Anatomical Background of Dynamic Causal Modeling and ... and its... · Anatomical Background of...
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Anatomical Background of Dynamic Causal Modeling and Effective
Connectivity Analyses
Jakob Heinzle
Translational Neuromodeling Unit (TNU),Institute for Biomedical Engineering
University and ETH Zürich
HBM 2014, Educational Course: Anatomy
Anatomical Background for DCM 2
• Relation between structure and function
• Effective connectivity
• Dynamic causal modeling (DCM)
Outline
Connectional fingerprints determine local function
Anatomical Background for DCM 3
• Unique anatomical connectivity patterns (connectional fingerprints) for cortical areas
• “Families” of cortical areas (clusters) with similar patterns
• Analogous results for electrophysio-logical response patterns
Anatomical connectivity is the major determinant for the response profile of neuronal ensembles.
Passingham et al., Nat Rev Neurosci, 2002
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Anatomical connections define processinghierarchies
Anatomical Background for DCM 4
Felleman & Van Essen, Cereb Cortex, 1991
Hilgetag et al, Phil Trans. B, 2000
Markov & Kennedy, TICS, 2014
Literature based database: http://cocomac.g-node.org/Stephan et al., Phil. Trans. B, 2001;
Kötter, Neuroinformatics, 2004
Weighted and directed connectivity matrix in macaque
Anatomical Background for DCM 5
Fraction of labeled neurons per area weightMarkov et al., Cereb Cortex, 2012; J Comp Neurol 2014;
Fro
ma
rea
To area
Activation, intrinsic functional connectivityand anatomy
Anatomical Background for DCM 6
Vincent et al, Nature, 2007
Spontaneous
correlation
pattern
Evoked response
pattern:
eye movement task
Anatomical
connectivity
pattern
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Tight link between functional and anatomical connectivity - human fMRI
Anatomical Background for DCM 7
Intrinsic functional connectivity in humans is visuotopicallyorganized matches monkey anatomy!
Heinzle et al, Neuroimage, 2011
Average CCRF
Some naming conventions
• Anatomical connectivity
- Fibre bundles, Close Contacts, Synapses
• Functional connectivity
- Statistical relation, e.g. Correlation, Mutual information
• Effective connectivity
- Directed influence, e.g. DCM, Transfer Entropy, Granger Causality
Anatomical Background for DCM 8
Outline
• Relation between structure and function
• Effective connectivity
• Dynamic causal modeling (DCM)
Anatomical Background for DCM 9
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Why effective connectivity?
Anatomical Background for DCM 10
Anatomical connectivity is critical for understanding brainfunction …
… but not sufficient on its own.
Functional connections synapses
Context dependent modulation of connection strengths, synaptic plasticity, neuronal adaptation mechanisms, etc. …
Synaptic connections show plasticity
Anatomical Background for DCM 11
• Numerous mechanisms at different time scales(ms to days) incl. very rapid changes!
• Regulated in several ways (e.g. modulatoryeffects of DA)
Reynolds et al., Nature, 2001
peak
PS
P (
mV
)
Matsuzaki et al., Nature, 2004
Connections are recruited in a context-dependent fashion
Anatomical Background for DCM 12
0 10 20 30 40 50 60 70 80 90 100
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Synaptic strengths are context-sensitive: They depend on the spatio-temporal distribution of presynaptic inputs and post-synaptic events.
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To understand brain (dys)function ...
… we need models of effective connectivity that:
• incorporate anatomical and physiological principles
• connect these to computational mechanisms
• allow for inference on neuronal mechanisms (e.g., synaptic plasticity) from measured brain responses
Anatomical Background for DCM 13
Anatomical Background for DCM 14
• Relation between structure and function
• Effective connectivity
• Dynamic causal modeling (DCM)
Outline
Dynamic causal modeling (DCM)
Anatomical Background for DCM 15
( , , )dx
f x udt
),(xgy
Model inversion:
Estimating neuronal mechanisms from brain
activity measures
Forward model:
Predicting measured activity given a putative
neuronal state
David et al., Neuroimage, 2006
Moran et al., NeuroImage, 2008
Friston et al., Neuroimage, 2003
Stephan et al., Neuroimage, 2008
Stephan et al., Neuroimage, 2010
EEG, MEG fMRI
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Nonlinear DCM for fMRI – neural model
Anatomical Background for DCM 16
x1 x2
x3
CuxDxBuAdt
dx n
j
jj
m
i
ii
1
)(
1
)(
u1
u2
0 10 20 30 40 50 60 70 80 90 100
0
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0 10 20 30 40 50 60 70 80 90 100
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Neu
ral p
opul
atio
n ac
tivity
0 10 20 30 40 50 60 70 80 90 100
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1
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0 10 20 30 40 50 60 70 80 90 100-1
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fMR
I sig
nal c
hang
e (%
)
Stephan et al., Neuroimage, 2008Weights are constrained / reflect by anatomy
Hemodynamics DCM – forward model
Anatomical Background for DCM 17
0 2 4 6 8 10 12 14
0
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0 2 4 6 8 10 12 14
0
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1
0 2 4 6 8 10 12 14
-0.6
-0.4
-0.2
0
0.2
RBMN, = 0.5
CBMN, = 0.5
RBMN, = 1
CBMN, = 1
RBMN, = 2
CBMN, = 2
sf
tionflow induc
(rCBF)
s
v
stimulus functions
v
q q/vvEf,EEfqτ /α
dHbchanges in
100 )( /αvfvτ
volumechanges in
1
f
q
)1(
fγsxs
signalryvasodilato
u
s
CuxBuAdt
dx m
j
jj
1
)(
t
neural state
equation
1
3.4
111),(
3
002
001
32100
k
TEErk
TEEk
vkv
qkqkV
S
Svq
hemodynamic
state equations f
Balloon model
BOLD signal change equation Stephan et al., Neuroimage, 2007
Conductance-based DCMs (for EEG)
Anatomical Background for DCM 18
pyramidal cells
pyramidal cells
spiny stellate
cells
inhibitory interneurons
pyramidal cells
( )1,3
E ( )3 ,1
E
( )2 ,3
E
( )3 ,2
I
(1) (1) (1) (1) (1) (1)
(1) ( ) (3) (3) (1)1,3
(1) ( ) (2) (2) (1)1,2
( ) ( ) ( )
( ( , ) )
( ( , ) )
L L E E I I V
EE E V R E E
EI I V R I I
CV g V V g V V g V V u
g V g
g V g
(2) ( ) (3) (3) (2)2,3
(2) ( ) (3) (3) (2)2,3
( ( , ) )
( ( , ) )
EE E V R E E
INMDA NMDA V R NMDA NMDA
g V g
g V g
VEMgNMDAEELL VVVfgVVgVVgVC ))(()()( )2()2()2()2()2()2(
(3) ( ) (1) (1) (3)3,1
(3) ( ) (2) (2) (3)3,2
(3) ( ) (1) (1) (3)3,1
( ( , ) )
( ( , ) )
( ( , ) )
EE E V R E E
II I V R I I
INMDA NMDA V R NMDA NMDA
g V g
g V g
g V g
VEMgNMDAIIEELL VVVfgVVgVVgVVgVC ))(()()()( )3()3()3()3()3()3()3()3(
( )1,2
I
Marreiros et al., Neuroimage, 2010Moran et al., Neuroimage, 2011
0i i iCV g V V
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Conductance-based DCMs (for EEG)
Anatomical Background for DCM 19
pyramidal cells
pyramidal cells
spiny stellate
cells
inhibitory interneurons
pyramidal cells
( )1,3
E ( )3 ,1
E
( )2 ,3
E
( )3 ,2
I
(1) (1) (1) (1) (1) (1)
(1) ( ) (3) (3) (1)1,3
(1) ( ) (2) (2) (1)1,2
( ) ( ) ( )
( ( , ) )
( ( , ) )
L L E E I I V
EE E V R E E
EI I V R I I
CV g V V g V V g V V u
g V g
g V g
(2) ( ) (3) (3) (2)2,3
(2) ( ) (3) (3) (2)2,3
( ( , ) )
( ( , ) )
EE E V R E E
INMDA NMDA V R NMDA NMDA
g V g
g V g
VEMgNMDAEELL VVVfgVVgVVgVC ))(()()( )2()2()2()2()2()2(
(3) ( ) (1) (1) (3)3,1
(3) ( ) (2) (2) (3)3,2
(3) ( ) (1) (1) (3)3,1
( ( , ) )
( ( , ) )
( ( , ) )
EE E V R E E
II I V R I I
INMDA NMDA V R NMDA NMDA
g V g
g V g
g V g
VEMgNMDAIIEELL VVVfgVVgVVgVVgVC ))(()()()( )3()3()3()3()3()3()3()3(
( )1,2
I
Marreiros et al., Neuroimage, 2010Moran et al., Neuroimage, 2011
0i i iCV g V V
Weights are constrained by anatomy
Generative models, model selection andmodel validation
Anatomical Background for DCM 20
Any given DCM = a particular generative model of how the measureddata (may) have been caused
Model selection = hypothesis testing = comparing competing models(i.e. different ideas about mechanisms underlying observed data)
Evaluate the relative plausibility of competing explanations for an established effect (e.g., activation)
Careful definition of model (hypothesis) space crucial!
Model validation requires external criteria (external to the measureddata)
model selection model validation!
Bayesian model selection (BMS)
Anatomical Background for DCM 21
log ( | ) log ( | , )
, |
, | ,
p y m p y m
KL q p m
KL q p y m
Model evidence:
accounts for both accuracy and complexity of the model
a measure of how well the model generalizes
all possible datasets
y
p(y|
m)
Gharamani, 2004
McKay, Neural Comp, 1992
Penny et al., Neuroimage, 2004
( | ) ( | , ) ( | ) p y m p y m p m d
Various approximations, e.g.:- negative free energy, AIC, BIC
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Examples for the use of DCM
Anatomical Background for DCM 22
• Anatomical priors for DCM for fMRI
• Modulation of connectivity by predictionerrors
• Conductance based DCM
• if time permits: DCM validation in patientsor layered DCM
Anatomically informed priors
Anatomical Background for DCM 23
LG LG
FGFG
DCM
LGleft
LGright
FGright
FGleft
13 15.7%
34 6.5%
24 43.6%
12 34.2%
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
Stephan et al., Neuroimage, 2009
anatomical probability
connection-specific priorsfor couplingparameters
Anatomically informed priors
Anatomical Background for DCM 24
0 10 20 30 40 50 600
0.1
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Posterior model probabilities
Stephan et al., Neuroimage, 2009
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
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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
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
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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
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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
anatomical probability
prio
r va
rianc
e
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
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0.6
0.8
1
1.2
1.4
1.6
Models with anatomically informed priors were clearly superior :
Bayes Factor >109
Stephan et al., Neuroimage, 2009
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Prediction errors drive synaptic plasticity
Anatomical Background for DCM 25
McLaren 1989 x1 x2
x3
PE(t)
01
t
t kk
w w PE
0
0
( )t
tw a PE d
0a
R
synaptic plasticity during learning = f (prediction error)
Learning of dynamic audio-visual associations
Anatomical Background for DCM 26
den Ouden et al., J Neurosci, 2010
Model behavior with a hierarchicalBayesian Model estimate ofprediction errors PE(Behrens et al., Nat Neurosci, 2007)
Prediction error (PE) activity in the putamen
Anatomical Background for DCM 27
PE duringRF learning
PE during incidentalsensory learning
O'Doherty et al., Science, 2004
den Ouden et al., Cereb Cortex, 2009
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 duringactive sensory
learning
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PE control plasticity during adaptive cognition
Anatomical Background for DCM 28
• Influence of visual areas on premotor cortex:– stronger for
surprising stimuli
– weaker for expected stimuli
den Ouden et al., J Neurosci, 2010
PPA FFA
PMd
Hierarchical Bayesian learning model
PUT
p = 0.010 p = 0.017
ongoing pharmacologicaland genetic studies
What is a good model?
Anatomical Background for DCM 29
“… essentially, all models are wrong,but some are useful.”
George E.P. Box
Strategies for model validation
Anatomical Background for DCM 30
numerical analysis & simulation studies
clinical facts
experimentally controlled system perturbations
in silico
animals &humans
patients
experiments of knowncognitive/neurophys. processes
humans
Examples: Validation ofDCM in animal studies:
• infers site of seizure origin(David et al. 2008)
• infers primary recipient ofvagal nerve stimulation (Reytet al. 2010)
• infers synaptic changes aspredicted by microdialysis(Moran et al. 2008)
• infers fear conditioninginduced plasticity in amygdala (Moran et al. 2009)
• tracks anaesthesia levels(Moran et al. 2011)
• predicts sensory stimulation(Brodersen et al. 2010)
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Dopaminergic modulation of AMPA/NMDA receptors
Anatomical Background for DCM 31
Moran et al., Curr Biol, 2011
• exogenousinputs to layer IV
• NMDA inputs tolayer III pyramidal cells andinterneurons
a AMPA NMDA GABA
Estimates of AMPA/NMDA correlate with behaviour
Anatomical Background for DCM 32
Moran et al., Curr Biol, 2011
Validating models against clinical facts
Anatomical Background for DCM 33
model of neuronal (patho)physiology individual diagnosis
individual therapeutic response
individual outcomepredicting
Brodersen et al., PLoS Comp Biol, 2011;Brodersen et al, Neuroimage Clin. 2013
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Summary
Anatomical Background for DCM 34
• Anatomical connectivity information is important, but not everything
• Models of effective connectivity neural system mechanisms can beinferred from neuroimaging data
• DCM is one (not the only) method for this:
– Neuronal interactions are modeled at the hidden neuronal level
– Bayesian system identification method
– Key role for model selection
– Can be integrated with measures of anatomical connectivity
– Can be integrated with computational models
• Validation is critical (for any modeling approach)
Acknowledgments
Anatomical Background for DCM 35
TNU-TeamE. AponteT. BaumgartnerD. ColeA. DiaconescuS. GrässliH. Haker RösslerQ. HuysS. IglesiasL. KasperE. LomakinaC. Mathys
S. PaliwalF. PetzschnerS. PrinczS. RamanD. RenzG. StefanicsK.E. StephanL. WeberT. WentzS. Wilde
Translational Neuromodeling Unit
CollaboratorsJ.-D. Haynes, BerlinT. Kahnt, ChicagoH. den Ouden, NijmegenP. Koopmans, OxfordK.A.C. Martin, Zürich
Many thanks to K.E. Stephan for sharing slides.