Which blood vessel runs along the dorsal surface of the brain stem?

The basilar artery runs along the dorsal surface of the brain stem, making it the correct choice. This artery is formed by the union of the two vertebral arteries and ascends along the midline of the brain stem, where it provides critical blood supply to various structures in the brain, including the cerebellum and parts of the brain stem itself. Its position on the dorsal surface is significant for understanding the vascular supply and potential areas of infarction in the brain stem, which can have wide-ranging effects on neurological function.

Other arteries listed, such as the anterior inferior cerebellar artery, pontine arteries, and vertebral arteries, have different specific paths and areas of supply. The anterior inferior cerebellar artery branches off from the basilar artery and supplies parts of the cerebellum and brain stem but does not run along the dorsal surface itself. The pontine arteries arise from the basilar artery and supply the pons directly, while vertebral arteries are primarily located in the neck region and merge to form the basilar artery before ascending, also not running along the dorsal surface of the brain stem. Understanding the specific anatomy and functions of these arteries helps clarify their roles and locations in relation to the brain stem.