**Core Concept**
The supracondylar fracture of the humerus is a type of elbow fracture that occurs just above the condyles of the humerus. The nerves in the vicinity of this fracture are at risk of injury, particularly those that run through the cubital tunnel and the anterior interosseous nerve, which is a branch of the median nerve.

**Why the Correct Answer is Right**
The anterior interosseous nerve is the most commonly injured nerve in supracondylar fractures of the humerus. This is because the nerve passes close to the fracture site and can be stretched or transected during the injury. The mechanism of injury often involves a fall onto an outstretched hand, which can cause a fracture and subsequent nerve damage. The anterior interosseous nerve is responsible for innervating the flexor digitorum profundus, flexor pollicis longus, and pronator quadratus muscles.

**Why Each Wrong Option is Incorrect**
**Option A:** The radial nerve is not typically involved in supracondylar fractures of the humerus, as it is located more laterally and is not as close to the fracture site.

**Option B:** The ulnar nerve is also not commonly injured in supracondylar fractures, as it is located more medially and is protected by the medial epicondyle of the humerus.

**Option C:** The median nerve is the parent nerve of the anterior interosseous nerve, but it is not the specific nerve most commonly injured in supracondylar fractures.

**Clinical Pearl / High-Yield Fact**
It is essential to carefully evaluate patients with supracondylar fractures for nerve injuries, particularly the anterior interosseous nerve, as early recognition and treatment can significantly improve outcomes.

**✓ Correct Answer: D. Anterior interosseus Nerve**