In the background of all human thinking—acting and reacting are sets of connections between different neurons or groups of neurons. We studied and evaluated these connections using electroencephalography (EEG) brain signals. In this paper, we propose the use of the complex Pearson correlation coefficient (CPCC), which provides information on connectivity with and without consideration of the volume conduction effect. Although the Pearson correlation coefficient is a widely accepted measure of the statistical relationships between random variables and the relationships between signals, it is not being used for EEG data analysis. Its meaning for EEG is not straightforward and rarely well understood. In this work, we compare it to the most commonly used undirected connectivity analysis methods, which are phase locking value (PLV) and weighted phase lag index (wPLI). First, the relationship between the measures is shown analytically. Then, it is illustrated by a practical comparison using synthetic and real EEG data. The relationships between the observed connectivity measures are described in terms of the correlation values between them, which are, for the absolute values of CPCC and PLV, not lower that 0.97, and for the imaginary component of CPCC and wPLI—not lower than 0.92, for all observed frequency bands. Results show that the CPCC includes information of both other measures balanced in a single complex-numbered index.

In this paper, we propose a new method to study and evaluate the time-varying brain network dynamics. The proposed RICI-imCPCC method (relative intersection of confidence intervals for the imaginary component of the complex Pearson correlation coefficient) is based on an adaptive window size and the imaginary part of the complex Pearson correlation coefficient. It reduces the weaknesses of the existing method of constant sliding window analysis with narrow and wide windows. These are the low temporal precision and low reliability for short connectivity periods for wide windows, and high susceptibility to noise for narrow windows, all resulting in low estimation accuracy. The proposed method overcomes these shortcomings by dynamically adjusting the window width using the RICI rule, which is based on the statistical properties of the area around the observed sample. In this paper, we compare the RICI-imCPCC with the existing constant sliding window analysis method and describe its advantages. First, the mathematical principles are established. Then, the comparison between the existing and the proposed method using synthetic and real electroencephalography (EEG) data is presented. The results show that the proposed RICI-imCPCC method has improved temporal resolution and estimation accuracy compared to the existing method and is less affected by the noise. The estimation error energy calculated for the RICI-imCPCC method on synthetic signals was lower by a factor of $1.22$ compared to the error of the constant sliding window analysis using narrow window size imCPCC, by a factor of $2.87$ compared to using wide window size imCPCC, by a factor of $6.69$ compared to using narrow window size wPLI, and by a factor of $4.72$ compared to using wide window size wPLI. Analysis of the real signals shows the ability of the proposed method to detect a P300 response and to detect a decrease in dynamic connectivity due to desynchronization and blockage of mu-rhythms.

In this article, we perform a case study of the impact of photobiomodulation (PBM) on brain power spectrum and connectivity in an elderly person with a Self Administered Gerocognitive Exam (SAGE) score indicating probable memory and thinking disorder. First, we designed and realized the prototype of a near-infrared (NIR) device for PBM. Analysing the alpha band of the power spectrum, we found a positive long-term effect in nine out of sixteen electrodes in the eyes-open condition (OE) and in twelve out of sixteen electrodes in the eyes-closed condition (CE), while in the theta band, a positive long-term effect was found in nine out of sixteen electrodes for OE and seven out of sixteen electrodes for CE. When considering the theta-alpha ratio (TAR), the positive long-term effect is found on thirteen of sixteen electrodes for OE and on fourteen of sixteen electrodes for CE. A connectivity analysis using the imaginary component of the complex Pearson correlation coefficient (imCPCC) was also performed, and a global efficiency measure based on connectivity matrices with thresholds was calculated. The global efficiency calculated for the long-term effect was higher than before stimulation by a factor of $5.24$ for the OE condition and by a factor of $1.25$ for the CE condition. This case study suggests that PBM could have positive effects on improving desired brain activity, measured as improvement in power spectrum and connectivity measures in theta and alpha bands, for elderly people with memory and thinking disorders.

This study presents a method for generating synthetic electroencephalography (EEG) signals to test dynamic directed brain connectivity estimation methods. Current methods for evaluating dynamic brain connectivity estimation techniques face challenges due to the lack of ground truth in real EEG signals. To address this, we propose a framework for generating synthetic EEG signals with predefined dynamic connectivity changes. Our approach allows for evaluating and optimizing dynamic connectivity estimation methods, particularly Granger causality (GC). We demonstrate the framework’s utility by identifying optimal window sizes and regression orders for GC analysis. The findings could guide the development of more accurate dynamic connectivity techniques.

In this paper, EEG data processing was conducted in order to define the parameters for neurofeedback. A new survey was conducted based on a brief review of previous research. Two groups of participants were chosen: ADHD (3) and nonADHD (14). The main part of this study includes EEG signal data pre-processing and processing. We have outlined statistical features of observed EEG signals such as mean value, grand-mean value and their ratios. It can be concluded that an increase in grand-mean values of power theta-low beta ratio on Cz electrode gives confirmation of previous research. The value of alpha-delta power ratio higher than 1 on C3, Cz, P3, Pz, P4 in ADHD group is proposed as a new approach to classification. Based on these conclusions we will design a neurofeedback protocol as a continuation of this work.

In this paper, the analysis of noise and sensitivity for different BP filter designs is observed. Calculation of the voltage noise spectral density, root mean square (RMS) value of the noise voltage, Schoeffler sensitivity and the multi-parameter sensitivity is done for the simply designed (SD) active RC, noise and sensitivity optimized (NO and SO) active RC, operational transconductance amplifiers (OTA-C) and switched capacitor (SC) filter designs. This is observed for the fourth-order Chebyshev band-pass filter, with central frequency f_c = 4 kHz, bandwidth 1 kHz and pass-band ripple α_max = −0.1 dB. Cascade of two second-order sections is used for fulfilment realization of all four observing designs. Programming tools, such as MATLAB and SPICE (LTspice), are also used for the analyses. Highlights