Zurich SPM Course 2014 14 February 2014 DCM: Advanced topics Klaas Enno Stephan

Zurich SPM Course 201414 February 2014

DCM: Advanced topics

Klaas Enno Stephan

Overview

• Generative models & analysis options

• Extended DCM for fMRI: nonlinear, two-state, stochastic

• Embedding computational models into DCMs

• Integrating tractography and DCM

• Applications of DCM to clinical questions

( | , )p y m

( | , ) ( | )p y m p m

Generative models

Advantages:

1. force us to think mechanistically: how were the data caused?

2. allow one to generate synthetic data.

3. Bayesian perspective → inversion & model evidence

),,( uxFdt

dx

Neural state equation:

Electromagneticforward model:

neural activityEEGMEGLFP

Dynamic Causal Modeling (DCM)

simple neuronal modelcomplicated forward model

complicated neuronal modelsimple forward model

fMRIfMRI EEG/MEGEEG/MEG

inputs

Hemodynamicforward model:neural activityBOLD

( , , )

( , )

dx dt f x u

y g x

)|(

),(),|(),|(

)(),|()|(

myp

mpmypmyp

dpmypmyp

),(),(

))(),((),|(

Nmp

gNmyp

Invert model

Make inferences

Define likelihood model

Specify priors

Neural dynamics

Observer function

Design experimental inputs)(tu

Inference on model structure

Inference on parameters

Bayesian system identification

VB in a nutshell (mean-field approximation)

, | ,p y q q q

( )

( )

exp exp ln , ,

exp exp ln , ,

q

q

q I p y

q I p y

Iterative updating of sufficient statistics of approx. posteriors by gradient ascent.

ln | , , , |

ln , , , , , |q

p y m F KL q p y

F p y KL q p m

Mean field approx.

Neg. free-energy approx. to model evidence.

Maximise neg. free energy wrt. q = minimise divergence,by maximising variational energies

Generative models

• any DCM = a particular generative model of how the data (may) have been caused

• modelling = comparing competing hypotheses about the mechanisms underlying observed data

model space: a priori definition of hypothesis set is crucial

model selection: determine the most plausible hypothesis (model), given the data

inference on parameters: e.g., evaluate consistency of how model mechanisms are implemented across subjects

• model selection model validation!

model validation requires external criteria (external to the measured data)

| , | , |p y m p y m p m

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

log ( | ) log ( | , )

, |

, | ,

p y m p y m

KL q p m

KL q p y m

Model evidence:

Bayesian model selection (BMS)

accounts for both accuracy and complexity of the model

a measure of generalizability

all possible datasets

y

p(y

|m)

Gharamani, 2004

McKay 1992, Neural Comput.Penny et al. 2004a, NeuroImage

( | ) ( | , ) ( | ) p y m p y m p m d

Various approximations, e.g.:- negative free energy, AIC, BIC

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. 2004a, NeuroImage

Approximations to the model evidence in DCM

No. of parameters

No. ofdata points

The (negative) free energy approximation

• Under Gaussian assumptions about the posterior (Laplace approximation):

log ( | )

log ( | , ) , | , | ,

p y m

p y m KL q p m KL q p y m

log ( | ) , | ,

log ( | , ) , |accuracy complexity

F p y m KL q p y m

p y m KL q p m

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: Since SPM8, only F is used for model selection !

y

Tyy CCC

mpqKL

|1

|| 2

1ln

2

1ln

2

1

)|(),(

inference on model structure or inference on model parameters?

inference on individual models or model space partition?

comparison of model families using

FFX or RFX BMS


FFX or RFX BMS

optimal model structure assumed to be identical across subjects?

FFX BMSFFX BMS RFX BMSRFX BMS

yes no

inference on parameters of an optimal model or parameters of all models?

BMABMA

definition of model spacedefinition of model space

FFX analysis of parameter estimates

(e.g. BPA)


(e.g. BPA)

RFX analysis of parameter estimates(e.g. t-test, ANOVA)



FFX BMS

yes no

RFX BMS

Stephan et al. 2010, NeuroImage

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

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

)|(~ pmpm kk

);(~ rDirr

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

Random effects BMS for heterogeneous groups

Dirichlet parameters = “occurrences” of models in the population

Dirichlet distribution of model probabilities r

Multinomial distribution of model labels m

Measured data y

Model inversion by Variational Bayes or MCMC

Stephan et al. 2009a, NeuroImagePenny et al. 2010, PLoS Comput. Biol.

• Gaussian assumptions about the posterior distributions of the parameters

• Use of the cumulative normal distribution to test the probability that a certain parameter (or contrast of parameters cT ηθ|y) is above a chosen threshold γ:

• By default, γ is chosen as zero ("does the effect exist?").

Inference about DCM parameters:Bayesian single-subject analysis

cCc

cp

yT

yT

N

Inference about DCM parameters:Random effects group analysis (classical)

• In analogy to “random effects” analyses in SPM, 2nd level analyses can be applied to DCM parameters:

Separate fitting of identical models for each subject

Separate fitting of identical models for each subject

Selection of model parameters of interest

Selection of model parameters of interest

one-sample t-test:

parameter > 0 ?

one-sample t-test:

parameter > 0 ?

paired t-test: parameter 1 > parameter 2 ?

paired t-test: parameter 1 > parameter 2 ?

rmANOVA: e.g. in case of

multiple sessions per subject

rmANOVA: e.g. in case of

multiple sessions per subject

Bayesian Model Averaging (BMA)

• uses the entire model space considered (or an optimal family of models)

• averages parameter estimates, weighted by posterior model probabilities

• particularly useful alternative when– none of the models (subspaces)

considered clearly outperforms all others

– when comparing groups for which the optimal model differs

1..

1..

|

| , |

n N

n n Nm

p y

p y m p m y

NB: p(m|y1..N) can be obtained by

either FFX or RFX BMS

Penny et al. 2010, PLoS Comput. Biol.

inference on model structure or inference on model parameters?

inference on individual models or model space partition?


FFX or RFX BMS


FFX or RFX BMS


FFX BMSFFX BMS RFX BMSRFX BMS

yes no

inference on parameters of an optimal model or parameters of all models?

BMABMA

definition of model spacedefinition of model space


(e.g. BPA)


(e.g. BPA)




FFX BMS

yes no

RFX BMS


Overview



• Embedding computational models into DCMs



The evolution of DCM in SPM

• DCM is not one specific model, but a framework for Bayesian inversion of dynamic system models

• The default implementation in SPM is evolving over time– improvements of numerical routines (e.g., for inversion)– change in parameterization (e.g., self-connections, hemodynamic states

in log space)– change in priors to accommodate new variants (e.g., stochastic DCMs,

endogenous DCMs etc.)

To enable replication of your results, you should ideally state which SPM version (release number) you are using when publishing papers.

The release number is stored in the DCM.mat file.

endogenous 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

The classical DCM:a deterministic, one-state, bilinear model

Factorial structure of model specification in DCM10• Three dimensions of model specification:

– bilinear vs. nonlinear

– single-state vs. two-state (per region)

– deterministic vs. stochastic

• Specification via GUI.

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

driving input

modulation

non-linear DCM

...)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)


u1

u2

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


uinput

Single-state DCM

1x

Intrinsic (within-region)

coupling

Extrinsic (between-region)

coupling

NNNN

N

ijijij

x

x

x

uBA

Cuxx

1

1

111

Two-state DCM

Ex1

IN

EN

I

E

IINN

IENN

EENN

EENN

EEN

IIIE

EEN

EIEE

ijijijij

x

x

x

x

x

uBA

Cuxx

1

1

1

1111

11111

00

0

00

0

)exp(

Ix1

I

E

x

x

1

1

Two-state DCM

Marreiros et al. 2008, NeuroImage

Estimates of hidden causes and states(Generalised filtering)

0 200 400 600 800 1000 1200-1

-0.5

0

0.5

1inputs or causes - V2

0 200 400 600 800 1000 1200-0.1

-0.05

0

0.05

0.1hidden states - neuronal

0 200 400 600 800 1000 12000.8

0.9

1

1.1

1.2

1.3hidden states - hemodynamic

0 200 400 600 800 1000 1200-3

-2

-1

0

1

2predicted BOLD signal

time (seconds)

excitatorysignal

flowvolumedHb

observedpredicted

Stochastic DCM

( ) ( )

( )

( )j xjj

v

dxA u B x Cv

dt

v u

Li et al. 2011, NeuroImage

• all states are represented in generalised coordinates of motion

• random state fluctuations w(x) account for endogenous fluctuations,have unknown precision and smoothness two hyperparameters

• fluctuations w(v) induce uncertainty about how inputs influence neuronal activity

• can be fitted to resting state data

Overview



• Embedding computational models in DCMs



Prediction errors drive synaptic plasticity

McLaren 1989

x1 x2

x3

PE(t)

01

t

t kk

w w PE

0

0

( )t

tw a PE d

0aR

synaptic plasticity during learning = f (prediction error)

Learning of dynamic audio-visual associations

CS Response

Time (ms)

0 200 400 600 800 2000 ± 650

or

Target StimulusConditioning Stimulus

or

TS

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

p(f

ace)

trial

CS1

CS2

den Ouden et al. 2010, J. Neurosci.

Hierarchical Bayesian learning model

observed events

probabilistic association

volatility

k

vt-1 vt

rt rt+1

ut ut+1

)exp(,~,|1 ttttt vrDirvrrp

)exp(,~,|1 kvNkvvp ttt

1kp

Behrens et al. 2007, Nat. Neurosci.

prior on volatility

Explaining RTs by different learning models

400 440 480 520 560 6000

0.2

0.4

0.6

0.8

1

Trial

p(F

)

TrueBayes VolHMM fixedHMM learnRW

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Categoricalmodel

Bayesianlearner

HMM (fixed) HMM (learn) Rescorla-Wagner

Exc

eed

ance

pro

b.

Bayesian model selection:

hierarchical Bayesian model performs best

5 alternative learning models:

• categorical probabilities

• hierarchical Bayesian learner

• Rescorla-Wagner

• Hidden Markov models (2 variants)

0.1 0.3 0.5 0.7 0.9390

400

410

420

430

440

450

RT

(m

s)

p(outcome)

Reaction times

den Ouden et al. 2010, J. Neurosci.

Putamen Premotor cortex

Stimulus-independent prediction error

p < 0.05 (SVC)

p < 0.05 (cluster-level whole- brain corrected)

p(F) p(H)-2

-1.5

-1

-0.5

0

BO

LD

re

sp.

(a.u

.)

p(F) p(H)-2

-1.5

-1

-0.5

0

BO

LD

re

sp.

(a.u

.)

den Ouden et al. 2010, J. Neurosci .

Prediction error (PE) activity in the putamen

PE during reinforcement learning

PE during incidentalsensory learning

O'Doherty et al. 2004, Science

den Ouden et al. 2009, Cerebral Cortex

Could the putamen be regulating trial-by-trial changes of task-relevant connections?

PE = “teaching signal” for synaptic plasticity during

learning

p < 0.05 (SVC)

PE during activesensory learning

Prediction errors control plasticity during adaptive cognition

• Influence of visual areas on premotor cortex:– stronger for

surprising stimuli – weaker for expected

stimuli

den Ouden et al. 2010, J. Neurosci .

PPA FFA

PMd

Hierarchical Bayesian learning model

PUT

p = 0.010 p = 0.017

Overview






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 et al. 2009, NeuroImage

LG LG

FGFG

DCM

LGleft

LGright

FGright

FGleft

13 15.7%

34 6.5%

24 43.6%

12 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

Proof of concept study

connection-specific priors for coupling parameters

Stephan, Tittgemeyer et al. 2009, NeuroImage

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

01 exp( )ijij

Connection-specific prior variance as a function of anatomical connection probability

• 64 different mappings by systematic search across hyper-parameters and

• yields anatomically informed (intuitive and counterintuitive) and uninformed priors

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

0.4

0.5

0.6

model

po

st.

mo

del

pro

b.

Models with anatomically informed priors (of an intuitive form)

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

Models with anatomically informed priors (of an intuitive form) were clearly superior to anatomically uninformed ones: Bayes Factor >109

Overview






model structure

Model-based predictions for single patients

set of parameter estimates

BMS

model-based decoding

BMS: Parkison‘s disease and treatment

Rowe et al. 2010,NeuroImage

Age-matched controls

PD patientson medication

PD patientsoff medication

DA-dependent functional disconnection of the SMA

Selection of action modulates connections between PFC and SMA

Model-based decoding by generative embedding

Brodersen et al. 2011, PLoS Comput. Biol.

step 2 —kernel construction

step 1 —model inversion

measurements from an individual subject

subject-specificinverted generative model

subject representation in the generative score space

A → B

A → C

B → B

B → C

A

CB

step 3 —support vector classification

separating hyperplane fitted to discriminate between groups

A

CB

jointly discriminativemodel parameters

step 4 —interpretation

Discovering remote or “hidden” brain lesions

Discovering remote or “hidden” brain lesions

Model-based decoding of disease status: mildly aphasic patients (N=11) vs. controls (N=26)

Connectional fingerprints from a 6-region DCM of auditory areas during speech perception


MGB

PT

HG (A1)

S

MGB

PT

HG (A1)

S

Model-based decoding of disease status: aphasic patients (N=11) vs. controls (N=26)

Classification accuracy


MGB

PT

HG(A1)

MGB

PT

HG(A1)

auditory stimuli

-10

0

10

-0.5

0

0.5

-0.1

0

0.1

0.2

0.3

0.4

-0.4-0.2

0 -0.5

0

0.5-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-10

0

10

-0.5

0

0.5

-0.1

0

0.1

0.2

0.3

0.4

-0.4-0.2

0 -0.5

0

0.5-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

gen

erative em

bedd

ing

L.H

G

L.H

G

Vo

xel (

64,-

24,4

) mm

L.MGB L.MGBVoxel (-42,-26,10) mmVoxel (-56,-20,10) mm R.HG L.HG

controlspatients

Voxel-based feature space Generative score space

Multivariate searchlightclassification analysis

Generative embedding using DCM

F

D

EC

B

A

Definition of ROIs

Are regions of interest definedanatomically or functionally?

anatomically functionally

Functional contrasts

Are the functional contrasts definedacross all subjects or between groups?

1 ROI definitionand nmodel inversions

unbiased estimate

Repeat n times:1 ROI definition and nmodel inversions

unbiased estimate

1 ROI definition and nmodel inversions

slightly optimistic estimate:voxel selection for training set and test set based on test data

Repeat n times:1 ROI definition and 1 model inversion

slightly optimistic estimate:voxel selection for training set based on test data and test labels

Repeat n times:1 ROI definition and nmodel inversions

unbiased estimate

1 ROI definition and nmodel inversions

highly optimistic estimate:voxel selection for training set and test set based on test data and test labels

across subjects

between groups


Generative embedding for detecting patient subgroups

Brodersen et al. 2014, NeuroImage: Clinical

Generative embedding of variational Gaussian Mixture Models


• 42 controls vs. 41 schizophrenic patients• fMRI data from working memory task (Deserno et al. 2012, J. Neurosci)

Supervised:SVM classification

Unsupervised:GMM clustering

number of clusters number of clusters

71%

Detecting subgroups of patients in schizophrenia

• three distinct subgroups (total N=41)

• subgroups differ (p < 0.05) wrt. negative symptoms on the positive and negative symptom scale (PANSS)

Optimal cluster solution


TAPAS

• PhysIO: physiological noise correction

• Hierarchical Gaussian Filter (HGF)

• Variational Bayesian linear regression

• Mixed effects inference for classification studies

Brodersen et al. 2011, PLoS CB Mathys et al. 2011, Front. Hum. Neurosci.

Brodersen et al. 2012, J Mach Learning Res

Kasper et al., in prep.

www.translationalneuromodeling.org/tapas

Methods papers: DCM for fMRI and BMS – part 1

• Brodersen KH, Schofield TM, Leff AP, Ong CS, Lomakina EI, Buhmann JM, Stephan KE (2011) Generative embedding for model-based classification of fMRI data. PLoS Computational Biology 7: e1002079.

• Brodersen KH, Deserno L, Schlagenhauf F, Lin Z, Penny WD, Buhmann JM, Stephan KE (2014) Dissecting psychiatric spectrum disorders by generative embedding. NeuroImage: Clinical 4: 98-111

• Daunizeau J, David, O, Stephan KE (2011) Dynamic Causal Modelling: A critical review of the biophysical and statistical foundations. NeuroImage 58: 312-322.

• Daunizeau J, Stephan KE, Friston KJ (2012) Stochastic Dynamic Causal Modelling of fMRI data: Should we care about neural noise? NeuroImage 62: 464-481.

• Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. NeuroImage 19:1273-1302.

• Friston K, Stephan KE, Li B, Daunizeau J (2010) Generalised filtering. Mathematical Problems in Engineering 2010: 621670.

• Friston KJ, Li B, Daunizeau J, Stephan KE (2011) Network discovery with DCM. NeuroImage 56: 1202–1221.

• Friston K, Penny W (2011) Post hoc Bayesian model selection. Neuroimage 56: 2089-2099.

• Kiebel SJ, Kloppel S, Weiskopf N, Friston KJ (2007) Dynamic causal modeling: a generative model of slice timing in fMRI. NeuroImage 34:1487-1496.

• Li B, Daunizeau J, Stephan KE, Penny WD, Friston KJ (2011). Stochastic DCM and generalised filtering. NeuroImage 58: 442-457

• Marreiros AC, Kiebel SJ, Friston KJ (2008) Dynamic causal modelling for fMRI: a two-state model. NeuroImage 39:269-278.

• Penny WD, Stephan KE, Mechelli A, Friston KJ (2004a) Comparing dynamic causal models. NeuroImage 22:1157-1172.

• Penny WD, Stephan KE, Mechelli A, Friston KJ (2004b) Modelling functional integration: a comparison of structural equation and dynamic causal models. NeuroImage 23 Suppl 1:S264-274.

Methods papers: DCM for fMRI and BMS – part 2

• Penny WD, Stephan KE, Daunizeau J, Joao M, Friston K, Schofield T, Leff AP (2010) Comparing Families of Dynamic Causal Models. PLoS Computational Biology 6: e1000709.

• Penny WD (2012) Comparing dynamic causal models using AIC, BIC and free energy. Neuroimage 59: 319-330.

• Stephan KE, Harrison LM, Penny WD, Friston KJ (2004) Biophysical models of fMRI responses. Curr Opin Neurobiol 14:629-635.

• Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38:387-401.

• Stephan KE, Harrison LM, Kiebel SJ, David O, Penny WD, Friston KJ (2007) Dynamic causal models of neural system dynamics: current state and future extensions. J Biosci 32:129-144.

• Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38:387-401.

• Stephan KE, Kasper L, Harrison LM, Daunizeau J, den Ouden HE, Breakspear M, Friston KJ (2008) Nonlinear dynamic causal models for fMRI. NeuroImage 42:649-662.

• Stephan KE, Penny WD, Daunizeau J, Moran RJ, Friston KJ (2009a) Bayesian model selection for group studies. NeuroImage 46:1004-1017.

• Stephan KE, Tittgemeyer M, Knösche TR, Moran RJ, Friston KJ (2009b) Tractography-based priors for dynamic causal models. NeuroImage 47: 1628-1638.

• Stephan KE, Penny WD, Moran RJ, den Ouden HEM, Daunizeau J, Friston KJ (2010) Ten simple rules for Dynamic Causal Modelling. NeuroImage 49: 3099-3109.

Thank you

Documents

Zurich SPM Course 2014 14 February 2014 DCM: Advanced topics Klaas Enno Stephan