Critical Reviews™ in Biomedical Engineering, 41(3):259–268 (2013)
Simulation of the Upper Urinary System Ghazaleh Hosseini,1 John J.R. Williams,1 Eldad J. Avital,1 A. Munjiza,1 Xu Dong,1 & James S.A. Green2 School of Engineering and Materials science, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom; 2Department of Urology, Barts Health NHS Trust, Whipps Cross University Hospital, Whipps Cross Road, London E11 1NR
1
*Address all correspondence to: Ghazaleh hosseini, e-mail:
[email protected], ProfessorJohn J.R Williams, e-mail: j.j.r.williams@qmul. ac.uk, Tel: +44 (0)20 7882 5306
ABSTRACT: The ureter and its peristalsis motions have long been of significant interest in biomechanics. In this article we review experimental, theoretical, and numerical studies of the behavior of the ureter together with its mechanical properties, emphasizing studies that contain information of importance in building a virtual simulation tool of the complete ureter that includes its complex geometry, nonlinear material properties, and interaction with urine flow. A new technique to model the contraction of a ureter, which directly applies wall forces to model pacemaker activities, is presented. The required further steps to capture the full complex movement of the peristalsis are discussed, aiming to construct a computational platform that will provide a reliable tool to assist in the investigation and design of material devices (stents) for the renal system. KEY WORDS: ureter, computational fluid dynamics, peristalsis movement
I.
INTRODUCTION
Ureters are muscular tubes that propel urine from the kidneys to the urinary bladder, with lengths that vary between 27 and 37cm. Two major problems can occur with the ureter: obstruction of the ureteropelvic junction and vesicoureteral reflux. The obstruction of the ureteropelvic junction is an obstruction of the flow of urine from the renal pelvis to the proximal ureter, and vesicoureteral reflux can occur when there is irregular movement of urine from the bladder into the ureters. Peristaltic movement causes urine transport and is initiated by the activity of a few pacemaker regions in the renal pelvis. Many researchers believe the location of the primary pacemaker is situated in the most proximal calyceal regions of the renal pelvis.1–5 However, others suggest they are located in the pelvis ureteric junction.6–9 The ureter, like the heart, has other areas that also have the ability to contract; these are called latent pacemakers sites.10 In vivo peristalsis contractions propagate in a way that is unaffected by use of any neuron blocking agents and therefore show myogenic properties.11–13 Furthermore, in vivo studies have shown
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that the pressure amplitude and frequency of peristalsis can be influenced by the volume of urine production. Thus, with small amounts of urine, the renal pelvis produces only a few muscle contractions, which then move down through the ureter. With a higher rate of diuresis, contractions from the renal pelvis develop until there is a one-to-one relationship.14–17 Peristalsis and transport of urine has long been of interest in biomechanics, and the theoretical and numerical modeling of such a system is one of the classic subjects studied by many researchers. It is worth mentioning that to simulate peristalsis, the mechanical properties of the ureter are also important, and in the majority of studies, the peristaltic movement has been considered a radial-wall deformation; only a few articles have linked this to the propagation of a control signal. This review article refers to the fundamentally important studies of the mechanical properties and the analytical and numerical modeling of ureters. However, it does not cover all original journal publications because of limited space. A new high-performance computational approach opening new aspect of research also is discussed. 259
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II. MECHANICAL PROPERTIES OF A URETER To computationally simulate a ureter we first need to investigate its mechanical properties such as wall elasticity or viscoelasticity. One attempt was made by Watanabe et al.,18 who studied tension and expansion effects through tests of a human ureter. Their research showed that tension in a longitudinal direction was stronger than that in a transverse direction, confirming that ureter injury first takes place along the latter direction. Yin and Fung19 also studied mechanical properties of isolated mammalian ureteral segments, including the human ureter. They investigated the passive elasticity parameters under simple elongation and stress relaxation. Creep and isometric contraction were also tested, and the experiments revealed that ureteral tissue shows behavior similar to that of other living tissues: creep and stress relaxation depend upon the initial amount of stretching. Typical stress-strain curves during loading and unloading for different species can be seen in Fig. 1. Such a complex process has led to various invasive and noninvasive methods to investigate urine dynamics and ureteric peristalsis, namely radiography, dynamic scintigraphy, Doppler ultrasonography, endo-
luminal ultrasonography, implantable magnetic sensing, electromyography, impedance measurement, and external pressure transduction.20–26 While noninvasive techniques offer evidence of peristaltic frequency, they are not able to produce useful further data on the upper urinary urodynamic system and consequently are not frequently used in routine clinical practice. Ureteric profilometry in both normal and pathologic ureters has been recorded in situ by means of pressure transducers,27,28 and Kiil27 made one of the first attempts to do this. The results showed that in general pressure remains at a constant level but increases periodically to a peak that can vary between 20 and 40 mmHg in a normal ureter. For most ureters, the more-or-less lower constant level is known to be between 1 and 6 mmHg. Ureteroarrhythmic and silent pressure profile patterns in pathologic ureters were recorded by Shafik.29 The results indicate that a normal caliber ureter, as detected by an excretory urogram, might be ureteroarrythmic, which could disturb urine transport. However, further confirmation using a larger number of patients, indicates that ureteric pressure profilometry could be a useful diagnostic tool for various pathologic conditions such as strictured or refluxing ureters.
FIGURE 1. Stress/strain curve of human and animal ureters.19
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There have been only a few methods that can record several parameters simultaneously. Young et al.30 introduced a novel intraluminal method in a pig and human ureter to study 3 parameters: intraluminal pressure, conduction velocity, and peristaltic frequency. The results are shown in Table 1 and Fig. 2, where P1 and P2 are intraureteral pressures at the tip and proximal transducers, respectively. It is worth mentioning that intraluminal devices disturb the normal function of a ureter and that the catheter might even completely block the ureter; therefore, such information may not provide highly accurate results. TABLE 1. Mean Ureterodynamic Parameters Pigs (n = 6)
Humans (n = 3)
Peristaltic interval (sec)
Parameters
16 (5.5–29)
24 (14–30)
Conduction velocity (cm/sec)
1.2 (1.1–1.3)
2.4 (1.7–2.9)
P1
18 (6–25)
11 (8–16)
P2
29 (14–51)
21 (18–24)
Intraureteral pressure (cm H2O)
Tilling and Constantinou31 used a video microscopic imaging method to determine the effect of drugs such as LY274614 and oxybutynin on peristalsis movement in rats in which peristaltic velocity and frequency, bolus length, and direction of propagation were evaluated. The results showed that oxy-
butynin caused a substantial increase in the length of the bolus; LY274614 decreased pelvic pressure and ureteral frequency and increased the bolus length. Although the imaging method used in this experiment is feasible for the evaluation of the anatomical aspect of the upper urinary system, the visualization of hidden structures within the renal pelvis is not very clear, and fat around both the kidney and ureter reduces transparency. The passage of urine from the renal pelvis into the bladder in humans is clearly a complex process that can be affected by many variables. For example, the effect of external pressures such as intra-amniotic and intra-abdominal pressures can be an important issue in the dynamics of urine flow. With this in mind, Karnak et al.32 conducted a study using an in vitro experiment on 9 adult cattle; a simple pressure recording system was designed to determine the effects of increments of intra-abdominal pressures on the pressure needed to transport fluid through ureters of different lengths at various flow rates. The study demonstrated that there is a high possibility of hydronephrosis as a result of increased external pressure influencing the flow of urine at a high flow rate. It is worth noting that this experiment was done in the absence of peristalsis contraction, and thus the diameter of the tube did not change. Also, human ureters are slightly different from animal ureters in terms of bolus flow. In humans, the contraction frequency depends on the flow rate and is related to posture, whereas in pigs and dogs the rate of contraction is increased when the flow rate increases.33–35
FIGURE 2. Ureteral recording from an experiment using pig ureters. The top tracing represents a P1 transducer in the upper ureter and the lower tracing represents a P2 transducer the mid-distal ureter. Each division of the y-axis represents 10 cm H2O.30
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III. MODELLING OF A TYPICAL URETER There are many parameters that need to be considered to model peristalsis transport, such as amplitude ratio, wave number, Reynolds number, and if the fluid to be considered is Newtonian or non-Newtonian. Simplified preliminary analyses of peristalsis motion have assumed a periodic sinusoidal wave with low Reynold numbers and wave numbers in an infinitely long tube. In 1986 Griffiths et al.36,37 presented a basic theoretical analysis and numerical solution for viscosity-dominated flow through a uniform, highly distensible tube with a slit-shaped crosssection undergoing peristalsis. Their studies showed that at flow rates below an intrinsic upper limit of the peristaltic carrying capacity of the tube, 2 different possible types of steady peristaltic flows (isolated boluses and boluses in contact ) were clearly evident. They assumed there was always at least one peristaltic contraction wave in the tube. Beyond this intrinsic upper limit, 2 other nonsteady types of flows were possible, where the boluses are not as well defined and the contraction waves were generally not completely occlusive. They stated that in flows with isolated boluses, boluses in contact with one another, and leaky boluses, the pressure/flow relation was determined by the active and passive properties of the tube and by the resistance at its outlet. Later, Griffiths37 found that the pelvic pressure/ flow and pressure/detrusor pressure relations depend upon the intrinsic peristaltic carrying capacity, the maximum tube pressure exerted in the contraction wave, and fT, where f is the peristaltic frequency and T is the time needed for a contraction wave to fully sweep through the ureter. They showed that the kidney was better isolated from bladder pressure variations when the peristaltic frequency was high. However, they also found that high peristaltic frequency could by itself lead to elevated renal pelvic pressures at high flow rates. Experimental analysis of pigs was performed and supported these conclusions; however, their model was based on a simple geometry and assumptions. Apter and Mason28 modeled viscoelastic muscular behavior of polymeric material. According to their model, oscillating muscular contractions reflect oscillating membrane permeability only if the move-
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ment of ions through the membrane is the reason for the changes in the macromolecules actin and myosin. Their model, however, failed to address the fact that the oscillating membrane potential is not always associated with contractions. Also, they did not consider the all-or-nothing principle by which a threshold level of selected ions can convert the macromolecules from a relaxed state to a contracted state. Another mathematical model introduced by Burns and Parkes38 modeled the peristaltic flow of a viscous fluid through axially symmetric pipes and symmetrical channels. The effect of pressure gradient with fixed walls together with peristaltic motion with no pressure gradient was investigated. Their results showed that the flux through the tube increased with the wave amplitude when there was peristaltic motion but the flux decreased when amplitude was increased at a prescribed pressure gradient. Shapiro et al.39 also investigated a peristalsis flow with a small Reynolds number and a long wave. The effects of the amplitude ratio from zero to full occlusion were studied for both plane and axisymmetric geometries. The infinite sinusoidal wave train with the wall coordinate follows the law in Eq. (1):
ξ
τ (1)
Where H, ξ, and τ are the dimensionless wall coordinates, transverse coordinates, and time, respectively. Their results showed that the theoretical increase in pressure per wavelength decreased linearly with increasing time and mean flow rate; an experiment with a quasi-2-dimensional apparatus confirmed the theoretical values. Manton40 investigated flow behavior from a long peristalsis wave of arbitrary shape using an asymptotic expansion for flow at a low Reynolds number. He assumed a wall profile based on an axisymmetric wave of a constant shape propagating at speed c, as in Eq. (2):
, (2)
where λ is the wave length, x = (x* – ct)/λ, and a0 is the root mean square radius of the tube, that is,
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The relationship between the mean pressure gradient and volume flux was investigated for the walls mean rate of working and shear stress. He showed that reflux occurred whenever there was an adverse mean pressure gradient, independent of the shape of the wave, and an estimate of the amount of reflux was expressed. Moreover, Zien and Ostrach41 investigated peristaltic motion in the limit of the long wave length and low frequency using the following traveling waves: , (4)
where a, λ, and c indicate the amplitude, wavelength, and phase speed of waves, respectively. By using an asymptotic expansion of the solution in terms of the was small parameter d/λ, a solution up to presented. They showed that reflux would not occur even in the presence of a resultant adverse mean pressure gradient of a certain magnitude if there was an additional pressure gradient that increased the mean flux volume. Table 2 summarizes analytical studies of peristaltic flow. TABLE 2. Summery of Analytical Studies of Peristaltic Flow References
Fluid Type
Reynolds Number
Wave Shape
Newtonian
0
S
Newtonian
Small
S
Zien & Ostrach
Newtonian
Small
S
Manton40
Newtonian
Small
Arb
Srivastava et al.42–44
Newtonian
0
S
Burns and Parkes38 Shapiro et al.39 41
Srivastava et al.42–44 further investigated peristaltic transport of fluid of variable viscosity in a nonuniform tube and channel. They showed that the pressure rise decreased as the fluid viscosity decreased at zero flow rate, that it was independent of viscosity variation at a fixed flow rate, and that it increased if the flow rate was further increased. Also, when the viscosity of the fluid decreased, the flow rate increased for a constant pressure. Takabatake and Ayukawa45,46 used a finite difference method to study peristalsis flow in a Volume 41, Number 3, 2013
circular cylindrical tube and found greater pumping efficiency for cylindrical tubes than for 2-dimensional plane channels. In terms of material properties, a nonlinear material model of the ureteral wall was studied by Vahidi and Fatouraee.47 A fifth order of the Arruda-Boyce model was used in their study. It was a non-Gaussian, 8-chain molecular network model with chains located along the diagonals of unit cell and deform with the cell, as shown in Eq. (5):
, (5)
where μ the initial is shear modulus and λm is the locking stretch. C1 = 0.5, C2 = 0.05, C3 = 0.001047, C4 = 0.00269, and C5 = 0.00077. Their model was based on Navier-Stokes equations and continuity in fluid domain as shown in Eqs. (6) and (7), where v is the flow velocity vector and ρ is fluid density, p is the static pressure , μ is the dynamic viscosity, and f represents body force:
(6)
(7)
A direct-coupling method of fluid-structure interaction (FSI) by applying the Newton-Raphson method was used to solve solid and fluid equations. A solid wall moving along a rigid tube was used to model ureteral peristaltic flow, and the results showed that when the wave moved downward, the possibility of ureteropelvic reflux decreased. Vahidi and Fatouraee They also showedd that ureterovesical reflux occurred during longitudinal propagation of a wave and quantitatively during the vital antireflux function of the ureteropelvic junction. Although this was a more realistic model because it considered intraluminal geometrical dynamic changes of the ureter, there are still many issues that have not been solved. One is that the cross-sectional shape of a ureter is stellate, and it varies along its length. Another is that the loads causing the ureteral wall to close completely are affected by the shape of the cross-section. Ureteral peristalsis consists of a complicated movement in multiple dimensions: a movement in a transverse direction can cause a
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change in diameter but it can also be associated with a movement in the axial direction and the rotation of the ureter. All of this makes a realistic simulation of peristalsis very challenging. Numerical methods also have been used to investigate peristalsis movement. Takabatake and Ayukawa45,46 used a successive overrelaxation method used to solve the Navier-Stokes equations, an upwind finite difference technique to solve the convective terms of vorticity transport equations, and a centered difference to solve the diffusive terms. Table 3 lists work carried out using numerical solutions based on the Navier-Stokes equations to model peristalsis motion.45–51 Rathish-Kumar and Naidu48 used the finite element method to investigate the influence of the magnitude of wave amplitude, wave length, and Reynolds number on urine flow. Their results indicated that progressive sinusoidal waves with high amplitude and low wave numbers caused peristaltic flows with high variations on wall shear stress and that an applied external magnetic field resulted in a decrease in wall shear stresses. There have been other studies in which the finite volume method has been used to compute urine flow assuming incompressible and Newtonian fluid. Using this approach, Xiao and Damodaran49 considered a
wide range of Reynolds numbers, wave amplitudes, and wavelengths in their computational model. Their results were in good agreement with the theoretical work of Shapiro et al.39 and the numerical results of Takabatake and Ayukawa.46 They showed that for small wave lengths, the inertial force could affect the peristaltic flow more than a ratio with a larger amplitude. They also showed that the velocity profile changed from being parabolic to one with flow separation and a reversed velocity when the Reynolds number increased to 1. With regard to the effect of Reynolds number on pressure distribution, Xiao and Damodaran suggested that the influence of inertial effects on the flow field increased with Reynolds number. A multi phase cycle of ureter contractions was suggested by Osman et al.50 (see Fig. 3). According to their study, a longitudinal contraction passively distends the highest part of the ureter in an axial direction; that distension actively spreads downward, developing ureteral diastole that helps with filling while the circular muscle is still in the relaxed state. Moreover, the longitudinal contraction of the lower part followed by contraction of the circular ring helps insert urine into the bladder. Such complex behavior has yet to be accurately modeled. Furthermore, the nature of reflux and the mechanisms of the ureteric pelvic valve also have
TABLE 3. Summary of Numerical Studies of Peristaltic Flow References Takabatake et al.
46
Rathish-Kumar et al. Xiao et al.49 Vahidi et al.
47
48
Fluid type
Reynolds number
Geometry
Method
Newtonian
Moderate
Axisym
Finite difference
Newtonian
10–100
2D-plane
Finite element
Newtonian
0.01–100
Axisym
Finite volume
Newtonian
Low
Axisym
Finite element
FIGURE 3. Suggested phases of the ureteral motion cycle.50
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to be considered. The method of applying a moving circular force to mimic a contraction wave has recently been used.51 The immersed boundary (IB) method was used to couple computational fluid dynamics and discrete element codes52–54; application of different inlet pressures revealed promising behavior. The IB method55 is used to tackle such complex FSI problems in an easy and straightforward manner. Fluid motion equations are discretized on a fixed Cartesian grid, and an extra singular body force is added into the momentum equation to take into account the solid boundary, as follows:
(8) (9)
Eq. (10) is the conservative form of a secondorder Adam-Bashforth temporal discretized governing equation of incompressible fluid flow using the IB method, where u is velocity, p is the pressure, = and comprises connective and diffusive terms, and f designates the body force. I ( , variables on the Cartesian grids) and D (Φ, variables on the IB points) represent interpolation and distribution functions, respectively. The interpolation function projects the physical field from the Cartesian grids to IB points. The distribution function maps the physical field from the IB points back to the Cartesian grids. The purpose of the IB method is to set the boundary conditions on the IB exactly (see Fig. 4). The initial simulation was a basic model of an elastic homogenous material with an outer circular shape for the tube’s cross-sectional area. The wavy motion of the tube shown in Fig. 5 was created by applying directly an external circular force moving from right to left, as indicated by a narrowing passage. Later, laminar urine flow was simulated in a tube using published mechanical properties of ureters.51 It was assumed that the fundamental reason for urine flow is the contraction of the ureter walls (pacemaker activity) and the pressure difference between the kidney and bladder. The pressure and velocity distribution along the ureter for 2 separated contractions were analyzed in the absence of a pressure difference and the existence of 2 pressure difVolume 41, Number 3, 2013
FIGURE 4. Illustration of a capturing circular body using a fixed Cartesian grid and the IB method.
ferences (0.007 and 4 cm H2O) between the outlet and the inlet of the tube. The velocity contours in both pressure differences show an increase in the velocity magnitude in the middle of the tube as the pressure difference condition is applied. However, the velocity magnitude is somewhat too high for the high pressure difference of 4 cm H2O; the flow rate of urine is around 0.1–3 mL urine/minute. This is likely due to the difference between the shape of the cross-sectional area of a ureter and our model. Also, the lack of pressure difference causes a significant backward flow, indicating the possibility of urine reflux. In comparison, the backward flow does not occur when the pressure difference is applied, pointing to a smaller possibility of reflux. A more realistic model can be built using computed tomography to capture ureter geometry and account for the viscoelatic behavior of the walls. This compelx FSI simulation requires dedicated high-performance computing resources; results from this effort will be reported in the near future. IV. DISCUSSION: Significant recent developments in the basic simulation of the urinary system have paved the way for both further research and insight into medical practice. Various analytical and numerical studies have made a promising start to understanding the full complicity of ureter behavior. However, there are still many issues yet to be resolved, for example, the nature of reflux; in addition, the process and
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FIGURE 5. Time sequence of wave propagation of the ureter under the action of application force. Higher pressure is clear around the contraction (Red color )
activation of pacemakers in different parts of the ureter are not clear and, as a consequence, they are very difficult to simulate. Moreover, because there are limitations in terms of computational tools and costs, solving FSI problems in ureter flow is not a straightforward process. The deformation of the ureter wall is a complicated mechanism; deformation occurs in different directions. Thus, the action of longitudinal and circular muscles is also difficult to simulate. In the majority of articles reviewed here, deformation was assumed to be a radial displacement and did not take into account other directions. Moreover, the actual star-shaped cross-sectional area of ureter can be an important factor to model in order to obtain realistic results. Most of the studies mentioned herein used a circular cross-section, which significantly affects the level of the force required to cause contraction and movement of urine. In comparison, a star-shaped cross-section most likely requires a smaller force to achieve a contraction. The application of mathematical and computational models can be used in medical diagnostics and physiological experiments. However, access to accurate experimental data to verify those models is another challenge. Also, techniques for measuring pressure still need to be improved. Pressure transducers also add an extra force inside the ureter during recording, which can affect urine flow and the normal contraction rate. At the moment, data can be collected from only 1 or 2 points, and it would be beneficial to obtain readings over multiple points simultaneously to obtain a more accurate verification at a given
time. Urodynamic properties including the flow rate of urine, the dimension of the bolus, and contraction rates should also be obtained by combining multiple techniques that use contact and noncontact methods. V. SUMMARY: Some significant recent developments have been made to understand and predict upper urinary flow. Various analytical and numerical studies have made a promising start to understanding the full complicity of ureter behavior. However, an accurate model of ureter function, in particular the effect of inserted medical devices, remains a significant challenge. Advances in computational technology suggest that the complex geometry of the ureter’s star shape, its viscoelastic behavior, and interaction with urinary flow can be taken into account. This requires using massive computational resources available at a national level and the continuous improvement of models describing the material properties of the ureter through experimental studies. Nevertheless, it is now possible to conduct many accurate computational studies to assist in the development of new medical devices such as stents to see how they perform under various flow and ureter conditions. This opens a new chapter of collaboration between the medical and engineering professions. REFERENCES 1. Constantinou CE. Renal pelvic pacemaker control of ureteral peristaltic rate. Am J Physiol. 1974;226:1413–9.
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Simulation of the Upper Urinary System 2. Constantinou CE. Contractility of the pyeloureteral pacemaker system. Urol Int. 1978;33(6):399–416. 3. Morita T, Ishizuka G, Tauchida S. Initiation and propagation of stimulus from the renal pelvic pacemaker in pig kidney. Invest Urol. 1981;19:157–60. 4. Golenhofen K, Hannappel J. Normal spontaneous activity of the pyeloureteral system in the guinea pig. Pflugers Arch. 1973;341(3):257–70. 5. Tsuchida S, Morita T, Harada T, Kimura Y. Initiation and propagation of canine renal pelvic peristalsis. Urol Int. 1981;36:307–14. 6. Shiratori T, Kinoshita H. Electromyographic studies on urinary tract. II. Electromyographic study on the genesis of peristaltic movement of the dog’s ureter. Tohoku J Exp Med. 1961;73:103–17. 7. Weiss RM, Wagner ML, Hoffman BF. Localisation of the pacemaker for peristalsis in the intact canine ureter. Invest Urol. 1967;5:42–8. 8. Manning DC, Snyder SH. 3H-bradykinin binding site localization in guinea pig urinary system. Adv Exp Med Biol. 1986;198:563–70. 9. Notley RG. The musculature of the human ureter. Brit J Urol. 1970;42:724–7. 10. Meini, S, Santicioli P, Maggi CA. Propagation of impulses in the guinea-pig ureter and its blockade by calcitoningene-related peptide (CGRP). Naunyn Schmiedebergs Arch Pharmacol. 1995;351(1): 79–86. 11. Golenhofen K, Hannappel J. Normal spontaneous activity of the pyeloureteral system in the guinea-pig. Pflugers Arch. 1973;341(3):257–70. 12. Santicioli P, Maggi CA. Myogenic and neurogenic factors in the control of pyeloureteral motility and ureteral peristalsis. Pharmacol Rev. 1998;50:683–721. 13. Teele ME, Lang RJ. Stretch-evoked inhibition of spontaneous migrating contractions in a whole mount preparation of the guinea pig upper urinary tract. Br J Pharmacol. 1998;123:1143–53. 14. Finberg JP, Peart WS. Function of smooth muscle of the rat renal pelvis–response of the isolated pelvis muscle to angiotensin and some other substances. Br J Pharmacol. 1970;39:373–81. 15. Hrynczuk JR, Schwartz TW. Rhythmic contractions in the renal pelvis correlated to ureteral peristalsis. Invest Urol. 1975;13:29–30. 16. Constantinou CE, Hrynczuk JR. The incidence of ectopic peristaltic contractions. Urol Int. 1976;31(6):476–88. 17. Constantinou CE, Hrynczuk JR. Urodynamics of the upper urinary tract. Invest Urol. 1976;14:233–40. 18. Watanabe H, Nakagawa Y, Uchida M. Tests to evaluate the mechanical properties of the ureter. ASTM Special Technical Publication 1173. Philadelphia: American Society for Testing and Materials; 1994. p. 275–82. 19. Yin FC, Fung YC. Mechanical properties of isolated mammalian ureter segments. Am J Physiol. 1971; 221(5):1484–93.
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