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.     

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.     

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.     

Interstitial cell of Cajal-like cells in the upper urinary tract

Autorhythmicity in the upper urinary tract (UUT) has long been considered to arise in specialized atypical smooth muscle cells (SMC) predominately situated in the most proximal regions of the pyeloureteric system. These atypical SMC pacemakers have been thought to trigger adjacent electrically-quiescent typical SMC to fire action potentials which allow an influx of Ca2+ and the generation of muscle contraction. More recently, the presence of cells with many of the morphological, electrical and immunohistochemical characteristics of interstitial cells of Cajal (ICC), the pacemaker cells of the gastrointestinal tract, have been located in many regions of both the upper and lower urinary tract. This article reviews the evidence from the literature and from our laboratory supporting a role of both atypical SMC and ICC-like cells in the initiation and propagation of pyeloureteric peristalsis in the UUT. We propose a new model in which there are 2 populations of pacemaker cells, high frequency atypical SMC and lower frequency ICC-like cells, both of which can drive electrically-quiescent typical SMC. The relative presence of these 2 populations of pacemaker cells and the relatively-long refractoriness of typical SMC determines the decreasing frequency of contraction with distance from the renal fornix. In the absence of the proximal pacemaker drive from atypical SMC after pyeloureteral/ureteral obstruction or surgery, ICC-like cell pacemaking provides a compensatory mechanism allowing the ureter to maintain rudimentary peristaltic waves and movement of urine from the pyelon towards the bladder.     

On the influence of wall properties and Poiseuille flow in peristalsis

The present study extends the two-dimensional analysis of peristaltic motion by Fung and Yih to include an elastic or viscoelastic wall, and a Poiseuille flow. This fluid-solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. The wall characteristics appear in their equations of motion, which are solved to represent boundary conditions of fluid motion. The influence of Poiseuille flow on pure peristalisis is also investigated.

The phenomenon of the ‘mean flow reversal’ is found to exist both at the center and at the boundaries of the channel. When the walls of the channel are elastic, pure peristalsis involves flow reversal only at the center. This position may shift drastically to the boundaries, if viscous damping forces are considered.     

Origin of the secondary peristalsis of the esophagus in sheep

Manometric and electromyographic methods were used for investigating oesophageal motor activity in conscious sheep. A contraction wave, the so-called "secondary peristalsis", was readily evoked by means of the fast inflation of a rubber balloon distending the oesophagus. This peristaltic wave travels onto the cardia at the same speed as the primary deglutitive peristalsis (28 m X sec-1, approximately). In that particular species, whose oesophageal muscular coat is all along entirely made of striated fibers, secondary peristalsis is always initiated at the origin of the cervical oesophagus, whatever the site, cervical or thoracic, of the distension.     

Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

The mechanical advantage of local longitudinal shortening on peristaltic transport

Whereas bolus transport along the esophagus results from peristaltic contractions of the circular muscle layer, it has been suggested that local shortening of the longitudinal muscle layer concentrates circular muscle fibers in the region where the highest contractile pressures are required. Here we analyze the mechanical consequences of local longitudinal shortening (LLS) through a mathematical model based on lubrication theory. We find that local pressure and shear stress in the contraction zone are greatly reduced by the existence of LLS. In consequence, peak contractile pressure is reduced by nearly 2/3 at physiological LLS, and this reduction is greatest when peak in LLS is well aligned with peak contractile pressure. We conclude that a peristaltic wave of local longitudinal muscle contraction coordinated with the circular muscle contraction wave has both a great physiological advantage (concentrating circular muscle fibers), and a great mechanical advantage (reducing the level of contractile force required to transport the bolus), which combine to greatly reduce circular muscle tone during esophageal peristalsis.     

Peristaltic Transport of Carreau-Yasuda Fluid in a Curved Channel with Slip Effects

The wide occurrence of peristaltic pumping should not be surprising at all since it results physiologically from neuro-muscular properties of any tubular smooth muscle. Of special concern here is to predict the rheological effects on the peristaltic motion in a curved channel. Attention is focused to develop and simulate a nonlinear mathematical model for Carreau-Yasuda fluid. The progressive wave front of peristaltic flow is taken sinusoidal (expansion/contraction type). The governing problem is challenge since it has nonlinear differential equation and nonlinear boundary conditions even in the long wavelength and low Reynolds number regime. Numerical solutions for various flow quantities of interest are presented. Comparison for different flow situations is also made. Results of physical quantities are interpreted with particular emphasis to rheological characteristics.     

Effect of dry swallows and wet swallows of different volumes on esophageal peristalsis.

The effect of dry swallows and wet swallows of various volumes on esophageal function was studied in normal subjects. An intraesophageal transducer assembly was used to measure the dynamics of esophageal peristalsis. The strength of esophageal contraction (amplitude) following a 1-ml liquid bolus was similar to that following a dry swallow but was significantly less than that following a wet swallow of a larger volume. There was no difference in strength of esophageal squeeze following swallows ranging from 2 to 20 ml. In addition, a wet swallow was associated with slower wave speed, greater duration of the contraction wave, and later time of appearance of the peristaltic wave in the distal esophagus than a dry swallow. Futhermore, the incidence of peristalsis was greater with a wet swallow than a dry swallow. The results of our studies indicate that although the act of swallowing alone in man initiates peristalsis, afferent information contributes to the regulation of primary peristalsis.     

Numerical simulation of the urine flow in a stented ureter

When a stent is implanted in a blocked ureter, the urine passing from the kidney to the bladder must traverse a very complicated flow path. That path consists of two parallel passages, one of which is the bore of the stent and the other is the annular space between the external surface of the stent and the inner wall of the ureter. The flow path is further complicated by the presence of numerous pass-through holes that are deployed along the length of the stent. These holes allow urine to pass between the annulus and the bore. Further complexity in the pattern of the urine flow occurs because the coiled "pig tails," which hold the stent in place, contain multiple ports for fluid ingress and egress. The fluid flow in a stented ureter has been quantitatively analyzed here for the first time using numerical simulation. The numerical solutions obtained here fully reveal the details of the urine flow throughout the entire stented ureter. It was found that in the absence of blockages, most of the pass-through holes are inactive. Furthermore, only the port in each coiled pig tail that is nearest the stent proper is actively involved in the urine flow. Only in the presence of blockages, which may occur due to encrustation or biofouling, are the numerous pass-through holes activated. The numerical simulations are able to track the urine flow through the pass-through holes as well as adjacent to the blockages. The simulations are also able to provide highly accurate results for the kidney-to-bladder urine flow rate. The simulation method presented here constitutes a powerful new tool for rational design of ureteral stents in the future.     

A mathematical model for the peristaltic flow of chyme movement in small intestine

A mathematical model based on viscoelastic fluid (fractional Oldroyd-B model) flow is considered for the peristaltic flow of chyme in small intestine, which is assumed to be in the form of an inclined cylindrical tube. The peristaltic flow of chyme is modeled more realistically by assuming that the peristaltic rush wave is a sinusoidal wave, which propagates along the tube. The governing equations are simplified by making the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions of problem are obtained by using homotopy analysis method and convergence of the obtained series solution is properly checked. For the realistic values of the emerging parameters such as fractional parameters, relaxation time, retardation time, Reynolds number, Froude number and inclination of tube, the numerical results for the pressure difference and the frictional force across one wavelength are computed and discussed the roles played by these parameters during the peristaltic flow. On the basis of this study, it is found that the first fractional parameter, relaxation time and Froude number resist the movement of chyme, while, the second fractional parameter, retardation time, Reynolds number and inclination of tube favour the movement of chyme through the small intestine during pumping. It is further revealed that size of trapped bolus reduces with increasing the amplitude ratio whereas it is unaltered with other parameters.     

Flow fields generated by peristaltic reflex in isolated guinea pig ileum: impact of contraction depth and shoulders

The guinea pig ileum responds to distension with characteristic wall movements, luminal pressure gradients, and outflow (the peristaltic reflex). To date, little is known about whether the peristaltic reflex generates flow events other than laminar flow. Here we used a numerical method to solve for the flow generated by moving walls to assess occlusive contractions (case 1), nonocclusive contractions (case 2), and contractions with steep shoulders (case 3) for which visual parameters of wall movements are published. We found that all three contraction cases produced pressure differentials across the coapting segment, downstream and reverse flow, and vortical flow patterns that redistributed particles and mixed liquids. Contractions generated pressures and shear stresses, particularly along the moving section of the wall. The nonocclusive contraction was much less effective than the occlusive contraction with the steep shoulders; the occlusive contraction with flat shoulders had an intermediate effect. Our analysis shows that even peristaltic contractions produce not only laminar flow but also many flow events likely to promote digestion and absorption. The visual patterns of contractions impact the patterns of luminal flow, and precise definition of wall movements is critical to quantify the fluid mechanical consequences of intestinal contractions.     

Development and differentiation of the ureteric bud into the ureter in the absence of a kidney collecting system

Six1-/- mice were found to have apparently normal ureters in the absence of a kidney, suggesting that the growth and development of the unbranched ureter is largely independent of the more proximal portions of the UB which differentiates into the highly branched renal collecting system. Culture of isolated urinary tracts (from normal and mutant mice) on Transwell filters was employed to study the morphogenesis of this portion of the urogenital system. Examination of the ureters revealed the presence of a multi-cell layered tubule with a lumen lined by cells expressing uroplakin (a protein exclusively expressed in the epithelium of the lower urinary tract). Cultured ureters of both the wild-type and Six1 mutant become contractile and undergo peristalsis, an activity preceded by the expression of alpha-smooth muscle actin (alphaSMA). Treatment with a number of inhibitors of signaling molecules revealed that inhibition of PI3 kinase dissociates the developmental expression of alphaSMA from ureter growth and elongation. Epidermal growth factor also perturbed smooth muscle differentiation in culture. Moreover, the peristalsis of the ureter in the absence of the kidney in the Six1-/- mouse indicates that the development of this clinically important function of ureter (peristaltic movement of urine) is not dependent on fluid flow through the ureter. In keeping with this, isolated ureters cultured in the absence of surrounding tissues elongate, differentiate and undergo peristalsis when cultured on a filter and undergo branching morphogenesis when cultured in 3-dimensional extracellular matrix gels in the presence of a conditioned medium derived from a metanephric mesenchyme (MM) cell line. In addition, ureters of Six1-/- urinary tracts (i.e., lacking a kidney) displayed budding structures from their proximal ends when cultured in the presence of GDNF and FGFs reminiscent of UB budding from the wolffian duct. Taken together with the above data, this indicates that, although the distal ureter (at least early in its development) retains some of the characteristics of the more proximal UB, the growth and differentiation (i.e., development of smooth muscle actin, peristalsis and uroplakin expression) of the distal non-branching ureter are inherent properties of this portion of the UB, occurring independently of detectable influences of either the undifferentiated MM (unlike the upper portion of the ureteric bud) or more differentiated metanephric kidney. Thus, the developing distal ureter appears to be a unique anatomical structure which should no longer be considered as simply the non-branching portion of the ureteric bud. In future studies, the ability to independently analyze and study the portion of the UB that becomes the renal collecting system and that which becomes the ureter should facilitate distinguishing the developmental nephrome (renal ontogenome) from the ureterome.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Mathematica numerical simulation of peristaltic biophysical transport of a fractional viscoelastic fluid through an inclined cylindrical tube

This paper studies the peristaltic transport of a viscoelastic fluid (with the fractional second-grade model) through an inclined cylindrical tube. The wall of the tube is modelled as a sinusoidal wave. The flow analysis is presented under the assumptions of long wave length and low Reynolds number. Caputo's definition of fractional derivative is used to formulate the fractional differentiation. Analytical solutions are developed for the normalized momentum equations. Expressions are also derived for the pressure, frictional force, and the relationship between the flow rate and pressure gradient. Mathematica numerical computations are then performed. The results are plotted and analysed for different values of fractional parameter, material constant, inclination angle, Reynolds number, Froude number and peristaltic wave amplitude. It is found that fractional parameter and Froude number resist the flow pattern while material constant, Reynolds number, inclination of angle and amplitude aid the peristaltic flow. Furthermore, frictional force and pressure demonstrate the opposite behaviour under the influence of the relevant parameters emerging in the equations of motion. The study has applications in uretral biophysics, and also potential use in peristaltic pumping of petroleum viscoelastic bio-surfactants in chemical engineering and astronautical applications involving conveyance of non-Newtonian fluids (e.g. lubricants) against gravity and in conduits with deformable walls.     

Mechanics and hemodynamics of esophageal varices during peristaltic contraction

Our hypothesis states that variceal pressure and wall tension increase dramatically during esophageal peristaltic contractions. This increase in pressure and wall tension is a natural consequence of the anatomy and physiology of the esophagus and of the esophageal venous plexus. The purpose of this study was to evaluate variceal hemodynamics during peristaltic contraction. A simultaneous ultrasound probe and manometry catheter was placed in the distal esophagus in nine patients with esophageal varices. Simultaneous esophageal luminal pressure and ultrasound images of varices were recorded during peristaltic contraction. Maximum variceal cross-sectional area and esophageal luminal pressures at which the varix flattened, closed, and opened were measured. The esophageal lumen pressure equals the intravariceal pressure at variceal flattening due to force balance laws. The mean flattening pressures (40.11 +/- 16.77 mmHg) were significantly higher than the mean opening pressures (11.56 +/- 25.56 mmHg) (P < or = 0.0001). Flattening pressures >80 mmHg were generated during peristaltic contractions in 15.5% of the swallows. Variceal cross-sectional area increased a mean of 41% above baseline (range 7-89%, P < 0.0001) during swallowing. The peak closing pressures in patients that experience future variceal bleeding were significantly higher than the peak closing pressures in patients that did not experience variceal bleeding (P < 0.04). Patients with a mean peak closing pressure >61 mmHg were more likely to bleed. In this study, accuracy of predicting future variceal bleeding, based on these criteria, was 100%. Variceal models were developed, and it was demonstrated that during peristaltic contraction there was a significant increase in intravariceal pressure over baseline intravariceal pressure and that the peak intravariceal pressures were directly proportional to the resistance at the gastroesophageal junction. In conclusion, esophageal peristalsis in combination with high resistance to blood flow through the gastroesophageal junction leads to distension of the esophageal varices and an increase in intravariceal pressure and wall tension.     

The relation between pelvic pressure and bladder pressure during pelvic perfusion with standardized flow rates

The aim of this study was to elucidate the relation between pelvic pressure and bladder pressure during pelvic perfusion with standardized flow rates. Anaesthetized Danish Landrace Breed pigs (n = 5) weighing 35-40 kg were studied. Transparenchymally two 6-F catheters were placed in both renal pelves for pressure measurement and perfusion. Transurethrally two catheters were placed in the bladder for pressure measurements and for urine collection and infusion. Bladder filling was done with a constant infusion rate of 45 ml/min during perfusion of both pelves with saline consecutively with the flow rates: 0, 2, 4, 6 and 8 ml/min during continuous measurement of bladder and bilateral pelvic pressure. The baseline diuresis varied from 0.4-1.0 ml/min. Without pelvic perfusion a negative pressure gradient between pelvis and bladder was seen demonstrating the importance of ureteral peristalsis. Pelvic perfusion with 2 ml/min showed that pelvic and bladder pressure were equal demonstrating weakening of ureteral peristalsis. During perfusion with higher flow rates pelvic pressure was higher than bladder pressure, showing that the positive gradient was important for urine transport. In conclusion ureteral peristalsis is important at low flow rates during increasing bladder pressure. At higher flow rates peristalsis weakens and the pressure gradient is the determining factor.