Truncus encephali

is to assist in breathing as grown frogs do not have gills
helps air flow to the lungs (used as an air way)
It most likely helps a frog breathe because the do not have gills when they are grown!

Truncus Arteriosus is a rare congenital heart defect. Instead of a baby having two main arteries (the aorta and pulmonary artery) they have only one large one. Their oxygen levels will usually be slightly lower than normal, and congestive heart failure (CHF) usually develops within the first week of life. Some of the symptoms of CHF are shortness of breath, wheezing, rapid and/or noisy breathing and restlessness.

1st is the carotids, then is the systemic arch that goes throughout the body, almost in a heart shape itself, then is the pulmocutaneous arteries