Optimal experimental designs for event-related functional magnetic resonance imaging
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The main foci of this dissertation are 1) developing efficient computational approaches for finding optimal experimental designs for event-related functional magnetic resonance imaging (ER-fMRI) and 2) studying the characteristics of optimal ER-fMRI designs obtained. Taking into account both statistical efficiencies and practical constraints, we develop an approach that includes rigorously formulated models, well defined design criteria, and an efficient, versatile search algorithm. Our algorithm incorporates knowledge about the performance of well known ER-fMRI designs, and can accommodate a variety of experimental settings. Through simulations, we show that our approach is more efficient than other methods. Designs found by our approach outperform other designs currently in use by fMRI researchers. Under the popular linear model framework, we adopt our approach to study cases where both individual stimulus effects and pairwise contrasts of stimulus types are of interest; these two effects are common interests of fMRI researchers. A practical situation where along scanning session is divided into multiple short scanning sessions is also investigated. We also take into account the warm-up period of an MR scanner when finding optimal ER-fMRI designs. These studies indicate that our approach can work reliably well for a variety of practical situations encountered in ER-fMRI experiments. A nonlinear model is also considered in our study. While previous studies use two linear models for the two common statistical objectives, namely estimating the hemodynamic response function and detecting brain activation, the nonlinear model approach that we propose provides a natural, unified setting for these two objectives. In addition to finding locally optimal designs and pseudo-Bayesian designs, we also adopt techniques for solving multi-objective optimization problems to obtain a set of designs for researchers to choose from based on their goals and needs.