If a person needs to eat on Yom Kippur for medical reasons, he should, if possible, limit his food intake to a Ke’zayit of food every nine minutes. This means he should eat a Ke’zayit, then wait nine minutes, and then eat another Ke’zayit. As for drinking, a patient who must drink should drink a "Melo Lugmav" – a cheek-full – every nine minutes. Since every person’s "cheek-full" is different, one who knows he will need to drink on Yom Kippur should "measure" this amount before Yom Kippur, by filling his cheek with water and then expelling the water into a measuring cup. One can also suck an ice cube every nine minutes instead of drinking the water.
Of course, this applies only if the person needs just a small amount of food and water to maintain his health. But if there is a real life-threatening condition, then it goes without saying that the individual should eat and drink as much and as often as he needs to avoid a risk to his life.
(Based on Hacham Bension Abba Shaul, in Ner Siyon)