Potentialities of the wavelet and multifractal techniques to evaluate changes in the functional state of the human brain

Classification of Mammographic ROI for Microcalcification Detection Using Multifractal Approach

Microcalcifications (MCs) are the main signs of precancerous cells. The development of aided-system for their detection has become a challenge for researchers in this field. In this paper, we propose a system for MCs detection based on the multifractal approach that classifies mammographic ROIs into normal (healthy) or abnormal ROIs containing MCs. The proposed method is divided into four main steps: a mammogram pre-processing step based on breast selection, breast density reduction using haze removal algorithm and contrast enhancement using multifractal measures. The second step consists of extracting the normal and abnormal ROIs and calculating the multifractal spectrum of each ROI. The next step represents the extraction of the multifractal features from the multifractal spectrum and the GLCM characteristics of each ROI. The last step is the classification of ROIs where three classifiers are tested (KNN, DT, and SVM). The system is evaluated on images from the INbreast database (308 images) with a total of 2688 extracted ROIs (1344 normal, 1344 with MC) from different BI-RADS classes. In this study, the SVM classifier gave the best classification results with a sensitivity, specificity, and precision of 98.66%, 97.77%, and 98.20% respectively. These results are very satisfactory and remarkable compared to the literature.

Fractal Structure of Brain Electrical Activity of Patients With Mental Disorders

This work was aimed at a comparative analysis of the degree of multifractality of electroencephalographic time series obtained from a group of healthy subjects and from patients with mental disorders. We analyzed long-term records of patients with paranoid schizophrenia and patients with depression. To evaluate the properties of multifractal scaling of various electroencephalographic time series, the method of maximum modulus of the wavelet transform and multifractal analysis of fluctuations without a trend were used. The stability of the width and position of the singularity spectrum for each of the test groups was revealed, and a relationship was established between the correlation and anticorrelation dynamics of successive values of the electroencephalographic time series and the type of mental disorders. It was shown that the main differences between the multifractal properties of brain activity in normal and pathological conditions lie in the different width of the multifractality spectrum and its location associated with the correlated or anticorrelated dynamics of the values of successive time series. It was found that the schizophrenia group is characterized by a greater degree of multifractality compared to the depression group. Thus, the degree of multifractality can be included in a set of tests for differential diagnosis and research of mental disorders.

EEG multifractal analysis correlates with cognitive testing scores and clinical staging in mild cognitive impairment

Alzheimer's disease and mild cognitive impairment are increasingly prevalent global health concerns in aging industrialized societies. There are only limited non-invasive biomarkers for the cognitive and functional impairment associated with dementia. Multifractal analysis of EEG has recently been proposed as having the potential to be an improved method of quantitative EEG analysis compared to existing techniques (e.g., spectral analysis). We utilized an existing database of a study of healthy elderly patients (N = 20) who were assessed with cognitive testing (Folstein Mini Mental Status Exam; MMSE) and resting state EEG (4 leads). Each subject's EEG was separated into two 30 s tracings for training and testing a statistical model against the MMSE scores. We compared multifractal detrended fluctuation analysis (MF-DFA) against Fourier Transform (FT) in the ability to produce an accurate classification and regression trees estimator for the testing EEG segments. The MF-DFA-based statistical model MMSE estimation strongly correlated with the actual MMSE when applied to the test EEG parameter dataset, whereas the corresponding FT-based model did not. Using a standardized cutoff value for MMSE-based clinical staging, the MF-DFA-based statistical model was both sensitive and specific for clinical staging of both mild Alzheimer's disease and mild cognitive impairment. MF-DFA shows promise as a method of quantitative EEG analysis to accurately estimate cognition in Alzheimer's disease.

A Novel MFDFA Algorithm and Its Application to Analysis of Harmonic Multifractal Features

A power grid harmonic signal is characterized as having both nonlinear and nonstationary features. A novel multifractal detrended fluctuation analysis (MFDFA) algorithm combined with the empirical mode decomposition (EMD) theory and template movement is proposed to overcome some shortcomings in the traditional MFDFA algorithm. The novel algorithm is used to study the multifractal feature of harmonic signals at different frequencies. Firstly, the signal is decomposed and the characteristics of wavelet transform multiresolution analysis are employed to obtain the components at different frequency bands. After this, the local fractal characteristic of the components is studied by utilizing the novel MFDFA algorithm. The experimental results show that the harmonic signals exhibit obvious multifractal characteristics and that the multifractal intensity is related to the signal frequency. Compared with the traditional MFDFA algorithm, the proposed method is more stable in curve fitting and can extract the multifractal features more accurately.

Generalized Information Equilibrium Approaches to EEG Sleep Stage Discrimination

Recent advances in neuroscience have raised the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG) signals is via power-law distributed neuronal avalanches, while EEG signals are nonstationary. Therefore, spectral analysis of EEG may miss many properties inherent in such signals. A complete understanding of such dynamical systems requires knowledge of the underlying nonequilibrium thermodynamics. In recent work by Fielitz and Borchardt (2011, 2014), the concept of information equilibrium (IE) in information transfer processes has successfully characterized many different systems far from thermodynamic equilibrium. We utilized a publicly available database of polysomnogram EEG data from fourteen subjects with eight different one-minute tracings of sleep stage 2 and waking and an overlapping set of eleven subjects with eight different one-minute tracings of sleep stage 3. We applied principles of IE to model EEG as a system that transfers (equilibrates) information from the time domain to scalp-recorded voltages. We find that waking consciousness is readily distinguished from sleep stages 2 and 3 by several differences in mean information transfer constants. Principles of IE applied to EEG may therefore prove to be useful in the study of changes in brain function more generally.

Multifractal detrended fluctuation analysis of human EEG: preliminary investigation and comparison with the wavelet transform modulus maxima technique

Recently, many lines of investigation in neuroscience and statistical physics have converged to raise the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG) signals is nonlinear, with self-affine dynamics, while scalp-recorded EEG signals themselves are nonstationary. Therefore, traditional methods of EEG analysis may miss many properties inherent in such signals. Similarly, fractal analysis of EEG signals has shown scaling behaviors that may not be consistent with pure monofractal processes. In this study, we hypothesized that scalp-recorded human EEG signals may be better modeled as an underlying multifractal process. We utilized the Physionet online database, a publicly available database of human EEG signals as a standardized reference database for this study. Herein, we report the use of multifractal detrended fluctuation analysis on human EEG signals derived from waking and different sleep stages, and show evidence that supports the use of multifractal methods. Next, we compare multifractal detrended fluctuation analysis to a previously published multifractal technique, wavelet transform modulus maxima, using EEG signals from waking and sleep, and demonstrate that multifractal detrended fluctuation analysis has lower indices of variability. Finally, we report a preliminary investigation into the use of multifractal detrended fluctuation analysis as a pattern classification technique on human EEG signals from waking and different sleep stages, and demonstrate its potential utility for automatic classification of different states of consciousness. Therefore, multifractal detrended fluctuation analysis may be a useful pattern classification technique to distinguish among different states of brain function.