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Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

Author

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  • Nieves Atienza

    (Departamento de Matemática Aplicada I, E.T.S. Ingeniería Informática, Universidad de Sevilla, Av. Reina Mercedes S.N., 41012 Sevilla, Spain
    These authors contributed equally to this work and are listed in alphabetical order.)

  • Maria-Jose Jimenez

    (Departamento de Matemática Aplicada I, E.T.S. Ingeniería Informática, Universidad de Sevilla, Av. Reina Mercedes S.N., 41012 Sevilla, Spain
    These authors contributed equally to this work and are listed in alphabetical order.)

  • Manuel Soriano-Trigueros

    (Departamento de Matemática Aplicada I, E.T.S. Ingeniería Informática, Universidad de Sevilla, Av. Reina Mercedes S.N., 41012 Sevilla, Spain
    These authors contributed equally to this work and are listed in alphabetical order.)

Abstract

We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial complexes) that are built from the regions representing the cells in the tissue. We use a complete and well-grounded set of numerical variables over those persistence barcodes, also known as topological summaries. A novel combination of normalization methods for both the set of input segmented images and the produced barcodes allows for the proven stability results for those variables with respect to small changes in the input, as well as invariance to image scale. Our study provides new insights to this problem, such as a possible novel indicator for the development of the drosophila wing disc tissue or the importance of centroids’ distribution to differentiate some tissues from their CVT-path counterpart (a mathematical model of epithelia based on Voronoi diagrams). We also show how the use of topological summaries may improve the classification accuracy of epithelial images using a Random Forest algorithm.

Suggested Citation

  • Nieves Atienza & Maria-Jose Jimenez & Manuel Soriano-Trigueros, 2021. "Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue," Mathematics, MDPI, vol. 9(15), pages 1-22, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1723-:d:599079
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    References listed on IDEAS

    as
    1. Daniel Sánchez-Gutiérrez & Aurora Sáez & Alberto Pascual & Luis M Escudero, 2013. "Topological Progression in Proliferating Epithelia Is Driven by a Unique Variation in Polygon Distribution," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-8, November.
    2. Sebastian A Sandersius & Manli Chuai & Cornelis J Weijer & Timothy J Newman, 2011. "Correlating Cell Behavior with Tissue Topology in Embryonic Epithelia," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-11, April.
    3. Luis M. Escudero & Luciano da F. Costa & Anna Kicheva & James Briscoe & Matthew Freeman & M. Madan Babu, 2011. "Epithelial organisation revealed by a network of cellular contacts," Nature Communications, Nature, vol. 2(1), pages 1-7, September.
    Full references (including those not matched with items on IDEAS)

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