Granger Causality in fmri connectivity analysis

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1 Granger Causalit in fmri connectivit analsis Alard Roebroeck Maastricht Brain Imaging Center (MBIC) Facult of Pscholog & Neuroscience Maastricht Universit

2 Overview fmri signal & connectivit Functional & Effective connectivit Structural model & Dnamical model Identification & model selection Granger causalit & fmri Granger causalit and its variants Granger causalit mapping Issues with variable hemodnamics Hemodnamic deconvolution

3 Integration and connectivit Brain Performance of comple tasks requires interaction of specialized brain sstems (functional integration) Interaction of specialized areas requires connectivit Investigation of comple tasks requires connectivit analsis

4 A problem for fmri connectivit In fmri our access to the neural activit is indirect We want to infer interaction between Area X and Y from observations [t] and [t] (time-series) Hemodnamics Hemodnamics MRI MRI scanner scanner signal [t] access Brain Hemodnamics Hemodnamics MRI MRI scanner scanner signal [t]

5 fmri: The BOLD signal Stimulus Neural pathwa Hemodnamics MR scanner % signal change ~0.5 2 ~4 time [s] ~10 stimulus

6 Overview fmri signal & connectivit Functional & Effective connectivit Structural model & Dnamical model Identification & model selection Granger causalit & fmri Granger causalit and its variants Granger causalit mapping Issues with variable hemodnamics Hemodnamic deconvolution

7 Functional & Effective Connectivit Functional connectivit Association (mutual information) Localization of whole networks Effective connectivit Uncover network mechanisms (causal influence) Directed vs. undirected Direct vs. indirect

8 Effective connectivit brain data measurement Effective connectivit modeling Inferred model Structural model& priors Dnamical model& priors

9 Effective connectivit ROI selection Graph selection Structural model& priors What interacts Dnamical model& priors = S ˆ Ë Ê = ˆ Ë Ê ˆ Ë Ê + ˆ Ë Ê - - = ˆ Ë Ê Â = cov ] [ ] [ ] [ ] [ p i i e e e e i t i t t t s s s s A Deterministic vs. stochastic models Linear vs. non-linear Forward observation models How does it interact: signal model

10 Problem: spurious influence A B A C B C Danger of strong structural models: When important regions are left out (of the anatomical model), ANY correct method will give wrong answers

11 Overview fmri signal & connectivit Functional & Effective connectivit Structural model & Dnamical model Identification & model selection Granger causalit & fmri Granger causalit and its variants Granger causalit mapping Issues with variable hemodnamics Hemodnamic deconvolution

12 = S ˆ Ë Ê = ˆ Ë Ê ˆ Ë Ê + ˆ Ë Ê - - = ˆ Ë Ê Â = cov ] [ ] [ ] [ ] [ p i i e e e e i t i t t t s s s s A Predictions are quantified with a linear multivariate autoregressive (AR) model Though not necessaril: non-linear AR or nonparametric (e.g. Dhamala et al., NI, 2008) AR Transfer function form gives frequenc distribution Various normalizations Geweke s decomposition (Geweke, 1982; Roebroeck, NI, 2005) Directed transfer function (DTF; Blinowska, PhsRevE, 2004; Deshpande, NI, 2008) Partial directed coherence (PDC; Sameshima, JNeuSciMeth, 1999; Sato, HBM, 2009) Granger causalit (G-causalit)

13 Sampling & Hemodnamics Granger causalit analsis X Y? Roebroeck, NI 2005

14 Structural model for GC ROI-based as in SEM, DCM E.g. Stilla, 2007; Sridharan, 2008; Udapha, 2008; Deshpande, 2008 Massivel multivariate based on parcelation of the corte Valdes Sosa, 2004, 2005 Granger causalit mapping Massivel bivariate without prior anatomical asumptions

15 Granger causalit mapping (GCM) Random effects level GCMs Roebroeck, NI 2005; Goebel, MRI 2004

16 Granger causalit mapping (GCM) Eperimental modulation: Functional assignment Avoid HRF confound Roebroeck, NI 2005; Goebel, MRI 2004

17 Overview fmri signal & connectivit Functional & Effective connectivit Structural model & Dnamical model Identification & model selection Granger causalit & fmri Granger causalit and its variants Granger causalit mapping Issues with variable hemodnamics Hemodnamic deconvolution

18 Hemodnamics & GC GC could be due purel to differences in hemodnamic latencies in different parts of the brain Which are estimated to be in the order of 100 s s ms (Aguirre, NI, 1998; Saad, HBM, 2001)

19 Hemodnamics & GC Caution needed in appling and interpreting temporal precedence Tools: Finding eperimental modulation of GC Studing temporall integrated signals for slow processes (e.g. fatigue; Deshpande, HBM, 2009) Combining fmri with EEG or MEG Hemodnamic deconvolution

20 Hemodnamic deconvolution m(t) = s(t) h(t) fmri signal = Deconvolve neuronal source signal s(t) and hemodnamic response h(t) from fmri signal E.g. b wiener deconvolution (Glover, NI, 1999) Onl possible if: Strong constraints on s(t) are assumed (e.g. DCM: stimulus functions), or An independent measure of s(t) is available (e.g. simultaneous EEG) and EEG/fMRI coupling can be assumed

21 Hemodnamic deconvolution Rat stud of epileps Simultaneous fmri/eeg S1BF HRF Gold standard model => Granger without deconvolution DCM Granger using deconvolution David, PLoS Biolog, 2008

22 Summar G-causalit and AR models are powerful tools in fmri effective connectivit analsis GC is ideal for massive eploration of the structural model Caution is needed with GC in the face of variable hemodnamics

Obtaining Knowledge. Lecture 7 Methods of Scientific Observation and Analysis in Behavioral Psychology and Neuropsychology.

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