Resampling spatial brain maps with geometric eigenmodes

Inferring the relationship between different brain maps is a topic of substantial interest. Identifying true associations requires knowledge about the distribution of correlations that arise by chance in the presence of smoothness (or spatial autocorrelation; SA) in these maps. This null distribution can be generated from an ensemble of surrogate brain maps that preserve the intrinsic SA but break the correlations between maps. This educational session introduces the use of “eigenstrapping”, a novel method involving the spectral decomposition of cortical and subcortical surfaces in terms of their geometric eigenmodes, and then random rotations of these modes to produce SA-preserving surrogate brain maps. The null distributions generated by this method properly reflect the null hypothesis of no association between brain maps in the presence of SA, offering a powerful tool for brain map inference.

This session will provide an accessible introduction to geometric eigenmodes, emphasising their role in brain mapping and their mathematical foundations. Participants will learn how the method works both theoretically and practically, and how it can be a powerful tool for improving the reliability of brain map analysis. A practical demonstration will involve participants in the step-by-step implementation of the method using Jupyter notebooks, with several applications to real-world brain-imaging data. Additionally, we will present a case study illustrating how this method enhances the statistical robustness of findings in neuroscience.

Designed for researchers, students, and clinicians in neuroscience and computational fields at all levels, this session bridges theoretical concepts with practical application. Participants will be engaged with quizzes and short problem-solving tasks and will leave with a deeper understanding of the potential of geometric eigenmodes in improving brain map analysis and statistical inference. The session will conclude with a guided discussion, inviting participants to explore how they can integrate this method into their own research.