Benchmarking spatial interpolation methods for brain maps

The human brain is a unique biological space that hosts complex processes unfolding at multiple scales. To study these processes, an abundance of imaging technologies evolved over many decades to produce large-scale, dense mappings of structural and functional features. In parallel, a rich universe of techniques for cellular and molecular biology supplies us with fine-scale, highly specific and reliable measurements in sparse tissue samples. To represent cortical processes integratively across scales, spatial interpolation is necessary for bridging dense and sparse data. The absence of a field consensus for realistic interpolation of features over the whole brain prompts a comprehensive comparison of existing frameworks from the broader scientific literature. Here, we benchmark the performance of multiple deterministic (Inverse Distance Weighting, K-Nearest Neighbours, and Radial Basis Function) and stochastic (Spatially-Weighted Regression, Ordinary Kriging, and Regression Kriging) strategies first with simulated or empirical ground truths. We then demonstrate two use cases with de novo sparse brain data (intracranial EEG and microarray gene expression). In these experiments, we investigate how differences in data characteristics, such as spatial dependency structure and sampling distribution, impact the performance of different interpolation methods. Throughout the results, we consistently find that maps interpolated through spatially-informed stochastic frameworks such as Ordinary Kriging and Regression Kriging are more accurate and biologically realistic across geometric constraints, data modalities, and sampling conditions. This invites continued development of spatially-informed statistical frameworks for analyzing brain data and, more fundamentally, the biological processes that produce them.