DCM for ERP/ERF: theory and practice

1. DCM for ERP/ERF: theory and practice Melanie Boly Based on slides from Chris Phillips, Klaas Stephan and Stefan Kiebel

2. ? ? Dynamical Causal Modelling A sophisticated technique to investigate effective connectivity of the brain for fMRI and EEG / MEG data: EEG / MEG data: The goal of DCM is to explain evoked responses as the output of an interacting network consisting of a few areas that receive an input stimulus.

3. Terminology: effective connectivity? Functional specialisation: Identification of a particular brain region with a specific function. Functional integration: Identifying interactions among specialised neural populations & how these depend on the context. Functional connectivity: Is defined as correlations between remote neuro-physiological events. Effective connectivity: Refers explicitly to the influence that one neuronal system exerts over another, either at a synaptic (i.e.synaptic efficacy) or population level.

4. Effective connectivity in DCM • the influence that one neural system exerts over another - how is this affected by experimental manipulations • considers the brain as a physical interconnected system • requires - an anatomical model of which regions are connected and - a mathematical model of how the different regions interact

5. DCM: generative model for fMRI and ERPs Hemodynamicforward model:neural activityBOLD Electric/magnetic forward model:neural activityEEGMEG LFP Neural state equation: fMRI ERPs Neural model: 1 state variable per region bilinear state equation no propagation delays Neural model: 8 state variables per region nonlinear state equation propagation delays inputs

12. Neural mass model of a cortical macrocolumn = POPULATION DYNAMICS CONNECTIVITY ORGANISATION E x t r i n s i c i n p u t s Excitatory Interneurons Function P mean firing rate  mean postsynaptic potential (PSP) Pyramidal Cells MEG/EEG signal Function S mean PSP mean firing rate Inhibitory Interneurons Excitatory connection Inhibitory connection

13. Neural mass model of a cortical macrocolumn = Function P E x t r i n s i c i n p u t s Excitatory Interneurons He, e mean firing rate  mean postsynaptic potential (PSP) ~H ~ 1 2 Pyramidal Cells He, e MEG/EEG signal Function S 3 4 mean PSP mean firing rate Inhibitory Interneurons Hi, i Excitatory connection Inhibitory connection • te, ti : synaptic time constant (excitatory and inhibitory) • He, Hi: synaptic efficacy (excitatory and inhibitory) • g1,…,g4: intrinsic connection strengths • propagation delays Parameters: Jansen & Rit (1995) Biol. Cybern. David et al. (2006) NeuroImage

14. Hierarchical Connections Bottom-up Top-down Lateral Excitatory Interneurons Excitatory Interneurons Excitatory Interneurons Excitatory Interneurons Excitatory Interneurons Excitatory Interneurons Pyramidal Cells Pyramidal Cells Pyramidal Cells Pyramidal Cells Pyramidal Cells Pyramidal Cells aF aB aL Inhibitory Interneurons Inhibitory Interneurons Inhibitory Interneurons Inhibitory Interneurons Inhibitory Interneurons Inhibitory Interneurons Excitatory connection Inhibitory connection

15. Model parameters (I) 1 2 neural mass model 3 area model Inhibitory IN 2 3 Excitatory IN 1 Pyramidal cells Intrinsic Forward Backward Lateral Extrinsic Input u David and Friston, 2003 David et al., 2005

16. Model parameters (I) within-area parameters 1 2 neural mass model 3 area model • te, ti : synaptic time constant (excitatory and inhibitory) • He, Hi: synaptic efficacy (excitatory and inhibitory) • g1,…,g4: connectivity constants ti , Hi Supra-granular 2 3 Layer 4 g1 g2 te, He Connectivity matrices g4 g3 1 Infra-granular ti , Hi between-area parameters Intrinsic Forward Backward Lateral Extrinsic Input u David and Friston, 2003 David et al., 2005

17. Hierarchical DCM for M/EEG inhibitory interneurons spiny stellate cells pyramidal cells State equations Extrinsic lateral connections Extrinsic forward connections Intrinsic connections Extrinsic backward connections Function S neuronal (source) model mean PSP mean firing rate

18. Hierarchical DCM for M/EEG inhibitory interneurons spiny stellate cells pyramidal cells State equations Extrinsic lateral connections Extrinsic forward connections Intrinsic connections Extrinsic backward connections Output equation neuronal (source) model Lead field

19. Electromagnetic forward model for M/EEG Forward model: lead field & gain matrix Depolarisation of pyramidal cells Scalp data Forward model

22. Practical Example …

23. Introduction Example: Mismatch Negativity Oddball paradigm standards deviants time pseudo-random auditory sequence 80% standard tones – 500 Hz 20% deviant tones – 550 Hz data SPM • convert to matlab file • filter • epoch • down sample • artifact correction • average ERPs of 12 subjects, 2 conditions (standard + deviant) raw data preprocessing 128 EEG scalp electrodes

24. 4 standards deviants 3 MMN 2 1 V m 0 -1 -2 -3 -4 -100 -50 0 50 100 150 200 250 300 350 400 ms Grand Mean (average over subjects) DCM: 1) Models the difference between two evoked responses … 2) … as a modulation of some of the inter-aereal connections.

25. Finally … SPM! DCM for Evoked Responses Also for steady-state responses (SSR) and induces responses (IND) …

26. Choose time window Trial indices Choose nr. of components

27. Depolarisation of pyramidal cells Spatial model Sensor data Spatial Forward Model Default: Each area that is part of the model is modeled by one equivalent current dipole (ECD).

28. STG A1 IFG Assumptions … MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002). • Assumed Sources: • Left A1 • Right A1 • Left STG • Right STG • Right IFG Find the coordinates of the sources … (in mm in MNI coordinates).

29. How to spatially model ER Sources’ coordinates Onset time for modelling Sources’ names

30. DCM specification … IFG STG STG Opitz et al., 2002 rIFG lA1 rA1 rSTG lSTG A1 A1 input Doeller et al., 2003 modulation of effective connectivity

31. IFG STG STG A1 A1 input modulation of effective connectivity e.g. from left A1 to left STG Specify extrinsic connections Input to Modulatory effect Intrinsic connections from Invert DCM

32. Then.. Optimization of the parameters inhibitory interneurons spiny stellate cells pyramidal cells State equations Extrinsic lateral connections Extrinsic forward connections Intrinsic connections Extrinsic backward connections Output equation neuronal (source) model Lead field

33. Observed (adjusted) 1 Predicted 6 6 4 4 2 2 0 0 -2 -2 -4 -4 input -6 -6 -8 -8 0 50 100 150 200 250 0 50 100 150 200 250 time (ms) time (ms) Model Inversion: fit the data Data Predicted data We need to estimate the extrinsic connectivity parameters and their modulation from data.

34. Coupling B Posterior means for gain modulations Probability ≠ prior means

35. Alternative Models for Comparison … IFG IFG IFG Forward and Forward - F Backward - B Backward - FB STG STG STG STG STG STG A1 A1 A1 A1 A1 A1 input input input Forward Forward Forward Backward Backward Backward Lateral Lateral Lateral modulation of effective connectivity

39. LD LD|LVF LD|RVF LD|LVF LD LD RVF stim. LD LVF stim. RVF stim. LD|RVF LVF stim. LG LG MOG MOG MOG MOG FG FG FG FG LG LG Group level BMS resistant to outliers m2 m1 Stephan et al. 2009

40. Estimates of Dirichlet parameters Post. expectations of model probabilities Exceedance probability Stephan et al. 2009

41. Conclusions • DCM is a sophisticated technique to investigate effective connectivity • Combines a biologically plausible neuronal mass model with a spatial forward model to generate a predicted data set • Allows us to estimate connectivity parameters & how they are modulated between conditions • And to compute the model evidence in order to single out the best model of the ones proposed. • Underlying theory is complex, but SPM analysis is comparatively simple. • But: requires a lot of previous knowledge. • DCM is not a method to do ERP source reconstruction but knowledge about possible sources is a prerequisite for applying DCM to a data set. • DCM is not exploratory!

42. 10 simple rules for dynamic causal modelling: • 1) Know what is causal about dynamic causal model • In EEG: inferences about conduction delays is allowed, not in fMRI • 2) Know your hypothesis and how to test it • anatomy of the network – inference on model structure or parameters • 3) Use Bayesian Model selection as a fist step • Results on connection parameters depend on the accuracy of the model • 4) Motivate model space carefully • parametrize model space – test systematically different models (factorial) • 5) Choose an appropriate method for group-level inference on model structure • - fixed/ random effects – family-level inference

43. 10 simple rules for dynamic causal modelling: • 6) Know what you can do and what you can’t do with bayesian model selection • model defined for one particular data set, • cannot change regions in fMRI, cannot change preprocessing steps in general • test an appropriate set of models • 7) Choose an appropriate method for group inference on parameters • RFX vs FFX, bayesian model averaging • 8) Optimize design and data acquisition • in EEG: record electrodes on the scalp – do first feature selection • 9) Use anatomical information and computational models to refine your DCM • can improve model evidence • 10) Report the modelling approach and results in detail

44. References: Jansen BH, Rit VG, (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics 73:357–366 David O, Friston KJ (2003). A neural mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage 20:1743–1755 Kiebel SJ, Garrido MI, Moran RJ, Friston KJ (2008). Dynamic causal modeling for EEG and MEG. Cognitive Neurodynamics (2008) 2:121–136 SPM8 Manual:http://www.fil.ion.ucl.ac.uk/spm/doc/manual.pdf

45.  Thanks to Marta Garrido & Rosalyn Moran