3D Valveless Pumping
Eunok Jung and Sookkyung Lim

A pumping heart generates a unidirectional blood flow in the circulatory system while the cardiac valves open and close to prevent reversal flow ensuring a unidirectional net flow. What if the valves do not function normally? If there is a unidirectional net flow in a circulating system without valves, we call this phenomenon valveless pumping (VP). There are examples of valveless pumping in nature. One is a unidirectional blood circulation in the human embryo before the development of the heart valves. Another is a thoracic pump mechanism during cardiopulmonary resuscitation (CPR). Two controversial theories have been proposed to explain the mechanism of blood flow during CPR: thoracic pump and cardiac pump. The fundamental difference between these two mechanisms is whether the mitral valve opens or closes during chest compression. In thoracic pump models, the heart acts as a passive conduit for blood flow with the mitral valve always open. Mathematical modeling of VP may explain how blood flows without valves.

[1] Eunok Jung and Charles S. Peskin, Two-dimensional simulations of valveless pumping using the immersed boundary method, SIAM. J. Sci. Comput. Vol. 25, No. 6, pp. 2066-2083, 2004

[2] Eunok Jung and Sookkyung Lim, Three-dimensional mathematical model of valveless pumping, submitted to Bulletin of Mathematical Biology