There are many ways to detect activation patterns in a time series of observations at a single voxel in a functional magnetic resonance imaging study. The critical problem is to estimate the statistical significance, which depends on the estimation of both the magnitude of the response to the stimulus and the serial dependence of the time series and especially on the assumptions made in that estimation. We show that for experimental designs with periodic stimuli, only a few aspects of the serial dependence are important and these can be estimated reliably via nonparametric estimation of the spectral density of the time series, whereas existing techniques are biased by their assumptions. The linear model with (stationary) serially dependent errors can be analyzed entirely in frequency domain, and doing so provides many insights. In particular, we introduce a technique to detect periodic activations and show that it has a distribution theory that enables us to assign significance levels down to 1 in 100,000, levels which are needed when a whole brain image is under consideration. Nonparametric spectral density estimation is shown to be self-calibrating and accurate when compared to several other time-domain approaches. The technique is especially resistant to high frequency artefacts that we have found in some datasets and we demonstrate that time-domain approaches may be sufficiently susceptible to these effects to give misleading results. The method is easily generalized to handle event-related designs. We found it necessary to consider the trends in the time series carefully and use nonlinear filters to remove the trends and robust techniques to remove "spikes." Using this in connection with our techniques allows us to detect activations in clumps of a few (even one) voxel in periodic designs, yet produce essentially no false positive detections at any voxels in null datasets.
Copyright 2000 Academic Press.