3d-OT: a deep geometry-aware framework for heterogeneous slices alignment of spatial multi-omics.

The rapid advancement of spatial multi-omics technologies has unveiled opportunities for deciphering the intricate spatial heterogeneity; however, current computational approaches struggle to comprehensively integrate diverse molecular and spatial information. Here we propose 3d-OT, a deep geometry-aware framework that leverages spatial geometric and multi-omics information for feature extraction, spatial domains identification and heterogeneous slices alignment. 3d-OT utilizes modality fusion representation to align spatial slices, bridging the gap in spatial multi-omics alignment methods. Meanwhile, we handle nonrigid deformations in heterogeneous slice alignment through soft correspondence optimal transport, and the chamfer distance is introduced to quantify its performance. 3d-OT outperforms existing methods in capturing anatomical details of mouse brain cortex layers and tracking nonrigid deformations of heart and neural crest tissues at different resolutions. Finally, we construct the 3D spatiotemporal trajectory of mouse embryonic development. Overall, 3d-OT enables comprehensive understanding of existing spatial multi-omics data, offering a powerful computational tool to decipher the spatial complexity of biological tissues.