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.

[1]  Stefan Skare,et al.  How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging , 2003, NeuroImage.

[2]  James G. Scott,et al.  Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem , 2010, 1011.2333.

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[5]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[6]  Catie Chang,et al.  Time–frequency dynamics of resting-state brain connectivity measured with fMRI , 2010, NeuroImage.

[7]  Steven C Cramer,et al.  Understanding the Impact of Stroke on Brain Motor Function: A Hierarchical Bayesian Approach , 2016, Journal of the American Statistical Association.

[8]  Martin J. McKeown,et al.  Dynamic Bayesian network modeling of fMRI: A comparison of group-analysis methods , 2008, NeuroImage.

[9]  T. Fearn,et al.  Multivariate Bayesian variable selection and prediction , 1998 .

[10]  Stamatios N. Sotiropoulos,et al.  Non-parametric representation and prediction of single- and multi-shell diffusion-weighted MRI data using Gaussian processes , 2015, NeuroImage.

[11]  Mingzhou Ding,et al.  Is Granger Causality a Viable Technique for Analyzing fMRI Data? , 2013, PloS one.

[12]  Hui Zhang,et al.  Realistic simulation of artefacts in diffusion MRI for validating post-processing correction techniques , 2016, NeuroImage.

[13]  Marina Vannucci,et al.  A Bayesian Approach for Estimating Dynamic Functional Network Connectivity in fMRI Data , 2018, Journal of the American Statistical Association.

[14]  B. Jennett,et al.  Assessment of coma and impaired consciousness. A practical scale. , 1974, Lancet.

[15]  Karl J. Friston,et al.  Variational Bayesian inference for fMRI time series , 2003, NeuroImage.

[16]  Kaustubh Supekar,et al.  Temporal Dynamics and Developmental Maturation of Salience, Default and Central-Executive Network Interactions Revealed by Variational Bayes Hidden Markov Modeling , 2016, PLoS Comput. Biol..

[17]  Mark W. Woolrich,et al.  Constrained linear basis sets for HRF modelling using Variational Bayes , 2004, NeuroImage.

[18]  Christopher M. Bishop,et al.  Variational Relevance Vector Machines , 2000, UAI.

[19]  James G. Scott,et al.  Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables , 2012, 1205.0310.

[20]  Ying Guo,et al.  Integrative Bayesian analysis of brain functional networks incorporating anatomical knowledge , 2018, NeuroImage.

[21]  Hernando Ombao,et al.  Investigating brain connectivity using mixed effects vector autoregressive models , 2012, NeuroImage.

[22]  Panayiota Poirazi,et al.  Computational modeling of the effects of amyloid-beta on release probability at hippocampal synapses , 2013, Front. Comput. Neurosci..

[23]  Rainer Goebel,et al.  Mapping directed influence over the brain using Granger causality and fMRI , 2005, NeuroImage.

[24]  Juan Zhou,et al.  Learning effective brain connectivity with dynamic Bayesian networks , 2007, NeuroImage.

[25]  Marina Vannucci,et al.  Temporal and spectral characteristics of dynamic functional connectivity between resting-state networks reveal information beyond static connectivity , 2018, PloS one.

[26]  J. Pekar,et al.  A method for making group inferences from functional MRI data using independent component analysis , 2001, Human brain mapping.

[27]  Gadi Goelman,et al.  Maximizing Negative Correlations in Resting-State Functional Connectivity MRI by Time-Lag , 2014, PloS one.

[28]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[29]  V. Calhoun,et al.  The Chronnectome: Time-Varying Connectivity Networks as the Next Frontier in fMRI Data Discovery , 2014, Neuron.

[30]  Marina Vannucci,et al.  Bayesian vector autoregressive model for multi‐subject effective connectivity inference using multi‐modal neuroimaging data , 2017, Human brain mapping.

[31]  Christopher Fonnesbeck,et al.  A Bayesian Double Fusion Model for Resting-State Brain Connectivity Using Joint Functional and Structural Data , 2017, Brain Connect..

[32]  Marina Vannucci,et al.  NPBayes-fMRI: Non-parametric Bayesian General Linear Models for Single- and Multi-Subject fMRI Data , 2019 .

[33]  Timothy Edward John Behrens,et al.  Characterization and propagation of uncertainty in diffusion‐weighted MR imaging , 2003, Magnetic resonance in medicine.

[34]  Steven C. Cramer,et al.  Hierarchical vector auto-regressive models and their applications to multi-subject effective connectivity , 2013, Front. Comput. Neurosci..

[35]  William D. Penny,et al.  Bayesian fMRI data analysis with sparse spatial basis function priors , 2007, NeuroImage.

[36]  Linda Ewing-Cobbs,et al.  Longitudinal diffusion tensor imaging after pediatric traumatic brain injury: Impact of age at injury and time since injury on pathway integrity , 2016, Human brain mapping.

[37]  Linda Ewing-Cobbs,et al.  Graph theory analysis of DTI tractography in children with traumatic injury , 2019, NeuroImage: Clinical.

[38]  Stamatios N. Sotiropoulos,et al.  An integrated approach to correction for off-resonance effects and subject movement in diffusion MR imaging , 2016, NeuroImage.

[39]  L. Kramer,et al.  Post-Traumatic Stress Symptoms after Pediatric Injury: Relation to Pre-Frontal Limbic Circuitry. , 2019, Journal of neurotrauma.

[40]  Marina Vannucci,et al.  A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data , 2016 .

[41]  T. Adali,et al.  A method for making group inferences from functional MRI data using independent component analysis , 2002 .

[42]  Stamatios N. Sotiropoulos,et al.  Incorporating outlier detection and replacement into a non-parametric framework for movement and distortion correction of diffusion MR images , 2016, NeuroImage.

[43]  David M. Blei,et al.  Variational Inference: A Review for Statisticians , 2016, ArXiv.

[44]  Karl J. Friston.  Functional and Effective Connectivity: A Review , 2011, Brain Connect..

[45]  Erin D. Bigler,et al.  Diffusion tensor imaging in moderate-to-severe pediatric traumatic brain injury: changes within an 18 month post-injury interval , 2012, Brain Imaging and Behavior.

[46]  M. Greicius,et al.  Resting-state functional connectivity reflects structural connectivity in the default mode network. , 2009, Cerebral cortex.

[47]  Karl J. Friston,et al.  The choice of basis functions in event-related fMRI , 2001, NeuroImage.

[48]  E. George,et al.  APPROACHES FOR BAYESIAN VARIABLE SELECTION , 1997 .

[49]  Roland Eils,et al.  circlize implements and enhances circular visualization in R , 2014, Bioinform..

[50]  Xiaoping Hu,et al.  Multivariate Granger causality analysis of fMRI data , 2009, Human brain mapping.

[51]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[52]  Matthew J. Beal.  Variational algorithms for approximate Bayesian inference , 2003 .

[53]  Miguel Lázaro-Gredilla,et al.  Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning , 2011, NIPS.

[54]  G. Deco,et al.  Emerging concepts for the dynamical organization of resting-state activity in the brain , 2010, Nature Reviews Neuroscience.