Urine is transported from the kidney to the urinary bladder through the ureter by peristalsis and pressure gradients. The contractile force acting on the ureter wall has drawn considerable interest in the field of biomechanics. Backflow of urine from bladder to the kidney can occur due to failure of the ureterovesical (ureteral-bladder) junction or blockage in the ureter passage because of recurrent urinary tract infection and also due to formation of stone in kidney. To understand the nature of the flow as well as its effect on the ureter wall, two-way fluid-solid interaction (FSI) modeling of the ureter peristaltic flow at different pressure is required. A transient 2D axisymmetric numerical calculation of ureteral wall peristalsis and urine flow is performed with a fully-coupled monolithic solver using an arbitrary Lagrangian-Eulerian (ALE) method. The ureter is assumed to be a circular tube with successive compression waves traveling downstream. The incompressible Navier-Stokes equations are solved to calculate the laminar flow of urine. The ureter wall is modeled as a non-linear hyper-elastic, nearly incompressible material, by curve fitting the biaxial test data of a human ureter, obtained from literature. Displacement due to peristalsis on ureteral wall is created with a compressive force having a Gaussian bell-curve variation along the length of the ureter, and a certain wavelength specified according to the data found from previous studies. It is observed that, as the compression wave travels from the abdominal part of the ureter towards to the pelvis, it is more likely for urine reflux to occur due to the failure of the ureteropelvic junction rather than the ureterovesical junction.

Urine moves from the kidney to the bladder through the ureter. A series of compression waves facilitates this transport. Due to the highly concentrated mineral deposits in urine, stones are formed in the kidney and travel down through the urinary tract. While passing, a larger stone can get stuck and cause severe damage to ureter wall. Also, stones in the ureter obstructing the urine flow can cause pain and backflow of urine which in turn might require surgical intervention. The current study develops a 2D axisymmetric numerical model to gain an understanding of the ureter obstruction and its effects on the flow, which are critical in assessing the different treatment options. Transient computational analysis involving a two-way fully coupled fluid-structure interaction with the arbitrary Lagrangian-Eulerian method between the ureteral wall and urine flow is conducted with an obstruction in the ureter. The ureter wall is modeled as an anisotropic hyperelastic material, data of which, is based on biaxial tests on human ureter from previous literature, while the incompressible Navier-Stokes equations are solved to calculate urine flow. A finite element-based monolithic solver is used for the simulations here. The obstruction is placed in the fluid domain as a circular stone at the proximal part of the ureter. One of the objectives of this study is to quantify the effect of the ureteral obstruction. A sharp jump in pressure gradient and wall shear stress, as well as retrograde urine flow, is observed as a result of the obstruction.

Obstruction in the ureter flow path is one of the most common problems in urinary-related diseases. As the ureter transports the urine using the expansion bolus created by the peristaltic pulses, an obstruction in its path can cause unwanted backflow and can also result in damage to the wall. But in order to understand this further, and specifically to quantify and parametrize the effect of the obstruction in the ureter, a detailed study investigating various level of obstructions in peristaltic ureter flow is necessary. In the current study, full 3D numerical simulations of peristalsis in an obstructed ureter are carried out using a finite element solver along with a two-way coupling between the fluid and structural domain with the arbitrary Eulerian-Lagrangian method. Analysis of the results shows that the larger the obstruction, the higher the wall shear stress and pressure gradient in the fluid. In addition, the amount of backflow increases with increase in the obstruction.

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