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 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 The Model u1 u2 q1 q2 a r2 r1 b Spatial Priors l W Y Y=XW+E [TxN] [TxK] [KxN] [TxN] Spatial Priors A Spatio-Temporal Model for fMRI Laplacian Prior on regression coefficients W Spatial domain General Linear Model Time domain Spatial domain, voxels g=1..G Time domain, at voxel g W Laplacian Prior: Spatial operator D Spatial precision a General Linear Model: Data yg Design matrix X Temporal precision lg Yg=Xwg+eg Spatial domain, voxels g=1..G Time domain, at voxel g rg Spatial operator D Spatial precision a g 1 Data yg Design matrix X Temporal precision lg l g X X diag (a ) D gg T w g g ( l g X y g diag (a ) r g ) T SPATIO-TEMPORAL DECONVOLUTION Synthetic Data: blobs True Smoothing Spatial prior Sensitivity 1-Specificity 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 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% 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 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 Using model evidence to select spatial noise model Tissue Specific Priors Spatial Smoothness Priors PAPER - 5 W. Penny. Bayesian Analysis of fMRI data with spatial Priors. To appear in Proceedings of the Joint Statistical Meeting (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 …… ?!!