Nonlinear voxel-based modelling of the haemodynamic response in fMRI

A common assumption for data analysis in functional magnetic resonance imaging is that the response signal can be modelled as the convolution of a haemodynamic response (HDR) kernel with a stimulus reference function. Early approaches modelled spatially constant HDR kernels, but more recently spatially varying models have been proposed. However, convolution limits the flexibility of these models and their ability to capture spatial variation. Here, a range of (nonlinear) parametric curves are fitted by least squares minimisation directly to individual voxel HDRs (i.e., without using convolution). A 'constrained gamma curve' is proposed as an efficient form for fitting the HDR at each individual voxel. This curve allows for spatial variation in the delay of the HDR, but places a global constraint on the temporal spread. The approach of directly fitting individual parameters of HDR shape is demonstrated to lead to an improved fit of response estimates.