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 - 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
AN - SCOPUS:85057444225
T3 - Association for Women in Mathematics Series
SP - 211
EP - 231
BT - Association for Women in Mathematics Series
PB - Springer
ER -