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Dynamic Causal Modelling: Inversion of Input-State-Output Systems

This tutorial focuses on the inversion of dynamic input-state-output systems using a Bayesian framework. It explores the analysis of effective connectivity in the brain through experimentally designed inputs and fMRI and EEG responses.

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Dynamic Causal Modelling: Inversion of Input-State-Output Systems

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  1. Imaging Clinic Tuesday 26th October: 10AM-4.30PM; Building 26, room 135; Clayton Campus Dynamic Causal Modelling (tutorial) Karl Friston, Wellcome Centre for Neuroimaging, UCL Abstract This tutorial is about the inversion of dynamic input-state-output systems. Identification of the systems parameters proceeds in a Bayesian framework given known, deterministic inputs and observed responses of the [neuronal] system. We develop this approach for the analysis of effective connectivity or coupling in the brain, using experimentally designed inputs and fMRI and EEG responses. In this context, the parameters correspond to effective connectivity and, in particular, bilinear parameters reflect the changes in connectivity induced by inputs. The ensuing framework allows one to characterise experiments, conceptually, as an experimental manipulation of integration among brain regions (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). As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling (c.f. psychophysiologic interactions). However, unlike previous approaches to connectivity in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.

  2. Dynamic Causal Modelling State and observation equations Model inversion DCMs for fMRI Bilinear models Hemodynamic models Attentional modulation Two-state models DCMs for EEG Neural-mass models Perceptual learning and MMN Backward connections DCMs for LFP Steady-state responses

  3. y y y y y Functional integration and the enabling of specific pathways Structural perturbations Stimulus-free - u e.g., attention, time neuronal network BA39 Dynamic perturbations Stimuli-bound u e.g., visual words STG V4 V1 BA37 measurement

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

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

  6. Dynamic Causal Modelling State and observation equations Model inversion DCMs for fMRI Bilinear models Hemodynamic models Attentional modulation Two-state models DCMs for EEG Neural-mass models Perceptual learning and MMN Backward connections Induced responses DCMs for LFP Steady-state responses

  7. Input The bilinear (neuronal) model Dynamic perturbation Structural perturbation average connectivity bilinear connectivity exogenous causes

  8. Hemodynamic models for fMRI basically, a convolution signal The plumbing flow volume dHb 0 8 16 24 sec Output: a mixture of intra- and extravascular signal

  9. Neural population activity 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 100 u2 0.6 0.4 A toy example x3 0.2 0 0 10 20 30 40 50 60 70 80 90 100 0.3 0.2 0.1 BOLD signal change (%) 0 0 10 20 30 40 50 60 70 80 90 100 x1 x2 u1 3 2 1 – – 0 0 10 20 30 40 50 60 70 80 90 100 4 3 2 1 0 -1 0 10 20 30 40 50 60 70 80 90 100 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100

  10. PPC V5+ An fMRI study of attention Stimuli 250 radially moving dots at 4.7 degrees/s Pre-Scanning 5 x 30s trials with 5 speed changes (reducing to 1%) Task: detect change in radial velocity Scanning(no speed changes) 4 100 scan sessions; each comprising 10 scans of 4 conditions F A F N F A F N S ................. F - fixation point A - motion stimuli with attention (detect changes) N - motion stimuli without attention S - no motion Buchel et al 1999

  11. 3) Attentional modulation of prefrontal connections sufficient to explain regionally specific attentional effects 1) Hierarchical architecture Attention .43 .53 SPC Photic .40 .49 .62 .92 V1 IFG .35 .53 2) Segregation of motion information to V5 Motion V5 .73 Friston et al 1999

  12. rivalry non-rivalry 0.02 -0.03 MFG 1.05 0.08 2.43 2.41 -0.31 0.51 0.30 PPA FFA -0.80 0.04 -0.03 0.02 0.06 faces houses faces houses Nonlinear DCM: modulation of connections in inferotemporal cortex under binocular rivalry FFA PPA MFG time (s) Stephan et al 2008

  13. Modeling excitatory and inhibitory dynamics Single-state DCM Two-state DCM input (bottom right). Extrinsic (between-region) coupling Intrinsic (within-region) coupling Andre Marreiros et al

  14. Model comparison: where is attention mediated? Model comparison Andre Marreiros et al

  15. Dynamic Causal Modelling State and observation equations Model inversion DCMs for fMRI Bilinear models Hemodynamic models Attentional modulation Two-state models DCMs for EEG Neural-mass models Perceptual learning and MMN Backward connections Induced responses DCMs for LFP Steady-state responses Hierarchical connections in the brain and laminar specificity

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

  17. 0 0 400 200 IFG A1 A1 0 STG STG 0 200 400 Comparing models (with and without backward connections) ERPs log-evidence FB vs. F IFG IFG FB F STG STG STG STG without with A1 A1 A1 A1 input input Garrido et al 2007

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

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

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

  21. 200 180 160 140 120 100 80 60 repetition effects 40 20 0 1 2 3 4 5 STG STG 250 A1 A1 200 150 subcortical input 100 1 2 3 4 5 1 2 3 4 5 50 0 1 2 3 4 5 Intrinsic connections The dynamics of plasticity: Repetition suppression monotonic phasic Extrinsic connections number of presentations Garrido et al 2009

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

  23. LF LF RF RF LV LV RV RV input input Frequency-specific coupling during face-processing CC Chen et al 2008

  24. FLBL FNBL FLBN FNBN 0 -10000 -16306 -16308 -11895 -20000 -30000 -40000 -50000 -60000 -59890 -70000 Functional asymmetries in forward and backward connections SPM tdf 72; FWHM 7.8 x 6.5 Hz 4 12 20 28 36 44 Frequency (Hz) 44 36 28 20 12 4 From 32 Hz (gamma) to 10 Hz (alpha) t = 4.72; p = 0.002 0.1 0.1 0.08 0.08 0.06 0.06 LF RF 0.04 0.04 0.02 0.02 0 0 LV RV -0.02 -0.02 -0.04 -0.04 Forward Backward Forward Backward -0.06 -0.06 -0.08 -0.08 input -0.1 -0.1 Left hemisphere Right hemisphere CC Chen et al 2008

  25. Dynamic Causal Modelling State and observation equations Model inversion DCMs for fMRI Bilinear models Hemodynamic models Attentional modulation Two-state models DCMs for EEG Neural-mass models Perceptual learning and MMN Backward connections DCMs for LFP Steady-state responses

  26. STN Striatum Cortex GPe 5 5 5 5 Cortex 0 0 0 0 0 20 40 0 20 40 0 20 40 0 20 40 5 5 5 Striatum 0 0 0 0 20 40 0 20 40 0 20 40 5 5 GPe 0 0 0 20 40 0 20 40 Glutamatergic stellate cells 5 GABAergic cells STN Glutamatergic Projection cells 0 D Data 40 0 20 DCMs for steady-state responses: characterizing coupling parameters Cross-spectral data features 6-OHDA lesion model of Parkinsonism D 1. Cortex D 2. Striatum D 3. External globus pallidus (GPe) 6. Thalamus D 5. Entopeduncular Nucleus (EPN) 4. Subthalamic Nucleus (STN) Moran et al

  27. * 8 * 7 6 5 4 3 2 1 0 Changes in the basal ganglia-cortical circuits D D 3.07 ± 0.17 1.44 ± 0.18 1 1 MAP estimates 3.43 ± 0.16 4.25 ± 0.17 D D 2 2 5.00 ± 0.15 5.24 ± 0.16 0.29 ± 0.31 0.74 ± 0.28 0.85 ± 0.36 1.03 ± 0.35 D D 3 3 6 6 1.04 ± 0.20 0.90 ± 0.21 0.72 ± 0.44 STN to GPe STN to EPN GPe to STN Striatum to EPN Ctx to STN Ctx to Striatum EPN to Thalamus Striatum to GPe Thalamus to Ctx 1.43 ± 0.38 5 1.18 ± 0.33 5 6. 91 ± 0.19 D 2.33 ± 0.21 D 4 4 Control 6-OHDA Lesioned Moran et al

  28. 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

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