1. Computational and physiological models Part 2 Daniel Renz Computational Psychiatry Seminar: Computational Neuropharmacology 14 March, 2014

2. Overview Dynamic Causal Modeling for fMRI Example: visuomotor modulation of putamen Dynamic Causal Modeling for EEG/MEG Example: Reduction of synaptic plasticity using ketamine Example: Dopaminergic modulation of neurotransmission

3. What is Dynamic Causal Modeling (DCM)? inference

4. Neural dynamics - effective connectivity Sporns 2007, Scholarpedia

5. DCM for fMRI – approximation to neural population dynamics

6. DCM for fMRI – neural population dynamics example x1x1 x2x2 u2u2 u1u1 a 21 a 12 - -

7. Non-linear DCM for fMRI

8. x1x1 x2x2 u2u2 u1u1 a 21 d 12 a 12 - -

9. DCM parameters are rate constants x1x1 - The coupling parameter thus describes the speed of the exponential change in x(t) Coupling parameter a is inversely proportional to the half life  of x(t):

10. Set of differential equations describing how neural activity causes the BOLD signal The forward model is important for model fitting, but of no interest for statistical inference. Computed separately for each region x1x1 x2x2 u2u2 u1u1 a 21 a 12 y1y1 y2y2 - - HRF

11. stimulus functions u neural state equation f Balloon model BOLD signal change equation 6 hemodynamic parameters: Friston et al. 2000, NeuroImage Stephan et al. 2007, NeuroImage v: blood volume q: deoxyhemoglobin content Hemodynamic model

12. Bayesian Inversion Make inferences Define likelihood model Specify priors Neural state function Observer function Inference on models Inference on parameters Iterative optimization using Expectation-Maximization: 1.Compute model response 2.Compare with data 3.Improve parameters, if possible Empirical prior Conservative shrinkage prior

13. Overview Dynamic Causal Modeling for fMRI Example: visuomotor modulation of putamen Dynamic Causal Modeling for EEG/MEG Example: Reduction of synaptic plasticity using ketamine Example: Dopaminergic modulation of neurotransmission

14. Modulation of visuomotor integration by putamen How do (failures of) learned predictions about visual stimuli influence subsequent motor responses? Hypothesis: Visuomotor connections are modulated by activity in the putamen This activity increases with the size of the prediction error (surprise; free energy) Den Ouden 2009

15. Bayesian learning model Speed and accuracy of motor responses increased significantly with predictability of stimulus Response speed is a good linear predictor of choice error, but unrealistic Hierarchical Bayesian model estimates posterior PDF of both the probabilistic associations and their volatility Den Ouden 2009

16. Imaging analysis Responses in putamen (and PMd) were negatively correlated with probability of any visual stimulus Responses in the fusiform face area (FFA) were negatively correlated with probability of faces Responses in the parahippocampal place area (PPA) were negatively correlated with probability of houses (and positively correlated with probability of faces) Den Ouden 2009

17. DCM analysis

18. Does putamen really gate visuomotor connections, or does PMd gate connections between visual areas and putamen?

19. DCM analysis Does putamen really gate visuomotor connections, or does PMd gate connections between visual areas and putamen? Den Ouden 2009

20. Overview Dynamic Causal Modeling for fMRI Example: visuomotor modulation of putamen Dynamic Causal Modeling for EEG/MEG Example: Reduction of synaptic plasticity using ketamine Example: Dopaminergic modulation of neurotransmission

21. David et al., NeuroImage, 2006

22. Kiebel et al., NeuroImage, 2006 Daunizeau et al., NeuroImage, 2009

23. Overview Dynamic Causal Modeling for fMRI Example: visuomotor modulation of putamen Dynamic Causal Modeling for EEG/MEG Example: Reduction of synaptic plasticity using ketamine Example: Dopaminergic modulation of neurotransmission

24. How does Ketamine modulate synaptic plasticity underlying mismatch negativity? Schmidt, Diaconescu, et al 2012 Roving paradigm Mismatch negativity (MMN): ERP component elicited when the brain detects that an established pattern in sensory input has been violated.

25. Mismatch negativity Functionally, MMN is thought to serve two roles: Current prediction error signal caused by previous neuronal spike-frequency adaptation (memory trace formation) in auditory cortex Model adjustment to minimize future prediction error, reflected by glutamatergic long-range connections (between temporal and frontal regions) Free-energy principle: Suggests an overarching physiological and computational process of minimizing prediction error that requires both adaptation and model adjustment

26. Mismatch negativity and pathopsychology MMN is a potential index for pathopsychology Patients with schizophrenia show deficits in auditory sensory memory. They show impaired ability to match tones, accompanied by deficient generation of MMN MMN can also be reduced using NMDA-antagonists, e.g. ketamine

27. Neurophysiology In animal studies it was shown that NMDAR plays a key role in MMN generation Both spike-frequency adaptation and glutamatergic plasticity are regulated by NMDARs Spike-frequency adaptation results from potassium channel-dependent hyperpolarization which relies on intracellular calcium influx modulated by NMDAR status NMDARs can lead to rapid changes in the strength of glutamatergic synapses, for example, via phosphorylation of AMPA receptors

28. Results Inter-regional Synaptic Coupling Adaptation and Inter-regional Synaptic Coupling Schmidt, Diaconescu, et al 2012

29. Results Inter-regional Synaptic Coupling Adaptation and Inter-regional Synaptic Coupling Schmidt, Diaconescu, et al 2012

30. Results Schmidt, Diaconescu, et al 2012

31. Overview Dynamic Causal Modeling for fMRI Example: visuomotor modulation of putamen Dynamic Causal Modeling for EEG/MEG Example: Reduction of synaptic plasticity using ketamine Example: Dopaminergic modulation of neurotransmission

32. Delayed match-to-sample How does dopamine influence WM? L-Dopa vs placebo in delayed match-to sample task MEG recordings Moran 2011

33. MEG results MEG measured greater activity during memory condition in delta, theta and alpha bands at predicted locations Prominent theta-activity in right superior frontal gyrus during memory maintenance. Spectra were boosted by L-Dopa Moran 2011

34. Dopaminergic Synaptic Effects - Hypotheses An enhancement in the conductance of GABA A and NMDA channels A decreased conductance at AMPA receptor-associated channels (at synapses between exogenous glutamatergic inputs and layer III pyramidal cells) Moran 2011

35. Dopaminergic Synaptic Effects - Results The only parameter with a differential contribution to theta band at peak of interaction under L-DOPA was the NMDA non-linearity parameter This was further enhanced during the memory condition NMDA nonlinear function. As alpha increases, the voltage-dependent magnesium switch becomes highly nonlinear.

36. Dopaminergic Synaptic Effects - Results Can we link WM performance to synaptic parameters? Greater L-Dopa mediated improvement in memory performance was correlated with increased NMDA signaling and decreased AMPA signaling