title: Intravesical tunnel length to ureteral diameter ratio insufficiently explains ureterovesical junction competence: A parametric simulation study.
abstract: OBJECTIVE
  In 1959, Paquin recommended a tunnel length five times the diameter of the ureter to prevent vesicoureteral reflux (VUR) during ureteral reimplants. In 1969, Lyon et al. challenged Paquin's conclusions and proposed that the ureteral orifice was more important than the intravesical tunnel for UVJ competence. It is not known if the two mechanisms of UVJ competence (tunnel length and UO spatial orientation) are interdependent or if one is more critical. Although in clinical practice Paquin's rule has stood the test of time, classical mechanics of materials would predict more coaptation (less reflux) with larger diameter ureters and this contradicts Paquin's rule. The aim of this study was to test Paquin's tunnel length theory by parametrically modeling the ureterovesical junction (UVJ) to determine variables critical for ureteral closure.
  
  
  METHODS
  LS-DYNA finite-element simulation software was use to model ureteral collapse (Figure). Intravesical tunnel length, ureteral diameter, ureteral thickness and ureteral stiffness were all modeled. Changes in the pressure required to collapse the ureter were studied as each variable was changed on the model. The modeled ureteral orifice was not affected by changes in bladder volume (in a real bladder, bladder distention would pull the ureteral office open) and had no constraints (which could occur by suturing the ureteral orifice to a stiff bladder).
  
  
  RESULTS
  As predicted by classical mechanics of materials, the pressure required to collapse the ureter was inversely related to its diameter. Above 1 cm tunnel length, pressures required to collapse a ureter did not decrease by any significant amount. Increasing ureteral thickness or ureteral stiffness did increase the pressure required to collapse the ureter, but only significantly for ureteral thicknesses not commonly seen in practice (i.e. wall thickness of 2.5 mm in a 6.4 mm ureter).
  
  
  CONCLUSIONS
  Our model showed that for most ureters seen in clinical practice (3-30 mm in diameter), and when the ureteral orifice is not constrained by the bladder mucosa, a 1 cm tunnel would allow the ureter to collapse under low pressures. Contrary to Paquin's belief, larger diameter ureters collapsed more easily. It is important to understand that our model's main limitation was that it did not study the effects of the ureteral orifice, which in light of our findings must play an important role in preventing reflux as suggested by Lyon et al., in 1969. For example, a 3 cm ureteral orifice sutured to the bladder mucosa would be difficult to collapse as the bladder distends and pulls open the orifice. One way of compensating for a difficult to collapse ureteral orifice would be creating a larger diameter tunnel, but another would be to create a better ureteral orifice, perhaps by narrowing the diameter of the UO (distal ureteral tapering) and making it protrude into the bladder like a volcano (i.e. advancement sutures, or creating an intravesical nipple).
  
  
  CONCLUSIONS
  We hope that this new understanding of the variables involved in ureterovesical junction competence can lead to further refinement in our surgical techniques to correct vesicoureteral reflux.
authors.affiliation: University of Nebraska Medical Center/Children's Hospital and Medical Center, Omaha, NE, USA. Electronic address: cvillanueva.uro@gmail.com.
authors.forename: Carlos A
authors.initials: CA
authors.lastname: Villanueva
authors.affiliation: Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA; Department of Surgery, University of Nebraska Medical Center, Lincoln, NE, USA. Electronic address: cnelson5@unl.edu.
authors.forename: Carl A
authors.initials: CA
authors.lastname: Nelson
authors.affiliation: Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, USA. Electronic address: cale.stolle@huskers.unl.edu.
authors.forename: Cale
authors.initials: C
authors.lastname: Stolle
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D020342:Finite Element Analysis; D006801:Humans; D011312:Pressure; D014513:Ureter / Q000473:pathology* / Q000503:physiopathology; D014718:Vesico-Ureteral Reflux / Q000209:etiology* / Q000473:pathology*
keywords: Ureter; Ureteral diseases; Vesico-ureteral reflux