Abstract

This talk will present a general approach (DCM) to the identification of dynamic input-state-output systems such as the network of equivalent current dipoles (sources) used to model electromagnetic brain responses. We develop this approach for the analysis of effective connectivity (coupling) using experimentally designed inputs and task-free designs. The ensuing framework allows one to characterize experiments conceptually as an experimental manipulation of integration among brain sources (by contextual or trial-free inputs, like time or attentional set) that is perturbed or probed using evoked responses (to trial-bound inputs like stimuli). The approach is illustrated using DCM for evoked responses, induced responses and steady-state activity, to illustrate the range of questions that can be addressed with informed forward modeling of MEG data

Swinbourne talk Wednesday 27th October, 10.30-11.30

Modelling distributed electromagnetic responsesKarl Friston, Wellcome Centre for Neuroimaging, UCL

Dynamic Causal ModellingState and observation equationsModel inversion

DCMs for evoked responsesNeural-mass modelsPerceptual learning and MMNBackward connections

DCMs for induced responsesNonlinear coupling Face processing

DCMs for ergodic responsesSynaptic coupling Beta oscillations in Parkinsonism

Functional connectivityStatistical dependence between systems

DCMDAG

Effective connectivityCausal influence among systems

1x

3 2

3 2 2 1 1

( )

( | ) ( | ) ( | ) ( )

x f x

p x m p x x p x x p x

2x

3x 1( )x t

2( )x t

3( )x t

( ) ( , )

( | ) ( | ) ( )

x t f x

p x m p x p d

1

exp( )t t

x

x Ax

A f

1 1( ) ( )T T T

x Ax

xx I A I A

( )u t

Tests for conditional independence:Structural causal modeling

Bayesian model comparison:Dynamic causal modeling

Bayesian networks

Path analysis (SEM) Ganger causality (MAR)

DCM

PCA and ICA1( )x I A

x W

Observed data

)(tu

ix

input

( , , )x f x u

),(xgy

Forward model (measurement)

Model inversion

Forward models and their inversion

Forward model (neuronal)

( | , , , )p y x u m ( , | , , )p x y u m

Model specification and inversion

),(

),,(

xgy

uxfx

( | , ) ( , )( | , ) ( )

( | )

ln ( | ) ln ( | , ) ( ) F

p y m p mp y m q

p y m

p y m p y m p d

( | , ) ( ( ), ( ))

( , ) ( , )

N

N

p y m g

p m

Invert modelInvert model

InferenceInference

Define likelihood modelDefine likelihood model

Specify priorsSpecify priors

Neural dynamics

Observer function

Design experimental inputsDesign experimental inputs)(tu

Inference on models

Inference on parameters( , ( )) ln ( | )y q p y m F

Hierarchical connections in the brain and laminar specificityDynamic Causal Modelling

State and observation equationsModel inversion

DCMs for evoked responsesNeural-mass modelsPerceptual learning and MMNBackward connections

DCMs for induced responsesNonlinear coupling Face processing

DCMs for ergodic responsesSynaptic coupling Beta oscillations in Parkinsonism

neuronal mass models of distributed sources

State equations

( , , ) x f x u

Output equation

(3)( , ) y g x LV

Exogenous input

E13

( )u t

Excitatory spiny cells in granular layers

Excitatory pyramidal cells in infragranular layers

Inhibitory cells in supragranular layers

Measured response

)( )3(Vg

(1) (1) (1) (1)

(1) (3) (3) (1)13

( ) ( )

( ( , ) )

L L E E V

EE E V R E E

CV g V V g V V u

g V g

E31

IIRVI

II

EERVE

EE

VIIEELL

gVg

gVg

VVgVVgVVgVC

)),((

)),((

)()()(

)2()2()2(22

)2(

)2()3()3(23

)2(

)2()2()2()2()2()2(

IIRVI

II

EERVE

EE

VIIEELL

gVg

gVg

VVgVVgVVgVC

)),((

)),((

)()()(

)3()2()2(32

)3(

)3()1()1(31

)3(

)3()3()3()3()3()3(

E23

I32 12

I

uinput

x

ERPs

Comparing models (with and without backward connections)

A1 A1

STG

input

STG

IFG

FB

A1 A1

STG

input

STG

IFG

F

0 200 400

0

0 200 400

0

FB vs. F

without with

A1A1

STGSTG

IFG

Garrido et al 2007

log-evidence

ln ( | ) Fp y m

The MMN and perceptual learning

MMN

standards deviants

ERP standardsERP deviantsdeviants - standards

Garrido et al 2008

Model comparison:Changes in forward and backward connections

A1 A1

STG STG

ForwardBackward

Lateral

input

A1 A1

STG STG

ForwardBackward

Lateral

input

A1 A1

STG

ForwardBackward

Lateral

input

-

STG

IFGIFGIFG

Forward (F) Backward (B) Forward and Backward (FB)

Garrido et al 2009

A1A1

STGSTG

IFGA1 A1

STG STG

ForwardBackward

Lateral

input

A1 A1

STG STG

ForwardBackward

Lateral

input

A1 A1

STG

ForwardBackward

Lateral

input

-

STG

IFGIFGIFG

Forward (F) Backward (B) Forward and Backward (FB)

FFB

log

evid

ence

Bayesian model comparison

subjects

Forward (F)

Backward (B)

Forward and Backward (FB)

Two subgroups

Garrido et al 2008

1 2 3 4 5 1 2 3 4 5

A1 A1

STG

subcortical input

STG

repetition effects

monotonic phasic

1 2 3 4 50

20

40

60

80

100

120

140

160

180

200

1 2 3 4 50

50

100

150

200

250

Intrinsic connections

Extrinsic connections

number of presentations

The dynamics of plasticity:Repetition suppression

Garrido et al 2009

Dynamic Causal ModellingState and observation equationsModel inversion

DCMs for evoked responsesNeural-mass modelsPerceptual learning and MMNBackward connections

DCMs for induced responsesNonlinear coupling Face processing

DCMs for ergodic responsesSynaptic coupling Beta oscillations in Parkinsonism

K frequencies in j-th source

KKij

Kij

Kijij

ij

AA

AA

A

1

111

Nonlinear (between-frequency) coupling

Linear (within-frequency) coupling

Extrinsic (between-source) coupling

Neuronal model for spectral features

)()()(1

1

1111

tu

C

C

tg

AA

AA

g

g

tg

JJJJ

J

J

Data in channel space

12

( ) ( )

( , )

( , ) ( ( ))

( , )

j

j j

j K

x t L d t

g t

g t FT x t

g t

)(td

Inversion of electromagnetic model L

)(tu

klijA

jg

input

Intrinsic (within-source) coupling

),( tgi

DCM for induced responses – a different sort of data feature

CC Chen et al 2008

LV RV

RFLF

input

LV RV

RFLF

input

Frequency-specific coupling during face-processing

CC Chen et al 2008

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 t df 72; FWHM 7.8 x 6.5 Hz

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

Right hemisphereLeft hemisphere

Forward Backward Forward BackwardFr

eque

ncy

(Hz)

LV RV

RFLF

input

FLBL FNBL FLBN FNBN

-59890

-16308 -16306 -11895

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

Functional asymmetries in forward and backward connections

CC Chen et al 2008

Dynamic Causal ModellingState and observation equationsModel inversion

DCMs for evoked responsesNeural-mass modelsPerceptual learning and MMNBackward connections

DCMs for induced responsesNonlinear coupling Face processing

DCMs for ergodic responsesSynaptic coupling Beta oscillations in Parkinsonism

2 3 4 5 6

A

Te3

Te2A1

7

= Silverball electrode, diameter: 1 mm

PAF

DCM for ergodic (steady-state) responses:Validation of synaptic coupling estimates in a rat model of anesthesia

Excitatory synaptic kernel

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10-3

Time ms

PSP

mV

Moran et al 2010

2

1

( ) | ( ) | ( , ) ( , )

( ) ( ( ) )

y x cg H g g

H s sI f x

The transfer function and likelihood model

eH

under white noise during silence

Frequency (Hz)Frequency (Hz)

Powe

r A1

Powe

r A1

Pow

er A

2

Pow

er A

2

Powe

r A1

- A2

Powe

r A1

- A2

0 5 10 15 20 25 300

0.02

0.04

0.06

0 5 10 15 20 25 300

0.02

0.04

0.06

0 5 10 15 20 25 300

0.02

0.04

0.06

1.4 %1.8 %2.4 %2.8 %

Predicted Observed

0 5 10 15 20 25 30

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25 30

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25 300

0.02

0.04

0.06

0.08

Predicted and observed cross-spectra

for different levels of isoflurane

( )y iig ( )y ijg

( )y jjg

m1

m2

m3

0

50

100

150

200

250

White Noise

Silence

Log

Gro

up B

ayes

Fac

tor

Model comparison and auditory hierarchies

m3

A1

PAF

lateral

lateral

m2

PAF

A1

forward

backward

m1

A1

PAF

forward

backward

Moran et al 2010

He A1: White NoiseHi A1: White Noise and He PAF: White NoiseHi PAF: White Noise and

He A1: SilenceHi A1: Silence and He PAF: SilenceHi PAF: Silence and

1.4 1.8 2.4 2.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

****

*

**

1.4 1.8 2.4 2.8-1.5

-1

-0.5

0

0.5

1

**

**

**

1.4 1.8 2.4 2.8-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

*

**

**

1.4 1.8 2.4 2.8-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

*

**

**

Isoflurane Dose Isoflurane Dose

Isoflurane DoseIsoflurane Dose

Do

se

Sp

ec

ific

Ga

inD

os

e S

pe

cif

ic G

ain

Do

se

Sp

ec

ific

Ga

inD

os

e S

pe

cif

ic G

ain

Moran et al 2010

Glutamatergic stellate cells

GABAergic cells

Glutamatergic Projection cells

Data

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

0 20 400

5

Cortex

GPe

StriatumSTN

Cortex GPeStriatum STN

DCMs for steady-state responses:characterizing coupling parameters Cross-spectral data features

6-OHDA lesion model of Parkinsonism

Moran et al 2010

1. Cortex

2. Striatum

3. External globus pallidus (GPe)

4. Subthalamic Nucleus (STN)

6. Thalamus

5. Entopeduncular Nucleus (EPN)

Changes in the basal ganglia-cortical circuits

Moran et al

Control 6-OHDA Lesioned

2

3

4.25 ± 0.17

1.44 ± 0.18

5.24 ± 0.16

6. 91 ± 0.190.90

± 0

.21

1.43 ± 0.38

0.29 ± 0.31

0.85 ± 0.36

5

0.72 ± 0.44

2

3

5

3.43 ± 0.16

3.07 ± 0.17

5.00 ± 0.15

2.33 ± 0.21 1.0

4 ±

0.20

1.18 ± 0.33

1.03 ± 0.35

0.74 ± 0.28

MAP estimates

EPN

to T

hala

mus

Thal

amus

to C

tx

Ctx

to S

triat

um

Ctx

to S

TN

Stria

tum

to G

Pe

Stria

tum

to E

PN

STN

to E

PN

STN

to G

Pe

GPe

to S

TN

0

1

2

3

4

5

6

7

8

**

Thank you

And thanks to

CC ChenJean Daunizeau Marta GarridoLee HarrisonStefan Kiebel

Andre MarreirosRosalyn Moran

Will PennyKlaas Stephan

And many others