An Efficient and Reliable Statistical Method for Estimating Functional Connectivity in Large Scale Brain Networks Using Partial Correlation

Differential network knockoff filter with application to brain connectivity analysis

The brain functional connectivity can typically be represented as a brain functional network, where nodes represent regions of interest (ROIs) and edges symbolize their connections. Studying group differences in brain functional connectivity can help identify brain regions and recover the brain functional network linked to neurodegenerative diseases. This process, known as differential network analysis focuses on the differences between estimated precision matrices for two groups. Current methods struggle with individual heterogeneity in measuring the brain connectivity, false discovery rate (FDR) control, and accounting for confounding factors, resulting in biased estimates and diminished power. To address these issues, we present a two-stage FDR-controlled feature selection method for differential network analysis using functional magnetic resonance imaging (fMRI) data. First, we create individual brain connectivity measures using a high-dimensional precision matrix estimation technique. Next, we devise a penalized logistic regression model that employs individual brain connectivity data and integrates a new knockoff filter for FDR control when detecting significant differential edges. Through extensive simulations, we showcase the superiority of our approach compared to other methods. Additionally, we apply our technique to fMRI data to identify differential edges between Alzheimer's disease and control groups. Our results are consistent with prior experimental studies, emphasizing the practical applicability of our method.

Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations, we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We further demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics in covariance.

A survey of brain functional network extraction methods using fMRI data

Functional network (FN) analyses play a pivotal role in uncovering insights into brain function and understanding the pathophysiology of various brain disorders. This paper focuses on classical and advanced methods for deriving brain FNs from functional magnetic resonance imaging (fMRI) data. We systematically review their foundational principles, advantages, shortcomings, and interrelations, encompassing both static and dynamic FN extraction approaches. In the context of static FN extraction, we present hypothesis-driven methods such as region of interest (ROI)-based approaches as well as data-driven methods including matrix decomposition, clustering, and deep learning. For dynamic FN extraction, both window-based and windowless methods are surveyed with respect to the estimation of time-varying FN and the subsequent computation of FN states. We also discuss the scope of application of the various methods and avenues for future improvements.

A Demographic-Conditioned Variational Autoencoder for fMRI Distribution Sampling and Removal of Confounds

Objective

fMRI and derived measures such as functional connectivity (FC) have been used to predict brain age, general fluid intelligence, psychiatric disease status, and preclinical neurodegenerative disease. However, it is not always clear that all demographic confounds, such as age, sex, and race, have been removed from fMRI data. Additionally, many fMRI datasets are restricted to authorized researchers, making dissemination of these valuable data sources challenging.

Methods

We create a variational autoencoder (VAE)-based model, DemoVAE, to decorrelate fMRI features from demographics and generate high-quality synthetic fMRI data based on user-supplied demographics. We train and validate our model using two large, widely used datasets, the Philadelphia Neurodevelopmental Cohort (PNC) and Bipolar and Schizophrenia Network for Intermediate Phenotypes (BSNIP).

Results

We find that DemoVAE recapitulates group differences in fMRI data while capturing the full breadth of individual variations. Significantly, we also find that most clinical and computerized battery fields that are correlated with fMRI data are not correlated with DemoVAE latents. An exception are several fields related to schizophrenia medication and symptom severity.

Conclusion

Our model generates fMRI data that captures the full distribution of FC better than traditional VAE or GAN models. We also find that most prediction using fMRI data is dependent on correlation with, and prediction of, demographics.

Significance

Our DemoVAE model allows for generation of high quality synthetic data conditioned on subject demographics as well as the removal of the confounding effects of demographics. We identify that FC-based prediction tasks are highly influenced by demographic confounds.

The Use of Generative Adversarial Network and Graph Convolution Network for Neuroimaging-Based Diagnostic Classification

Functional connectivity (FC) obtained from resting-state functional magnetic resonance imaging has been integrated with machine learning algorithms to deliver consistent and reliable brain disease classification outcomes. However, in classical learning procedures, custom-built specialized feature selection techniques are typically used to filter out uninformative features from FC patterns to generalize efficiently on the datasets. The ability of convolutional neural networks (CNN) and other deep learning models to extract informative features from data with grid structure (such as images) has led to the surge in popularity of these techniques. However, the designs of many existing CNN models still fail to exploit the relationships between entities of graph-structure data (such as networks). Therefore, graph convolution network (GCN) has been suggested as a means for uncovering the intricate structure of brain network data, which has the potential to substantially improve classification accuracy. Furthermore, overfitting in classifiers can be largely attributed to the limited number of available training samples. Recently, the generative adversarial network (GAN) has been widely used in the medical field for its generative aspect that can generate synthesis images to cope with the problems of data scarcity and patient privacy. In our previous work, GCN and GAN have been designed to investigate FC patterns to perform diagnosis tasks, and their effectiveness has been tested on the ABIDE-I dataset. In this paper, the models will be further applied to FC data derived from more public datasets (ADHD, ABIDE-II, and ADNI) and our in-house dataset (PTSD) to justify their generalization on all types of data. The results of a number of experiments show the powerful characteristic of GAN to mimic FC data to achieve high performance in disease prediction. When employing GAN for data augmentation, the diagnostic accuracy across ADHD-200, ABIDE-II, and ADNI datasets surpasses that of other machine learning models, including results achieved with BrainNetCNN. Specifically, in ADHD, the accuracy increased from 67.74% to 73.96% with GAN, in ABIDE-II from 70.36% to 77.40%, and in ADNI, reaching 52.84% and 88.56% for multiclass and binary classification, respectively. GCN also obtains decent results, with the best accuracy in ADHD datasets at 71.38% for multinomial and 75% for binary classification, respectively, and the second-best accuracy in the ABIDE-II dataset (72.28% and 75.16%, respectively). Both GAN and GCN achieved the highest accuracy for the PTSD dataset, reaching 97.76%. However, there are still some limitations that can be improved. Both methods have many opportunities for the prediction and diagnosis of diseases.

Causal functional connectivity in Alzheimer's disease computed from time series fMRI data

Functional connectivity between brain regions is known to be altered in Alzheimer's disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an un-directed network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer's disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer's and cognitively normal groups, based on edge-wise p-values obtained by Welch's t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer's disease, published by researchers from clinical/medical institutions.

Topological Data Analysis for Multivariate Time Series Data

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent homology (PH), which can extract topological properties from data at various scales. The aim of this article is to introduce TDA concepts to a statistical audience and provide an approach to analyzing multivariate time series data. The application's focus will be on multivariate brain signals and brain connectivity networks. Finally, this paper concludes with an overview of some open problems and potential application of TDA to modeling directionality in a brain network, as well as the casting of TDA in the context of mixed effect models to capture variations in the topological properties of data collected from multiple subjects.

Network-based diagnostic probability estimation from resting-state functional magnetic resonance imaging

Brain functional connectivity is a useful biomarker for diagnosing brain disorders. Connectivity is measured using resting-state functional magnetic resonance imaging (rs-fMRI). Previous studies have used a sequential application of the graphical model for network estimation and machine learning to construct predictive formulas for determining outcomes (e.g., disease or health) from the estimated network. However, the resulting network had limited utility for diagnosis because it was estimated independent of the outcome. In this study, we proposed a regression method with scores from rs-fMRI based on supervised sparse hierarchical components analysis (SSHCA). SSHCA has a hierarchical structure that consists of a network model (block scores at the individual level) and a scoring model (super scores at the population level). A regression model, such as the multiple logistic regression model with super scores as the predictor, was used to estimate diagnostic probabilities. An advantage of the proposed method was that the outcome-related (supervised) network connections and multiple scores corresponding to the sub-network estimation were helpful for interpreting the results. Our results in the simulation study and application to real data show that it is possible to predict diseases with high accuracy using the constructed model.

R-Mixup: Riemannian Mixup for Biological Networks

Biological networks are commonly used in biomedical and healthcare domains to effectively model the structure of complex biological systems with interactions linking biological entities. However, due to their characteristics of high dimensionality and low sample size, directly applying deep learning models on biological networks usually faces severe overfitting. In this work, we propose R-Mixup, a Mixup-based data augmentation technique that suits the symmetric positive definite (SPD) property of adjacency matrices from biological networks with optimized training efficiency. The interpolation process in R-Mixup leverages the log-Euclidean distance metrics from the Riemannian manifold, effectively addressing the swelling effect and arbitrarily incorrect label issues of vanilla Mixup. We demonstrate the effectiveness of R-Mixup with five real-world biological network datasets on both regression and classification tasks. Besides, we derive a commonly ignored necessary condition for identifying the SPD matrices of biological networks and empirically study its influence on the model performance. The code implementation can be found in Appendix E.

Classification of human chronotype based on fMRI network-based statistics

Chronotype-the relationship between the internal circadian physiology of an individual and the external 24-h light-dark cycle-is increasingly implicated in mental health and cognition. Individuals presenting with a late chronotype have an increased likelihood of developing depression, and can display reduced cognitive performance during the societal 9-5 day. However, the interplay between physiological rhythms and the brain networks that underpin cognition and mental health is not well-understood. To address this issue, we use rs-fMRI collected from 16 people with an early chronotype and 22 people with a late chronotype over three scanning sessions. We develop a classification framework utilizing the Network Based-Statistic methodology, to understand if differentiable information about chronotype is embedded in functional brain networks and how this changes throughout the day. We find evidence of subnetworks throughout the day that differ between extreme chronotypes such that high accuracy can occur, describe rigorous threshold criteria for achieving 97.3% accuracy in the Evening and investigate how the same conditions hinder accuracy for other scanning sessions. Revealing differences in functional brain networks based on extreme chronotype suggests future avenues of research that may ultimately better characterize the relationship between internal physiology, external perturbations, brain networks, and disease.

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.

SCALAR ON NETWORK REGRESSION VIA BOOSTING

Neuroimaging studies have a growing interest in learning the association between the individual brain connectivity networks and their clinical characteristics. It is also of great interest to identify the sub brain networks as biomarkers to predict the clinical symptoms, such as disease status, potentially providing insight on neuropathology. This motivates the need for developing a new type of regression model where the response variable is scalar, and predictors are networks that are typically represented as adjacent matrices or weighted adjacent matrices, to which we refer as scalar-on-network regression. In this work, we develop a new boosting method for model fitting with sub-network markers selection. Our approach, as opposed to group lasso or other existing regularization methods, is essentially a gradient descent algorithm leveraging known network structure. We demonstrate the utility of our methods via simulation studies and analysis of the resting-state fMRI data in a cognitive developmental cohort study.

Statistical perspective on functional and causal neural connectomics: The Time-Aware PC algorithm

The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm—a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.

Deriving causal relationships in resting-state functional connectivity using SSFO-based optogenetic fMRI

Objective.The brain network has been extensively studied as a collection of brain regions that are functionally inter-connected. However, the study of the causal relationship in brain-wide functional connectivity, which is critical to the brain function, remains challenging. We aim to examine the feasibility of using (SSFO)-based optogenetic functional magnetic resonance imaging to infer the causal relationship (i.e. directional information) in the brain network.Approach.We combined SSFO-based optogenetics with fMRI in a resting-state rodent model to study how a local increase of excitability affects brain-wide neural activity and resting-state functional connectivity (RSFC). We incorporated Pearson's correlation and partial correlation analyses in a graphic model to derive the directional information in connections exhibiting RSFC modulations.Main results. When the dentate gyrus (DG) was sensitized by SSFO activation, we found significantly changed activity and connectivity in several brain regions associated with the DG, particularly in the medial prefrontal cortex Our causal inference result shows an 84%-100% accuracy rate compared to the directional information based on anatomical tracing data.Significance.This study establishes a system to investigate the relationship between local region activity and RSFC modulation, and provides a way to analyze the underlying causal relationship between brain regions.

Combination of structural and functional connectivity explains unique variation in specific domains of cognitive function

The relationship between structural and functional brain networks has been characterised as complex: the two networks mirror each other and show mutual influence but they also diverge in their organisation. This work explored whether a combination of structural and functional connectivity can improve the fit of regression models of cognitive performance. Principal Component Analysis (PCA) was first applied to cognitive data from the Human Connectome Project to identify latent cognitive components: Executive Function, Self-regulation, Language, Encoding and Sequence Processing. A Principal Component Regression approach with embedded Step-Wise Regression (SWR-PCR) was then used to fit regression models of each cognitive domain based on structural (SC), functional (FC) or combined structural-functional (CC) connectivity. Executive Function was best explained by the CC model. Self-regulation was equally well explained by SC and FC. Language was equally well explained by CC and FC models. Encoding and Sequence Processing were best explained by SC. Evaluation of out-of-sample models' skill via cross-validation showed that SC, FC and CC produced generalisable models of Language performance. SC models performed most effectively at predicting Language performance in unseen sample. Executive Function was most effectively predicted by SC models, followed only by CC models. Self-regulation was only effectively predicted by CC models and Sequence Processing was only effectively predicted by FC models. The present study demonstrates that integrating structural and functional connectivity can help explaining cognitive performance, but that the added explanatory value (in sample) may be domain-specific and can come at the expense of reduced generalisation performance (out-of-sample).

Simultaneous differential network analysis and classification for matrix-variate data with application to brain connectivity

Growing evidence has shown that the brain connectivity network experiences alterations for complex diseases such as Alzheimer's disease (AD). Network comparison, also known as differential network analysis, is thus particularly powerful to reveal the disease pathologies and identify clinical biomarkers for medical diagnoses (classification). Data from neurophysiological measurements are multidimensional and in matrix-form. Naive vectorization method is not sufficient as it ignores the structural information within the matrix. In the article, we adopt the Kronecker product covariance matrices framework to capture both spatial and temporal correlations of the matrix-variate data while the temporal covariance matrix is treated as a nuisance parameter. By recognizing that the strengths of network connections may vary across subjects, we develop an ensemble-learning procedure, which identifies the differential interaction patterns of brain regions between the case group and the control group and conducts medical diagnosis (classification) of the disease simultaneously. Simulation studies are conducted to assess the performance of the proposed method. We apply the proposed procedure to the functional connectivity analysis of an functional magnetic resonance imaging study on AD. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies, and satisfactory out-of-sample classification performance is achieved for medical diagnosis of AD.

Generalized Connectivity Matrix Response Regression with Applications in Brain Connectivity Studies

Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose a new generalized matrix response regression model, where the observed network is treated as a matrix-valued response and the subject covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the effect of subject covariates through a sparse slope tensor. We develop an efficient alternating gradient descent algorithm for parameter estimation, and establish the non-asymptotic error bound for the actual estimator from the algorithm, which quantifies the interplay between the computational and statistical errors. We further show the strong consistency for graph community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through simulations and two brain connectivity studies.

A Multimodal Multilevel Neuroimaging Model for Investigating Brain Connectome Development

Recent advancements of multimodal neuroimaging such as functional MRI (fMRI) and diffusion MRI (dMRI) offers unprecedented opportunities to understand brain development. Most existing neurodevelopmental studies focus on using a single imaging modality to study microstructure or neural activations in localized brain regions. The developmental changes of brain network architecture in childhood and adolescence are not well understood. Our study made use of dMRI and resting-state fMRI imaging data sets from Philadelphia Neurodevelopmental Cohort (PNC) study to characterize developmental changes in both structural as well as functional brain connectomes. A multimodal multilevel model (MMM) is developed and implemented in PNC study to investigate brain maturation in both white matter structural connection and intrinsic functional connection. MMM addresses several major challenges in multimodal connectivity analysis. First, by using a first-level data generative model for observed measures and a second-level latent network modeling, MMM effectively infers underlying connection states from noisy imaging-based connectivity measurements. Secondly, MMM models the interplay between the structural and functional connections to capture the relationship between different brain connectomes. Thirdly, MMM incorporates covariate effects in the network modeling to investigate network heterogeneity across subpopoulations. Finally, by using a module-wise parameterization based on brain network topology, MMM is scalable to whole-brain connectomics. MMM analysis of the PNC study generates new insights in neurodevelopment during adolescence including revealing the majority of the white fiber connectivity growth are related to the cognitive networks where the most significant increase is found between the default mode and the executive control network with a 15% increase in the probability of structural connections. We also uncover functional connectome development mainly derived from global functional integration rather than direct anatomical connections. To the best of our knowledge, these findings have not been reported in the literature using multimodal connectomics. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Functional connectome of brainstem nuclei involved in autonomic, limbic, pain and sensory processing in living humans from 7 Tesla resting state fMRI

Despite remarkable advances in mapping the functional connectivity of the cortex, the functional connectivity of subcortical regions is understudied in living humans. This is the case for brainstem nuclei that control vital processes, such as autonomic, limbic, nociceptive and sensory functions. This is because of the lack of precise brainstem nuclei localization, of adequate sensitivity and resolution in the deepest brain regions, as well as of optimized processing for the brainstem. To close the gap between the cortex and the brainstem, on 20 healthy subjects, we computed a correlation-based functional connectome of 15 brainstem nuclei involved in autonomic, limbic, nociceptive, and sensory function (superior and inferior colliculi, ventral tegmental area-parabrachial pigmented nucleus complex, microcellular tegmental nucleus-prabigeminal nucleus complex, lateral and medial parabrachial nuclei, vestibular and superior olivary complex, superior and inferior medullary reticular formation, viscerosensory motor nucleus, raphe magnus, pallidus, and obscurus, and parvicellular reticular nucleus - alpha part) with the rest of the brain. Specifically, we exploited 1.1mm isotropic resolution 7 Tesla resting-state fMRI, ad-hoc coregistration and physiological noise correction strategies, and a recently developed probabilistic template of brainstem nuclei. Further, we used 2.5mm isotropic resolution resting-state fMRI data acquired on a 3 Tesla scanner to assess the translatability of our results to conventional datasets. We report highly consistent correlation coefficients across subjects, confirming available literature on autonomic, limbic, nociceptive and sensory pathways, as well as high interconnectivity within the central autonomic network and the vestibular network. Interestingly, our results showed evidence of vestibulo-autonomic interactions in line with previous work. Comparison of 7 Tesla and 3 Tesla findings showed high translatability of results to conventional settings for brainstem-cortical connectivity and good yet weaker translatability for brainstem-brainstem connectivity. The brainstem functional connectome might bring new insight in the understanding of autonomic, limbic, nociceptive and sensory function in health and disease.

Hypothesis Testing for Network Data with Power Enhancement

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Numerous existing network inference solutions focus on global testing of entire networks, without comparing individual network links. The observed data often take the form of vectors or matrices, and the problem is formulated as comparing two covariance or precision matrices under a normal or matrix normal distribution. Moreover, many tests suffer from a limited power under a small sample size. In this article, we tackle the problem of network comparison, both global and simultaneous inferences, when the data come in a different format, i.e., in the form of a collection of symmetric matrices, each of which encodes the network structure of an individual subject. Such data format commonly arises in applications such as brain connectivity analysis and clinical genomics. We no longer require the underlying data to follow a normal distribution, but instead impose some moment conditions that are easily satisfied for numerous types of network data. Furthermore, we propose a power enhancement procedure, and show that it can control the false discovery, while it has the potential to substantially enhance the power of the test. We investigate the efficacy of our testing procedure through both an asymptotic analysis and a simulation study under a finite sample size. We further illustrate our method with examples of brain connectivity analysis.

Estimating Functional Connectivity by Integration of Inherent Brain Function Activity Pattern Priors

Brain functional connectivity (FC) has shown great potential in becoming biomarkers of brain status. However, the problem of accurately estimating FC from complex-noisy fMRI time series remains unsolved. Usually, a regularization function is more appropriate in fitting the real inherent properties of the brain function activity pattern, which can further limit noise interference to improve the accuracy of the estimated result. Recently, the neuroscientists widely suggested that the inherent brain function activity pattern indicates sparse, modular and overlapping topology. However, previous studies have never considered this factual characteristic. Thus, we propose a novel method by integration of these inherent brain function activity pattern priors to estimate FC. Extensive experiments on synthetic data demonstrate that our method can more accurately estimate the FC than previous. Then, we applied the estimated FC to predict the symptom severity of depressed patients, the symptom severity is related to subtle abnormal changes in the brain function activity, a more accurate FC can more effectively capture the subtle abnormal brain function activity changes. As results, our method better than others with a higher correlation coefficient of 0.4201. Moreover, the overlapping probability of each brain region can be further explored by the proposed method.

Conditional Functional Graphical Models

Graphical modeling of multivariate functional data is becoming increasingly important in a wide variety of applications. The changes of graph structure can often be attributed to external variables, such as the diagnosis status or time, the latter of which gives rise to the problem of dynamic graphical modeling. Most existing methods focus on estimating the graph by aggregating samples, but largely ignore the subject-level heterogeneity due to the external variables. In this article, we introduce a conditional graphical model for multivariate random functions, where we treat the external variables as conditioning set, and allow the graph structure to vary with the external variables. Our method is built on two new linear operators, the conditional precision operator and the conditional partial correlation operator, which extend the precision matrix and the partial correlation matrix to both the conditional and functional settings. We show that their nonzero elements can be used to characterize the conditional graphs, and develop the corresponding estimators. We establish the uniform convergence of the proposed estimators and the consistency of the estimated graph, while allowing the graph size to grow with the sample size, and accommodating both completely and partially observed data. We demonstrate the efficacy of the method through both simulations and a study of brain functional connectivity network.

Feasibility of Auricular Field Stimulation in Fibromyalgia: Evaluation by Functional Magnetic Resonance Imaging, Randomized Trial

OBJECTIVE

To evaluate the feasibility of recruitment, preliminary efficacy, and acceptability of auricular percutaneous electrical nerve field stimulation (PENFS) for the treatment of fibromyalgia in veterans, using neuroimaging as an outcome measure and a biomarker of treatment response.

DESIGN

Randomized, controlled, single-blind.

SETTING

Government hospital.

SUBJECTS

Twenty-one veterans with fibromyalgia were randomized to standard therapy (ST) control or ST with auricular PENFS treatment.

METHODS

Participants received weekly visits with a pain practitioner over 4 weeks. The PENFS group received reapplication of PENFS at each weekly visit. Resting-state functional connectivity magnetic resonance imaging (rs-fcMRI) data were collected within 2 weeks prior to initiating treatment and 2 weeks following the final treatment. Analysis of rs-fcMRI used a right posterior insula seed. Pain and function were assessed at baseline and at 2, 6, and 12 weeks post-treatment.

RESULTS

At 12 weeks post-treatment, there was a nonsignificant trend toward improved pain scores and significant improvements in pain interference with sleep among the PENFS treatment group as compared with the ST controls. Neuroimaging data displayed increased connectivity to areas of the cerebellum and executive control networks in the PENFS group as compared with the ST control group following treatment.

CONCLUSIONS

There was a trend toward improved pain and function among veterans with fibromyalgia in the ST + PENFS group as compared with the ST control group. Pain and functional outcomes correlated with altered rs-fcMRI network connectivity. Neuroimaging results differed between groups, suggesting an alternative underlying mechanism for PENFS analgesia.

Multivariate Correlation Measures Reveal Structure and Strength of Brain-Body Physiological Networks at Rest and During Mental Stress

In this work, we extend to the multivariate case the classical correlation analysis used in the field of network physiology to probe dynamic interactions between organ systems in the human body. To this end, we define different correlation-based measures of the multivariate interaction (MI) within and between the brain and body subnetworks of the human physiological network, represented, respectively, by the time series of δ, θ, α, and β electroencephalographic (EEG) wave amplitudes, and of heart rate, respiration amplitude, and pulse arrival time (PAT) variability (η, ρ, π). MI is computed: (i) considering all variables in the two subnetworks to evaluate overall brain-body interactions; (ii) focusing on a single target variable and dissecting its global interaction with all other variables into contributions arising from the same subnetwork and from the other subnetwork; and (iii) considering two variables conditioned to all the others to infer the network topology. The framework is applied to the time series measured from the EEG, electrocardiographic (ECG), respiration, and blood volume pulse (BVP) signals recorded synchronously via wearable sensors in a group of healthy subjects monitored at rest and during mental arithmetic and sustained attention tasks. We find that the human physiological network is highly connected, with predominance of the links internal of each subnetwork (mainly η-ρ and δ-θ, θ-α, α-β), but also statistically significant interactions between the two subnetworks (mainly η-β and η-δ). MI values are often spatially heterogeneous across the scalp and are modulated by the physiological state, as indicated by the decrease of cardiorespiratory interactions during sustained attention and by the increase of brain-heart interactions and of brain-brain interactions at the frontal scalp regions during mental arithmetic. These findings illustrate the complex and multi-faceted structure of interactions manifested within and between different physiological systems and subsystems across different levels of mental stress.

Network Modeling in Biology: Statistical Methods for Gene and Brain Networks

The rise of network data in many different domains has offered researchers new insight into the problem of modeling complex systems and propelled the development of numerous innovative statistical methodologies and computational tools. In this paper, we primarily focus on two types of biological networks, gene networks and brain networks, where statistical network modeling has found both fruitful and challenging applications. Unlike other network examples such as social networks where network edges can be directly observed, both gene and brain networks require careful estimation of edges using covariates as a first step. We provide a discussion on existing statistical and computational methods for edge esitimation and subsequent statistical inference problems in these two types of biological networks.

Link predictions for incomplete network data with outcome misclassification

Link prediction is a fundamental problem in network analysis. In a complex network, links can be unreported and/or under detection limits due to heterogeneous sources of noise and technical challenges during data collection. The incomplete network data can lead to an inaccurate inference of network based data analysis. We propose a parametric link prediction model and consider latent links as misclassified binary outcomes. We develop new algorithms to optimize model parameters and yield robust predictions of unobserved links. Theoretical properties of the predictive model are also discussed. We apply the new method to a partially observed social network data and incomplete brain network data. The results demonstrate that our method outperforms the existing latent-link prediction methods.

Modulation of SI and ACC response to noxious and non-noxious electrical stimuli after the spared nerve injury model of neuropathic pain

BACKGROUND

The current knowledge on the role of SI and ACC in acute pain processing and how these contribute to the development of chronic pain is limited. Our objective was to investigate differences in and modulation of intracortical responses from SI and ACC in response to different intensities of peripheral presumed noxious and non-noxious stimuli in the acute time frame of a peripheral nerve injury in rats.

METHODS

We applied non-noxious and noxious electrical stimulation pulses through a cuff electrode placed around the sciatic nerve and measured the cortical responses (six electrodes in each cortical area) before and after the spared nerve injury model.

RESULTS

We found that the peak response correlated with the stimulation intensity and that SI and ACC differed in both amplitude and latency of cortical response. The cortical response to both noxious and non-noxious stimulation showed a trend towards faster processing of non-noxious stimuli in ACC and increased cortical processing of non-noxious stimuli in SI after SNI.

CONCLUSIONS

We found different responses in SI and ACC to different intensity electrical stimulations based on two features and changes in these features following peripheral nerve injury. We believe that these features may be able to assist to track cortical changes during the chronification of pain in future animal studies.

SIGNIFICANCE

This study showed distinct cortical processing of noxious and non-noxious peripheral stimuli in SI and ACC. The processing latency in ACC and accumulated spiking activity in SI appeared to be modulated by peripheral nerve injury, which elaborated on the function of these two areas in the processing of nociception.

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.

Partial Similarity Reveals Dynamics in Brainstem-Midbrain Networks during Trigeminal Nociception

Imaging studies help us understand the important role of brainstem and midbrain regions in human trigeminal pain processing without solving the question of how these regions actually interact. In the current study, we describe this connectivity and its dynamics during nociception with a novel analytical approach called Partial Similarity (PS). We developed PS specifically to estimate the communication between individual hubs of the network in contrast to the overall communication within that network. Partial Similarity works on trial-to-trial variance of neuronal activity acquired with functional magnetic resonance imaging. It discovers direct communication between two hubs considering the remainder of the network as confounds. A similar method to PS is Representational Similarity, which works with ordinary correlations and does not consider any external influence on the communication between two hubs. Particularly the combination of Representational Similarity and Partial Similarity analysis unravels brainstem dynamics involved in trigeminal pain using the spinal trigeminal nucleus (STN)—the first relay station of peripheral trigeminal input—as a seed region. The combination of both methods can be valuable tools in discovering the network dynamics in fMRI and an important instrument for future insight into the nature of various neurological diseases like primary headaches.

Reproducibility of graph measures at the subject level using resting-state fMRI

INTRODUCTION

Graph metrics have been proposed as potential biomarkers for diagnosis in clinical work. However, before it can be applied in a clinical setting, their reproducibility should be evaluated.

METHODS

This study systematically investigated the effect of two denoising pipelines and different whole-brain network constructions on reproducibility of subject-specific graph measures. We used the multi-session fMRI dataset from the Brain Genomics Superstruct Project consisting of 69 healthy young adults.

RESULTS

In binary networks, the test-retest variability for global measures was large at low density irrespective of the denoising strategy or the type of correlation. Weighted networks showed very low test-retest values (and thus a good reproducibility) for global graph measures irrespective of the strategy used. Comparing the test-retest values for different strategies, there were significant main effects of the type of correlation (Pearson correlation vs. partial correlation), the (partial) correlation value (absolute vs. positive vs. negative), and weight calculation (based on the raw (partial) correlation values vs. based on transformed Z-values). There was also a significant interaction effect between type of correlation and weight calculation. Similarly as for the binary networks, there was no main effect of the denoising pipeline.

CONCLUSION

Our results demonstrated that normalized global graph measures based on a weighted network using the absolute (partial) correlation as weight were reproducible. The denoising pipeline and the granularity of the whole-brain parcellation used to define the nodes were not critical for the reproducibility of normalized graph measures.

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.

Heart Rate Variability as an Index of Differential Brain Dynamics at Rest and After Acute Stress Induction

The brain continuously receives input from the internal and external environment. Using this information, the brain exerts its influence on both itself and the body to facilitate an appropriate response. The dynamic interplay between the brain and the heart and how external conditions modulate this relationship deserves attention. In high-stress situations, synchrony between various brain regions such as the prefrontal cortex and the heart may alter. This flexibility is believed to facilitate transitions between functional states related to cognitive, emotional, and especially autonomic activity. This study examined the dynamic temporal functional association of heart rate variability (HRV) with the interaction between three main canonical brain networks in 38 healthy male subjects at rest and directly after a psychosocial stress task. A sliding window approach was used to estimate the functional connectivity (FC) among the salience network (SN), central executive network (CEN), and default mode network (DMN) in 60-s windows on time series of blood-oxygen-level dependent (BOLD) signal. FC between brain networks was calculated by Pearson correlation. A multilevel linear mixed model was conducted to examine the window-by-window association between the root mean square of successive differences between normal heartbeats (RMSSD) and FC of network-pairs across sessions. Our findings showed that the minute-by-minute correlation between the FC and RMSSD was significantly stronger between DMN and CEN than for SN and CEN in the baseline session [b = 4.36, t(5025) = 3.20, p = 0.006]. Additionally, this differential relationship between network pairs and RMSSD disappeared after the stress task; FC between DMN and CEN showed a weaker correlation with RMSSD in comparison to baseline [b = −3.35, t(5025) = −3.47, p = 0.006]. These results suggest a dynamic functional interplay between HRV and the functional association between brain networks that varies depending on the needs created by changing conditions.

Gaussian Graphical Models Reveal Inter-Modal and Inter-Regional Conditional Dependencies of Brain Alterations in Alzheimer's Disease

Alzheimer's disease (AD) is characterized by a sequence of pathological changes, which are commonly assessed in vivo using various brain imaging modalities such as magnetic resonance imaging (MRI) and positron emission tomography (PET). Currently, the most approaches to analyze statistical associations between regions and imaging modalities rely on Pearson correlation or linear regression models. However, these models are prone to spurious correlations arising from uninformative shared variance and multicollinearity. Notably, there are no appropriate multivariate statistical models available that can easily integrate dozens of multicollinear variables derived from such data, being able to utilize the additional information provided from the combination of data sources. Gaussian graphical models (GGMs) can estimate the conditional dependency from given data, which is conceptually expected to closely reflect the underlying causal relationships between various variables. Hence, we applied GGMs to assess multimodal regional brain alterations in AD. We obtained data from N = 972 subjects from the Alzheimer's Disease Neuroimaging Initiative. The mean amyloid load (AV45-PET), glucose metabolism (FDG-PET), and gray matter volume (MRI) were calculated for each of the 108 cortical and subcortical brain regions. GGMs were estimated using a Bayesian framework for the combined multimodal data and the resulted conditional dependency networks were compared to classical covariance networks based on Pearson correlation. Additionally, graph-theoretical network statistics were calculated to determine network alterations associated with disease status. The resulting conditional dependency matrices were much sparser (≈10% density) than Pearson correlation matrices (≈50% density). Within imaging modalities, conditional dependency networks yielded clusters connecting anatomically adjacent regions. For the associations between different modalities, only few region-specific connections were detected. Network measures such as small-world coefficient were significantly altered across diagnostic groups, with a biphasic u-shape trajectory, i.e., increased small-world coefficient in early mild cognitive impairment (MCI), similar values in late MCI, and decreased values in AD dementia patients compared to cognitively normal controls. In conclusion, GGMs removed commonly shared variance among multimodal measures of regional brain alterations in MCI and AD, and yielded sparser matrices compared to correlation networks based on the Pearson coefficient. Therefore, GGMs may be used as alternative to thresholding-approaches typically applied to correlation networks to obtain the most informative relations between variables.

Heterogeneity of Preictal Dynamics in Human Epileptic Seizures

It is generally understood that there is a preictal phase in the development of a seizure and this precictal period is the basis for seizure prediction attempts. The focus of this study is the preictal global spatiotemporal dynamics and its intra-patient variability. We analyzed preictal broadband brain connectivity from human electrocorticography (ECoG) recordings of 185 seizures (which included 116 clinical seizures) collected from 12 patients. ECoG electrodes record from only a part of the cortex, leaving large regions of the brain unobserved. Brain connectivity was therefore estimated using the sparse-plus-latent-regularized precision matrix (SLRPM) method, which calculates connectivity from partial correlations of the conditional statistics of the observed regions given the unobserved latent regions. Brain connectivity was quantified using eigenvector centrality (EC), from which a degree of heterogeneity was calculated for the preictal periods of all seizures in each patient. Results from the SLRPM method are compared to those from the sparse-regularized precision matrix (SRPM) and correlation methods, which do not account for the unobserved inputs when estimating brain connectivity. The degree of heterogeneity estimated by the SLRPM method is higher than those estimated by the SRPM and correlation methods for the preictal periods in most patients. These results reveal substantial heterogeneity or desynchronization among brain areas in the preictal period of human epileptic seizures. Furthermore, the SLRPM method identifies more onset channels from the preictal active electrodes compared to the SRPM and correlation methods. Finally, the correlation between the degree of heterogeneity and seizure severity of patients for SLRPM and SRPM methods were lower than that obtained from the correlation method. These results support recent findings suggesting that inhibitory neurons can have anti-seizure effects by inducing variability or heterogeneity across seizures. Understanding how this variability is linked to seizure initiation may lead to better predictions and controlling therapies.

Mixed-Effect Time-Varying Network Model and Application in Brain Connectivity Analysis

Time-varying networks are fast emerging in a wide range of scientific and business applications. Most existing dynamic network models are limited to a single-subject and discrete-time setting. In this article, we propose a mixed-effect network model that characterizes the continuous time-varying behavior of the network at the population level, meanwhile taking into account both the individual subject variability as well as the prior module information. We develop a multistep optimization procedure for a constrained likelihood estimation and derive the associated asymptotic properties. We demonstrate the effectiveness of our method through both simulations and an application to a study of brain development in youth. Supplementary materials for this article are available online.

Capturing the Forest but Missing the Trees: Microstates Inadequate for Characterizing Shorter-Scale EEG Dynamics

The brain is known to be active even when not performing any overt cognitive tasks, and often it engages in involuntary mind wandering. This resting state has been extensively characterized in terms of fMRI-derived brain networks. However, an alternate method has recently gained popularity: EEG microstate analysis. Proponents of microstates postulate that the brain discontinuously switches between four quasi-stable states defined by specific EEG scalp topologies at peaks in the global field potential (GFP). These microstates are thought to be “atoms of thought,” involved with visual, auditory, salience, and attention processing. However, this method makes some major assumptions by excluding EEG data outside the GFP peaks and then clustering the EEG scalp topologies at the GFP peaks, assuming that only one microstate is active at any given time. This study explores the evidence surrounding these assumptions by studying the temporal dynamics of microstates and its clustering space using tools from dynamical systems analysis, fractal, and chaos theory to highlight the shortcomings in microstate analysis. The results show evidence of complex and chaotic EEG dynamics outside the GFP peaks, which is being missed by microstate analysis. Furthermore, the winner-takes-all approach of only one microstate being active at a time is found to be inadequate since the dynamic EEG scalp topology does not always resemble that of the assigned microstate, and there is competition among the different microstate classes. Finally, clustering space analysis shows that the four microstates do not cluster into four distinct and separable clusters. Taken collectively, these results show that the discontinuous description of EEG microstates is inadequate when looking at nonstationary short-scale EEG dynamics.

Paired test of matrix graphs and brain connectivity analysis

Inferring brain connectivity network and quantifying the significance of interactions between brain regions are of paramount importance in neuroscience. Although there have recently emerged some tests for graph inference based on independent samples, there is no readily available solution to test the change of brain network for paired and correlated samples. In this article, we develop a paired test of matrix graphs to infer brain connectivity network when the groups of samples are correlated. The proposed test statistic is both bias corrected and variance corrected, and achieves a small estimation error rate. The subsequent multiple testing procedure built on this test statistic is guaranteed to asymptotically control the false discovery rate at the pre-specified level. Both the methodology and theory of the new test are considerably different from the two independent samples framework, owing to the strong correlations of measurements on the same subjects before and after the stimulus activity. We illustrate the efficacy of our proposal through simulations and an analysis of an Alzheimer's Disease Neuroimaging Initiative dataset.

A difference degree test for comparing brain networks

Recently, there has been a proliferation of methods investigating functional connectivity as a biomarker for mental disorders. Typical approaches include massive univariate testing at each edge or comparisons of network metrics to identify differing topological features. Limitations of these methods include low statistical power due to the large number of comparisons and difficulty attributing overall differences in networks to local variation. We propose a method to capture the difference degree, which is the number of edges incident to each region in the difference network. Our difference degree test (DDT) is a two-step procedure for identifying brain regions incident to a significant number of differentially weighted edges (DWEs). First, we select a data-adaptive threshold which identifies the DWEs followed by a statistical test for the number of DWEs incident to each brain region. We achieve this by generating an appropriate set of null networks which are matched on the first and second moments of the observed difference network using the Hirschberger-Qi-Steuer algorithm. This formulation permits separation of the network's true topology from the nuisance topology induced by the correlation measure that alters interregional connectivity in ways unrelated to brain function. In simulations, the proposed approach outperforms competing methods in detecting differentially connected regions of interest. Application of DDT to a major depressive disorder dataset leads to the identification of brain regions in the default mode network commonly implicated in this ruminative disorder.

The Functional Brain Organization of an Individual Allows Prediction of Measures of Social Abilities Transdiagnostically in Autism and Attention-Deficit/Hyperactivity Disorder

BACKGROUND

Autism spectrum disorder and attention-deficit/hyperactivity disorder (ADHD) are associated with complex changes as revealed by functional magnetic resonance imaging. To date, neuroimaging-based models are not able to characterize individuals with sufficient sensitivity and specificity. Further, although evidence shows that ADHD traits occur in individuals with autism spectrum disorder, and autism spectrum disorder traits in individuals with ADHD, the neurofunctional basis of the overlap is undefined.

METHODS

Using individuals from the Autism Brain Imaging Data Exchange and ADHD-200, we apply a data-driven, subject-level approach, connectome-based predictive modeling, to resting-state functional magnetic resonance imaging data to identify brain-behavior associations that are predictive of symptom severity. We examine cross-diagnostic commonalities and differences.

RESULTS

Using leave-one-subject-out and split-half analyses, we define networks that predict Social Responsiveness Scale, Autism Diagnostic Observation Schedule, and ADHD Rating Scale scores and confirm that these networks generalize to novel subjects. Networks share minimal overlap of edges (<2%) but some common regions of high hubness (Brodmann areas 10, 11, and 21, cerebellum, and thalamus). Further, predicted Social Responsiveness Scale scores for individuals with ADHD are linked to ADHD symptoms, supporting the hypothesis that brain organization relevant to autism spectrum disorder severity shares a component associated with attention in ADHD. Predictive connections and high-hubness regions are found within a wide range of brain areas and across conventional networks.

CONCLUSIONS

An individual's functional connectivity profile contains information that supports dimensional, nonbinary classification in autism spectrum disorder and ADHD. Furthermore, we can determine disorder-specific and shared neurofunctional pathology using our method.

Characterizing Brain Connectivity From Human Electrocorticography Recordings With Unobserved Inputs During Epileptic Seizures

Epilepsy is a neurological disorder characterized by the sudden occurrence of unprovoked seizures. There is extensive evidence of significantly altered brain connectivity during seizure periods in the human brain. Research on analyzing human brain functional connectivity during epileptic seizures has been limited predominantly to the use of the correlation method. However, spurious connectivity can be measured between two brain regions without having direct connection or interaction between them. Correlations can be due to the apparent interactions of the two brain regions resulting from common input from a third region, which may or may not be observed. Hence, researchers have recently proposed a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions, thus identifying observed regions that are conditionally independent of both the observed and latent regions. We evaluate the performance of the methods using a spring-mass artificial network and assuming that some nodes cannot be observed, thus constituting the latent variables in the example. Several cases have been considered, including both sparse and dense connections, short-range and long-range connections, and a varying number of latent variables. The SLRPM method is then applied to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seventy-four clinical seizures from five patients, all having complex partial epilepsy, were analyzed using SLRPM, and brain connectivity was quantified using modularity index, clustering coefficient, and eigenvector centrality. Furthermore, using a measure of latent inputs estimated by the SLRPM method, it was possible to automatically detect 72 of the 74 seizures with four false positives and find six seizures that were not marked manually.

Variability of Resting-State Functional MRI Graph Theory Metrics across 3T Platforms

BACKGROUND AND PURPOSE

Graph theory analysis of brain connectivity data is a promising tool for studying the function of the healthy and diseased brain. The consistency of resting-state functional MRI (rsfMRI) connectivity measures across multiple scanner types is an important factor in designing multi-institutional research studies and has important implications for the potential use of this technique in a heterogeneous clinical setting. We sought to quantitatively study the interscanner variability of rsfMRI graph theory metrics obtained from healthy volunteers scanned on three different scanner platforms.

METHODS

In this prospective Institutional Review Board approved study, 9 healthy volunteers were enrolled for brain MRI on three 3T scanners (Magnetom Prisma, Skyra, and Trio, Siemens, Erlangen, Germany) in three separate scan sessions within approximately 1 week. Standard preprocessing of rsfMRI was performed with SPM12. Subject scans were normalized to Montreal Neurologic Institute (MNI) space, and connectivity of 116 regions-of-interests based on the automated anatomic labeling (AAL) atlas was calculated using Conn toolbox. Whole-network graph theory metrics were calculated using Brain Connectivity Toolbox, and intraclass correlation (ICC) across three scan sessions was assessed.

RESULTS

A total of 25 rsfMRI exams were completed in 9 subjects with a median-intersession time of 3 days. Among all three sessions, there was good to excellent agreement in characteristic path length and global efficiency (ICC: .79, .79) and good agreement in the transitivity, local efficiency, and clustering coefficient (ICC = .72, .69, .62).

CONCLUSIONS

There was high consistency of graph theory metrics of rsfMRI connectivity networks among healthy volunteers scanned on three different generation 3T MRI scanners.

A Comparison of Static and Dynamic Functional Connectivities for Identifying Subjects and Biological Sex Using Intrinsic Individual Brain Connectivity

Functional magnetic resonance imaging has revealed correlated activities in brain regions even in the absence of a task. Initial studies assumed this resting-state functional connectivity (FC) to be stationary in nature, but recent studies have modeled these activities as a dynamic network. Dynamic spatiotemporal models better model the brain activities, but are computationally more involved. A comparison of static and dynamic FCs was made to quantitatively study their efficacies in identifying intrinsic individual connectivity patterns using data from the Human Connectome Project. Results show that the intrinsic individual brain connectivity pattern can be used as a 'fingerprint' to distinguish among and identify subjects and is more accurately captured with partial correlation and assuming static FC. It was also seen that the intrinsic individual brain connectivity patterns were invariant over a few months. Additionally, biological sex identification was successfully performed using the intrinsic individual connectivity patterns, and group averages of male and female FC matrices. Edge consistency, edge variability and differential power measures were used to identify the major resting-state networks involved in identifying subjects and their sex.

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.

Differential pattern of brain functional connectome in obsessive-compulsive disorder versus healthy controls

Researchers believe that recognition of functional impairment in some of brain networks such as frontal-parietal, default mode network (DMN), anterior medial prefrontal cortex (MPFC) and striatal structures could be a beneficial biomarker for diagnosis of obsessive-compulsive disorder (OCD). Although it is well recognized brain functional connectome in OCD patients shows changes, debate still remains on characteristics of the changes. In this regard, little has been done so far to statistically assess the altered pattern using whole brain electroencephalography. In this study, resting state EEG data of 39 outpatients with OCD and 19 healthy controls (HC) were recorded. After, brain functional network was estimated from the cleaned EEG data using the weighted phase lag index algorithm. Output matrices of OCD group and HCs were then statistically compared to represent meaningful differences. Significant differences in functional connectivity pattern were demonstrated in several regions. As expected the most significant changes were observed in frontal cortex, more significant in frontal-temporal connections (between F3 and F7, and T5 regions). These results in OCD patients are consistent with previous studies and confirm the role of frontal and temporal brain regions in OCD.

Graph theory approaches to functional network organization in brain disorders: A critique for a brave new small-world

Over the past two decades, resting-state functional connectivity (RSFC) methods have provided new insights into the network organization of the human brain. Studies of brain disorders such as Alzheimer's disease or depression have adapted tools from graph theory to characterize differences between healthy and patient populations. Here, we conducted a review of clinical network neuroscience, summarizing methodological details from 106 RSFC studies. Although this approach is prevalent and promising, our review identified four challenges. First, the composition of networks varied remarkably in terms of region parcellation and edge definition, which are fundamental to graph analyses. Second, many studies equated the number of connections across graphs, but this is conceptually problematic in clinical populations and may induce spurious group differences. Third, few graph metrics were reported in common, precluding meta-analyses. Fourth, some studies tested hypotheses at one level of the graph without a clear neurobiological rationale or considering how findings at one level (e.g., global topology) are contextualized by another (e.g., modular structure). Based on these themes, we conducted network simulations to demonstrate the impact of specific methodological decisions on case-control comparisons. Finally, we offer suggestions for promoting convergence across clinical studies in order to facilitate progress in this important field.