The cause for most Alzheimer's cases is still mostly unknown except for 1% to 5% of cases where genetic differences have been identified.
According to the Alzheimer's Association:
While scientists know Alzheimer's disease involves progressive brain cell failure, the reason cells fail isn't clear.
As for the claims by Dr. Perlmutter's book, there is an interesting article by James Hamblin where Epidemiologist Dr. David Katz, founding director of Yale University's Prevention Research Center, has criticized Grain Brain, saying "Perlmutter is way ahead of any justifiable conclusion" and that many of its claims are "wildly preposterous".
An article by Nathanael Johnson on grist.org also refers to this article:
Here’s a key exchange between Hamblin (who speaks first) and Perlmutter:
I asked for some clarity on that. “We don’t have clinical studies linking gluten to Alzheimer’s, ADHD, or —”
“With all due respect, we do. That information is well established. It was actually published by the Mayo Clinic, that gluten can in fact be related to risk for dementia. So I would beg to differ with you on that point. Gluten, certainly in patients with celiac disease, is strongly associated with risk for dementia. As was described in the proceedings of the Mayo Clinic, it was a treatable cause of dementia. So I think that’s pretty revolutionary and exciting.”
That study didn’t appear in my inbox. I asked him for it later, and he promptly sent me a 2006 case series that identified 13 patients in a review of Mayo Clinic records from January 1, 1970, to December 31, 2005. That is an interesting correlation — the study’s authors called it a “possible association” — but is far from well-established causation that gluten is a mechanism for dementia in people with celiac disease, much less all people.
Got that? Under Perlmutter’s prism, a single study, of 13 people, with a finding of “possible association,” turns into a near certainty. Hyperbole is a good way to sell diet books and start fads, but it’s not good for dieters.
So in conclusion, there is not enough research to confirm these claims, definitely not enough to warrant an extreme change to somebody's diet like avoiding grains.