A simple analytical solution to the three-compartment pharmacokinetic model suitable for computer-controlled infusion pumps

The disposition of many drugs following an intravenous bolus injection can be described by a biexponential or triexponential equation. Computer-controlled infusion pumps have been developed which dose intravenous drugs based on models of drug disposition. These pumps can maintain steady plasma drug concentrations and facilitate controlled increases and decreases in drug concentration, enhancing titration of intravenous drugs. Several investigators have proposed analytical solutions to the biexponential and triexponential disposition functions for use in computer-controlled infusion pumps. Because of the complexity of these analytical solutions, other investigators have used numerical techniques to approximate the analytical solution. The authors have derived an extremely simple analytical solution to polyexponential disposition functions. This solution simplifies both the prediction of the plasma drug concentration by a computer-controlled infusion pump and the stepwise calculation of the infusion rate required to maintain constant plasma drug concentrations.