Urinary flow through urethras with a rough lumen

Abstract

Aims: This study investigates how lumen roughness and urethral length influence urinary flow speed.

Methods: We used micro-computed tomography scans to measure the lumen roughness and dimensions for rabbits, cats, and pigs. We designed and fabricated three-dimensional-printed urethra mimics of varying roughness and length to perform flow experiments. We also developed a corresponding mathematical model to rationalize the observed flow speed.

Results: We update the previously reported relationship between body mass and urethra length and diameter, now including 41 measurements for urethra length and 10 measurements for diameter. We report the relationship between lumen diameter and roughness as a function of position down the urethra for rabbits, cats, and pigs. The time course of urinary speed from our mimics is reported, as well as the average speed as a function of urethra length.

Conclusions: Based on the behavior of our mimics, we conclude that the lumen roughness in mammals reduces flow speed by up to 25% compared to smooth urethras. Urine flows fastest when the urethra length exceeds 25 times its diameter. Longer urethras do not drain faster due to viscous effects counteracting the additional gravitational head. However, flows with our urethra mimics are still 6 times faster than those observed in nature, suggesting that further work is needed to understand flow resistance in the urethra.

Keywords: major loss; roughness; urethra.