How to bootstrap fMRI data?

Over the last decade the bootstrap procedure is gaining popularity in the statistical analysis of neuro- imaging data. As fMRI data are complexly structured with both temporal and spatial dependencies, such bootstrap procedures may indeed offer an elegant and powerful solution. We provide a thorough investigation on the most appropriate bootstrapping procedure for fMRI data. Friman and Westin (2005, NeuroImage) showed that a bootstrap procedure based on pre-whitening the temporal structure of fMRI time series is superior to procedures based on wavelets or Fourier de- composition of the signal, especially in the case of blocked fMRI designs. Several bootstrap schemes can be exploited though for the re-sampling of residuals from a fitted general linear model. We examine here the differences between 1) bootstrapping pre-whitened residuals which are based on parametric as- sumptions of the temporal structure, 2) a blocked bootstrapping which avoids making such assumptions (with several variants like the circular bootstrap,...), and 3) a combination of both bootstrap procedures. Because the dependence in the residuals of a misspecified GLM might differ in blocked and event-related fMRI designs we investigated the bootstrapping schemes for both design types. Based on real data and simulation studies, we discuss the temporal and spatial properties of the different bootstrap procedures.