INVESTIGATING DIFFERENCES IN BRAIN FUNCTIONAL NETWORKS USING HIERARCHICAL COVARIATE-ADJUSTED INDEPENDENT COMPONENT ANALYSIS

Identifying covariate-related subnetworks for whole-brain connectome analysis

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Sparse Bayesian modeling of hierarchical independent component analysis: Reliable estimation of individual differences in brain networks

Independent component analysis (ICA) is one of the leading approaches for studying brain functional networks. There is increasing interest in neuroscience studies to investigate individual differences in brain networks and their association with demographic characteristics and clinical outcomes. In this work, we develop a sparse Bayesian group hierarchical ICA model that offers significant improvements over existing ICA techniques for identifying covariate effects on the brain network. Specifically, we model the population-level ICA source signals for brain networks using a Dirichlet process mixture. To reliably capture individual differences on brain networks, we propose sparse estimation of the covariate effects in the hierarchical ICA model via a horseshoe prior. Through extensive simulation studies, we show that our approach performs considerably better in detecting covariate effects in comparison with the leading group ICA methods. We then perform an ICA decomposition of a between-subject meditation study. Our method is able to identify significant effects related to meditative practice in brain regions that are consistent with previous research into the default mode network, whereas other group ICA approaches find few to no effects.

LOCUS: A REGULARIZED BLIND SOURCE SEPARATION METHOD WITH LOW-RANK STRUCTURE FOR INVESTIGATING BRAIN CONNECTIVITY

Network-oriented research has been increasingly popular in many scientific areas. In neuroscience research, imaging-based network connectivity measures have become the key for understanding brain organizations, potentially serving as individual neural fingerprints. There are major challenges in analyzing connectivity matrices, including the high dimensionality of brain networks, unknown latent sources underlying the observed connectivity, and the large number of brain connections leading to spurious findings. In this paper we propose a novel blind source separation method with low-rank structure and uniform sparsity (LOCUS) as a fully data-driven decomposition method for network measures. Compared with the existing method that vectorizes connectivity matrices ignoring brain network topology, LOCUS achieves more efficient and accurate source separation for connectivity matrices using low-rank structure. We propose a novel angle-based uniform sparsity regularization that demonstrates better performance than the existing sparsity controls for low-rank tensor methods. We propose a highly efficient iterative node-rotation algorithm that exploits the block multiconvexity of the objective function to solve the nonconvex optimization problem for learning LOCUS. We illustrate the advantage of LOCUS through extensive simulation studies. Application of LOCUS to Philadelphia Neurodevelopmental Cohort neuroimaging study reveals biologically insightful connectivity traits which are not found using the existing method.

BrainGB: A Benchmark for Brain Network Analysis With Graph Neural Networks

Mapping the connectome of the human brain using structural or functional connectivity has become one of the most pervasive paradigms for neuroimaging analysis. Recently, Graph Neural Networks (GNNs) motivated from geometric deep learning have attracted broad interest due to their established power for modeling complex networked data. Despite their superior performance in many fields, there has not yet been a systematic study of how to design effective GNNs for brain network analysis. To bridge this gap, we present BrainGB, a benchmark for brain network analysis with GNNs. BrainGB standardizes the process by (1) summarizing brain network construction pipelines for both functional and structural neuroimaging modalities and (2) modularizing the implementation of GNN designs. We conduct extensive experiments on datasets across cohorts and modalities and recommend a set of general recipes for effective GNN designs on brain networks. To support open and reproducible research on GNN-based brain network analysis, we host the BrainGB website at https://braingb.us with models, tutorials, examples, as well as an out-of-box Python package. We hope that this work will provide useful empirical evidence and offer insights for future research in this novel and promising direction.

Bayesian Spatial Blind Source Separation via the Thresholded Gaussian Process

Blind source separation (BSS) aims to separate latent source signals from their mixtures. For spatially dependent signals in high dimensional and large-scale data, such as neuroimaging, most existing BSS methods do not take into account the spatial dependence and the sparsity of the latent source signals. To address these major limitations, we propose a Bayesian spatial blind source separation (BSP-BSS) approach for neuroimaging data analysis. We assume the expectation of the observed images as a linear mixture of multiple sparse and piece-wise smooth latent source signals, for which we construct a new class of Bayesian nonparametric prior models by thresholding Gaussian processes. We assign the vMF priors to mixing coefficients in the model. Under some regularity conditions, we show that the proposed method has several desirable theoretical properties including the large support for the priors, the consistency of joint posterior distribution of the latent source intensity functions and the mixing coefficients, and the selection consistency on the number of latent sources. We use extensive simulation studies and an analysis of the resting-state fMRI data in the Autism Brain Imaging Data Exchange (ABIDE) study to demonstrate that BSP-BSS outperforms the existing method for separating latent brain networks and detecting activated brain activation in the latent sources.

Template independent component analysis with spatial priors for accurate subject-level brain network estimation and inference

Independent component analysis is commonly applied to functional magnetic resonance imaging (fMRI) data to extract independent components (ICs) representing functional brain networks. While ICA produces reliable group-level estimates, single-subject ICA often produces noisy results. Template ICA is a hierarchical ICA model using empirical population priors to produce more reliable subject-level estimates. However, this and other hierarchical ICA models assume unrealistically that subject effects are spatially independent. Here, we propose spatial template ICA (stICA), which incorporates spatial priors into the template ICA framework for greater estimation efficiency. Additionally, the joint posterior distribution can be used to identify brain regions engaged in each network using an excursions set approach. By leveraging spatial dependencies and avoiding massive multiple comparisons, stICA has high power to detect true effects. We derive an efficient expectation-maximization algorithm to obtain maximum likelihood estimates of the model parameters and posterior moments of the latent fields. Based on analysis of simulated data and fMRI data from the Human Connectome Project, we find that stICA produces estimates that are more accurate and reliable than benchmark approaches, and identifies larger and more reliable areas of engagement. The algorithm is computationally tractable, achieving convergence within 12 hours for whole-cortex fMRI analysis.

Rejoinder to discussions of "distributional independent component analysis for diverse neuroimaging modalities"

We thank the editors for organizing the discussions and the discussants for insightful comments. Our rejoinder provides results and comments to address the questions raised in the discussions. Specifically, we present results showing DICA largely demonstrates better or comparable stability as compared with standard ICA. We also validate the DICA in real fMRI application by showing DICA generally shows higher reliability in reproducibly recovering major brain functional networks as compared with the standard ICA. We provide details on the computational complexity of the method. The computational cost of DICA is very reasonable with the analysis of the fMRI and DTI data easily implementable on a PC or laptop. Finally, we include discussions on several directions for extending the DICA framework in the future.

Distributional independent component analysis for diverse neuroimaging modalities

Recent advances in neuroimaging technologies have provided opportunities to acquire brain images of different modalities for studying human brain organization from both functional and structural perspectives. Analysis of images derived from various modalities involves some common goals such as dimension reduction, denoising, and feature extraction. However, since these modalities have vastly different data characteristics, the current analysis is usually performed using distinct analytical tools that are only suitable for a specific imaging modality. In this paper, we present a Distributional Independent Component Analysis (DICA) that represents a new approach that performs decomposition on the distribution level, providing a unified framework for extracting features across imaging modalities with different scales and representations. When applying DICA to fMRI images, we successfully recover well-established brain functional networks in neuroscience literature, providing empirical validation that DICA delivers neurologically relevant findings. More importantly, we discover several structural network components when applying DICA to DTI images. Through fiber tracking, we find these DICA-derived structural components correspond to several major white fiber bundles. To the best of our knowledge, this is the first time these fiber bundles are successfully identified via blind source separation on single subject DTI images. We also evaluate the performance of DICA as compared with existing ICA methods through extensive simulation studies.

Hierarchical modelling of functional brain networks in population and individuals from big fMRI data

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We introduce stochastic PROFUMO (sPROFUMO) for inferring functional brain networks from big data.

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sPROFUMO hierarchically estimates fMRI networks for the population and every individual.

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We characterised high dimensional resting state fMRI networks from UK Biobank.

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Model outperforms ICA and dual regression for estimation of individual-specific network topography.

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We demonstrate the model's utility for predicting cognitive traits, and capturing subject variability in network topographies versus connectivity.

A major goal of large-scale brain imaging datasets is to provide resources for investigating heterogeneous populations. Characterisation of functional brain networks for individual subjects from these datasets will have an enormous potential for prediction of cognitive or clinical traits. We propose for the first time a technique, Stochastic Probabilistic Functional Modes (sPROFUMO), that is scalable to UK Biobank (UKB) with expected 100,000 participants, and hierarchically estimates functional brain networks in individuals and the population, while allowing for bidirectional flow of information between the two. Using simulations, we show the model's utility, especially in scenarios that involve significant cross-subject variability, or require delineation of fine-grained differences between the networks. Subsequently, by applying the model to resting-state fMRI from 4999 UKB subjects, we mapped resting state networks (RSNs) in single subjects with greater detail than has been possible previously in UKB (>100 RSNs), and demonstrate that these RSNs can predict a range of sensorimotor and higher-level cognitive functions. Furthermore, we demonstrate several advantages of the model over independent component analysis combined with dual-regression (ICA-DR), particularly with respect to the estimation of the spatial configuration of the RSNs and the predictive power for cognitive traits. The proposed model and results can open a new door for future investigations into individualised profiles of brain function from big data.

Integrative learning for population of dynamic networks with covariates

Although there is a rapidly growing literature on dynamic connectivity methods, the primary focus has been on separate network estimation for each individual, which fails to leverage common patterns of information. We propose novel graph-theoretic approaches for estimating a population of dynamic networks that are able to borrow information across multiple heterogeneous samples in an unsupervised manner and guided by covariate information. Specifically, we develop a Bayesian product mixture model that imposes independent mixture priors at each time scan and uses covariates to model the mixture weights, which results in time-varying clusters of samples designed to pool information. The computation is carried out using an effcient Expectation-Maximization algorithm. Extensive simulation studies illustrate sharp gains in recovering the true dynamic network over existing dynamic connectivity methods. An analysis of fMRI block task data with behavioral interventions reveal subgroups of individuals having similar dynamic connectivity, and identifies intervention-related dynamic network changes that are concentrated in biologically interpretable brain regions. In contrast, existing dynamic connectivity approaches are able to detect minimal or no changes in connectivity over time, which seems biologically unrealistic and highlights the challenges resulting from the inability to systematically borrow information across samples.

Impact of inter-individual variability on the estimation of default mode network in temporal concatenation group ICA

Temporal concatenation group ICA (TC-GICA) is a widely used data-driven method to extract common functional brain networks among individuals. TC-GICA concatenates the time series of individual fMRI data and applies dimension reduction and ICA algorithms to decompose the data into group-level components. The default mode network (DMN) estimated using TC-GICA at relatively high model orders (i.e., large numbers of components) is split into multiple components. The split DMNs are topographically different from those estimated using other methods (e.g., seed-based correlation, clustering, graph theoretical analysis, and other ICA methods like gRAICAR and IVA-GL) and are inconsistent with the existing knowledge of DMN. We hypothesize that the "DMN-splitting'' phenomenon reflects the impact of inter-individual variability in data, which is propagated into the ICA decomposition via the data-concatenation step of TC-GICA. By systematically manipulating the amount of variability involved in the temporal concatenation in both simulated and several realistic datasets, we observed that as more variability was involved, the estimated DMN became less similar to the averaged functional connectivity (FC) pattern obtained using seed-based correlation analysis. The performance of the DMN estimation in TC-GICA also exhibited remarkable dependence on the model order settings. Further analyses revealed that the "DMN-splitting" in TC-GICA could be reproduced when involving large variability in the data-concatenation and performing ICA at high model orders. These results were replicated across multiple datasets and various software implementations. When applying ICA approaches that avoid temporal concatenation, such as gRAICAR and IVA-GL, to the same datasets, the estimated group-level DMN was more consistent with the seed-based FC pattern and was more robust to various model order settings. This study calls for caution when applying TC-GICA to datasets expected to have large inter-individual variability, such as pooling different experimental groups of subjects.

HINT: A hierarchical independent component analysis toolbox for investigating brain functional networks using neuroimaging data

BACKGROUND

Independent component analysis (ICA) is a popular tool for investigating brain organization in neuroscience research. In fMRI studies, an important goal is to study how brain networks are modulated by subjects' clinical and demographic variables. Existing ICA methods and toolboxes don't incorporate subjects' covariates effects in ICA estimation of brain networks, which potentially leads to loss in accuracy and statistical power in detecting brain network differences between subjects' groups.

NEW METHOD

We introduce a Matlab toolbox, HINT (Hierarchical INdependent component analysis Toolbox), that provides a hierarchical covariate-adjusted ICA (hc-ICA) for modeling and testing covariate effects and generates model-based estimates of brain networks on both the population- and individual-level. HINT provides a user-friendly Matlab GUI that allows users to easily load images, specify covariate effects, monitor model estimation via an EM algorithm, specify hypothesis tests, and visualize results. HINT also has a command line interface which allows users to conveniently run and reproduce the analysis with a script.

COMPARISON TO EXISTING METHODS

HINT implements a new multi-level probabilistic ICA model for group ICA. It provides a statistically principled ICA modeling framework for investigating covariate effects on brain networks. HINT can also generate and visualize model-based network estimates for user-specified subject groups, which greatly facilitates group comparisons.

RESULTS

We demonstrate the steps and functionality of HINT with an fMRI example data to estimate treatment effects on brain networks while controlling for other covariates. Results demonstrate estimated brain networks and model-based comparisons between the treatment and control groups. In comparisons using synthetic fMRI data, HINT shows desirable statistical power in detecting group differences in networks especially in small sample sizes, while maintaining a low false positive rate. HINT also demonstrates similar or increased accuracy in reconstructing both population- and individual-level source signal maps as compared to some state-of-the-art group ICA methods.

CONCLUSION

HINT can provide a useful tool for both statistical and neuroscience researchers to evaluate and test differences in brain networks between subject groups.

Template Independent Component Analysis: Targeted and Reliable Estimation of Subject-level Brain Networks using Big Data Population Priors

Large brain imaging databases contain a wealth of information on brain organization in the populations they target, and on individual variability. While such databases have been used to study group-level features of populations directly, they are currently underutilized as a resource to inform single-subject analysis. Here, we propose leveraging the information contained in large functional magnetic resonance imaging (fMRI) databases by establishing population priors to employ in an empirical Bayesian framework. We focus on estimation of brain networks as source signals in independent component analysis (ICA). We formulate a hierarchical "template" ICA model where source signals-including known population brain networks and subject-specific signals-are represented as latent variables. For estimation, we derive an expectation maximization (EM) algorithm having an explicit solution. However, as this solution is computationally intractable, we also consider an approximate subspace algorithm and a faster two-stage approach. Through extensive simulation studies, we assess performance of both methods and compare with dual regression, a popular but ad-hoc method. The two proposed algorithms have similar performance, and both dramatically outperform dual regression. We also conduct a reliability study utilizing the Human Connectome Project and find that template ICA achieves substantially better performance than dual regression, achieving 75-250% higher intra-subject reliability.

A hierarchical independent component analysis model for longitudinal neuroimaging studies

In recent years, longitudinal neuroimaging study has become increasingly popular in neuroscience research to investigate disease-related changes in brain functions, to study neurodevelopment or to evaluate treatment effects on neural processing. One of the important goals in longitudinal imaging analysis is to study changes in brain functional networks across time and how the changes are modulated by subjects' clinical or demographic variables. In current neuroscience literature, one of the most commonly used tools to extract and characterize brain functional networks is independent component analysis (ICA), which separates multivariate signals into linear mixture of independent components. However, existing ICA methods are only applicable to cross-sectional studies and not suited for modeling repeatedly measured imaging data. In this paper, we propose a novel longitudinal independent component model (L-ICA) which provides a formal modeling framework for extending ICA to longitudinal studies. By incorporating subject-specific random effects and visit-specific covariate effects, L-ICA is able to provide more accurate estimates of changes in brain functional networks on both the population- and individual-level, borrow information across repeated scans within the same subject to increase statistical power in detecting covariate effects on the networks, and allow for model-based prediction for brain networks changes caused by disease progression, treatment or neurodevelopment. We develop a fully traceable exact EM algorithm to obtain maximum likelihood estimates of L-ICA. We further develop a subspace-based approximate EM algorithm which greatly reduce the computation time while still retaining high accuracy. Moreover, we present a statistical testing procedure for examining covariate effects on brain network changes. Simulation results demonstrate the advantages of our proposed methods. We apply L-ICA to ADNI2 study to investigate changes in brain functional networks in Alzheimer disease. Results from the L-ICA provide biologically insightful findings which are not revealed using existing methods.

INVESTIGATING DIFFERENCES IN BRAIN FUNCTIONAL NETWORKS USING HIERARCHICAL COVARIATE-ADJUSTED INDEPENDENT COMPONENT ANALYSIS

Human brains perform tasks via complex functional networks consisting of separated brain regions. A popular approach to characterize brain functional networks in fMRI studies is independent component analysis (ICA), which is a powerful method to reconstruct latent source signals from their linear mixtures. In many fMRI studies, an important goal is to investigate how brain functional networks change according to specific clinical and demographic variabilities. Existing ICA methods, however, cannot directly incorporate covariate effects in ICA decomposition. Heuristic post-ICA analysis to address this need can be inaccurate and inefficient. In this paper, we propose a hierarchical covariate-adjusted ICA (hc-ICA) model that provides a formal statistical framework for estimating covariate effects and testing differences between brain functional networks. Our method provides a more reliable and powerful statistical tool for evaluating group differences in brain functional networks while appropriately controlling for potential confounding factors. We present an analytically tractable EM algorithm to obtain maximum likelihood estimates of our model. We also develop a subspace-based approximate EM that runs significantly faster while retaining high accuracy. To test the differences in functional networks, we introduce a voxel-wise approximate inference procedure which eliminates the need of computationally expensive covariance matrix estimation and inversion. We demonstrate the advantages of our methods over the existing method via simulation studies. We apply our method to an fMRI study to investigate differences in brain functional networks associated with post-traumatic stress disorder (PTSD).