DCM Advanced, Part II Will Penny (Klaas Stephan) Wellcome Trust Centre for Neuroimaging Institute of Neurology University College London SPM Course FIL

Overview Extended DCM for fMRI: nonlinear, two-state, stochastic Embedding computational models in DCMs Clinical Applications

endogenous connectivity direct inputs modulation of connectivity Neural state equation hemodynamic model λ x y integration BOLD yy y activity x 1 (t) activity x 2 (t) activity x 3 (t) neuronal states t driving input u 1 (t) modulatory input u 2 (t) t    The classical DCM: a deterministic, one-state, bilinear model

Factorial structure of model specification in DCM Three dimensions of model specification: –bilinear vs. nonlinear –single-state vs. two-state (per region) –deterministic vs. stochastic Specification via GUI.

bilinear DCM Bilinear state equation: driving input modulation driving input modulation non-linear DCM Two-dimensional Taylor series (around x 0 =0, u 0 =0): Nonlinear state equation:

Neural population activity fMRI signal change (%) x1x1 x2x2 x3x3 Nonlinear dynamic causal model (DCM) Stephan et al. 2008, NeuroImage u1u1 u2u2

V1 V5 stim PPC attention motion MAP = 1.25 Stephan et al. 2008, NeuroImage

V1 V5 PPC observed fitted motion & attention motion & no attention static dots

input Single-state DCM Intrinsic (within-region) coupling Extrinsic (between-region) coupling Two-state DCM Marreiros et al. 2008, NeuroImage

Estimates of hidden causes and states (Generalised filtering) Stochastic DCM Li et al. 2011, NeuroImage random state fluctuations w (x) account for endogenous fluctuations, fluctuations w (v) induce uncertainty about how inputs influence neuronal activity can be fitted to resting state data

Estimates of hidden causes and states (Generalised filtering) Stochastic DCM Good working knowledge of dDCM sDCMs (esp. for nonlinear models) can have richer dynamics than dDCM Model selection may be easier than with dDCM See Daunizeau et al. ‘sDCM: Should we care about neuronal noise ?’, Neuroimage, 2012

Overview Extended DCM for fMRI: nonlinear, two-state, stochastic Embedding computational models in DCMs Clinical Applications

Learning of dynamic audio-visual associations CS Response Time (ms) ± 650 or Target StimulusConditioning Stimulus or TS p(face) trial CS 1 2 den Ouden et al. 2010, J. Neurosci.

Hierarchical Bayesian learning model observed events probabilistic association volatility k v t-1 vtvt rtrt r t+1 utut u t+1 Behrens et al. 2007, Nat. Neurosci. prior on volatility

Explaining RTs by different learning models Trial p(F) True Bayes Vol HMM fixed HMM learn RW Bayesian model selection: hierarchical Bayesian model performs best 5 alternative learning models: categorical probabilities hierarchical Bayesian learner Rescorla-Wagner Hidden Markov models (2 variants) RT (ms) p(outcome) Reaction times den Ouden et al. 2010, J. Neurosci.

PutamenPremotor cortex Stimulus-independent prediction error p < 0.05 (SVC ) p < 0.05 (cluster-level whole- brain corrected) p(F) p(H) BOLD resp. (a.u.) p(F)p(H) BOLD resp. (a.u.) den Ouden et al. 2010, J. Neurosci.

Prediction error (PE) activity in the putamen PE during reinforcement learning PE during incidental sensory learning O'Doherty et al. 2004, Science den Ouden et al. 2009, Cerebral Cortex Could the putamen be regulating trial-by-trial changes of task-relevant connections? PE = “teaching signal” for synaptic plasticity during learning p < 0.05 (SVC ) PE during active sensory learning

Prediction errors control plasticity during adaptive cognition Modulation of visuo- motor connections by striatal prediction error activity Influence of visual areas on premotor cortex: –stronger for surprising stimuli –weaker for expected stimuli den Ouden et al. 2010, J. Neurosci. PPAFFA PMd Hierarchical Bayesian learning model PUT p = p = 0.017

Overview Extended DCM for fMRI: nonlinear, two-state, stochastic Embedding computational models in DCMs Clinical Applications

model structure Model-based predictions for single patients set of parameter estimates BMS model-based decoding

BMS: Parkison‘s disease and treatment Rowe et al. 2010, NeuroImage Age-matched controls PD patients on medication PD patients off medication DA-dependent functional disconnection of the SMA Selection of action modulates connections between PFC and SMA

Model-based decoding by generative embedding Brodersen et al. 2011, PLoS Comput. Biol. step 2 — kernel construction step 1 — model inversion measurements from an individual subject subject-specific inverted generative model subject representation in the generative score space A → B A → C B → B B → C A C B step 3 — support vector classification separating hyperplane fitted to discriminate between groups A C B jointly discriminative model parameters step 4 — interpretation

Model-based decoding of disease status: mildly aphasic patients (N=11) vs. controls (N=26) Connectional fingerprints from a 6-region DCM of auditory areas during speech perception Brodersen et al. 2011, PLoS Comput. Biol.

Model-based decoding of disease status: aphasic patients (N=11) vs. controls (N=26) Classification accuracy Brodersen et al. 2011, PLoS Comput. Biol. MGB PT HG (A1) MGB PT HG (A1) auditory stimuli

Multivariate searchlight classification analysis Generative embedding using DCM

Summary Model Selection Extended DCM for fMRI: nonlinear, two-state, stochastic Embedding computational models in DCMs Clinical Applications