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, UCLhttp://www.fil.ion.ucl.ac.uk/~wpenny

(2) Cuban Neuroscience Center, Havana, Cuba.

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

Motivation

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) ?

AR(1)

Aim: For SPM5 to remove the need for spatial smoothing just as SPM2 removed the need for temporal smoothing

Contrast

A

q1 q2

W

Y

u1 u2

Y=XW+E[TxN] [TxK] [KxN] [TxN]

r1 r2

The Model

SpatialPriors

SpatialPriors

General Linear ModelLaplacian Prior on regression coefficients W

Time domainSpatial domain

Spatio-Temporal Model for fMRI

General Linear Model:

Data yg

Design matrix XTemporal precision g

Laplacian Prior:

Spatial operator DSpatial precision

Time domain, at voxel gSpatial domain, voxels g=1..G

W

Yg=Xwg+eg

Data yg

Design matrix XTemporal precision g

Spatial operator DSpatial precision

Time domain, at voxel gSpatial domain, voxels g=1..G

))((

)(1

ggT

ggg

ggT

gg

rdiagyXw

DdiagXX

rg

SPATIO-TEMPORAL DECONVOLUTION

Synthetic Data: blobs

True Smoothing

Spatial prior

1-Specificity

Sen

sitiv

ity

Face data

Convolve event-stream with basis functions to account for the hemodynamic response function

Event-related fMRI: Faces versus chequerboard

Smoothing

Spatial Prior

Event-related fMRI: Familiar faces versus unfamiliar faces

Smoothing

Spatial Prior

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

PAPER - 1

• 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%

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.

• Spatial prior for regression coefficients

• Shown to be more sensitive than ‘smoothing the data’

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)

PAPER - 4

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

• 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

Using model evidence to select hemodynamic basis sets

Nested ModelComparison

Non-nestedmodelcomparison

Optimality of non-nested model comparison

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

BayesianCluster ofInterest Analysis

Using model evidence to select spatial noise model

TissueSpecificPriors

SpatialSmoothnessPriors

PAPER - 5

W. Penny. Bayesian Analysis of fMRI data with spatial Priors. To appear in Proceedings of the Joint StatisticalMeeting (JSM), 2005.

• 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 - 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 …… ?!!