IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v21y1979i4p340-351.html
   My bibliography  Save this article

Accuracy of simple difference-differential equations for blood flow in arteries

Author

Listed:
  • Lefevre, J.
  • Magnus, A.

Abstract

This paper presents an analysis of the numerical accuracy of the representation of an arterial segment by difference-differential equations (dde) of low order (N). The analysis is done by comparing, in the linear autonomous case, the two-port representations of the exact solution (Womersley) and of the lumped approximation (Rideout) of the flow by N annuli of constant flows. For low N (2, 3) it is shown that the dde's overestimate greatly the longitudinal impedance of the artery. For higher N, we give a closed-form expression for this longitudinal impedance approximation and show that it converges toward the Womersley solution for N → ∞. However for N ⩽ 5 (which are the only practical cases) the error in longitudinal impedance remains large. Finally, the practical influence of these errors, is shown on a model of the pulmonary vascular bed of the dog for which the use of Rideout's method completely destroys the input impedance pattern shown by the Womersley solution.

Suggested Citation

  • Lefevre, J. & Magnus, A., 1979. "Accuracy of simple difference-differential equations for blood flow in arteries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(4), pages 340-351.
    • Handle: RePEc:eee:matcom:v:21:y:1979:i:4:p:340-351
    DOI: 10.1016/0378-4754(79)90003-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037847547990003X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(79)90003-X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rideout, V.C. & Beneken, J.E.W., 1975. "Parameter estimation applied to physiological systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 17(1), pages 23-36.
    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.

      More about this item

      Statistics

      Access and download statistics

      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:eee:matcom:v:21:y:1979:i:4:p:340-351. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      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.