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

The brain expresses activity in complex spatiotemporal patterns, reflected in the influence of spatially distributed cytoarchitectural, biochemical, and genetic properties. The correspondence between these multimodal "brain maps" may reflect underlying causal pathways and is hence 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 internal SA but break correlations between maps. The present work introduces "eigenstrapping", using a spectral decomposition of cortical and subcortical surfaces in terms of 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 similar or superior false positive control to current state-of-the-art procedures. Eigenstrapping is fast, eschews the need for parametric assumptions about the nature of the SA, and works with maps defined on smooth surfaces with or without a boundary. It 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. ### Competing Interest Statement The authors have declared no competing interest.