CRIS Workshop: Computational Neuroscience and Bayesian Modelling Monday 25th October; 2-5PM; Building 26, room 135; Clayton Campus Effective and functional connectivity Karl Friston, Wellcome Centre for Neuroimaging, UCL Abstract This talk will highlight the fundamental difference between effective and functional connectivity by demonstrating the nature of biophysical models used to infer effective connectivity. I will use DCM studies of reciprocal connections in the brain to illustrate what can be achieved using anatomically and physiologically informed models of distributed neuronal interactions. The examples chosen will focus on functional asymmetries in forward and backward connections and try to cover (i) different data features (e.g., fMRI and ERPs) and (ii) different scales (macroscopic and microscopic).

Functional and Effective connectivity Dynamic Causal Modelling DCM and fMRI DCM and EEG DCM and DTI

Functional connectivity Effective connectivity Statistical dependence between systems Effective connectivity Causal influence among systems DAG DCM Tests for conditional independence: Structural causal modeling Bayesian model comparison: Dynamic causal modeling Bayesian networks DCM PCA and ICA Path analysis (SEM) Ganger causality (MAR)

Functional and Effective connectivity Dynamic Causal Modelling DCM and fMRI DCM and EEG DCM and DTI

Forward models and their inversion Observed data Forward model (measurement) Model inversion Forward model (neuronal) input

Model specification and inversion Design experimental inputs Neural dynamics Define likelihood model Observer function Specify priors Invert model Inference on parameters Inference on models Inference

The bilinear (neuronal) model Input Dynamic perturbation Structural perturbation average connectivity bilinear and nonlinear connectivity exogenous causes

Functional and Effective connectivity Dynamic Causal Modelling DCM and fMRI DCM and EEG DCM and DTI

Output: a mixture of intra- and extravascular signal Hemodynamic models for fMRI basically, a convolution signal The plumbing flow volume dHb 0 8 16 24 sec Output: a mixture of intra- and extravascular signal

A toy example u2 x3 u1 x1 x2 – – Neural population activity 0.4 0.3 0.2 0.1 10 20 30 40 50 60 70 80 90 100 u2 0.6 0.4 A toy example x3 0.2 10 20 30 40 50 60 70 80 90 100 0.3 0.2 0.1 BOLD signal change (%) 10 20 30 40 50 60 70 80 90 100 u1 x1 x2 3 2 1 – – 10 20 30 40 50 60 70 80 90 100 4 3 2 1 -1 10 20 30 40 50 60 70 80 90 100 3 2 1 10 20 30 40 50 60 70 80 90 100

An fMRI study of attention 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) 4 100 scan sessions; each comprising 10 scans of 4 conditions F A F N F A F N S ................. F - fixation point A - motion stimuli with attention (detect changes) N - motion stimuli without attention S - no motion V5+ PPC Buchel et al 1999

1) Hierarchical architecture 3) Attentional modulation of prefrontal connections sufficient to explain regionally specific attentional effects Attention .43 .53 Photic SPC .40 .49 .62 V1 .92 .35 IFG .53 2) Segregation of motion information to V5 Motion V5 .73 Friston et al 1999

Functional and Effective connectivity Dynamic Causal Modelling DCM and fMRI DCM and EEG DCM and DTI

neuronal mass models of distributed sources input Inhibitory cells in supragranular layers Exogenous input Excitatory spiny cells in granular layers State equations Output equation Excitatory pyramidal cells in infragranular layers Measured response

FB F Comparing models (with and without backward connections) ERPs log-evidence A1 STG IFG FB vs. F IFG IFG FB F STG STG STG STG 200 400 without with A1 A1 A1 A1 input input Garrido et al 2007

Functional and Effective connectivity Dynamic Causal Modelling DCM and fMRI DCM and EEG DCM and DTI

Probabilistic constraints (priors) on effective connectivity LD LD LD|LVF FG (x3) FG (x4) Probabilistic constraints (priors) on effective connectivity LD LD LG (x1) LG (x2) LD|RVF RVF stim. LVF stim. BVF stim. FG FG DTI data and tractography LG LG Probabilistic structural connectivity

Model-space search (scoring) Optimizing structural constraints Model-space search (scoring)

Model-space search - results 1

Thank you And thanks to CC Chen Jean Daunizeau Marta Garrido Lee Harrison Stefan Kiebel Andre Marreiros Rosalyn Moran Will Penny Klaas Stephan And many others