Fitness level implies good blood flow which the brain needs. Newer diseases like Alzheimer’s is just the brain's version of hardening of the arteries that lead to strokes and heart attack, or again, PAD and even certain manly "dysfunctions" you hear about these days. They are all related.
Problem is (and here goes my rant again), they scare people into wanting to stay healthy, so here comes the prescription pad for Lipitor or the likes to keep those arteries from getting clogged. But even the medical personnel know to stay away from that stuff. Once a guy is put on such pills, nurses jokingly say to each other that he has been put on the "dumb pill" as in a pill that makes one mentally slower --- the very thing we are trying to prevent!! I mean, the medical doctors and nurses and others in the field are staying away from what they are putting their patients on and then laughing behind their backs, all for $$$ apparently.
So yes. Stay fit and get proper nourishment by all means. But if they find a "problem", I'll bet dollars to donuts you'll be mentally sharper if you just let the "problem" go rather than "treating" it. As long as you are already doing the right things by diet and exercise you probably are as good as you will ever be.