Mathematical Modeling of the Ureteral Peristaltic Flow with Fluid Structure Interaction

INTRODUCTION Urine 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 [1]. 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 and it may result in the ingress of bacteria and toxins from the bladder into the renal pelves and then into the kidneys [2]. The problem of correctly modeling the smooth muscle of the ureter is to a large extent unsolved [3,4]. A theoretical analysis and numerical solutions were accomplished for peristaltic flow through a distensible tube of limited length [5]. The results showed that in flow with isolated boluses pressure/flow relation was determined by the active and passive properties of the tube undergoing peristaltis and not by the outlet condition. 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 [6] but none of them included wall extensibility in their studies. Here a two-dimensional non-linear fluid structure interaction (FSI) model using ureteral real data is presented.