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Hagen-Poiseuille equation: A non-invasive tool for detecting renal pelvic pressure

Yansheng Li, Yancheng Wang, Xiuwu Han, Xuhui Zhu, Tao Li, Peng Zhang, Hui Shan, Xiaodong Zhang

Flexible Ureteroscopy (F-URS) has become an effective modality for treatment of upper urinary tract stone. This study aims to assess the feasibility of using Hagen-Poiseuille equation as a tool for speculating Renal Pelvic Pressure (RPP) during F-URS. The ureteral access sheath and polyscope were placed in the upper urinary tract model in a standard fashion. A tube was placed in the renal pelvis transparenchymally for pressure measurement. A saline bag surrounded by the pressure cuff of a mercurial sphygmomanometer provided the irrigating fluid at a constant flow rate in the Polyscope under a given pressure. The 20 mmHg pressure gradient was set from 100 mmHg to 300 mmHg. After building the in vitro model, the pressure drop (ΔP) across Polyscope was measured (ΔPm), or was calculated according to the Hagen-Poiseuille Equation (ΔPc). The flow rate (Q) was calculated by perfused fluid volume divided by the perfusion time. The variable (l) was obtained by length measuring. The radius (R) was available in the published literature. The viscosity of water and saline was tested. Finally, the ΔPc and ΔPm was compared statistically. Results showed that, ΔPc from Hagen-Poiseuille Equation failed to fit perfectly with ΔPm, but the regression model showed there was a strong linear relationship (R2=0.977) between them. The linear regression equation was established as ΔPm=0.992 ΔPc-29.498. Hagen-Poiseuille equation can be hopeful as a non-invasive validated tool for predicting the RPP during F-URS.