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The pharmacokinetic behavior of intravenous anesthetic drugs can be described by two- or three-compartment models. Rapid achievement and maintenance of steady plasma concentrations of these drugs requires a complicated delivery scheme, perhaps best controlled by a computer. The authors developed a method of simulating the performance of a computer-controlled infusion pump from the differential equations describing drug transfer between compartments. They also derived a mathematically simple and flexible approximate solution to these equations using Euler's numerical method. They incorporated this approximate solution into a computer-controlled infusion pump for intravenous drugs. They tested their pump by simulating the administration of fentanyl to a hypothetical patient whose fentanyl pharmacolunetics were described by a three-compartment model. The exact analytical solution served as the standard of comparison. The approximation technique, using a 15-s interval between model updates, had a maximum error of 0.35 ng·ml-1, and rapidly converged on the exact solution. The simulations revealed oscillations in the system. The authors suggest that such simulations be used to evaluate computer-controlled infusion pumps prior to clinical trials of these devices.