We describe a mathematical model of digestion in the small intestine. The main interest of our work is to consider simultaneously the different aspects of digestion i.e. 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 several numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy regarding the overall behavior of the model and also when challenged versus experimental data. The main feature and interest of this model are its genericity. Even if we are at an early stage of development, our approach can be adapted to deal with contrasted feedstuffs in nonruminant animal to predict the composition and velocity of bolus in the small intestine.

In this work, the modeling of the digestion in the small intestine is developed by investigating specifically the effects of dietary fiber. As our previous model, this new version takes into account the three main phenomena of digestion: transit of the bolus, degradation of feedstuffs and absorption through the intestinal wall. However the two main physiochemical characteristics of dietary fiber, namely viscosity and water holding capacity, lead us to substantially modify our initial model by emphasizing the role of water and its intricated dynamics with dry matter in the bolus. Various numerical simulations given by this new model are qualitatively in agreement with the positive effect of insoluble dietary fiber on the velocity of bolus and on its degradation all along the small intestine. These simulations reproduce the negative effect of soluble dietary fiber on digestion as it has been experimentally observed. Although, this model is generic and contains a large number of parameters but, to the best of our knowledge, it is among the first qualitative dynamical models of fiber influence on intestinal digestion.