Zurich SPM Course 2014 14 February 2014
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Transcript of Zurich SPM Course 2014 14 February 2014
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
),,( uxFdtdx
Neural state equation:
Electromagneticforward model:
neural activityEEGMEGLFP
Dynamic Causal Modeling (DCM)
simple neuronal modelcomplicated forward model
complicated neuronal modelsimple forward model
fMRI EEG/MEG
inputs
Hemodynamicforward model:neural activityBOLD
( , , )
( , )
dx dt f x u
y g x
)|(),(),|(),|(
)(),|()|(
mypmpmypmyp
dpmypmyp
),(),())(),((),|(
NmpgNmyp
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 selectionGiven 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
mcomplexitymypmcomplexitymaccuracymyp
In SPM2 & SPM5, interface offers 2 approximations:
NpmypBIC 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
|| 21ln
21ln
21
)|(),(
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
optimal model structure assumed to be identical across subjects?
FFX BMS RFX BMS
yes no
inference on parameters of an optimal model or parameters of all models?
BMA
definition of model space
FFX analysis of parameter estimates
(e.g. BPA)
RFX analysis of parameter estimates(e.g. t-test, ANOVA)
optimal model structure assumed to be identical across subjects?
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
Selection of model parameters of interest
one-sample t-test:
parameter > 0 ?
paired t-test: parameter 1 > parameter 2 ?
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?
comparison of model families using
FFX or RFX BMS
optimal model structure assumed to be identical across subjects?
FFX BMS RFX BMS
yes no
inference on parameters of an optimal model or parameters of all models?
BMA
definition of model space
FFX analysis of parameter estimates
(e.g. BPA)
RFX analysis of parameter estimates(e.g. t-test, ANOVA)
optimal model structure assumed to be identical across subjects?
FFX BMS
yes no
RFX BMS
Stephan et al. 2010, NeuroImage
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
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 )( )(
uxC
xx
uB
xxA
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
CuxDxBuAdtdx m
i
n
j
jj
ii
1 1
)()(CuxBuAdtdx m
i
ii
1
)(
Bilinear state equation:
driving input
modulation
driving input
modulationnon-linear DCM
...)0,(),(2
0
uxuxfu
ufx
xfxfuxf
dtdx
Two-dimensional Taylor series (around x0=0, u0=0):
Nonlinear state equation:
...2
)0,(),(2
2
22
0
x
xfux
uxfu
ufx
xfxfuxf
dtdx
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 1000
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
CuxDxBuAdtdx n
j
jj
m
i
ii
1
)(
1
)(
Nonlinear dynamic causal model (DCM)
Stephan et al. 2008, NeuroImage
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
0.390.26
0.50
0.26
0.10MAP = 1.25
Stephan et al. 2008, NeuroImage
uinput
Single-state DCM
1x
Intrinsic (within-region)
coupling
Extrinsic (between-region)
coupling
NNNN
N
ijijij
x
xx
uBACuxx
1
1
111
Two-state DCM
Ex1
IN
EN
I
E
IINN
IENN
EENN
EENN
EEN
IIIE
EEN
EIEE
ijijijij
xx
xx
x
uBA
Cuxx
1
1
1
1111
11111
000
000
)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
dx A u B x Cvdt
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
• Generative models & analysis options• Extended DCM for fMRI: nonlinear, two-state, stochastic • Embedding computational models in DCMs• Integrating tractography and DCM• Applications of DCM to clinical questions
Prediction errors drive synaptic plasticity
McLaren 1989
x1 x2
x3
PE(t)
01
t
t kk
w w PE
00
( )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(fa
ce)
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
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0.6
0.7
Categoricalmodel
Bayesianlearner
HMM (fixed) HMM (learn) Rescorla-Wagner
Exce
edan
ce p
rob.
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
(ms)
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
• Generative models & analysis options• Extended DCM for fMRI: nonlinear, two-state, stochastic • Embedding computational models in DCMs• Integrating tractography and DCM• Applications of DCM to clinical questions
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
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1m2: a=-16,b=-32
0 0.5 10
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1m3: a=-16,b=-28
0 0.5 10
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1m4: a=-12,b=-32
0 0.5 10
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1m5: a=-12,b=-28
0 0.5 10
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1m6: a=-12,b=-24
0 0.5 10
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1m7: a=-12,b=-20
0 0.5 10
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1m8: a=-8,b=-32
0 0.5 10
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1m9: a=-8,b=-28
0 0.5 10
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1m10: a=-8,b=-24
0 0.5 10
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1m11: a=-8,b=-20
0 0.5 10
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1m12: a=-8,b=-16
0 0.5 10
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1m13: a=-8,b=-12
0 0.5 10
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1m14: a=-4,b=-32
0 0.5 10
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1m15: a=-4,b=-28
0 0.5 10
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1m16: a=-4,b=-24
0 0.5 10
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1m17: a=-4,b=-20
0 0.5 10
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1m18: a=-4,b=-16
0 0.5 10
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1m19: a=-4,b=-12
0 0.5 10
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1m20: a=-4,b=-8
0 0.5 10
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1m21: a=-4,b=-4
0 0.5 10
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1m22: a=-4,b=0
0 0.5 10
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1m23: a=-4,b=4
0 0.5 10
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1m24: a=0,b=-32
0 0.5 10
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1m25: a=0,b=-28
0 0.5 10
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1m26: a=0,b=-24
0 0.5 10
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1m27: a=0,b=-20
0 0.5 10
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1m28: a=0,b=-16
0 0.5 10
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1m29: a=0,b=-12
0 0.5 10
0.5
1m30: a=0,b=-8
0 0.5 10
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1m31: a=0,b=-4
0 0.5 10
0.5
1m32: a=0,b=0
0 0.5 10
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1m33: a=0,b=4
0 0.5 10
0.5
1m34: a=0,b=8
0 0.5 10
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1m35: a=0,b=12
0 0.5 10
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1m36: a=0,b=16
0 0.5 10
0.5
1m37: a=0,b=20
0 0.5 10
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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
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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
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1m46: a=4,b=16
0 0.5 10
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1m47: a=4,b=20
0 0.5 10
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1m48: a=4,b=24
0 0.5 10
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1m49: a=4,b=28
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1m50: a=4,b=32
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1m51: a=8,b=12
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1m52: a=8,b=16
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1m53: a=8,b=20
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1m54: a=8,b=24
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1m55: a=8,b=28
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1m56: a=8,b=32
0 0.5 10
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1m57: a=12,b=20
0 0.5 10
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1m58: a=12,b=24
0 0.5 10
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1m59: a=12,b=28
0 0.5 10
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1m60: a=12,b=32
0 0.5 10
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1m61: a=16,b=28
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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
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grou
p B
ayes
fact
or
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Models with anatomically informed priors (of an intuitive form)
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1m1: a=-32,b=-32
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1m2: a=-16,b=-32
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1m3: a=-16,b=-28
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1m4: a=-12,b=-32
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1m5: a=-12,b=-28
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1m6: a=-12,b=-24
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1m7: a=-12,b=-20
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1m8: a=-8,b=-32
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1m9: a=-8,b=-28
0 0.5 10
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1m10: a=-8,b=-24
0 0.5 10
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1m11: a=-8,b=-20
0 0.5 10
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1m12: a=-8,b=-16
0 0.5 10
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1m13: a=-8,b=-12
0 0.5 10
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1m14: a=-4,b=-32
0 0.5 10
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1m15: a=-4,b=-28
0 0.5 10
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1m16: a=-4,b=-24
0 0.5 10
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1m17: a=-4,b=-20
0 0.5 10
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1m18: a=-4,b=-16
0 0.5 10
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1m19: a=-4,b=-12
0 0.5 10
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1m20: a=-4,b=-8
0 0.5 10
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1m21: a=-4,b=-4
0 0.5 10
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1m22: a=-4,b=0
0 0.5 10
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1m23: a=-4,b=4
0 0.5 10
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1m24: a=0,b=-32
0 0.5 10
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1m25: a=0,b=-28
0 0.5 10
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1m26: a=0,b=-24
0 0.5 10
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1m27: a=0,b=-20
0 0.5 10
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1m28: a=0,b=-16
0 0.5 10
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1m29: a=0,b=-12
0 0.5 10
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1m30: a=0,b=-8
0 0.5 10
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1m31: a=0,b=-4
0 0.5 10
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1m32: a=0,b=0
0 0.5 10
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1m33: a=0,b=4
0 0.5 10
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1m34: a=0,b=8
0 0.5 10
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1m35: a=0,b=12
0 0.5 10
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1m36: a=0,b=16
0 0.5 10
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1m37: a=0,b=20
0 0.5 10
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1m38: a=0,b=24
0 0.5 10
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1m39: a=0,b=28
0 0.5 10
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1m40: a=0,b=32
0 0.5 10
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1m41: a=4,b=-32
0 0.5 10
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1m42: a=4,b=0
0 0.5 10
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1m43: a=4,b=4
0 0.5 10
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1m44: a=4,b=8
0 0.5 10
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1m45: a=4,b=12
0 0.5 10
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1m46: a=4,b=16
0 0.5 10
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1m47: a=4,b=20
0 0.5 10
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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
• Generative models & analysis options• Extended DCM for fMRI: nonlinear, two-state, stochastic • Embedding computational models in DCMs• Integrating tractography and DCM• Applications of DCM to clinical questions
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 → BA → CB → BB → 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
Brodersen et al. 2011, PLoS Comput. Biol.
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
Brodersen et al. 2011, PLoS Comput. Biol.
MGB
PT
HG(A1)
MGB
PT
HG(A1)
auditory stimuli
-10
0
10
-0.50
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
-0.50
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
generative em
bedding
L.H
G
L.H
G
Voxe
l (64
,-24,
4) m
m
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 ROIsAre regions of interest definedanatomically or functionally?
anatomically functionally
Functional contrastsAre the functional contrasts defined
across all subjects or between groups?
1 ROI definitionand nmodel inversionsunbiased estimate
Repeat n times:1 ROI definition and nmodel inversionsunbiased estimate
1 ROI definition and nmodel inversionsslightly optimistic estimate:voxel selection for training set and test set based on test data
Repeat n times:1 ROI definition and 1 model inversionslightly optimistic estimate:voxel selection for training set based on test data and test labels
Repeat n times:1 ROI definition and nmodel inversionsunbiased estimate
1 ROI definition and nmodel inversionshighly optimistic estimate:voxel selection for training set and test set based on test data and test labels
across subjects
between groups
Brodersen et al. 2011, PLoS Comput. Biol.
Generative embedding for detecting patient subgroups
Brodersen et al. 2014, NeuroImage: Clinical
Generative embedding of variational Gaussian Mixture Models
Brodersen et al. 2014, NeuroImage: Clinical
• 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
Brodersen et al. 2014, NeuroImage: Clinical
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