Efficiency, power, and entropy in event-related fMRI with multiple trial types. Part II: design of experiments.

The performance of an experimental design for functional magnetic resonance imaging (fMRI) can be characterized by its estimation efficiency, which is the ability to make an estimate of the hemodynamic response, its detection power, which is the ability to detect an activation, and its conditional entropy, which is a measure of the randomness of the design. In Liu and Frank [Neuroimage 21 (2004) 387-400], it is shown that there is a fundamental theoretical trade-off between estimation efficiency and detection power for experiments with multiple trial types and that there is an empirical relation between estimation efficiency and conditional entropy. This paper provides an intuitive interpretation of the theoretical results and examines the practical implications of these results for the optimal design of fMRI experiments with multiple trial types. The properties of block designs, permuted block designs, m-sequence designs, clustered m-sequence designs, and mixed designs are explored. It is shown that these designs nearly achieve the theoretically predicted performance and can be used in practice to obtain advantageous trade-offs among efficiency, power, and entropy.