Exploring ureteroscope design with computational fluid dynamics for improved intra-pelvic pressure

High intra-pelvic pressure (IPP) during ureteroscopy can lead to complications including pyelovenous backflow, bleeding, and infection. Our primary goal was to identify the best cross-section and orientation of a ureteroscope within a Ureteral Access Sheath (UAS) to minimize IPP and maximize outflow. Our secondary goal was to validate our findings with a UAS prototype. To determine the optimal ureteroscope cross-section within a UAS, four ureteroscopes of equivalent cross-sectional area were simulated within a 10 Fr UAS using computational fluid dynamics software COMSOL. We then created a corresponding prototype by securing a 3-0 monofilament suture at the inferior aspect of the 12 Fr outer UAS, inducing an offset to the ureteroscope. Mean flow volumes through a 10/12 Fr UAS occupied by a 9.5-Fr single-use flexible ureteroscope were compared (17 iterations) to those through our prototype UAS. During the simulation, the lowest IPP and highest outflow were seen with an offset circular ureteroscope (41% resistance) compared to a ureteroscope centered in the UAS. The unmodified UAS had an average volume of 30.0 mL/min (SD ± 0.35) compared to 33.76 mL/min (SD ± 0.90) for the modified UAS (p < 0.05). We found that using a circular ureteroscope positioned along the sidewall maximizes outflow through a circular UAS. We made a prototype UAS to offset the ureteroscope and observed a 12.5% increase in outflow. This approach can potentially decrease IPP during ureteroscopy without impacting inflow or the working channel. Although modifying a ureteroscope is more difficult, it could create an offset without reducing UAS cross-section.

One effective approach to regulating IPP during ureteroscopy is to utilize a ureteral access sheath (UAS) [9,10,15].Experimental evidence suggests that the diameter of the UAS is one critical parameter in outflow until a plateau at 10-12 Fr inner diameter, depending on the size of the ureteroscope used [5,11].While a larger inner diameter is also important for stone fragment retrieval, the size of the access sheath is often limited by the diameter of a patient's ureter.As such, using a smaller ureteroscope can be preferable [11], but technical limitations require a certain minimal cross-sectional area of a ureteroscope to house the internal components and maintain functionality [16].Currently, there exists a comprehensive understanding of the mathematical impact of factors such as irrigation pressure and technique, as well as variations in the diameter of the ureteroscope and access sheath, on intrarenal pressure.However, the optimal cross-sectional shape and orientation of a UAS and ureteroscope to achieve the lowest IPP remains unknown.The primary goal of our study was to identify the optimal cross-sectional shape and orientation within a UAS by conducting a finite-element analysis to simulate fluid flow in a UAS while manipulating the shape of the ureteroscope.Following the identification of the optimal cross-sectional shape within a UAS, our secondary goal was to develop a corresponding prototype to further test and validate our simulation findings.

Simulated equipment rationale
To ensure a fair comparison between different ureteroscopes, we estimated the minimum cross-sectional area to be that of a circular 7.5-Fr ureteroscope, which is considered the upper limit for an ideally sized device and the lower limit for commercially available ureteroscopes [17].We selected a 10-Fr inner diameter for the access sheath based on previous studies that suggested it is large enough for clinical use, yet small enough for fluid flow patterns to have a meaningful impact [5,11,13].

Ureteroscope configurations
We simulated four different ureteroscope cross-sections to maintain a 7.5 Fr "minimum cross-sectional area" in a 10 Fr UAS.The following ureteroscope shapes met the cross-sectional area and diameter criteria while maintaining plausible clinical utility: circle, "D" shaped circle with a 90-degree chord angle, oval, and offset circle.Unfortunately, other shapes, such as squares and triangles do not simultaneously meet the required cross-sectional area and fit within the 10 Fr sheath due to their small fractional areas.For example, the maximum fractional area that a square will occupy is 2/π (where the formula of a square inscribed within a circle is 2r 2 , that of the circle is πr 2 , with an absolute difference of (π − 2)r 2 ).The triangle would occupy an even smaller fraction.

Finite element analysis
The computational fluid dynamics software COMSOL (COMSOL Inc., Stockholm, Sweden) was used to perform finite-element analysis.The volumetric flow rate in the working channel of the ureteroscope is given by Q = P irr − P p ∕R US where P irr is the irrigation pressure at the entrance of the ureteroscope, P p is IPP, and R US is hydrodynamic resistance.Assuming laminar flow, resistance is estimated using the standard Hagen-Poiseuille equation, 4 ).Here, is the viscosity of water, and l SC and d SC are the length and the diameter of the scope, respectively.The outflow of irrigation fluid between the ureteroscope and the UAS is expressed as Q U = P p ∕R UAS .Resistance when the cross-sections of both UAS and ureteroscope are concentric and circular has been previously described [5,11].For other configurations, this resistance was determined by solving the equations of motion in COMSOL.The steady-state IPP is reached when the inflow equals outflow.

Prototype analysis
Once the optimal cross-sectional area within a UAS was determined, we created a corresponding UAS prototype.We decided to create a UAS prototype rather than a ureteroscope prototype as the modification of a ureteroscope is more technically challenging, understanding that flow rates should be ambivalent to the origin of the displacing structure.Our prototype was created by modifying a 10/12 Fr UAS (Olympus, Center Valley, PA, USA) by securing a taut 3-0 Prolene ® suture (J&J Medical Devices, New Brunswick, NJ, USA) at the inferior aspect of the sheath's lumen (Fig. 1).The distal end of the suture was glue to the funnel of the UAS (as shown in Fig. 1), the suture was then pulled proximally through the UAS lumen and looped out of the proximal end of the UAS where it was glued to the outside of the sheath.This prototype UAS was then placed horizontally Fig. 1 Prototype UAS, modified by securing a taut 3-0 Prolene ® suture to the inside of the UAS on an elevated surface at a height of 5 cm.The proximal end of the UAS was attached to vinyl tubing, which hung vertically and attached to a 1 L bag of normal saline (NS) at a height of 155 cm.The prototype UAS was occupied by a Boston Scientific (Marlborough, MA, USA) LithoVue ® single-use flexible ureteroscope (circular 9.5 Fr cross-section).We recorded the outflow volume after allowing NS to flow through the tubing for one minute.This was repeated for 17 total iterations.The same procedure was then repeat with the unmodified UAS for a total of 17 iterations.Mean flow volumes were compared using 2-tailed Student's t tests with significance set to p = 0.05.

Results
Volumetric flow rates between a ureteroscope and access sheath for given irrigation pressures as modeled within a 10 Fr UAS are depicted in the bottom pane of Fig. 2. Irrigation pressure was directly proportional to both IPP and flowrate.In the top pane of Fig. 2, a gradient of color depicts relative fluid flow velocity with blue representing low velocity, yellow representing medium velocity, and red representing high velocity.A 7.5 Fr circular ureteroscope centered within an access sheath with an inner diameter of 10 Fr demonstrated the highest IPP and the lowest outflow rate (Fig. 2A).Modification of the ureteroscope cross-section to an ellipse (Fig. 2B), measuring 8.5 × 6.6 Fr without compromising the cross-sectional area, resulted in reduction in the resistance to outflow to 84% of baseline and a comparable improvement in irrigation outflow.By modifying the shape of the ureteroscope to a circle with a 90° chord angle (Fig. 2C), the cross-sectional area of the ureteroscope is reduced by 9%.We observed that outflow resistance dropped to 60%, and the fluid outflow rate improved comparably.Finally, for any given irrigation pressure, the lowest IPP and highest outflow was seen with an offset circular ureteroscope (Fig. 2D).This configuration had only 41% of the outflow resistance of a ureteroscope in the center of a UAS.Time to steady state in the simulation was roughly 5 min.
With regard to our prototype analysis, the control UAS, which does not offset the ureteroscope, allowed for an average volume of 30.0 mL in 1 min (SD ± 0.35) compared to a volume of 33.76 in 1 min (SD ± 0.90) for the modified UAS, which does offset the ureteroscope (p < 0.05).

Discussion
Studies have shown that as IPP rises, rates of sepsis and complications may increase with one randomized controlled trial suggesting a 50% reduction in post-ureteroscopy sepsis with UAS utilization [5,18].Unfortunately, UAS size is often limited by the diameter of the patient's ureter and is, therefore, a non-modifiable factor.As such, modification of the ureteroscope's position within a UAS may allow for improvement in fluid outflow within a smaller UAS.Over the past several decades, significant improvements have been made in flexible ureteroscope technology.We have seen decreased diameters, disposable ureteroscopes, increased visualization, improvements in durability, and a wide variety of instruments developed to fit within increasingly large working channels [16].It is essential to weigh the benefits of miniaturization against the potential costs and impact on device functionality.
In our study, we found that for a fixed cross-sectional area of 7.5 Fr, offsetting a ureteroscope in a UAS is the most effective way to reduce IPP.We discovered that while the circular ureteroscope has the smallest diameter of any shape for a given cross-sectional area, it creates the highest resistance to flow when placed in the center of the sheath.However, placing the circular ureteroscope off-center in the sheath significantly decreased resistance to flow; more so than the "D" shaped ureteroscope with a 90-degree chord and the ellipse-shaped ureteroscope.
To improve irrigation outflow during ureteroscopy, modifying the ureteroscope or UAS to offset the ureteroscope to the side of the access sheath would be the most feasible in contrast to further miniaturization.This could be achieved by creating a UAS with a notch within the lumen which spans the length of the sheath.We propose a prototype UAS with a similar modification, which showed improved outflow compared to a standard UAS without affecting inflow or the working channel.However, this design may limit the maximal diameter of a stone which could be removed.The offset ureteroscope may also be achieved by placing a continuous band or small, tapered bumps or knobs along the length of the ureteroscope (Fig. 3), which would not disturb laminar fluid flow.Placing the lengthwise projection on the ureteroscope would not limit the diameter of the stone which could be removed, however, it would limit the use of the modified ureteroscope to concurrent utilization of a UAS as use without a UAS may cause damage to the ureter.Further study will focus on constructing model ureteral access sheaths and ureteroscopes and evaluating the difference in outflow measures between such prototypes in vitro.

Conclusions
Reducing intra-pelvic pressure during ureteroscopic procedures may limit the rate of postoperative sepsis or other pressure-related complications and improvements in technology may achieve this goal.Significant improvements in ureteroscope technology are limited by the irreducible constraints of miniaturization.Modification of the UAS or ureteroscope, such that the circular cross-section of a ureteroscope is offset within the access sheath, can increase outflow and reduce intra-pelvic pressure without a substantial re-design.The current study reports on computational modeling and a corresponding UAS prototype that improves ureteral irrigation outflow without costly miniaturization of the ureteroscope.Such design modifications may result in decreased IPP and, therefore, potential decrease post-procedural sepsis or other pressurerelated complications.
Author contributions C.M and A.S. wrote the main manuscript text and S.W. prepared figures 1-3.C.M. and S.W. reviewed the manuscript as well as made changes in response to the reviewers.

Fig. 2
Fig. 2 Top pane: a gradient of color depicts fluid flow velocity (blue: low, yellow: medium, red: high).A A circular 7.5 Fr ureteroscope has the highest resistance to flow (100% relative resistance).B An elliptical ureteroscope measuring 8.5 × 6.6 Fr demonstrates 84% relative resistance.C A 7.5 Fr circle with a 90° chord reduces cross-sectional area by 9% and has a 60% relative resistance.D A circular 7.5 Fr ure-

Fig. 3
Fig. 3 Schematic representation of an idealized flexible ureteroscope with radially oriented projections to produce the offset within a ureteral access sheath.A Cross-section, B side view