08 dcm induced phase

8/3/2019 08 DCM Induced Phase

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DCM for Time Frequency

Will Penny

Wellcome Trust Centre for Neuroimaging,

University College London, UK

SPM MEG/EEG Course, Oct 27, 2009


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DCM for Induced Responses

Region 1

Region 3

Region 2

??

How does slow activityin one region affectfast activity in another ?

Relate change of powerin one region and frequencyto change in power in others.


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Single region 1 11 1 1z a z cu

u2

u1

z1

z2

z

1

u1

a11c

DCM for fMRI


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Multiple regions

1 11 1 1

2 21 22 2 2

0

0z a z ucz a a z u

u2

u1

z1

z2

z

1

z2

u1

a11

a22

c

a21


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Modulatory inputs

1 11 1 1 12

2 21 22 2 21 2 2

0 0 0

0 0

z a z z ucu

z a a z b z u

u2

u1

z1

z2

u2

z1

z2

u

1

a11

a22

c

a21

b21


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Reciprocal connections

1 11 12 1 1 1

2

2 21 22 2 21 2 2

0 0

0 0

z a a z z ucu

z a a z b z u

u2

u1

z1

z2

u2

z1

z2

u1

a11

a22

c

a12

a21

b21


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Single Region

dg(t)/dt=Ag(t)+Cu(t)

DCM for induced responses

Where g(t) is a K x 1 vector of spectral responsesA is a K x K matrix of frequency coupling parametersDiagonal elements of A (linear within freq)Off diagonal (nonlinear between freq)Also allow A to be changed by experimental condition


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DCM for induced responses

Specify the DCM: 2 areas (A1 and A2) 2 frequencies (F and S) 2 inputs (Ext. and Con.) Extrinsic and intrinsic coupling

Integratethe state equations

A1 A2

2

1

2

1

),(

),(

),(

),(

A

A

A

A

tSx

tSx

tFx

tFx


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Differential equation model for spectral energy

KK

ij

K

ij

K

ijij

ij

AA

AA

A

1

111

Nonlinear (between-frequency) coupling

Linear (within-frequency) coupling

Extrinsic (between-source) coupling

)()()(

1

1

1111

tu

C

C

tg

AA

AA

g

g

tg

JJJJ

J

J

Intrinsic (within-source) coupling

How frequency K inregion j affectsfrequency 1 in region i


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Modulatory connections

Intrinsic (within-source) coupling

Extrinsic (between-source) coupling

state equation

JJJJ

J

JJJ

J

JC

C

tutwx

BB

BB

tu

AA

AA

x

x

W, tx

1

1

111

1

1111

)(),()()(.


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Connection to Neurobiology

First and

Second orderVolterra kernelsFrom NeuralMass model.

Strong

(saturating)input leads tocross-frequencycoupling


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Single Region

G=USV

Use of Frequency Modes

Where G is a K x T spectrogramU is KxK matrix with K frequency modesV is K x T and contains spectral mode responsesHence A is only K x K, not K x K


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MEG Data


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15

81

39

z

y

x

15

81

42

z

y

x

27

45

42

z

y

x

24

51

39

z

y

x

OFA OFA

FFAFFA

input

The core system


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nonlinear (and linear)

linear

Forward

Backwar

d

linear nonlinear

linear

nonlinear

FLBL FNBL

FLNB FNBN

OFA OFA

Input

FFAFFA

FLBL

Input

FNBL

OFA OFA

FFAFFA

FLBN

OFA OFA

Input

FFAFFA

FNBN

OFA OFA

Input

FFAFFA


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FLBL FNBL FLBN *FNBN

-59890

-16308 -16306 -11895

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

01000 backward linear backward nonlinear

forward linear

forward nonlinear

Inference on model I

Both forward and backward connections arenonlinear


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From 32 Hz (gamma) to 10 Hz (alpha)

t= 4.72; p = 0.002

4 12 20 28 36

44

44

36

28

20

12

4

SPM tdf 72; FWHM 7.8 x 6.5 Hz

Frequency(Hz)

Right hemisphereLeft hemisphere

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Forward Backward

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Forward Backward

Left forward excitatory -- activating effect of

gamma- alpha coupling in the forward connections

Right backward - inhibitory -- suppressive effect ofgamma- alpha coupling in backward connections

Gamma affects Alpha


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Gamma activity in input areas induces slower

dynamics in higher areas as prediction error is accumulated. Nonlinear

coupling in high-level area induces gamma activity in that higherarea which then accelerates the decay of activity in the lower level.

This decay is manifest as damped alpha oscillations.

C.C. Chen , S. Kiebel, KJ Friston , Dynamic causal modelling ofinduced responses. NeuroImage, 2008; (41):1293-1312.

C.C. Chen, R.N. Henson, K.E. Stephan, J.M. Kilner, and K.J.Friston1. Forward and backward connections in the brain: A DCMstudy of functional asymmetries in face processing. NeuroImage,2009 Apr 1;45(2):453-62


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For studying synchronization among brain regions

Relate change of phase in one region to phase in others

Region 1

Region 3

Region 2

?

?

DCM for Phase Coupling

( )i i jj

g


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Connection to Neurobiology:Septo-Hippocampal theta rhythm

Denham et al. 2000: Hippocampus

Septum

1

1 1 1 13 3 3

2

2 2 2 21 1

1

3 3 3 34 4 3

4

4 4 4 42 2

( ) ( )

( ) ( )

( ) ( )

( ) ( )

e e CA

i i

i e CA

i i S

dxx k x z w x P

dt

dxx k x z w x

dt

dxx k x z w x P

dt

dxx k x z w x P

dt

1x

2x 3x

4xWilson-Cowan style model


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Four-dimensional state space


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Hippocampus

Septum

A

A

B

B

Hopf Bifurcation


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cossin)( baz

For a generic Hopf bifurcation (Erm & Kopell)

See Brown et al. 04, for PRCs corresponding to other bifurcations


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0

1sin( ) cos( )

2

iij i j ij i j

j

df a b

dt

3

2

1

12a

13a

DCM for Phase Coupling

12b

13b


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MEG Example Fuentemilla et al 09

+

+

+

1 sec 3 sec 5 sec 5 sec

1) No retention (control condition): Discrimination task

2) Retention I (Easy condition): Non-configural task

3) Retention II (Hard condition): Configural task

ENCODING MAINTENANCE PROBE


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Delay activity (4-8Hz)


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Questions

Duzel et al. find different patterns of theta-coupling in the delay perioddependent on task.

Pick 3 regions based on [previous source reconstruction]

1. Right MTL [27,-18,-27] mm

2. Right VIS [10,-100,0] mm3. Right IFG [39,28,-12] mm

Fit models to control data (10 trials) and hard data (10 trials). Each trialcomprises first 1sec of delay period.

Find out if structure of network dynamics is Master-Slave (MS) or(Partial/Total) Mutual Entrainment (ME)

Which connections are modulated by (hard) memory task ?


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Data Preprocessing

Source reconstruct activity in areas of interest (with fewer sources thansensors and known location, then pinv will do; Baillet 01)

Bandpass data into frequency range of interest

Hilbert transform data to obtain instantaneous phase

Use multiple trials per experimental condition


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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


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LogEv

Model

1 2 3 4 5 6 70

50

100

150

200

250

300

350

400

450


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MTL

VISIFG

2.89

2.46

0.89

0.77


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MTL-VIS

IFG-VIS

Control


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MTL-VIS

IFG-VIS

Memory


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08 dcm induced phase

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