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. Some authors even reported that no sedation (analgesia only) provides better outcome than light sedation, because it further shortens the durations of mechanical ventilation and ICU stay. In the above studies of the investigators, the recruited patients were less severe because the Acute Physiology and Chronic Health Evaluation II (APACHE II) score was low (mean score from 10.2 to 10.6) and the duration of mechanical ventilation was short (median 6.9 hours in the control group). 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 improving sleep and 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).