  Functional magnetic resonance imaging (fMRI) technology is popularly used in
many fields for studying how the brain reacts to mental stimuli. The
identification of optimal fMRI experimental designs is crucial for rendering
precise statistical inference on brain functions, but research on this topic is
very lacking. We develop a general theory to guide the selection of fMRI
designs for estimating a hemodynamic response function (HRF) that models the
effect over time of the mental stimulus, and for studying the comparison of two
HRFs. We provide a useful connection between fMRI designs and circulant biased
weighing designs, establish the statistical optimality of some well-known fMRI
designs and identify several new classes of fMRI designs. Construction methods
of high-quality fMRI designs are also given.
