1. Abstract This talk will present a general approach (DCM) to the identification of dynamic input-state-output systems such as the network of equivalent current dipoles (sources) used to model electromagnetic brain responses. We develop this approach for the analysis of effective connectivity (coupling) using experimentally designed inputs and task-free designs. The ensuing framework allows one to characterize experiments conceptually as an experimental manipulation of integration among brain sources (by contextual or trial-free inputs, like time or attentional set) that is perturbed or probed using evoked responses (to trial-bound inputs like stimuli). The approach is illustrated using DCM for evoked responses, induced responses and steady-state activity, to illustrate the range of questions that can be addressed with informed forward modeling of MEG data Swinbourne talk Wednesday 27th October, 10.30-11.30 Modelling distributed electromagnetic responses Karl Friston, Wellcome Centre for Neuroimaging, UCL

2. Dynamic Causal Modelling State and observation equations Model inversion DCMs for evoked responses Neural-mass models Perceptual learning and MMN Backward connections DCMs for induced responses Nonlinear coupling Face processing DCMs for ergodic responses Synaptic coupling Beta oscillations in Parkinsonism

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

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

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

6. Hierarchical connections in the brain and laminar specificity Dynamic Causal Modelling State and observation equations Model inversion DCMs for evoked responses Neural-mass models Perceptual learning and MMN Backward connections DCMs for induced responses Nonlinear coupling Face processing DCMs for ergodic responses Synaptic coupling Beta oscillations in Parkinsonism

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

8. ERPs Comparing models ( with and without backward connections) A1 STG input STG IFG FB A1 STG input STG IFG F 0 200 400 0 0200 400 0 FB vs. F withoutwith A1 STG IFG Garrido et al 2007 log-evidence

9. The MMN and perceptual learning MMN standardsdeviants ERP standards ERP deviants deviants - standards Garrido et al 2008

10. Model comparison: Changes in forward and backward connections A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input - STG IFG Forward (F) Backward (B) Forward and Backward (FB) Garrido et al 2009 A1 STG IFG A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input - STG IFG Forward (F) Backward (B) Forward and Backward (FB)

11. F FB log evidence Bayesian model comparison subjects Forward (F) Backward (B) Forward and Backward (FB) Two subgroups Garrido et al 2008

12. 1234512345 A1 STG subcortical input STG repetition effects monotonicphasic Intrinsic connections Extrinsic connections number of presentations The dynamics of plasticity: Repetition suppression Garrido et al 2009

13. Dynamic Causal Modelling State and observation equations Model inversion DCMs for evoked responses Neural-mass models Perceptual learning and MMN Backward connections DCMs for induced responses Nonlinear coupling Face processing DCMs for ergodic responses Synaptic coupling Beta oscillations in Parkinsonism

14. K frequencies in j -th source Nonlinear (between-frequency) coupling Linear (within-frequency) coupling Extrinsic (between-source) coupling Neuronal model for spectral features Data in channel space Inversion of electromagnetic model L input Intrinsic (within-source) coupling DCM for induced responses – a different sort of data feature CC Chen et al 2008

15. LVRV RF LF input LVRV RF LF input Frequency-specific coupling during face-processing CC Chen et al 2008

16. From 32 Hz (gamma) to 10 Hz (alpha) t = 4.72 ; p = 0.002 4 12 20 28 36 44 44 36 28 20 12 4 SPM t df 72; FWHM 7.8 x 6.5 Hz -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Right hemisphereLeft hemisphere Forward Backward Frequency (Hz) LVRV RF LF input FLBLFLBL FNBLFNBL FLBNFLBN FNBNFNBN -59890 -16308 -16306 -11895 -70000 -60000 -50000 -40000 -30000 -20000 -10000 0 Functional asymmetries in forward and backward connections CC Chen et al 2008

17. Dynamic Causal Modelling State and observation equations Model inversion DCMs for evoked responses Neural-mass models Perceptual learning and MMN Backward connections DCMs for induced responses Nonlinear coupling Face processing DCMs for ergodic responses Synaptic coupling Beta oscillations in Parkinsonism

18. 2345 6 A Te3 Te2 A1 7 = Silverball electrode, diameter: 1 mm PAF DCM for ergodic (steady-state) responses: Validation of synaptic coupling estimates in a rat model of anesthesia Excitatory synaptic kernel 02468101214161820 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10 -3 Time ms PSP mV Moran et al 2010 The transfer function and likelihood model

19. under white noise during silence Frequency (Hz) Power A1 Power A2 Power A1 - A2 051015202530 0 0.02 0.04 0.06 051015202530 0 0.02 0.04 0.06 0510152025 30 0 0.02 0.04 0.06 1.4 % 1.8 % 2.4 % 2.8 % Predicted Observed 051015202530 0 0.02 0.04 0.06 0.08 051015202530 0 0.02 0.04 0.06 0.08 051015202530 0 0.02 0.04 0.06 0.08 Predicted and observed cross-spectra for different levels of isoflurane

20. Model comparison and auditory hierarchies m3 A1 PAF lateral m2 PAF A1 forward backward m1 A1PAF forward backward Moran et al 2010

21. H e A1: White Noise H i A1: White Noise and H e PAF: White Noise H i PAF: White Noise and H e A1: Silence H i A1: Silence and H e PAF: Silence H i PAF: Silence and 1.41.82.42.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ** * 1.41.82.42.8 -1.5 -0.5 0 0.5 1 ** 1.41.82.42.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 * ** 1.41.82.42.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 * ** Isoflurane Dose Dose Specific Gain Moran et al 2010

22. Glutamatergic stellate cells GABAergic cells Glutamatergic Projection cells Data DCMs for steady-state responses: characterizing coupling parameters Cross-spectral data features 6-OHDA lesion model of Parkinsonism Moran et al 2010 1. Cortex 2. Striatum 3. External globus pallidus (GPe) 4. Subthalamic Nucleus (STN) 6. Thalamus 5. Entopeduncular Nucleus (EPN)

23. Changes in the basal ganglia-cortical circuits Moran et al Control6-OHDA Lesioned 2 3 4.25 ± 0.17 1.44 ± 0.18 5.24 ± 0.16 6. 91 ± 0.19 0.90 ± 0.21 1.43 ± 0.38 0.29 ± 0.31 0.85 ± 0.36 5 0.72 ± 0.44 2 3 5 3.43 ± 0.16 3.07 ± 0.17 5.00 ± 0.15 2.33 ± 0.21 1.04 ± 0.20 1.18 ± 0.33 1.03 ± 0.35 0.74 ± 0.28 MAP estimates EPN to Thalamus Thalamus to Ctx Ctx to Striatum Ctx to STN Striatum to GPe Striatum to EPN STN to EPN STN to GPe GPe to STN 0 1 2 3 4 5 6 7 8 * *

24. 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