Longitudinal wall motion during peristalsis and its effect on reflux

In this study, for the first time, we consider longitudinal motion of the walls during peristalsis in a distensible tube and how this affects backward (or retrograde) flow, i.e. peristaltic reflux. Building on the analytical model developed by Shapiro et al. (J. Fluid Mech., vol. 37, no. 4, 1969, pp. 799–825) based on lubrication theory, we model peristalsis as a two-dimensional infinite sinusoidal wavetrain. We develop an objective function with high mechanical pumping efficiency and low reflux to find optimal peristalsis conditions. We show that optimal wall longitudinal motion contributes substantially to limiting reflux during peristalsis. The results suggest that the optimal form of wall longitudinal velocity is a linear function of the wall transverse coordinate, moving forward with the wave when the tube is distended and retracting when contracted. Our results are in general agreement with clinical observations of ureteral peristalsis.