Sodium ion transport in the intestinal wall: A mathematical model

A theoretical approach to study the uptake of sodium ions acrossthe gastrointestinal mucosa and the concentrations at whichthey are taken up into the underlying blood capillaries hasbeen attempted. A two-phase model of the mucosa is considered,consisting of an extracellular phase and a cellular phase. Themodel takes into account two important modes of transport: diffusionunder concentration gradient and potential gradient (electrodiffusion)and active transport which is ATPase enzyme mediated. Appropriatepartial differential equations for the two mechanisms of transportare derived and are solved by iterative methods. An approximatedistance from the lumen where the capillaries lie is somewherebetween 10 and 15% of the total wall length. The mean concentrationof sodium ions made available for absorption at the capillariesis studied with time. A functional form for the variation ofpotential with respect to distance is proposed, and by comparingmodel solutions with experimental data it is calculated explicitly.