Tor D' Wager

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Functional connectivityand path models

• Tor D. Wager
• Columbia University

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Functional Connectivity
Human brain mapping has been primarily used to
provide maps that show which regions of the brain
are activated by specific tasks.
Recently, there has been an increased interest in
augmenting this type of analysis by functional
connectivity studies which describe how the
various regions interact and how these
interactions depend on experimental conditions.
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A network?

• Current fashion to call any set of regions
  activated in a task a network
• But what does it mean to be a network?
• Set of interconnected regions information
  transfer among regions

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Connectivity
Functional Connectivity Undirected
association between two or more fMRI time series
Effective Connectivity Directed influence of
one brain region on the physiological activity
recorded in other brain regions
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Functional Connectivity
Functional connectivity analysis is usually
performed using data-driven methods which make
few assumptions about the underlying biology.

• Methods
• Seed analyses
• Psychophysiological interaction analyses
• Eigenimage analysis (PCA)
• Independent Components Analysis
• Partial Least Squares

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Effective Connectivity
Effective connectivity analysis is performed
using statistical models which make anatomically
motivated assumptions and restricts inference to
networks comprising of a number of pre-selected
regions of interest.
These methods are hypothesis driven rather than
data-driven and most applicable when it is
possible to specify a complete set of the
relevant functional areas.

• Methods
• Structural Equation Modeling
• Dynamic Causal Modeling

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Connectivity Levels of analysis
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Levels of analysisTypes of inference
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Levels of analysisTypes of inference
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Types of connectivity

• Simple functional connectivity
• Two regions, A B Seed analysis
• Pathways mediation
• Interactions moderation/modulation
• psychophysiological interactions
• Granger causality
• More complex structural equation models DCM

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Functional connectivity
A
B

• Simple functional connectivity
• Region A is correlated with Region B
• Provides information about relationships among
  regions
• Can specify a seed region and search for voxels
  with correlated data
• Can be performed on timeseries data within a
  subject, or individual differences (contrast
  maps, one per subject)

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Timeseries connectivity Simple analysis strategy
Brain
Heart rate
r
Z
Subj 1
r
Z
Subj 2
r
Z
Subj 3
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Correlations between brain activity and
heart-rate increases
Timeseries connectivity analysis Does VMPFC
correlate with heart rate? Yes VMPFC is the
strongest positively-correlated region.
Time (TRs, 2 s)
Threshold p lt .005
Display subjects randomly with respect to
brain-heart connectivity
Average within-subject correlation (r)
Six subjects out of 24 selected at random for
display
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Issue with timeseries connectivity

• Different hemodynamic lag in different regions
• Timeseries from different regions may not match
  up, even if neural activity pattern does match up
• If lags are estimated from data, temporal order
  may be caused by vascular (uninteresting) or
  neural (interesting) response

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Temporal relationship of VMPFC and heart
Are VMPFC changes associated with autonomic
control or feedback? VMPFC changes precede
changes in heart rate, implicating it in control.
Pos Heart earlier
Neg Brain earlier
Regions showing significant lag
Blue Brain precedes heart Red Heart precedes
brain
MPFC precedes heart autonomic control
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Mediation
A
B
M

• Mediation (Baron Kenny, 1986 Shrout Bolger,
  2003)
• The relationship between regions A and B is
  mediated by M
• Can identify functional pathways spanning gt 2
  regions
• Can be performed on timeseries data within a
  subject, or individual differences (contrast
  maps, one per subject)
• Also Test of whether task-related activations in
  B are mediated, or explained, by M.

Task
B
M
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Moderation/Modulation
A
M
B

• Moderation (Baron Kenny, 1986)
• The relationship between regions A and B is
  moderated by M
• Connectivity between A and B depends on state
  (level) of M
• Can be performed on timeseries data within a
  subject, or individual differences (contrast
  maps, one per subject)
• M can be task state or other variable (e.g.,
  prefrontal cortex, PFC)
• In SPM, on timeseries data Psychophysiological
  interaction (PPI)

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Timeseries connectivity Simple analysis strategy
Brain
Heart rate
r
Z
Subj 1
r
Z
Subj 2
r
Z
Subj 3
Task modulation of connectivity brain x task
state (green - red, rest - speech prep) For each
subject bB,H green - bB,H red
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Task-modulated connectivity
Are VMPFC - Heart Rate correlations stronger
during speech preparation than baseline?
Red Stronger correlation during speech
T-value for Speech - Baseline
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Granger Causality
A
B

• Directional connectivity model
• Activity in A predicts subsequent activity in B
• Used on timeseries data
• Good for handling correlations when A and B have
  different hysteresis (impulse response functions)
  
• Does not itself provide evidence for causality.
• Rooster crowing may Granger cause the sun to
  rise
• Implemented in BrainVoyager software

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Structural Equation Models
A
D
B
E
C

• Confirmatory model specification and comparison
• Allows a priori specification of regions and
  relationships based on anatomical data
• Models total covariance matrix among variables
  using smaller set of modeled relationships
• Can compare nested models or test goodness of fit
  of a model
• Good for single subjects, difficult to make group
  inferences

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Functional vs. EffectiveScope of inference

• A goal of functional connectivity analysis is to
  make inferences on the structure of relationships
  among brain regions
• These regions form a network
• Regions are more connected during task A than
  B
• This task is associated with activation of pain
  pathways
• A goal of effective connectivity analysis is to
  make statements about causal effects among tasks
  and regions.
• Frontal cortex enhances connectivity between
  visual areas and hippocampus.
• VMPFC inhibits the amygdala

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Functional vs. EffectiveScope of inference

• A goal of functional connectivity analysis is to
  make inferences on the structure of relationships
  among brain regions
• A goal of effective connectivity analysis is to
  make statements about causal effects among tasks
  and regions.
• Effective connectivity provides more
  theoretically powerful inference, but much
  stronger assumptions!
• Validity of causal inference depends strongly on
  assumptions being correct.
• Data is the same in either case massively
  observational.
• Assumptions are often poorly specified and hard
  to check
• !

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To claim causal effect

• You must be willing to claim that there are no
  unmodeled or improperly modeled variables
• Relationships are linear
• No other brain regions that are correlated with
  those in model
• If observational data You must be willing to
  assume that arrows in model capture correct
  direction of causality, based on other sources of
  evidence

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Example
A
B

• If A and B are brain regions in an fMRI study,
  the data is that A and B are correlated.
• If I make a claim about A causing B, I must
  assume
• There is no other variable C that influences both
  A and B
• B does not cause A

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Example II
b2
A
B
b1
C

• In some cases, I may be able to estimate
  coefficients for effects of A on B and B on A.
• I must assume that there is some variable C that
  affects B, but not A. Note the strong assumption!
  
• In this case, any observed association between C
  and A is attributable to b2, whereas the
  observed association between A and B is
  determined by both b1 and b2.

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Causal inference

• Inferences about causality are very dicey when
  made from observational data (e.g., Rubin) --
  e.g., inferences about effects of one region on
  another
• Even anatomical pathways are massively
  bidirectional, so little help from anatomy.
• Causal relationships can be inferred for some
  effects, with careful experimental design.
  Properly randomized experimental treatments can
  be said to have causal effects on brain
  activity.

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The end.
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Example
A
B

• If A and B are brain regions in an fMRI study,
  the data is that A and B are correlated.
• If I make a claim about A causing B, I must
  assume
• There is no other variable C that influences both
  A and B
• B does not cause A

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• The brain pathway is a natural unit of analysis
• Multiple levels, with different interpretations
• Each is useful because they have complementary
  problems
• Need for complementary approaches
• Testing relationships among defined areas
• Pathway-building when all exact regions are
  unknown

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Connectivity
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Brain-heart connectivity
Activation t-value
Now how is the network differ for resilient
subjects?
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Resilience effects in VMPFC
Significant (p lt .05)
Resilience
Onset estimates
Observed t
Other sig. effects Nonresilient gt Resilient in
DLPFC Resilient gt Non in ventral striatum
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Example
A
B

• If A and B are brain regions in an fMRI study,
  the data is that A and B are correlated.
• If I make a claim about A causing B, I must
  assume
• There is no other variable C that influences both
  A and B
• B does not cause A