The ureter provides a way for urine to flow from the kidney to the bladder. Peristalsis in the ureter partially forces the urine flow, along with hydrostatic pressure. Ureteral diseases and a double J stent, which is commonly inserted in a ureteral stenosis or occlusion, disturb normal peristalsis. Ineffective or no peristalsis could make the contour of the ureter a tube, a funnel, or a combination of the two. In this study, we investigated urine flow in the abnormal situation. We made three different, curved tubular, funnel-shaped, and undulated ureter models that were based on human anatomy. A numerical analysis of the urine flow rate and pattern in the ureter was performed for a combination of the three different ureters, with and without a ureteral stenosis and with four different types of double J stents. The three ureters showed a difference in urine flow rate and pattern. Luminal flow rate was affected by ureter shape. The side holes of a double J stent played a different role in detour, which depended on ureter geometry.
The ureter is part of the upper urinary system and provides a way for urine to flow from the kidney to the bladder. The shape of the whole length of the ureter could be described as a tube, a funnel, or a combination of the two. The flow of urine is partially achieved through peristalsis along with hydrostatic pressure [
A ureteral stenosis or occlusion caused by stones or a malignancy requires a temporary or permanent urinary diversion or insertion of a ureteral stent, a thin hollow tube inserted temporarily or permanently into the ureter to prevent or treat obstruction of the urine flow from the kidney, to relieve the hydronephrosis that results from the pressure increase in the renal pelvis. The placement of a double J stent is a common treatment for stenosis, along with percutaneous nephrostomy, although various complications, such as urinary infection, migration, fracture, encrustation, and vesicoureteral reflux, have been reported with these treatments [
A ureter model with a double J stent. The ureter was (a) tubular, (b) funnel-shaped, or (c) undulated.
Urine flow in a ureter in which there is ineffective or no peristalsis must be different from urine flow in a ureter with normal peristalsis. In this study, we investigate urine flow in the abnormal situation. We made three different, curved tubular, funnel-shaped, and undulated ureter models based on human anatomy. Numerical analysis of urine flow rate and pattern in the ureter were performed for a combination of the three different ureters, with and without a ureteral stenosis, and using four different types of double J stents, for a total of 18 CFD models.
Most CFD studies [
The ureter models used in this study were based on data collected from 19 men who did not have any diseases in their urinary systems. The collection of the data was described in detail in our previous studies [
The double J stent used in the study was based on data collected from a study on a double J stent by a medical company. The stent consisted of two coils at both ends and a shaft in the middle. Each coil was round with a 10 mm diameter and had one end hole and four side holes, which were called ports to differentiate them from the side holes in the shaft. The shaft went along with the ureter and shared the same axis; the shaft had no side holes or it had multiple side holes. The inner and outer diameters of the stent were 1 mm and 2 mm, respectively. Double J stents are manufactured by various companies, and the number and geometry of the side holes in the stent depend on the manufacturer. Our previous studies [
Description of the ureter models used in the study.
Case | Ureter | Number of side holes | Angular position of side holes | Interval of side holes | Stenosis |
---|---|---|---|---|---|
1 | Tubular | 0 | — | — | None |
2 | Tubular | 11 | 0°, 180° | 2 cm | None |
3 | Tubular | 22 | 0°, 180° | 1 cm | None |
4 | Tubular | 45 | 0°, 180° | 0.5 cm | None |
5 | Tubular | 11 | 0°, 180° | 2 cm | One in ureter (at sixth side hole), 75% stenosis |
6 | Tubular | 11 | 0°, 180° | 2 cm | One in stent (at sixth side hole), 30% stenosis |
7 | Funnel | 0 | — | — | None |
8 | Funnel | 11 | 0°, 180° | 2 cm | None |
9 | Funnel | 22 | 0°, 180° | 1 cm | None |
10 | Funnel | 45 | 0°, 180° | 0.5 cm | None |
11 | Funnel | 11 | 0°, 180° | 2 cm | One in ureter (at sixth side hole), 75% stenosis |
12 | Funnel | 11 | 0°, 180° | 2 cm | One in stent (at sixth side hole), 30% stenosis |
13 | Undulated | 0 | — | — | None |
14 | Undulated | 11 | 0°, 180° | 2 cm | None |
15 | Undulated | 22 | 0°, 180° | 1 cm | None |
16 | Undulated | 45 | 0°, 180° | 0.5 cm | None |
17 | Undulated | 11 | 0°, 180° | 2 cm | One in ureter (at sixth side hole), 75% stenosis |
18 | Undulated | 11 | 0°, 180° | 2 cm | One in stent (at sixth side hole), 30% stenosis |
A stenosis in the ureter and an in-stent encrustation were made in all three ureters in the midureter, at the level of the 6th side hole of a stent with 11 side holes. A ureter model with a double J stent is shown in Figure
The continuity equation and the Navier–Stokes equation, which were the governing equations used in the study, were converted into algebraic equations with the discretization method using the finite volume method. We analyzed the flow rates and patterns in the ureter using Ansys CFX and a pressure-based AMG coupled solver. The continuity and momentum equations are shown below:
The urine viscosity and density applied in the study were 0.654 mPa·s and 1,003 kg/m3, respectively. Urine is similar to water in density and dynamic viscosity because it consists mostly of water. At a temperature of 37°C, the density and dynamic viscosity of urine are 1,003–1,035 kg/m3 and 0.635–0.797 mPa·s, respectively. The viscosity changes according to temperature, although the change is negligible in the range of normal body temperatures from 35°C to 40.5°C. Urine was considered a noncompressible and Newtonian fluid. Pressure was applied for the boundary condition where the inlet (97.8 Pa) and outlet (0 Pa) were specified based on the reference data [
Ansys ICEM was used for mesh generation. The ureter models had the same scale factor and seed size. Tetrahedron and prism meshes were used for the ports and side holes of the stents. As the number of side holes increased, the area for meshing decreased. The number of nodes and elements for a model depended on the model type; the number of nodes ranged from 1 million to 2.5 million, while the number of elements ranged from 5.7 million to 14.5 million. The grid dependency test was conducted to minimize the influence of the grid. To protect the phenomena that mesh is broken at the small side holes of a stent, global element scale factor and seed size were set as 0.975 and 0.32, respectively. Since geometry of a side hole was complex, factor of curvature based refinement was limited to 0.325. Thus, the average quality of the created grid was 0.75.
The flow rates and pattern in the renal pelvis, ureter, and bladder were investigated. In the stented ureter, urine flows through both the inner bore space of the stent (stent lumen) and the outer ureter space of the stent. The luminal flow rate was defined as the flow rate measured in the stent lumen; the extraluminal flow rate was defined as the flow rate in the ureter except in the stent lumen. The total flow rate was defined as the sum of the luminal and the extraluminal flow rates. The flow pattern in the stent lumen and ureter, especially around the ureteral stenosis and in-stent stenosis, was observed.
The total flow rate in each ureter with a double J stent was 23.4~23.6 ml/h for the tubular ureter, 17.5~17.9 ml/h for the funnel-shaped ureter, and 20.1~20.4 ml/h for the undulated ureter (Figure
Total flow rates in three different ureters with four different types of double J stents. (a) Cases
The total flow rate in ureters with a double J stent with side holes was higher than the total flow rate in ureters with a double J stent without side holes. Of the ureters with a double J stent with side holes, the highest rate was in the stent with 45 side holes and the lowest rate was in the stent with 11 side holes (Figure
The luminal flow rates in the three different ureters with a double J stent without side holes showed similar patterns (Figure
Luminal flow rates in three different ureters with a double J stent without side holes (Cases
The luminal flow rates in the three different ureters with a double J stent with multiple side holes showed different features (Figure
Luminal flow rates in three different ureters with a double J stent with multiple side holes (Cases
The luminal flow rate in the undulated ureter fluctuated along the whole ureter. It had two peaks in the proximal and distal ureter (Figure
The total flow rates in three different ureters with ureteral and in-stent stenoses are demonstrated in Figure
Total flow rates in three different ureters with no stenosis (Cases
The total flow rate in the tubular ureter with a ureteral stenosis was less than the total flow rate in the funnel-shaped ureter with a ureteral stenosis. The total flow rate in the undulated stented ureter with a ureteral stenosis was less than that in the tubular ureter with a ureteral stenosis. This could be explained by the diameters in the midureter where the ureteral stenosis was located. The ureter diameter in the funnel-shaped ureter was 4.64 mm (average of 5.69 mm and 3.59 mm), which was larger than the diameters in the tubular ureter (4.57 mm) and the undulated ureter (4.48 mm).
The luminal flow rates in three different ureters with a double J stent with 11 side holes and no stenosis, ureteral stenosis, and in-stent stenosis are demonstrated in Figures
Luminal flow rates in three different ureters with no stenosis, ureteral stenosis, and in-stent stenosis. (a) Tubular ureters (Cases
Total, luminal, and extraluminal flow rates in undulated ureters with (a) no stenosis, (b) ureteral stenosis, and (c) in-stent stenosis (Cases
In the tubular ureter, the role of the side holes in the stent shaft was limited to the first and last side holes of the double J stent; the other side holes did not play any significant role in the detour from the extraluminal to luminal spaces or the luminal to extraluminal spaces, although there was minimal fluctuation in luminal flow rates (Figure
Flow vectors in proximal, mid, and distal segment of the tubular ureter with no stenosis (Case
Flow vectors in proximal, mid, and distal segment of the funnel ureter with no stenosis (Case
Flow vectors in proximal, mid, and distal segment of the undulated ureter with no stenosis (case
Flow vectors in proximal, mid, and distal segment of the undulated ureter with a ureteral stenosis (Case
Flow vectors in proximal, mid, and distal segment of the undulated ureters with an in-stent stenosis (Case
Table
Reynold number in the ureter models.
Tubular | Funnel | Undulated | ||||
---|---|---|---|---|---|---|
|
|
|
|
|
|
|
No stenosis | 27.73 | 27.73 | 26.45 | 16.67 | 30.31 | 19.13 |
Ureteral stenosis | 12.21 | 8.55 | 14.53 | 7.49 | 11.43 | 6.21 |
In-stent stenosis | 27.70 | 27.70 | 26.73 | 16.85 | 30.42 | 19.19 |
Table
Pressure change at side holes in the ureter models.
Hole 1 | Hole 2 | Hole 3 | Hole 4 | Hole 5 | Hole 6 | Hole 7 | Hole 8 | Hole 9 | Hole 10 | Hole 11 | |
---|---|---|---|---|---|---|---|---|---|---|---|
Tubular [Pa] | |||||||||||
|
|||||||||||
No stenosis | 48.85 | 43.98 | 40.11 | 35.23 | 31.34 | 27.13 | 22.85 | 18.21 | 14.12 | 5.72 | 0.03 |
Ureteral stenosis | 48.89 | 47.38 | 46.18 | 44.67 | 43.46 | 42.09 | 24.89 | 5.71 | 4.35 | 1.76 | 0.01 |
In-stent stenosis | 48.85 | 43.98 | 40.11 | 35.22 | 31.32 | 27.13 | 18.15 | 14.08 | 5.71 | 1.48 | 0.03 |
|
|||||||||||
Funnel [Pa] | |||||||||||
|
|||||||||||
No stenosis | 48.88 | 47.78 | 46.51 | 45.07 | 43.15 | 40.84 | 37.95 | 34.29 | 29.33 | 14.63 | 0.06 |
Ureteral stenosis | 48.89 | 48.40 | 47.84 | 47.20 | 46.35 | 45.26 | 30.70 | 15.42 | 13.14 | 6.55 | 0.03 |
In-stent stenosis | 48.88 | 47.78 | 46.51 | 45.07 | 43.15 | 40.85 | 34.24 | 29.29 | 14.59 | 4.47 | 0.06 |
|
|||||||||||
Undulated [Pa] | |||||||||||
|
|||||||||||
No stenosis | 48.88 | 47.46 | 43.57 | 36.37 | 29.85 | 25.01 | 20.90 | 16.25 | 12.80 | 7.70 | 0.06 |
Ureteral stenosis | 48.89 | 48.44 | 47.17 | 44.84 | 42.71 | 41.07 | 5.36 | 4.14 | 2.49 | 1.42 | 0.02 |
In-stent stenosis | 48.88 | 47.47 | 43.58 | 36.40 | 29.89 | 25.07 | 16.23 | 12.80 | 7.71 | 4.39 | 0.06 |
Here, CFD was capable of studying the flows through double J stents with various side holes in different types of ureter and it could be a great help in selecting the most suitable stent with an optimal position of side holes with respect to a stenosis. In this study, we found that the three different ureters showed a difference in urine flow rate and pattern. Luminal flow rate was affected by the shape of the ureter. The side holes of a double J stent played a different role in the detour depending on ureter geometry. The findings suggest that we should use a ureter model closest to the human anatomy for more accurate studies of the ureter.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2014R1A1A1003987).