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On the Dynamic Suction Pumping of Blood Cells in Tubular Hearts

  • Nicholas A. BattistaEmail author
  • Andrea N. Lane
  • Laura A. Miller
Conference paper
Part of the Association for Women in Mathematics Series book series (AWMS, volume 8)

Abstract

Around the third week after gestation in embryonic development, the human heart consists only of a valveless tube, unlike a fully developed adult heart, which is multi-chambered. At this stage in development, the heart valves have not formed and so net flow of blood through the heart must be driven by a different mechanism. It is hypothesized that there are two possible mechanisms that drive blood flow at this stage—Liebau pumping (dynamic suction pumping (DSP) or valveless pumping) and peristaltic pumping. We implement the immersed boundary method (IBM) with adaptive mesh refinement (IBAMR) to numerically study the effect of hematocrit on the circulation around a valveless tube. Both peristalsis and DSP are considered. In the case of DSP, the heart and circulatory system is simplified as a flexible tube attached to a relatively rigid racetrack. For some Womersley number (Wo) regimes, there is significant net flow around the racetrack. We find that the addition of flexible blood cells does not significantly affect flow rates within the tube forWo ≤ 10, except in the case forWo ≈ 1. 5 where we see a decrease in average flow with increasing volume fraction. On the other hand, peristalsis consistently drives blood around the racetrack for allWo and for all hematocrit considered.

Notes

Acknowledgements

The authors would like to thank Steven Vogel for conversations on scaling in various hearts. We would also like to thank Lindsay Waldrop, Austin Baird, Jiandong Liu, Leigh Ann Samsa, and William Kier for discussions on embryonic hearts. This project was funded by NSF DMS CAREER #1151478 awarded to L.A.M. Funding for N.A.B. was provided from an National Institutes of Health T32 grant [HL069768-14; PI, Christopher Mack].

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Copyright information

© The Author(s) and the Association for Women in Mathematics 2017

Authors and Affiliations

  • Nicholas A. Battista
    • 1
    Email author
  • Andrea N. Lane
    • 2
  • Laura A. Miller
    • 1
  1. 1.Departments of Mathematics and BiologyUniversity of North CarolinaChapel HillUSA
  2. 2.Departments of Biostatistics and MathematicsUNC Gillings School of Global Public HealthChapel HillUSA

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