bernadette van wijk dcm for time-frequency 1. dcm for induced responses 2. dcm for phase coupling
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Bernadette van WijkBernadette van Wijk
DCM for Time-Frequency
1. DCM for Induced Responses
2. DCM for Phase Coupling
Dynamic Causal Models
Physiological PhenomenologicalNeurophysiological model
• DCM for ERP
• DCM for SSR
• DCM for Induced Responses• DCM for Phase Coupling
spiny stellate
cells
inhibitory interneuron
s
PyramidalCells
Models a particular data feature
Time
Freq
uenc
y
Phase
Source locations not optimizedElectromagnetic forward model included
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
?
?
Single region 1 11 1 1z a z cu
u2
u1
z1
z2
z1
u1
a11c
cf. Neural state equations in DCM for fMRI
Multiple regions
1 11 1 1
2 21 22 2 2
00
z a z ucz a a z u
u2
u1
z1
z2
z1
z2
u1
a11
a22
c
a21
cf. DCM for fMRI
Modulatory inputs
1 11 1 1 12
2 21 22 2 21 2 2
0 0 00 0
z a z z ucu
z a a z b z u
u2
u1
z1
z2
u2
z1
z2
u1
a11
a22
c
a21
b21
cf. DCM for fMRI
u1 u2
z1
z2
a11
a22
c
a12
a21
b21
Reciprocal connections
1 11 12 1 1 12
2 21 22 2 21 2 2
0 00 0
z a a z z ucu
z a a z b z u
u2
u1
z1
z2
cf. DCM for fMRI
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
Freq
uenc
y
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
Freq
uenc
y
KKij
Kij
Kijij
ij
AA
AAA
1
111
Nonlinear (between-frequency) coupling
Linear (within-frequency) coupling
Extrinsic (between-source) coupling
)()()(1
1
1111
tuC
Ctg
AA
AA
g
gtg
JJJJ
J
J
Intrinsic (within-source) coupling
How frequency K in region j affects frequency 1 in region i
Differential equation model
Modulatory connections
Extrinsic (between-source) coupling
1 11 1 11 1 1
1 1
( ) ( ) ( )J J
J J JJ J JJ J
g A A B B Cg t v g t u t
g A A B B C
Intrinsic (within-source) coupling
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
Sources in Motor and Occipital areas
M
O
MNI coordinates[34 -28 37] [-37 -25 39][14 -69 -2] [-18 -71 -5]
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?
• 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 OAttenuation is weaker for slow reaction times
O M
Interactions are mainly within frequency bands
Slow reaction timesaccompanied by a
negative beta to gamma coupling
from M to O
• How do (cross-)frequency couplings lead to the observed time-frequency modulations?
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
( )i i jj
2. DCM for Phase Coupling
?
?
f1
One oscillator
f1
f2
Two oscillators
f1
)sin(3.0 122 f
0.3
Two coupled oscillators
f1
)sin(3.0 122 f
0.3
Different initial phases
f1
2 2 10.6sin( )f
0.6
Stronger coupling
)sin(3.0 122 f
0.30.3
)sin(3.0 211 f
Bidirectional coupling
j
j
i
DCM for Phase Coupling
)sin( jij
ijii af
sin( [ ]) cos( [ ])i i ijK i j ijK i jK j K j
f a K b K
Phase interaction function is an arbitrary order Fourier series
Allow connections to depend on experimental condition
ija
ija
Fuentemilla et al, Current Biology, 2010
Example: MEG data
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] mm2. Right VIS [10,-100,0] mm3. 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
VISIFG
MTL
VISIFG
MTL
VISIFG
MTL
VISIFG
MTL
VISIFG
MTL
VISIFG1
MTL
VISIFG2
3
4
5
6
7
Master-Slave
PartialMutualEntrainment
TotalMutualEntrainment
MTL Master VIS Master IFG Master
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
LogEv
Model
1 2 3 4 5 6 70
50
100
150
200
250
300
350
400
450
MTL
VISIFG3
MTL
VISIFG
2.89
2.46
0.89
0.77
sin([ ]) cos([ ])i i ij i j ij i jj j
f a b
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