Multiscale domain identification for spatial transcriptomics via persistent homology

Spatial transcriptomics (ST) measures gene expression at a set of spatial locations in a tissue. Communities of nearby cells that express similar genes form spatial domains. Specialized clustering algorithms have been developed to identify spatial domains. These methods often locate spatial domains at a single morphological scale, and interactions across multiple scales are often overlooked. For example, large domains often contain smaller substructures and heterogeneous regions may lie between homogeneous domains. Topological data analysis (TDA) is an emerging mathematical toolkit that studies the underlying features of data at various geometric scales, especially useful for analyzing biological datasets with multiscale characteristics. Using TDA, we develop persistent homology for domains at multiple scales (PHD-MS) to locate tissue structures that persist across morphological scales. We apply PHD-MS to highlight multiscale spatial domains across tissue types and ST technologies. We compare PHD-MS domains against expert-annotated ground truth, where PHD-MS outperforms traditional clustering approaches.