Dynamic Causal Modelling Will Penny Wellcome Department of Imaging Neuroscience, University College London, UK FMRIB, Oxford, May

Outline §Functional specialisation and integration §DCM theory §Attention Data §Model comparison

Outline §Functional specialisation and integration §DCM theory §Attention Data §Model comparison

Attention to Visual Motion 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 S – stationary dots N – moving dots A – attended moving dots 1.Photic Stimulation, S,N,A 2.Motion, N,A 3.Attention, A Experimental Factors Buchel et al. 1997

Functional Specialisation Q. In what areas does the ‘motion’ factor change activity ? Univariate Analysis

Attention V2 attention no attention V2 activity V5 activity SPM{Z} time V5 activity Functional Integration Q. In what areas is activity correlated with activity in V2 ? Q. In what areas does the ‘attention’ factor change this correlation ? Multivariate Analysis

Functional Integration Q. In what areas is activity correlated with activity in V2 ? Q. In what areas does the ‘attention’ factor change this correlation ? Q. In what areas is activity related to the correlation between V2 and V5 ? Psycho-Physiological (PPI) Interaction Physio-Physiological (PPI) Interaction Physiological correlation

Larger networks Structural Equation Modelling (SEM) Multivariate Autoregressive (MAR) Dynamic Causal Modelling (DCM) Connections = ‘Hemodynamic’ (SEM/MAR) = ‘Neuronal’ (PPI/DCM) Z2Z2 Z4Z4 Z3Z3 Z5Z5

Outline §Functional specialisation and integration §DCM theory §Attention Data §Model comparison

To estimate and make inferences about (1) the influence that one neural system exerts over another (i.e. effective connectivity) (2) how this is affected by the experimental context Aim of DCM Z2Z2 Z4Z4 Z3Z3 Z5Z5

DCM Theory §A Model of Neuronal Activity §A Model of Hemodynamic Activity §Fitting the Model §Making inferences §Model Comparison

Model of Neuronal Activity Z2Z2 Z1Z1 Z2Z2 Z4Z4 Z3Z3 Z5Z5 Stimuli u 1 Set u 2 Nonlinear, systems-level model

Bilinear Dynamics a53 Set u 2 Stimuli u 1

Bilinear Dynamics: Oscillatory transients Z2Z2 Stimuli u 1 Set u 2 Z1Z u 1 Z 1 u 2 Z 2 Seconds

Bilinear Dynamics: Positive transients - Z2Z2 Stimuli u 1 Set u 2 Z1Z u 1 Z 1 u 2 Z 2

DCM: A model for fMRI Set u 2 Stimuli u 1 Causality: set of differential equations relating change in one area to change in another

The hemodynamic model Buxton, Mandeville, Hoge, Mayhew.

Hemodynamics Impulse response BOLD is sluggish

Neuronal Transients and BOLD: I 300ms500ms More enduring transients produce bigger BOLD signals Seconds

Neuronal Transients and BOLD: II BOLD is sensitive to frequency content of transients Seconds Relative timings of transients are amplified in BOLD

Model estimation and inference Unknown neural parameters, N={A,B,C} Unknown hemodynamic parameters, H Vague priors and stability priors, p(N) Informative priors, p(H) Observed BOLD time series, B. Data likelihood, p(B|H,N) = Gauss (B-Y) Bayesian inference p(N|B)  p(B|N) p(N) Laplace Approximation

Posterior Distributions A1 A2 WA   CC P(A(ij)) = N (  A (i,j),    ij) ) P(B(ij)) = N (  B (i,j),    ij) ) P(C(ij)) = N (  C (i,j),  C  ij) ) Show connections for which A(i,j) > Thresh with probability > 90%

Outline §Functional specialisation and integration §DCM theory §Attention Data §Model comparison

Attention to Visual Motion 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 S – stationary dots N – moving dots A – attended moving dots 1.Photic Stimulation, S,N,A 2.Motion, N,A 3.Attention, A Experimental Factors Buchel et al. 1997

V1IFG V5SPC Motion Photic Attention..82 (100%).42 (100%).37 (90%).69 (100%).47 (100%).65 (100%).52 (98%).56 (99%) Motion modulates bottom-up V1-V5 connection Attention modulates top-down IFG-SPC and SPC-V5 connections Friston et al. 2003

Outline §Functional specialisation and integration §DCM theory §Attention Data §Model comparison

First level of Bayesian Inference First level of Inference: What are the best parameters ? We have data, y, and some parameters,  Parameters are of model, M, ….

First and Second Levels The first level again, writing in dependence on M: Second level of Inference: What’s the best model ?

Model Comparison We need to compute the Bayesian Evidence: We can’t always compute it exactly, but we can approximate it: Log p(y|M) ~ F(M) Evidence = Accuracy - Complexity

m=1 V1PFC V5 PPC Motion Photic Attention Motion Photic Attention Motion Photic Attention Motion Photic Attention m=2 V1PFC V5 PPC Motion Photic Attention V1PFCV5PPC Motion Photic Attention V1PFCV5PPC Motion Photic Attention m=3 m=4

m=1 V1PFC V5 PPC Motion Photic Attention Motion Photic Attention Motion Photic Attention Motion Photic Attention m=2 V1PFC V5 PPC Motion Photic Attention V1PFC V5 PPC Motion Photic Attention V1PFC V5 PPC Motion Photic Attention m=3 m=4

Summary §Studies of functional integration look at experimentally induced changes in connectivity §In PPI’s and DCM this connectivity is at the neuronal level §DCM: Neurodynamics and hemodynamics §Inferences about large-scale neuronal networks §Model comparison/averaging

Single word processing at different rates SPM{F} “Dog” “Mountain” “Gate” Functional localisation of primary and secondary auditory cortex and Wernicke’s area Friston et al. 2003

Time Series A1 WA A2 Auditory stimulus, u1 Adaptation variable, u2

Dynamic Causal Model A2 WA A1.. Auditory stimulus, u1 Model allows for full intrinsic connectivity u1 Adaptation variable, u2 u1 enters A1 and is also allowed to affect all intrinsic self-connections u2 is allowed to affect all intrinsic connections between regions

Inferred Neural Network A2 WA A1.92 (100%).38 (94%).47 (98%).37 (91%) -.62 (99%) -.51 (99%).37 (100%) Intrinsic connections are feed-forward Neuronal saturation with increasing stimulus frequency in A1 & WA Time-dependent change in A1-WA connectivity

Two central problems §The problem of the hidden level We measure hemodynamics but wish to make inferences about neurodynamics §The problem of the hidden variable Association between A and B can be mediated by causal influence from C