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A vascular transport operator

R B King1, A Deussen, G M Raymond

  • 1Center for Bioengineering, University of Washington, Seattle 98195.

The American Journal of Physiology
|December 1, 1993
PubMed
Summary
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Blood flow dispersion in vessels is less than predicted by Newtonian flow due to cross-stream mixing and heart pulsations. A novel two-parameter operator models this intravascular mass transport effectively.

Area of Science:

  • Physiology
  • Biomedical Engineering
  • Fluid Dynamics

Background:

  • Blood flow exhibits dispersion of tracers/substrates within vessels.
  • Vascular transport is influenced by cross-stream mixing and heart pulsations.
  • Newtonian flow models (parabolic velocity profile) do not fully capture intravascular transport dynamics.

Purpose of the Study:

  • To develop a simplified model for intravascular mass transport.
  • To describe blood transport using a two-parameter differential operator.
  • To characterize the dispersion of substances in blood flow.

Main Methods:

  • A one-dimensional, two-parameter differential operator was formulated.
  • The operator comprises a pure delay and a fourth-order linear differential operator.

Related Experiment Videos

  • The operator's transport function was analyzed for skewness and kurtosis.

    • Main Results:

    • The developed operator accurately describes intravascular mass transport.
    • The operator accounts for blunter velocity profiles compared to Newtonian flow.
    • Relative dispersion (RD) values of 15-20% were observed in the human leg arterial system.

    Conclusions:

    • A simple two-parameter operator effectively models intravascular transport.
    • The model's parameters (mean transit time and relative dispersion) are crucial.
    • This model provides a suitable representation for blood transport dynamics in arterial systems.