Mathematical Homogenization in the Modelling of Digestion in the Small Intestine

TL;DR

This paper demonstrates that a simplified macroscopic model of small intestine digestion can be derived from more detailed models using homogenization techniques, linking different scales of biological processes.

Contribution

It shows how a simplified ODE model of digestion is a limit case of more complex models through homogenization, bridging multiple biological scales.

Findings

The simplified model accurately represents complex biological phenomena.

Homogenization methods connect detailed models to macroscopic descriptions.

The approach validates the simplified model as a limit of realistic models.

Abstract

Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the transport and degradation-absorption processes during the digestion. The present article sustains this simplified model by showing that it can be seen as a macroscopic version of more realistic models including biological phenomena at lower scales. In other words, our simplified model can be considered as a limit of more realistic ones by averaging-homogenization methods on biological processes representation.