Model determination for use in automated control of drug dosages: application to d-tubocurarine

To implement a feedback control system to achieve satisfactory muscle relaxation during surgical procedures, a mathematical formalism, based on linear compartmental theory, is derived to model the input/output response between the dosage of a drug administered and its neuromuscular effect as measured by the train-of-four (T4) ratio twitch response. The effect (T4 ratio) is related directly to the dosage schedule, and no attempt is made to include the plasma concentration of the neuromuscular blocking drug in the formalism. The neuromuscular blocking data of 24 patients, in whom the muscle relaxant d-tubocurarine (curare) was used, were fitted using a nonlinear least-squares data fitting routine. The number of compartments necessary to fit the data for each patient was determined using the general linear test. In all but three cases a biexponential model was sufficient to fit the data. Simulation studies also show that a biexponential model gives satisfactory control even for those patients for whom a triexponential model was necessary to fit the data. Further simulation shows that because of interindividual variation the application of adaptive control techniques will be needed.