Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study

Authors Andrew Aukerman , Mathieu Carrière, Chao Chen , Kevin Gardner, Raúl Rabadán , Rami Vanguri

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Andrew Aukerman
  • Department of Pathology & Cell Biology, Columbia University, New York, NY, United States
Mathieu Carrière
  • Department of Systems Biology, Columbia University, New York, NY, United States
Chao Chen
  • Department of Biomedical Informatics, Stony Brook University, NY, United States
Kevin Gardner
  • Department of Pathology & Cell Biology, Columbia University, New York, NY, United States
Raúl Rabadán
  • Department of Systems Biology, Columbia University, New York, NY, United States
Rami Vanguri
  • Department of Pathology & Cell Biology, Columbia University, New York, NY, United States

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Andrew Aukerman, Mathieu Carrière, Chao Chen, Kevin Gardner, Raúl Rabadán, and Rami Vanguri. Persistent Homology Based Characterization of the Breast Cancer Immune Microenvironment: A Feasibility Study. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Persistent homology is a common tool of topological data analysis, whose main descriptor, the persistence diagram, aims at computing and encoding the geometry and topology of given datasets. In this article, we present a novel application of persistent homology to characterize the spatial arrangement of immune and epithelial (tumor) cells within the breast cancer immune microenvironment. More specifically, quantitative and robust characterizations are built by computing persistence diagrams out of a staining technique (quantitative multiplex immunofluorescence) which allows us to obtain spatial coordinates and stain intensities on individual cells. The resulting persistence diagrams are evaluated as characteristic biomarkers of cancer subtype and prognostic biomarker 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. This provides new insights and possibilities on the general problem of building (topology-based) biomarkers that are characteristic and predictive of cancer subtype, overall survival and response to therapy.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Topological data analysis
  • persistence diagrams


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