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

Abnormal brain entropy dynamics in ADHD

BACKGROUND

Brain entropy (BEN) is a novel measure for irregularity and complexity of brain activities, which has been used to characterize abnormal brain activities in many brain disorders including attention-deficit/hyperactivity disorder (ADHD). While most research assumes BEN is stationary during scan sessions, the brain in resting state is also a highly dynamic system. The BEN dynamics in ADHD has not been explored.

METHODS

We used a sliding window approach to derive the dynamical brain entropy (dBEN) from resting-state functional magnetic resonance imaging (rfMRI) dataset that includes 98 ADHD patients and 111 healthy controls (HCs). We identified 3 reoccurring BEN states. We tested whether the BEN dynamics differ between ADHD and HC, and whether they are associated with ADHD symptom severity.

RESULTS

One BEN states, characterized by low overall BEN and low within-state BEN located in SMN (sensorimotor network) and VN (visual network), its FW (fractional window) and MDT (mean dwell time) were increased in ADHD and positively correlated with ADHD severity; another state characterized by high overall BEN and low within-state BEN located in DMN (default mode network) and ECN (executive control network), its FW and MDT were decreased in ADHD and negatively correlated with ADHD severity.

LIMITATIONS

The window length of dBEN analysis can be further optimized to suit more datasets. The co-variation between dBEN and other dynamical brain metrics was not explored.

CONCLUSION

Our findings revealed abnormal BEN dynamics in ADHD, providing new insights into clinical diagnosis and neuropathology of ADHD.

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.

Cognitive protection and brain entropy changes from omega-3 polyunsaturated fatty acids supplement in late-life depression: A 52-week randomized controlled trial

BACKGROUND

Late-life depression (LLD) is associated with risk of dementia, yet intervention of LLD provides an opportunity to attenuate subsequent cognitive decline. Omega-3 polyunsaturated fatty acids (PUFAs) supplement is a potential intervention due to their beneficial effect in depressive symptoms and cognitive function. To explore the underlying neural mechanism, we used resting-state functional MRI (rs-fMRI) before and after omega-3 PUFAs supplement in older adults with LLD.

METHODS

A 52-week double-blind randomized controlled trial was conducted. We used multi-scale sample entropy to analyze rs-fMRI data. Comprehensive cognitive tests and inflammatory markers were collected to correlate with brain entropy changes.

RESULTS

A total of 20 patients completed the trial with 11 under omega-3 PUFAs and nine under placebo. While no significant global cognitive improvement was observed, a marginal enhancement in processing speed was noted in the omega-3 PUFAs group. Importantly, participants receiving omega-3 PUFAs exhibited decreased brain entropy in left posterior cingulate gyrus (PCG), multiple visual areas, the orbital part of the right middle frontal gyrus, and the left Rolandic operculum. The brain entropy changes of the PCG in the omega-3 PUFAs group correlated with improvement of language function and attenuation of interleukin-6 levels.

LIMITATIONS

Sample size is small with only marginal clinical effect.

CONCLUSION

These findings suggest that omega-3 PUFAs supplement may mitigate cognitive decline in LLD through anti-inflammatory mechanisms and modulation of brain entropy. Larger clinical trials are warranted to validate the potential therapeutic implications of omega-3 PUFAs for deterring cognitive decline in patients with late-life depression.

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.

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.

Entropy, complexity, and maturity in children’s neural responses to naturalistic video lessons

Temporal characteristics of neural signals are often overlooked in traditional fMRI developmental studies but are critical to studying brain functions in ecologically valid settings. In the present study, we explore the temporal properties of children's neural responses during naturalistic mathematics and grammar tasks. To do so, we introduce a novel measure in developmental fMRI: neural entropy, which indicates temporal complexity of BOLD signals. We show that temporal patterns of neural activity have lower complexity and greater variability in children than in adults in the association cortex but not in the sensory-motor cortex. We also show that neural entropy is associated with both child-adult similarity in functional connectivity and neural synchrony, and that neural entropy increases with the size of functionally connected networks in the association cortex. In addition, neural entropy increases with functional maturity (i.e., child-adult neural synchrony) in content-specific regions. These exploratory findings suggest the hypothesis that neural entropy indexes the increasing breadth and diversity of neural processes available to children for analyzing mathematical information over development.

FMRI Complexity Correlates with Tau-PET and Cognitive Decline in Late-Onset and Autosomal Dominant Alzheimer's Disease

BACKGROUND

Neurofibrillary tangle pathology detected with tau-PET correlates closely with neuronal injury and cognitive symptoms in Alzheimer's disease (AD). Complexity of rs-fMRI has been demonstrated to decrease with cognitive decline in AD.

OBJECTIVE

We hypothesize that the rs-fMRI complexity provides an index for tau-related neuronal injury and cognitive decline in the AD process.

METHODS

Data was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI3) and the Estudio de la Enfermedad de Alzheimer en Jalisciences (EEAJ) study. Associations between tau-PET and rs-fMRI complexity were calculated. Potential pathways relating complexity to cognitive function mediated through tau-PET were assessed by path analysis.

RESULTS

We found significant negative correlations between rs-fMRI complexity and tau-PET in medial temporal lobe of both cohorts, and associations of rs-fMRI complexity with cognitive scores were mediated through tau-PET.

CONCLUSION

The association of rs-fMRI complexity with tau-PET and cognition, suggests that a reduction in complexity is indicative of tau-related neuropathology and cognitive decline in AD processes.

Cross-Scale Dynamicity of Entropy and Connectivity in the Sleeping Brain

Introduction: The concept of local sleep refers to the phenomenon of local brain activity that modifies neural networks during unresponsive global sleep. Such network rewiring may differ across spatial scales; however, the global and local alterations in brain systems remain elusive in human sleep. Materials and Methods: We examined cross-scale changes of brain networks in sleep. Functional magnetic resonance imaging data were acquired from 28 healthy participants during nocturnal sleep. We adopted both metrics of connectivity (functional connectivity [FC] and regional homogeneity [ReHo]) and complexity (multiscale entropy) to explore the global and local functionality of the neural assembly across nonrapid eye movement sleep stages. Results: Long-range FC decreased with sleep depth, whereas local ReHo peaked at the N2 stage and reached its lowest level at the N3 stage. Entropy exhibited a general decline at the local scale (Scale 1) as sleep deepened, whereas the coarse-scale entropy (Scale 3) was consistent across stages. Discussion: The negative correlation between Scale-1 entropy and ReHo reflects the enhanced signal regularity and synchronization in sleep, identifying the information exchange at the local scale. The N2 stage showed a distinctive pattern toward local information processing with scrambled long-distance information exchange, indicating a specific time window for network reorganization. Collectively, the multidimensional metrics indicated an imbalanced global-local relationship among brain functional networks across sleep-wake stages.

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

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

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.

Multiscale Entropy of Resting-State Functional Magnetic Resonance Imaging Differentiates Progressive Supranuclear Palsy and Multiple System Atrophy

Distinguishing progressive supranuclear palsy (PSP) from multiple system atrophy (MSA) in the early clinical stages is challenging; few sensitive and specific biomarkers are available for their differential diagnosis. Resting-state functional magnetic resonance imaging (rs-fMRI) is used to study the fluctuations in blood oxygen level-dependent (BOLD) signals at rest, which provides evidence for aberrant brain functional networks in neurodegenerative diseases. We aimed to examine whether rs-fMRI data could differentiate between PSP and MSA via a multiscale entropy (MSE) analysis of BOLD signals, which estimates the complexity of temporal fluctuations in brain activity. We recruited 14 and 18 patients with PSP and MSA, respectively, who underwent neuropsychological tests and rs-fMRI. PSP patients demonstrated greater cognitive function impairments, particularly in the frontal executive function. The bilateral prefrontal cortex revealed lower entropy BOLD signal values in multiple time scales for PSP, compared to the values observed in MSA patients; however, the functional connectivity of the representative brain networks was comparable between the diseases. The reduced complexity of BOLD signals in the prefrontal cortex was associated with frontal dysfunction. Thus, an MSE analysis of rs-fMRI could differentiate between PSP and MSA, and the reduced complexity of BOLD signals could be associated with cognitive impairment.

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.

Altered network stability in progressive supranuclear palsy

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We investigated network dynamics in the tauopathy progressive supranuclear palsy

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Abnormal temporal properties of large-scale networks are related to phenotype

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Progressive supranuclear palsy paradoxically increases frontoparietal state time

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Reductions in neural signal complexity relate to altered network dynamics

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Dynamic network and topological changes occur distally to primary sites of atrophy

The clinical syndromes of Progressive Supranuclear Palsy (PSP) may be mediated by abnormal temporal dynamics of brain networks, due to the impact of atrophy, synapse loss and neurotransmitter deficits. We tested the hypothesis that alterations in signal complexity in neural networks influence short-latency state transitions. Ninety-four participants with PSP and 64 healthy controls were recruited from two independent cohorts. All participants underwent clinical and neuropsychological testing and resting-state functional MRI. Network dynamics were assessed using hidden Markov models and neural signal complexity measured in terms of multiscale entropy. In both cohorts, PSP increased the proportion of time in networks associated with higher cognitive functions. This effect correlated with clinical severity as measured by the PSP-rating-scale, and with reduced neural signal complexity. Regional atrophy influenced abnormal brain-state occupancy, but abnormal network topology and dynamics were not restricted to areas of atrophy. Our findings show that the pathology of PSP causes clinically relevant changes in neural temporal dynamics, leading to a greater proportion of time in inefficient brain-states.

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.

Comparative Analysis of the Permutation and Multiscale Entropies for Quantification of the Brain Signal Variability in Naturalistic Scenarios

As alternative entropy estimators, multiscale entropy (MSE) and permutation entropy (PE) are utilized for quantification of the brain function and its signal variability. In this context, their applications are primarily focused on two specific domains: (1) the effect of brain pathology on its function (2) the study of altered states of consciousness. As a result, there is a paucity of research on applicability of these measures in more naturalistic scenarios. In addition, the utility of these measures for quantification of the brain function and with respect to its signal entropy is not well studied. These shortcomings limit the interpretability of the measures when used for quantification of the brain signal entropy. The present study addresses these limitations by comparing MSE and PE with entropy of human subjects' EEG recordings, who watched short movie clips with negative, neutral, and positive content. The contribution of the present study is threefold. First, it identifies a significant anti-correlation between MSE and entropy. In this regard, it also verifies that such an anti-correlation is stronger in the case of negative rather than positive or neutral affects. Second, it finds that MSE significantly differentiates between these three affective states. Third, it observes that the use of PE does not warrant such significant differences. These results highlight the level of association between brain's entropy in response to affective stimuli on the one hand and its quantification in terms of MSE and PE on the other hand. This, in turn, allows for more informed conclusions on the utility of MSE and PE for the study and analysis of the brain signal variability in naturalistic scenarios.

Altered complexity of resting-state BOLD activity in Alzheimer's disease-related neurodegeneration: a multiscale entropy analysis

Brain complexity, which reflects the ability of the brain to adapt to a changing environment, has been found to be significantly changed with age. However, there is less evidence on the alterations of brain complexity in neurodegenerative disorders such as Alzheimer's disease (AD). Here we investigated the altered complexity of resting-state blood oxygen level-dependent signals in AD-related neurodegeneration using multiscale entropy (MSE) analysis. All participants were recruited from the Alzheimer's Disease Neuroimaging Initiative, including healthy controls (HC, n=62), amnestic mild cognitive impairment (aMCI, n =81) patients, and Alzheimer's disease (AD, n=25) patients. Our results showed time scale-dependent MSE differences across the three groups. In scale=1, significantly changed MSE patterns (HC>aMCI>AD) were found in four brain regions, including the hippocampus, middle frontal gyrus, intraparietal lobe, and superior frontal gyrus. In scale=4, reversed MSE patterns (HC<aMCI<AD) were found in the middle frontal gyrus and middle occipital gyrus. Furthermore, the values of regional entropy were significantly associated with cognitive functions positively on the short time scale, while negatively on the longer time scale. Our findings suggest that MSE could be a reliable measure for characterizing brain deterioration in AD, and may provide insights into the neural mechanism of AD-related neurodegeneration.

Reduced Dynamic Complexity of BOLD Signals Differentiates Mild Cognitive Impairment From Normal Aging

Mild cognitive impairment (MCI) is characterized as a transitional phase between cognitive decline associated with normal aging and Alzheimer’s disease (AD). Resting-state functional magnetic resonance imaging (fMRI) measuring blood oxygenation level-dependent (BOLD) signals provides complementary information considered essential for understanding disease progression. Previous studies suggested that multi-scale entropy (MSE) analysis quantifying the complexity of BOLD signals is a novel and promising method for investigating neurodegeneration associated with cognitive decline in different stages of MCI. Therefore, the current study used MSE to explore the changes in the complexity of resting-state brain BOLD signals in patients with early MCI (EMCI) and late MCI (LMCI). We recruited 345 participants’ data from the Alzheimer’s Disease Neuroimaging Initiative database, including 176 normal control (NC) subjects, 87 patients with EMCI and 82 patients with LMCI. We observed a significant reduction of brain signal complexity toward regularity in the left fusiform gyrus region in the EMCI group and in the rostral anterior cingulate cortex in the LMCI group. Our results extend prior work by revealing that significant reductions of brain BOLD signal complexity can be detected in different stages of MCI independent of age, sex and regional atrophy. Notably, the reduction of BOLD signal complexity in the rostral anterior cingulate cortex was significantly associated with greater risk of progression to AD. The present study thus identified MSE as a potential imaging biomarker for the early diagnosis of pre-clinical Alzheimer’s disease and provides further insights into the neuropathology of cognitive decline in prodromal AD.

The functional implications and modifiability of resting-state brain network complexity in older adults

The dynamics of the resting-state activity in brain functional networks are complex, containing meaningful patterns over multiple temporal scales. Such physiologic complexity is often diminished in older adults. Here we aim to examine if the resting-state complexity within functional brain networks is sensitive to functional status in older adults and if repeated exposure to transcranial direct current stimulation (tDCS) would modulate such complexity. Twelve older adults with slow gait and mild-to-moderate executive dysfunction and 12 age- and sex-matched controls completed a baseline resting-state fMRI (rs-fMRI). Ten participants in the functionally-limited group then completed ten 20-minute sessions of real (n = 6) or sham (n = 4) tDCS targeting the left prefrontal cortex over a two-week period as well as a follow-up rs-fMRI. The resting-state complexity associated with seven functional networks was quantified by averaging the multiscale entropy (MSE) of the blood oxygen level-dependent (BOLD) time-series for all voxels within each network. Compared to controls, functionally-limited group exhibited lower complexity in the motor, ventral attention, limbic, executive and default mode networks (F > 6.3, p < 0.02). Within this group, those who received tDCS exhibited greater complexity within the ventral, executive and limbic networks (p < 0.04) post intervention as compared to baseline, while no significant changes in sham group was observed. This study provides preliminary evidence that older adults with functional limitations had diminished complexity of resting-state brain network activity and repeated exposure to tDCS may increase that resting-state complexity, warranting future studies to establish such complexity as a marker of brain health in older adults.

Differences in high-definition transcranial direct current stimulation over the motor hotspot versus the premotor cortex on motor network excitability

The effectiveness of transcranial direct current stimulation (tDCS) placed over the motor hotspot (thought to represent the primary motor cortex (M1)) to modulate motor network excitability is highly variable. The premotor cortex-particularly the dorsal premotor cortex (PMd)-may be a promising alternative target to reliably modulate motor excitability, as it influences motor control across multiple pathways, one independent of M1 and one with direct connections to M1. This double-blind, placebo-controlled preliminary study aimed to differentially excite motor and premotor regions using high-definition tDCS (HD-tDCS) with concurrent functional magnetic resonance imaging (fMRI). HD-tDCS applied over either the motor hotspot or the premotor cortex demonstrated high inter-individual variability in changes on cortical motor excitability. However, HD-tDCS over the premotor cortex led to a higher number of responders and greater changes in local fMRI-based complexity than HD-tDCS over the motor hotspot. Furthermore, an analysis of individual motor hotspot anatomical locations revealed that, in more than half of the participants, the motor hotspot is not located over anatomical M1 boundaries, despite using a canonical definition of the motor hotspot. This heterogeneity in stimulation site may contribute to the variability of tDCS results. Altogether, these preliminary findings provide new considerations to enhance tDCS reliability.

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.

Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ. Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ, only general recommendations such as N>>m!, τ=1, or m=3,…,7. This paper deals specifically with the study of the practical implications of N>>m!, since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N>>m! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

BOLD signal variability and complexity in children and adolescents with and without autism spectrum disorder

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Resting-state BOLD signal variability and complexity were examined.

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No significant group differences were observed in youth with and without autism.

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A continuum of brain-behavior relationships was observed across diagnostic groups.

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Positive correlations were found between brain measures, age and global efficiency.

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Negative correlations were found between the brain measures and behavioral severity.

Variability of neural signaling is an important index of healthy brain functioning, as is signal complexity, which relates to information processing capacity. Alterations in variability and complexity may underlie certain brain dysfunctions. Here, resting-state fMRI was used to examine variability and complexity in children and adolescents with and without autism spectrum disorder (ASD). Variability was measured using the mean square successive difference (MSSD) of the time series, and complexity was assessed using sample entropy. A categorical approach was implemented to determine if the brain measures differed between diagnostic groups (ASD and controls). A dimensional approach was used to examine the continuum of relationships between each brain measure and behavioral severity, age, IQ, and the global efficiency (GE) of each participant’s structural connectome, which reflects the structural capacity for information processing. Using the categorical approach, no significant group differences were found for neither MSSD nor entropy. The dimensional approach revealed significant positive correlations between each brain measure, GE, and age. Negative correlations were observed between each brain measure and the severity of ASD behaviors across all participants. These results reveal the nature of variability and complexity of BOLD signals in children and adolescents with and without ASD.