DCM for Time-FrequencyDCM for Time-Frequency

1. DCM for Induced Responses2. DCM for Phase Coupling

Bernadette van Wijk

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

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?

?

?

Single regioncf. Neural state equations in DCM for fMRI

1 11 1 1z a z cu

u2

u1

z1

z2

z1

u1

a11c

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

a12a21

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

DCM for induced responses

dg(t)/dt=A g(t)∙+C u(t)∙

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

Use of Frequency Modes

Time

Freq

uenc

y

G=USV’

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

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

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

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]

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?

1

2

3

4

5

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

One oscillator

f1

Two oscillators

f1

f2

Different initial phases

)sin(3.0 122 f

0.3

f1

Stronger coupling

0.6

f1

2 2 10.6sin( ) f

Bidirectional coupling

)sin(3.0 122 f

0.30.3

)sin(3.0 211 f

DCM for Phase Coupling

j

j

i

)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

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] 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