**Core Concept**
Posterior dislocation of the knee is a serious injury that poses significant risks to surrounding structures, particularly the popliteal artery. The popliteal artery is the primary blood supply to the lower leg, and its injury can lead to severe complications.

**Why the Correct Answer is Right**
The popliteal artery is closely associated with the posterior aspect of the knee joint and is vulnerable to injury during a posterior dislocation. The artery passes through the popliteal fossa, a small, triangular space at the back of the knee, making it susceptible to damage from the dislocated femur. The injury can cause a sudden interruption of blood flow, leading to ischemia of the lower leg. Prompt recognition and treatment are essential to prevent long-term damage. The popliteal artery's proximity to the joint and its critical role in limb perfusion make it the most likely structure to be injured in a posterior knee dislocation.

**Why Each Wrong Option is Incorrect**
**Option B:** Sciatic nerve injury, while possible, is less common than popliteal artery injury in posterior knee dislocations. The sciatic nerve is more laterally located and has a greater capacity for stretch without injury.

**Option C:** Ischemia of the lower leg compartment is a potential consequence of popliteal artery injury but is not the primary complication of posterior knee dislocation. It is a downstream effect of the more immediate threat to the popliteal artery.

**Option D:** Femoral artery injury is less likely in posterior knee dislocations, as the femoral artery is more proximally located and has a more robust collateral circulation.

**Clinical Pearl / High-Yield Fact**
In cases of suspected posterior knee dislocation, it is essential to immediately assess the popliteal pulse and consider imaging studies to evaluate the integrity of the popliteal artery. Prompt intervention can prevent long-term limb ischemia and associated complications.

**✓ Correct Answer: A. Popliteal artery injury**