**Core Concept**
The hypophysis cerebri, also known as the pituitary gland, is a crucial endocrine gland that regulates various bodily functions, including growth, metabolism, and reproductive processes. It receives its blood supply from a unique vascular network that is distinct from the general cerebral circulation.

**Why the Correct Answer is Right**
The pituitary gland is supplied by the hypophyseal portal system, which is a specialized network of blood vessels that allows for the transport of hormones from the hypothalamus to the pituitary gland. This system is essential for the regulation of hormone secretion by the pituitary gland. The hypophyseal portal system arises from the superior and inferior hypophyseal arteries, which are branches of the internal carotid artery. The hormones produced by the hypothalamus are transported to the pituitary gland through this portal system, where they regulate the secretion of various hormones.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the hypophysis cerebri is not supplied by the middle meningeal artery, which primarily supplies the dura mater.
**Option B:** This option is incorrect because the anterior cerebral artery does not directly supply the pituitary gland, although it does supply the anterior part of the hypothalamus.
**Option C:** This option is incorrect because the posterior cerebral artery primarily supplies the posterior part of the hypothalamus and the thalamus, but not the pituitary gland.

**Clinical Pearl / High-Yield Fact**
The hypophyseal portal system is a unique feature of the pituitary gland that allows for the regulation of hormone secretion by the hypothalamus. This system is essential for maintaining homeostasis in the body.

**Correct Answer: D. The hypophyseal portal system arises from the superior and inferior hypophyseal arteries.**