**Core Concept**
The question tests the knowledge of a specific complication associated with a common medical procedure, namely, arterial dissection following arteriography by the femoral route. Arteriography involves the injection of a contrast agent into an artery to visualize the vascular system, and it is performed using various access routes, including the femoral artery in the groin.

**Why the Correct Answer is Right**
The femoral artery is located in the thigh and is a common site for accessing the aorta and its branches during arteriography. The risk of arterial dissection following arteriography is higher when the procedure is performed through the femoral artery due to the higher pressure and manipulation required to access the aorta. The dissection occurs when the intimal layer of the artery is torn, leading to separation of the intima from the media and potentially causing a false lumen to form. The most commonly dissected artery in this scenario is the **External Iliac Artery**, which is the artery that arises from the Common Iliac Artery and supplies blood to the lower limb.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **Internal Iliac Artery** is not the most commonly dissected artery following arteriography by the femoral route. While it can be affected, the external iliac artery is more prone to dissection due to its direct connection to the aorta and the higher pressure required to access the aorta.
* **Option B:** The **Superficial Femoral Artery** is a branch of the femoral artery and is not the most commonly dissected artery following arteriography by the femoral route. While it can be affected, the external iliac artery is more prone to dissection.
* **Option C:** The **Popliteal Artery** is not the most commonly dissected artery following arteriography by the femoral route. It is a branch of the femoral artery that supplies blood to the lower limb, but it is not directly involved in the procedure.

**Clinical Pearl / High-Yield Fact**
It is essential to note that the risk of arterial dissection following arteriography can be minimized by using smaller catheters, lower contrast agent volumes, and more precise technique. Additionally, patients with a history of atherosclerosis or other vascular diseases are at a higher risk of arterial dissection.

**Correct Answer: C. External Iliac Artery.**