Sodium ion transport in the intestinal wall: a mathematical model

A theoretical approach to study the uptake of sodium ions across the gastrointestinal mucosa and the concentrations at which they are taken up into the underlying blood capillaries has been attempted. A two-phase model of the mucosa is considered, consisting of an extracellular phase and a cellular phase. The model takes into account two important modes of transport: diffusion under concentration gradient and potential gradient (electrodiffusion) and active transport which is ATPase enzyme mediated. Appropriate partial differential equations for the two mechanisms of transport are derived and are solved by iterative methods. An approximate distance from the lumen where the capillaries lie is somewhere between 10 and 15% of the total wall length. The mean concentration of sodium ions made available for absorption at the capillaries is studied with time. A functional form for the variation of potential with respect to distance is proposed, and by comparing model solutions with experimental data it is calculated explicitly.