“All of the things are good for you to do in general,” Dr. Elizabeth Edgerly, a clinical psychologist with the Alzheimer’s Association, said. “Do I have concerns? Yes. We’re very cautious. Is it going to mean you can remember where you left your car keys? We can’t say that.”

Still, the appeal of the programs is strong.

Epoch Senior Living in Providence is among the many assisted living facilities with “brain fitness centers.” Surrounded by posters of Einstein, Rodin’s “Thinker,” and “Brain Facts” (“one billion glial cells in the human brain”), residents spend an hour a day for eight weeks doing computer exercises involving recalling story details and distinguishing similar-sounding syllables.

David Horvitz, 92, an Epoch resident, said, “It did improve my concentration, particularly when I read. Before, my mind would wander and I’d have to reread passages several times. It also seems to me that I’m remembering names a little bit better.”

Emeritus Assisted Living, a chain, started a brain health program for residents, their families, staff members and people in the community. So far, centers in Florida, Massachusetts and South Carolina offer “brain-healthy” foods like salmon and walnuts, activities like spelling bees and reminiscing games, prizes to staff members for recalling brain health trivia, and a “brain health self-assessment” questionnaire asking, among other things, if people play challenging board games, walk 10,000 steps a day, or eat flax seed three times a week.

The brain program at the Isle at Emerald Court in Tewksbury, Mass., an Emeritus facility, includes a five-day-a-week regimen of leg lifts and stretches on the burgundy jacquard lobby chairs, influenced Ray Decker to choose the center for his mother, Joan, 75, who is in the early stage of Alzheimer’s.

“Those types of things may stimulate her brain and, despite her debilitating disease, she actually may come back a little,” said Mr. Decker, 57, who plans to adopt brain-healthy activities. “I think that this will keep my mother healthy for some time to come, actually extend her life in a mental and physical manner.”