In interviews, dt have stated that the "Medicate" section of the song was inspired by the Robin Williams film "Awakenings," which in turn was based on real-life events. The common thread between all 3 stories is that they feature a doctor using a drug to bring a patient out of a longstanding coma, only to have the patient relapse shortly thereafter.
And yes, in the end, it ties back to the overlying Octavarium theme: "The story ends where it began;" in this case, the story ends with the patient relapsing into the coma they had been pulled from.