The effect of ureteric stents on urine flow: Reflux

If the ureter becomes blocked, the resultant increased pressure may be relieved by inserting a double-J stent (a polymer tube, usually punctuated with holes). A major clinical problem associated with stent use is reflux (retrograde flow of urine from the bladder to the kidney), which may result in infections, scarring, and even renal failure. We develop a mathematical model, treating the ureter as an elastic tube and the stent as a permeable rigid tube within it. We investigate how the number of holes in the stent wall affects the total amount of reflux that occurs when bladder pressure rises, by considering the limits of a highly-permeable stent, and an impermeable stent. We find that, in the scenarios we consider, the highly-permeable stent gives rise to less total reflux than the impermeable one.Revised version: 8 August 2003     

Finite-element modeling of the hemodynamics of stented aneurysms

BACKGROUND: Computational fluid dynamics (CFD) simulations are used to analyze the wall shear stress distribution and flow streamlines near the throat of a stented basilar side-wall aneurysm. Previous studies of stented aneurysm flows used low mesh resolution, did not include mesh convergence analyses, and depended upon conformal meshing techniques that apply only to very artificial stent geometries. METHOD OF APPROACH: We utilize general-purpose computer assisted design and unstructured mesh generation tools that apply in principle to stents and vasculature of arbitrary complexity. A mesh convergence analysis for stented steady flow is performed, varying node spacing near the stent. Physiologically realistic pulsatile simulations are then performed using the converged mesh. RESULTS: Artifact-free resolution of the wall shear stress field on stent wires requires a node spacing of approximately 1/3 wire radius. Large-scale flow features tied to the velocity field are, however, captured at coarser resolution (nodes spaced by about one wire radius or more). CONCLUSIONS: Results are consistent with previous work, but our methods yield more detailed insights into the complex flow dynamics. However, routine applications of CFD to anatomically realistic cases still depend upon further development of dedicated algorithms, most crucially to handle geometry definition and mesh generation for complicated stent deployments.     

A two way fully coupled fluid structure simulation of human ureter peristalsis

Abstract

Numerical simulations of ureter peristalsis have been carried out in the past to understand both the flow field and ureter wall mechanics. The main objective of the current investigations is to have a better understanding of the urine transport due to the peristalsis in the ureter, thus making the information helpful for a better treatment and diagnosis of ureteral complications like urine reflux. In the current study, a numerical simulation is performed using a finite-element-based solver with a two-way fully coupled fluid structure interaction approach between the ureter wall and urine. For the first time, the ureter wall is modeled as an anisotropic hyper-elastic material based on experiments performed in previous literature on the human ureter. Peristalsis in the ureter is modeled as a series of isolated boluses. By observing the flow field it is clear that the peristalsis mechanism has a natural tendency to create a backflow as the isolated bolus moves forward. As a result, the urine can flow back from the bladder to the ureter at the ureterovesical (ureter-bladder) junctions, if the one-way valve starts to malfunction.     

Flow-tissue interaction with compliance mismatch in a model stented artery

The insertion of an endovascular prosthesis is known to have a thrombogenic effect that is also a consequence of the interaction between the flowing blood and the stented arterial segment; in fact the prosthesis induces a compliance mismatch and a possible small expansion along the vessel that eventually gives rise to an anomalous distribution of wall shear stresses. The fluid dynamics inside a rectilinear elastic vessel with compliance and section variation is studied here numerically. A recently introduced perturbative approach is employed to model the interaction between the fluid and the elastic tissue; this approximate technique is first validated by comparison with a complete solution within a simple one-dimensional model of the same system. Then it is applied to an axisymmetric model in order to evaluate the flow dynamics and the distribution of wall shear stress in the stented vessel. Compliance mismatch is shown to produce more intense negative wall shear stresses in the stented segment while rapid variations of wall shear stress are found at the stent ends. These effects are enhanced when the prosthesis is accompanied by a small increase of the vessel lumen.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

Reproducibility of haemodynamical simulations in a subject-specific stented aneurysm model--a report on the Virtual Intracranial Stenting Challenge 2007

This paper presents the results of the Virtual Intracranial Stenting Challenge (VISC) 2007, an international initiative whose aim was to establish the reproducibility of state-of-the-art haemodynamical simulation techniques in subject-specific stented models of intracranial aneurysms (IAs). IAs are pathological dilatations of the cerebral artery walls, which are associated with high mortality and morbidity rates due to subarachnoid haemorrhage following rupture. The deployment of a stent as flow diverter has recently been indicated as a promising treatment option, which has the potential to protect the aneurysm by reducing the action of haemodynamical forces and facilitating aneurysm thrombosis. The direct assessment of changes in aneurysm haemodynamics after stent deployment is hampered by limitations in existing imaging techniques and currently requires resorting to numerical simulations. Numerical simulations also have the potential to assist in the personalized selection of an optimal stent design prior to intervention. However, from the current literature it is difficult to assess the level of technological advancement and the reproducibility of haemodynamical predictions in stented patient-specific models. The VISC 2007 initiative engaged in the development of a multicentre-controlled benchmark to analyse differences induced by diverse grid generation and computational fluid dynamics (CFD) technologies. The challenge also represented an opportunity to provide a survey of available technologies currently adopted by international teams from both academic and industrial institutions for constructing computational models of stented aneurysms. The results demonstrate the ability of current strategies in consistently quantifying the performance of three commercial intracranial stents, and contribute to reinforce the confidence in haemodynamical simulation, thus taking a step forward towards the introduction of simulation tools to support diagnostics and interventional planning.     

Flow of urine through the ureter: a collapsible, muscular tube undergoing peristalsis

In steady flow through nonuniform collapsible tubes a key concept is the compressive zone, at which flow limitation can occur at both high and low Reynolds numbers. Ureteral peristalsis can be considered as a series of compressive zones, corresponding to waves of active muscular contraction, that move at near-constant speed along the ureter towards the bladder. One-dimensional, lubrication-theory analysis shows that peristalsis can pump urine from kidney into the bladder only at relatively low mean rates of urine flow. Under these circumstances isolated boluses of urine are propelled steadily through the ureter (assumed uniform) by the contraction waves. At higher mean rates of flow the behavior depends on whether the frequency of peristalsis is higher or lower than a critical value. For frequencies above the critical value steady propagation of boluses that are in contact with contraction waves at both ends is possible. As the flow rate rises the urine begins to leak through the contraction waves and steady peristaltic flow breaks down. There is an upper limit to the mean flow rate that can be carried by steady peristalsis, which depends on the mechanical properties of the ureter. At high flow rates the peristaltic contractions do not pump but hinder the flow of urine through the ureter.     

Compound Ex Vivo and In Silico Method for Hemodynamic Analysis of Stented Arteries

Hemodynamic factors such as low wall shear stress have been shown to influence endothelial healing and atherogenesis in stent-free vessels. However, in stented vessels, a reliable quantitative analysis of such relations has not been possible due to the lack of a suitable method for the accurate acquisition of blood flow. The objective of this work was to develop a method for the precise reconstruction of hemodynamics and quantification of wall shear stress in stented vessels. We have developed such a method that can be applied to vessels stented in or ex vivo and processed ex vivo. Here we stented the coronary arteries of ex vivo porcine hearts, performed vascular corrosion casting, acquired the vessel geometry using micro-computed tomography and reconstructed blood flow and shear stress using computational fluid dynamics. The method yields accurate local flow information through anatomic fidelity, capturing in detail the stent geometry, arterial tissue prolapse, radial and axial arterial deformation as well as strut malapposition. This novel compound method may serve as a unique tool for spatially resolved analysis of the relationship between hemodynamic factors and vascular biology. It can further be employed to optimize stent design and stenting strategies.     

Local hemodynamic analysis after coronary stent implantation based on Euler-Lagrange method

Coronary stents are deployed to treat the coronary artery disease (CAD) by reopening stenotic regions in arteries to restore blood flow, but the risk of the in-stent restenosis (ISR) is high after stent implantation. One of the reasons is that stent implantation induces changes in local hemodynamic environment, so it is of vital importance to study the blood flow in stented arteries. Based on regarding the red blood cell (RBC) as a rigid solid particle and regarding the blood (including RBCs and plasma) as particle suspensions, a non-Newtonian particle suspensions model is proposed to simulate the realistic blood flow in this work. It considers the blood’s flow pattern and non-Newtonian characteristic, the blood cell-cell interactions, and the additional effects owing to the bi-concave shape and rotation of the RBC. Then, it is compared with other four common hemodynamic models (Newtonian single-phase flow model, Newtonian Eulerian two-phase flow model, non-Newtonian single-phase flow model, non-Newtonian Eulerian two-phase flow model), and the comparison results indicate that the models with the non-Newtonian characteristic are more suitable to describe the realistic blood flow. Afterwards, based on the non-Newtonian particle suspensions model, the local hemodynamic environment in stented arteries is investigated. The result shows that the stent strut protrusion into the flow stream would be likely to produce the flow stagnation zone. And the stent implantation can make the pressure gradient distribution uneven. Besides, the wall shear stress (WSS) of the region adjacent to every stent strut is lower than 0.5 Pa, and along the flow direction, the low-WSS zone near the strut behind is larger than that near the front strut. What’s more, in the regions near the struts in the proximal of the stent, the RBC particle stagnation zone is easy to be formed, and the erosion and deposition of RBCs are prone to occur. These hemodynamic analyses illustrate that the risk of ISR is high in the regions adjacent to the struts in the proximal and the distal ends of the stent when compared with struts in other positions of the stent. So the research can provide a suggestion on the stent design, which indicates that the strut structure in these positions of a stent should be optimized further.

     

Evaluation of the effect of stent strut profile on shear stress distribution using statistical moments

Background  

In-stent restenosis rates have been closely linked to the wall shear stress distribution within a stented arterial segment, which in turn is a function of stent design. Unfortunately, evaluation of hemodynamic performance can only be evaluated with long term clinical trials. In this work we introduce a set of metrics, based on statistical moments, that can be used to evaluate the hemodynamic performance of a stent in a standardized way. They are presented in the context of a 2D flow study, which analyzes the impact of different strut profiles on the wall shear stress distribution for stented coronary arteries.     

Comparison of devices used for stent-assisted coiling of intracranial aneurysms

Introduction

Two self-expandable stents, the Neuroform and the Enterprise stent, are widely used for stent-assisted coiling (SAC) of complex shaped intracranial aneurysms. However, comparative knowledge about technical feasibility, peri- and post-procedural morbidity and mortality, packing densities as well as follow-up data is limited.

Material and Methods

We conducted a retrospective study to investigate differences in aneurysms stented with the Enterprise or Neuroform stents. Angiographic follow-up (mean 19.42 months) was available in 72.6% (61/84) of aneurysms treated with stent-assisted coiling. We further sought to compare stent-assisted coiling to a matched patient population with aneurysms treated by conventional coil embolization.

Results

The stenting success rate of the Enterprise was higher compared to the Neuroform stent (46/48 and 42/51, respectively). In 5 of 9 cases in which the Neuroform stent was not navigable to the landing zone, we successfully deployed an Enterprise stent instead. Eventually, 42 aneurysms were coiled after stenting in each group. We observed no significant differences in peri-procedural complication rate, post-procedural hospital stay, packing density, recurrence rate or number of in-stent stenosis. Strikingly, 36.1% of followed aneurysms in the SAC group showed progressive occlusion on angiographic follow-up imaging. The packing density was significantly higher in aneurysms treated by SAC as compared to conventionally coiled aneurysms, while recanalization rate was significantly lower in the SAC group.

Conclusion

The procedural success rate is higher using the Enterprise, but otherwise both stents exhibited similar characteristics. Lower recurrence frequency and complication rates comparable to conventional coil embolization emphasize the importance of stent-assisted coiling in the treatment of complex aneurysms. Progressive occlusion on angiographic follow-up was a distinct and frequent observation in the SAC group and may in part be due to flow diversion.     

Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

Background  

The success of stent implantation in the restoration of blood flow through areas of vascular narrowing is limited by restenosis. Several recent studies have suggested that the local geometric environment created by a deployed stent may influence regional blood flow characteristics and alter distributions of wall shear stress (WSS) after implantation, thereby rendering specific areas of the vessel wall more susceptible to neointimal hyperplasia and restenosis. Stents are most frequently implanted in curved vessels such as the coronary arteries, but most computational studies examining blood flow patterns through stented vessels conducted to date use linear, cylindrical geometric models. It appears highly probable that restenosis occurring after stent implantation in curved arteries also occurs as a consequence of changes in fluid dynamics that are established immediately after stent implantation.     

Luminal Flow Amplifies Stent-Based Drug Deposition in Arterial Bifurcations

Background

Treatment of arterial bifurcation lesions using drug-eluting stents (DES) is now common clinical practice and yet the mechanisms governing drug distribution in these complex morphologies are incompletely understood. It is still not evident how to efficiently determine the efficacy of local drug delivery and quantify zones of excessive drug that are harbingers of vascular toxicity and thrombosis, and areas of depletion that are associated with tissue overgrowth and luminal re-narrowing.

Methods and Results

We constructed two-phase computational models of stent-deployed arterial bifurcations simulating blood flow and drug transport to investigate the factors modulating drug distribution when the main-branch (MB) was treated using a DES. Simulations predicted extensive flow-mediated drug delivery in bifurcated vascular beds where the drug distribution patterns are heterogeneous and sensitive to relative stent position and luminal flow. A single DES in the MB coupled with large retrograde luminal flow on the lateral wall of the side-branch (SB) can provide drug deposition on the SB lumen-wall interface, except when the MB stent is downstream of the SB flow divider. In an even more dramatic fashion, the presence of the SB affects drug distribution in the stented MB. Here fluid mechanic effects play an even greater role than in the SB especially when the DES is across and downstream to the flow divider and in a manner dependent upon the Reynolds number.

Conclusions

The flow effects on drug deposition and subsequent uptake from endovascular DES are amplified in bifurcation lesions. When only one branch is stented, a complex interplay occurs – drug deposition in the stented MB is altered by the flow divider imposed by the SB and in the SB by the presence of a DES in the MB. The use of DES in arterial bifurcations requires a complex calculus that balances vascular and stent geometry as well as luminal flow.     

Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries

Restenosis resulting from neointimal hyperplasia (NH) limits the effectiveness of intravascular stents. Rates of restenosis vary with stent geometry, but whether stents affect spatial and temporal distributions of wall shear stress (WSS) in vivo is unknown. We tested the hypothesis that alterations in spatial WSS after stent implantation predict sites of NH in rabbit iliac arteries. Antegrade iliac artery stent implantation was performed under angiography, and blood flow was measured before casting 14 or 21 days after implantation. Iliac artery blood flow domains were obtained from three-dimensional microfocal X-ray computed tomography imaging and reconstruction of the arterial casts. Indexes of WSS were determined using three-dimensional computational fluid dynamics. Vascular histology was unchanged proximal and distal to the stent. Time-dependent NH was localized within the stented region and was greatest in regions exposed to low WSS and acute elevations in spatial WSS gradients. The lowest values of WSS spatially localized to the stented area of a theoretical artery progressively increased after 14 and 21 days as NH occurred within these regions. This NH abolished spatial disparity in distributions of WSS. The results suggest that stents may introduce spatial alterations in WSS that modulate NH in vivo.     

Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were 'treated' with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

A numerical assessment of wall shear stress changes after endovascular stenting

This theoretical/numerical study aims at assessing the haemodynamic changes induced by endovascular stenting. By using the classical one-dimensional linear pressure waves theory in elastic vessels, we first show that the modulus of the reflection coefficient induced by an endovascular prosthesis is most likely small since it is proportional to the stent-to-wavelength ratio. As a direct consequence, the wall motion of the elastic (stented) artery can be prescribed a priori and the coupled fluid-structure problem does not have to be solved for assessing the haemodynamic changes due to stenting. Several 2D axisymetric calculations are performed to solve the unsteady incompressible Navier-Stokes equations on moving meshes for different types of (stented) arteries. The numerical results suggest that endovascular stenting increases the systo-diastolic variations of the wall shear stress (by 35% at the middle of the stent, by almost 50% in the proximal transition region). Additional calculations show that over-dilated stents produce less haemodynamic perturbations. Indeed, the increase of the amplitude of the wall shear stress variations over the cardiac cycle is only 10% when the stent radius is equal to the radius of the elastic artery at systole (instead of being equal to the mean artery radius).     

Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were ‘treated’ with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

Beyond the Virtual Intracranial Stenting Challenge 2007: Non-Newtonian and flow pulsatility effects

The Virtual Intracranial Stenting Challenge 2007 (VISC’07) is becoming a standard test case in computational minimally invasive cerebrovascular intervention. Following views expressed in the literature and consistent with the recommendations of a report, the effects of non-Newtonian viscosity and pulsatile flow are reported. Three models of stented cerebral aneurysms, originating from VISC’07 are meshed and the flow characteristics simulated using commercial computational fluid dynamics (CFD) software. We conclude that non-Newtonian and pulsatile effects are important to include in order to discriminate more effectively between stent designs.     

Hydrodynamic effects of compliance mismatch in stented arteries

Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and development of treatment options imperative. The most common modality for treatment of occlusive coronary artery diseases is the use of stents. Stent design profoundly influences the postprocedural hemodynamic and solid mechanical environment of the stented artery. However, despite their wide acceptance, the incidence of stent late restenosis is still high (Zwart et al., 2010, "Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment," Current Treatment Options in Cardiovascular Medicine, 12(1), pp. 46-57), and it is most prevailing at the proximal and distal ends of the stent. In this work, we focus our investigation on the localized hemodynamic effects of compliance mismatch due to the presence of a stent in an artery. The compliance mismatch in a stented artery is maximized at the proximal and distal ends of the stent. Hence, it is our objective to understand and reveal the mechanism by which changes in compliance contribute to the generation of nonphysiological wall shear stress (WSS). Such adverse hemodynamic conditions could have an effect on the onset of restenosis. Three-dimensional, spatiotemporally resolved computational fluid dynamics simulations of pulsatile flow with fluid-structure interaction were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with uniform elastic modulus is used as the baseline control case. In order to study the effect of compliance variation on local hemodynamics, this baseline model is compared with models where the elastic modulus was increased by two-, five-, and tenfold in the middle of the vessel. The simulations provided detailed information regarding the recirculation zone dynamics formed during flow reversals. The results suggest that discontinuities in compliance cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients. The change in pressure gradient at the discontinuity was as high as 90%. The corresponding changes in WSS and oscillatory shear index calculated were 9% and 15%, respectively. We demonstrate that these changes are attributed to the physical mechanism associating the pressure gradient discontinuities to the production of vorticity (vorticity flux) due to the presence of the stent. The pressure gradient discontinuities and augmented vorticity flux are affecting the wall shear stresses. As a result, this work reveals how compliance variations act to modify the near wall hemodynamics of stented arteries.     

A mathematical simulation of the ureter: effects of the model parameters on ureteral pressure/flow relations

Ureteral peristaltic mechanism facilitates urine transport from the kidney to the bladder. Numerical analysis of the peristaltic flow in the ureter aims to further our understanding of the reflux phenomenon and other ureteral abnormalities. Fluid-structure interaction (FSI) plays an important role in accuracy of this approach and the arbitrary Lagrangian-Eulerian (ALE) formulation is a strong method to analyze the coupled fluid-structure interaction between the compliant wall and the surrounding fluid. This formulation, however, was not used in previous studies of peristalsis in living organisms. In the present investigation, a numerical simulation is introduced and solved through ALE formulation to perform the ureteral flow and stress analysis. The incompressible Navier-Stokes equations are used as the governing equations for the fluid, and a linear elastic model is utilized for the compliant wall. The wall stimulation is modeled by nonlinear contact analysis using a rigid contact surface since an appropriate model for simulation of ureteral peristalsis needs to contain cell-to-cell wall stimulation. In contrast to previous studies, the wall displacements are not predetermined in the presented model of this finite-length compliant tube, neither the peristalsis needs to be periodic. Moreover, the temporal changes of ureteral wall intraluminal shear stress during peristalsis are included in our study. Iterative computing of two-way coupling is used to solve the governing equations. Two phases of nonperistaltic and peristaltic transport of urine in the ureter are discussed. Results are obtained following an analysis of the effects of the ureteral wall compliance, the pressure difference between the ureteral inlet and outlet, the maximum height of the contraction wave, the contraction wave velocity, and the number of contraction waves on the ureteral outlet flow. The results indicate that the proximal part of the ureter is prone to a higher shear stress during peristalsis compared with its middle and distal parts. It is also shown that the peristalsis is more efficient as the maximum height of the contraction wave increases. Finally, it is concluded that improper function of ureteropelvic junction results in the passage of part of urine back flow even in the case of slow start-up of the peristaltic contraction wave.