1. People who get migraines are probably chewing too much gum (that is, chewing too much in general.)

2. There's a sharp increase in dementia when people lose their teeth, and this is likely because they aren't chewing enough.

Neither of these were particularly strong studies (the first of the two only had a sample-size of 30, if I recall) but they do support one-another on a general hypothesis: chewing plays a large and necessary part in oxygenating your brain.