IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i19p2459-d649047.html
   My bibliography  Save this article

Comparison of Non-Newtonian Models of One-Dimensional Hemodynamics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/19/2459/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/19/2459/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Krivovichev, Gerasim V., 2022. "Comparison of inviscid and viscid one-dimensional models of blood flow in arteries," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    2. Bhaumik, Bivas & De, Soumen & Changdar, Satyasaran, 2024. "Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 21-36.
    3. Leidy Tatiana Contreras & Omar Dario Lopez & Santiago Lain, 2018. "Computational Fluid Dynamics Modelling and Simulation of an Inclined Horizontal Axis Hydrokinetic Turbine," Energies, MDPI, vol. 11(11), pages 1-23, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2459-:d:649047. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.