When it comes to the brain, it turns out, size does matter. But as we age, our brains get smaller and our memories suffer.

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Dr. Carolyn Brockington, director of the Stroke Center at New York’s St. Luke’s Roosevelt Hospital says, “As we get older, everyone’s brain shrinks.”

And that shrinkage, “Early Show” Contributing Correspondent Taryn Winter Brill reports, can lead to dementia and absent-mindedness later in life.

But a new study by the University of Pittsburgh and appearing in the journal Neurology suggests that just six miles a week on your feet can actually protect your brain, and improve your memory.

After tracking the physical activity of older adults over a nine-year period, researchers found the subjects with more active lifestyles maintained more brain mass.

Brockington said, “People who are exercising on a regular basis, their brains did not shrink at the same rate that other brains did.”

CBS News Medical Correspondent Dr. Jennifer Ashton added on “The Early Show” that walking has been associated with overall good health.

She said, “What’s good for your heart, what’s good for your waistline, also likely is good for your brain. The fact of matter is, we really don’t understand fully what causes dementia and Alzheimer’s, so right now the best we have are associations and factors that seem to be associated with a protective effect.”

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Ashton continued, “What this study actually found, the gray matter, the part of the brain that holds the nerve cell bodies responsible for things like memory and speech and emotion, did not shrink as likely they do with all of us as we age in the people who tended to walk the most.”

“Early Show” co-anchor Harry Smith asked, What are other things beyond walking that are good for the brain?”

Ashton said, “Exercise is very important. You really want to exercise your whole body. We’ve heard a lot recently about brain-boosting foods. These are fruits and vegetables, particularly green leafy vegetables, fruits with dark skins. You want to stay socially engaged. People who have a good social network, even who have pets who are talking to people, who are involved with other living things tend to have less dementia. … Lastly, stay mentally active in middle age. You want to do things that really engage your brain and stimulate new connections within the brain, crossword puzzles and things like that. They don’t help as much when you already have dementia, but in middle-age they can.”

Smith remarked, “It all ties together, help me a bit — the notion sometimes people retire and, you know, they take themselves out of using their brains and maybe as active as they were and kinds of the worst things can happen.”

Ashton said, “All of the things we think are aggravation when we were working actually may be stimulating our brains.”

Smith said, “Be well young brain.”

Ashton said, “And walk to work.”

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