fMRI brain mapping with kernels

Functional Magnetic Resonance Imaging is a technique for the study of the human brain that can detect the regionally specific effects of brain stimuli or activity through the detection of the activity related BOLD signal. The standard fMRI techniques include the use of the so called General Linear Model (GLM), which assumes that the combination of different activity in the brain present linear behavior. We present here a nonlinear counterpart of the GLM that does not contain that assumption and that is based on the use of Mercer's kernels, thus keeping the simplicity and reasonable computational burden of the of the linear model. We show the advantages of this model in analysis of real fMRI data in multistimuli experiments.

I. Introduction

Functional magnetic resonance imaging (fMRI), based on the Blood Oxygenation Level Dependent (BOLD) signal, is considered as a consolidated technique for a system level understanding of the human brain. Since its first description by [1], the number of BOLD fMRI reports has sharply increased [2], underling the importance of this technique. FMRI allows a characterization of the functional anatomy, the localization of functional areas and the localization of distributed networks necessary for the functional integration. fMRI detects the variations between dehydrogenated and oxygenated haemoglobine inside each voxel of the brain tissue, that are a function of the brain behaviour, for example, in response to sensorial stimuli or sensorimotor or cognitive activities.