Efficient design of event-related fMRI experiments using M-sequences.

Rapid event-related fMRI (erfMRI) allows estimation of the shape of hemodynamic responses (HDR) associated with transient brain activation evoked by various sensory, motor, and cognitive events. Choosing a sequence of events that maximizes efficiency of estimating the HDR is essential for conducting event-related brain imaging experiments, since increasing efficiency is essentially equivalent to reducing scanning time or increasing the strength of the principal magnetic field. The efficiency of an erfMRI design depends critically on the temporal arrangement of the sequence of events and the noise in the fMRI signal. We introduce to erfMRI a simple method for generating efficient event sequences based on maximum-length shift register sequences, or m-sequences. We show that under the assumption of white uncorrelated MRI noise, efficiency of erfMRI experimental designs that employ m-sequences exceeds efficiency of the best randomly generated sequences. This is true for single and multiple event type experiments, which allow either parallel events (overlapping events design) or designs in which only one event occurs at a time (nonoverlapping events design). HDR estimation efficiency afforded by m-sequences grows with the number of event types, and is greatest when event sequences are relatively short, albeit within commonly used scan times (i.e., 63-255 total events per scan). The improvement in efficiency, however, comes at a cost of constraints imposed by m-sequence generation rules, such as predetermined sequence lengths; for nonoverlapping events design m-sequence-based designs are not available for all possible numbers of event types. Nevertheless, designs that are available with m-sequences cover a large subset of commonly used erfMRI experimental designs. Under conditions of characteristic time-correlated fMRI noise, randomly generated sequences may yield efficiencies that exceed those afforded by m-sequences for single event-type designs, since in this case one can generate random sequences that partially decorrelate MRI noise by chance. Our simulations suggest that for designs of realistic sequence lengths that use more than one event type, m-sequence based designs tend to outperform random designs, thus making the knowledge of noise inessential. Finally, within an r-th order m-sequence (generated by a shift register of length r) all possible combinations of subsequences of length r occur, and thus these subsequences are exactly counterbalanced. This property is essential for minimizing effects of psychological and neuronal adaptation and expectation.