Hi,
How is your daughter? After the Fontan operation, most children will continue to require some medications and may be placed on anti-coagulant medications to reduce the chances of clot formation in the circulatory system. With your child's history, it is best to sedate her as if she is undergoing a surgery procedure in the hospital setting. It is also important that both cardiologist and anesthesiologist are present to monitor your child during the procedure. Aside from this, antibiotics are given prior to certain dental and surgical procedures to minimize the risk of cardiac infections.
Although nitrous oxide, is generally safe, it is a mild and fast-acting sedative but it is also a weak anesthetic and has low potency. Patients are quick to recover and may also lead to myocardial depression in sick patients. Discuss any doubts with your doctor to alleviate all your worries prior to this procedure. Take care and regards.
What kind of dental work is she having done?