Graph Theory for Modeling and Analysis of the Human Lymphatic System

Rostislav Savinkov, Dmitry Grebennikov, Darya Puchkova, Valery Chereshnev, Igor Sazonov and Gennady Bocharov
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Rostislav Savinkov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
Dmitry Grebennikov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
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

Mathematics, 2020, vol. 8, issue 12, 1-18

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.

Keywords: graph theory; networks; mathematical modeling; lymphatic system; immunology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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