Fractal Analysis of BOLD Time Series in a Network Associated With Waiting Impulsivity

A novel technique for delineating the effect of variation in the learning rate on the neural correlates of reward prediction errors in model-based fMRI

Introduction

Computational models play an increasingly important role in describing variation in neural activation in human neuroimaging experiments, including evaluating individual differences in the context of psychiatric neuroimaging. In particular, reinforcement learning (RL) techniques have been widely adopted to examine neural responses to reward prediction errors and stimulus or action values, and how these might vary as a function of clinical status. However, there is a lack of consensus around the importance of the precision of free parameter estimation for these methods, particularly with regard to the learning rate. In the present study, I introduce a novel technique which may be used within a general linear model (GLM) to model the effect of mis-estimation of the learning rate on reward prediction error (RPE)-related neural responses.

Methods

Simulations employed a simple RL algorithm, which was used to generate hypothetical neural activations that would be expected to be observed in functional magnetic resonance imaging (fMRI) studies of RL. Similar RL models were incorporated within a GLM-based analysis method including derivatives, with individual differences in the resulting GLM-derived beta parameters being evaluated with respect to the free parameters of the RL model or being submitted to other validation analyses.

Results

Initial simulations demonstrated that the conventional approach to fitting RL models to RPE responses is more likely to reflect individual differences in a reinforcement efficacy construct (lambda) rather than learning rate (alpha). The proposed method, adding a derivative regressor to the GLM, provides a second regressor which reflects the learning rate. Validation analyses were performed including examining another comparable method which yielded highly similar results, and a demonstration of sensitivity of the method in presence of fMRI-like noise.

Conclusion

Overall, the findings underscore the importance of the lambda parameter for interpreting individual differences in RPE-coupled neural activity, and validate a novel neural metric of the modulation of such activity by individual differences in the learning rate. The method is expected to find application in understanding aberrant reinforcement learning across different psychiatric patient groups including major depression and substance use disorder.

A pattern of cognitive resource disruptions in childhood psychopathology

The Hurst exponent (H) isolated in fractal analyses of neuroimaging time series is implicated broadly in cognition. Within this literature, H is associated with multiple mental disorders, suggesting that H is transdimensionally associated with psychopathology. Here, we unify these results and demonstrate a pattern of decreased H with increased general psychopathology and attention-deficit/hyperactivity factor scores during a working memory task in 1,839 children. This pattern predicts current and future cognitive performance in children and some psychopathology in 703 adults. This pattern also defines psychological and functional axes associating psychopathology with an imbalance in resource allocation between fronto-parietal and sensorimotor regions, driven by reduced resource allocation to fronto-parietal regions. This suggests the hypothesis that impaired working memory function in psychopathology follows from a reduced cognitive resource pool and a reduction in resources allocated to the task at hand.

Estimating dynamic individual coactivation patterns based on densely sampled resting-state fMRI data and utilizing it for better subject identification

As a complex dynamic system, the brain exhibits spatially organized recurring patterns of activity over time. Coactivation patterns (CAPs), which analyzes data from each single frame, have been utilized to detect transient brain activity states recently. However, previous CAP analyses have been conducted at the group level, which might neglect meaningful individual differences. Here, we estimated individual CAP states at both subject- and scan-level based on a densely sampled dataset: Midnight Scan Club. We used differential identifiability, which measures the gap between intra- and inter-subject similarity, to evaluate individual differences. We found individual CAPs at the subject-level achieved the best fingerprinting ability by maintaining high intra-subject similarity and enlarging inter-subject differences, and brain regions of association networks mainly contributed to the identifiability. On the other hand, scan-level CAP states were unstable across scans for the same participant. Expectedly, we found subject-specific CAPs became more reliable and discriminative with more data (i.e., longer duration). As the acquisition time of each participant is limited in practice, our results recommend a data collection strategy that collects more scans with appropriate duration (e.g., 12 ~ 15 min/scan) to obtain more reliable subject-specific CAPs, when total acquisition time is fixed (e.g., 150 min). In summary, this work has constructed reliable subject-specific CAP states with meaningful individual differences, and recommended an appropriate data collection strategy, which can guide subsequent investigations into individualized brain dynamics.

Fractal Characterization of the Mass Loss of Bronze by Erosion-Corrosion in Seawater

The fractal approach is one of the nondestructive techniques for analyzing corrosion's effects on different materials. This article utilizes it to analyze the erosion-corrosion produced by cavitation on two types of bronze introduced into an ultrasonic cavitation field to investigate the differences between their behavior in saline water. The aim is to check the hypothesis that the fractal/multifractal measures significantly differ for the studied materials that belong to the same class (bronze) as a step in applying fractal techniques to distinguish between two materials. The study emphasizes the multifractal characteristics of both materials. While the fractal dimensions do not significantly differ, the highest multifractal dimensions correspond to the sample of bronze with Sn.

Monofractal analysis of functional magnetic resonance imaging: An introductory review

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

Fractal-Based Analysis of fMRI BOLD Signal During Naturalistic Viewing Conditions

Background: Temporal fractals are characterized by prominent scale-invariance and self-similarity across time scales. Monofractal analysis quantifies this scaling behavior in a single parameter, the Hurst exponent (H). Higher H reflects greater correlation in the signal structure, which is taken as being more fractal. Previous fMRI studies have observed lower H during conventional tasks relative to resting state conditions, and shown that H is negatively correlated with task difficulty and novelty. To date, no study has investigated the fractal dynamics of BOLD signal during naturalistic conditions. Methods: We performed fractal analysis on Human Connectome Project 7T fMRI data (n = 72, 41 females, mean age 29.46 ± 3.76 years) to compare H across movie-watching and rest. Results: In contrast to previous work using conventional tasks, we found higher H values for movie relative to rest (mean difference = 0.014; p = 5.279 × 10^-7; 95% CI [0.009, 0.019]). H was significantly higher in movie than rest in the visual, somatomotor and dorsal attention networks, but was significantly lower during movie in the frontoparietal and default networks. We found no cross-condition differences in test-retest reliability of H. Finally, we found that H of movie-derived stimulus properties (e.g., luminance changes) were fractal whereas H of head motion estimates were non-fractal. Conclusions: Overall, our findings suggest that movie-watching induces fractal signal dynamics. In line with recent work characterizing connectivity-based brain state dynamics during movie-watching, we speculate that these fractal dynamics reflect the configuring and reconfiguring of brain states that occurs during naturalistic processing, and are markedly different than dynamics observed during conventional tasks.

Impact of concatenating fMRI data on reliability for functional connectomics

Compelling evidence suggests the need for more data per individual to reliably map the functional organization of the human connectome. As the notion that 'more data is better' emerges as a golden rule for functional connectomics, researchers find themselves grappling with the challenges of how to obtain the desired amounts of data per participant in a practical manner, particularly for retrospective data aggregation. Increasingly, the aggregation of data across all fMRI scans available for an individual is being viewed as a solution, regardless of scan condition (e.g., rest, task, movie). A number of open questions exist regarding the aggregation process and the impact of different decisions on the reliability of resultant aggregate data. We leveraged the availability of highly sampled test-retest datasets to systematically examine the impact of data aggregation strategies on the reliability of cortical functional connectomics. Specifically, we compared functional connectivity estimates derived after concatenating from: 1) multiple scans under the same state, 2) multiple scans under different states (i.e. hybrid or general functional connectivity), and 3) subsets of one long scan. We also varied connectivity processing (i.e. global signal regression, ICA-FIX, and task regression) and estimation procedures. When the total number of time points is equal, and the scan state held constant, concatenating multiple shorter scans had a clear advantage over a single long scan. However, this was not necessarily true when concatenating across different fMRI states (i.e. task conditions), where the reliability from the aggregate data varied across states. Concatenating fewer numbers of states that are more reliable tends to yield higher reliability. Our findings provide an overview of multiple dependencies of data concatenation that should be considered to optimize reliability in analysis of functional connectivity data.

Impulsive prepotent actions and tics in Tourette disorder underpinned by a common neural network

Tourette disorder (TD), which is characterized by motor and vocal tics, is not in general considered as a product of impulsivity, despite a frequent association with attention deficit hyperactivity disorder and impulse control disorders. It is unclear which type of impulsivity, if any, is intrinsically related to TD and specifically to the severity of tics. The waiting type of motor impulsivity, defined as the difficulty to withhold a specific action, shares some common features with tics. In a large group of adult TD patients compared to healthy controls, we assessed waiting motor impulsivity using a behavioral task, as well as structural and functional underpinnings of waiting impulsivity and tics using multi-modal neuroimaging protocol. We found that unmedicated TD patients showed increased waiting impulsivity compared to controls, which was independent of comorbid conditions, but correlated with the severity of tics. Tic severity did not account directly for waiting impulsivity, but this effect was mediated by connectivity between the right orbito-frontal cortex with caudate nucleus bilaterally. Waiting impulsivity in unmedicated patients with TD also correlated with a higher gray matter signal in deep limbic structures, as well as connectivity with cortical and with cerebellar regions on a functional level. Neither behavioral performance nor structural or functional correlates were related to a psychometric measure of impulsivity or impulsive behaviors in general. Overall, the results suggest that waiting impulsivity in TD was related to tic severity, to functional connectivity of orbito-frontal cortex with caudate nucleus and to structural changes within limbic areas.

Variance and Scale-Free Properties of Resting-State Blood Oxygenation Level-Dependent Signal After Fear Memory Acquisition and Extinction

Recently, the dynamic properties of brain activity rather than its stationary values have attracted more interest in clinical applications. It has been shown that brain signals exhibit scale-free dynamics or long-range temporal correlations (LRTC) that differ between rest and cognitive tasks in healthy controls and clinical groups. Little is known about how fear-inducing tasks may influence dispersion and the LRTC of subsequent resting-state brain activity. In this study, we aimed to explore the changes in the variance and scale-free properties of the brain’s blood oxygenation level-dependent (BOLD) signal during the resting-state sessions before and after fear learning and fear memory extinction. During a 1-h break between magnetic resonance imaging (MRI) scanning, 23 healthy, right-handed volunteers experienced a fear extinction procedure, followed by Pavlovian fear conditioning that included partial reinforcement using mild electrical stimulation. We extracted the average time course of the BOLD signal from 245 regions of interest (ROIs) taken from the resting-state functional atlas. The variance of the BOLD signal and the Hurst exponent (H), which reflects the scale-free dynamic, were compared in the resting states before and after fear learning and fear memory extinction. After fear extinction, six ROIs showed a difference in H at the uncorrected level of significance, including areas associated with fear processing. H decreased during fear extinction but then became higher than before fear learning, specifically in areas related to the fear extinction network (FEN). However, activity in the other ROIs restored the H to its initial level. The variance of the BOLD signal in six ROIs demonstrated a significant increase from initial rest to the post-task rest. A limited number of ROIs showed changes in both H and variance. Our results imply that the variability and scale-free properties of the BOLD signal might serve as additional indicators of changes in spontaneous brain activity related to recent experience.

Regional Hurst Exponent Reflects Impulsivity-Related Alterations in Fronto-Hippocampal Pathways Within the Waiting Impulsivity Network

In general, the Hurst exponent. is used as a measure of long-term memory of time series. In previous neuroimaging studies, H has been introduced as one important parameter to define resting-state networks, reflecting upon global scale-free properties emerging from a network. H has been examined in the waiting impulsivity (WI) network in an earlier study. We found that alterations of H in the anterior cingulate cortex (H^ACC) and the nucleus accumbens (H^NAcc) were lower in high impulsive (highIMP) compared to low impulsive (lowIMP) participants. Following up on those findings, we addressed the relation between altered fractality in H^ACC and H^NAcc and brain activation and neural network connectivity. To do so, brain activation maps were calculated, and network connectivity was determined using the Dynamic Causal Modeling (DCM) approach. Finally, 1–H scores were determined to quantify the alterations of H. This way, the focus of the analyses was placed on the potential effects of alterations of H on neural network activation and connectivity. Correlation analyses between the alterations of H^ACC/H^NAcc and activation maps and DCM estimates were performed. We found that the alterations of H predominantly correlated with fronto-hippocampal pathways and correlations were significant only in highIMP subjects. For example, alterations of H^ACC was associated with a decrease in neural activation in the right HC in combination with increased ACC-hippocampal connectivity. Alteration inH^NAcc, in return, was related to an increase in bilateral prefrontal activation in combination with increased fronto-hippocampal connectivity. The findings, that the WI network was related to H alteration in highIMP subjects indicated that impulse control was not reduced per se but lacked consistency. Additionally, H has been used to describe long-term memory processes before, e.g., in capital markets, energy future prices, and human memory. Thus, current findings supported the relation of H toward memory processing even when further prominent cognitive functions were involved.

Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives

Despite significant effort on understanding complex biological systems, we lack a unified theory for modeling, inference, analysis, and efficient control of their dynamics in uncertain environments. These problems are made even more challenging when considering that only limited and noisy information is accessible for modeling, which can prove insufficient for explaining, and predicting the behavior of complex systems. For instance, missing information hampers the capabilities of analytical tools to uncover the true degrees of freedom and infer the model structure and parameters of complex biological systems. Toward this end, in this paper, we discuss several important mathematical challenges that could open new theoretical avenues in studying complex systems: (1) By understanding the universal laws characterizing the asymmetric statistics of magnitude increments and the complex space-time interdependency within one process and across many processes, we can develop a class of compact yet accurate mathematical models capable to potentially providing higher degree of predictability, and more efficient control strategies. (2) In order to better predict the onset of disease and their root cause, as well as potentially discover more efficient quality-of-life (QoL)-control strategies, we need to develop mathematical strategies that not only are capable to discover causal interactions and their corresponding mathematical expressions for space and time operators acting on biological processes, but also mathematical and algorithmic techniques to identify the number of unknown unknowns (UUs) and their interdependency with the observed variables. (3) Lastly, to improve the QoL of control strategies when facing intra- and inter-patient variability, the focus should not only be on specific values and ranges for biological processes, but also on optimizing/controlling knob variables that enforce a specific spatiotemporal multifractal behavior that corresponds to an initial healthy (patient specific) behavior. All in all, the modeling, analysis and control of complex biological collective systems requires a deeper understanding of the multifractal properties of high dimensional heterogeneous and noisy data streams and new algorithmic tools that exploit geometric, statistical physics, and information theoretic concepts to deal with these data challenges.

Increased scale-free dynamics in salience network in adult high-functioning autism

Autism spectrum disorder (ASD) is clinically characterized by extremely slow and inflexible behavior. The neuronal mechanisms of these symptoms remain unclear though. Using fMRI, we investigate the resting state's temporal structure in the frequency domain (scale-free activity as measured with Power-Law Exponent, PLE, and Spectral Entropy, SE) and temporal variance (neural variability) in high-functioning, adult ASD comparing them with schizophrenic and neurotypical subjects. We show that ASD is characterized by high PLE in salience network, especially in dorsal anterior cingulate. This increase in PLE was 1) specific for salience network; 2) independent of other measures such as neuronal variability/SD and functional connectivity, which did not show any significant difference; 3) detected in two independent samples of ASD but not in the schizophrenia sample. Among salience network subregions, dorsal anterior cingulate cortex exhibited PLE differences between ASD and neurotypicals in both samples, showing high robustness in ROC curves values. Salience network abnormal temporal structure was confirmed by SE, which was strongly anticorrelated with PLE and thus decreased in ASD. Taken together, our findings show abnormal temporal structure (but normal temporal variance) in resting state salience network in adult high-functioning ASD. The abnormally high PLE indicates a relative predominance of slower over faster frequencies, which may underlie the slow adaptation to unexpected changes and the inflexible behavior observed in autistic individuals. The specificity of abnormal PLE in salience network suggests its potential utility as biomarker in ASD.