Final answer:
The axillary artery and specifically the Posterior humeral circumflex artery (option B) , which is one of its branches, may be injured in a fracture of the surgical neck of the humerus. This is due to the anatomical proximity of these arterial structures to the surgical neck region.
Step-by-step explanation:
In a fracture of the surgical neck of the humerus, the artery that may be injured is the axillary artery, particularly its branches known as the humeral circumflex arteries. This region is supplied blood by the axillary artery, after it exits the thorax and is renamed from the subclavian artery. The axillary artery, upon supplying the region near the head of the humerus via the humeral circumflex arteries, continues into the upper arm as the brachial artery.
The Posterior humeral circumflex artery, which is one of the humeral circumflex arteries branching from the axillary artery, is positioned in proximity to the surgical neck of the humerus. Thus, it is the artery most at risk of being injured during a fracture to this specific area of the humerus. Other choices, such as the Subscapular, Radial recurrent, Deep brachial, and Circumflex scapular arteries are less likely to be involved in this type of injury.