SPM short course Functional integration and connectivity Christian Büchel Karl Friston The Wellcome Department of Cognitive Neurology, UCL London UK http//:

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

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

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

Effective vs. functional connectivity Model: A = V1 fMRI time-series B = 0.5 * A + e1 C = 0.3 * A + e2 Model: A = V1 fMRI time-series B = 0.5 * A + e1 C = 0.3 * A + e2 Correlations: ABC Correlations: ABC ABC  2 =0.5, ns. Correct model

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’

Eigenimages and SVD Y (DATA) time voxels Y = USV T = s 1 U 1 V 1 T + s 2 U 2 V 2 T +... APPROX. OF Y U1U1U1U1 = APPROX. APPROX. + s 2 + s s1s1s1s1 U2U2U2U2 U3U3U3U3 V1V1V1V1 V2V2V2V2 V3V3V3V3

An example from PET Eigenimage analysis of a PET word generation study Word generation G Word repetitionR R G R G R G

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

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%) 5 x 30s trials with 5 speed changes (reducing to 1%) Task - detect change in radial velocity Scanning (no speed changes) 6 normal subjects, 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

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

Regression with time-varying coefficients Fixed regression model (one coefficient for entire time-series) y = x*b + e y = x*b + e Time varying regression model (coefficient changes over time) y t = x t.b t + e t b t = b t-1 +h t Coefficient b of the explanatory variable (V5) is modelled as a time-varying random walk. Estimation by Kalman filter. Fixed regression model (one coefficient for entire time-series) y = x*b + e y = x*b + e Time varying regression model (coefficient changes over time) y t = x t.b t + e t b t = b t-1 +h t Coefficient b of the explanatory variable (V5) is modelled as a time-varying random walk. Estimation by Kalman filter. Attention Fixation No attention btbtbtbt x = V5 y = PP Time (scans) regression coefficient

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

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 + z x= 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: x T. x =  = (I-B) -T. C.(I-B) -1 where C= z T z x T.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  Structural equation modelling (SEM) U W V a b c u v w

Attention - No attention Attention No attention

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

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

Changes in effective connectivity over time: Learning Changes in effective connectivity over time: Learning Paired associates learningPaired associates learning PairingPairing –Object (Snodgrass) with –Location fMRI, 48 axial slices, TR 4.1s, 8 scans/condfMRI, 48 axial slices, TR 4.1s, 8 scans/cond 8 cycles (E)ncoding (C)ontrol (R)etrieval8 cycles (E)ncoding (C)ontrol (R)etrieval 3 sessions (each with new objects & locations)3 sessions (each with new objects & locations) Paired associates learningPaired associates learning PairingPairing –Object (Snodgrass) with –Location fMRI, 48 axial slices, TR 4.1s, 8 scans/condfMRI, 48 axial slices, TR 4.1s, 8 scans/cond 8 cycles (E)ncoding (C)ontrol (R)etrieval8 cycles (E)ncoding (C)ontrol (R)etrieval 3 sessions (each with new objects & locations)3 sessions (each with new objects & locations) CCC ERER V1 ITp ITa PP LP V1 ITp DE

SEM: Encoding Early vs. Late V1DEPP LPITpITa Early V1DEPP LPITpITa Late  2 =6.3 p<0.05 diff. = 0.16 Single subjects: +0.27*, +0.21, +0.37*, +0.24*, +0.19, +0.31* * p < 0.05

Changes in effective connectivity predict learning Length of EARLY (in learning blocks) that maximised the EARLY vs. LATE difference in connectivity (PP -> ITP) learning rate k r = learning block k =.35 k =.60 k =.63 k=.95 k =.71 k =.44 % correct

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

Volterra series approximation Trying to explain activity in region A byTrying to explain activity in region A by –past and present activity in other regions (1st order) direct effects (eg. effect of B on A)direct effects (eg. effect of B on A) –past and present activity in other regions (pairwise = 2nd order) non-linear (eg. effect of B 2 on A)non-linear (eg. effect of B 2 on A) modulatory (eg. effect of AB on A)modulatory (eg. effect of AB on A) –A = a 1 B + a 2 C + a 3 AA + a 4 BB + a 5 CC + a 6 AB + a 7 AC + a 8 BC –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 Trying to explain activity in region A byTrying to explain activity in region A by –past and present activity in other regions (1st order) direct effects (eg. effect of B on A)direct effects (eg. effect of B on A) –past and present activity in other regions (pairwise = 2nd order) non-linear (eg. effect of B 2 on A)non-linear (eg. effect of B 2 on A) modulatory (eg. effect of AB on A)modulatory (eg. effect of AB on A) –A = a 1 B + a 2 C + a 3 AA + a 4 BB + a 5 CC + a 6 AB + a 7 AC + a 8 BC –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

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

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