Sample entropy reveals high discriminative power between young and elderly adults in short fMRI data sets

Smoking affects global and regional brain entropy in depression patients regardless of depression: Preliminary findings

OBJECTIVE

This study examines the effect of smoking on global and regional brain entropy in patients with Major Depressive Disorder (MDD), aiming to elucidate the relationship between smoking habits and brain network complexity in depression.

METHODS

The study enrolled 24 MDD patients, divided into smokers and non-smokers, from Alanya Alaaddin Keykubat University and Istanbul Medipol University. Resting-state fMRI data were acquired and processed. The complexity of neuronal activity was assessed using dispersion entropy, with statistical significance determined by a suite of tests including Kolmogorov-Smirnov, Student's t-test, and Mann-Whitney U test.

RESULTS

The smoking cohort exhibited higher global brain entropy compared to the non-smoking group (p = 0.033), with significant differences in various brain networks, indicating that smoking may alter global brain activity and network dynamics in individuals with MDD.

CONCLUSION

The study provides evidence that smoking is associated with increased brain entropy in MDD patients, suggesting that chronic smoking may influence cognitive and emotional networks. This underscores the importance of considering smoking history in the treatment and prognosis of MDD. The findings call for further research to understand the mechanistic links between smoking, brain entropy, and depression.

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.

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.

From local properties to brain-wide organization: A review of intraregional temporal features in functional magnetic resonance imaging data

Based on the fluctuations ensembled over neighbouring neurons, blood oxygen level-dependent (BOLD) signal is a mesoscale measurement of brain signals. Intraregional temporal features (IRTFs) of BOLD signal, extracted from regional neural activities, are utilized to investigate how the brain functions in local brain areas. This literature highlights four types of IRTFs and their representative calculations including variability in the temporal domain, variability in the frequency domain, entropy, and intrinsic neural timescales, which are tightly related to cognitions. In the brain-wide spatial organization, these brain features generally organized into two spatial hierarchies, reflecting structural constraints of regional dynamics and hierarchical functional processing workflow in brain. Meanwhile, the spatial organization gives rise to the link between neuronal properties and cognitive performance. Disrupted or unbalanced spatial conditions of IRTFs emerge with suboptimal cognitive states, which improved our understanding of the aging process and/or neuropathology of brain disease. This review concludes that IRTFs are important properties of the brain functional system and IRTFs should be considered in a brain-wide manner.

Altered brain entropy and functional connectivity patterns in generalized anxiety disorder patients

BACKGROUND

Generalized anxiety disorder (GAD) is a highly prevalent disease characterized by chronic, pervasive, and intrusive worry. Previous resting-state functional MRI (fMRI) studies on GAD have mainly focused on conventional static linear features. Entropy analysis of resting-state functional magnetic resonance imaging (rs-fMRI) has recently been adopted to characterize brain temporal dynamics in some neuropsychological or psychiatric diseases. However, the nonlinear dynamic complexity of brain signals has been rarely explored in GAD.

METHODS

We measured the approximate entropy (ApEn) and sample entropy (SampEn) of the resting-state fMRI data from 38 GAD patients and 37 matched healthy controls (HCs). The brain regions with significantly different ApEn and SampEn values between the two groups were extracted. Using these brain regions as seed points, we also investigated whether there are differences in whole brain resting-state function connectivity (RSFC) pattern between GADs and HCs. Correlation analysis was subsequently conducted to investigate the association between brain entropy, RSFC and the severity of anxiety symptoms. A linear support vector machine (SVM) was used to assess the discriminative power of BEN and RSFC features among GAD patients and HCs.

RESULTS

Compared to the HCs, patients with GAD showed increased levels of ApEn in the right angular cortex (AG) and increased levels of SampEn in the right middle occipital gyrus (MOG) as well as the right inferior occipital gyrus (IOG). Contrarily, compared to the HCs, patients with GAD showed decreased RSFC between the right AG and the right inferior parietal gyrus (IPG). The SVM-based classification model achieved 85.33 % accuracy (sensitivity: 89.19 %; specificity: 81.58 %; and area under the receiver operating characteristic curve: 0.9018). The ApEn of the right AG and the SVM-based decision value was positively correlated with the Hamilton Anxiety Scale (HAMA).

LIMITATIONS

This study used cross-sectional data and sample size was small.

CONCLUSION

Patients with GAD showed increased level of nonlinear dynamical complexity of ApEn in the right AG and decreased linear features of RSFC in the right IPG. Combining the linear and nonlinear features of brain signals may be used to effectively diagnose psychiatric disorders.

Reorganization of resting-state brain network functional connectivity across human brain developmental stages

Cognitive brain aging can either be healthy or degenerative in nature. Multiple alterations occur in brain networks with healthy aging. Much of this has yet to be investigated. This study seeks to understand the typical healthy human brain's developmental stages using a publicly available dataset from the human connectome project. As the human brain's developmental stage varies, we also intend to identify a pattern of reorganization in the resting state functional connectivity of several brain networks. The results are specifically presented based on the resting state BOLD signals of 1096 healthy volunteers between the age group of 7-89 years. The k-means clustering method has been used to determine the various human brain developmental stages. Using the t-SNE technique, the clusters are visually separated. BrainNet Viewer is used to study the changes in resting state functional connectivity of the entire brain as the human brain developmental stages vary. The age-related pattern of change in the resting state functional connectivity of six Dosenbasch brain networks that were grouped using the k-means elbow approach has been additionally presented. For performance evaluation, three metrics of brain network connection including network segregation, between network connectivity, and within-network connectivity are used. As the age cohort changes, a consistent pattern in the variance of these connection indices is seen for different Dosenbasch brain networks. Thus, the study's findings suggest that healthy aging causes a functional reorganization of the resting state brain network connections.

A Feasibility Study of Bilateral Wrist Sensors for Measuring Motor Traits in Children With Autism

Direct, quantitative measures of hyperactivity and motor coordination, two motor characteristics associated with impairment in autism, are limited. Wearable sensors can objectively index real-world movement variables that may relate to these behaviors. Here, we explored the feasibility of bilateral wrist accelerometers for measuring upper limb activity in 3-10-year-olds with autism (n = 22; 19 boys, 3 girls; M age = 5.64, SD = 2.73 years) and without autism (n = 26; 15 boys, 11 girls; M age = 6.26, SD = 2.47 years). We investigated the relationships between movement characteristics related to duration, intensity, complexity, and symmetry on the one hand and parent-reported hyperactivity and motor coordination on the other. Participants with and without autism wore the sensors for 12-hour periods. Sensor variables varied by age but not sex, with movement intensity and complexity moderately related to motor coordination. These findings lend preliminary support to wearable sensors as a means of providing ecologically-valid metrics of motor characteristics that impact adaptive function in children with autism.

Brain function complexity during dual-tasking is associated with cognitive impairment and age

BACKGROUND AND PURPOSE

Early diagnosis of cognitive impairment is important because symptoms can be delayed through therapies. Synaptic disconnections are the key characteristics of dementia, and through nonlinear complexity analysis of brain function, it is possible to identify long-range synaptic disconnections in the brain.

METHODS

We investigated the capability of a novel upper-extremity function (UEF) dual-task paradigm in the functional MRI (fMRI) setting, where the participant flexes and extends their arm while counting, to differentiate between cognitively normal (CN) and those with mild cognitive impairment (MCI). We used multiscale entropy (MSE) complexity analysis of the blood oxygen-level dependent time-series across neural networks and brain regions. Outside of the fMRI, we used the UEF dual-task test, while the elbow kinematics were measured using motion sensors, to record the motor function score.

RESULTS

Results showed 34% lower MSE values in MCI compared to CN (p<.04 for all regions and networks except cerebellum when counting down by one; effect size = 1.35±0.15) and a negative correlation between MSE values and age (average r2 of 0.30 for counting down by one and 0.36 for counting backward by three). Results also showed an improvement in the logistic regression model sensitivity by 14-24% in predicting the presence of MCI when brain function measure was added to the motor function score (kinematics data).

CONCLUSIONS

Current findings suggest that combining measures of neural network and motor function, in addition to neuropsychological testing, may provide an accurate tool for assessing early-stage cognitive impairment and age-related decline in cognition.

Nonlinear Analyses Distinguish Load Carriage Dynamics in Walking and Standing: A Systematic Review

Load carriage experiments are typically performed from a linear perspective that assumes that movement variability is equivalent to error or noise in the neuromuscular system. A complimentary, nonlinear perspective that treats variability as the object of study has generated important results in movement science outside load carriage settings. To date, no systematic review has yet been conducted to understand how load carriage dynamics change from a nonlinear perspective. The goal of this systematic review is to fill that need. Relevant literature was extracted and reviewed for general trends involving nonlinear perspectives on load carriage. Nonlinear analyses that were used in the reviewed studies included sample, multiscale, and approximate entropy; the Lyapunov exponent; fractal analysis; and relative phase. In general, nonlinear tools successfully distinguish between unloaded and loaded conditions in standing and walking, although not in a consistent manner. The Lyapunov exponent and entropy were the most used nonlinear methods. Two noteworthy findings are that entropy in quiet standing studies tends to decrease, whereas the Lyapunov exponent in walking studies tends to increase, both due to added load. Thus, nonlinear analyses reveal altered load carriage dynamics, demonstrating promise in applying a nonlinear perspective to load carriage while also underscoring the need for more research.

Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis

Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.

Dynamical Complexity Fingerprints of Occupation-Dependent Brain Functional Networks in Professional Seafarers

The complexity derived from resting-state functional magnetic resonance imaging (rs-fMRI) data has been applied for exploring cognitive states and occupational neuroplasticity. However, there is little information about the influence of occupational factors on dynamic complexity and topological properties of the connectivity networks. In this paper, we proposed a novel dynamical brain complexity analysis (DBCA) framework to explore the changes in dynamical complexity of brain activity at the voxel level and complexity topology for professional seafarers caused by long-term working experience. The proposed DBCA is made up of dynamical brain entropy mapping analysis and complex network analysis based on brain entropy sequences, which generate the dynamical complexity of local brain areas and the topological complexity across brain areas, respectively. First, the transient complexity of voxel-wise brain map was calculated; compared with non-seafarers, seafarers showed decreased dynamic entropy values in the cerebellum and increased values in the left fusiform gyrus (BA20). Further, the complex network analysis based on brain entropy sequences revealed small-worldness in terms of topological complexity in both seafarers and non-seafarers, indicating that it is an inherent attribute of human the brain. In addition, seafarers showed a higher average path length and lower average clustering coefficient than non-seafarers, suggesting that the information processing ability is reduced in seafarers. Moreover, the reduction in efficiency of seafarers suggests that they have a less efficient processing network. To sum up, the proposed DBCA is effective for exploring the dynamic complexity changes in voxel-wise activity and region-wise connectivity, showing that occupational experience can reshape seafarers’ dynamic brain complexity fingerprints.

Multivariate Classification of Brain Blood-Oxygen Signal Complexity for the Diagnosis of Children with Tourette Syndrome

Tourette syndrome (TS) is a childhood-onset neuropsychiatric disorder characterized by the presence of multiple motor and vocal tics. Because of its varied clinical expressions and lack of reliable diagnostic biomarker, present TS diagnosis still depends on qualitative descriptions of symptoms. Our study aimed to investigate whether the complexity of resting state brain activity can serve as a potential biomarker for TS diagnosis, since it has been used successfully in various neuropsychiatric disorders, including two common TS comorbidities: attention-deficit hyperactivity disorder (ADHD) and obsessive-compulsive disorder (OCD). In the current study, we used both univariate analysis and multivariate searchlight analysis with both linear and non-linear classification methods to explore the group differences in the complexity of resting state brain blood oxygen level-dependent (BOLD) signals between 25 TS boys without comorbidity and 25 sex, age and educational years matched healthy controls (HCs). We also investigated the relation between symptom severity in TS patients (YGTSS scores) and complexity indices derived from different analysis methods. We found: i) univariate analysis revealed reduced complexity in TS patients in the left cerebellum, left superior frontal gyrus, and left medial frontal gyrus; ii) multivariate analysis with non-linear classification method achieved the highest performance (accuracy: 0.94, sensitivity: 0.96, specificity: 0.92, AUC: 0.95) in bilateral supplementary motor areas; iii) significant correlations were found between complexity index derived from multivariate analysis with non-linear classification method and Tic severity (YGTSS scores) in the left cerebellum (r = 0.523, with YGTSS phonic) and in the right supplementary motor area (r = 0.767, with YGTSS motor). Taken together, these results suggested that complexity of resting state BOLD activity is a highly effective index for differentiating TS patients from normal controls. It has a good potential to be a quantitative biomarker for TS diagnosis.

The Application of Complexity Analysis in Brain Blood-Oxygen Signal

One of the daunting features of the brain is its physiology complexity, which arises from the interaction of numerous neuronal circuits that operate over a wide range of temporal and spatial scales, enabling the brain to adapt to the constantly changing environment and to perform various cognitive functions. As a reflection of the complexity of brain physiology, the complexity of brain blood-oxygen signal has been frequently studied in recent years. This paper reviews previous literature regarding the following three aspects: (1) whether the complexity of the brain blood-oxygen signal can serve as a reliable biomarker for distinguishing different patient populations; (2) which is the best algorithm for complexity measure? And (3) how to select the optimal parameters for complexity measures. We then discuss future directions for blood-oxygen signal complexity analysis, including improving complexity measurement based on the characteristics of both spatial patterns of brain blood-oxygen signal and latency of complexity itself. In conclusion, the current review helps to better understand complexity analysis in brain blood-oxygen signal analysis and provide useful information for future studies.

Interindividual Signatures of fMRI Temporal Fluctuations

The complexity and variability of human brain activity, such as quantified from Functional Magnetic Resonance Imaging (fMRI) time series, have been widely studied as potential markers of healthy and pathological states. However, the extent to which fMRI temporal features exhibit stable markers of inter-individual differences in brain function across healthy young adults is currently an open question. In this study, we draw upon two widely used time-series measures-a nonlinear complexity measure (sample entropy; SampEn) and a spectral measure of low-frequency content (fALFF)-to capture dynamic properties of resting-state fMRI in a large sample of young adults from the Human Connectome Project. We observe that these two measures are closely related, and that both generate reproducible patterns across brain regions over four different fMRI runs, with intra-class correlations of up to 0.8. Moreover, we find that both metrics can uniquely differentiate subjects with high identification rates (ca. 89%). Canonical correlation analysis revealed a significant relationship between multivariate brain temporal features and behavioral measures. Overall, these findings suggest that regional profiles of fMRI temporal characteristics may provide stable markers of individual differences, and motivate future studies to further probe relationships between fMRI time series metrics and behavior.

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

"Unrest while Resting"? Brain entropy in autism spectrum disorder

Biological systems typically exhibit complex behavior with nonlinear dynamic properties. Nonlinear signal processing techniques such as sample entropy is a novel approach to characterize the temporal dynamics of brain connectivity. Estimating entropy is especially important in clinical populations such as autism spectrum disorder (ASD) as differences in entropy may signal functional alterations in the brain. Considering the models of disrupted brain network connectivity in ASD, sample entropy would provide a novel direction to understand brain organization. Resting state fMRI data from 45 high-functioning children with ASD and 45 age-and-IQ-matched typically developing (TD) children were obtained from the Autism Brain Imaging Data Exchange (ABIDE-II) database. Data were preprocessed using the CONN toolbox. Sample entropy was then calculated using the complexity toolbox, in a whole-brain voxelwise manner as well as in regions of interests (ROIs) based methods. ASD participants demonstrated significantly increased entropy in left angular gyrus, superior parietal lobule, and right inferior temporal gyrus; and reduced sample entropy in superior frontal gyrus compared to TD participants. Positive correlations of average entropy in clusters of significant group differences scores across all subjects were found. Finally, ROI analysis revealed a main effect of lobes. Differences in entropy between the ASD and TD groups suggests that entropy may provide another important index of brain dysfunction in clinical populations like ASD. Further, the relationship between increased entropy and ASD symptoms in our study underscores the role of optimal brain synchronization in cognitive and behavioral functions.

Spatial variability of low frequency brain signal differentiates brain states

Temporal variability of the neural signal has been demonstrated to be closely related to healthy brain function. Meanwhile, the evolving brain functions are supported by dynamic relationships among brain regions. We hypothesized that the spatial variability of brain signal might provide important information about brain function. Here we used the spatial sample entropy (SSE) to investigate the spatial variability of neuroimaging signal during a steady-state presented face detection task. Lower SSE was found during task state than during resting state, associating with more repetitive functional interactions between brain regions. The standard deviation (SD) of SSE during the task was negatively related to the SD of reaction time, suggesting that the spatial pattern of neural activity is reorganized according to particular cognitive function and supporting the previous theory that greater variability is associated with better task performance. These results were replicated with reordered data, implying the reliability of SSE in measuring the spatial organization of neural activity. Overall, the present study extends the research scope of brain signal variability from the temporal dimension to the spatial dimension, improving our understanding of the spatiotemporal characteristics of brain activities and the theory of brain signal variability.

Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study

Bipolar Disorder (BD) is an illness with high prevalence and a huge social and economic impact. It is recurrent, with a long-term evolution in most cases. Early treatment and continuous monitoring have proven to be very effective in mitigating the causes and consequences of BD. However, no tools are currently available for a massive and semi-automatic BD patient monitoring and control. Taking advantage of recent technological developments in the field of wearables, this paper studies the feasibility of a BD episodes classification analysis while using entropy measures, an approach successfully applied in a myriad of other physiological frameworks. This is a very difficult task, since actigraphy records are highly non-stationary and corrupted with artifacts (no activity). The method devised uses a preprocessing stage to extract epochs of activity, and then applies a quantification measure, Slope Entropy, recently proposed, which outperforms the most common entropy measures used in biomedical time series. The results confirm the feasibility of the approach proposed, since the three states that are involved in BD, depression, mania, and remission, can be significantly distinguished.

Fever Time Series Analysis Using Slope Entropy. Application to Early Unobtrusive Differential Diagnosis

Fever is a readily measurable physiological response that has been used in medicine for centuries. However, the information provided has been greatly limited by a plain thresholding approach, overlooking the additional information provided by temporal variations and temperature values below such threshold that are also representative of the subject status. In this paper, we propose to utilize continuous body temperature time series of patients that developed a fever, in order to apply a method capable of diagnosing the specific underlying fever cause only by means of a pattern relative frequency analysis. This analysis was based on a recently proposed measure, Slope Entropy, applied to a variety of records coming from dengue and malaria patients, among other fever diseases. After an input parameter customization, a classification analysis of malaria and dengue records took place, quantified by the Matthews Correlation Coefficient. This classification yielded a high accuracy, with more than 90% of the records correctly labelled in some cases, demonstrating the feasibility of the approach proposed. This approach, after further studies, or combined with more measures such as Sample Entropy, is certainly very promising in becoming an early diagnosis tool based solely on body temperature temporal patterns, which is of great interest in the current Covid-19 pandemic scenario.

Entropy and the Brain: An Overview

Entropy is a powerful tool for quantification of the brain function and its information processing capacity. This is evident in its broad domain of applications that range from functional interactivity between the brain regions to quantification of the state of consciousness. A number of previous reviews summarized the use of entropic measures in neuroscience. However, these studies either focused on the overall use of nonlinear analytical methodologies for quantification of the brain activity or their contents pertained to a particular area of neuroscientific research. The present study aims at complementing these previous reviews in two ways. First, by covering the literature that specifically makes use of entropy for studying the brain function. Second, by highlighting the three fields of research in which the use of entropy has yielded highly promising results: the (altered) state of consciousness, the ageing brain, and the quantification of the brain networks' information processing. In so doing, the present overview identifies that the use of entropic measures for the study of consciousness and its (altered) states led the field to substantially advance the previous findings. Moreover, it realizes that the use of these measures for the study of the ageing brain resulted in significant insights on various ways that the process of ageing may affect the dynamics and information processing capacity of the brain. It further reveals that their utilization for analysis of the brain regional interactivity formed a bridge between the previous two research areas, thereby providing further evidence in support of their results. It concludes by highlighting some potential considerations that may help future research to refine the use of entropic measures for the study of brain complexity and its function. The present study helps realize that (despite their seemingly differing lines of inquiry) the study of consciousness, the ageing brain, and the brain networks' information processing are highly interrelated. Specifically, it identifies that the complexity, as quantified by entropy, is a fundamental property of conscious experience, which also plays a vital role in the brain's capacity for adaptation and therefore whose loss by ageing constitutes a basis for diseases and disorders. Interestingly, these two perspectives neatly come together through the association of entropy and the brain capacity for information processing.

Acute Alcohol Intake Produces Widespread Decreases in Cortical Resting Signal Variability in Healthy Social Drinkers

BACKGROUND

Acute alcohol intoxication has wide-ranging neurobehavioral effects on psychomotor, attentional, inhibitory, and memory-related cognitive processes. These effects are mirrored in disruption of neural metabolism, functional activation, and functional network coherence. Metrics of intraregional neural dynamics such as regional signal variability (RSV) and brain entropy (BEN) may capture unique aspects of neural functional capacity in healthy and clinical populations; however, alcohol's influence on these metrics is unclear. The present study aimed to elucidate the influence of acute alcohol intoxication on RSV and to clarify these effects with subsequent BEN analyses.

METHODS

26 healthy adults between 25 and 45 years of age (65.4% women) participated in 2 counterbalanced sessions. In one, participants consumed a beverage containing alcohol sufficient to produce a breath alcohol concentration of 0.08 g/dl. In the other, they consumed a placebo beverage. Approximately 35 minutes after beverage consumption, participants completed a 9-minute resting-state fMRI scan. Whole-brain, voxel-wise standard deviation was used to assess RSV, which was compared between sessions. Within clusters displaying alterations in RSV, sample entropy was calculated to assess BEN.

RESULTS

Compared to the placebo, alcohol intake resulted in widespread reductions in RSV in the bilateral middle frontal, right inferior frontal, right superior frontal, bilateral posterior cingulate, bilateral middle temporal, right supramarginal gyri, and bilateral inferior parietal lobule. Within these clusters, significant reductions in BEN were found in the bilateral middle frontal and right superior frontal gyri. No effects were noted in subcortical or cerebellar areas.

CONCLUSIONS

Findings indicate that alcohol intake produces diffuse reductions in RSV among structures associated with attentional processes. Within these structures, signal complexity was also reduced in a subset of frontal regions. Neurobehavioral effects of acute alcohol consumption may be partially driven by disruption of intraregional neural dynamics among regions involved in higher-order cognitive and attentional processes.

Entropy of Real-World Gait in Parkinson's Disease Determined from Wearable Sensors as a Digital Marker of Altered Ambulatory Behavior

Parkinson’s disease (PD) is a common age-related neurodegenerative disease. Gait impairment is frequent in the later stages of PD contributing to reduced mobility and quality of life. Digital biomarkers such as gait velocity and step length are predictors of motor and cognitive decline in PD. Additional gait parameters may describe different aspects of gait and motor control in PD. Sample entropy (SampEnt), a measure of signal predictability, is a nonlinear approach that quantifies regularity of a signal. This study investigated SampEnt as a potential biomarker for PD and disease duration. Real-world gait data over a seven-day period were collected using an accelerometer (Axivity AX3, York, UK) placed on the low back and gait metrics extracted. SampEnt was determined for the stride time, with vector length and threshold parameters optimized. People with PD had higher stride time SampEnt compared to older adults, indicating reduced gait regularity. The range of SampEnt increased over 36 months for the PD group, although the mean value did not change. SampEnt was associated with dopaminergic medication dose but not with clinical motor scores. In conclusion, this pilot study indicates that SampEnt from real-world data may be a useful parameter reflecting clinical status although further research is needed involving larger populations.

Reduced Complexity in Stroke with Motor Deficits: A Resting-State fMRI Study

Recently, alterations of complexity due to brain disorders have been demonstrated using brain entropy (BEN), while the changes of brain complexity in stroke, a common cerebrovascular disease, remain unclear. In this research, resting-state functional magnetic resonance imaging (fMRI) was performed to explore the alterations of brain complexity using BEN in twenty stroke patients with motor deficits and nineteen matched healthy controls. The sample entropy (SampEn) was applied to build the BEN mapping for each participant. Compared with healthy controls, stroke patients exhibited lower BEN values in the contralesional precentral gyrus (preCG), bilateral dorsolateral frontal gyrus (SFGdor) and bilateral supplementary motor area (SMA). Moreover, significantly positive correlations between BEN values and Fugl-Meyer Assessment scores were detected in the ipsilesional SFGdor and ipsilesional SMA. Mutual information independence was observed between BEN and regional homogeneity (ReHo), amplitude of low-frequency fluctuations (ALFF), respectively, in the stroke patients. Our findings implied that brain complexity had been impacted after stroke, and also suggested that BEN could be a complementary tool for evaluating the motor impairment after stroke.

Sample Entropy Combined with the K-Means Clustering Algorithm Reveals Six Functional Networks of the Brain

Identifying brain regions contained in brain functional networks and functions of brain functional networks is of great significance in understanding the complexity of the human brain. The 160 regions of interest (ROIs) in the human brain determined by the Dosenbach’s template have been divided into six functional networks with different functions. In the present paper, the complexity of the human brain is characterized by the sample entropy (SampEn) of dynamic functional connectivity (FC) which is obtained by analyzing the resting-state functional magnetic resonance imaging (fMRI) data acquired from healthy participants. The 160 ROIs are clustered into six clusters by applying the K-means clustering algorithm to the SampEn of dynamic FC as well as the static FC which is also obtained by analyzing the resting-state fMRI data. The six clusters obtained from the SampEn of dynamic FC and the static FC show very high overlap and consistency ratios with the six functional networks. Furthermore, for four of six clusters, the overlap ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC, and for five of six clusters, the consistency ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC. The results show that the combination of machine learning methods and the FC obtained using the blood oxygenation level-dependent (BOLD) signals can identify the functional networks of the human brain, and nonlinear dynamic characteristics of the FC are more effective than the static characteristics of the FC in identifying brain functional networks and the complexity of the human brain.

Evidence for Maintained Post-Encoding Memory Consolidation Across the Adult Lifespan Revealed by Network Complexity

Memory consolidation is well known to occur during sleep, but might start immediately after encoding new information while awake. While consolidation processes are important across the lifespan, they may be even more important to maintain memory functioning in old age. We tested whether a novel measure of information processing known as network complexity might be sensitive to post-encoding consolidation mechanisms in a sample of young, middle-aged, and older adults. Network complexity was calculated by assessing the irregularity of brain signals within a network over time using multiscale entropy. To capture post-encoding mechanisms, network complexity was estimated using functional magnetic resonance imaging (fMRI) during rest before and after encoding of picture pairs, and subtracted between the two rest periods. Participants received a five-alternative-choice memory test to assess associative memory performance. Results indicated that aging was associated with an increase in network complexity from pre- to post-encoding in the default mode network (DMN). Increases in network complexity in the DMN also were associated with better subsequent memory across all age groups. These findings suggest that network complexity is sensitive to post-encoding consolidation mechanisms that enhance memory performance. These post-encoding mechanisms may represent a pathway to support memory performance in the face of overall memory declines.

Resting-state brain entropy in right temporal lobe epilepsy and its relationship with alertness

BACKGROUND

To date, no functional MRI (fMRI) studies have focused on brain entropy in right temporal lobe epilepsy (rTLE) patients. Here, we characterized brain entropy (BEN) alterations in patients with rTLE using resting-state functional MRI(rs-fMRI) and explored the relationship between BEN and alertness.

METHOD

Thirty-one rTLE patients and 33 controls underwent MRI scanning to investigate differences in BEN and resting-state functional connectivity (rs-FC) in regions of interest (ROIs) between patients and controls. Correlation analyses were performed to examine relationships between the BEN of each ROI and alertness reaction times (RTs) in rTLE patients.

RESULTS

Compared with controls, the BEN of rTLE patients was significantly increased in the right middle temporal gyrus, inferior temporal gyrus, and other regions of the left hemisphere and significantly decreased in the right middle frontal gyrus and left supplementary motor area (p < .05). The rs-FCs between the ROIs (at p < .01, with the left superior parietal lobule and right precentral gyrus defined as ROI1 and ROI2, respectively) and the whole brain showed an increasing trend in rTLE patients. In addition, the BEN of ROI2 was associated with the intrinsic alertness and phasic alertness RTs of patients with rTLE.

CONCLUSIONS

Our findings suggest that BEN is altered in patients with rTLE and that decreased BEN in the right precentral gyrus is positively related to intrinsic and phasic alertness; the abnormal FC in the brain regions with altered entropy suggests a reconstruction of brain functional connectivity. These findings suggest that BEN mapping may provide a useful tool for probing brain mechanisms related to TLE.

A Study of Brain Neuronal and Functional Complexities Estimated Using Multiscale Entropy in Healthy Young Adults

Brain complexity estimated using sample entropy and multiscale entropy (MSE) has recently gained much attention to compare brain function between diseased or neurologically impaired groups and healthy control groups. Using resting-state functional magnetic resonance imaging (rfMRI) blood oxygen-level dependent (BOLD) signals in a large cohort (n = 967) of healthy young adults, the present study maps neuronal and functional complexities estimated by using MSE of BOLD signals and BOLD phase coherence connectivity, respectively, at various levels of the brain’s organization. The functional complexity explores patterns in a higher dimension than neuronal complexity and may better discern changes in brain functioning. The leave-one-subject-out cross-validation method is used to predict fluid intelligence using neuronal and functional complexity MSE values as features. While a wide range of scales was selected with neuronal complexity, only the first three scales were selected with functional complexity. Fewer scales are advantageous as they preclude the need for long BOLD signals to calculate good estimates of MSE. The presented results corroborate with previous findings and provide a baseline for other studies exploring the use of MSE to examine changes in brain function related to aging, diseases, and clinical disorders.

Motion During Acquisition is Associated With fMRI Brain Entropy

Measures of fMRI brain entropy have been used to investigate age and disease related neural changes. However, it is unclear if movement in the scanner is associated with brain entropy after geometric correction for movement. As age and disease can affect motor control, quantifying and correcting for the influence of movement will avoid false findings. This paper examines the influence of head motion on fMRI brain entropy. Resting-state and task-based fMRI data from 281 individuals born in Aberdeen between 1950 and 1956 were analyzed. The images were realigned, followed by nuisance regression of the head motion parameters. The images were either high-pass filtered (0.008 Hz) or band-pass (0.008-0.1 Hz) filtered in order to compare the two methods; fuzzy approximate entropy and fuzzy sample entropy were calculated for every voxel. Motion was quantified as the mean displacement and mean rotation in three dimensions. Greater mean motion was correlated with decreased entropy for all four methods of calculating entropy. Different movement characteristics produce different patterns of associations, which appear to be artefact. However, across all motion metrics, entropy calculation methods, and scan conditions, a number of regions consistently show a significant negative association: the right cerebellar crus, left precentral gyrus (primary motor cortex), the left postcentral gyrus (primary somatosensory cortex), and the opercular part of the left inferior frontal gyrus. The robustness of our findings at these locations suggests that decreased entropy in specific brain regions may be a marker for decreased motor control.

Spatial complexity of brain signal is altered in patients with generalized anxiety disorder

BACKGROUND

Is it healthy to be chaotic? Recent studies have argued that mental disorders are associated with more orderly neural activities, corresponding to a less flexible functional system. These conclusions were derived from altered temporal complexity. However, the relationship between spatial complexity and health is unknown, although spatial configuration is of importance for normal brain function.

METHODS

Based on resting-state functional magnetic resonance imaging data, we used Sample entropy (SampEn) to evaluate the altered spatial complexity in patients with generalized anxiety disorder (GAD; n = 47) compared to healthy controls (HCs; n = 38) and the relationship between spatial complexity and anxiety level.

RESULTS

Converging results showed increased spatial complexity in patients with GAD, indicating more chaotic spatial configuration. Interestingly, inverted-U relationship was revealed between spatial complexity and anxiety level, suggesting complex relationship between health and the chaos of human brain.

LIMITATIONS

Anxiety-related alteration of spatial complexity should be verified at voxel level in a larger sample and compared with results of other indices to clarify the mechanism of spatial chaotic of anxiety.

CONCLUSIONS

Altered spatial complexity in the brain of GAD patients mirrors inverted-U relationship between anxiety and behavioral performance, which may reflect an important characteristic of anxiety. These results indicate that SampEn is a good reflection of human health or trait mental characteristic.

Validating team communication data using a transmission-duration threshold and voice activity detection algorithm

The processes underlying team effectiveness can be understood by analyzing the temporal dynamics of team communication sequences. The results of such analyses have shown that the complexity of team communication is associated with team performance on task-related variables, and hence communication complexity statistics have been proposed for use as measures for real-time feedback on team performance. In two analyses of historical team communication sequences, we found that filtering via use of a transmission-duration threshold and voice activity detection algorithm resulted in significant changes in complexity relative to not filtering the data or using a transmission-duration filter alone. The use of these filtering techniques showed significant effects on the complexity of communication sequences in both a laboratory-based experiment, with participants with little experience with voice communication protocols, and in a mission simulation with trained military operators. There was also a significant non-linear relationship between the complexity of communication sequences and task performance. However, an analysis of the impact of the changes in communication dynamics gained through filtering did not demonstrate that the changed temporal dynamics of filtered data better explained team performance. It is concluded that pre-filtering of invalid communication data should be included during the data cleaning stage of statistical analysis as a matter of good scientific practice. Furthermore, such use of filtering will ensure that inferences made about the relationship between the complexity of communication between team members and their performance are not confounded by the presence of invalid communication events.

Default Mode Network Complexity and Cognitive Decline in Mild Alzheimer's Disease

The human resting-state is characterized by spatially coherent brain activity at a low temporal frequency. The default mode network (DMN), one of so-called resting-state networks, has been associated with cognitive processes that are directed toward the self, such as introspection and autobiographic memory. The DMN's integrity appears to be crucial for mental health. For example, patients with Alzheimer's disease or other psychiatric conditions show disruptions of functional connectivity within the brain regions of the DMN. However, in prodromal or early stages of Alzheimer's disease, physiological alterations are sometimes elusive, despite manifested cognitive impairment. While functional connectivity assesses the signal correlation between brain areas, multi-scale entropy (MSE) measures the complexity of the blood-oxygen level dependent signal within an area and thus might show local changes before connectivity is affected. Hence, we investigated alterations of functional connectivity and MSE within the DMN in fifteen mild Alzheimer's disease patients as compared to fourteen controls. Potential associations of MSE with functional connectivity and cognitive abilities [i.e., mini-mental state examination (MMSE)] were assessed. A moderate decrease of DMN functional connectivity between posterior cingulate cortex and right hippocampus in Alzheimer's disease was found, whereas no differences were evident for whole-network functional connectivity. In contrast, the Alzheimer's disease group yielded lower global DMN-MSE than the control group. The most pronounced regional effects were localized in left and right hippocampi, and this was true for most scales. Moreover, MSE significantly correlated with functional connectivity, and DMN-MSE correlated positively with the MMSE in Alzheimer's disease. Most interestingly, the right hippocampal MSE was positively associated with semantic memory performance. Thus, our results suggested that cognitive decline in Alzheimer's disease is reflected by decreased signal complexity in DMN nodes, which might further lead to disrupted DMN functional connectivity. Additionally, altered entropy in Alzheimer's disease found in the majority of the scales indicated a disturbance of both local information processing and information transfer between distal areas. Conclusively, a loss of nodal signal complexity potentially impairs synchronization across nodes and thus preempts functional connectivity changes. MSE presents a putative functional marker for cognitive decline that might be more sensitive than functional connectivity alone.

A Strategy to Reduce Bias of Entropy Estimates in Resting-State fMRI Signals

Complexity analysis of resting-state blood oxygen level-dependent (BOLD) signals using entropy methods has attracted considerable attention. However, investigation on the bias of entropy estimates in resting-state functional magnetic resonance imaging (fMRI) signals and a general strategy for selecting entropy parameters is lacking. In this paper, we present a minimizing error approach to reduce the bias of sample entropy (SampEn) and multiscale entropy (MSE) in resting-state fMRI data. The strategy explored a range of parameters that minimized the relative error of SampEn of BOLD signals in cerebrospinal fluids where minimal physiologic information was present, and applied these parameters to calculate SampEn of BOLD signals in gray matter regions. We examined the effect of various parameters on the results of SampEn and MSE analyses of a large normal aging adult cohort (354 healthy subjects aged 21-89 years). The results showed that a tradeoff between pattern length m and tolerance factor r was necessary to maintain the accuracy of SampEn estimates. Furthermore, an increased relative error of SampEn was associated with an increased coefficient of variation in voxel-wise statistics. Overall, the parameters m = 1 and r = 0.20-0.45 provided reliable MSE estimates in short resting-state fMRI signals. For a single-scale SampEn analysis, a wide range of parameters was available with data lengths of at least 97 time points. This study provides a minimization error strategy for future studies on the non-linear analysis of resting-state fMRI signals to account for the bias of entropy estimates.

Brain function characteristics of chronic fatigue syndrome: A task fMRI study

The mechanism underlying neurological dysfunction in chronic fatigue syndrome/myalgic encephalomyelitis (CFS/ME) is yet to be established. This study investigated the temporal complexity of blood oxygenation level dependent (BOLD) changes in response to the Stroop task in CFS patients. 43 CFS patients (47.4 ± 11.8 yrs) and 26 normal controls (NCs, 43.4 ± 13.9 yrs) were included in this study. Their mental component summary (MCS) and physical component summary (PCS) from the 36-item Short Form Health Survey (SF-36) questionnaire were recorded. Their Stroop colour-word task performance was measured by accuracy and response time (RT). The BOLD changes associated with the Stroop task were evaluated using a 2-level general linear model approach. The temporal complexity of the BOLD responses, a measure of information capacity and thus adaptability to a challenging environment, in each activated region was measured by sample entropy (SampEn). The CFS patients showed significantly longer RTs than the NCs (P < 0.05) but no significant difference in accuracy. One sample t-tests for the two groups (Family wise error adjusted PFWE < 0.05) showed more BOLD activation regions in the CFS, although a two sample group comparison did not show significant difference. BOLD SampEns in ten regions were significantly lower (FDR-q < 0.05) in CFS patients. BOLD SampEns in 15 regions were significantly associated with PCS (FDR-q < 0.05) and in 9 regions were associated with MCS (FDR-q < 0.05) across all subjects. SampEn of the BOLD signal in the medioventral occipital cortex could explain 40% and 31% of the variance in the SF-36 PCS and MCS scores, and those in the precentral gyrus could explain an additional 16% and 7% across all subjects. This is the first study to investigate BOLD signal SampEn in response to tasks in CFS. The results suggest the brain responds differently to a cognitive challenge in patients with CFS, with recruitment of wider regions to compensate for lower information capacity.

Occupational functional plasticity revealed by brain entropy: A resting-state fMRI study of seafarers

Recently, functional magnetic resonance imaging (fMRI) has been increasingly used to assess brain function. Brain entropy is an effective model for evaluating the alteration of brain complexity. Specifically, the sample entropy (SampEn) provides a feasible solution for revealing the brain's complexity. Occupation is one key factor affecting the brain's activity, but the neuropsychological mechanisms are still unclear. Thus, in this article, based on fMRI and a brain entropy model, we explored the functional complexity changes engendered by occupation factors, taking the seafarer as an example. The whole-brain entropy values of two groups (i.e., the seafarers and the nonseafarers) were first calculated by SampEn and followed by a two-sample t test with AlphaSim correction (p < .05). We found that the entropy of the orbital-frontal gyrus (OFG) and superior temporal gyrus (STG) in the seafarers was significantly higher than that of the nonseafarers. In addition, the entropy of the cerebellum in the seafarers was lower than that of the nonseafarers. We conclude that (1) the lower entropy in the cerebellum implies that the seafarers' cerebellum activity had strong regularity and consistency, suggesting that the seafarer's cerebellum was possibly more specialized by the long-term career training; (2) the higher entropy in the OFG and STG possibly demonstrated that the seafarers had a relatively decreased capability for emotion control and auditory information processing. The above results imply that the seafarer occupation indeed impacted the brain's complexity, and also provided new neuropsychological evidence of functional plasticity related to one's career.

Multiscale energy reallocation during low-frequency steady-state brain response

Traditional task-evoked brain activations are based on detection and estimation of signal change from the mean signal. By contrast, the low-frequency steady-state brain response (lfSSBR) reflects frequency-tagging activity at the fundamental frequency of the task presentation and its harmonics. Compared to the activity at these resonant frequencies, brain responses at nonresonant frequencies are largely unknown. Additionally, because the lfSSBR is defined by power change, we hypothesize using Parseval's theorem that the power change reflects brain signal variability rather than the change of mean signal. Using a face recognition task, we observed power increase at the fundamental frequency (0.05 Hz) and two harmonics (0.1 and 0.15 Hz) and power decrease within the infra-slow frequency band (<0.1 Hz), suggesting a multifrequency energy reallocation. The consistency of power and variability was demonstrated by the high correlation (r > .955) of their spatial distribution and brain-behavior relationship at all frequency bands. Additionally, the reallocation of finite energy was observed across various brain regions and frequency bands, forming a particular spatiotemporal pattern. Overall, results from this study strongly suggest that frequency-specific power and variability may measure the same underlying brain activity and that these results may shed light on different mechanisms between lfSSBR and brain activation, and spatiotemporal characteristics of energy reallocation induced by cognitive tasks.

Signal Complexity of Human Intracranial EEG Tracks Successful Associative-Memory Formation across Individuals

Memory performance is highly variable among individuals. Most studies examining human memory, however, have largely focused on the neural correlates of successful memory formation within individuals, rather than the differences among them. As such, what gives rise to this variability is poorly understood. Here, we examined intracranial EEG (iEEG) recordings captured from 43 participants (23 male) implanted with subdural electrodes for seizure monitoring as they performed a paired-associates verbal memory task. We identified three separate but related signatures of neural activity that tracked differences in successful memory formation across individuals. High-performing individuals consistently exhibited less broadband power, flatter power spectral density slopes, and greater complexity in their iEEG signals. Furthermore, within individuals across three separate time scales ranging from seconds to days, successful recall was positively associated with these same metrics. Our data therefore suggest that memory ability across individuals can be indexed by increased neural signal complexity.SIGNIFICANCE STATEMENT We show that participants whose intracranial EEG exhibits less low-frequency power, flatter power spectrums, and greater sample entropy overall are better able to memorize associations, and that the same metrics track fluctuations in memory performance across time within individuals. These metrics together signify greater neural signal complexity, which may index the brain's ability to flexibly engage with information and generate separable memory representations. Critically, the current set of results provides a unique window into the neural markers of individual differences in memory performance, which have hitherto been underexplored.

Study of memory deficit in Alzheimer's disease by means of complexity analysis of fNIRS signal

Working memory deficit is a signature of Alzheimer's disease (AD). The free and cued selective reminding test (FCSRT) is a clinical test that quantifies memory deficit for AD diagnosis. However, the diagnostic accuracy of FCSRT may be increased by accompanying it with neuroimaging. Since the test requires doctor-patient interaction, brain monitoring is challenging. Functional near-infrared spectroscopy (fNIRS) could be suited for such a purpose because of the fNIRS flexibility. We investigated whether the complexity, based on sample entropy and multiscale entropy metrics, of the fNIRS signal during FCSRT was correlated with memory deficit in early AD. fNIRS signals were recorded over the prefrontal cortex of healthy and early AD participants. Group differences were tested through Wilcoxon-Mann-Whitney test ([Formula: see text]). At group level, we found significant differences for Brodmann areas 9 and 46. The results, although preliminary, demonstrate the feasibility of performing ecological studies on early AD with fNIRS. This approach may provide a potential neuroimaging-based method for diagnosis of early AD, viable at the doctor's office level, improving test-based diagnosis. The increased entropy of the fNIRS signal in early AD suggests the opportunity for further research on the neurophysiological status in AD and its relevance for clinical symptoms.

Predicting clinical symptoms of attention deficit hyperactivity disorder based on temporal patterns between and within intrinsic connectivity networks

Attention deficit hyperactivity disorder (ADHD) is a common brain disorder with high prevalence in school-age children. Previously developed machine learning-based methods have discriminated patients with ADHD from normal controls by providing label information of the disease for individuals. Inattention and impulsivity are the two most significant clinical symptoms of ADHD. However, predicting clinical symptoms (i.e., inattention and impulsivity) is a challenging task based on neuroimaging data. The goal of this study is twofold: to build predictive models for clinical symptoms of ADHD based on resting-state fMRI and to mine brain networks for predictive patterns of inattention and impulsivity. To achieve this goal, a cohort of 74 boys with ADHD and a cohort of 69 age-matched normal controls were recruited from the ADHD-200 Consortium. Both structural and resting-state fMRI images were obtained for each participant. Temporal patterns between and within intrinsic connectivity networks (ICNs) were applied as raw features in the predictive models. Specifically, sample entropy was taken asan intra-ICN feature, and phase synchronization (PS) was used asan inter-ICN feature. The predictive models were based on the least absolute shrinkage and selectionator operator (LASSO) algorithm. The performance of the predictive model for inattention is r=0.79 (p<10^-8), and the performance of the predictive model for impulsivity is r=0.48 (p<10^-8). The ICN-related predictive patterns may provide valuable information for investigating the brain network mechanisms of ADHD. In summary, the predictive models for clinical symptoms could be beneficial for personalizing ADHD medications.

Sample entropy reveals an age-related reduction in the complexity of dynamic brain

Dynamic reconfiguration of the human brain is characterized by the nature of complexity. The purpose of this study was to measure such complexity and also analyze its association with age. We modeled the dynamic reconfiguration process by dynamic functional connectivity, which was established by resting-state functional magnetic resonance imaging (fMRI) data, and we measured complexity within the dynamic functional connectivity by sample entropy (SampEn). A brainwide map of SampEn in healthy subjects shows larger values in the caudate, the olfactory gyrus, the amygdala, and the hippocampus, and lower values in primary sensorimotor and visual areas. Association analysis in healthy subjects indicated that SampEn of the amygdala-cortical connectivity decreases with advancing age. Such age-related loss of SampEn, however, disappears in patients with schizophrenia. These findings suggest that SampEn of the dynamic functional connectivity is a promising indicator of normal aging.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics

This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.

Aging and cardiovascular complexity: effect of the length of RR tachograms

As we age, our hearts undergo changes that result in a reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, three complexity measures are used, namely Lempel-Ziv complexity (LZ), Sample Entropy (SampEn) and Effort-To-Compress (ETC). We determined the minimum length of RR tachogram required for characterizing complexity of healthy young and healthy old hearts. All the three measures indicated significantly lower complexity values for older subjects than younger ones. However, the minimum length of heart-beat interval data needed differs for the three measures, with LZ and ETC needing as low as 10 samples, whereas SampEn requires at least 80 samples. Our study indicates that complexity measures such as LZ and ETC are good candidates for the analysis of cardiovascular dynamics since they are able to work with very short RR tachograms.

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

A retrospective analysis of the effect of blood transfusion on cerebral oximetry entropy and acute kidney injury

Purpose:

Acute anemia is associated with both cerebral dysfunction and acute kidney injury and is often treated with red blood cell transfusion. We sought to determine if blood transfusion changed the cerebral oximetry entropy, a measure of the complexity or irregularity of the oximetry values, and if this change was associated with subsequent acute kidney injury.

Methods:

This was a retrospective, case-control study of patients undergoing cardiac surgery with cardiopulmonary bypass at a tertiary care hospital, comparing those who received a red blood cell transfusion to those who did not. Acute kidney injury was defined as a perioperative increase in serum creatinine by ⩾26.4 μmol/L or by ⩾50% increase. Entropy was measured using approximate entropy, sample entropy, forbidden word entropy and basescale4 entropy in 500-point sets.

Results:

Forty-four transfused patients were matched to 88 randomly selected non-transfused patients. All measures of entropy had small changes in the transfused group, but increased in the non-transfused group (p<0.05, for all comparisons). Thirty-five of 132 patients (27%) suffered acute kidney injury. Based on preoperative factors, patients who suffered kidney injury were similar to those who did not, including baseline cerebral oximetry levels. After analysis with hierarchical logistic regression, the change in basescale4 entropy (odds ratio = 1.609, 95% confidence interval = 1.057–2.450, p = 0.027) and the interaction between basescale entropy and transfusion were significantly associated with subsequent development of acute kidney injury.

Conclusions:

The transfusion of red blood cells was associated with a smaller rise in entropy values compared to non-transfused patients, suggesting a change in the regulation of cerebral oxygenation, and these changes in cerebral oxygenation are also associated with acute kidney injury.

An explorative investigation of functional differences in plantar center of pressure of four foot types using sample entropy method

In the study of biomechanics of different foot types, temporal or spatial parameters derived from plantar pressure are often used. However, there is no comparative study of complexity and regularity of the center of pressure (CoP) during the stance phase among pes valgus, pes cavus, hallux valgus and normal foot. We aim to analyze whether CoP sample entropy characteristics differ among these four foot types. In our experiment participated 40 subjects with normal feet, 40 with pes cavus, 19 with pes valgus and 36 with hallux valgus. A Footscan^® system was used to collect CoP data. We used sample entropy to quantify several parameters of the investigated four foot types. These are the displacement in medial–lateral (M/L) and anterior–posterior (A/P) directions, as well as the vertical ground reaction force of CoP during the stance phase. To fully examine the potential of the sample entropy method for quantification of CoP components, we provide results for two cases: calculating the sample entropy of normalized CoP components, as well as calculating it using the raw data of CoP components. We also explored what are the optimal values of parameters m (the matching length) and r (the tolerance range) when calculating the sample entropy of CoP data obtained during the stance phases. According to statistical results, some factors significantly influenced the sample entropy of CoP components. The sample entropies of non-normalized A/P values for the left foot, as well as for the right foot, were different between the normal foot and pes valgus, and between the normal foot and hallux valgus. The sample entropy of normalized M/L displacement of the right foot was different between the normal foot and pes cavus. The measured variable for A/P and M/L displacements could serve for the study of foot function.

Exploiting Complexity Information for Brain Activation Detection

We present a complexity-based approach for the analysis of fMRI time series, in which sample entropy (SampEn) is introduced as a quantification of the voxel complexity. Under this hypothesis the voxel complexity could be modulated in pertinent cognitive tasks, and it changes through experimental paradigms. We calculate the complexity of sequential fMRI data for each voxel in two distinct experimental paradigms and use a nonparametric statistical strategy, the Wilcoxon signed rank test, to evaluate the difference in complexity between them. The results are compared with the well known general linear model based Statistical Parametric Mapping package (SPM12), where a decided difference has been observed. This is because SampEn method detects brain complexity changes in two experiments of different conditions and the data-driven method SampEn evaluates just the complexity of specific sequential fMRI data. Also, the larger and smaller SampEn values correspond to different meanings, and the neutral-blank design produces higher predictability than threat-neutral. Complexity information can be considered as a complementary method to the existing fMRI analysis strategies, and it may help improving the understanding of human brain functions from a different perspective.

Identifying Dysfunctional Cortex: Dissociable Effects of Stroke and Aging on Resting State Dynamics in MEG and fMRI

Spontaneous signals in neuroimaging data may provide information on cortical health in disease and aging, but the relative sensitivity of different approaches is unknown. In the present study, we compared different but complementary indicators of neural dynamics in resting-state MEG and BOLD fMRI, and their relationship with blood flow. Participants included patients with post-stroke aphasia, age-matched controls, and young adults. The complexity of brain activity at rest was quantified in MEG using spectral analysis and multiscale entropy (MSE) measures, whereas BOLD variability was quantified as the standard deviation (SDBOLD), mean squared successive difference (MSSD), and sample entropy of the BOLD time series. We sought to assess the utility of signal variability and complexity measures as markers of age-related changes in healthy adults and perilesional dysfunction in chronic stroke. The results indicate that reduced BOLD variability is a robust finding in aging, whereas MEG measures are more sensitive to the cortical abnormalities associated with stroke. Furthermore, reduced complexity of MEG signals in perilesional tissue were correlated with hypoperfusion as assessed with arterial spin labeling (ASL), while no such relationship was apparent with BOLD variability. These findings suggest that MEG signal complexity offers a sensitive index of neural dysfunction in perilesional tissue in chronic stroke, and that these effects are clearly distinguishable from those associated with healthy aging.

Fuzzy approximate entropy analysis of resting state fMRI signal complexity across the adult life span

In this study, we present a method for measuring functional magnetic resonance imaging (fMRI) signal complexity using fuzzy approximate entropy (fApEn) and compare it with the established sample entropy (SampEn). Here we use resting state fMRI dataset of 86 healthy adults (41 males) with age ranging from 19 to 85 years. We expect the complexity of the resting state fMRI signals measured to be consistent with the Goldberger/Lipsitz model for robustness where healthier (younger) and more robust systems exhibit more complexity in their physiological output and system complexity decrease with age. The mean whole brain fApEn demonstrated significant negative correlation (r = -0.472, p<0.001) with age. In comparison, SampEn produced a non-significant negative correlation (r = -0.099, p = 0.367). fApEn also demonstrated a significant (p < 0.05) negative correlation with age regionally (frontal, parietal, limbic, temporal and cerebellum parietal lobes). There was no significant correlation regionally between the SampEn maps and age. These results support the Goldberger/Lipsitz model for robustness and have shown that fApEn is potentially a sensitive new method for the complexity analysis of fMRI data.

Brain Dynamics of Aging: Multiscale Variability of EEG Signals at Rest and during an Auditory Oddball Task

Recently, the study of brain signal fluctuations is widely put forward as a promising entry point to characterize brain dynamics in health and disease. Although interesting results have been reported regarding how variability of brain activations can serve as an indicator of performance and adaptability in elderly, many uncertainties and controversies remain with regard to the comparability, reproducibility, and generality of the described findings, as well as the ensuing interpretations.

The present work focused on the study of fluctuations of cortical activity across time scales in young and older healthy adults. The main objective was to offer a comprehensive characterization of the changes of brain (cortical) signal variability during aging, and to make the link with known underlying structural, neurophysiological, and functional modifications, as well as aging theories. We analyzed electroencephalogram (EEG) data of young and elderly adults, which were collected at resting state and during an auditory oddball task. We used a wide battery of metrics that typically are separately applied in the literature, and we compared them with more specific ones that address their limits. Our procedure aimed to overcome some of the methodological limitations of earlier studies and verify whether previous findings can be reproduced and extended to different experimental conditions. In both rest and task conditions, our results mainly revealed that EEG signals presented systematic age-related changes that were time-scale-dependent with regard to the structure of fluctuations (complexity) but not with regard to their magnitude. Namely, compared with young adults, the cortical fluctuations of the elderly were more complex at shorter time scales, but less complex at longer scales, although always showing a lower variance. Additionally, the elderly showed signs of spatial, as well as between, experimental conditions dedifferentiation. By integrating these so far isolated findings across time scales, metrics, and conditions, the present study offers an overview of age-related changes in the fluctuation electrocortical activity while making the link with underlying brain dynamics.