A Mathematical Treatment of Multiple Intermittent Intravenous Infusions in a One-Compartment Model

Abstract

Compartment models in pharmacokinetics are generally described for a single dose and can only simulate drug concentration as a function of the first dosing interval. Our objective was to create a one-compartment model for constant rate repetitive intravenous intermittent infusions where drug concentration can be simulated as a function of real time. The analytical solutions to differential equations that were set for the time periods of drug infusion and elimination after an intermittent intravenous infusion were used to derive sequences patterns and determine the partial sums of mathematical series for multiple intermittent infusion doses. The model's original theory was supplemented with explicit solutions to the concentration and AUC, at non steady state conditions, with and without a loading dose, for both the infusion and elimination time periods after repetitive intermittent intravenous infusions. The validity and accuracy of these formulas in calculating drug concentration and AUC was verified by mathematical proofs, numerical methods and the principle of superposition. Drug concentration and AUC can be simulated using the newly described one-compartment pharmacokinetic model in the entire time-domain of therapy after multiple and repetitive intermittent intravenous infusions and not just within the first dosing interval.