Dynamic Causal Modelling DCM: Applications

1
Dynamic Causal Modelling (DCM) Applications

• Klaas Enno Stephan Functional Imaging Lab
• Wellcome Dept. of Imaging Neuroscience
• University College London
• k.stephan_at_fil.ion.ucl.ac.uk

Connectivity Workshop, Melbourne17 February 2005
2
Overview

• Refresher DCM in a nutshell
• Practical steps of a DCM study
• Example 1 attention to visual motion
• Example 2 interhemispheric interactions
• Getting connectivity data CoCoMac

3
Conceptual overview
Neural state equation
The bilinear model
effective connectivity
modulation of connectivity
Input u(t)
direct inputs
c1
b23
integration
neuronal states
a12
activity z2(t)
activity z3(t)
activity z1(t)
hemodynamic model
y
y
y
BOLD
Friston et al.,NeuroImage 2003
4
stimulus function u
Overviewparameter estimation
neural state equation

• Combining the neural and hemodynamic states gives
  the complete forward model.
• An observation model includes measurement error
  e and confounds X (e.g. drift).
• Bayesian parameter estimation by means of a
  Levenberg-Marquardt gradient ascent, embedded
  into an EM algorithm.
• ResultGaussian a posteriori parameter
  distributions, characterised by mean ??y and
  covariance C?y.

parameters
hidden states
state equation
observation model
modelled BOLD response
5
Overview

• Refresher DCM in a nutshell
• Practical steps of a DCM study
• Example 1 attention to visual motion
• Example 2 interhemispheric interactions
• Getting connectivity data CoCoMac

6
The DCM cycle
Hypothesis abouta neural system
Statistical test on parameters of optimal model
Definition of DCMs as systemmodels
Bayesian modelselection of optimal DCM
Design a study thatallows to investigatethat
system
Parameter estimationfor all DCMs considered
Data acquisition
Extraction of time seriesfrom SPMs
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Planning a DCM-compatible study

• Suitable experimental design
• preferably multi-factorial (e.g. 2 x 2)
• e.g. one factor that varies the driving (sensory)
  input
• and one factor that varies the contextual input
• TR
• as short as possible (optimal lt 2 s)
• Hypothesis and model
• define specific a priori hypothesis
• which parameters are relevant to test this
  hypothesis?
• ensure that intended model is suitable to test
  this hypothesis ? simulations before experiment
• define criteria for inference

8
Timing problems at long TRs

• Two potential timing problems in DCM
• wrong timing of inputs
• temporal shift between regional time series
  because of multi-slice acquisition

2
slice acquisition
1
visualinput

• DCM is robust against timing errors up to approx.
  1 s
• compensatory changes of s and ?h
• Possible corrections
• slice-timing (not for long TRs)
• restriction of the model to neighbouring regions
• in both cases adjust temporal reference bin in
  SPM defaults (defaults.stats.fmri.t0)

9
Practical steps of a DCM study - I

• Conventional SPM analysis (subject-specific)
• DCMs are fitted separately for each session ?
  consider concatenation of sessions or adequate
  2nd level analysis
• Definition of the model (on paper!)
• Structure which areas, connections and inputs?
• Which parameters represent my hypothesis?
• How can I demonstrate the specificity of my
  results?
• What are the alternative models to test?
• Defining criteria for inference
• single-subject analysis stat. threshold?
  contrast?
• group analysis which 2nd-level model?

10
Practical steps of a DCM study - II

• Extraction of time series, e.g. via VOI tool in
  SPM
• cave anatomical functional standardisation
  important for group analyses!
• Possibly definition of a new design matrix, if
  the normal design matrix does not represent the
  inputs appropriately.
• NB DCM only reads timing information of each
  input from the design matrix, no parameter
  estimation necessary.
• Definition of model
• via DCM-GUI or directlyin MATLAB

11
Practical steps of a DCM study - III

• DCM parameter estimation
• cave models with many regions scans can crash
  MATLAB!
• Model comparison and selection
• Which of all models considered is the optimal
  one?? Bayesian model selection tool
• Testing the hypothesis Statistical test onthe
  relevant parametersof the optimal model

12
Overview

• Refresher DCM in a nutshell
• Practical steps of a DCM study
• Example 1 attention to visual motion
• Example 2 interhemispheric interactions
• Getting connectivity data CoCoMac

13
Attention to motion in the visual system
Stimuli 250 radially moving dots at 4.7
degrees/s Pre-Scanning 5 x 30s trials with 5
speed changes (reducing to 1) Task - detect
change in radial velocity Scanning (no speed
changes) 6 normal subjects, 4 x 100 scan
sessions each session comprising 10 scans of 4
different conditions F A F N F A F N S
................. F - fixation point only A -
motion stimuli with attention (detect changes) N
- motion stimuli without attention S - no motion
PPC
V3A
V5
Attention No attention
Büchel Friston 1997, Cereb. Cortex Büchel et
al. 1998, Brain
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A simple DCM of the visual system
Attention

• Visual inputs drive V1, activity then spreads to
  hierarchically arranged visual areas.
• Motion modulates the strength of the V1?V5
  forward connection.
• The intrinsic connection V1?V5 is insignificant
  in the absence of motion (a21-0.05).
• Attention increases the backward-connections
  IFG?SPC and SPC?V5.

0.55
0.26
0.72
0.37
0.56
0.42
Motion
0.66
0.88
-0.05
Photic
0.48
Re-analysis of data fromFriston et al.,
NeuroImage 2003
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Comparison of three simple models
Model 1attentional modulationof V1?V5
Model 2attentional modulationof SPC?V5
Model 3attentional modulationof V1?V5 and
SPC?V5
Attention
Attention
Photic
Photic
Photic
SPC
0.55
0.03
0.85
0.86
0.85
0.70
0.75
0.70
0.84
1.36
1.42
1.36
0.89
0.85
V1
-0.02
-0.02
-0.02
0.56
0.57
0.57
V5
Motion
Motion
Motion
0.23
0.23
Attention
Attention
Bayesian model selection Model 1 better than
model 2, model 1 and model 3 equal ?
Decision for model 1 in this experiment,
attention primarily modulates V1?V5
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DCM
Neurophysiology
Modelling with DCM bottom-up gain control
effects
V5

V1
V1
bottom-up- effect
Depending on the nature of the contextual factor,
modulation of a forward-connection can both
represent bottom-up- and top-down-effects.
MOT
VIS STIM
ATT_MOT
X
top-down- effect (gain control)
V5

V1
V1
VIS STIM
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Modellingwith DCM baseline shifts
A
B
C
ATT_MOT
ATT_MOT
ATT_GEN
ATT_MOT
c23
c22
Model Atests the existence of a baseline shift
(BS) under ATT_MOT in V5Hypothesis c22gt ?
Model Btests whether there is a BS under
ATT_MOT in SPC that is conveyed to V5 via the
backward connectionHypothesis c23gt ?1, a23gt
?2 Model C tests whether a general attentional
BS occurs in SPC that is conveyed to V5 via the
backward connection during ATT_MOTHypothesis
b223gt?
SPC
SPC
a23
b223
V5
V5
V5
V1
V1
V1
VIS STIM
VIS STIM
VIS STIM
VIS STIM visual stimuli (u1) ATT_MOT
attention to motion (u2) ATT_GEN general
attention of arbitrary modality (u3) ? chosen
statistical threshold
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DCM
Neurophysiology
Physio-physiologicalinteractions in DCM
X
ATT_MOT
V5

The parameter estimation scheme can currently not
deal with physio-physiologicalinteractions. This
will be implemented in the near future, however.
V1
Psycho-physiologicalinteraction bilinear
effect
V1
VIS STIM
SPC
Physio-physiologicalinteraction quadratic
effect
V5

V1
V1
VIS STIM
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Overview

• Refresher DCM in a nutshell
• Practical steps of a DCM study
• Example 1 attention to visual motion
• Example 2 interhemispheric interactions
• Getting connectivity data CoCoMac

20
Callosal connectivity

• There appear to be fairly general rules for the
  anatomical connectivity of the corpus callosum
• homotopic regions always seem to be connected
  (exception parts of V1 representing the
  peripheral VF)
• callosal connections mirror the intra-hemispheric
  connections(Cavada Goldman-Rakic 1989)
• tight integration with intra-hemispheric
  connections(McGuire et al. 1991)
• mirror-symmetric point-to-point connections in
  the visual system(Abel et al. 2000)
• The functional roles of callosal connections are
  quite diverse
• information transfer
• competition mutual inhibition
• transcallosal inhibition in the motor system
• inter-hemispheric competition in spatial
  attention
• complexity-dependent processing mode setting,
  particularly during selective attention (Banich)

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Experimental design
Letter decisions Does the word contain the
letter A or not?
time
Visuospatial decisions Is the red letter left or
right from the midline of the word?
Reaction time task (baseline) Press button as
quickly as possible when stimulus appears.
extrafoveal (6) dur. 150 ms SOA 1,5-2,5
s size 2.3 x 10
left vs. right visual field
left vs. rightresponse hand
task
2 x 3 x 2
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Main effectof task
Does the word contain the letter A or not?
letter decisions gt spatial decisions
group analysis (random effects),n16, plt0.05
corrected analysis with SPM2
time
Is the red letter left or right from the midline
of the word?
spatial decisions gt letter decisions
Stephan et al., Science 2003
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Inter-hemispheric interactions in the ventral
stream of the visual system

• What experimental factors modulate transcallosal
  connectivity?
• task?
• visual field?
• task conditional on visual field?
• task and visual field, independently?
• Are these modulations symmetric or asymmetric?
• Is this modulation equally present for all visual
  areas involved in the letter decision task?

word in LVF
wordin RVF
left fusiform gyrus (FG)
rightlingualgyrus(LG)
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Predictions
Information transfer(left-lateralised task)
Inhibition/Competition
Processing mode setting
T
T
TRVF
-

??

-

TLVF
T
T
LVF
RVF
Predictions modulation by task conditional on
visual field asymmetric connection strengths
Predictions modulation by task only negative
symmetricconnection strengths
Predictions modulation by task only positive
symmetricconnection strengths
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Procedure for this study

• Derive a set of 16 competing models from the
  systematic combination of experimental factors as
  modulators of connection strengths in the visual
  system.
• Select subject-specific time series from the
  individual SPMs (see below).
• Fit all 16 DCMs to data from each subject.
• Across subjects, find the optimal model using
  Bayesian model selection.
• 2nd level analysis of the parameters from the
  optimal model
• Which parameters are consistently larger than
  zero across subjects?
• Are modulatory effects on callosal connections
  symmetric or asymmetric?
• Is this modulation present for any pair of
  homotopic areas?

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A
C
VF
RVF
LVF
LD
LD
LD
Bind
LD,RVF
LD,LVF
Bcond
LDRVF
LDLVF
RVF stim.
LVF stim.
B
VF
LD
Bind
Bcond
D
LD
LVF
LD
LVF
LDLVF
RVF
RVF
LDRVF
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Selection of anatomically functionally
standardised time series

• maxima of random effects group analysis as
  starting points
• choose closest subject-specific local maximum (at
  plt0.05 uncorrected) within 2?FWHM 16 mm
• anatomical functional constraints
• maximum within the same gyrus
• LG probability of maximum in V2 ?? 0.4
  (according to probabilistic cytoarchitectonic
  atlas)
• LG VF-specific response (masking with VF
  contrast)

12 out of 16 subjects fulfill all criteriafor
all areas
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Bayesian model selection

• For each of S12 subjects, Bayesian model
  comparison of all M16 models? subject- and
  model-specific Bayes factors (BFs).
• Subject-specific models are independent from each
  other. For any given model i, the average Bayes
  factor across subjects is
• The optimal model was Bcond-LD, i.e.
• modulation of callosal connections by LD
  conditional on VF
• modulation of intra-hemispheric connections by LD
• Subject-specific BFs for comparing Bcond-LD vs.
  all other models

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Ventral stream letter decisionsBcond-LD model
(4 areas)
LDLVF
Right FG 38,-52,-20
Left FG -44,-52,-18
0.24 ? 0.13
0.12 ? 0.09
LD
LD
plt0.001 uncorrected
plt0.01 uncorrected
0.35 ? 0.23
0.17 ? 0.19
Left LG -12,-64,-4
Right LG 14,-68,-2
0.03 ? 0.09
0.02 ? 0.06
RVF stim.
LVF stim.
LDRVF
mean parameter estimates ? SD (n12)
plt0.001 unc., masked incl. by RVFgtLVF at plt0.05
unc.
plt0.001 unc., masked incl. by LVFgtRVF at plt0.05
unc.
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Ventral stream letter decisionsBcond-LD model
(6 areas)
Left MOG -38,-90,-4
Right MOG -38,-94,0
LDLVF
0.19 ? 0.13
0.00 ? 0.04
0.08 ? 0.06
plt0.001 uncorrected
plt0.01 uncorrected
0.24 ? 0.19
0.08 ? 0.15
LD
LD
0.02 ? 0.09
-0.01 ? 0.15
0.01 ? 0.02
0.05 ? 0.08
0.01 ? 0.02
RVF stim.
LVF stim.
LDRVF
mean parameter estimates ? SD (n12)
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Dorsal stream spatial decisionsSD-SD model (6
areas)
Right PPC 22,-74,58
Right OPC 40,-80,-36
Left PPC -22,-74,58
SD
mean parameter estimates ? SD (n12)
Left OPC -44,-74,-42
0.09 ? 0.09
0.02 ? 0.04
plt0.001 uncorrected
0.06 ? 0.15
0.10 ? 0.09
SD
SD
0.05 ? 0.08
-0.04 ? 0.09
Left V1 -12,-96,4
Right V1 18,-96,12
0.06 ? 0.07
0.00 ? 0.05
RVF stim.
LVF stim.
SD
RVFgtLVF, plt0.001 unc., masked excl. by LDgtSD at
plt0.05 unc.
LVFgtRVF, plt0.001 unc., masked excl. by LDgtSD at
plt0.05 unc.
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Summary

• The functional role of callosal connections in
  the visual system depends on the neural system
  and the cognitive context.
• Ventral stream letter decision task
• callosal connections depend on task and VF
• asymmetric information transfer from non-dominant
  to dominant hemisphere
• Dorsal stream spatial decision task
• task-dependent symmetric increase in
  interhemispheric coupling
• consistent with Banich's hypothesis on
  complexity-dependent processing mode setting

33
Overview

• Refresher DCM in a nutshell
• Practical steps of a DCM study
• Example 1 attention to visual motion
• Example 2 interhemispheric interactions
• Getting connectivity data CoCoMac

34
CoCoMac Collection of Connectivity data on the
Macaque brain

• Relational database of published tract tracing
  studies on anatomical connectivity of the Macaque
  brain
• Public access via web interface www.cocomac.org
• Uses Objective Relational Transformation (ORT)
  for coordinate-independent mapping
• Currently contains
• 37,000 individual descriptions of connections
  from
• 2,500 experiments described in
• 390 papers
• Use of CoCoMac
• Statistical analyses of connectivity patterns
• Basis for neurobiologically realistic network
  models, e.g. DCM

35
Connectional fingerprints

• Cortical areas have unique anatomical
  connectivity patterns
• but form families (clusters) with similar
  patterns.
• Similar constellations were found for functional
  connectivity and electrophysiological response
  patterns obtained from experiments in the Macaque
  brain.

Connectivity is the major anatomical constraint
for the formation of context-specific ensembles
in the brain.
Passingham, Stephan Kötter,Nat. Rev. Neurosci.
2002
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Cortical functional connectivity shows small
world properties
Small world networks (SWNs)Lreal?Lrnd and
CrealgtgtCrnd ? local specialisation and global
integration.
Analysis of functional connectivity data from
CoCoMac demonstrates that Macaque cortex has SWN
properties
Stephan et al., Phil. Trans. B 2000
37
CoCoMac DCM

• DCM requires that one specifies a system model in
  terms of
• the experimental perturbation (inputs) ? design
  matrix
• time series of system elements ?? extracted from
  SPMs
• connectivity of the system
• Data on human connectivity is very sparse ?
  inference from primate data often necessary
• CoCoMac can serve as a powerful tool to search
  for primate connectivity data ? online
  demonstration

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Many thanks to my colleagues
DCM Karl Friston Lee Harrison Will Penny
fMRI experiment Gereon Fink John Marshall Afra
Ritzl James Rowe Karl Zilles
CoCoMac Rolf Kötter Malcolm Young
Supported by the Wellcome Trust.