Multi-Resolution Graph Based Volumetric Cortical Basis Functions From Local Anatomic Features

Objective: Modern clinical MRI collects millimeter scale anatomic information, but scalp electroencephalography source localization is ill posed, and cannot resolve individual sources at that resolution. Dimensionality reduction in the space of cortical sources is needed to improve computational and storage complexity, yet volumetric methods still employ simplistic grid coarsening that eliminates fine scale anatomic structure. We present an approach to extend near-arbitrary spatial scaling to volumetric localization. Methods: Starting from a voxelwise brain parcellation, sub-parcels are identified from local cortical connectivity with an iterated graph cut approach. Spatial basis functions in each parcel are constructed using either a decomposition of the local leadfield matrix or spectral basis functions of local cortical connectivity graphs. Results: We present quantitative evaluation with extensive simulations and use multiple sets of real data to highlight how parameter changes impact computed reconstructions. Our results show that volumetric basis functions can improve accuracy by as much as 30%, while reducing computational complexity by over two orders of magnitude. In real data from epilepsy surgical candidates, accurate localization of seizure onset regions is demonstrated. Conclusion: Spatial dimensionality reduction with volumetric basis functions improves reconstruction accuracy while reducing computational complexity. Significance: Near-arbitrary spatial dimensionality reduction will enable volumetric reconstruction with modern computationally intensive algorithms and anatomically driven multi-resolution methods.