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## DCM for Time-Frequency

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**DCM for Time-Frequency**DCM for Induced Responses DCM for Phase Coupling Bernadette van Wijk**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**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 fMRI**Single region u1 c u1 a11 z1 u2 z1 z2**u1**c a11 z1 a21 z2 a22 cf. DCM for fMRI Multiple regions u1 u2 z1 z2**cf. DCM for fMRI**Modulatory inputs u1 u2 c u1 a11 z1 u2 b21 z1 a21 z2 z2 a22**cf. DCM for fMRI**Reciprocal connections u1 u2 c u1 a11 z1 u2 b21 a12 z1 a21 z2 z2 a22**DCM for induced 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**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**Linear (within-frequency) coupling**Intrinsic (within-source) coupling Nonlinear (between-frequency) coupling Extrinsic (between-source) coupling Differential equation model for spectral energy How frequency K in region j affects frequency 1 in region i**Intrinsic (within-source) coupling**Extrinsic (between-source) coupling Modulatory connections**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] [-37 -25 39] [14 -69 -2] [-18 -71 -5]**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**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 Interactions are mainly within frequency bands 4 2 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**Bidirectional coupling**0.3 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 (4-8Hz)**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**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**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 LogEv Model**0.77**2.46 IFG VIS 0.89 2.89 MTL