Efficient orthogonal functional magnetic resonance imaging designs in the presence of drift

To study brain activity, by measuring changes associated with the blood flow in the brain, functional magnetic resonance imaging techniques are employed. The design problem in event-related functional magnetic resonance imaging studies is to find the best sequence of stimuli to be shown to subjects for precise estimation of the brain activity. Previous analytical studies concerning optimal functional magnetic resonance imaging designs often assume a simplified model with independent errors over time. Optimal designs under this model are called g-lag orthogonal designs. Recently, it has been observed that g-lag orthogonal designs also perform well under simplified models with auto-regressive error structures. However, these models do not include drift. We investigate the performance of g-lag orthogonal designs for models that incorporate drift parameters. Identifying g-lag orthogonal designs that perform best in the presence of a drift is important because a drift is typically assumed for the analysis of event-related functional magnetic resonance imaging data.