Mathematical Modeling of Transport and Degradation of Feedstuffs in the Small Intestine

We describe a mathematical modeling of the digestion in the small intestine. The main interest of our work is to consider, at the same time, different aspects of the digestion i.e. the transport of the bolus all along the intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. A system of coupled ordinary differential equations is used to model these phenomena. The major unknowns of this system are the position of the bolus and its composition. This system of equations is solved numerically. We present different numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy with experimental data. The main feature and interest of this model are its generality. Even if we are at an early stage of development, our approach can be adapted to treat any kind of feedstuffs in any non-ruminant animal to predict the composition and velocity of bolus in the small intestine

The concept of a functional unit of the gut

The concept of a functional unit (FU) as the basic element of the gut as a mechanical structure is presented. The FU is a geometrically and morphofunctionally defined part of the gut modeled as a soft cylindrical orthotropic shell. The wall of the shell formed of the two distinct layers of muscle - the longitudinal and circular, respectively. The myoelectrical activity of both layers is controlled by pacemaker cells, analogous to interstitial cells of Cajal type MP (ICC-MP). The mechanical properties of the wall of the FU are nonlinear and deformations are finite. The dynamics of the generation of coupled electromechanical waves of contraction/relaxation as a response to a discharge of ICC-MP and an increased in intraluminal pressure is studied numerically

Intestinal propulsion of a solid non-deformable bolus

A mathematical model of a segment of the gut with an enclosed pellet is constructed. The gut is represented as a thin deformable soft biological shell with the pellet modeled as a non-deformable solid. Mechanical properties of the gut wall were represented as longitudinal and circular smooth muscle layers embedded in stroma that satisfies the general type of nonlinear orthotropy. Deformations of the wall are finite. Bolus propulsion is numerically simulated by generation and propagation of an electromechanical wave along the syncytia. Pharmacological manipulation is applied to model 5-HT type 3 antagonist (Lotronex, GlaxoSmithKline) and 5-HT type 4 agonist (Zelnorm, Novartis, AB) drugs on the dynamics of bolus progression. The results lead to new quantitative insights into the complex spatio-temporal patterns of gastrointestinal transit. It is demonstrated that the reciprocal relationship in contraction of the longitudinal and circular smooth muscle syncytia is necessary to provide the "mixing" type of movements during the preparatory phase of propulsion. Strong simultaneous contractions of the both smooth muscle layers are required to expel the "mixed" pellet from the segment. The model is implemented as an interactive software system, Gut Discovery© (www.aincompany.com), and accurately predicts the effects of drugs on gut motility. © 2005 Elsevier Ltd. All rights reserved