DCM for Time-Frequency

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

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

3. 1. DCM for Induced Responses ? ? 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?

4. cf. Neural state equations in DCM for fMRI Single region u1 c u1 a11 z1 u2 z1 z2

5. cf. DCM for fMRI u1 c a11 z1 a21 z2 a22 Multiple regions u1 u2 z1 z2

6. cf. DCM for fMRI Modulatory inputs u1 u2 c u1 a11 z1 u2 b21 z1 a21 z2 z2 a22

7. cf. DCM for fMRI Reciprocal connections u1 u2 c u1 a11 z1 u2 b21 a12 z1 a21 z2 z2 a22

8. DCM for induced responses Single Region dg(t)/dt=A∙g(t)+C∙u(t) Frequency Time 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

9. Use of Frequency Modes Single Region G=USV’ Frequency Time 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

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

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

12. Example: MEG Data Motor imagery through mental hand rotation De Lange et al. 2008 • 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. Do trials with fast and slow reaction times differ in time-frequency modulations? Slow reaction times: - Stronger increase in gamma power in O - Stronger decrease in beta power in O

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

16. Results for Model Bforward/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. O M • How do (cross-)frequency couplings lead to the observed time-frequency modulations? Interactions are mainly within frequency bands Slow reaction times accompanied by a negative beta to gamma coupling from M to O

20. 2. DCM for Phase Coupling Region 2 Region 1 ? ? 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

21. One oscillator

22. Two oscillators

23. Two coupled oscillators 0.3

24. Different initial phases 0.3

25. Stronger coupling 0.6

26. Bidirectional coupling 0.3 0.3

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

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

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 Master VIS Master IFG Master 1 IFG 3 5 VIS IFG VIS IFG VIS Master- Slave MTL MTL MTL IFG 6 VIS 2 IFG VIS 4 IFG VIS Partial Mutual Entrainment MTL MTL MTL 7 IFG VIS Total Mutual Entrainment MTL

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. 3 IFG VIS MTL LogEv Model

35. 0.77 2.46 IFG VIS 0.89 2.89 MTL