DCM Advanced, Part II
Will Penny (Klaas Stephan)
Wellcome Trust Centre for Neuroimaging
Institute of Neurology
University College London
SPM Course 2014 @ FIL
Overview
•Extended DCM for fMRI: nonlinear, two-state, stochastic
•Embedding computational models in DCMs
•Clinical Applications
endogenousconnectivity
direct inputs
modulation of
connectivity
Neural state equation
hemodynamic
model
λ
x
y
integration
BOLD
y
y
y
activity
x1(t)
activity
x2(t)
activity
x3(t)
neuronal
states
t
driving
input u1(t)
modulatory
input u2(t)
t
The classical DCM:
a deterministic, one-state,bilinear model
Factorial structure of model specification in DCM
•Three dimensions of model specification:
–bilinear vs. nonlinear
–single-state vs. two-state (per region)
–deterministic vs. stochastic
•Specification via GUI.
bilinear DCM
Bilinear state equation:
driving
input
modulation
driving
input
modulation
non-linear DCM
Two-dimensional Taylor series (around x0=0, u0=0):
Nonlinear state equation:
Neural population activity
fMRI signal change (%)
x1
x2
x3
Nonlinear dynamic causal model (DCM)
Stephan et al. 2008, NeuroImage
u1
u2
V1
V5
stim
PPC
attention
motion
1.25
0.13
0.46
0.39
0.26
0.50
0.26
0.10
MAP = 1.25
Stephan et al. 2008, NeuroImage
V1
V5
PPC
observed
fitted
motion &
attention
motion &
no attention
static
dots
input
Single-state DCM
Intrinsic(within-region)coupling
Extrinsic(between-region)coupling
Two-state DCM
Two-state DCM
Marreiros et al. 2008, NeuroImage
Estimates of hidden causes and states
(Generalised filtering)
Stochastic DCM
Li et al. 2011, NeuroImage
•random state fluctuations w(x) account forendogenous fluctuations,
•fluctuations w(v) induce uncertainty abouthow inputs influence neuronal activity
•can be fitted to resting state data
Estimates of hidden causes and states
(Generalised filtering)
Stochastic DCM
•Good working knowledge of dDCM
•sDCMs (esp. for nonlinear models) canhave richer dynamics than dDCM
•Model selection may be easier than withdDCM
•See Daunizeau et al. ‘sDCM: Should wecare about neuronal noise ?’,Neuroimage, 2012
Overview
•Extended DCM for fMRI: nonlinear, two-state, stochastic
•Embedding computational models in DCMs
•Clinical Applications
Learning of dynamic audio-visual associations
CS
Response
Time (ms)
0
200
400
600
800
2000±650
or
Target Stimulus
Conditioning Stimulus
or
TS
0
200
400
600
800
1000
0
0.2
0.4
0.6
0.8
1
p(face)
trial
CS
1
CS
2
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
Behrens et al. 2007, Nat. Neurosci.
prior on volatility
Explaining RTs by different learning models
400
440
480
520
560
600
0
0.2
0.4
0.6
0.8
1
Trial
p(F)
True
Bayes Vol
HMM fixed
HMM learn
RW
Bayesian model selection:
hierarchical Bayesian modelperforms 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
0.9
390
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
BOLD resp. (a.u.)
p(F)
p(H)
-2
-1.5
-1
-0.5
0
BOLD resp. (a.u.)
den Ouden et al. 2010, J. Neurosci .
Prediction error (PE) activity in the putamen
PE during
reinforcement learning
PE during incidental
sensory learning
O'Doherty et al. 2004,Science
den Ouden et al. 2009,Cerebral Cortex
Could the putamen be regulating trial-by-trial changes oftask-relevant connections?
Could the putamen be regulating trial-by-trial changes oftask-relevant connections?
PE = “teaching signal” forsynaptic plasticity duringlearning
PE = “teaching signal” forsynaptic plasticity duringlearning
p < 0.05(SVC)
PE during active
sensory learning
Prediction errors controlplasticity during adaptivecognition
•Modulation of visuo-motor connections bystriatal predictionerror activity
•Influence of visualareas on premotorcortex:
–stronger forsurprising stimuli
–weaker for expectedstimuli
den Ouden et al. 2010, J. Neurosci .
PPA
FFA
PMd
HierarchicalBayesianlearning model
PUT
p = 0.010
p = 0.017
Overview
•Extended DCM for fMRI: nonlinear, two-state, stochastic
•Embedding computational models in DCMs
•Clinical Applications
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-matchedcontrols
PD patients
on medication
PD patients
off 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 froman individual subject
subject-specificinverted generative model
subject representation in thegenerative score space
A → B
A → C
B → B
B → C
A
C
B
step 3 —
support vector classification
separating hyperplane fitted todiscriminate between groups
A
C
B
jointly discriminative
model parameters
step 4 —
interpretation
Model-based decoding of disease status:mildly aphasic patients (N=11) vs. controls (N=26)
Connectional fingerprintsfrom a 6-region DCM ofauditory areas during speechperception
Brodersen et al. 2011, PLoS Comput. Biol.
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
Multivariate searchlight
classification analysis
Generative embedding
using DCM
Summary
•Model Selection
•Extended DCM for fMRI: nonlinear, two-state, stochastic
•Embedding computational models in DCMs
•Clinical Applications