Final answer:
The best method to prevent trachea-innominate artery fistula is to avoid prolonged intubation, as it reduces the pressure on the tracheal wall which is the main cause of fistula formation.
Step-by-step explanation:
The question pertains to the prevention of trachea-innominate artery fistula, a serious complication that can arise from procedures like prolonged intubation. The fistula can happen when the tracheostomy tube exerts constant pressure against the tracheal wall, leading to necrosis and fistula formation with major arteries nearby, such as the innominate artery. Among the listed options, avoiding prolonged intubation serves as the most effective measure for preventing this complication, as it directly addresses the issue of prolonged pressure on the tracheal wall. While antibiotics administration and continuous suctioning might be beneficial in preventing infection and managing secretions respectively, these do not specifically prevent fistula formation. High-pressure cuff inflation is contrary to what should be done, as it may actually increase the risk of fistula development.