Combined spatial and non-spatial prior for inference on MRI time-series.
When modelling FMRI and other MRI time-series data, a Bayesian approach based on adaptive spatial smoothness priors is a compelling alternative to using a standard generalized linear model (GLM) on presmoothed data. Another benefit of the Bayesian approach is that biophysical prior information can be incorporated in a principled manner; however, this requirement for a fixed non-spatial prior on a parameter would normally preclude using spatial regularization on that same parameter. We have developed a Gaussian-process-based prior to apply adaptive spatial regularization while still ensuring that the fixed biophysical prior is correctly applied on each voxel. A parameterized covariance matrix provides separate control over the variance (the diagonal elements) and the between-voxel correlation (due to off-diagonal elements). Analysis proceeds using evidence optimization (EO), with variational Bayes (VB) updates used for some parameters. The method can also be applied to non-linear forward models by using a linear Taylor expansion centred on the latest parameter estimates. Applying the method to FMRI with a constrained haemodynamic response function (HRF) shape model shows improved fits in simulations, compared to using either the non-spatial or spatial-smoothness prior alone. We also analyse multi-inversion arterial spin labelling data using a non-linear perfusion model to estimate cerebral blood flow and bolus arrival time. By combining both types of prior information, this new prior performs consistently well across a wider range of situations than either prior alone, and provides better estimates when both types of prior information are relevant.
Groves
Adrian R
AR
FMRIB Centre, Department of Clinical Neurology, John Radcliffe Hospital, Oxford, UK. adriang@fmrib.ox.ac.uk
Chappell
Michael A
MA
Woolrich
Mark W
MW
D000465:Algorithms; D001921:Brain / Q000502:physiology; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D008959:Models, Neurological