Abstract: We consider an experimental design problem in functional magnetic resonance imaging (fMRI), a dominant technology for studying brain activity in response to mental stimuli presented to the experimental subject. In contrast to previous studies, we develop analytical results on optimal designs for comparing hemodynamic response functions, each describing the effect of the corresponding type of stimulus. In particular, for studies with two stimulus types, we derive a sufficient condition for an fMRI design to be universally optimal, and show that designs constructed via m-sequences or Paley difference sets satisfy this sufficient condition.

Key words and phrases: Difference sets, experimental designs, Hadamard matrix, m-sequences, universal optimality.