DCM for TimeFrequency 1 DCM for Induced Responses

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

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

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?

cf. Neural state equations in DCM for f. MRI Single region u 1 c z 1 a 11 u 2 z 1 z 2

cf. DCM for f. MRI Multiple regions u 1 c a 11 z 2 a 22 u 1 u 2 a 21 z 2

cf. DCM for f. MRI Modulatory inputs u 1 u 2 c u 1 a 11 z 1 b 21 z 2 a 21 u 2 z 1 z 2

cf. DCM for f. MRI Reciprocal connections u 1 u 2 c a 11 z 1 b 21 a 12 z 2 a 22 u 1 a 21 u 2 z 1 z 2

Frequency DCM for induced responses dg(t)/dt=A∙g(t)+C∙u(t) 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

Frequency Use of Frequency Modes G=USV’ 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

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

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

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

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

• Do trials with fast and slow reaction times differ in timefrequency modulations? Slow reaction times: - Stronger increase in gamma power in O - Stronger decrease in beta power in O

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

Results for Model Bforward/backward Good correspondence between observed and predicted time-frequency spectra

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

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

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

One oscillator

Two oscillators

Different initial phases 0. 3

Stronger coupling 0. 6

Bidirectional coupling 0. 3

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

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

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

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?

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

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

3 IFG VIS MTL Log. Ev Model

0. 77 IFG 2. 46 VIS 2. 89 MTL 0. 89