Anatomical Background of Dynamic Causal Modeling and ... and its... · Anatomical Background of Dynamic Causal Modeling and Effective Connectivity Analyses Jakob Heinzle Translational

1

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


• 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

2

Anatomical connections define processinghierarchies


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


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


Vincent et al, Nature, 2007

Spontaneous

correlation

pattern

Evoked response

pattern:

eye movement task

Anatomical

connectivity

pattern

3

Tight link between functional and anatomical connectivity - human fMRI


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


- Directed influence, e.g. DCM, Transfer Entropy, Granger Causality


Outline





4

Why effective connectivity?


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


• 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


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

Synaptic strengths are context-sensitive: They depend on the spatio-temporal distribution of presynaptic inputs and post-synaptic events.

5

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






Outline

Dynamic causal modeling (DCM)


( , , )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


EEG, MEG fMRI

6

Nonlinear DCM for fMRI – neural model


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

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

Neu

ral p

opul

atio

n ac

tivity

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

fMR

I sig

nal c

hang

e (%

)

Stephan et al., Neuroimage, 2008Weights are constrained / reflect by anatomy

Hemodynamics DCM – forward model


0 2 4 6 8 10 12 14

0

0.2

0.4

0 2 4 6 8 10 12 14

0

0.5

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)


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


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

7

Conductance-based DCMs (for EEG)


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


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


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


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)


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

8

Examples for the use of DCM


• 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


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


anatomical probability

connection-specific priorsfor couplingparameters

Anatomically informed priors


0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

Posterior model probabilities


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

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

0.4

0.6

0.8

1

1.2

1.4

1.6

Models with anatomically informed priors were clearly superior :

Bayes Factor >109


9

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

0a

R

synaptic plasticity during learning = f (prediction error)

Learning of dynamic audio-visual associations


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


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

10

PE control plasticity during adaptive cognition


• 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?


“… essentially, all models are wrong,but some are useful.”

George E.P. Box

Strategies for model validation


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)

11

Dopaminergic modulation of AMPA/NMDA receptors


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


Moran et al., Curr Biol, 2011

Validating models against clinical facts


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

12

Summary


• 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


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.

Documents

Anatomical Background of Dynamic Causal Modeling and ... and its... · Anatomical Background of Dynamic Causal Modeling and Effective Connectivity Analyses Jakob Heinzle Translational