DCM: Advanced issues

Klaas Enno Stephan

Laboratory for Social & Neural Systems Research Institute for Empirical Research in EconomicsUniversity of Zurich

Functional Imaging Laboratory (FIL)Wellcome Trust Centre for NeuroimagingUniversity College London

Methods & models for fMRI data analysis, University of Zurich27 May 2009

Overview

• Bayesian model selection (BMS)

• Nonlinear DCM for fMRI

• Timing errors & sampling accuracy

• Integrating tractography and DCM

• DCMs for electrophysiological data

Model comparison and selection

Given competing hypotheses on structure & functional mechanisms of a system, which model is the best?

For which model m does p(y|m) become maximal?

Which model represents thebest balance between model fit and model complexity?

Pitt & Miyung (2002) TICS

dmpmypmyp )|(),|()|( Model evidence:

Bayesian model selection (BMS)

)|(

)|(),|(),|(

myp

mpmypmyp

Bayes’ rule:

accounts for both accuracy and complexity of the model

allows for inference about structure (generalisability)of the model

integral usually not analytically solvable, approximations necessary

dmpmypmyp )|(),|()|(

Model evidence p(y|m)Gharamani, 2004

p(y

|m

)

all possible datasets y

a specific y

Balance between fit and complexity

Generalisability of the model

Model evidence: probability of generating data y from parameters that are randomly sampled from the prior p(m).

Maximum likelihood: probability of the data y for the specific parameter vector that maximises p(y|,m).

pmypAIC ),|(log

Logarithm is a monotonic function

Maximizing log model evidence= Maximizing model evidence

)(),|(log

)()( )|(log

mcomplexitymyp

mcomplexitymaccuracymyp

In SPM2 & SPM5, interface offers 2 approximations:

Np

mypBIC log2

),|(log

Akaike Information Criterion:

Bayesian Information Criterion:

Log model evidence = balance between fit and complexity

Penny et al. 2004, NeuroImage

Approximations to the model evidence in DCM

No. of parameters

No. ofdata points

AIC favours more complex models,BIC favours simpler models.

Bayes factors

)|(

)|(

2

112 myp

mypB

positive value, [0;[

But: the log evidence is just some number – not very intuitive!

A more intuitive interpretation of model comparisons is made possible by Bayes factors:

To compare two models, we can just compare their log evidences.

B12 p(m1|y) Evidence

1 to 3 50-75% weak

3 to 20 75-95% positive

20 to 150 95-99% strong

150 99% Very strong

Kass & Raftery classification:

Kass & Raftery 1995, J. Am. Stat. Assoc.

The negative free energy approximation

• Under Gaussian assumptions about the posterior (Laplace approximation), the negative free energy F is a lower bound on the log model evidence:

mypqKLF

mypqKLmpqKLmyp

myp

,|,

,|,|,),|(log

)|(log

mypqKLmypF ,|,)|(log

The complexity term in F

• In contrast to AIC & BIC, the complexity term of the negative free energy F accounts for parameter interdependencies.

• The complexity term of F is higher– the more independent the prior parameters ( effective DFs)

– the more dependent the posterior parameters

– the more the posterior mean deviates from the prior mean

• NB: SPM8 only uses F for model selection !

y

Tyy CCC

mpqKL

|1

|| 2

1ln

2

1ln

2

1

)|(),(

V1 V5stim

PPCM2

attention

V1 V5stim

PPCM1

attention

V1 V5stim

PPCM3attention

V1 V5stim

PPCM4attention

BF 2966F = 7.995

M2 better than M1

BF 12F = 2.450

M3 better than M2

BF 23F = 3.144

M4 better than M3

M1 M2 M3 M4

BMS in SPM8: an example

Fixed effects BMS at group level

Group Bayes factor (GBF) for 1...K subjects:

Average Bayes factor (ABF):

Problems:- blind with regard to group heterogeneity- sensitive to outliers

k

kijij BFGBF )(

( )kKij ij

k

ABF BF

)|(~ 111 mypy)|(~ 111 mypy

)|(~ 222 mypy)|(~ 111 mypy

)|(~ pmpm kk

);(~ rDirr

)|(~ pmpm kk )|(~ pmpm kk),1;(~1 rmMultm

Random effects BMS for group studies: a variational Bayesian approach

Dirichlet parameters= “occurrences” of models in the population

Dirichlet distribution of model probabilities

Multinomial distribution of model labels

Measured data

Stephan et al. 2009, NeuroImage

Is the red letter left or right from the midline of the word?

group analysis (random effects),n=16, p<0.05

whole-brain corrected

group analysis (random effects),n=16, p<0.05

whole-brain corrected

Task-driven lateralisation

letter decisions > spatial decisions

time

•••

Does the word contain the letter A or not?

spatial decisions > letter decisions

Stephan et al. 2003, Science

MOGleft

LGleft

LGright

RVFstim.

LVFstim.

FGright

FGleft

LD|RVF

LD|LVF

LD LD

0.20 0.04

0.06 0.02

0.00 0.01

0.01 0.01

0.27 0.06

0.11 0.03

MOGright

0.00 0.04

0.01 0.03

0.07 0.02

0.01 0.01

Inter-hemispheric connectivity in the visual ventral stream

LD>SD, p<0.05 cluster-level corrected(p<0.001 voxel-level cut-off)

Left MOG-38,-90,-4

Left FG-44,-52,-18

Right MOG-38,-94,0

p<0.01 uncorrected

Left LG-12,-70,-6

Left LG-14,-68,-2

LD>SD masked incl. with RVF>LVFp<0.05 cluster-level corrected(p<0.001 voxel-level cut-off)

LD>SD masked incl. with LVF>RVFp<0.05 cluster-level corrected

(p<0.001 voxel-level cut-off)

Right FG38,-52,-20

Stephan et al. 2007, J. Neurosci.

-35 -30 -25 -20 -15 -10 -5 0 5

Su

bje

cts

Log model evidence differences

MOG

LG LG

RVFstim.

LVFstim.

FGFG

LD|RVF

LD|LVF

LD LD

MOGMOG

LG LG

RVFstim.

LVFstim.

FGFG

LD

LD

LD|RVF LD|LVF

MOG

m2 m1

Stephan et al. 2009, NeuroImage

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

r1

p(r 1

|y)

p(r1>0.5 | y) = 0.997

157.0,843.0

194.2,806.11

21

21

rr

Simulation study: sampling subjects from a

heterogenous population

• Population where 70% of all subjects' data are generated by model m1 and 30% by model m2

• Random sampling of subjects from this population and generating synthetic data with observation noise

• Fitting both m1 and m2 to all data sets and performing BMS

MOG

LG LG

RVFstim.

LVFstim.

FGFG

LD|RVF

LD|LVF

LD LD

MOG

MOG

LG LG

RVFstim.

LVFstim.

FGFG

LD

LD

LD|RVF LD|LVF

MOG

m1

m2

Stephan et al. 2009, NeuroImage

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

100

200

300

400

500

600

700

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

B

0

2

4

6

8

10

12

14

16

18A

m1 m2

m1 m2 m1 m2

log GBF12

C D

<r>

true values:1=220.7=15.42=220.3=6.6

mean estimates:1=15.4, 2=6.6

true values:r1 = 0.7, r2=0.3

mean estimates:r1 = 0.7, r2=0.3

true values:1 = 1, 2=0

mean estimates:1 = 0.89, 2=0.11

Overview

• Bayesian model selection (BMS)

• Nonlinear DCM for fMRI

• Timing errors & sampling accuracy

• Integrating tractography and DCM

• DCMs for electrophysiological data

intrinsic connectivity

direct inputs

modulation ofconnectivity

Neural state equation CuxBuAx jj )( )(

u

xC

x

x

uB

x

xA

j

j

)(

hemodynamicmodelλ

x

y

integration

BOLDyyy

activityx1(t)

activityx2(t) activity

x3(t)

neuronalstates

t

drivinginput u1(t)

modulatoryinput u2(t)

t

Stephan & Friston (2007),Handbook of Brain Connectivity

bilinear DCM

CuxDxBuAdt

dx m

i

n

j

jj

ii

1 1

)()(CuxBuA

dt

dx m

i

ii

1

)(

Bilinear state equation:

driving input

modulation

non-linear DCM

driving input

modulation

...)0,(),(2

0

uxux

fu

u

fx

x

fxfuxf

dt

dx

Two-dimensional Taylor series (around x0=0, u0=0):

Nonlinear state equation:

...2

)0,(),(2

2

22

0

x

x

fux

ux

fu

u

fx

x

fxfuxf

dt

dx

0 10 20 30 40 50 60 70 80 90 100

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80 90 100

0

0.2

0.4

0.6

0 10 20 30 40 50 60 70 80 90 100

0

0.1

0.2

0.3

Neural population activity

0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

0 10 20 30 40 50 60 70 80 90 100-1

0

1

2

3

4

0 10 20 30 40 50 60 70 80 90 100

0

1

2

3

fMRI signal change (%)

x1 x2

x3

CuxDxBuAdt

dx n

j

jj

m

i

ii

1

)(

1

)(

Nonlinear dynamic causal model (DCM):

Stephan et al. 2008, NeuroImage

u1

u2

Nonlinear DCM: Attention to motion

V1 IFG

V5

SPC

Motion

Photic

Attention

.82(100%)

.42(100%)

.37(90%)

.69 (100%).47

(100%)

.65 (100%)

.52 (98%)

.56(99%)

Stimuli + Task

250 radially moving dots (4.7 °/s)

Conditions:F – fixation onlyA – motion + attention (“detect changes”)N – motion without attentionS – stationary dots

Previous bilinear DCM

Friston et al. (2003)

Friston et al. (2003):attention modulates backward connections IFG→SPC and SPC→V5.

Q: Is a nonlinear mechanism (gain control) a better explanation of the data?

Büchel & Friston (1997)

modulation of back-ward or forward connection?

additional drivingeffect of attentionon PPC?

bilinear or nonlinearmodulation offorward connection?

V1 V5stim

PPCM2

attention

V1 V5stim

PPCM1

attention

V1 V5stim

PPCM3attention

V1 V5stim

PPCM4attention

BF = 2966

M2 better than M1

M3 better than M2

BF = 12

M4 better than M3

BF = 23

Stephan et al. 2008, NeuroImage

V1 V5stim

PPC

attention

motion

-2 -1 0 1 2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

%1.99)|0( 1,5 yDp PPCVV

1.25

0.13

0.46

0.39

0.26

0.50

0.26

0.10MAP = 1.25

Stephan et al. 2008, NeuroImage

V1

V5PPC

observedfitted

motion &attention

motion &no attention

static dots

Stephan et al. 2008, NeuroImage

FFA PPA

MFG

-0.80

-0.31

faces houses faces houses

rivalry non-rivalry

1.05 0.08

0.300.51

2.43 2.41

0.04 -0.03 0.02 0.06

0.02 -0.03

-2 -1 0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-2 -1 0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

%9.99)|0( , yDp MFGFFAPPA

%9.99)|0( , yDp MFGPPAFFA

Nonlinear DCM: Binocular rivalry

Stephan et al. 2008, NeuroImage

BR nBR

FFA

PPAMFG

time (s)

Stephan et al. 2008, NeuroImage

Overview

• Bayesian model selection (BMS)

• Nonlinear DCM for fMRI

• Timing errors & sampling accuracy

• Integrating tractography and DCM

• DCMs for electrophysiological data

Timing problems at long TRs/TAs

• Two potential timing problems in DCM:

1. wrong timing of inputs2. temporal shift between

regional time series because of multi-slice acquisition

• DCM is robust against timing errors up to approx. ± 1 s – compensatory changes of σ and θh

• Possible corrections:– slice-timing in SPM (not for long TAs)– restriction of the model to neighbouring regions– in both cases: adjust temporal reference bin in SPM defaults

(defaults.stats.fmri.t0)• Best solution: Slice-specific sampling within DCM

1

2

slic

e a

cquis

itio

n

visualinput

Slice timing in DCM: three-level model

),,( hhxxgv

),( Tvhz

),,( uxfx n

3rd level

2nd level

1st level

sampled BOLD response

BOLD response

neuronal response

x = neuronal states u = inputsxh = hemodynamic states v = BOLD responsesn, h = neuronal and hemodynamic parameters T = sampling time points

Kiebel et al. 2007, NeuroImage

Slice timing in DCM: an example

t

1 TR 2 TR 3 TR 4 TR 5 TR

t

1 TR 2 TR 3 TR 4 TR 5 TR

Defaultsampling

Slice-specific sampling

1T

2T1T

2T1T

2T1T

2T1T

2T

1T 1T 1T 1T 1T2T 2T 2T 2T 2T

Kiebel et al. 2007, NeuroImage

Overview

• Bayesian model selection (BMS)

• Nonlinear DCM for fMRI

• Timing errors & sampling accuracy

• Integrating tractography and DCM

• DCMs for electrophysiological data

Diffusion-weighted imaging

Parker & Alexander, 2005, Phil. Trans. B

Probabilistic tractography: Kaden et al. 2007, NeuroImage

• computes local fibre orientation density by spherical deconvolution of the diffusion-weighted signal

• estimates the spatial probability distribution of connectivity from given seed regions

• anatomical connectivity = proportion of fibre pathways originating in a specific source region that intersect a target region

• If the area or volume of the source region approaches a point, this measure reduces to method by Behrens et al. (2003)

R2R1

R2R1

-2 -1 0 1 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-2 -1 0 1 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

low probability of anatomical connection small prior variance of effective connectivity parameter

high probability of anatomical connection large prior variance of effective connectivity parameter

Integration of tractography and DCM

Stephan, Tittgemeyer, Knoesche, Moran, Friston, in revision

LG(x1)

LG(x2)

RVFstim.

LVFstim.

FG(x4)

FG(x3)

LD|LVF

LD LD

BVFstim.

LD|RVF DCM structure

LGleft

LGright

FGright

FGleft

* 313

13

5.37 10

15.7%

* 334

34

2.23 10

6.5%

* 224

24

1.50 10

43.6%

* 212

12

1.17 10

34.2%

anatomical connectivity

probabilistictractography

-3 -2 -1 0 1 2 30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

6.5%

0.0384v

15.7%

0.1070v

34.2%

0.5268v

43.6%

0.7746v

connection-specific priors for coupling parameters

0 0.5 10

0.5

1m1: a=-32,b=-32

0 0.5 10

0.5

1m2: a=-16,b=-32

0 0.5 10

0.5

1m3: a=-16,b=-28

0 0.5 10

0.5

1m4: a=-12,b=-32

0 0.5 10

0.5

1m5: a=-12,b=-28

0 0.5 10

0.5

1m6: a=-12,b=-24

0 0.5 10

0.5

1m7: a=-12,b=-20

0 0.5 10

0.5

1m8: a=-8,b=-32

0 0.5 10

0.5

1m9: a=-8,b=-28

0 0.5 10

0.5

1m10: a=-8,b=-24

0 0.5 10

0.5

1m11: a=-8,b=-20

0 0.5 10

0.5

1m12: a=-8,b=-16

0 0.5 10

0.5

1m13: a=-8,b=-12

0 0.5 10

0.5

1m14: a=-4,b=-32

0 0.5 10

0.5

1m15: a=-4,b=-28

0 0.5 10

0.5

1m16: a=-4,b=-24

0 0.5 10

0.5

1m17: a=-4,b=-20

0 0.5 10

0.5

1m18: a=-4,b=-16

0 0.5 10

0.5

1m19: a=-4,b=-12

0 0.5 10

0.5

1m20: a=-4,b=-8

0 0.5 10

0.5

1m21: a=-4,b=-4

0 0.5 10

0.5

1m22: a=-4,b=0

0 0.5 10

0.5

1m23: a=-4,b=4

0 0.5 10

0.5

1m24: a=0,b=-32

0 0.5 10

0.5

1m25: a=0,b=-28

0 0.5 10

0.5

1m26: a=0,b=-24

0 0.5 10

0.5

1m27: a=0,b=-20

0 0.5 10

0.5

1m28: a=0,b=-16

0 0.5 10

0.5

1m29: a=0,b=-12

0 0.5 10

0.5

1m30: a=0,b=-8

0 0.5 10

0.5

1m31: a=0,b=-4

0 0.5 10

0.5

1m32: a=0,b=0

0 0.5 10

0.5

1m33: a=0,b=4

0 0.5 10

0.5

1m34: a=0,b=8

0 0.5 10

0.5

1m35: a=0,b=12

0 0.5 10

0.5

1m36: a=0,b=16

0 0.5 10

0.5

1m37: a=0,b=20

0 0.5 10

0.5

1m38: a=0,b=24

0 0.5 10

0.5

1m39: a=0,b=28

0 0.5 10

0.5

1m40: a=0,b=32

0 0.5 10

0.5

1m41: a=4,b=-32

0 0.5 10

0.5

1m42: a=4,b=0

0 0.5 10

0.5

1m43: a=4,b=4

0 0.5 10

0.5

1m44: a=4,b=8

0 0.5 10

0.5

1m45: a=4,b=12

0 0.5 10

0.5

1m46: a=4,b=16

0 0.5 10

0.5

1m47: a=4,b=20

0 0.5 10

0.5

1m48: a=4,b=24

0 0.5 10

0.5

1m49: a=4,b=28

0 0.5 10

0.5

1m50: a=4,b=32

0 0.5 10

0.5

1m51: a=8,b=12

0 0.5 10

0.5

1m52: a=8,b=16

0 0.5 10

0.5

1m53: a=8,b=20

0 0.5 10

0.5

1m54: a=8,b=24

0 0.5 10

0.5

1m55: a=8,b=28

0 0.5 10

0.5

1m56: a=8,b=32

0 0.5 10

0.5

1m57: a=12,b=20

0 0.5 10

0.5

1m58: a=12,b=24

0 0.5 10

0.5

1m59: a=12,b=28

0 0.5 10

0.5

1m60: a=12,b=32

0 0.5 10

0.5

1m61: a=16,b=28

0 0.5 10

0.5

1m62: a=16,b=32

0 0.5 10

0.5

1m63 & m64

0 10 20 30 40 50 600

200

400

600

model

log

gro

up

Bay

es f

acto

r

0 10 20 30 40 50 60

680

685

690

695

700

model

log

gro

up

Bay

es f

acto

r

0 10 20 30 40 50 600

0.1

0.2

0.3

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0.5

0.6

model

po

st.

mo

del

pro

b.

0 0.5 10

0.5

1m1: a=-32,b=-32

0 0.5 10

0.5

1m2: a=-16,b=-32

0 0.5 10

0.5

1m3: a=-16,b=-28

0 0.5 10

0.5

1m4: a=-12,b=-32

0 0.5 10

0.5

1m5: a=-12,b=-28

0 0.5 10

0.5

1m6: a=-12,b=-24

0 0.5 10

0.5

1m7: a=-12,b=-20

0 0.5 10

0.5

1m8: a=-8,b=-32

0 0.5 10

0.5

1m9: a=-8,b=-28

0 0.5 10

0.5

1m10: a=-8,b=-24

0 0.5 10

0.5

1m11: a=-8,b=-20

0 0.5 10

0.5

1m12: a=-8,b=-16

0 0.5 10

0.5

1m13: a=-8,b=-12

0 0.5 10

0.5

1m14: a=-4,b=-32

0 0.5 10

0.5

1m15: a=-4,b=-28

0 0.5 10

0.5

1m16: a=-4,b=-24

0 0.5 10

0.5

1m17: a=-4,b=-20

0 0.5 10

0.5

1m18: a=-4,b=-16

0 0.5 10

0.5

1m19: a=-4,b=-12

0 0.5 10

0.5

1m20: a=-4,b=-8

0 0.5 10

0.5

1m21: a=-4,b=-4

0 0.5 10

0.5

1m22: a=-4,b=0

0 0.5 10

0.5

1m23: a=-4,b=4

0 0.5 10

0.5

1m24: a=0,b=-32

0 0.5 10

0.5

1m25: a=0,b=-28

0 0.5 10

0.5

1m26: a=0,b=-24

0 0.5 10

0.5

1m27: a=0,b=-20

0 0.5 10

0.5

1m28: a=0,b=-16

0 0.5 10

0.5

1m29: a=0,b=-12

0 0.5 10

0.5

1m30: a=0,b=-8

0 0.5 10

0.5

1m31: a=0,b=-4

0 0.5 10

0.5

1m32: a=0,b=0

0 0.5 10

0.5

1m33: a=0,b=4

0 0.5 10

0.5

1m34: a=0,b=8

0 0.5 10

0.5

1m35: a=0,b=12

0 0.5 10

0.5

1m36: a=0,b=16

0 0.5 10

0.5

1m37: a=0,b=20

0 0.5 10

0.5

1m38: a=0,b=24

0 0.5 10

0.5

1m39: a=0,b=28

0 0.5 10

0.5

1m40: a=0,b=32

0 0.5 10

0.5

1m41: a=4,b=-32

0 0.5 10

0.5

1m42: a=4,b=0

0 0.5 10

0.5

1m43: a=4,b=4

0 0.5 10

0.5

1m44: a=4,b=8

0 0.5 10

0.5

1m45: a=4,b=12

0 0.5 10

0.5

1m46: a=4,b=16

0 0.5 10

0.5

1m47: a=4,b=20

0 0.5 10

0.5

1m48: a=4,b=24

0 0.5 10

0.5

1m49: a=4,b=28

0 0.5 10

0.5

1m50: a=4,b=32

0 0.5 10

0.5

1m51: a=8,b=12

0 0.5 10

0.5

1m52: a=8,b=16

0 0.5 10

0.5

1m53: a=8,b=20

0 0.5 10

0.5

1m54: a=8,b=24

0 0.5 10

0.5

1m55: a=8,b=28

0 0.5 10

0.5

1m56: a=8,b=32

0 0.5 10

0.5

1m57: a=12,b=20

0 0.5 10

0.5

1m58: a=12,b=24

0 0.5 10

0.5

1m59: a=12,b=28

0 0.5 10

0.5

1m60: a=12,b=32

0 0.5 10

0.5

1m61: a=16,b=28

0 0.5 10

0.5

1m62: a=16,b=32

0 0.5 10

0.5

1m63 & m64

Overview

• Bayesian model selection (BMS)

• Nonlinear DCM for fMRI

• Timing errors & sampling accuracy

• Integrating tractography and DCM

• DCMs for electrophysiological data

),,( uxFx Neural state equation:

Electric/magneticforward model:

neural activityEEGMEGLFP

(linear)

DCM: generative model for fMRI and ERPs

Neural model:1 state variable per regionbilinear state equationno propagation delays

Neural model:8 state variables per region

nonlinear state equationpropagation delays

fMRIfMRI ERPsERPs

inputs

Hemodynamicforward model:neural activityBOLD(nonlinear)

DCMs for M/EEG and LFPs

• can be fitted both to frequency spectra and ERPs

• models different neuronal cell types, different synaptic types (and their plasticity) and spike-frequency adaptation (SFA)

• ongoing model validation by LFP recordings in rats, combined with pharmacological manipulations

standards deviants

A1

A2

Tombaugh et al. 2005, J.Neurosci.

Example of single-neuron SFA

Neural mass model of a cortical macrocolumn

ExcitatoryInterneurons

He, e

PyramidalCells

He, e

InhibitoryInterneurons

Hi, e

Extrinsic inputs

Excitatory connection

Inhibitory connection

e, i : synaptic time constant (excitatory and inhibitory) He, Hi: synaptic efficacy (excitatory and inhibitory) 1,…,: intrinsic connection strengths propagation delays

21

43

MEG/EEGsignal

MEG/EEGsignal

Parameters:

Parameters:

Jansen & Rit (1995) Biol. Cybern.David et al. (2003) NeuroImage

mean firing rate

mean

postsynaptic potential (PSP)

mean PSP

mean firing rate

43

12

12

4914

41

2))(( xxuaxsHx

xx

eeee

Excitatory spiny cells in granular layers

Exogenous input u

43

12

Intrinsicconnections

5

Excitatory spiny cells in granular layers

Excitatory pyramidal cells in agranular layers

Inhibitory cells in agranular layers

),( uxfx

11812

102

1112511

1110

72

8938

87

2)(

2)()(

xxx

xxxSHx

xx

xxxSAAHx

xx

iiii

eeLB

ee

12

4914

41

2))()(( xxCuxSAAHx

xx

eeLF

ee

Synaptic ‘alpha’ kernelSynaptic ‘alpha’ kernel

Sigmoid functionSigmoid function

659

32

61246

63

22

51295

52

2)(

2))()()((

xxx

xxxSHx

x

xxxSxSAAHx

xx

iiii

eeLB

ee

Extrinsic

Connections:

Forward

Backward

Lateral

David et al. 2006, NeuroImage Kiebel et al. 2007, NeuroImage Moran et al. 2009, NeuroImage

Electromagnetic forward model for M/EEG

Depolarisation of

pyramidal cells

Forward model:lead field & gain

matrixScalp data

),,(0 uxfx LK 0),( LKxxgy

Forward model

Kiebel et al. 2006, NeuroImage

DCM for steady-state responses

• models the cross-spectral density of recorded data

• feature extraction by means of p-order VAR model

• spectral form of neuronal innovations (i.e. baseline cortical activity) are estimated using a mixture of white and pink (1/f) components

• assumes quasi-stationary responses (i.e. changes in neuronal states are approximated by small perturbations around some fixed point)

10

20

30

Fre

qu

en

cy

(H

z)

Time (s)

0 10

Moran et al. 2009, NeuroImage

Validation study using microdialysis (in collaboration with Conway Inst., UC Dublin)

Low GlutamateRegular Glutamate

Isolated mPFCControls mPFC

Low GlutamateRegular Glutamate

Isolated mPFCControls mPFC

mPFC

VTA

-0.06

0

0.06

0.12

mV

mPFC EEG

-0.06

0

0.06

0.12

mV

- two groups of rats with different rearing conditions

- LFP recordings and microdialysis measurements (Glu & GABA) from mPFC

Moran et al. 2008, NeuroImage

Experimental data

FFT 10 mins time series: one area (mPFC)

blue: control animalsred: isolated animals

* p<0.05, Bonferroni-corrected

Moran et al. 2008, NeuroImage

Predictions about expected parameter estimates from the microdialysis

measurements

chronic reduction in extracellular

glutamate levels

upregulation of AMPA receptors

sensitisation of postsynaptic mechanisms

EPSPs

amplitude of synaptic kernels

( He)

activation of voltage-sensitive Ca2+ channels → intracellular Ca2+ → Ca-dependent K+ currents → IAHP

SFA(2)

Van den Pool et al. 1996, NeuroscienceSanchez-Vives et al. 2000, J. Neurosci.

Extrinsicforward

connections

4

1 2u

5

Excitatory spiny cells in granular layers

Excitatory pyramidal cells in infragranular layers

Extrinsicforward

connections

4 3

u

5

Excitatory spiny cells in granular layers

Inhibitory cells in supragranular layers

[161, 210]

[29,37]

[195, 233]

(0.4)

(0.37)(0. 13)

[3.8 6.3]

[0.76,1.34] (0.0003)

(0.04)eH

2

Control group estimates in blue,isolated animals in red,p values in parentheses.

sensitization of post-synaptic mechanisms

Increased neuronal adaption:decreased firing rate

Moran et al. 2008, NeuroImage

Take-home messages

• Bayesian model selection (BMS):generic approach to selecting an optimal model from an arbitrarily large number of competing models

• random effects BMS for group studies:posterior model probabilities and exceedance probabilities

• nonlinear DCM:enables one to investigate synaptic gating processes via activity-dependent changes in connection strengths

• DCM & tractography: probabilities of anatomical connections can be used to inform the prior variance of DCM coupling parameters

• DCMs for electrophysiology:based on neurophysiologically fairly detailed neural mass models

Thank you