For patients undergoing mechanical ventilation, light sedation is better than deep sedation for the outcomes, which is manifested as shortened length of ICU stay, shortened duration of mechanical ventilation, and decreased mortality. In a recent study of the investigators, low-dose dexmedetomidine without sedative effects (0.1 ug/kg/h) improved sleep quality and reduced the incidence of delirium in elderly patients admitted to the ICU after surgery. The investigators hypothesize that, for ICU patients with prolonged mechanical ventilation, low-dose dexmedetomidine infusion (0.1 ug/kg/h) may also be effective in decreasing delirium. The purpose of this study is to investigate whether low-dose dexmedetomidine infusion can reduce the incidence of delirium in ICU patients with prolonged duration of mechanical ventilation (>= 24 hours).