Topography Aware Optimal Transport for Alignment of Spatial Omics Data

Understanding the spatial organization of tissues is essential for uncovering cellular communication, developmental processes, and disease mechanisms. Recent advances in spatial omics technologies have provided unprecedented insight into tissue spatial organization, but challenges remain in aligning spatial slices and integrating complementary single-cell and spatial data. Here, we propose TOAST (Topography-aware Optimal Alignment of Spatially-resolved Tissues), a novel OT-based framework that extends the classical Fused Gromov-Wasserstein (FGW) objective to more comprehensively model the heterogeneity of local molecular interactions. By introducing spatial coherence, quantified through the entropy of local neighborhoods, and neighborhood consistency, which preserves the expression profiles of neighboring spots, TOASTs objective function significantly improves the alignment of spatially resolved tissue slices and the mapping between single-cell and spatial data. Through comprehensive evaluations on both simulated and real-world datasets, including human brain cortex Visium data, Axolotl brain Stereo-seq data, mouse embryo seqFISH data, and Imaging Mass Cytometry from multiple cancer types, we demonstrate that our method consistently outperforms traditional FGW and other OT-based alignment methods. Specifically, TOAST improves the accuracy of spatial slice alignment, better preserves cell type compositions, recovers lineage trajectories in developmental brain data, and reconstructs spatial relationships in spatial transcriptomics mouse embryo data. By integrating spatial constraints into OT, our framework provides a principled approach to enhance the biological interpretability of spatially resolved omics data and facilitate multimodal data integration.