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Comparison of Non-Newtonian Models of One-Dimensional Hemodynamics

Author

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  • Gerasim Vladimirovich Krivovichev

    (Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russian)

Abstract

The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated.

Suggested Citation

  • Gerasim Vladimirovich Krivovichev, 2021. "Comparison of Non-Newtonian Models of One-Dimensional Hemodynamics," Mathematics, MDPI, vol. 9(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2459-:d:649047
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    References listed on IDEAS

    as
    1. Elhanafy, Ahmed & Guaily, Amr & Elsaid, Ahmed, 2019. "Numerical simulation of blood flow in abdominal aortic aneurysms: Effects of blood shear-thinning and viscoelastic properties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 55-71.
    2. Taha Sochi, 2016. "The flow of power law fluids in elastic networks and porous media," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 19(3), pages 324-329, February.
    3. A.D. Caballero & S. Laín, 2015. "Numerical simulation of non-Newtonian blood flow dynamics in human thoracic aorta," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(11), pages 1200-1216, August.
    4. Ameenuddin, Mohammed & Anand, Mohan & Massoudi, Mehrdad, 2019. "Effects of shear-dependent viscosity and hematocrit on blood flow," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 299-311.
    Full references (including those not matched with items on IDEAS)

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