This is a great question for the anesthesiologist. It is important to make sure that your afib is well controlled and monitored by a cardiologist. Clearance from your cardiologist would be required prior to the procedure. The anesthesiologist would then review your chart and determine what the safest form of anesthesia is for you.
It is best to have atrial fibrillation controlled with medications prior to undergoing elective cosmetic surgery. Patient's cardiologist should also give clearance to undergo elective anesthesia and surgery. The medications given while the patient's are asleep under anesthesia Is up to each individual anesthesiologist.