Some Limit Results for Efficiency in Stochastic fMRI Designs

Functional magnetic resonance imaging (fMRI) provides an indirect measure of neural activity changes in the brain. fMRI designs use a sequence of events (such as the presentation of a picture to the subject). A common goal of fMRI data analysis is to estimate the amplitudes of local brain responses to these experimental events. Designs involving a random component in the temporal structure of the event sequence are called stochastic. Stochastic designs are favored in situations where predictability of the event sequence is a potential confound. In this paper, discrete-time models of the efficiency of response amplitude estimation (using generalized least-squares) in single event-type, stationary stochastic fMRI designs (Friston et al., 1999) are extended to continuous-time. This allows one to determine certain results concerning efficiency as the average spacing between experimental events gets very small. Furthermore, we derive expressions for efficiency in the frequency domain. This provides a direct connection between efficiency and formulations of designs and noise in the frequency domain. This is useful from a signal processing and filtering perspective. These results can be used, given other constraints, to optimize fMRI stochastic design parameters.