Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity

Bayesian varying-effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury

In this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi-subject Bayesian vector autoregressive model that estimates group-specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group-specific networks and selection of relevant covariate effects. We show improved performance over competing two-stage approaches on simulated data. We apply our method on resting-state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group-level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.

High-dimensional multisubject time series transition matrix inference with application to brain connectivity analysis

Brain-effective connectivity analysis quantifies directed influence of one neural element or region over another, and it is of great scientific interest to understand how effective connectivity pattern is affected by variations of subject conditions. Vector autoregression (VAR) is a useful tool for this type of problems. However, there is a paucity of solutions when there is measurement error, when there are multiple subjects, and when the focus is the inference of the transition matrix. In this article, we study the problem of transition matrix inference under the high-dimensional VAR model with measurement error and multiple subjects. We propose a simultaneous testing procedure, with three key components: a modified expectation-maximization (EM) algorithm, a test statistic based on the tensor regression of a bias-corrected estimator of the lagged auto-covariance given the covariates, and a properly thresholded simultaneous test. We establish the uniform consistency for the estimators of our modified EM, and show that the subsequent test achieves both a consistent false discovery control, and its power approaches one asymptotically. We demonstrate the efficacy of our method through both simulations and a brain connectivity study of task-evoked functional magnetic resonance imaging.

Macroscopic resting-state brain dynamics are best described by linear models

It is typically assumed that large networks of neurons exhibit a large repertoire of nonlinear behaviours. Here we challenge this assumption by leveraging mathematical models derived from measurements of local field potentials via intracranial electroencephalography and of whole-brain blood-oxygen-level-dependent brain activity via functional magnetic resonance imaging. We used state-of-the-art linear and nonlinear families of models to describe spontaneous resting-state activity of 700 participants in the Human Connectome Project and 122 participants in the Restoring Active Memory project. We found that linear autoregressive models provide the best fit across both data types and three performance metrics: predictive power, computational complexity and the extent of the residual dynamics unexplained by the model. To explain this observation, we show that microscopic nonlinear dynamics can be counteracted or masked by four factors associated with macroscopic dynamics: averaging over space and over time, which are inherent to aggregated macroscopic brain activity, and observation noise and limited data samples, which stem from technological limitations. We therefore argue that easier-to-interpret linear models can faithfully describe macroscopic brain dynamics during resting-state conditions.

Through the looking glass: Deep interpretable dynamic directed connectivity in resting fMRI

Brain network interactions are commonly assessed via functional (network) connectivity, captured as an undirected matrix of Pearson correlation coefficients. Functional connectivity can represent static and dynamic relations, but often these are modeled using a fixed choice for the data window Alternatively, deep learning models may flexibly learn various representations from the same data based on the model architecture and the training task. However, the representations produced by deep learning models are often difficult to interpret and require additional posthoc methods, e.g., saliency maps. In this work, we integrate the strengths of deep learning and functional connectivity methods while also mitigating their weaknesses. With interpretability in mind, we present a deep learning architecture that exposes a directed graph layer that represents what the model has learned about relevant brain connectivity. A surprising benefit of this architectural interpretability is significantly improved accuracy in discriminating controls and patients with schizophrenia, autism, and dementia, as well as age and gender prediction from functional MRI data. We also resolve the window size selection problem for dynamic directed connectivity estimation as we estimate windowing functions from the data, capturing what is needed to estimate the graph at each time-point. We demonstrate efficacy of our method in comparison with multiple existing models that focus on classification accuracy, unlike our interpretability-focused architecture. Using the same data but training different models on their own discriminative tasks we are able to estimate task-specific directed connectivity matrices for each subject. Results show that the proposed approach is also more robust to confounding factors compared to standard dynamic functional connectivity models. The dynamic patterns captured by our model are naturally interpretable since they highlight the intervals in the signal that are most important for the prediction. The proposed approach reveals that differences in connectivity among sensorimotor networks relative to default-mode networks are an important indicator of dementia and gender. Dysconnectivity between networks, specially sensorimotor and visual, is linked with schizophrenic patients, however schizophrenic patients show increased intra-network default-mode connectivity compared to healthy controls. Sensorimotor connectivity was important for both dementia and schizophrenia prediction, but schizophrenia is more related to dysconnectivity between networks whereas, dementia bio-markers were mostly intra-network connectivity.

Model-based stationarity filtering of long-term memory data applied to resting-state blood-oxygen-level-dependent signal

Resting-state blood-oxygen-level-dependent (BOLD) signal acquired through functional magnetic resonance imaging is a proxy of neural activity and a key mechanism for assessing neurological conditions. Therefore, practical tools to filter out artefacts that can compromise the assessment are required. On the one hand, a variety of tailored methods to preprocess the data to deal with identified sources of noise (e.g., head motion, heart beating, and breathing, just to mention a few) are in place. But, on the other hand, there might be unknown sources of unstructured noise present in the data. Therefore, to mitigate the effects of such unstructured noises, we propose a model-based filter that explores the statistical properties of the underlying signal (i.e., long-term memory). Specifically, we consider autoregressive fractional integrative process filters. Remarkably, we provide evidence that such processes can model the signals at different regions of interest to attain stationarity. Furthermore, we use a principled analysis where a ground-truth signal with statistical properties similar to the BOLD signal under the injection of noise is retrieved using the proposed filters. Next, we considered preprocessed (i.e., the identified sources of noise removed) resting-state BOLD data of 98 subjects from the Human Connectome Project. Our results demonstrate that the proposed filters decrease the power in the higher frequencies. However, unlike the low-pass filters, the proposed filters do not remove all high-frequency information, instead they preserve process-related higher frequency information. Additionally, we considered four different metrics (power spectrum, functional connectivity using the Pearson’s correlation, coherence, and eigenbrains) to infer the impact of such filter. We provided evidence that whereas the first three keep most of the features of interest from a neuroscience perspective unchanged, the latter exhibits some variations that could be due to the sporadic activity filtered out.

Recommendations and publication guidelines for studies using frequency domain and time-frequency domain analyses of neural time series

Since its beginnings in the early 20th century, the psychophysiological study of human brain function has included research into the spectral properties of electrical and magnetic brain signals. Now, dramatic advances in digital signal processing, biophysics, and computer science have enabled increasingly sophisticated methodology for neural time series analysis. Innovations in hardware and recording techniques have further expanded the range of tools available to researchers interested in measuring, quantifying, modeling, and altering the spectral properties of neural time series. These tools are increasingly used in the field, by a growing number of researchers who vary in their training, background, and research interests. Implementation and reporting standards also vary greatly in the published literature, causing challenges for authors, readers, reviewers, and editors alike. The present report addresses this issue by providing recommendations for the use of these methods, with a focus on foundational aspects of frequency domain and time-frequency analyses. It also provides publication guidelines, which aim to (1) foster replication and scientific rigor, (2) assist new researchers who wish to enter the field of brain oscillations, and (3) facilitate communication among authors, reviewers, and editors.

BVAR-Connect: A Variational Bayes Approach to Multi-Subject Vector Autoregressive Models for Inference on Brain Connectivity Networks

In this paper we propose BVAR-connect, a variational inference approach to a Bayesian multi-subject vector autoregressive (VAR) model for inference on effective brain connectivity based on resting-state functional MRI data. The modeling framework uses a Bayesian variable selection approach that flexibly integrates multi-modal data, in particular structural diffusion tensor imaging (DTI) data, into the prior construction. The variational inference approach we develop allows scalability of the methods and results in the ability to estimate subject- and group-level brain connectivity networks over whole-brain parcellations of the data. We provide a brief description of a user-friendly MATLAB GUI released for public use. We assess performance on simulated data, where we show that the proposed inference method can achieve comparable accuracy to the sampling-based Markov Chain Monte Carlo approach but at a much lower computational cost. We also address the case of subject groups with imbalanced sample sizes. Finally, we illustrate the methods on resting-state functional MRI and structural DTI data on children with a history of traumatic injury.

A Hierarchical Bayesian Model for Differential Connectivity in Multi-trial Brain Signals

There is a strong interest in the neuroscience community to measure brain connectivity and develop methods that can differentiate connectivity across patient groups and across different experimental stimuli. The development of such statistical tools is critical to understand the dynamics of functional relationships among brain structures supporting memory encoding and retrieval. However, the challenge comes from the need to incorporate within-condition similarity with between-conditions heterogeneity in modeling connectivity, as well as how to provide a natural way to conduct trial- and condition-level inference on effective connectivity. A Bayesian hierarchical vector autoregressive (BH-VAR) model is proposed to characterize brain connectivity and infer differences in connectivity across conditions. Within-condition connectivity similarity and between-conditions connectivity heterogeneity are accounted for by the priors on trial-specific models. In addition to the fully Bayesian framework, an alternative two-stage computation approach is also proposed which still allows straightforward uncertainty quantification of between-trial conditions via MCMC posterior sampling, but provides a fast approximate procedure for the estimation of trial-specific VAR parameters. A novel aspect of the approach is the use of a frequency-specific measure, partial directed coherence (PDC), to characterize effective connectivity under the Bayesian framework. More specifically, PDC allows inferring directionality and explaining the extent to which the present oscillatory activity at a certain frequency in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the brain network. The proposed model is applied to a large electrophysiological dataset collected as rats performed a complex sequence memory task. This unique dataset includes local field potentials (LFPs) activity recorded from an array of electrodes across hippocampal region CA1 while animals were presented with multiple trials from two main conditions. The proposed modeling approach provided novel insights into hippocampal connectivity during memory performance. Specifically, it separated CA1 into two functional units, a lateral and a medial segment, each showing stronger functional connectivity to itself than to the other. This approach also revealed that information primarily flowed in a lateral-to-medial direction across trials (within-condition), and suggested this effect was stronger on one trial condition than the other (between-conditions effect). Collectively, these results indicate that the proposed model is a promising approach to quantify the variation of functional connectivity, both within- and between-conditions, and thus should have broad applications in neuroscience research.

Statistical model-based approaches for functional connectivity analysis of neuroimaging data

We present recent literature on model-based approaches to estimating functional connectivity from neuroimaging data. In contrast to the typical focus on a particular scientific question, we reframe a wider literature in terms of the underlying statistical model used. We distinguish between directed versus undirected and static versus time-varying connectivity. There are numerous advantages to a model-based approach, including easily specified inductive bias, handling limited data scenarios, and building complex models from simpler building blocks.

Bayesian hierarchical vector autoregressive models for patient-level predictive modeling

Predicting health outcomes from longitudinal health histories is of central importance to healthcare. Observational healthcare databases such as patient diary databases provide a rich resource for patient-level predictive modeling. In this paper, we propose a Bayesian hierarchical vector autoregressive (VAR) model to predict medical and psychological conditions using multivariate time series data. Compared to the existing patient-specific predictive VAR models, our model demonstrated higher accuracy in predicting future observations in terms of both point and interval estimates due to the pooling effect of the hierarchical model specification. In addition, by adopting an elastic-net prior, our model offers greater interpretability about the associations between variables of interest on both the population level and the patient level, as well as between-patient heterogeneity. We apply the model to two examples: 1) predicting substance use craving, negative affect and tobacco use among college students, and 2) predicting functional somatic symptoms and psychological discomforts.

Changes in brain activity following intensive voice treatment in children with cerebral palsy

Eight children (3 females; 8-16 years) with motor speech disorders secondary to cerebral palsy underwent 4 weeks of an intensive neuroplasticity-principled voice treatment protocol, LSVT LOUD^® , followed by a structured 12-week maintenance program. Children were asked to overtly produce phonation (ah) at conversational loudness, cued-phonation at perceived twice-conversational loudness, a series of single words, and a prosodic imitation task while being scanned using fMRI, immediately pre- and post-treatment and 12 weeks following a maintenance program. Eight age- and sex-matched controls were scanned at each of the same three time points. Based on the speech and language literature, 16 bilateral regions of interest were selected a priori to detect potential neural changes following treatment. Reduced neural activity in the motor areas (decreased motor system effort) before and immediately after treatment, and increased activity in the anterior cingulate gyrus after treatment (increased contribution of decision making processes) were observed in the group with cerebral palsy compared to the control group. Using graphical models, post-treatment changes in connectivity were observed between the left supramarginal gyrus and the right supramarginal gyrus and the left precentral gyrus for the children with cerebral palsy, suggesting LSVT LOUD enhanced contributions of the feedback system in the speech production network instead of high reliance on feedforward control system and the somatosensory target map for regulating vocal effort. Network pruning indicates greater processing efficiency and the recruitment of the auditory and somatosensory feedback control systems following intensive treatment. Hum Brain Mapp 38:4413-4429, 2017. © 2017 Wiley Periodicals, Inc.

A variance components model for statistical inference on functional connectivity networks

We propose a variance components linear modeling framework to conduct statistical inference on functional connectivity networks that directly accounts for the temporal autocorrelation inherent in functional magnetic resonance imaging (fMRI) time series data and for the heterogeneity across subjects in the study. The novel method estimates the autocorrelation structure in a nonparametric and subject-specific manner, and estimates the variance due to the heterogeneity using iterative least squares. We apply the new model to a resting-state fMRI study to compare the functional connectivity networks in both typical and reading impaired young adults in order to characterize the resting state networks that are related to reading processes. We also compare the performance of our model to other methods of statistical inference on functional connectivity networks that do not account for the temporal autocorrelation or heterogeneity across the subjects using simulated data, and show that by accounting for these sources of variation and covariation results in more powerful tests for statistical inference.

Bayesian vector autoregressive model for multi-subject effective connectivity inference using multi-modal neuroimaging data

In this article a multi-subject vector autoregressive (VAR) modeling approach was proposed for inference on effective connectivity based on resting-state functional MRI data. Their framework uses a Bayesian variable selection approach to allow for simultaneous inference on effective connectivity at both the subject- and group-level. Furthermore, it accounts for multi-modal data by integrating structural imaging information into the prior model, encouraging effective connectivity between structurally connected regions. They demonstrated through simulation studies that their approach resulted in improved inference on effective connectivity at both the subject- and group-level, compared with currently used methods. It was concluded by illustrating the method on temporal lobe epilepsy data, where resting-state functional MRI and structural MRI were used. Hum Brain Mapp 38:1311-1332, 2017. © 2016 Wiley Periodicals, Inc.

Understanding the Impact of Stroke on Brain Motor Function: A Hierarchical Bayesian Approach

Stroke is a disturbance in blood supply to the brain resulting in the loss of brain functions, particularly motor function. A study was conducted by the UCI Neurorehabilitation Lab to investigate the impact of stroke on motor-related brain regions. Functional MRI (fMRI) data were collected from stroke patients and healthy controls while the subjects performed a simple motor task. In addition to affecting local neuronal activation strength, stroke might also alter communications (i.e., connectivity) between brain regions. We develop a hierarchical Bayesian modeling approach for the analysis of multi-subject fMRI data that allows us to explore brain changes due to stroke. Our approach simultaneously estimates activation and condition-specific connectivity at the group level, and provides estimates for region/subject-specific hemodynamic response functions. Moreover, our model uses spike and slab priors to allow for direct posterior inference on the connectivity network. Our results indicate that motor-control regions show greater activation in the unaffected hemisphere and the midline surface in stroke patients than those same regions in healthy controls during the simple motor task. We also note increased connectivity within secondary motor regions in stroke subjects. These findings provide insight into altered neural correlates of movement in subjects who suffered a stroke.

A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity

OBJECTIVE

This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions.

METHODS

To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages.

RESULTS

The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods.

CONCLUSION

The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality.

SIGNIFICANCE

The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

Bayesian Models for fMRI Data Analysis

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.