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Dynamic Causal Modelling of Evoked Responses in EEG/MEG

This study explores principles of functional segregation and integration in the brain using EEG/MEG data. It investigates the power of signal and source localization, as well as the interactions between distant brain areas. The study focuses on EEG/MEG signals and their interactions with neuronal activity, current density, and effective connectivity. The Jansen's model for cortical area and spatial forward modelling techniques are used to estimate ERP/ERF parameters and solve for brain sources.

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Dynamic Causal Modelling of Evoked Responses in EEG/MEG

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

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

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

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

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

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

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

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

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

  10. Jansen‘s model for a cortical area E x t r i n s i c i n p u t s Excitatory Interneurons He, te g1 g2 Pyramidal Cells He, te MEG/EEG signal g4 g3 Inhibitory Interneurons Hi, ti Excitatory connection Inhibitory connection • te, ti : synaptic time constant (excitatory and inhibitory) • He, Hi: synaptic efficacy (excitatory and inhibitory) • g1,…,g4: connectivity constants Parameters: Jansen & Rit, Biol. Cybern., 1995

  11. Jansen‘s model for a cortical area MEG/EEG signal = dendritic signal of pyramidal cells Output : y(t)=v1-v2 Input : p(t) cortical noise Jansen & Rit, Biol. Cybern., 1995

  12. Connectivity between areas 1 2 Bottom-up Top-Down Lateral Supra granular Layer IV Cortex Infra granular 2 1 2 1 1 2 Felleman & Van Essen, Cereb. Cortex, 1991

  13. Connectivity between areas Pyramidal cells Inhibitory interneurons Supra granular Excitatory interneurons Layer IV Cortex Pyramidal cells Inhibitory interneurons Infra granular Bottom-up Top-Down Lateral Exc. Inter. Exc. Inter. Exc. Inter. Exc. Inter. Exc. Inter. Exc. Inter. Pyr. Cells Pyr. Cells Pyr. Cells Pyr. Cells Pyr. Cells Pyr. Cells abu atd ala Inh. Inter. Inh. Inter. Inh. Inter. Inh. Inter. Inh. Inter. Inh. Inter. Area 1 Area 2 Area 1 Area 2 Area 1 Area 2 David et al., NeuroImage, 2005

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

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

  16. Propagation delays There is short delay within-area between subareas (~2 ms). Excitatory Interneurons He, te There is delay between areas. We found that these delays are important parameters (~10-30 ms). g1 g2 Pyramidal Cells He, te 1 2 g4 g3 Inhibitory Interneurons Hi, ti Delayed differential equations

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

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

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

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

  21. Spherical model Idea: Each area is spatially modelled by one equivalent current dipole. Advantages of 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 Spatial parameters

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

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

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

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

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

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

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

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

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

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

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