillations in several frequency ranges. This transition from a disordered to an ordered state is accompanied by a resonance phenomenon and results in frequency stabilization, synchronization, and enhancement of the ongoing EEG activity. Among multiple EEG frequencies, only those related to information processing contribute to ongoing EEG reorganization and give rise to event-related brain potentials (ERPs). The interest is to investigate how brain electric oscillations get synchronized by external stimulation. The objective of this chapter is to analyze the stimulus-related resonance and synchronization EEG processes by quantifying complex signal behavior in the ERP. The aim is to show stimulus effects on electrical events in terms of EEG frequency synchronization or tuning, to identify temporal and spatial regions of synchrony/desynchrony, and to reveal temporal regions of event-related frequency reorganization by comparing prestimulus and poststimulus epochs. A new method has been applied for quantifying entropy in short-lasting EEG signals to reflect temporal evolution of order/disorder states in neuroelectric activity. The data analysis from the experiments implies that wavelet energy (WE) quantifiers can identify a bioelectric process that is consistently involved with auditory stimulus processing. WE are capable of detecting changes in a non-stationary signal because of the localization characteristics of the wavelet transform. The computational time of WE is short, because the algorithm involves the use of wavelet transform in a multi-resolution frame-work, and the WE is parameter-free. Wavelet analysis is a method that relies on the introduction of an appropriate basis and a characterization of the signal by the distribution of amplitude in the basis. The chapter discusses wavelet transform, wavelet energy and wavelet entropy, and quantifiers based on wavelet entropy.

AN ENTROPY BASED IN WAVELET LEADERS TO QUANTIFY THE LOCAL REGULARITY OF A SIGNAL AND ITS APPLICATION TO ANALIZE THE DOW JONES INDEX

Local regularity analysis is useful in many fields, such as financial analysis, fluid mechanics, PDE theory, signal and image processing. Different quantifiers have been proposed to measure the local regularity of a function. In this paper we present a new quantifier of local regularity of a signal: the pointwise wavelet leaders entropy. We define this new measure of regularity by combining the concept of entropy, coming from the information theory and statistical mechanics, with the wavelet leaders coefficients. Also we establish its inverse relation with one of the well-known regularity exponents, the pointwise Holder exponent. Finally, we apply this methodology to the financial data series of the Dow Jones Industrial Average Index, registered in the period 1928–2011, in order to compare the temporal evolution of the pointwise Holder exponent and the pointwise wavelet leaders entropy. The analysis reveals that temporal variation of these quantifiers reflects the evolution of the Dow Jones Industrial Ave...