Numerical approximation of mathematical model for absorption of subcutaneously injected insulin

Abstract

A pharmacokinetic model is modified to enable quantitation of subcutaneous insulin absorption following insulin injections of soluble insulin and monomeric insulin analogues. The model for soluble insulin includes diffusion, equilibration between hexameric and dimeric insulin and absorption of dimeric insulin molecules. Numerical approximation is carried out by modelling the whole system as a capacitor-resistor network with lumped elements and discrete sources and sinks. By means of the analytical solution for monomeric-insulin absorption, it can be shown that the approximation scheme yields sufficiently accurate results. The modified model for soluble insulin demonstrates dose- and concentration-dependent insulin absorption within the range of therapeutic concentrations and volumes. Additionally, parameters are estimated from published glucose-clamp data. The results of the data fitting indicate that the model presented is adequate for pharmacological studies. The model is suitable for individual parameter estimation from the time course of plasma insulin or from the disappearance curves of radiolabelled injected insulin.