This clinical trial of three dose rates of dexmedetomine will determine the pharmacokinetics of the drug in infants who remain tracheally intubated postoperatively. An exploratory pharmacodynamic study of a non-invasive device measuring sedation will be performed. Although the pharmacokinetics of dexmedetomine have been described for pediatric patients, the drug disposition in infants has not been well described. A range of doses has been studied, yet there are no reports describing the optimal dose for post-operative pediatric patients. This study will provide data that may allow for improved dosing recommendations in this critically ill population of children.