Constrained linear basis sets for HRF modelling using Variational Bayes

• Published in: NeuroImage (Orlando, Fla.) Vol. 21; no. 4; pp. 1748 - 1761
• Main Authors: Woolrich, Mark W., Behrens, Timothy E.J., Smith, Stephen M.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.04.2004; Elsevier Limited
• Subjects: Algorithms; Basis sets; Bayes Theorem; Bayesian analysis; Brain - physiology; Brain Mapping; Computer Simulation; Economic models; Evoked Potentials - physiology; FMRI; GLM; HRF; Humans; Image Interpretation, Computer-Assisted; Linear Models; Magnetic Resonance Imaging - statistics & numerical data; Markov Chains; Markov random field; Mathematical Computing; Models, Statistical; Noise; Pain Threshold - physiology; Pattern Recognition, Visual - physiology; Power plants; Sensitivity and Specificity; Thermosensing - physiology; Variational Bayes; GLM; Basis sets; Markov random field; Variational Bayes; HRF; FMRI
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2003.12.024

FMRI modelling requires flexible haemodynamic response function (HRF) modelling, with the HRF being allowed to vary spatially and between subjects. To achieve this flexibility, voxelwise parameterised HRFs have been proposed; however, inference on such models is very slow. An alternative approach is to use basis functions allowing inference to proceed in the more manageable General Linear Model (GLM) framework. However, a large amount of the subspace spanned by the basis functions produces nonsensical HRF shapes. In this work we propose a technique for choosing a basis set, and then the means to constrain the subspace spanned by the basis set to only include sensible HRF shapes. Penny et al. [NeuroImage (2003)] showed how Variational Bayes can be used to infer on the GLM for FMRI. Here we extend the work of Penny et al. to give inference on the GLM with constrained HRF basis functions and with spatial Markov Random Fields on the autoregressive noise parameters. Constraining the subspace spanned by the basis set allows for far superior separation of activating voxels from nonactivating voxels in FMRI data. We use spatial mixture modelling to produce final probabilities of activation and demonstrate increased sensitivity on an FMRI dataset.