**Core Concept**
The oblique popliteal ligament is a fibrous structure located in the posterior compartment of the knee joint. It plays a crucial role in providing stability to the knee by forming a part of the posterior capsule. The ligament is also known to be pierced by a specific branch of the popliteal artery.

**Why the Correct Answer is Right**
The middle genicular branch of the popliteal artery is responsible for supplying blood to the structures within the knee joint, including the ligaments and the synovial membrane. As the middle genicular artery passes through the knee joint, it pierces the oblique popliteal ligament, providing a vital blood supply to the surrounding tissues. This branch is a key structure in the anatomy of the knee, and its relationship with the oblique popliteal ligament is an important detail to remember.

**Why Each Wrong Option is Incorrect**
* **Option A:** The anterior branch of the popliteal artery is primarily involved in supplying blood to the muscles and structures of the anterior compartment of the thigh. It is not directly related to the oblique popliteal ligament.
* **Option B:** The medial inferior genicular branch of the popliteal artery supplies blood to the structures of the medial aspect of the knee, including the medial meniscus and the medial collateral ligament. It is not the correct answer in this context.
* **Option C:** The medial superior genicular branch of the popliteal artery supplies blood to the structures of the medial aspect of the knee, including the quadriceps femoris muscle. It is not the correct answer in this context.

**Clinical Pearl / High-Yield Fact**
The middle genicular branch of the popliteal artery is one of the three branches of the popliteal artery, along with the anterior and posterior branches. Understanding the anatomy of this branch and its relationship with the oblique popliteal ligament is crucial for surgeons and physicians performing procedures in the knee joint.

**✓ Correct Answer:** D. Middle genicular branch of popliteal artery