A Method to Custom-build Equations of Drug Concentration as a Function of Real Time in the One-Compartment Open Model and Their Application in Multiple Intravenous Bolus and Multiple Oral Doses

Abstract

A method to custom-build expressions of drug concentration as a function of total time in a one-compartment pharmacokinetic model for multiple-dose schedules is developed and successfully applied in four dosing schedules that combined administration of multiple IV bolus and oral maintenance and loading doses. The method consists of writing the terms of the mathematical sequence from the analytical solutions to drug concentration using total time, instead of time within dosing interval, extracting the pattern of the respective sequences, and finally, determining the partial sums of the series that relate to drug concentration to dose number and real-time, for each particular administration route and dosing schedule. Multiple subroutines written in Fortran language demonstrated the potential of these equations to investigate the effect of dose size on peak plasma drug concentration and peak time after multiple oral administrations and for calculating and refining experimentally determined time-dependent pharmacokinetic parameters such as non steady-state average concentration values and Area Under the Curve (AUC). It is shown that the only truly independent of dose size peak time is that of the first oral dose (). A mathematical expression was derived that relates the time to reach non steady-state peak times after multiple oral doses to the absorption and elimination rate constants for the first time. For repetitive oral dose administration, the will always be the longest peak time, while the shortest time to reach maximum plasma drug concentration will be at steady-state conditions.