Renewl

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Dynamic Causal Modelling
Karl Friston, Lee Harrison, Will Penny
Wellcome Department of Imaging Neuroscience,
University College London, UK
Neuronal Variability and Noise Challenges and
Promises NIMH, Washington,
September 2002
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Neuronal Variability

• Neurons often vary in their response to
• identical stimuli
• Multi-unit recordings suggest that variability
• previously attributed to single neuron noise
  may instead reflect system-wide changes
• Noise in linear systems analysis may be
  signal in nonlinear systems analysis

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The brain as a nonlinear dynamical system
Nonlinear, systems-level model
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Bilinear Dynamics
a53
Set u2
Stimuli u1
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Bilinear Dynamics Oscillatory transients
Stimuli u1
Set u2
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Z1
-
-

Z2
-
Seconds
-
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Bilinear Dynamics Positive transients
Stimuli u1
Set u2
-

Z1
-


Z2
-
-
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DCM A model for fMRI
Set u2
Stimuli u1
Causality set of differential equations
relating change in one area to change in another
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The hemodynamic model
Buxton, Mandeville, Hoge, Mayhew.
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Impulse response
Hemodynamics
BOLD is sluggish
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Neuronal Transients and BOLD I
300ms
500ms
Seconds
Seconds
More enduring transients produce bigger BOLD
signals
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Neuronal Transients and BOLD II
Seconds
BOLD is sensitive to frequency content of
transients
Seconds
Relative timings of transients are amplified in
BOLD
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Model estimation and inference
Unknown neural parameters, NA,B,C Unknown
hemodynamic parameters, H Vague (stability)
priors, p(N) Informative priors, p(H) Observed
BOLD time series, B. Data likelihood, p(BH,N)
Gauss (B-Y) Bayesian inference p(NB) a p(BN)
p(N)
Laplace Approximation
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Single word processing at different rates
Functional localisation of primary and secondary
auditory cortex and Wernickes area
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Time Series
Auditory stimulus, u1
Adaptation variable, u2
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Dynamic Causal Model
u1 allowed to affect all intrinsic
self-connections
A2
Model allows for full intrinsic connectivity
.
A1
u1
u2 allowed to affect all intrinsic connections
between regions
.
WA
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Posterior Distributions
mA
mB
mC
Show connections for which A(i,j) gt
Thresh with probability gt 90
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Inferred Neural Network
Intrinsic connections are feed-forward
Neuronal saturation with increasing stimulus
frequency in A1 WA
Time-dependent change in A1-WA connectivity
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Summary

• Brain as a nonlinear dynamical system
• Bilinear neural dynamics, hemodynamic model
• Bayesian estimation and inference to detect
  changes in connectivity

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Bilinear Dynamics Positive transients
Stimuli u1
Set u2
a230.2
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Z1
-

Z3
Z3


a23
Z2
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-
a230.1