Additional Study Information: This study is for patients who have severe migraine headaches that might be a result of a hole in the heart wall called a Patent Foreman Ovale, or PFO. It is known that as many as 40% of patients with migraine headaches also have a PFO. It is not well understood how the two are related, or how having a hole in the heart wall could cause headaches. In this study, we will test a drug, called ticagrelor (Brilanta), which is FDA approved for patients who have had heart attacks and are found to have blockages in their coronary arteries, but has never been tested as a treatment for migraines.