Valveless pumping: the reflected pulse wave hypothesis

Valveless pumping refers to nonzero mean flow of fluid within a closed loop of viscoelastic tubing, when a compliant section of the loop is rhythmically compressed at particular frequencies. Valveless pumping is thought to play a role in blood circulation in embryos and in cardiopulmonary resuscitation (CPR). Heretofore, the physical mechanism causing valveless pumping has remained a mystery. We consider closed loops composed of one length of soft, compliant tubing and one length of stiff, non-compliant tubing having equal internal diameters. The loops are filled with water and are compressed toward one end of the soft section. To model such pumps we characterize pulse (pressure) waves in the soft section using the classical wave equation assuming complete reflection of the pulse waves at the soft/stiff boundaries. Pulse wave velocity is specified by the Moens-Korteweg equation. The resulting instantaneous pressure difference across the fluid in the stiff segment is computed, and Newton’s second law is used to describe the instantaneous and time averaged movement of fluid through the stiff segment and around the loop. Mean flow equals zero if compression is performed at the midpoint of the soft segment. However, when changes in pulse wave velocity caused by expansion of the uncompressed regions of the soft segment are properly accounted for, nonzero mean flow develops during asymmetrical compression of the soft segment. The magnitude and direction of mean flow depend upon the compression frequency and can be reversed simply by changing from one compression frequency to another. Other parameters, such as compression point location and stiffness constants also act to determine the magnitude and direction of flow. Reflected pulse waves explain the existence and major features of valveless pumping on the basis of classical Newtonian physics.