Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis

Abstract

Inference from fMRI data faces the challenge that the hemodynamic system, that relates the underlying neural activity to the observed BOLD fMRI signal, is not known. We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD time series, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way. The prior mean function may be generated from a standard LTI system, based on a canonical hemodynamic response function, or a more elaborate physiological model such as the Balloon model. This gives us the nonparametric flexibility of the GP, but allows the posterior to fall back on the physiologically based prior when the data are weak. Results on simulated data show that even with an erroneous prior for the GP, the proposed model is still able to discriminate between active and non-active voxels in a satisfactory way. The proposed model is also applied to real fMRI data, where our Gaussian process model in several cases finds brain activity where previously proposed LTI models, parametric and nonparametric, does not.