1. Bernadette van Wijk DCM for Time-Frequency 1. DCM for Induced Responses 2. DCM for Phase Coupling

2. Dynamic Causal Models PhysiologicalPhenomenological Neurophysiological model DCM for ERP DCM for SSR DCM for Induced Responses DCM for Phase Coupling spiny stellate cells inhibitory interneurons Pyramidal Cells Models a particular data feature Time Frequency Phase Source locations not optimizedElectromagnetic forward model included

3. Changes in power caused by external input and/or coupling with other regions Model comparisons: Which regions are connected? E.g. Forward/backward connections (Cross-)frequency coupling: Does slow activity in one region affect fast activity in another? 1. DCM for Induced Responses ? ?

4. Single region u2u2 u1u1 z1z1 z2z2 z1z1 u1u1 a 11 c cf. Neural state equations in DCM for fMRI

5. Multiple regions u2u2 u1u1 z1z1 z2z2 z1z1 z2z2 u1u1 a 11 a 22 c a 21 cf. DCM for fMRI

6. Modulatory inputs u2u2 u1u1 z1z1 z2z2 u2u2 z1z1 z2z2 u1u1 a 11 a 22 c a 21 b 21 cf. DCM for fMRI

7. u1u1 u2u2 z1z1 z2z2 a 11 a 22 c a 12 a 21 b 21 Reciprocal connections u2u2 u1u1 z1z1 z2z2 cf. DCM for fMRI

8. Single Region dg(t)/dt=A∙g(t)+C∙u(t) DCM for induced responses Where g(t) is a K x 1 vector of spectral responses A is a K x K matrix of frequency coupling parameters Also allow A to be changed by experimental condition Time Frequency

9. G=USV’ Use of Frequency Modes Where G is a K x T spectrogram U is K x K’ matrix with K frequency modes V is K x T and contains spectral mode responses over time Hence A is only K’ x K’, not K x K Single Region Time Frequency

10. Nonlinear (between-frequency) coupling Linear (within-frequency) coupling Extrinsic (between-source) coupling Intrinsic (within-source) coupling How frequency K in region j affects frequency 1 in region i Differential equation model

11. Modulatory connections Extrinsic (between-source) coupling Intrinsic (within-source) coupling

12. Motor imagery through mental hand rotation De Lange et al. 2008 Example: MEG Data Do trials with fast and slow reaction times differ in time- frequency modulations? Are slow reaction times associated with altered forward and/or backward information processing? How do (cross-)frequency couplings lead to the observed time- frequency modulations? van Wijk et al, Neuroimage, 2013

13. Sources in Motor and Occipital areas M O MNI coordinates [34 -28 37][-37 -25 39] [14 -69 -2][-18 -71 -5]

14. Slow reaction times: - Stronger increase in gamma power in O - Stronger decrease in beta power in O Do trials with fast and slow reaction times differ in time- frequency modulations?

15. Are slow reaction times associated with altered forward and/or backward information processing?

16. Results for Model B forward/backward Good correspondence between observed and predicted time-frequency spectra

17. Decomposing contributions to the time-frequency spectra Feedback loop with M acts to attenuate gamma and beta modulations in O Attenuation is weaker for slow reaction times

18. OM Interactions are mainly within frequency bands Slow reaction times accompanied by a negative beta to gamma coupling from M to O How do (cross-)frequency couplings lead to the observed time-frequency modulations?

20. Synchronization achieved by phase coupling between regions Model comparisons: Which regions are connected? E.g. ‘master-slave’/mutual connections Parameter inference: (frequency-dependent) coupling values Region 1 Region 2 2. DCM for Phase Coupling ? ?

21. One oscillator

22. Two oscillators

23. 0.3 Two coupled oscillators

24. 0.3 Different initial phases

25. 0.6 Stronger coupling

26. 0.3 Bidirectional coupling

27. DCM for Phase Coupling Phase interaction function is an arbitrary order Fourier series Allow connections to depend on experimental condition

28. Fuentemilla et al, Current Biology, 2010 Example: MEG data

29. Delay activity (4-8Hz) Visual Cortex (VIS) Medial Temporal Lobe (MTL) Inferior Frontal Gyrus (IFG)

31. Questions Duzel et al. find different patterns of theta-coupling in the delay period dependent on task. Pick 3 regions based on previous source reconstruction 1. Right MTL [27,-18,-27] mm 2. Right VIS [10,-100,0] mm 3. Right IFG [39,28,-12] mm Find out if structure of network dynamics is Master-Slave (MS) or (Partial/Total) Mutual Entrainment (ME) Which connections are modulated by memory task ?

32. MTL VISIFG MTL VISIFG MTL VISIFG MTL VIS IFG MTL VISIFG MTL VIS IFG 1 MTL VISIFG 2 3 4 5 6 7 Master- Slave Partial Mutual Entrainment Total Mutual Entrainment MTL MasterVIS MasterIFG Master

33. Analysis Source reconstruct activity in areas of interest Bandpass data into frequency range of interest Hilbert transform data to obtain instantaneous phase Use multiple trials per experimental condition Model inversion

34. LogEv Model MTL VISIFG 3

35. MTL VISIFG 2.89 2.46 0.89 0.77