TY - CHAP
T1 - On the Dynamic Suction Pumping of Blood Cells in Tubular Hearts
AU - Battista, Nicholas A.
AU - Lane, Andrea N.
AU - Miller, Laura A.
N1 - Funding Information: 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]. Funding Information: 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]. Publisher Copyright: © 2017, The Author(s) and the Association for Women in Mathematics.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-319-60304-9_11
DO - 10.1007/978-3-319-60304-9_11
M3 - Chapter
T3 - Association for Women in Mathematics Series
SP - 211
EP - 231
BT - Association for Women in Mathematics Series
PB - Springer
ER -