Spatial analysis of malignant-immune cell interactions in the tumor microenvironment using topological data analysis

The spatial interactions between malignant and immune cells in the tumor microenvironment are important for tumor immunobiology and patient outcomes. However, analytical tools that can extract rigorous yet interpretable spatial features and link them to patient outcomes remain limited. We propose a framework integrating TDA with statistical approaches to extract interpretable spatial features characterizing malignant-immune interactions. We introduce Topological Malignant Region (TopMR), which uses topological persistence to automatically define regions of malignant cells, providing an objective reference for spatial analysis even when tumor boundaries are ambiguous. Global-scale infiltration is quantified using signed distances from immune cells to the TopMR boundary and local-scale interactions are captured via malignant cell density around individual immune cells. These global and local features are integrated into a unified signed distance-density ($s\mathrm{DD}$) space, enabling comprehensive characterization of spatial patterns. We apply this framework to high-resolution multiplex immunofluorescence images of diffuse large B-cell lymphoma, analyzing both malignant-enriched and tumor border regions. Two-stage hierarchical clustering stratifies patients based on spatial interaction patterns, revealing associations with survival outcomes. This framework provides an end-to-end pipeline from spatial feature extraction to clinical interpretation, suggesting how region-aware spatial analysis can capture biologically meaningful patterns linked to patient survival.