I know many people on vegetarian diets who follow the principles of the anti-inflammatory diet, it's basically a Mediterranean diet. The only concern on the vegetarian diet would be if you are getting enough omega-3 fatty acids; there are certainly many plant sources of them and I might try to persuade people to take supplements of fish oil. There are some algae-based supplements of omega-3 fatty acids and I think in the near future there will be many more, but that's really the only problem I would say.