Key properties of D-optimal designs for event-related functional MRI experiments with application to nonlinear models

To properly formulate functional magnetic resonance imaging (fMRI) experiments with complex mental activity, it is advantageous to permit great flexibility in the statistical components of the design of these studies. The length of an experiment, the placement of various stimuli and the modeling approach used all affect the ability to detect mental activity. Major advances in understanding the implications of various designs of fMRI experiments have taken place over the last decade. Nevertheless, new and increasingly difficult issues relating to the modeling of hemodynamic responses and the detection of activated brain regions continue to arise because of the increasing complexity of the experiments. In this article, the D-optimality criterion is used in conjunction with a genetic algorithm to create probability-based design generators for the selection of designs in event-related fMRI experiments where the hemodynamic response function is modeled with a function that is nonlinear in the parameters. The designs produced by these generators are shown to perform well compared with locally D-optimal designs and provide insight into optimal design characteristics that investigators can utilize in the selection of interstimulus intervals. Designs with these characteristics are shown to be applicable to fMRI studies involving one or two stimulus types. The designs are also shown to be robust with respect to misspecification of an AR(1) error autocorrelation and compare favorably with a maximin procedure.