Convolution Models for fMRI

This chapter reviews issues specific to the analysis of functional magnetic resonance imaging (fMRI) data. It extends the general linear model (GLM) introduced in Chapter 8 to convolution models, in which the blood oxygenation-level-dependent (BOLD) signal is modelled by neuronal causes that are expressed via a haemodynamic response function (HRF). We begin by considering linear convolution models and introduce the concept of temporal basis functions. We then consider the related issues of temporal filtering and temporal autocorrelation. Finally, we extend the convolution model to include nonlinear terms and conclude with some example analyses of fMRI data.