Okay, let's tackle this question. The patient has symptoms like facial pain, numbness, and impaired sensation on half the face. Then there's ataxia, nystagmus, dysphagia, hoarseness, and impaired pain/thermal sensation on the opposite side. Also, Horner's syndrome is present. The question is asking which vessel's thrombosis is causing this.

First, I need to recall the brain regions and their blood supply. The symptoms suggest a posterior circulation issue. Let's break down the signs. The facial pain and numbness point to a cranial nerve issue. Ataxia and nystagmus are cerebellar signs. Dysphagia and hoarseness suggest involvement of the vagus and glossopharyngeal nerves. The crossed sensory loss (ipsilateral face, contralateral body) is a classic sign of a lateral medullary syndrome, also known as Wallenberg syndrome. This is typically caused by occlusion of the posterior inferior cerebellar artery (PICA), which is a branch of the vertebral artery.

Horner's syndrome in this context would be due to damage to the sympathetic pathway passing through the lateral medulla. The PICA supplies the lateral medulla, so its thrombosis would lead to these symptoms. Let's check the options again. The correct answer is likely PICA. The other options might be other arteries like the anterior inferior cerebellar artery (AICA) or vertebral artery itself. AICA infarct would cause different symptoms, like hearing loss and facial weakness. Thrombosis of the vertebral artery might present with more extensive symptoms, but PICA is the direct supplier to the lateral medulla. So the answer should be PICA.

**Core Concept**
This question tests knowledge of posterior circulation stroke syndromes, specifically lateral medullary infarction (Wallenberg syndrome). The key clinical features include crossed sensory loss, cranial nerve deficits (CN IX-XII), ataxia, and Horner's syndrome, which localize to the lateral medulla supplied by the posterior inferior cerebellar artery (PICA).

**Why the Correct Answer is Right**
Posterior inferior cerebellar artery (PICA) thrombosis causes lateral medullary infarction. This artery supplies the lateral medulla, where the spinal trigeminal nucleus (responsible for facial pain/thermal sensation), descending sympathetic fibers (Horner’s syndrome), and nuclei of CN IX–XII (dysphagia, hoarseness) reside. Crossed sensory loss occurs due to spinothalamic tract involvement in the contralateral spinal cord.

**Why Each Wrong Option is Incorrect**
**Option A:** Anterior inferior cerebellar artery (AICA) infarction causes hearing loss, vertigo, and facial weakness (ipsilateral), not crossed sensory deficits.
**Option B:** Vertebral artery occlusion would cause more diffuse symptoms, including consciousness changes, due to bilateral posterior circulation compromise.
**Option C:** Middle cerebral artery (MCA) infarction presents with contralateral motor/sensory deficits, aphasia, and neglect, not brainstem signs.

**Clinical Pearl / High-Yield Fact**
"Wallenberg syndrome" = PICA territory infarction. Remember the "4 Ds": Dysphagia, Dys

✓ Correct Answer: B. PICA (Posterior inferior cerebellar aery)