Finite-element analysis of flow induced by contractions like those of the intestine

Abstract

After a brief description of the wall movements of the small intestine, the simplifications introduced to allow an analysis of the fluid mechanics of intestinal contractions are described. These simplifications, bearing mainly on the fluid properties, led to the use of the biharmonic equation as the governing equation of fluid flow. This is considered valid without excluding essential flow features. The kinematics of the wall cannot, however, be simplified so radically without too much loss, so that the use of numerical techniques was unavoidable. The versatility of the finite element method led to adoption of that procedure. It was necessary to make some changes because of the complexity of the flow patterns. This was accomplished by the careful use of the fifth-degree polynomial. It was thus possible to obtain reliable flow patterns, accurate velocity profiles and values for the flow rates. It was shown that isolated propagative transverse contractions over a finite length of the conduit can pump. The results of the numerical integrations are given in the form of velocity profiles, streamlines, and pumping characteristics. Although, so far, these results are for two-dimensional channels, the results represent a general behavior, so that further work with circular tubes should yield similar results.