PERSISTENT HOMOLOGY BASED CHARACTERIZATION OF THE BREAST CANCER IMMUNE MICROENVIRONMENT: A FEASIBILITY STUDY

Persistent homology is a powerful tool in topological data analysis. The main output, persistence diagrams, encode the geometry and topology of given datasets. We present a novel application of persistent homology to characterize the biological environ-ment surrounding breast cancers, known as the tumor microenvironment. Specifically, we will characterize the spatial arrangement of immune and malignant epithelial (tumor) cells within the breast cancer immune microenvironment. Quantitative and robust characteriza-tions are built by computing persistence diagrams from quantitative multiplex immunoflu-orescence, which is a technology which allows us to obtain spatial coordinates and protein intensities on individual cells. The resulting persistence diagrams are evaluated as characteristic biomarkers predictive of cancer subtype and prognostic of overall survival. For a cohort of approximately 700 breast cancer patients with median 8.5-year clinical follow-up, we show that these persistence diagrams outperform and complement the usual descriptors which capture spatial relationships with nearest neighbor analysis. Our results thus suggest new methods which can be used to build topology-based biomarkers which are characteristic and predictive of cancer subtype and response to therapy as well as prognostic of overall survival.