1. Dynamic Causal Modelling of Evoked Responses in EEG/MEG Wellcome Dept. of Imaging Neuroscience University College London Stefan Kiebel

2. Principles of organisation Varela et al. 2001, Nature Rev Neuroscience Varela et al. 2001, Nature Rev Neuroscience Functional segregation Functional integration Power of signal, source localisation Power of signal, source localisation Interactions between distant brain areas

3. EEG and MEG MEG - ~1929 (Hans Berger) - Neurophysiologists - From 10-20 clinical system to 64, 127, 256 sensors - Potential V: ~10 µV - ~1929 (Hans Berger) - Neurophysiologists - From 10-20 clinical system to 64, 127, 256 sensors - Potential V: ~10 µV EEG - ~1968 (David Cohen) - Physicists - From ~ 30 to more than 150 sensors - Magnetic field B: ~10 -13 T - ~1968 (David Cohen) - Physicists - From ~ 30 to more than 150 sensors - Magnetic field B: ~10 -13 T

4. MEG experiment Faces (F) vs. Scrambled faces (S) M170 S F 150-190ms fT RL Example data

5. average... single trials estimated event-related potential/field (ERP/ERF) ERP/ERF

6. Forward model Sensor data Current density Neuronal activity Neuronal activity Magnetic field Interactions between areas

7. Inverse problems Sensor data Current density Neuronal activity Neuronal activity Source reconstruction Effective connectivity

8. Dynamics f ERP/ERF Input u Spatial forward model g Generative model data y parameters θ states x

9. Neural mass model Neuronal assembly Time [ms] v [mV] Mean firing rate m(t) Mean firing rate m(t) Mean membrane potential v(t) Mean membrane potential v(t) Mean firing rate m(t) Mean firing rate m(t) m h

10. Jansen‘s model for a cortical area Excitatory Interneurons H e,  e Pyramidal Cells H e,  e Inhibitory Interneurons H i,  i Extrinsic inputsExtrinsic inputs Excitatory connection Inhibitory connection   e,  i : synaptic time constant (excitatory and inhibitory)  H e, H i :synaptic efficacy (excitatory and inhibitory)   1,…,   : connectivity constants 22 11 33 44 MEG/EEG signal MEG/EEG signal Parameters: Jansen & Rit, Biol. Cybern., 1995

11. Output : y(t)=v 1 -v 2 Input : p(t) cortical noise Jansen‘s model for a cortical area Jansen & Rit, Biol. Cybern., 1995 MEG/EEG signal = dendritic signal of pyramidal cells

12. Connectivity between areas 1 2 121 2 12 Cortex Bottom-upTop-DownLateral Supra granular Layer IV Infra granular Felleman & Van Essen, Cereb. Cortex, 1991

13. Inh. Inter. Inh. Inter. Exc. Inter. a bu Exc. Inter. Pyr. Cells Inh. Inter. Pyr. Cells Inh. Inter. Exc. Inter. a td Exc. Inter. Pyr. Cells Inh. Inter. Pyr. Cells Exc. Inter. a la Exc. Inter. Pyr. Cells Inh. Inter. Pyr. Cells Pyramidal cells Inhibitory interneurons Excitatory interneurons Pyramidal cells Inhibitory interneurons Area 1Area 2Area 1Area 2Area 1Area 2 Connectivity between areas Cortex Supra granular Layer IV Infra granular Bottom-upTop-Down Lateral David et al., NeuroImage, 2005

14. Connectivity model (no delay) Pyramidal cells Excit. IN Inhib. IN jth state for all areas Connectivity matrices

15. Input Input is modelled by an impulse at peri-stimulus time t=0 convolved with some input kernel. Gamma function Low-frequent change in input

16. Propagation delays There is short delay within-area between subareas (~2 ms). There is delay between areas. We found that these delays are important parameters (~10-30 ms). 1 2 Excitatory Interneurons H e,  e Pyramidal Cells H e,  e Inhibitory Interneurons H i,  i 22 11 33 44 Delayed differential equations

17. Connectivity parameters Within-area parameters Between-area parameters Input parameters

18. Spatial forward model Depolarisation of pyramidal cells Spatial model Sensor data

19. Forward modelling 3 main approaches lead to forward model 2D realistic model Spherical model 3D realistic model -Analytic solution (Sarvas 1987) -Isotropy and homogeneity -Analytic solution (Sarvas 1987) -Isotropy and homogeneity -Numerical solution (Mosher 1999) -2D meshes -Isotropy and homogeneity -Numerical solution (Mosher 1999) -2D meshes -Isotropy and homogeneity -Numerical solution (Marin 1998) -3D meshes -Numerical solution (Marin 1998) -3D meshes

20. Linear equation = x +  data Forward model K Sources J (over time) Sources J (over time) Error  Error  =x + Spatiotemporal characterization of the sensor data in terms of brain sources Question: How to solve for sources J?

21. Spherical model -Analytic solution (fast) -Easy to use -Good model for MEG (said to be less so for EEG) -Easy to parameterise -Seems to explains data well for early to medium latencies -Analytic solution (fast) -Easy to use -Good model for MEG (said to be less so for EEG) -Easy to parameterise -Seems to explains data well for early to medium latencies Spatial parameters Idea: Each area is spatially modelled by one equivalent current dipole. Advantages of spherical model:

22. One area - one dipole A1 OF PC STG input Forward Backward Lateral Left A1 Right A1 Left OF Right OF PC Right STG

23. Modulation by context MMN ERP standards ERP deviants deviants - standards Mismatch negativity (MMN) Different responses for two auditory stimuli Model: Explain 2 nd ERP/ERF by modulation of connectivity between areas Gain modulation matrix

24. Parameters Within-area parameters Between-area parameters Input parameters Spatial parameters

25. Network of areas MEG/EEG scalp data Input (Stimuli) Posterior distributions of parameters Modulation of connectivity differences between ERP/ERFs Dynamic causal modelling

26. Observation equation Observation equation: low-frequency drift term Normal likelihood

27. Estimation of model parameters Parameters Neurodynamics Connections (stability) Known parameters: Source locations Network connections Gain matrix K Source locations Network connections Gain matrix K Unknown parameters: Synaptic time constants and efficacies Coupling parameters Propagation delays between areas Input parameters Spatial parameters Synaptic time constants and efficacies Coupling parameters Propagation delays between areas Input parameters Spatial parameters Bayesian estimation Likelihood: Neural mass model Spatial forward model Likelihood: Neural mass model Spatial forward model Priors: Neurodynamic constants Connections Spatial parameters Priors: Neurodynamic constants Connections Spatial parameters Expectation/ Maximization

28. Model comparison models p(y|m i ) 1 2 3 Which model is the best among a set of competing models? Penny et al. 2004, NeuroImage

29. A1 STG IFG Forward Backward Lateral input MMN ERP standards ERP deviants deviants - standards Inferior frontal gyrus Superior temporal gyrus Primary auditory cortex Mismatch negativity Garrido et al., in preparation

30. forward backward forward & backward Model comparison Garrido et al., in preparation

31. Somatosensory evoked potential SI SII input Forward Backward Lateral 27.68 (100%) 2.67 (100%) 3.57 (99%) 0.95 (53%) mode 3 mode 1 mode 2 Contra SI Contra SII Ipsi SII

32. Fit to scalp data observed predicted

33. Conclusions Dynamic Causal Modelling (DCM) for EEG/MEG is physiologically grounded model. Context-induced differences in ERPs are modelled as modulation of connectivity between areas. Spherical head model is useful spatial model. DCM can alternatively be seen as source reconstruction device with temporal constraints.