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Dynamic Causal Modelling of Evoked Responses in EEG/MEG. Stefan Kiebe l. Wellcome Dept. of Imaging Neuroscience University College London. Principles of organisation. Functional segregation. Functional integration. Varela et al. 2001, Nature Rev Neuroscience. Power of signal,
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Dynamic Causal Modelling of Evoked Responses in EEG/MEG Stefan Kiebel Wellcome Dept. of Imaging Neuroscience University College London
Principles of organisation Functional segregation Functional integration Varela et al. 2001, Nature Rev Neuroscience Power of signal, source localisation Interactions between distant brain areas
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
S F Faces (F) vs. Scrambled faces (S) fT 150-190ms L R Example data MEG experiment M170
ERP/ERF single trials . . . average estimated event-related potential/field (ERP/ERF)
Forward model Interactions between areas Magnetic field Neuronal activity Sensor data Current density
Inverse problems Effective connectivity Source reconstruction Neuronal activity Sensor data Current density
Generative model Dynamics f Spatial forward model g states x ERP/ERF parameters θ Input u data y
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]
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
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
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
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
Connectivity model (no delay) Pyramidal cells jth state for all areas Excit. IN Connectivity matrices Inhib. IN
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
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
Connectivity parameters Within-area parameters Between-area parameters Input parameters
Spatial forward model Depolarisation of pyramidal cells Sensor data Spatial model
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
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?
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
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
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
Parameters Within-area parameters Between-area parameters Spatial parameters Input parameters
Dynamic causal modelling MEG/EEG scalp data Network of areas Input (Stimuli) Posterior distributions of parameters Modulation of connectivity differences between ERP/ERFs
Observation equation Observation equation: low-frequency drift term Normal likelihood
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
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
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
forward backward forward & backward Model comparison Garrido et al., in preparation
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
Fit to scalp data observed predicted
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.