before vowels an-, word-forming element meaning: 1. "upward, up in place or time," 2. "back, backward, against," 3. "again, anew," from Greek ana (prep.) "up, on, upon; up to, toward; throughout; back, backwards; again, anew," from an extended form of PIE root *an- (1) "on, upon, above" (see on, which is the English cognate). In old medical prescriptions, ana by itself meant "an equal quantity of each."
before vowels phren-, word-forming element meaning "mind," also, in medical use, "diaphragm, muscle which parts the abdomen from the thorax;" from Greek phrēn, phrenos "the mind, spirit," also "the midriff, diaphragm," also (in plural, phrenes) "the parts around the heart, the breast," and hence "wits, sense, sanity, mind" on the notion of the breast or heart as the seat of thoughts and passions.
The word is of uncertain origin; Watkins has it under a proposed PIE root *gwhren- "to think." Beekes finds the connection with phrassein "to fence or hedge in" "semantically attractive," but there are phonetic difficulties, and he finds "quite feasible" a relationship with phrazomai "to think, consider" (later phrazein; see phrase (n.)), itself an isolated word.