A mathematical analysis of intestinal peristaltic waves

Gut motility is usually investigated by introducing probes in the intestinal lumen. Image analysis could be used instead of intraluminal pressure measurements to avoid the inconvenience of this invasive procedure. The present study exposes the theoretical principles of intestinal peristalsis in terms of indirect intraluminal pressure and content velocity measurements. A geometrical model of intestinal contractions is mathematically described by using Stokes' equations in order to evaluate velocities and pressures in the equations established by quantitative analysis of cinematography pictures. The couple velocity-pressure is calculated at each point of the geometrical model for a viscous and non-compressible fluid. This fluid flows in a geometrical structure, the boundaries of which vary with time and behave in a periodic and regular way by simulating the movements of intestinal contractions. A comparison is made between experimental pressure recordings in isolated rat intestines and pressure values calculated by utilizing the geometrical model. Velocity values calculated at every grid node show positive and negative zones in the geometrical model output. The position of these zones vary from one geometrical model to another. Moreover, the calculated pressure and velocity values change according to the applied vector efforts. The similarity of the results obtained shows the efficiency of the finite element technique in the case of Stokes' equations.