Stochastic Designs in Event-Related fMRI

This article considers the efficiency of event-related fMRI designs in terms of the optimum temporal pattern of stimulus or trial presentations. The distinction between “stochastic” and “deterministic” is used to distinguish between designs that are specified in terms of the probability that an event will occur at a series of time points (stochastic) and those in which events always occur at prespecified time (deterministic). Stochastic designs may be “stationary,” in which the probability is constant, or nonstationary, in which the probabilities change with time. All these designs can be parameterized in terms of a vector of occurrence probabilities and a prototypic design matrix that embodies constraints (such as the minimum stimulus onset asynchrony) and the model of hemodynamic responses. A simple function of these parameters is presented and used to compare the relative efficiency of different designs. Designs with slow modulation of occurrence probabilities are generally more efficient than stationary designs. Interestingly the most efficient design is a conventional block design. A critical point, made in this article, is that the most efficient design for one effect may not be the most efficient for another. This is particularly important when considering evoked responses and the differences among responses. The most efficient designs for evoked responses, as opposed to differential responses, require trial-free periods during which baseline levels can be attained. In the context of stochastic, rapid-presentation designs this is equivalent to the inclusion of “null events.”