The Application of Complexity Analysis in Brain Blood-Oxygen Signal

The brain entropy dynamics in resting state

As a novel measure for irregularity and complexity of the spontaneous fluctuations of brain activities, brain entropy (BEN) has attracted much attention in resting-state functional magnetic resonance imaging (rs-fMRI) studies during the last decade. Previous studies have shown its associations with cognitive and mental functions. While most previous research assumes BEN is approximately stationary during scan sessions, the brain, even at its resting state, is a highly dynamic system. Such dynamics could be characterized by a series of reoccurring whole-brain patterns related to cognitive and mental processes. The present study aims to explore the time-varying feature of BEN and its potential links with general cognitive ability. We adopted a sliding window approach to derive the dynamical brain entropy (dBEN) of the whole-brain functional networks from the HCP (Human Connectome Project) rs-fMRI dataset that includes 812 young healthy adults. The dBEN was further clustered into 4 reoccurring BEN states by the k-means clustering method. The fraction window (FW) and mean dwell time (MDT) of one BEN state, characterized by the extremely low overall BEN, were found to be negatively correlated with general cognitive abilities (i.e., cognitive flexibility, inhibitory control, and processing speed). Another BEN state, characterized by intermediate overall BEN and low within-state BEN located in DMN, ECN, and part of SAN, its FW, and MDT were positively correlated with the above cognitive abilities. The results of our study advance our understanding of the underlying mechanism of BEN dynamics and provide a potential framework for future investigations in clinical populations.

Complexity Measures for EEG Microstate Sequences: Concepts and Algorithms

EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel-Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al., Neural Comput 16:717-736, https://doi.org/10.1162/089976604322860677 , 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Microstate jump sequences, where duplicate states have been removed, show higher randomness, lower statistical complexity, and no long-range correlations. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.

Exploring Physiological Differences in Brain Areas Using Statistical Complexity Analysis of BOLD Signals

The brain is a fundamental organ for the human body to function properly, for which it needs to receive a continuous flow of blood, which explains the existence of control mechanisms that act to maintain this flow as constant as possible in a process known as cerebral autoregulation. One way to obtain information on how the levels of oxygen supplied to the brain vary is through of BOLD (Magnetic Resonance) images, which have the advantage of greater spatial resolution than other forms of measurement, such as transcranial Doppler. However, they do not provide good temporal resolution nor allow for continuous prolonged examination. Thus, it is of great importance to find a method to detect regional differences from short BOLD signals. One of the existing alternatives is complexity measures that can detect changes in the variability and temporal organisation of a signal that could reflect different physiological states. The so-called statistical complexity, created to overcome the shortcomings of entropy alone to explain the concept of complexity, has shown potential with haemodynamic signals. The aim of this study is to determine by using statistical complexity whether it is possible to find differences between physiologically distinct brain areas in healthy individuals. The data set includes BOLD images of 10 people obtained at the University Hospital of Leicester NHS Trust with a 1.5 Tesla magnetic resonance imaging scanner. The data were captured for 180 s at a frequency of 1 Hz. Using various combinations of statistical complexities, no differences were found between hemispheres. However, differences were detected between grey matter and white matter, indicating that these measurements are sensitive to differences in brain tissues.

Complexity changes in functional state dynamics suggest focal connectivity reductions

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013; Adhikari et al., 2017; Li et al., 2018). However, many of these studies have not accounted for the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivity via a Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations.

Optimized Multiscale Entropy Model Based on Resting-State fMRI for Appraising Cognitive Performance in Healthy Elderly

Many studies have indicated that an entropy model can capture the dynamic characteristics of resting-state functional magnetic resonance imaging (rfMRI) signals. However, there are problems of subjectivity and lack of uniform standards in the selection of model parameters relying on experience when using the entropy model to analyze rfMRI. To address this issue, an optimized multiscale entropy (MSE) model was proposed to confirm the parameters objectively. All healthy elderly volunteers were divided into two groups, namely, excellent and poor, by the scores estimated through traditional scale tests before the rfMRI scan. The parameters of the MSE model were optimized with the help of sensitivity parameters such as receiver operating characteristic (ROC) and area under the ROC curve (AUC) in a comparison study between the two groups. The brain regions with significant differences in entropy values were considered biomarkers. Their entropy values were regarded as feature vectors to use as input for the probabilistic neural network in the classification of cognitive scores. Classification accuracy of 80.05% was obtained using machine learning. These results show that the optimized MSE model can accurately select the brain regions sensitive to cognitive performance and objectively select fixed parameters for MSE. This work was expected to provide the basis for entropy to test the cognitive scores of the healthy elderly.