Dynamic Causal Modelling

Dynamic Causal Modelling Will Penny Karl Friston, Lee Harrison, Klaas Stephan, Andrea Mechelli Wellcome Department of Imaging Neuroscience, University College London, UK Loughborough University Nov 25th 2003

Outline • Functional specialisation and integration • DCM theory • Attention to visual motion fMRI study • Model comparison

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

Attention to Visual Motion fMRI 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, 360 whole-brain scans, one every 3.2 seconds; each session comprising 4 different conditions e.g. F A F N F A F N S ................. F – fixation S – stationary dots N – moving dots A – attended moving dots Buchel et al. 1997 Experimental Factors • Photic Stimulation, S,N,A • Motion, N,A • Attention, A

Functional Specialisation Q. In what areas does the ‘motion’ factor change activity ? Univariate Analysis Spatial resolution – millimetres Temporal resolution – seconds

Attention V2 Functional Integration Multivariate Analysis SPM Q. In what areas is activity correlated with activity in V2 ? Q. In what areas does the ‘attention’ factor change this correlation ? V5 activity 300 600 900 Seconds attention V5 activity no attention V2 activity

Larger networks fMRI time series Structural Equation Modelling (SEM) Y(4)t Y(1)t Y(2)t Y(3)t Multivariate Autoregressive (MAR)

Z4 Z5 Z2 Z3 Aim of DCM To estimate and make inferences about (1) the influence that one neural system exerts over another (2) how this is affected by the experimental context Logothetis: fMRI is most strongly correlated with Local Field Potential

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

Z2 Set u2 Stimuli u1 Z4 Z5 Z1 Z2 Z3 Model of Neuronal Activity Systems-level model

Bilinear Dynamics a53 Set u2 Stimuli u1

u 1 u 2 Z 1 Z 2 Bilinear dynamics: oscillatory transients Stimuli u1 Set u2 - + Z1 - - + Z2 - Seconds -

u 1 u 2 Z 1 Z 2 Bilinear dynamics: positive transients Stimuli u1 Set u2 - + Z1 - + + Z2 - -

DCM: A model for fMRI Set u2 Stimuli u1

The hemodynamic model Buxton, Mandeville, Hoge, Mayhew.

Impulse response Hemodynamics BOLD is sluggish

Neuronal Transients and BOLD: I 300ms 500ms Seconds Seconds More enduring transients produce bigger BOLD signals

Seconds Neuronal Transients and BOLD: II Seconds 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) a p(B|N) p(N) Laplace Approximation

Photic SPC 0.85 0.70 0.84 1.36 V1 -0.02 0.57 V5 Motion 0.23 Attention V1 V5 Results SPC P(B{Attention-V1,V5} |Data) Attention Motion Photic

First level of Bayesian Inference We have data, y, and some parameters, b First level of Inference: What are the best 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

Photic Photic SPC SPC SPC SPC 0.96 0.85 0.70 0.84 1.36 0.96 V1 V1 V1 V1 0.06 -0.02 V5 V5 0.39 0.57 V5 V5 Motion Motion 0.23 0.58 Attention Attention Photic 0.86 0.75 1.42 0.89 Attention 0.55 -0.02 0.56 Motion Photic 0.85 0.70 1.36 0.85 Attention 0.03 -0.02 0.57 Motion 0.23 Attention Model 1 Model 3 Model 2 Model 4

Summary • Studies of functional integration look at experimentally induced changes in connectivity • In DCM this connectivity is at the neuronal level • DCM: Neurodynamics and hemodynamics • Inferences about large-scale neuronal networks • Model comparison • Future Work: DCMs for EEG and fMRI

Dynamic Causal Modelling