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.     

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.     

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.     

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.     

Opioids modulate periodicity rather than efficacy of peristaltic waves in the guinea pig ileum in vitro

The influence of opioid receptor blockade by naloxone and opioid receptor activation by opioids on peristalsis was studied in isolated segments of the guinea pig ileum.1. (-)Naloxone, but not (+)naloxone, increased the mean number of peristaltic waves per min within periods of elevated intraluminal pressure. Naloxone tended to modify intermittent peristalsis into ongoing peristalsis, whereas opioids worked in an opposite fashion. 2. Maximum amplitudes of luminal volume displacement during single peristaltic waves were not decreased by opioids. (-)Naloxone, however, applied to non-pretreated segments, decreased transitorily the efficacy of single peristaltic waves to a small, but statistically significant degree 3. Enhancement of peristalsis by naloxone decreased over time, although enough naloxone was present to occupy all opioid receptors. This suggests that opioid receptor blockade induces some compensatory mechanism.     

High definition mapping of circular and longitudinal motility in the terminal ileum of the brushtail possum <Emphasis Type="Italic">Trichosurus vulpecula</Emphasis> with watery and viscous perfusates

Longitudinal and radial movements during spontaneous contractions of isolated segments of terminal ileum of the brushtail possum, a species of arboreal folivore, were studied using high definition spatiotemporal maps. Segments obtained from specimens were continuously perfused with solutions of various apparent viscosities at 3 cm and 5 cm hydrostatic pressure. A series of sustained tetrodotoxin-sensitive peristaltic events occurred during perfusion. The leading edge of each peristaltic event progressed by a succession of rhythmic surges of circular contraction with concerted concurrent phasic longitudinal contractions. Three types of peristaltic event were observed, with differing durations of occlusion and patterns of cyclic, in phase, circular and longitudinal contractions. Each peristaltic event was preceded by a change of shade on the D map that indicated circumferential dilatation. Differences in the slopes of these phasic shade changes from those occurring during peristalsis indicate that this distension is passive and likely results from aboral displacement of fluid. Tetradotoxin insensitive longitudinal contraction waves of frequency 9.2 min⁻¹ occurred during and in the absence of peristalsis, originating at a variety of sites, and propagating either in an orad or aborad direction but predominantly in the latter. Perfusion with 1% guar gum, at 5 cm hydrostatic pressure caused the lumen to become distended and the generation of peristaltic events to cease pending reduction of the hydrostatic head to 3 cm but longitudinal contractile activity was preserved. Neither the frequencies nor the rates of progression of circular and longitudinal contractile events, nor the temporal coordination between these events, varied with the apparent viscosity of the perfusate or altered in a manner that could facilitate mixing.     

Ureteral motility in sheep

Ureteral motility was studied in twenty-five sodium pentobarbital-anaesthetized sheep. Mean frequency of the peristaltic waves was 15 per min and the range was 11-19. Frequency was the same throughout the length of the ureter. Mean contraction pressure (cm H2O) was 40 in the upper ureter, 35 in the middle ureter and 31 in the lower ureter. Mean concentration time was 1 sec and range was 0.6-1.5. Mean relaxation time was 1.1 sec and range was 0.7-1.5. Diuresis induced by rapid intravenous administration of physiologic sodium chloride solution abolished the peristaltic activity.     

Similarities and differences in the propagation of slow waves and peristaltic waves

The relationship between slow waves and peristaltic reflexes has not been well analyzed. In this study, we have recorded the electrical activity of slow waves together with that generated by spontaneous peristaltic contractions at 240 extracellular sites simultaneously. Recordings were made from five isolated tubular and six sheet segments of feline duodenum superfused in vitro. In all preparations, slow waves propagated as broad wave fronts along the longitudinal axis of the preparation in either the aborad or the orad direction. Electrical potentials recorded during peristalsis (peristaltic waves) also propagated as broad wave fronts in either directions. Peristaltic waves often spontaneously stopped conducting (46%), in contrast to slow waves that never did. Peristaltic waves propagated at a lower velocity than the slow waves (0.98 +/- 0.25 and 1.29 +/- 0.28 cm/s, respectively; P < 0.001; n = 24) and in a direction independent of the preceding slow wave direction (64% in the same direction, 46% in the opposite direction). In conclusion, slow waves and peristaltic waves in the isolated feline duodenum seem to constitute two separate electrical events that may drive two different mechanisms of contraction in the small intestine.     

The development of the bladder trigone, the center of the anti-reflux mechanism

The urinary tract is an outflow system that conducts urine from the kidneys to the bladder via the ureters that propel urine to the bladder via peristalsis. Once in the bladder, the ureteral valve, a mechanism that is not well understood, prevents backflow of urine to the kidney that can cause severe damage and induce end-stage renal disease. The upper and lower urinary tract compartments form independently, connecting at mid-gestation when the ureters move from their primary insertion site in the Wolffian ducts to the trigone, a muscular structure comprising the bladder floor just above the urethra. Precise connections between the ureters and the trigone are crucial for proper function of the ureteral valve mechanism; however, the developmental events underlying these connections and trigone formation are not well understood. According to established models, the trigone develops independently of the bladder, from the ureters, Wolffian ducts or a combination of both; however, these models have not been tested experimentally. Using the Cre-lox recombination system in lineage studies in mice, we find, unexpectedly, that the trigone is formed mostly from bladder smooth muscle with a more minor contribution from the ureter, and that trigone formation depends at least in part on intercalation of ureteral and bladder muscle. These studies suggest that urinary tract development occurs differently than previously thought, providing new insights into the mechanisms underlying normal and abnormal development.     

Characterization of spontaneous electrical activity of the urinary tract: Ureter,bladder, urethra

The study aimed to characterize spontaneous electrical activity of the ureter, urinary bladder and urethra as well as their interrelationship. The basic parameters of pacemaker activity (amplitude, frequency, peak rise rate, peak rise time, peak half-width) were comparatively analyzed in each of the active areas. Out of the three areas compared, the ureteral rhythmogenic zone displayed the maximum amplitude and apex formation rate. Under conditions of urine influx from the ureter into the bladder and isolation of these organs from the urethra, the amplitude and peak rise rate in the latter decreased by almost 20%. At the same time, all the parameters of the ureter and bladder remained intact. Complete block of urine influx into the bladder by transecting the ureter at the appropriate area led to a slight decrease in the amplitude of action potentials, peak rise rate and rhythmogenicity frequency in the bladder, respectively, by 14.2, 12.5 and 16% at the constancy of other parameters of its activity. Subsequent isolation of the bladder from the urethra had no appreciable effect on the altered parameters of the former. The similar tendency towards a reduction of the parameters was observed under the same conditions in the urethra. Thus, a relationship was revealed between autonomous activities of the ureter, bladder and urethra. The regulatory role in this process is provided by the urine flow through these organs.     

Relative contributions of "pressure pump" and "peristaltic pump" to gastric emptying

The relative contributions to gastric emptying from common cavity antroduodenal pressure difference ("pressure pump") vs. propagating high-pressure waves in the distal antrum ("peristaltic pump") were analyzed in humans by high-resolution manometry concurrently with time-resolved three-dimensional magnetic resonance imaging during intraduodenal nutrient infusion at 2 kcal/min. Gastric volume, space-time pressure, and contraction wave histories in the antropyloroduodenal region were measured in seven healthy subjects. The subjects fell into two distinct groups with an order of magnitude difference in levels of antral pressure activity. However, there was no significant difference in average rate of gastric emptying between the two groups. Antral pressure history was separated into "propagating high-pressure events" (HPE), "nonpropagating HPEs," and "quiescent periods." Quiescent periods dominated, and average pressure during quiescent periods remained unchanged with decreasing gastric volume, suggesting that common cavity pressure levels were maintained by increasing wall muscle tone with decreasing volume. When propagating HPEs moved to within 2-3 cm of the pylorus, pyloric resistance was found statistically to increase with decreasing distance between peristaltic waves and the pylorus. We conclude that transpyloric flow tends to be blocked when antral contraction waves are within a "zone of influence" proximal to the pylorus, suggesting physiological coordination between pyloric and antral contractile activity. We further conclude that gastric emptying of nutrient liquids is primarily through the "pressure pump" mechanism controlled by pyloric opening during periods of relative quiescence in antral contractile wave activity.     

Computational model for the transition from peristaltic to pulsatile flow in the embryonic heart tube

Early in development, the heart is a single muscle-wrapped tube without formed valves. Yet survival of the embryo depends on the ability of this tube to pump blood at steadily increasing rates and pressures. Developmental biologists historically have speculated that the heart tube pumps via a peristaltic mechanism, with a wave of contraction propagating from the inflow to the outflow end. Physiological measurements, however, have shown that the flow becomes pulsatile in character quite early in development, before the valves form. Here, we use a computational model for flow though the embryonic heart to explore the pumping mechanism. Results from the model show that endocardial cushions, which are valve primordia arising near the ends of the tube, induce a transition from peristaltic to pulsatile flow. Comparison of numerical results with published experimental data shows reasonably good agreement for various pressure and flow parameters. This study illustrates the interrelationship between form and function in the early embryonic heart.     

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.     

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.     

Pharmacology of ureter.

Ureter which performs the important function of transport of urine from kidney to the bladder is not a passive tube, but exhibits characteristic spontaneous (peristaltic) activity. This peristaltic activity is characterized by coordinated muscular contractions, which after originating from a spontaneously active primary pacemaker, situated in the vicinity of the pelvi ureteric junction, propagate downwards along the entire length of the ureter. In addition, the ureter, like the heart, possesses certain cells which become activated when the primary pacemaker is suppressed or there is an interruption of conduction, thereby, acting as latent pacemakers. (1) The peristaltic activity of the ureter is modified by several pharmacologically active substances. Moreover, some of these substances are occasionally able to initiate spontaneous activity even in quiescent ureters. This article briefly reviews the effects of catecholamines (adrenaline, noradrenaline and isoprenaline) and acetylcholine on the ureters of human beings and some domestic and laboratory animals.     

Evaluation of peristalsis in multiple segments of the guinea-pig isolated small intestine: optimisation of tissue use by refined in vitro methodology

Peristalsis is the aboral movement by which the intestine propels its contents. Since pharmacological research requires an experimental model with which drug-induced modifications of peristalsis can be reliably quantified, we set out to develop and validate an in vitro method for studying peristalsis in multiple gut segments. In our arrangement, up to four 10cm segments isolated from the guinea-pig jejunum and ileum can be set up in parallel and their lumens perfused. Peristalsis was elicited by pressure-evoked wall distension, and the peristalsis-induced changes in the intraluminal pressure were evaluated with software that determined the peristaltic pressure threshold, the frequency, maximal acceleration and amplitude of the peristaltic waves, and the residual baseline pressure. Validation experiments showed that the peristalsis parameters at baseline and after modification by morphine (0.01-10microM) did not differ between segments from the jejunum and ileum, or between segments examined in a consecutive manner. In conclusion, our work succeeded in optimising the use of the guinea-pig jejunum and ileum for multiple recordings of peristalsis in vitro, and in refining the recording and evaluation of peristaltic motility. This system promises to be particularly useful in the pharmacological screening and testing of drugs which modify peristalsis.     

Peristaltic waves of tubicolous worms and the problem of irrigation in Sabella pavonina

A simple scheme is presented to illustrate four possible kinds of locomotory peristalsis in worm-like animals. The application of this scheme to real animals is discussed. Peristaltic waves may be of constriction or dilatation. A continuous body cavity enables the worm to regulate both speed and direction of travel by controlling the relative tonus of its body wall muscles. Thus peristaltic waves can be used to pump water without causing locomotion.
Sabella irrigates its tube by peristaltic swellings but the coelom and intestine are sub-divided by entire septa. Anatomical and morphological features which allow the shortest, widest segments forming a "piston" to slide down the tube and the narrower elongated segments to grip its walls are considered. In this way the construction of the typical body segment is given a functional explanation.
The functions of septa in annelids are discussed.     

Dynamics of human milk extraction: A comparative study of breast feeding and breast pumping

We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.     

On the flow of a non-Newtonian liquid induced by intestine-like contractions

This paper considers the flow of an inelastic liquid which is generated by contractions like those of the intestine. Unlike regular peristaltic motion, these contractions occur locally over a finite length and have a finite amplitude. We adopt a contraction model due to Macagno and Christensen and repeat their analysis for an inelastic liquid. Our analysis, which is based on a Boundary Element Method, indicates that the net flow rate depends very weakly on the power-law index. The pumping action is therefore similar to that of a positive displacement pump.