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SPM short course Functional integration and connectivity

SPM short course Functional integration and connectivity. Christian Büchel Karl Friston The Wellcome Department of Cognitive Neurology, UCL London UK http//:www.fil.ion.ucl.ac.uk/spm. p <0.05. Data analysis. Design matrix. fMRI time-series. Kernel.

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SPM short course Functional integration and connectivity

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  1. SPM short course Functional integration and connectivity Christian Büchel Karl Friston The Wellcome Department of Cognitive Neurology, UCL London UK http//:www.fil.ion.ucl.ac.uk/spm

  2. p <0.05 Data analysis Design matrix fMRI time-series Kernel Inference with Gaussian field theory Realignment Smoothing General linear model Normalisation Adjusted regional data spatial modes and effective connectivity Template Parameter estimates

  3. Functional brain architectures • Functional segregation • Univariate analyses of regionally specific effects • Functional integration • Multivariate analyses of regional interactions • Functional connectivity • “the temporal correlation between neurophysiological events” • an operational definition • Effective connectivity • “the influence one neuronal system exerts over another” • a model-dependent definition

  4. Issues in functional integration • Functional Connectivity • Eigenimage analysis and PCA • Effective Connectivity • Psychophysiological Interactions • State space Models (Variable parameter regression) • Structural Equation Modelling • Volterra series

  5. B A C Effective vs. functional connectivity Model: A = V1 fMRI time-series B = 0.5 * A + e1 C = 0.3 * A + e2 Correlations: A B C 1 0.49 1 0.30 0.12 1 0.49 Correct model -0.02 2=0.5, ns. 0.31

  6. Eigenimages - the basic concept A time-series of 1D images 128 scans of 40 “voxels” Expression of 1st 3 “eigenimages” Eigenvalues and spatial “modes” The time-series ‘reconstituted’

  7. Eigenimages and SVD V1 V2 V3 voxels APPROX. OF Y U1 U2 APPROX. OF Y U3 APPROX. OF Y s1 + s2 + s3 = + ... Y (DATA) time Y = USVT = s1U1V1T + s2U2V2T + ...

  8. An example from PET Eigenimage analysis of a PET word generation study Word generation G Word repetition R R G R G R G.........

  9. Dynamic changes in effective connectivityAttentional modulation of V5 responses to visual motion • Psychophysiological interactions • Attentional modulation of V2 to V5 connections • State space models and variable parameter regression • Attentional modulation of V5 to PPC connections • Models of effective connectivity • The mediating role of posterior parietal cortex • in attentional modulation • Structural Equation modelling • Volterra formulation

  10. The fMRI study Stimuli 250 radially moving dots at 4.7 degrees/s Pre-Scanning 5 x 30s trials with 5 speed changes (reducing to 1%) Task - detect change in radial velocity Scanning (no speed changes) 6 normal subjects, 4 100 scan sessions; each session comprising 10 scans of 4 different condition e.g. F A F N F A F N S ................. F - fixation point only A - motion stimuli with attention (detect changes) N - motion stimuli without attention S - no motion

  11. Psychophysiological interactions: Attentional modulation of V2 -> V5 influences SPM{Z} V5 activity Attention time attention V2 V5 activity V5 no attention V2 activity

  12. AttentionFixation No attention 0.8 regression coefficient 0.5 • bt Time (scans) x = V5y = PP Regression with time-varying coefficients Fixed regression model (one coefficient for entire time-series) y = x*b + e Time varying regression model (coefficient changes over time) yt = xt.bt + et bt = bt-1+ht Coefficient b of the explanatory variable (V5) is modelled as a time-varying random walk. Estimation by Kalman filter.

  13. The source of modulatory afferents Anterior cingulate Dorsolateral prefrontal cortex “Modulatory” sources identified as regions correlated with bt R R p<0.05 corrected

  14. u v a V U c b W w Structural equation modelling (SEM) Minimise the difference between the observed (S) and implied () covariances by adjusting the path coefficients (a, b, c) The implied covariance structure: x = x.B + zx = z.(I - B)-1 x : matrix of time-series of regions U, V and W B: matrix of unidirectional path coefficients (a,b,c) Variance-covariance structure: xT . x =  = (I-B)-T. C.(I-B)-1 where C = zT z xT.x is the implied variance covariance structure  C contains the residual variances (u,v,w) and covariances The free parameters are estimated by minimising a [maximum likelihood] function of S and 

  15. 0.43 0.75 0.47 0.76 No attention Attention Attention - No attention

  16. PP V1 0.14 V5 V1xPP V5 The use of moderator or interaction variables 2 =11, p<0.01 = Modulatory influence of parietal cortex on V1 to V5

  17. PP 0.2 V5 PFC 2=13.6, p<0.01 0.1 2=5.9, p<0.01 V1 LGN Hierarchical architectures

  18. PP ITa ITp LP V1 DE V1 ITp E R E R Changes in effective connectivity over time: Learning • Paired associates learning • Pairing • Object (Snodgrass) with • Location • fMRI, 48 axial slices, TR 4.1s, 8 scans/cond • 8 cycles (E)ncoding (C)ontrol (R)etrieval • 3 sessions (each with new objects & locations) C C C

  19. PP PP LP LP DE DE V1 V1 ITp ITp ITa ITa SEM: Encoding Early vs. Late 0.59 0.61 0.37 0.41 0.46 2 =6.3p<0.05diff. = 0.16 0.26 0.57 0.15 0.13 -0.03 Late Early 0.38 0.45 0.27 0.35 Single subjects: +0.27*, +0.21, +0.37*, +0.24*, +0.19, +0.31** p < 0.05

  20. Changes in effective connectivity predict learning 1 k = .60 k = .35 learning rate k k=.95 k = .63 k = .71 0.4 k =.44 r = 0.64 % correct learning block 1 2 3 4 5 6 7 Length of EARLY (in learning blocks) that maximised the EARLY vs. LATE difference in connectivity (PP -> ITP)

  21. [u(t)] input[s] u(t) response y(t) Regional activities estimate kernels (h) Volterra series - a general nonlinear input-output model y(t) = 1[u(t)] + 2[u(t)] + .... + n[u(t)] + .... n[u(t)] = ....  hn(t1,..., tn)u(t - t1) .... u(t - tn)d t1 .... d tn

  22. Volterra series approximation • Trying to explain activity in region A by • past and present activity in other regions (1st order) • direct effects (eg. effect of B on A) • past and present activity in other regions (pairwise = 2nd order) • non-linear (eg. effect of B2 on A) • modulatory (eg. effect of AB on A) • A = a1B + a2C + a3AA + a4BB + a5CC + a6AB + a7AC + a8BC • All terms can be seen as regressors and their impact can be tested with the general linear model • direct effect of B on A : B and BB as covariates of interests, others confounds • modulatory effect of B on A : AB and BC as covariates of interest, others confounds

  23. PPC FEF IFS PPC V3a V5 areas showing attentional effects PPC V1/V2 V5 Pul regional interactions examined

  24. Changes in V5 response to V2 inputs with PPC activity i.e. a modulatory (activity-dependent) component of V5 responses PPC activity = 1 SPM{F} PPC activity = 0

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