Functional MRI Signal Complexity Analysis Using Sample Entropy

The heritability and structural correlates of resting-state fMRI complexity

The complexity of fMRI signals quantifies temporal dynamics of spontaneous neural activity, which has been increasingly recognized as providing important insights into cognitive functions and psychiatric disorders. However, its heritability and structural underpinnings are not well understood. Here, we utilize multi-scale sample entropy to extract resting-state fMRI complexity in a large healthy adult sample from the Human Connectome Project. We show that fMRI complexity at multiple time scales is heritable in broad brain regions. Heritability estimates are modest and regionally variable. We relate fMRI complexity to brain structure including surface area, cortical myelination, cortical thickness, subcortical volumes, and total brain volume. We find that surface area is negatively correlated with fine-scale complexity and positively correlated with coarse-scale complexity in most cortical regions, especially the association cortex. Most of these correlations are related to common genetic and environmental effects. We also find positive correlations between cortical myelination and fMRI complexity at fine scales and negative correlations at coarse scales in the prefrontal cortex, lateral temporal lobe, precuneus, lateral parietal cortex, and cingulate cortex, with these correlations mainly attributed to common environmental effects. We detect few significant associations between fMRI complexity and cortical thickness. Despite the non-significant association with total brain volume, fMRI complexity exhibits significant correlations with subcortical volumes in the hippocampus, cerebellum, putamen, and pallidum at certain scales. Collectively, our work establishes the genetic basis and structural correlates of resting-state fMRI complexity across multiple scales, supporting its potential application as an endophenotype for psychiatric disorders.

Divergent functional connectivity changes associated with white matter hyperintensities

Age-related white matter hyperintensities are a common feature and are known to be negatively associated with structural integrity, functional connectivity, and cognitive performance. However, this has yet to be fully understood mechanistically. We analyzed multiple MRI modalities acquired in 465 non-demented individuals from the Swedish BioFINDER study including 334 cognitively normal and 131 participants with mild cognitive impairment. White matter hyperintensities were automatically quantified using fluid-attenuated inversion recovery MRI and parameters from diffusion tensor imaging were estimated in major white matter fibre tracts. We calculated fMRI resting state-derived functional connectivity within and between predefined cortical regions structurally linked by the white matter tracts. How change in functional connectivity is affected by white matter lesions and related to cognition (in the form of executive function and processing speed) was explored. We examined the functional changes using a measure of sample entropy. As expected hyperintensities were associated with disrupted structural white matter integrity and were linked to reduced functional interregional lobar connectivity, which was related to decreased processing speed and executive function. Simultaneously, hyperintensities were also associated with increased intraregional functional connectivity, but only within the frontal lobe. This phenomenon was also associated with reduced cognitive performance. The increased connectivity was linked to increased entropy (reduced predictability and increased complexity) of the involved voxels' blood oxygenation level-dependent signal. Our findings expand our previous understanding of the impact of white matter hyperintensities on cognition by indicating novel mechanisms that may be important beyond this particular type of brain lesions.

Reliability of variability and complexity measures for task and task-free BOLD fMRI

Brain activity continuously fluctuates over time, even if the brain is in controlled (e.g., experimentally induced) states. Recent years have seen an increasing interest in understanding the complexity of these temporal variations, for example with respect to developmental changes in brain function or between-person differences in healthy and clinical populations. However, the psychometric reliability of brain signal variability and complexity measures-which is an important precondition for robust individual differences as well as longitudinal research-is not yet sufficiently studied. We examined reliability (split-half correlations) and test-retest correlations for task-free (resting-state) BOLD fMRI as well as split-half correlations for seven functional task data sets from the Human Connectome Project to evaluate their reliability. We observed good to excellent split-half reliability for temporal variability measures derived from rest and task fMRI activation time series (standard deviation, mean absolute successive difference, mean squared successive difference), and moderate test-retest correlations for the same variability measures under rest conditions. Brain signal complexity estimates (several entropy and dimensionality measures) showed moderate to good reliabilities under both, rest and task activation conditions. We calculated the same measures also for time-resolved (dynamic) functional connectivity time series and observed moderate to good reliabilities for variability measures, but poor reliabilities for complexity measures derived from functional connectivity time series. Global (i.e., mean across cortical regions) measures tended to show higher reliability than region-specific variability or complexity estimates. Larger subcortical regions showed similar reliability as cortical regions, but small regions showed lower reliability, especially for complexity measures. Lastly, we also show that reliability scores are only minorly dependent on differences in scan length and replicate our results across different parcellation and denoising strategies. These results suggest that the variability and complexity of BOLD activation time series are robust measures well-suited for individual differences research. Temporal variability of global functional connectivity over time provides an important novel approach to robustly quantifying the dynamics of brain function. PRACTITIONER POINTS: Variability and complexity measures of BOLD activation show good split-half reliability and moderate test-retest reliability. Measures of variability of global functional connectivity over time can robustly quantify neural dynamics. Length of fMRI data has only a minor effect on reliability.

Refined composite multiscale slope entropy and its application in rolling bearing fault diagnosis

Rolling bearing is the key component of rotating machinery, and its vibration signal usually exhibits nonlinear and nonstationary characteristics when failure occurs. Multiscale permutation entropy (MPE) is an effective nonlinear dynamics analysis tool, which has been successfully applied to rolling bearing fault diagnosis in recent years. However, MPE ignores the deep amplitude information when measuring the complexity of the time series and the original multiscale coarse-graining is insufficient, which requires further research and improvement. In order to protect the integrity of information structure, a novel nonlinear dynamic analysis method termed refined composite multiscale slope entropy (RCMSlE) is proposed in this paper, which introduced the concept of refined composite to further boost the performance of MPE in nonlinear dynamical complexity analysis. Furthermore, RCMSlE utilizes a novel symbolic representation that takes full account of mode and amplitude information, which overcomes the weaknesses in describing the complexity and regularity of bearing signals. Based on this, a GWO-SVM multi-classifier is introduced to fulfill mode recognition, and then a new intelligent fault diagnosis method for rolling bearing based on RCMSlE and GWO-SVM is proposed. The experimental results show that the proposed method can not only accurately identify different fault types and degrees of rolling bearing, but also has a short computation time and better performance than other comparative methods.

Sex differences of signal complexity at resting-state functional magnetic resonance imaging and their associations with the estrogen-signaling pathway in the brain

Sex differences in the brain have been widely reported and may hold the key to elucidating sex differences in many medical conditions and drug response. However, the molecular correlates of these sex differences in structural and functional brain measures in the human brain remain unclear. Herein, we used sample entropy (SampEn) to quantify the signal complexity of resting-state functional magnetic resonance imaging (rsfMRI) in a large neuroimaging cohort (N = 1,642). The frontoparietal control network and the cingulo-opercular network had high signal complexity while the cerebellar and sensory motor networks had low signal complexity in both men and women. Compared with those in male brains, we found greater signal complexity in all functional brain networks in female brains with the default mode network exhibiting the largest sex difference. Using the gene expression data in brain tissues, we identified genes that were significantly associated with sex differences in brain signal complexity. The significant genes were enriched in the gene sets that were differentially expressed between the brain cortex and other tissues, the estrogen-signaling pathway, and the biological function of neural plasticity. In particular, the G-protein-coupled estrogen receptor 1 gene in the estrogen-signaling pathway was expressed more in brain regions with greater sex differences in SampEn. In conclusion, greater complexity in female brains may reflect the interactions between sex hormone fluctuations and neuromodulation of estrogen in women.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09954-y.

Diverging functional connectivity timescales: Capturing distinct aspects of cognitive performance in early psychosis

Background

Psychosis spectrum disorders (PSDs) are marked by cognitive impairments, the neurobiological correlates of which remain poorly understood. Here, we investigate the entropy of time-varying functional connectivity (TVFC) patterns from resting-state fMRI (rfMRI) as potential biomarker for cognitive performance in PSDs. By combining our results with multimodal reference data, we hope to generate new insights into the mechanisms underlying cognitive dysfunction in PSDs. We hypothesized that low-entropy TVFC patterns (LEN) would be more behaviorally informative than high-entropy TVFC patterns (HEN), especially for tasks that require extensive integration across diverse cognitive subdomains.

Methods

rfMRI and behavioral data from 97 patients in the early phases of psychosis and 53 controls were analyzed. Positron-Emission Tomography (PET) and magnetoencephalography (MEG) data were taken from a public repository (Hansen et al., 2022). Multivariate analyses were conducted to examine relationships between TVFC patterns at multiple spatial scales and cognitive performance in patients.

Results

Compared to HEN, LEN explained significantly more cognitive variance on average in PSD patients, driven by superior encoding of information on psychometrically more integrated tasks. HEN better captured information in specific subdomains of executive functioning. Nodal HEN-LEN transitions were spatially aligned with neurobiological gradients reflecting monoaminergic transporter densities and MEG beta power. Exploratory analyses revealed a close statistical relationship between LEN and positive PSD symptoms.

Conclusion

Our entropy-based analysis of TVFC patterns dissociates distinct aspects of cognition in PSDs. By linking topographies of neurotransmission and oscillatory dynamics with cognitive performance, it enhances our understanding of the mechanisms underlying cognitive deficits in PSDs.

CRediT Authorship Contribution Statement

Fabian Hirsch: Conceptualization, Methodology, Software, Formal analysis, Writing - Original Draft, Writing - Review & Editing, Visualization; Ângelo Bumanglag: Methodology, Software, Formal analysis, Writing - Review & Editing; Yifei Zhang: Methodology, Software, Formal analysis, Writing - Review & Editing; Afra Wohlschlaeger: Methodology, Writing - Review & Editing, Supervision, Project administration.

Changed brain entropy and functional connectivity patterns induced by electroconvulsive therapy in majoy depression disorder

OBJECTIVE

Our objective is to innovatively integrate both linear and nonlinear characteristics of brain signals in Electroconvulsive Therapy (ECT) research, with the goal of uncovering deeper insights into the pathogenesis of Major Depressive Disorder (MDD) and identifying novel targets for other physical intervention therapies.

METHODS

We measured brain entropy (BEN) in 42 MDD patients and 42 matched healthy controls (HC) using rs-fMRI data. Brain regions that differed significantly in patients with MDD before and after ECT were extracted. Then, we use these brain regions as seed points to investigate the differences in whole-brain resting-state functional connectivity (RSFC) patterns before and after ECT.

RESULTS

Compared to HCs, patients had higher BEN levels in the right precuneus (PCUN.R) and right angular gyrus (ANG.R). After ECT, patients had lower BEN levels in the PCUN.R and ANG.R. Compared with before ECT, patients showed significantly increased RSFC after ECT between the PCUN.R and right middle temporal gyrus and ANG.R. Significantly increased RSFC was observed between the ANG.R and right middle frontal gyrus and right supramarginal gyrus after ECT.

CONCLUSION

Combining the linear and nonlinear characteristics of brain signals can effectively explore the pathogenesis of depression and provide new targets for ECT.

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.

Optimizing the measurement of sample entropy in resting-state fMRI data

Introduction

The complexity of brain signals may hold clues to understand brain-based disorders. Sample entropy, an index that captures the predictability of a signal, is a promising tool to measure signal complexity. However, measurement of sample entropy from fMRI signals has its challenges, and numerous questions regarding preprocessing and parameter selection require research to advance the potential impact of this method. For one example, entropy may be highly sensitive to the effects of motion, yet standard approaches to addressing motion (e.g., scrubbing) may be unsuitable for entropy measurement. For another, the parameters used to calculate entropy need to be defined by the properties of data being analyzed, an issue that has frequently been ignored in fMRI research. The current work sought to rigorously address these issues and to create methods that could be used to advance this field.

Methods

We developed and tested a novel windowing approach to select and concatenate (ignoring connecting volumes) low-motion windows in fMRI data to reduce the impact of motion on sample entropy estimates. We created utilities (implementing autoregressive models and a grid search function) to facilitate selection of the matching length m parameter and the error tolerance r parameter. We developed an approach to apply these methods at every grayordinate of the brain, creating a whole-brain dense entropy map. These methods and tools have been integrated into a publicly available R package ("powseR"). We demonstrate these methods using data from the ABCD study. After applying the windowing procedure to allow sample entropy calculation on the lowest-motion windows from runs 1 and 2 (combined) and those from runs 3 and 4 (combined), we identified the optimal m and r parameters for these data. To confirm the impact of the windowing procedure, we compared entropy values and their relationship with motion when entropy was calculated using the full set of data vs. those calculated using the windowing procedure. We then assessed reproducibility of sample entropy calculations using the windowed procedure by calculating the intraclass correlation between the earlier and later entropy measurements at every grayordinate.

Results

When applying these optimized methods to the ABCD data (from the subset of individuals who had enough windows of continuous "usable" volumes), we found that the novel windowing procedure successfully mitigated the large inverse correlation between entropy values and head motion seen when using a standard approach. Furthermore, using the windowed approach, entropy values calculated early in the scan (runs 1 and 2) are largely reproducible when measured later in the scan (runs 3 and 4), although there is some regional variability in reproducibility.

Discussion

We developed an optimized approach to measuring sample entropy that addresses concerns about motion and that can be applied across datasets through user-identified adaptations that allow the method to be tailored to the dataset at hand. We offer preliminary results regarding reproducibility. We also include recommendations for fMRI data acquisition to optimize sample entropy measurement and considerations for the field.

Task-induced changes in brain entropy

Entropy indicates irregularity of a dynamic system, with higher entropy indicating higher irregularity and more transit states. In the human brain, regional brain entropy (BEN) has been increasingly assessed using resting state fMRI (rs-fMRI), while changes of regional BEN during task-based fMRI have been scarcely studied. The purpose of this study is to characterize task-induced regional BEN alterations using the large Human Connectome Project (HCP) data. To control the potential modulation by the block design, BEN of task-fMRI was calculated from the fMRI images acquired during the task conditions only (task BEN) and then compared to BEN of rs-fMRI (resting BEN). Moreover, BEN was separately calculated from the control blocks of the task-fMRI runs (control BEN) and compared to task BEN. Finally, control BEN was compared to resting BEN to test for residual task effects in the control condition. With respect to resting state, task performance unanimously induced BEN reduction in the peripheral cortical area and BEN increase in the centric part of the sensorimotor and perception networks. Control compared to resting BEN showed similar entropy alterations, suggesting large residual task effects. Task compared to control BEN was characterized by reduced entropy in occipital, orbitofrontal, and parietal regions.

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.

Predicting suicidality in late-life depression by 3D convolutional neural network and cross-sample entropy analysis of resting-state fMRI

BACKGROUND

Predicting suicide is a pressing issue among older adults; however, predicting its risk is difficult. Capitalizing on the recent development of machine learning, considerable progress has been made in predicting complex behavior such as suicide. As depression remained the strongest risk for suicide, we aimed to apply deep learning algorithms to identify suicidality in a group with late-life depression (LLD).

METHODS

We enrolled 83 patients with LLD, 35 of which were non-suicidal and 48 were suicidal, including 26 with only suicidal ideation and 22 with past suicide attempts, for resting-state functional magnetic resonance imaging (MRI). Cross-sample entropy (CSE) analysis was conducted to examine the complexity of MRI signals among brain regions. Three-dimensional (3D) convolutional neural networks (CNNs) were used, and the classification accuracy in each brain region was averaged to predict suicidality after sixfold cross-validation.

RESULTS

We found brain regions with a mean accuracy above 75% to predict suicidality located mostly in default mode, fronto-parietal, and cingulo-opercular resting-state networks. The models with right amygdala and left caudate provided the most reliable accuracy in all cross-validation folds, indicating their neurobiological importance in late-life suicide.

CONCLUSION

Combining CSE analysis and the 3D CNN, several brain regions were found to be associated with suicidality.

Psilocybin-induced default mode network hypoconnectivity is blunted in alcohol-dependent rats

Alcohol Use Disorder (AUD) adversely affects the lives of millions of people, but still lacks effective treatment options. Recent advancements in psychedelic research suggest psilocybin to be potentially efficacious for AUD. However, major knowledge gaps remain regarding (1) psilocybin's general mode of action and (2) AUD-specific alterations of responsivity to psilocybin treatment in the brain that are crucial for treatment development. Here, we conducted a randomized, placebo-controlled crossover pharmaco-fMRI study on psilocybin effects using a translational approach with healthy rats and a rat model of alcohol relapse. Psilocybin effects were quantified with resting-state functional connectivity using data-driven whole-brain global brain connectivity, network-based statistics, graph theory, hypothesis-driven Default Mode Network (DMN)-specific connectivity, and entropy analyses. Results demonstrate that psilocybin induced an acute wide-spread decrease in different functional connectivity domains together with a distinct increase of connectivity between serotonergic core regions and cortical areas. We could further provide translational evidence for psilocybin-induced DMN hypoconnectivity reported in humans. Psilocybin showed an AUD-specific blunting of DMN hypoconnectivity, which strongly correlated to the alcohol relapse intensity and was mainly driven by medial prefrontal regions. In conclusion, our results provide translational validity for acute psilocybin-induced neural effects in the rodent brain. Furthermore, alcohol relapse severity was negatively correlated with neural responsivity to psilocybin treatment. Our data suggest that a clinical standard dose of psilocybin may not be sufficient to treat severe AUD cases; a finding that should be considered for future clinical trials.

Multivariate multiscale entropy (mMSE) as a tool for understanding the resting-state EEG signal dynamics: the spatial distribution and sex/gender-related differences

BACKGROUND

The study aimed to determine how the resting-state EEG (rsEEG) complexity changes both over time and space (channels). The complexity of rsEEG and its sex/gender differences were examined using the multivariate Multiscale Entropy (mMSE) in 95 healthy adults. Following the probability maps (Giacometti et al. in J Neurosci Methods 229:84-96, 2014), channel sets have been identified that correspond to the functional networks. For each channel set the area under curve (AUC), which represents the total complexity, MaxSlope-the maximum complexity change of the EEG signal at thefine scales (1:4 timescales), and AvgEnt-to the average entropy level at coarse-grained scales (9:12 timescales), respectively, were extracted. To check dynamic changes between the entropy level at the fine and coarse-grained scales, the difference in mMSE between the #9 and #4 timescale (DiffEnt) was also calculated.

RESULTS

We found the highest AUC for the channel sets corresponding to the somatomotor (SMN), dorsolateral network (DAN) and default mode (DMN) whereas the visual network (VN), limbic (LN), and frontoparietal (FPN) network showed the lowest AUC. The largest MaxSlope were in the SMN, DMN, ventral attention network (VAN), LN and FPN, and the smallest in the VN. The SMN and DAN were characterized by the highest and the LN, FPN, and VN by the lowest AvgEnt. The most stable entropy were for the DAN and VN while the LN showed the greatest drop of entropy at the coarse scales. Women, compared to men, showed higher MaxSlope and DiffEnt but lower AvgEnt in all channel sets.

CONCLUSIONS

Novel results of the present study are: (1) an identification of the mMSE features that capture entropy at the fine and coarse timescales in the channel sets corresponding to the main resting-state networks; (2) the sex/gender differences in these features.

Task-induced changes in brain entropy

Entropy indicates irregularity of a dynamic system with higher entropy indicating higher irregularity and more transit states. In the human brain, regional entropy has been increasingly assessed using resting state fMRI. Response of regional entropy to task has been scarcely studied. The purpose of this study is to characterize task-induced regional brain entropy (BEN) alterations using the large Human Connectome Project (HCP) data. To control the potential modulation by the block-design, BEN of task-fMRI was calculated from the fMRI images acquired during the task conditions only and then compared to BEN of rsfMRI. Compared to resting state, task-performance unanimously induced BEN reduction in the peripheral cortical area including both the task activated regions and task non-specific regions such as the task negative area and BEN increase in the centric part of the sensorimotor and perception networks. Task control condition showed large residual task effects. After controlling the task non-specific effects using the control BEN vs task BEN comparison, regional BEN showed task specific effects in target regions.

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Entropy of left ventricular late gadolinium enhancement and its prognostic value in hypertrophic cardiomyopathy a new CMR assessment method

PURPOSE

As a novel metric, entropy generated from late gadolinium enhancement (LGE) cardiac magnetic resonance (CMR) can be utilized to assess tissue heterogeneity. However, it is unknown if it can be utilized for risk stratification in hypertrophic cardiomyopathy (HCM). In addition, it is unknown if LGE entropy correlates with LGE mass%, which is commonly utilized for fibrosis assessment. This research was done to investigate these issues.

MATERIALS AND METHODS

Patients with HCM who underwent 3.0-T CMR between January 2015 and January 2020 were prospectively enrolled and classified into low- and high-risk groups according to the AHA/ACC risk stratification guideline for 2020. The LGE entropy was automatically estimated using a generic Python package algorithm. On CMR imaging, the LGE mass% was determined using the CVI 42 software. Endpoint events included sudden cardiac death (SCD), hospital readmission owing to heart failure, and implantable cardioverter defibrillator (ICD) treatment for ventricular arrhythmias.

RESULTS

A total of 109 HCM participants (70 males) were included. During the follow-up (23 ± 7 months), the patients in the high-risk group had higher LGE entropy (p < 0.001) and LGE mass% (p < 0.001) than those in the low-risk group, and patients with endpoint events had higher LGE entropy (p < 0.001) and LGE mass% (p < 0.001) than those without endpoint events. In all participants, there was a link between LGE entropy and LGE mass%, according to the Spearman rank correlation analysis (p < 0.001; r = 0.667). In ROC analysis, the area under the curve (AUC) of LGE entropy was 0.893 (95% CI, 0.794-0.993; P<0.001), AUC of LGE mass% was 0.826 (95% CI, 0.737-0.914; P<0.001), AUC of LVEF was 0.610 (95% CI, 0.473-0.748; P = 0.117) and AUC of 2020 AHA/ACC guideline for risk stratification was 0.716 (95% CI, 0.617-0.815; P = 0.002). According to Kaplan-Meier curves, HCM with a higher LGE entropy (≥cutoff value (<5.873) or ≥ thied tertile (5.540)) were more likely to experience the endpoint events. Following adjustment for the 2020 AHA/ACC guideline for risk categorization, LGE mass%, or decreased LVEF, Cox analysis showed that LGE entropy was independently linked with endpoint events.

CONCLUSIONS

The variability and extent of LGE pictures can be reflected by LGE entropy, which is a reliable, usable, and repeatable metric for risk classification in HCM. It is a prognostic indicator of endpoint events that is independent of other risk indicators.

Progressive brain abnormalities in schizophrenia across different illness periods: a structural and functional MRI study

Schizophrenia is a chronic brain disorder, and neuroimaging abnormalities have been reported in different stages of the illness for decades. However, when and how these brain abnormalities occur and evolve remains undetermined. We hypothesized structural and functional brain abnormalities progress throughout the illness course at different rates in schizophrenia. A total of 115 patients with schizophrenia were recruited and stratified into three groups of different illness periods: 5-year group (illness duration: ≤5 years), 15-year group (illness duration: 12-18 years), and 25-year group (illness duration: ≥25 years); 230 healthy controls were matched by age and sex to the three groups, respectively. All participants underwent resting-state MRI scanning. Each group of patients with schizophrenia was compared with the corresponding controls in terms of voxel-based morphometry (VBM), fractional anisotropy (FA), global functional connectivity density (gFCD), and sample entropy (SampEn) abnormalities. In the 5-year group we observed only SampEn abnormalities in the putamen. In the 15-year group, we observed VBM abnormalities in the insula and cingulate gyrus and gFCD abnormalities in the temporal cortex. In the 25-year group, we observed FA abnormalities in nearly all white matter tracts, and additional VBM and gFCD abnormalities in the frontal cortex and cerebellum. By using two structural and two functional MRI analysis methods, we demonstrated that individual functional abnormalities occur in limited brain areas initially, functional connectivity and gray matter density abnormalities ensue later in wider brain areas, and structural connectivity abnormalities involving almost all white matter tracts emerge in the third decade of the course in schizophrenia.

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.

Lower resting brain entropy is associated with stronger task activation and deactivation

Brain entropy (BEN) calculated from resting state fMRI has been the subject of increasing research interest in recent years. Previous studies have shown the correlations between rest BEN and neurocognition and task performance, but how this relates to task-evoked brain activations and deactivations remains unknown. The purpose of this study is to address this open question using large data (n = 862). Voxel wise correlations were calculated between rest BEN and task activations/deactivations of five different tasks. For most of the assessed tasks, lower rest BEN was found to be associated with stronger activations (negative correlations) and stronger deactivations (positive correlations) only in brain regions activated or deactivated by the tasks. Higher workload evoked spatially more extended negative correlations between rest BEN and task activations. These results not only confirm that resting brain activity can predict brain activity during task performance but also for the first time show that resting brain activity may facilitate both task activations and deactivations. In addition, the results provide a clue to understanding the individual differences of task performance and brain activations.

Aberrant functional brain network dynamics in patients with functional constipation

The aberrant static functional connectivity of brain network has been widely investigated in patients with functional constipation (FCon). However, the dynamics of brain functional connectivity in FCon patients remained unknown. This study aimed to detect the brain dynamics of functional connectivity states and network topological organizations of FCon patients and investigate the correlations of the aberrant brain dynamics with symptom severity. Eighty-three FCon patients and 80 healthy subjects (HS) were included in data analysis. The spatial group independent component analysis, sliding-window approach, k-means clustering, and graph-theoretic analysis were applied to investigate the dynamic temporal properties and coupling patterns of functional connectivity states, as well as the time-variation of network topological organizations in FCon patients. Four reoccurring functional connectivity states were identified in k-means clustering analysis. Compared to HS, FCon patients manifested the lower occurrence rate and mean dwell time in the state with a complex connection between default mode network and cognitive control network, as well as the aberrant anterior insula-cortical coupling patterns in this state, which were significantly correlated with the symptom severity. The graph-theoretic analysis demonstrated that FCon patients had higher sample entropy at the nodal efficiency of anterior insula than HS. The current findings provided dynamic perspectives for understanding the brain connectome of FCon and laid the foundation for the potential treatment of FCon based on brain connectomics.

Complexity Analysis of Resting-State and Task fMRI Using Multiscale Sample Entropy

Functional magnetic resonance imaging (fMRI) is a powerful tool that allows for analysis of neural activity via the measurement of blood-oxygenation-level-dependent (BOLD) signal. The BOLD fluctuations can exhibit different levels of complexity, depending upon the conditions under which they are measured. We examined the complexity of both resting-state and task-based fMRI using sample entropy (SampEn) as a surrogate for signal predictability. We found that within most tasks, regions of the brain that were deemed task-relevant displayed significantly low levels of SampEn, and there was a strong negative correlation between parcel entropy and amplitude.

Relationship Between Basic Properties of BOLD Fluctuations and Calculated Metrics of Complexity in the Human Connectome Project

Resting state functional MRI (rs-fMRI) creates a rich four-dimensional data set that can be analyzed in a variety of ways. As more researchers come to view the brain as a complex dynamical system, tools are increasingly being drawn from other fields to characterize the complexity of the brain's activity. However, given that the signal measured with rs-fMRI arises from the hemodynamic response to neural activity, the extent to which complexity metrics reflect neural complexity as compared to signal properties related to image quality remains unknown. To provide some insight into this question, correlation dimension, approximate entropy and Lyapunov exponent were calculated for different rs-fMRI scans from the same subject to examine their reliability. The metrics of complexity were then compared to several properties of the rs-fMRI signal from each brain area to determine if basic signal features could explain differences in the complexity metrics. Differences in complexity across brain areas were highly reliable and were closely linked to differences in the frequency profiles of the rs-fMRI signal. The spatial distributions of the complexity and frequency metrics suggest that they are both influenced by location-dependent signal properties that can obscure changes related to neural activity.