Optimal intravenous bolus-infusion drug-dosage regimen based on two-compartment pharmacokinetic models

An orthogonal collocation on finite elements-based regression method was applied to help design optimal drug-dosage regimens. The approach, suitable for two-compartment models, would allow clinicians to design multiple boluses followed by a constant-rate infusion of a medicament to patients in order to assure a desired plasma concentration. The algorithm was tested on theophylline, a drug that has been described by both linear and Michaelis-Menten elimination pharmacokinetics. In the linear case, increasing the number of boluses, from 1 to 4, decreased the normalized square root of the integral square error from 1.80 to 0.58 when a target concentration of 10 μg/mL was selected in the central compartment. When applied to the nonlinear metabolism, the procedure, implemented in Mathematica^® (Wolfram Research, Inc.), effectively computed optimal dose sizes, injection times and infusion rates. Estimations, based on linear interpolation, provided a good time-saving alternative to the full optimization methodology.