Single subject image analysis using the complex general linear model—An application to functional magnetic resonance imaging with multiple inputs

A linear time invariant model is applied to functional fMRI blood flow data. Based on traditional time series analysis, this model assumes that the fMRI stochastic output sequence can be determined by a constant plus a linear filter (hemodynamic response function) of several fixed deterministic inputs and an error term assumed stationary with zero mean. The input function consists of multiple exponential distributed (time delay between images) visual stimuli consisting of negative and erotic images. No a priori assumptions are made about the hemodynamic response function that, in essence, is calculated at each spatial position from the data. The sampling rate for the experiment is 400 ms in order to allow for filtering out higher frequencies associated with the cardiac rate. Since the statistical analysis is carried out in the Fourier domain, temporal correlation problems associated with inference in the time domain are avoided. This formal model easily lends itself to further development based on previously developed statistical techniques.