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New Boundary Conditions for One-Dimensional Network Models of Hemodynamics

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Abstract

New boundary conditions in the regions of vessel junctions for a one-dimensional network model of hemodynamics are proposed. It is shown that these conditions ensure the continuity of the solution and its derivatives at the points of vessel junctions. In the asymptotic limit, they give solutions that coincide with the solution in one continuous vessel. Nonreflecting boundary conditions at the endpoints of the terminal vessels are proposed. Results of numerical experiments that confirm the results of theoretical analysis are presented.

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Funding

This work was supported by the Russian Science Foundation, project no. 21-41-00029.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, 141700, Dolgoprudnyi, Moscow oblast, Russia

    S. S. Simakov

  2. Sechenov University, 119991, Moscow, Russia

    S. S. Simakov

  3. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia

    S. S. Simakov

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Correspondence to S. S. Simakov.

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Translated by A. Klimontovich

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Simakov, S.S. New Boundary Conditions for One-Dimensional Network Models of Hemodynamics. Comput. Math. and Math. Phys. 61, 2102–2117 (2021). https://doi.org/10.1134/S0965542521120125

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