Blood flow in venules: A mathematical model including valves inertia

  • Matteo Cardini Department of Mathematics and Informatics, University of Firenze, Italy.
  • Angiolo Farina | angiolo.farina@unifi.it Department of Mathematics and Informatics, University of Firenze, Italy.
  • Antonio Fasano Department of Mathematics and Informatics, University of Firenze; Scientific Manager and R&D Director, FIAB, Firenze; Associated to IASICNR, Roma, Italy.
  • Alberto Caggiati Department of Anatomy, La Sapienza University, Roma, Italy.

Abstract

It is well known that venules equipped with valves play a critical role in regulating blood flow. Essentially they are peristaltic pumps that increase the efficiency of venous blood return to the heart, thanks to the presence of valves preventing backflow. Inspired by two recent papers, we have modeled the venule as a vessel with valves placed at its ends and walls animated by radial oscillations that are independent of heart pulsation and respiratory rhythm. Differently from the previous papers, the present model takes into account the valves inertia allowing, for progressive closing/opening stages. The numerical simulations produce a pressure pulse and a velocity profile which agree almost perfectly with the experimental data of Dongaonkar et al., eliminating the discrepancies found in Farina et al., arising from the hypothesis that valves act instantaneously.

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Published
2019-09-09
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Original Articles
Keywords:
Vasomotion, blood flow in venules, mathematical modeling.
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How to Cite
Cardini, M., Farina, A., Fasano, A., & Caggiati, A. (2019). Blood flow in venules: A mathematical model including valves inertia. Veins and Lymphatics, 8(3). https://doi.org/10.4081/vl.2019.7946