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. 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

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

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

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

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

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

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

Output: a mixture of intra- and extravascular signal sec Hemodynamic models for fMRI basically, a convolution signal flow dHbvolume The plumbing

Neural population activity BOLD signal change (%) x1x1 x2x2 u1u1 x3x3 u2u2 –– A toy example

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) 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 V5+ PPC An fMRI study of attention

V1IFG V5 Photic Attention ) Attentional modulation of prefrontal connections sufficient to explain regionally specific attentional effects 2) Segregation of motion information to V5 1) Hierarchical architecture Friston et al 1999 SPC Motion

FFA PPA MFG faceshouses faceshouses rivalrynon-rivalry FFA PPA MFG time (s) Stephan et al 2008 Nonlinear DCM: modulation of connections in inferotemporal cortex under binocular rivalry

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

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

Hierarchical connections in the brain and laminar specificity 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

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

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

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

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

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

A1 STG subcortical input STG repetition effects monotonicphasic Intrinsic connections Extrinsic connections number of presentations The dynamics of plasticity: Repetition suppression Garrido et al 2009

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

LVRV RF LF input LVRV RF LF input Frequency-specific coupling during face-processing CC Chen et al 2008

From 32 Hz (gamma) to 10 Hz (alpha) t = 4.72 ; p = SPM t df 72; FWHM 7.8 x 6.5 Hz Right hemisphereLeft hemisphere Forward Backward Frequency (Hz) LVRV RF LF input FLBLFLBL FNBLFNBL FLBNFLBN FNBNFNBN Functional asymmetries in forward and backward connections CC Chen et al 2008

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

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

Changes in the basal ganglia-cortical circuits Moran et al Control6-OHDA Lesioned ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.28 MAP estimates EPN to Thalamus Thalamus to Ctx Ctx to Striatum Ctx to STN Striatum to GPe Striatum to EPN STN to EPN STN to GPe GPe to STN * *

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