Title: Renewl
1Dynamic 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
2Neuronal 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
3The brain as a nonlinear dynamical system
Nonlinear, systems-level model
4Bilinear Dynamics
a53
Set u2
Stimuli u1
5Bilinear Dynamics Oscillatory transients
Stimuli u1
Set u2
-
Z1
-
-
Z2
-
Seconds
-
6Bilinear Dynamics Positive transients
Stimuli u1
Set u2
-
Z1
-
Z2
-
-
7DCM A model for fMRI
Set u2
Stimuli u1
Causality set of differential equations
relating change in one area to change in another
8The hemodynamic model
Buxton, Mandeville, Hoge, Mayhew.
9Impulse response
Hemodynamics
BOLD is sluggish
10Neuronal Transients and BOLD I
300ms
500ms
Seconds
Seconds
More enduring transients produce bigger BOLD
signals
11Neuronal Transients and BOLD II
Seconds
BOLD is sensitive to frequency content of
transients
Seconds
Relative timings of transients are amplified in
BOLD
12Model 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
13Single word processing at different rates
Functional localisation of primary and secondary
auditory cortex and Wernickes area
14Time Series
Auditory stimulus, u1
Adaptation variable, u2
15Dynamic 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
16Posterior Distributions
mA
mB
mC
Show connections for which A(i,j) gt
Thresh with probability gt 90
17Inferred Neural Network
Intrinsic connections are feed-forward
Neuronal saturation with increasing stimulus
frequency in A1 WA
Time-dependent change in A1-WA connectivity
18Summary
- Brain as a nonlinear dynamical system
- Bilinear neural dynamics, hemodynamic model
- Bayesian estimation and inference to detect
changes in connectivity
19Bilinear Dynamics Positive transients
Stimuli u1
Set u2
a230.2
-
Z1
-
Z3
Z3
a23
Z2
-
-
a230.1