Generation of surrogate brain maps preserving spatial autocorrelation through random rotation of geometric eigenmodes

The brain expresses activity in complex spatiotemporal patterns, reflecting the influence of spatially distributed cytoarchitectural, biochemical, and genetic properties. The correspondence between these different "brain maps" is a topic of substantial interest. However, these maps possess intrinsic smoothness (spatial autocorrelation, SA) which can inflate spurious cross-correlations, leading to false positive associations. Identifying true associations requires knowledge about the distribution of correlations that arise by chance in the presence of SA. This null distribution can be generated from an ensemble of surrogate brain maps that preserve the intrinsic SA but break the correlations between maps. The present work introduces the "eigenstrapping" method, which performs a spectral decomposition of brain maps, such as fMRI activation patterns, expressed on cortical and subcortical surfaces, using geometric eigenmodes, and then randomly rotating these modes to produce SA-preserving surrogate brain maps. It is shown that these surrogates appropriately represent the null distribution of chance pairwise correlations, with expected false positive control superior to current state-of-the-art procedures. Eigenstrapping is fast, eschews the need for parametric assumptions about the nature of a map's SA, and works with maps defined on smooth surfaces with a boundary, such as a single cortical hemisphere when the medial wall has been removed. Moreover, eigenstrapping generalizes to broader classes of null models than existing techniques, offering a unified approach for inference on cortical and subcortical maps, spatiotemporal processes, and complex patterns possessing higher-order correlations.