Critical size of kidney stone through ureter: A mechanical analysis

Blockage of ureter caused by kidney stone, accompanied by severe pain/infections, is a high incidence urinary tract disease that has received extensive attention. Currently, in clinics, a kidney stone with diameter less than ∼5 mm is considered capable of passing through ureter. However, this critical size (∼5 mm) is empirically based, lacking quantitative analysis. In this study, we proposed a stone-ureter interaction model to quantificationally estimate the critical size of kidney stone passing through ureter. We revealed that the critical size of kidney stone is related to ureter size, about 11%-22% larger than the inner diameter of ureter. Further, based upon the Winkler elastic foundation beam model, we developed a simplified stone-ureter interaction model to evaluate how this critical size is dependent upon the stiffness of ureter and the surface roughness of kidney stone. The proposed model may help urologists improve the accuracy of personalized diagnosis and treatment.