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Even without applied spatial smoothing, activation maps (and maps of eg. AR coefficients) have spatial structure - PowerPoint PPT Presentation


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Bayesian fMRI models with Spatial Priors Will Penny (1), Nelson Trujillo-Barreto (2) Guillaume Flandin (1) Stefan Kiebel(1), Karl Friston (1) (1) Wellcome Department of Imaging Neuroscience, UCL http://www.fil.ion.ucl.ac.uk/~wpenny (2) Cuban Neuroscience Center, Havana, Cuba. Motivation.

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slide1
Bayesian fMRI models with Spatial PriorsWill Penny (1), Nelson Trujillo-Barreto (2)Guillaume Flandin (1) Stefan Kiebel(1), Karl Friston (1)(1) Wellcome Department of Imaging Neuroscience, UCLhttp://www.fil.ion.ucl.ac.uk/~wpenny(2) Cuban Neuroscience Center, Havana, Cuba.
slide2
Motivation

Even without applied spatial smoothing, activation maps

(and maps of eg. AR coefficients) have spatial structure

Contrast

AR(1)

We can increase the sensitivity of our inferences by smoothing

data with Gaussian kernels (SPM2). This is worthwhile, but crude.

Can we do better with a spatial model (SPM5) ?

Aim: For SPM5 to remove the need for spatial smoothing just as

SPM2 removed the need for temporal smoothing

slide3
q1

q2

a

b

u1

u2

l

W

A

Y

The Model

r2

r1

Spatial

Priors

Spatial

Priors

Y=XW+E

[TxN] [TxK] [KxN] [TxN]

slide4
Spatio-Temporal Model for fMRI

Laplacian Prior on

regression coefficients W

General Linear Model

Spatial domain

Time domain

slide5
Spatial domain, voxels g=1..G

Time domain, at voxel g

W

General Linear Model:

Data yg

Design matrix X

Temporal precision lg

Laplacian Prior:

Spatial operator D

Spatial precision a

Yg=Xwg+eg

slide6
Spatial domain, voxels g=1..G

Time domain, at voxel g

rg

Spatial operator D

Spatial precision a

Data yg

Design matrix X

Temporal precision lg

SPATIO-TEMPORAL DECONVOLUTION

slide7
Synthetic Data: blobs

Smoothing

True

Spatial prior

slide8
Sensitivity

1-Specificity

face data
Face data

Convolve event-stream with basis functions to account for

the hemodynamic response function

slide12
PAPER - 1

W. Penny, S. Kiebel and K. Friston (2003) Variational Bayesian Inference for fMRI time series. NeuroImage 19, pp 727-741.

  • GLMs with voxel-wise AR(p) models
  • Model order selection shows p=0,1,2 or 3 is sufficient
  • Voxel-wise AR(p) modelling can improve effect size
  • estimation accuracy by 15%
slide13
Spatial prior for regression coefficients
  • Shown to be more sensitive than ‘smoothing the data’

PAPER - 2

W.Penny, N. Trujillo-Barreto and K. Friston (2005). Bayesian fMRI time series analysis with spatial priors. NeuroImage 24(2), pp 350-362.

slide14
PAPER - 3

W.Penny and G. Flandin (2005). Bayesian analysis of single-subject fMRI: SPM implementation. Technical Report. WDIN, UCL.

  • Describes more efficient implementation of algorithm in papers
  • 1 and 2.
  • Describes how contrasts are evaluated when specified post-hoc
  • Roadmap to code (? Erm, OK, not done yet)
slide15
ROI-based Bayesian model comparison for selecting optimal
  • hemodynamic basis set.
  • Above Bayesian approach can be twice as sensitive as the
  • classical F-test method
  • Defined spatial priors for AR coefficients
  • Bayesian model comparison shows these to be better than
  • (i) global AR value, (ii) tissue-specific AR values

PAPER - 4

W.Penny, G. Flandin and N.Trujillo-Barreto. Bayesian Comparison of Spatially Regularised General Linear Models. Human Brain Mapping, Accepted for publication.

slide17
Optimality of non-nested model comparison

Bayesian

Cluster of

Interest

Analysis

Non-nested

model

comparison

Nested Model

Comparison

FIR basis (truth) versus Inf-3 basis in low SNR environment

slide18
Using model evidence to select spatial noise model

Tissue

Specific

Priors

Spatial

Smoothness

Priors

slide19
Describes Bayesian inference for multivariate contrasts based
  • on chi-squared statistics
  • Describes `default thresholds’ for generating PPMs: effect size
  • threshold is 0, probability threshold is 1-1/S where S is the number
  • of voxels in the search volume
  • This gives approximately 0, 1 or 2 False Positives per PPM
  • Describes a recent bug-fix !!! ?

PAPER - 5

W. Penny. Bayesian Analysis of fMRI data with spatial

Priors. To appear in Proceedings of the Joint Statistical

Meeting (JSM), 2005.

slide20
PAPER - 6

G. Flandin and W. Penny. Bayesian Analysis of fMRI data with spatial

basis set priors. Proceedings of Human Brain Mapping Conference, 2005.

  • Uses spatial prior based on spatial basis functions eg.
  • wavelets
  • This is much faster than previous approach
  • And provides yet more sensitivity …… ?!!
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