Practically perfect peristaltic pump performance

The ureter transports urine from the kidney to the bladder through peristalsis. The musculature of its wall is often considered as multiple layers of helically-oriented smooth muscle: an inner layer oriented primarily longitudinally and other layers oriented more circumferentially. While observation of the ureter during peristalsis shows both lateral and longitudinal movement, the first model to include longitudinal motion was developed by Kalayeh et al. (2023), expanding on Shapiro's (1967) earlier 2D sinusoidal wall motion using lubrication theory. Shapiro's model had impracticalities, such as achieving near 100% efficiency only for near zero pressure rise and having reflux at high efficiency. Kalayeh's model improved performance modestly. We now show that a slight modification of the form of longitudinal motion leads to almost 100% efficiency without reflux over the entire pressure range. We discuss further model refinements and propose future in vivo experimental verification.