Functional neuroimaging and brain connectivity

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Functional neuroimaging and brain connectivity

• A set of slides used during a discussion at the
  Centre for Speech and Language April 2003
• Many of the ideas discussed here are covered in
  greater detail, and with far greater elegance and
  erudition, by the group led by Karl Friston at
  the Institute of Cognitive Neuroscience,
  www.fil.ion.ucl.ac.uk.
• I also draw attention to the excellent early
  papers by McIntosh and Gonzales-Lima (Hum. Brain
  Mapp., 1994)

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Functional neuroimaging and brain connectivity

• Why bother?
• Brain adheres to certain principles of functional
  segregation but these are insufficient to
  describe its operations satisfactorily
• A description of regional patterns of activity in
  terms of causal relationships with other brain
  regions obviates some of the theoretical
  constraints in the simple brain mapping approach
• A better model for some brain disorders?

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Functional Connectivity vs. Effective Connectivity

• Functional Connectivity
• the temporal correlation of spatially remote
  neurophysiological events
• Effective Connectivity
• The influential relationship between one brain
  region and another

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An observed inter-regional correlation
r
These two regions are functionally connected. The
observation of correlation is an observation of
functional connectivity. They may be Effectively
connected. The observation of correlation is
compatible with this but also with other
possibilities.
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Why might we observe functional connectivity?
Because of effective connectivity i.e. a uni-or
bi-directional influential (effective)
relationship
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Why might we observe functional connectivity?
No effective connectivity between the two
regions. Correlation arises due to the common
influence of a third factor (region or task)
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How do we represent connectivity?
Functional
Data-led

• Descriptive
• Correlative
• Psychophysiological interaction/physiophysiologica
  l interaction
• Path analysis/structural equation modelling/DCM

Effective
Model-based
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Observation of task-related coactivation is a
rather unsatisfying index of inter-regional
connectivity

• Produced by a standard analysis of task-related
  activation, representing simply a different
  theoretical treatment of the results
• Regions thus implicated may not be directly
  correlated (correlation is not transitive)

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Non-transitivity of separate regional
task-associated activations
Task
Baseline
Region 1
Region 2
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Correlative analysis
Requires some a priori model (albeit a simple one)
Y (1-n) c ß.X (1-n) ?
X voxel/region of interest Y every other
region ß functional connectivity between X and Y
Ultimately, this approach - though it ensures
that two regions do indeed correlate - adds
little to a simple description of regional
co-activation.
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Psychophysiological interaction/Physiophysiologic
al interaction (PPI)

• The observation of task- or context-dependent
  inter-regional covariance
• Measures the ways in which a given region
  predicts activity in other brain regions.
• This has been referred to as the
  (context-dependent) contribution of activity in
  one area to that in another (here contribution is
  used used in a statistical sense contributes to
  an explanation of the variance)

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Task
Baseline
PFC
STG
Here, a simple correlation analysis would show a
negative correlation between PFC and STG. A PPI
asks the question does the strength of
correlation between the regions within the time
series associated with one task differ from that
associated with the time series in the other
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Practical implementation of this PPI analysis
the old approach.Block designs only

• Choose the voxel/region of interest (i.e. some a
  priori theorising is necessary) and obtain y
• Mean-correct voxel/region values (separately for
  task and baseline conditions)
• Multiply the mean-corrected time series vector by
  a column vector in which task is specified by 1
  and baseline by 1.
• Enter this vector as a covariate with a 1
  weighting to identify task-specific positive
  contributions from the ROI and 1 for the
  reverse.

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PPI the new approach (SPM2b) Gitelman et al,
NeuroImage 2003

• addresses two problems -
• The inadequacy of using an interaction between
  filtered/convolved signals as a measure of a
  neuronal interaction.
• A problem specific to event-related designs
  specifying the context of the measurement.

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The convolved signal

• A burst of neuronal firing is succeeded by a
  haemodynamic response (the form of which we think
  that we know in advance).
• In setting up our analytical model, we imagine
  that our psychological variable is controlling
  the neuronal firing and that we can specify when
  the neuronal bursts will occur with reference to
  when our cognitive events occurred.
• These two pieces of information enable us,
  through convolution of the neuronal burst with
  the HRF, to predict the changes in BOLD signal
  that should occur in activated areas.

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Effects of convolution

• The signal that we work with in standard fMRI
  analyses is quite a long way removed from the
  effects that interest us (i.e. the neuronal
  firing).
• This becomes a serious issue when we consider
  interactions between brain regions or between
  psychological context and regional activity.

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PPI and convolution

• Imagine two regions A and B
• Their activity is given by xA and xB
  respectively.
• The convolved signals, i.e. BOLD signals, from
  each are given by
• yA HxA and yB HxB
• A neuronal (physio-physiological) interaction is
  expressed by xA xB
• yA yB (i.e. HxA HxB) is not equivalent to H(xA xB
  )
• Likewise for psychophysiological interactions,
• HPyA (i.e.(HP)(HxA)) is not equivalent to H(PxA)

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PPI and convolution block design
Box-car design
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Neuronal firing
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Expected and actual BOLD signal
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PPI regressor produced by multiplying BOLD signal
by task design (yPX HP x HX)
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PPI regressor produced by multiplying neuronal
signal by task design and then convolving - yPX
H(P x X)
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PPI and block design - summary

• The use of the convolved signal in setting up the
  PPI does not seem too problematic.
• The resultant regressor differs only a little
  from that produced in the more correct way (using
  the convolved product of the task vector and the
  neuronal firing vector).

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PPI event-related designs

• Two problems
• The use of the convolved signal in producing the
  PPI regressor is much less satisfactory
• A given BOLD measurement is produced by
  convolution with a history of neuronal events,
  which have been stimulated under a number of
  different contexts.

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Activity Xa
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Activity Xb
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BOLD response HXa
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BOLD response - HXb
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PPI regressor produced by multiplying BOLD signal
by task design (yXaXb HXa x HXb)
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PPI regressor produced by multiplying neuronal
signal by task design and then convolving (yXaXb
H(Xa x Xb)
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PPI and event-related design - summary

• The use of the convolved signal in setting up the
  PPI is an inaccurate reflection of the (task x
  neuronal) or (neuronal x neuronal) interaction.
• The convolved response loses its context in the
  setting of rapidly changing events.

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PPI and e-r fMRInew approach

• Gitelman et al 2003
• Take the BOLD signal from the region of interest
• Deconvolve (PEB) to produce an educated guess at
  the train of neuronal firing that may have
  generated it
• Express the interaction between, say, task and
  neuronal firing as the product of the task design
  and the deconvolved signal
• Reconvolve the interaction with HRF.
• Use this new signal as the regressor in a
  standard implementation of GLM

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Closer to causal relationships Structural
Equation Modelling

• This is a much more intricately specified model,
  less data-led requiring the inclusion of more a
  priori information
• It is, like the other analysis options, based
  upon regression analysis (this time estimated
  simultaneously as an interlocked system of
  relationships).
• See McIntosh and Gonzales-Lima, 1994, Hum Brain
  Mapp. for very clear discussion

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The value of this simultaneous estimation lies in
the possibility that it offers a move from
correlational analysis (inherently
bi-directional) to uni-directional connections
(paths) which imply causality
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SEM requires

• An anatomical model
• Specified regions and directionally specified
  connections
• A functional model
• A correlation matrix generating, through the path
  equations, the path strengths

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SEM therefore involves

• A much fuller (but, ultimately, highly
  simplistic) model than previously described
  approaches.
• Assumptions that, though they may be backed by
  known neuroanatomy, are sometimes difficult to
  justify.

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But

• Lack of temporal information
• Causality exists within the model. The model may
  or may not be compatible with the real world (the
  data) but never proves the state of affairs in
  the real world.

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And now

• Dynamic Causal Modelling (DCM)
• Friston et al www.fil.ion.ucl.ac.uk
• The central idea behind DCM is to treat the brain
  as a "deterministic, nonlinear, dynamic system"

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Deterministic?

• DCM seeks to evaluate coupling of activity across
  different regions as a response to an input that
  is known and is produced by the experimental
  manipulation. Most models of connectivity, while
  they strive for context-specificity (and, indeed,
  must be represented in context-specific terms)
  actually treat the input as unknown and
  stochastic.

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Non-Linear?

• The majority of models are linear in the sense
  that they assume that the brains responses are
  additive. That is, a response is a weighted
  linear mixture of the inputs. Thus, while easy to
  analyse, they have a limited repertoire.
• Non-linear models on the other hand are complex
  and may be intractable.
• DCM uses a bilinear model, in which inputs may
  have two sorts of effect
• perturbation and modulation.

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Dynamic?

• DCM is concerned primarily with changes in
  effective connectivity in response to inputs to
  the system.
• These inputs correspond to experimental
  manipulations.

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SEM and DCM

• SEM
• Output Activation (intrinsic) plus activation
  (connected regions forward and backward)
• DCM
• Output Activation (intrinsic) plus activation
  (connected regions forward and backward)
• plus
• Perturbation by exp. manipulation (cu)
• Modulation by exp. manipulation (bu)