Topological Data Analysis Reveals Robust Alterations in the Whole-Brain and Frontal Lobe Functional Connectomes in Attention-Deficit/Hyperactivity Disorder

Who is WithMe? EEG features for attention in a visual task, with auditory and rhythmic support

Introduction

The study of attention has been pivotal in advancing our comprehension of cognition. The goal of this study is to investigate which EEG data representations or features are most closely linked to attention, and to what extent they can handle the cross-subject variability.

Methods

We explore the features obtained from the univariate time series from a single EEG channel, such as time domain features and recurrence plots, as well as representations obtained directly from the multivariate time series, such as global field power or functional brain networks. To address the cross-subject variability in EEG data, we also investigate persistent homology features that are robust to different types of noise. The performance of the different EEG representations is evaluated with the Support Vector Machine (SVM) accuracy on the WithMe data derived from a modified digit span experiment, and is benchmarked against baseline EEG-specific models, including a deep learning architecture known for effectively learning task-specific features.

Results

The raw EEG time series outperform each of the considered data representations, but can fall short in comparison with the black-box deep learning approach that learns the best features.

Discussion

The findings are limited to the WithMe experimental paradigm, highlighting the need for further studies on diverse tasks to provide a more comprehensive understanding of their utility in the analysis of EEG data.

Persistent homology reveals robustness loss in inhaled substance abuse rs-fMRI networks

Analyzing functional brain activity through functional magnetic resonance imaging (fMRI) is commonly done using tools from graph theory for the analysis of the correlation matrices. A drawback of these methods is that the networks must be restricted to values of the weights of the edges within certain thresholds and there is no consensus about the best choice of such thresholds. Topological data analysis (TDA) is a recently-developed tool in algebraic topology which allows us to analyze networks through combinatorial spaces obtained from them, with the advantage that all the possible thresholds can be considered at once. In this paper we applied TDA, in particular persistent homology, to study correlation matrices from rs-fMRI, and through statistical analysis, we detected significant differences between the topological structures of adolescents with inhaled substance abuse disorder (ISAD) and healthy controls. We interpreted the topological differences as indicative of a loss of robustness in the functional brain networks of the ISAD population.

Functional connectivity is linked to working memory differences in children with reading learning disability

Reading learning disability (RLD) is characterized by a specific difficulty in learning to read that is not better explained by an intellectual disability, lack of instruction, psychosocial adversity, or a neurological disorder. According to the domain-general hypothesis, a working memory deficit is the primary problem. Working memory in this population has recently been linked to altered resting-state functional connectivity within the default mode network (DMN), salience network (SN), and frontoparietal network (FPN) compared to that in typically developing individuals. The main purpose of the present study was to compare the within-network functional connectivity of the DMN, SN, FPN, and reading network in two groups of children with RLD: a group with lower-than-average working memory (LWM) and a group with average working memory (AWM). All subjects underwent resting-state functional magnetic resonance imaging (fMRI), and data were analyzed from a network perspective using the network brain statistics framework. The results showed that the LWM group had significantly weaker connectivity in a network that involved brain regions in the DMN, SN, and FPN than the AWM group. Although there was no significant difference between groups in reading network in the present study, other studies have shown relationship of the connectivity of the angular gyrus, supramarginal gyrus, and inferior parietal lobe with the phonological process of reading. The results suggest that although there are significant differences in functional connectivity in the associated networks between children with LWM and AWM, the distinctive cognitive profile has no specific effect on the reading network.

Altered topological structure of the brain white matter in maltreated children through topological data analysis

Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood. In this study, we propose an analytical pipeline for modeling the altered topological structure of brain white matter in maltreated and typically developing children. We perform topological data analysis (TDA) to assess the alteration in the global topology of the brain white matter structural covariance network among children. We use persistent homology, an algebraic technique in TDA, to analyze topological features in the brain covariance networks constructed from structural magnetic resonance imaging and diffusion tensor imaging. We develop a novel framework for statistical inference based on the Wasserstein distance to assess the significance of the observed topological differences. Using these methods in comparing maltreated children with a typically developing control group, we find that maltreatment may increase homogeneity in white matter structures and thus induce higher correlations in the structural covariance; this is reflected in the topological profile. Our findings strongly suggest that TDA can be a valuable framework to model altered topological structures of the brain. The MATLAB codes and processed data used in this study can be found at https://github.com/laplcebeltrami/maltreated.

Tree representations of brain structural connectivity via persistent homology

The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the structural connectome varies across individuals in relation to their traits, ranging from age and gender to neuropsychiatric outcomes. After applying tractography to dMRI to get white matter fiber bundles, a key question is how to represent the brain connectome to facilitate statistical analyses relating connectomes to traits. The current standard divides the brain into regions of interest (ROIs), and then relies on an adjacency matrix (AM) representation. Each cell in the AM is a measure of connectivity, e.g., number of fiber curves, between a pair of ROIs. Although the AM representation is intuitive, a disadvantage is the high-dimensionality due to the large number of cells in the matrix. This article proposes a simpler tree representation of the brain connectome, which is motivated by ideas in computational topology and takes topological and biological information on the cortical surface into consideration. We demonstrate that our tree representation preserves useful information and interpretability, while reducing dimensionality to improve statistical and computational efficiency. Applications to data from the Human Connectome Project (HCP) are considered and code is provided for reproducing our analyses.

Simple topological task-based functional connectivity features predict longitudinal behavioral change of fluid reasoning in the RANN cohort

Recent attention has been given to topological data analysis (TDA), and more specifically persistent homology (PH), to identify the underlying shape of brain network connectivity beyond simple edge pairings by computing connective components across different connectivity thresholds (see Sizemore et al., 2019). In the present study, we applied PH to task-based functional connectivity, computing 0-dimension Betti (B0) curves and calculating the area under these curves (AUC); AUC indicates how quickly a single connected component is formed across correlation filtration thresholds, with lower values interpreted as potentially analogous to lower whole-brain system segregation (e.g., Gracia-Tabuenca et al., 2020). One hundred sixty-three participants from the Reference Ability Neural Network (RANN) longitudinal lifespan cohort (age 20-80 years) were tested in-scanner at baseline and five-year follow-up on a battery of tests comprising four domains of cognition (i.e., Stern et al., 2014). We tested for 1.) age-related change in the AUC of the B0 curve over time, 2.) the predictive utility of AUC in accounting for longitudinal change in behavioral performance and 3.) compared system segregation to the PH approach. Results demonstrated longitudinal age-related decreases in AUC for Fluid Reasoning, with these decreases predicting longitudinal declines in cognition, even after controlling for demographic and brain integrity factors; moreover, change in AUC partially mediated the effect of age on change in cognitive performance. System segregation also significantly decreased with age in three of the four cognitive domains but did not predict change in cognition. These results argue for greater application of TDA to the study of aging.

Persistent homology-based functional connectivity and its association with cognitive ability: Life-span study

Brain-segregation attributes in resting-state functional networks have been widely investigated to understand cognition and cognitive aging using various approaches [e.g., average connectivity within/between networks and brain system segregation (BSS)]. While these approaches have assumed that resting-state functional networks operate in a modular structure, a complementary perspective assumes that a core-periphery or rich club structure accounts for brain functions where the hubs are tightly interconnected to each other to allow for integrated processing. In this article, we apply a novel method, persistent homology (PH), to develop an alternative to standard functional connectivity by quantifying the pattern of information during the integrated processing. We also investigate whether PH-based functional connectivity explains cognitive performance and compare the amount of variability in explaining cognitive performance for three sets of independent variables: (1) PH-based functional connectivity, (2) graph theory-based measures, and (3) BSS. Resting-state functional connectivity data were extracted from 279 healthy participants, and cognitive ability scores were generated in four domains (fluid reasoning, episodic memory, vocabulary, and processing speed). The results first highlight the pattern of brain-information flow over whole brain regions (i.e., integrated processing) accounts for more variance of cognitive abilities than other methods. The results also show that fluid reasoning and vocabulary performance significantly decrease as the strength of the additional information flow on functional connectivity with the shortest path increases. While PH has been applied to functional connectivity analysis in recent studies, our results demonstrate potential utility of PH-based functional connectivity in understanding cognitive function.

Development of the Functional Connectome Topology in Adolescence: Evidence from Topological Data Analysis

Adolescence is a crucial developmental period in terms of behavior and mental health. Therefore, understanding how the brain develops during this stage is a fundamental challenge for neuroscience. Recent studies have modeled the brain as a network or connectome, mainly applying measures from graph theory, showing a change in its functional organization, such as an increase in its segregation and integration. Topological Data Analysis (TDA) complements such modeling by extracting high-dimensional features across the whole range of connectivity values instead of exploring a fixed set of connections. This study inquires into the developmental trajectories of such properties using a longitudinal sample of typically developing human participants (N = 98; 53/45 female/male; 6.7-18.1 years), applying TDA to their functional connectomes. In addition, we explore the effect of puberty on individual developmental trajectories. Results showed that the adolescent brain has a more distributed topology structure compared with random networks but is more densely connected at the local level. Furthermore, developmental effects showed nonlinear trajectories for the topology of the whole brain and fronto-parietal networks, with an inflection point and increasing trajectories after puberty onset. These results add to the insights into the development of the functional organization of the adolescent brain.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Lifespan associations of resting-state brain functional networks with ADHD symptoms

Attention-deficit/hyperactivity disorder (ADHD) is increasingly being diagnosed in both children and adults, but the neural mechanisms that underlie its distinct symptoms and whether children and adults share the same mechanism remain poorly understood. Here, we used a nested-spectral partition approach to study resting-state brain networks of ADHD patients (n = 97) and healthy controls (HCs, n = 97) across the lifespan (7-50 years). Compared to the linear lifespan associations of brain segregation and integration with age in HCs, ADHD patients have a quadratic association in the whole-brain and in most functional systems, whereas the limbic system dominantly affected by ADHD has a linear association. Furthermore, the limbic system better predicts hyperactivity, and the salient attention system better predicts inattention. These predictions are shared in children and adults with ADHD. Our findings reveal a lifespan association of brain networks with ADHD and provide potential shared neural bases of distinct ADHD symptoms in children and adults.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Persistent homology of tumor CT scans is associated with survival in lung cancer

PURPOSE

Radiomics, the objective study of nonvisual features in clinical imaging, has been useful in informing decisions in clinical oncology. However, radiomics currently lacks the ability to characterize the overall topological structure of the data. This niche can be filled by persistent homology, a form of topological data analysis that analyzes high-level structure. We hypothesized that persistent homology features quantified using cubical complexes could be extracted from lung tumor scans and related to survival.

METHODS

We obtained segmented computed tomography (CT) lung scans (n = 565) from the NSCLC-Radiomics and NSCLC-Radiogenomics datasets in The Cancer Imaging Archive. These scans are three-dimensional images whose pixel intensity corresponds to a number of Hounsfield units. Cubical complexes are a topological image analysis method that effectively analyzes the number of topological features in an image as the image is thresholded at different intensities. We calculated a novel output called a feature curve by plotting the number of zero-dimensional (0D) topological features counted from the cubical complex filtration against each Hounsfield value. This curve's first moment of distribution was utilized as a summary statistic to show association with survival in a Cox proportional hazards model. We hypothesized that persistent homology features quantified using cubical complexes could be extracted from lung tumor scans and related to survival.

RESULTS

After controlling for tumor image size, age, and stage, the first moment of the 0D topological feature curve was associated with poorer survival (HR = 1.118; 95% CI = 1.026-1.218; p = 0.01). The patients in our study with the lowest first moment scores had significantly better survival (1238 days; 95% CI = 936-1599) compared to the patients with the highest first moment scores (429 days; 95% CI = 326-601; p = 0.0015).

CONCLUSIONS

We have shown that persistent homology can generate useful clinical correlates from tumor CT scans. Our 0D topological feature curve statistic predicts survival in lung cancer patients. This novel statistic may be used in tandem with standard radiomics variables to better inform clinical oncology decisions.

Persistent homology as a new method of the assessment of heart rate variability

Heart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent homology is a novel data analysis tool developed in the recent decades that is rooted at algebraic topology. The Topological Data Analysis (TDA) approach focuses on examining the shape of the data in terms of connectedness and holes, and has recently proved to be very effective in various fields of research. In this paper we propose the use of persistent homology to the hrv analysis. We recall selected topological descriptors used in the literature and we introduce some new topological descriptors that reflect the specificity of hrv, and we discuss their relation to the standard hrv measures. In particular, we show that this novel approach provides a collection of indices that might be at least as useful as the classical parameters in differentiating between series of beat-to-beat intervals (RR-intervals) in healthy subjects and patients suffering from a stroke episode.

Development of the brain functional connectome follows puberty-dependent nonlinear trajectories

Adolescence is a developmental period that dramatically impacts body and behavior, with pubertal hormones playing an important role not only in the morphological changes in the body but also in brain structure and function. Understanding brain development during adolescence has become a priority in neuroscience because it coincides with the onset of many psychiatric and behavioral disorders. However, little is known about how puberty influences the brain functional connectome. In this study, taking a longitudinal human sample of typically developing children and adolescents (of both sexes), we demonstrate that the development of the brain functional connectome better fits pubertal status than chronological age. In particular, centrality, segregation, efficiency, and integration of the brain functional connectome increase after the onset of the pubertal markers. We found that these effects are stronger in attention and task control networks. Lastly, after controlling for this effect, we showed that functional connectivity between these networks is related to better performance in cognitive flexibility. This study points out the importance of considering longitudinal nonlinear trends when exploring developmental trajectories, and emphasizes the impact of puberty on the functional organization of the brain in adolescence.

Multi-dimensional persistent feature analysis identifies connectivity patterns of resting-state brain networks in Alzheimer's disease

OBJECTIVE

The characterization of functional brain network is crucial to understanding the neural mechanisms associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI). Some studies have shown that graph theoretical analysis could reveal changes of the disease-related brain networks by thresholding edge weights. But the choice of threshold depends on ambiguous cognitive conditions, which leads to the lack of interpretability. Recently, persistent homology (PH) was proposed to record the persistence of topological features of networks across every possible thresholds, reporting a higher sensitivity than graph theoretical features in detecting network-level biomarkers of AD. However, most research on PH focused on 0-dimensional features (persistence of connected components) reflecting the intrinsic topology of the brain network, rather than 1-dimensional features (persistence of cycles) with an interesting neurobiological communication pattern. Our aim is to explore the multi-dimensional persistent features of brain networks in the AD and MCI patients, and further to capture valuable brain connectivity patterns.

APPROACH

We characterized the change rate of the connected component numbers across graph filtration using the functional derivative curves, and examined the persistence landscapes that vectorize the persistence of cycle structures. After that, the multi-dimensional persistent features were validated in disease identification using a K-nearest neighbor algorithm. Furthermore, a connectivity pattern mining framework was designed to capture the disease-specific brain structures.

MAIN RESULTS

We found that the multi-dimensional persistent features can identify statistical group differences, quantify subject-level distances, and yield disease-specific connectivity patterns. Relatively high classification accuracies were received when compared with graph theoretical features.

SIGNIFICANCE

This work represents a conceptual bridge linking complex brain network analysis and computational topology. Our results can be beneficial for providing a complementary objective opinion to the clinical diagnosis of neurodegenerative diseases.