**Core Concept**
The brachial artery is the main artery of the upper limb, supplying blood to the arm through its branches, including the profunda brachii artery. The origin of the brachial artery is from the axillary artery, and ligating it at its origin would affect blood flow to the upper limb.

**Why the Correct Answer is Right**
The profunda brachii artery is a branch of the brachial artery that supplies blood to the deep muscles of the arm. In the event of brachial artery ligation, the posterior circumflex humeral artery and the anterior circumflex humeral artery, which are branches of the axillary artery, would provide collateral circulation to the profunda brachii artery through the anastomoses between the deep and superficial branches of the brachial artery.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the superior ulnar collateral artery is not directly involved in supplying blood to the profunda brachii artery.
* **Option B:** This option is incorrect because the radial collateral artery is not responsible for supplying blood to the profunda brachii artery in the event of brachial artery ligation.
* **Option D:** This option is incorrect because the inferior ulnar collateral artery does not provide significant collateral circulation to the profunda brachii artery.

**Clinical Pearl / High-Yield Fact**
The anastomoses between the deep and superficial branches of the brachial artery provide a rich network of collateral circulation that can compensate for the loss of blood flow to the upper limb in the event of brachial artery ligation.

**Correct Answer:** C.