The Relationship of Discrete DCM and Directed Information in fMRI-Based Causality Analysis

This paper explores the conditional equivalence between discrete dynamic causal modeling (DDCM) and directed information (DI) for fMRI-based causality analysis. First, we briefly revisit the DDCM and its relationship with the conventional continuous time dynamic causal modeling. Second, we prove the conditional equivalence between DDCM and DI in characterizing the causal relationship and identifying the causal side of two brain regions based on the fMRI data. Third, we show that the DI-based causal relationship between the neurostates of two brain regions is equivalent to that between the observed BOLD signals. More specifically, in the noise free case, the DI inference is invariant under hemodynamic convolution as long as the system is invertible. The theoretical results are demonstrated using fMRI data obtained under both resting state and stimulus-based state. Our numerical analysis is consistent with that reported in previous study. Our results further confirm the convergence or conditional equivalences among existing causality analysis tools.

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

[2]  Karl J. Friston,et al.  Dynamic causal modeling , 2010, Scholarpedia.

[3]  Y. Shtarkov,et al.  The context-tree weighting method: basic properties , 1995, IEEE Trans. Inf. Theory.

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

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

[6]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[7]  Karl J. Friston,et al.  Effective connectivity: Influence, causality and biophysical modeling , 2011, NeuroImage.

[8]  Ying Liu,et al.  The relationship between transfer entropy and directed information , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[9]  Pramod K. Varshney,et al.  Quantifying EEG synchrony using copulas , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[10]  Karl J. Friston,et al.  Analysing connectivity with Granger causality and dynamic causal modelling , 2013, Current Opinion in Neurobiology.

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

[12]  Daniele Marinazzo,et al.  Kernel method for nonlinear granger causality. , 2007, Physical review letters.

[13]  Ying Liu,et al.  Quantification of Effective Connectivity in the Brain Using a Measure of Directed Information , 2012, Comput. Math. Methods Medicine.

[14]  Olivier J. J. Michel,et al.  On directed information theory and Granger causality graphs , 2010, Journal of Computational Neuroscience.

[15]  A. Seth,et al.  Granger causality and transfer entropy are equivalent for Gaussian variables. , 2009, Physical review letters.

[16]  Kuncheng Li,et al.  Altered Causal Connectivity of Resting State Brain Networks in Amnesic MCI , 2014, PloS one.

[17]  Hualou Liang,et al.  A copula approach to assessing Granger causality , 2014, NeuroImage.

[18]  Zhe Wang,et al.  Causality Analysis of fMRI Data Based on the Directed Information Theory Framework , 2016, IEEE Transactions on Biomedical Engineering.

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

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

[21]  Haim H. Permuter,et al.  Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing , 2009, IEEE Transactions on Information Theory.

[22]  Karl J. Friston.  Dynamic causal modeling and Granger causality Comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution , 2011, NeuroImage.

[23]  Todd P. Coleman,et al.  Estimating the directed information to infer causal relationships in ensemble neural spike train recordings , 2010, Journal of Computational Neuroscience.

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

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

[26]  Marcin Wolski,et al.  Nonlinear Granger Causality: Guidelines for Multivariate Analysis , 2013 .

[27]  Panos J. Antsaklis,et al.  A Linear Systems Primer , 2007 .

[28]  Negar Kiyavash,et al.  Measuring Causal Relationships in Dynamical Systems through Recovery of Functional Dependencies , 2017, IEEE Transactions on Signal and Information Processing over Networks.

[29]  Karl J. Friston,et al.  Comparing hemodynamic models with DCM , 2007, NeuroImage.

[30]  Karl J. Friston,et al.  Dynamic causal models of neural system dynamics: current state and future extensions , 2007, Journal of Biosciences.

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

[32]  Fei-Fei Li,et al.  Exploring Functional Connectivities of the Human Brain using Multivariate Information Analysis , 2009, NIPS.

[33]  Andrea J. Goldsmith,et al.  Inferring neural connectivity via measured delay in directed information estimates , 2013, 2013 IEEE International Symposium on Information Theory.

[34]  Riaz A. Usmani,et al.  Inversion of a tridiagonal jacobi matrix , 1994 .

[35]  Haim H. Permuter,et al.  Universal Estimation of Directed Information , 2010, IEEE Transactions on Information Theory.

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

[37]  Negar Kiyavash,et al.  Directed Information Graphs: A generalization of Linear Dynamical Graphs , 2014, 2014 American Control Conference.

[38]  Peter A. Tass,et al.  Modeling nonlinear oscillatory systems and diagnostics of coupling between them using chaotic time series analysis: applications in neurophysiology , 2008 .