Final answer:
The major branches off the aortic arch, specifically the brachiocephalic artery, the left common carotid artery, and the left subclavian artery, are most susceptible to damage first during an aortic dissection. The coronary arteries can also be affected if the dissection is near the root of the ascending aorta.
Step-by-step explanation:
In aortic dissection, the condition occurs when there is a tear in the inner layer of the aorta, leading to blood flowing between the layers of the wall of the aorta and forcing the layers apart. The aortic arch gives rise to three major branching arteries: the brachiocephalic artery, the left common carotid artery, and the left subclavian artery.
These vessels are particularly susceptible to being damaged first during an aortic dissection due to their proximity to the heart and their classification as elastic arteries, which are the types of arteries that can expand when the blood pressure is high. As the ascending aorta gives rise to the right and left coronary arteries, an aortic dissection occurring near its root could also potentially affect these arteries that supply the heart muscle itself.