But we’ve know this for years…
“A new review concludes that a Mediterranean diet is good for the brain, after finding that people who follow the diet are less likely to experience cognitive decline and develop Alzheimer’s disease.
Researchers say greater adherence to a Mediterranean diet may benefit cognitive function for younger and older adults.Lead author Roy Hardman, from the Centre for Human Psychopharmacology at Swinburne University of Technology in Melbourne, Australia, and his team publish their findings in the journal Frontiers in Nutrition.
The Mediterranean diet incorporates a high intake of plant-based foods, such as fruits, vegetables, whole grains, legumes, and nuts, while limiting intake of red meat and replacing butter with healthy fats, such as olive oil.The diet also emphasizes eating fish or poultry at least twice a week and using herbs and spices rather than salt to flavor food.”
Source: Mediterranean diet may slow cognitive decline, prevent Alzheimer’s – Medical News Today
Advanced Mediterranean Diet 
I suggest that writing “while replacing red meat and butter with healthy fats” is something you should consider no longer doing, as there is no evidence to support the fantasy that red meat or butter in and of themselves are unhealthy.
Perhaps advocating for the addition of olive oil as part of the diet, replacing trans fats, is more accurate.
Additionally, I suspect any diet that is equally low inflammation–such as one completely free of grains–would have identical or better health markers as the Mediterranean, don’t you?
I don’t know. I’d have to see the evidence. Someone has probably looked at inflammatory markers in celiac disease patients eating gluten-free.