DCM for Time-Frequency responses

1. DCM for Time-Frequency responses • DCM for Induced Responses • DCM for Phase Coupling Bernadette van Wijk Wellcome Trust Centre for Neuroimaging University College London

2. DCM for EEG/MEG Physiological Phenomenological Neurophysiological model Models a particular data feature x~(t) Phase  Frequency x(t) Time Electromagnetic forward model included States x different from data y Source locations not optimized States x and data y in the same “format” • DCM for event-related potentials • DCM for cross-spectral density • DCM for Induced Responses • DCM for Phase Coupling

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. u1 c a11 z1 a21 z2 a22 cf. DCM for fMRI 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. Time-Frequency Responses 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 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 Nonlinear (between-frequency) coupling Extrinsic (between-source) coupling Generative 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? Do slow/fast reaction times differ in forward and/or backward processing? How do (cross-)frequency couplings lead to the observed time-frequency responses? 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. 1) 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. Do slow/fast reaction times differ in forward and/or backward processing?

16. Results for Model Bforward/backward Good correspondence between observed and predicted spectra

17. Simulations with estimated model parameters  Feedback loop with M acts to attenuate modulations in O  Attenuation is weaker for slow reaction times

18. How do (cross-)frequency couplings lead to the observed time-frequency responses? O M 3 2 4  Interactions are mainly within frequency bands  Slow reaction times accompanied by a negative beta to gamma coupling from M to O 5 1

20. 2. DCM for Phase Coupling Region 2 Region 1 x~(t) x~(t) ? Phase  ? x(t) x(t) Phase  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. Different initial phases 0.3

24. Stronger coupling 0.6

25. Bidirectional coupling 0.3 0.3

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

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

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

29. Source activity (4-8Hz)

30. Phase time series

31. Different patterns of theta-coupling in the delay period dependent on task 1) Find out if structure of network dynamics is Master-Slave (MS) or (Partial/Total) Mutual Entrainment (ME) 2) How are connections modulated by the memory task? Questions

32. Analysis • Source reconstruct activity in areas of interest • 1. Right MTL [27,-18,-27] mm • 2. Right VIS [10,-100,0] mm • 3. Right IFG [39,28,-12] mm • Bandpass data into frequency range of interest • Hilbert transform data to obtain instantaneous phase • Use multiple trials per experimental condition • Model specification • Model inversion • Model comparisons

33. 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

34. 1) Find out if structure of network dynamics is Master-Slave (MS) or (Partial/Total) Mutual Entrainment (ME) 3 IFG VIS MTL LogEv  Driving role for visual cortex Model

35. 0.77 2.46 IFG VIS 0.89 2.89 MTL 2) How are connections modulated by the memory task?  Stronger coupling during working memory