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Graph Theory for Modeling and Analysis of the Human Lymphatic System

Author

Listed:
  • Rostislav Savinkov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Nikolsky Mathematical Institute, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
    These authors contributed equally to this work.)

  • Dmitry Grebennikov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute for Personalized Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
    These authors contributed equally to this work.)

  • Darya Puchkova

    (Moscow Institute of Physics and Technology, National Research University, 141700 Dolgoprudny, Moscow Region, Russia)

  • Valery Chereshnev

    (Institute of Immunology and Physiology, Ural Branch of Russian Academy of Sciences, 620000 Yekaterinburg, Russia)

  • Igor Sazonov

    (College of Engineering, Swansea University, Swansea SA1 8EN, UK)

  • Gennady Bocharov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute for Personalized Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia)

Abstract

The human lymphatic system (HLS) is a complex network of lymphatic organs linked through the lymphatic vessels. We present a graph theory-based approach to model and analyze the human lymphatic network. Two different methods of building a graph are considered: the method using anatomical data directly and the method based on a system of rules derived from structural analysis of HLS. A simple anatomical data-based graph is converted to an oriented graph by quantifying the steady-state fluid balance in the lymphatic network with the use of the Poiseuille equation in vessels and the mass conservation at vessel junctions. A computational algorithm for the generation of the rule-based random graph is developed and implemented. Some fundamental characteristics of the two types of HLS graph models are analyzed using different metrics such as graph energy, clustering, robustness, etc.

Suggested Citation

  • Rostislav Savinkov & Dmitry Grebennikov & Darya Puchkova & Valery Chereshnev & Igor Sazonov & Gennady Bocharov, 2020. "Graph Theory for Modeling and Analysis of the Human Lymphatic System," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2236-:d:463784
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    Cited by:

    1. Narjes Firouzkouhi & Reza Ameri & Abbas Amini & Hashem Bordbar, 2022. "Semihypergroup-Based Graph for Modeling International Spread of COVID- n in Social Systems," Mathematics, MDPI, vol. 10(23), pages 1-14, November.

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