Okay, let's tackle this question. The patient has prostate cancer that has spread to the T10 and T11 vertebrae. The question is about the route of metastasis.

First, I need to recall how prostate cancer typically spreads. Prostate cancer often metastasizes via the bloodstream. The lymphatic system is another route, but for bone metastasis, hematogenous spread is more common. The vertebral column is a common site for bone metastases in prostate cancer.

The specific pathway here would involve the veins. The prostatic veins drain into the internal iliac veins, which then connect to the common iliac veins and into the inferior vena cava. However, there's another pathway called the Batson's paravertebral venous plexus. This plexus is valveless, allowing retrograde flow, which is a common route for cancer cells to reach the vertebrae. So, Batson's plexus is the key here.

Now, looking at the options (even though they aren't listed), the correct answer would be Batson's paravertebral venous plexus. The other options might include lymphatic spread, direct extension, or other venous systems. Lymphatic spread is possible but less common for bone metastases. Direct extension would be if the cancer spread locally, not hematogenous. So the incorrect options would be wrong because they don't align with the typical route for prostate cancer to reach the vertebrae.

Clinical pearl: Remember that prostate cancer tends to metastasize to the axial skeleton (spine, pelvis) via Batson's plexus. This is a high-yield fact for exams.

**Core Concept**
Prostate cancer commonly metastasizes to the axial skeleton via **Batson's paravertebral venous plexus**, a valveless network allowing retrograde spread of malignant cells to vertebral bodies. This route is critical for hematogenous dissemination to the spine.

**Why the Correct Answer is Right**
The **Batson's venous plexus** connects pelvic veins (e.g., prostatic veins) to the vertebral venous system. Its valveless structure permits retrograde blood flow, enabling cancer cells from the prostate to bypass the heart and directly access spinal veins. This explains the metastasis to T10-T11 vertebrae observed in the x-ray. Prostate cancer's predilection for axial skeleton metastasis via this pathway is well-documented.

**Why Each Wrong Option is Incorrect**
**Option A:** *Lymphatic spread* is less common for vertebral metastases in prostate cancer, which preferentially uses hematogenous routes.
**Option B:** *Direct extension* would involve adjacent structures (e.g., bladder, rectum), not distant vertebrae.
**Option C:** *Portal system* is irrelevant here; the liver is a common site for other cancers (e.g., colorectal), not prostate.

**Clinical Pearl / High-Yield Fact**
Prostate cancer's vertebral metastases are typically **osteoblastic** (sclerotic), unlike osteolytic lesions seen in breast cancer. Remember **"Batson's plexus"** as the exam-relevant pathway for spinal metastasis in prostate cancer. Mnemonic: **"Prostate to Spine via Batson's Valveless Ride."**

✓ Correct Answer: C. Internal vertebral plexus of veins