The fluid mechanics of the ureter from a lubrication theory point of view

Abstract

The function of a healthy ureter is analyzed in terms of a fluid-mechanical model. To the extent that the Reynolds number is of the order of one, the fundamental equations are shown to reduce to those of the theory of lubrication. It is found that from the point of view of the pressure variation with time (the urometrogram) the important part of the peristaltic wave is the constricting part. For this reason this part of the wave is represented with an algebraic expression of the form h ∼ xn making it possible to find closed form solutions. Using Fourier analysis in defining the complete wave shape of the ureter it was also possible to obtain numerical solutions. For both cases it is shown that there is good agreement between the theoretical and experimental pressure distributions, this not being the case for sinusoidal wave shapes. An approximate equation for the flux is developed and a universal relation is presented connecting the maximum pressure, flux and kinematic behaviour of the ureter.