Variational Bayesian causal connectivity analysis for fMRI

The ability to accurately estimate effective connectivity among brain regions from neuroimaging data could help answering many open questions in neuroscience. We propose a method which uses causality to obtain a measure of effective connectivity from fMRI data. The method uses a vector autoregressive model for the latent variables describing neuronal activity in combination with a linear observation model based on a convolution with a hemodynamic response function. Due to the employed modeling, it is possible to efficiently estimate all latent variables of the model using a variational Bayesian inference algorithm. The computational efficiency of the method enables us to apply it to large scale problems with high sampling rates and several hundred regions of interest. We use a comprehensive empirical evaluation with synthetic and real fMRI data to evaluate the performance of our method under various conditions.

[1]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[2]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[3]  Victor Solo,et al.  Identifying fMRI Model Violations With Lagrange Multiplier Tests , 2012, IEEE Transactions on Medical Imaging.

[4]  Victor Solo,et al.  On causality I: Sampling and noise , 2007, 2007 46th IEEE Conference on Decision and Control.

[5]  Anders M. Dale,et al.  Automatic parcellation of human cortical gyri and sulci using standard anatomical nomenclature , 2010, NeuroImage.

[6]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

[7]  Anil K. Seth,et al.  A MATLAB toolbox for Granger causal connectivity analysis , 2010, Journal of Neuroscience Methods.

[8]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[9]  Mark Jenkinson,et al.  The minimal preprocessing pipelines for the Human Connectome Project , 2013, NeuroImage.

[10]  Mark D'Esposito,et al.  Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses , 2004, NeuroImage.

[11]  Anil K. Seth,et al.  Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling , 2013, NeuroImage.

[12]  C. Segebarth,et al.  Identifying Neural Drivers with Functional MRI: An Electrophysiological Validation , 2008, PLoS biology.

[13]  Michael E. Tipping.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001, J. Mach. Learn. Res..

[14]  R. Buxton,et al.  Modeling the hemodynamic response to brain activation , 2004, NeuroImage.

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

[16]  Martin Luessi.  Bayesian Approaches to Inverse Problems in Functional Neuroimaging , 2011 .

[17]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[18]  Zoubin Ghahramani,et al.  Propagation Algorithms for Variational Bayesian Learning , 2000, NIPS.

[19]  Karl J. Friston,et al.  Bilinear dynamical systems , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[20]  Bruce Fischl,et al.  FreeSurfer , 2012, NeuroImage.

[21]  Bhaskar D. Rao,et al.  An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem , 2007, IEEE Transactions on Signal Processing.

[22]  T. Moon,et al.  Mathematical Methods and Algorithms for Signal Processing , 1999 .

[23]  Karl J. Friston.  Functional and effective connectivity in neuroimaging: A synthesis , 1994 .

[24]  A. Seth,et al.  Behaviour of Granger causality under filtering: Theoretical invariance and practical application , 2011, Journal of Neuroscience Methods.

[25]  Aggelos K. Katsaggelos,et al.  Sparse Bayesian Methods for Low-Rank Matrix Estimation , 2011, IEEE Transactions on Signal Processing.

[26]  Wei Liao,et al.  Nonlinear connectivity by Granger causality , 2011, NeuroImage.

[27]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine Learning.

[28]  Paulo Fernandes,et al.  Efficient descriptor-vector multiplications in stochastic automata networks , 1998, JACM.

[29]  FernandesPaulo,et al.  Efficient descriptor-vector multiplications in stochastic automata networks , 1998 .

[30]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[31]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[32]  森田 陸司,et al.  Dynamic MR imagingを用いた腎機能評価法 , 1996 .

[33]  D. Tank,et al.  Brain magnetic resonance imaging with contrast dependent on blood oxygenation. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Lotfi Chaâri,et al.  Fast Joint Detection-Estimation of Evoked Brain Activity in Event-Related fMRI Using a Variational Approach , 2013, IEEE Transactions on Medical Imaging.

[35]  Steen Moeller,et al.  The Human Connectome Project: A data acquisition perspective , 2012, NeuroImage.

[36]  Karl J. Friston,et al.  Analysis of fMRI Time-Series Revisited , 1995, NeuroImage.

[37]  Mark W. Woolrich,et al.  Bayesian deconvolution fMRI data using bilinear dynamical systems , 2008, NeuroImage.

[38]  Stefan Haufe,et al.  Sparse Causal Discovery in Multivariate Time Series , 2008, NIPS Causality: Objectives and Assessment.

[39]  Guido Gerig,et al.  Patient-Tailored Connectomics Visualization for the Assessment of White Matter Atrophy in Traumatic Brain Injury , 2011, Front. Neur..

[40]  Anirban DasGupta.  Maximum Likelihood Estimates , 2008 .

[41]  J. Frahm,et al.  Dynamic MR imaging of human brain oxygenation during rest and photic stimulation , 1992, Journal of magnetic resonance imaging : JMRI.

[42]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001 .

[43]  Steven L. Bressler,et al.  Wiener–Granger Causality: A well established methodology , 2011, NeuroImage.

[44]  G L Shulman,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:A default mode of brain function , 2001 .

[45]  P. Bühlmann,et al.  The group lasso for logistic regression , 2008 .

[46]  Geoffrey E. Hinton,et al.  Parameter estimation for linear dynamical systems , 1996 .

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

[48]  Kewei Chen,et al.  Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems , 2010, NeuroImage.

[49]  D. Cox.  Causality : some statistical aspects , 1992 .

[50]  Kaustubh Supekar,et al.  Multivariate dynamical systems models for estimating causal interactions in fMRI , 2011, NeuroImage.

[51]  Xiaoping Hu,et al.  Effect of hemodynamic variability on Granger causality analysis of fMRI , 2010, NeuroImage.

[52]  Bo Wang,et al.  Lack of Consistency of Mean Field and Variational Bayes Approximations for State Space Models , 2004, Neural Processing Letters.

[53]  DE CS.TU-BERLIN.,et al.  Sparse Causal Discovery in Multivariate Time Series , 2010 .

[54]  Hagai Attias,et al.  A Variational Bayesian Framework for Graphical Models , 1999 .

[55]  Lester Melie-García,et al.  Estimating brain functional connectivity with sparse multivariate autoregression , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[56]  Thomas T. Liu,et al.  A component based noise correction method (CompCor) for BOLD and perfusion based fMRI , 2007, NeuroImage.

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

[58]  Zoubin Ghahramani,et al.  The variational Kalman smoother , 2001 .

[59]  Alard Roebroeck,et al.  Causal Time Series Analysis of Functional Magnetic Resonance Imaging Data , 2009, NIPS Mini-Symposium on Causality in Time Series.