Figure 1.
Fabrication of the ureter model.
A) Phases of ureter model (UM) fabrication. The male mold (MM) was inserted coaxially into a plastic hallow cylinder. A mixture of PDMS and curing agent was poured into the cylinder and cured at 80°C for 1 hr. The MM was then extracted from the cylinder and the resulting ureter model was further cured at 100°C for 30 min. B) Final UM with double-J stent (blue colour) placed inside. C) Particular of the terminal part of UM, in proximity to the vesico-ureter junction (VUJ). Note the presence of side holes and a curling “J” end of the stent.
Figure 2.
A) Syringe pump and pressure transducer were connected to the renal pelvis compartment of the ureter model. A microscope and a CCD camera were used for flow visualisation experiments. B) Schematic of the ureter model. The stent was inserted within UM, with its curling ends positioned in the renal pelvis and bladder compartment. C) A plastic sphere was used as a model of ureteric obstruction, with the stent passing through its hole so that the severity of ureteric obstruction (OB%) could be quantified from Eq. 1.
Table 1.
Summary of the experimental parameters values investigated in the present study to test the effects on the renal pelvic pressure.
Figure 3.
Schematic of the computational domain and boundary conditions.
A) Schematic representation of the two-dimensional computational domain. Colours correspond to different boundary conditions: red wall boundary; green outflow; light blue velocity inlet. B) Summary of the geometrical characteristics of the computational domain, and boundary conditions applied to each individual edge.
Figure 4.
Reconstruction of pig ureter geometry.
Average pig ureter internal diameters (Di, in mm; N = 8), along the longitudinal coordinate i (i = 0 at UP; i = 15 at VUJ) classified in Upper, Middle and Lower ureter (left). UPJ = ureteropelvic junction, VUJ = vesicoureteric junction. On the right, computer-aided design of the ureter employed as an input geometry for 3D printing.
Figure 5.
Renal pelvic pressure vs urine properties and severity of obstruction.
Renal pelvic pressure (P) in the ureteric model increases linearly with A) flow rate (Q in ml/min) and B) severity of obstruction in the upper UM (OB%, calculated using Eq. 1). Fixed values of OB% = 100 and Q = 20 ml/min were considered for the experimental data reported in A) and B), respectively. The fluid dynamic viscosity is equal to 1 cP. The equation of the least square regression line, the R-squared values and error bars are reported (N = 3). The slope of regression line in panel A represents the hydraulic resistance of the system. The horizontal red line indicates the critical value of renal pelvic pressure (P = 20 cmH2O).
Table 2.
Hydraulic resistances (in cmH2O*60 s/ml) measured from the slope (m) of the linear regression (R-squared values, R2, are also reported) of renal pelvic pressure versus flow rate values (example in Figure 5A) for each combination of viscosity and severity of obstruction (OB%).
Figure 6.
Dependence of UM renal pelvic pressure on fluid flow rate, dynamic viscosity and severity of obstruction.
Colourmaps show the dependence of ureteric model (UM) renal pelvic pressure on both the fluid flow rate (Q in ml/min, y-axis) and the fluid dynamic viscosity (μ in cP, x-axis). Colours correspond to different pressure values (in cmH2O) reported in the colourbar on the right hand side. A) OB% = 0, corresponding to unobstructed UM (absence of both plastic sphere and stent). B) refers to the condition of obstruction-causing effects, due to the stent only (absence of plastic sphere). Adding the plastic sphere, two values of severity of obstruction were considered: C) OB% = 88 and D) OB% = 100 (stent+plastic sphere, with hole size according to Eq. 1). Iso-pressure lines (in cmH2O) are reported (black lines). The green area corresponds to the safe region (P<15 cmH2O), the yellow area to the warning region (15<P<20 cmH2O) while the orange/red area to the dangerous region (P>20 cmH2O) for correct kidney functioning. N = 3.
Figure 7.
Two-dimensional numerical model of the flow field in close proximity to a stent side hole.
A–B) Numerical fluid pathlines in a region of the extra-luminal space of the stent positioned in close proximity to the 6th side hole, located after the plastic sphere. The mean velocity of the fluid exiting the stent side hole was set to: A) 0.01 m/sec and B) 0.1 m/sec. C) Magnitude of fluid velocity (in Log scale) along the centreline of the fluidic domain (in the x-direction), at vh = 0.01 m/sec (black squares) and 0.1 m/sec (red circles). x = 0 mm corresponds to the position of UM obstruction (i.e. plastic sphere) and x = 10.8 mm to the outflow boundary. Velocity minima correspond to the approximate position of eddies centre, as indicated by the black dashed lines. Changes in eddies velocity and size with increasing vh can be appreciated. D) formation of laminar eddies has been observed experimentally using fluorescent tracers, thus qualitatively corroborating with the numerical results. The direction of fluid flowing from the intra-luminal to the extra-luminal region of the stent is indicated by the blue arrow. SW = Stent wall; UMW = Ureter model wall.
Figure 8.
Severity of UM obstruction induced solely by stent insertion.
Severity of obstruction (OBi%) calculated along the longitudinal coordinate of the UM (D0–15, see Figure 4 for reference) introduced by the double-J stent only (absence of plastic sphere). For the calculations, Eq. 4 was considered. UPJ and VUJ indicate the urteropelvic and vesicureteric junctions, respectively.