Impact of gas bubble size on peristaltic blood flow dynamics in renal vein: an analytical study of venous embolism

Abstract This study presents an analytical investigation of the hemodynamic influence of gas bubbles on concentration, velocity, pressure, streamlines and flow rate of Newtonian blood plasma within the peristaltic horizontal renal vein. We used the assumption that the governing equations are solved analytically under the long-wavelength approximation ( δ → 0). The pathological presence of a gas phase adversely affects all vital parameters. The flow is governed by the coupled conservation equation for mass, momentum, volume flow rate, and concentration, in conjunction with the Navier–Stokes equations. This investigation simulates the scenario where a gas embolus develops in a vein, a condition that directly leads to venous embolism and potential vascular occlusion. The analysis demonstrates that the growing gas phase exerts a significant influence on the blood concentration, volume flow rate, velocity profile, and pressure gradient. Specifically, these hemodynamic variables exhibit significant sensitivity to minute variations in the gas bubble radius ( R 0 ) and the Grashof number ( G r ). The presence of the gas–blood mixture results in a substantial decay of the blood plasma velocity and volume flow rate when compared to the healthy (single-phase) flow, providing insight into the mechanism of vascular blockage. Our results demonstrate that increasing the gas bubble radius from R 0 = 0 to R 0 = 6×10 −3 m reduces the blood flow velocity by approximately near 0 and decreases the volume flow rate from 300 mL min −1 , for the right kidney flow, to nearly 0 mL min −1 . Additionally, the plasma pressure gradient between the right renal vein and inferior vena cava exceeds 1.0 mm Hg, indicating severe gas occlusion and flow disruption. This study provides the first analytical investigation of biphasic peristaltic flow in a horizontal renal vein, extending our previous work on vertical mesenteric veins to address transverse buoyancy effects and critical blockage thresholds.