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A report on the development of a model for the computer-guided administration of sufentanil throughout surgical procedures involving cardiopulmonary-bypass (CB) is presented. The authors approach the effects of hypothermia on sufentanil clearance by applying a continuous temperature correction to the ultimate elimination rate constant (the terminal eigenvalue). This correction is based primarily on the anticipated effects of temperature on the enzyme-catalyzed reactions which are essential for the elimination of the drug from the body. An algorithm for the application of the model is also presented.