Statistical models for image sequences

Identi cation of brain activity using functional magnetic resonance imaging (fMRI) depends on blood ow replenishing activated neuronal sites. In this paper we describe how previous studies have sought to model the hemo-dynamic response function with restricted parametric models, and examine some of the inadequacies imposed by the implicit restrictions. We investigate more exible estimation of hemodynamic response using cubic spline basis expansions, both of the time course itself and of the hemodynamic response function. In the latter, a deconvolution estimate of hemodynamic response is estimated from the observed fMRI time series at each pixel location and the designed temporal input stimulus. The estimated hemodynamic responses include both monophasic and biphasic forms, comparable with the more limited model proposed in Friston et al. [1995b]. Bootstrapping allows us to show that for our data, a Poisson-based convolution model performs no better than tting a sinusoid to the data, but that for regions of activation, both the spline-based convolution model and periodic spline models do. A study of primary visual cortex activation is used to illustrate these ndings.