Numerical simulation of the peristaltic reflex of the small bowel

Abstract

A mathematical model and results of numerical simulation of the peristaltic reflex development of the small bowel are presented. The organ is modeled as a soft orthotropic cylindrical biological shell, reinforced by the smooth muscle elements. Their mechanical activity is under the control of a simple reflex arc represented by a single cholinergic neurone. The dynamical reaction starts as a response to the depolarization wave propagating along the smooth muscle layers. The muscle layers contract independently but in a coordinated way with the generation of active forces. The mechanical properties of the wall are supposed to be nonlinear. Deformations of the bioshell are finite. The governing system of equations is obtained and solved numerically. The finite-difference method of second-order accuracy over the time and space variables has been used. The dynamics of stress-strain distribution in the biological shell and shape changes are analyzed. It is shown that there is no axial symmetry in the organ’s deformation during the first (preliminary) stage of motor reaction. Only with the development of propulsive contractions is the symmetry observed.