A Numerical Simulation of Peristaltic motion in the Ureter Using Fluid Structure Interactions Bahman Vahidi and Nasser Fatouraee
of the muscle depends on the load against which it is contracting as well as on its current geometry and its state of activation, and that load consists largely of the hydrodynamic (viscous) forces required to move the urine. A theoretical analysis and numerical solutions were reported for peristaltic flow through a distensible tube of limited length . Their results showed that in flow with isolated boluses, the pressure/flow relation was determined by the active and passive properties of the tube undergoing peristalsis and not by the outlet. Dynamics of the upper urinary tract and the effect of variations of bladder pressure on pyeloureteral pressure/flow relations have been studied by many researchers  but none of them included wall properties in their studies. Here an axisymmetric non-linear FSI model using ureteral real data is presented. II. THEORY A. The Fluid Model We consider transient viscous flow in an axisymmetric tube (Fig.1.). The flow is assumed to be laminar, Newtonian, viscous and incompressible. The incompressible NavierStokes equations are used as the governing equations. For boundary conditions, we assume that the tube have no axial motion, that no slipping takes place between the fluid and the wall and that no penetration of the fluid through the tube wall occurs. The pressures at the inlet and outlet of the tube are prescribed. This yields the following:
Abstract—An axisymmetric model with fluid-structure interactions (FSI) is introduced and solved to perform ureter flow and stress analysis. The Navier-Stokes equations are solved for the fluid and a linear elastic model for ureter is used. The finite element equations for both the structure and the fluid were solved by the Newton-Raphson iterative method. Our results indicated that shear stresses were high around the throat of moving contracted wall. The pressure gradient magnitude along the ureter wall and the symmetry line had the maximum value around the throat of moving contracted wall which decreased as the peristalsis propagates toward the bladder. The flow rate at the ureter outlet at the end of the peristaltic motion was about 650 mm3/s. During propagation of the peristalsis toward the bladder, the inlet backward flow region was limited to the areas near symmetry line but the inner ureter backward flow regions extended to the whole ureter contraction part. The backward flow was vanished after 1.5 seconds of peristalsis propagation start up and after that time the urine flow was forward in the whole ureter length, so reflux is more probable to be present at the beginning of the wall peristaltic motion.
RINE transport from the kidneys into the urinary bladder is one of the classical subjects of applied peristaltic transport theory with which the modeling of ureteral flow practically began . Despite active research, the mechanism by which urine is transported from the kidneys into the urinary bladder remains unclear. In general, the ureteral flow is not purely peristaltic and includes a component which depends on the pressure difference between the renal pelves and the urinary bladder. Thus reflux might be caused by an increase in the pressure inside the bladder. Reflux may result in the ingress of bacteria and toxins from the bladder into the renal pelves and then into the kidneys . In the absence of peristalsis, the ureter behaves as a nonuniform passively distensible tube and the flow through it may be taken as approximately steady. The problem of correctly modeling the smooth muscle of the ureter (like that of many other organs: esophagus, bowels, seminal duct, etc.) is to a large extent unsolved , . The rate of contraction Manuscript received June 22,...