What is there to suggest that it's the diets of these countries that are keeping their inhabitants' brains young, and not a genetic history, or some other aspect of their lifestyle? Dr Estep points to the fact that obesity and diseases including heart disease and dementia are growing in countries such as Japan and Italy as their traditional diets are replaced with more modern, processed foods - but older people in rural parts of these countries, which haven't been so exposed to Western influences, seem to remain as healthy as ever.
The cuisines of these countries might not seem to have a lot in common, but Dr Estep has identified one vital component - and it's not, as you might expect, olive oil or even oily fish. Instead he believes these populations' low rates of dementia come down to something they don't eat, and that's red meat or, more specifically, iron.
Some research suggests that iron reacts with oxygen to cause "rusting" in the body, leading to the deposit of waste products, such as the plaques in brain cells seen in people with dementia.
"We always hear about antioxidants, whose job is to counter the work of 'pro-oxidants' in the body," says Dr Estep. "Iron is the most abundant and potent pro-oxidant in the body, and the more we have of it in our bodies, the more oxidative stress and damage."
Iron, from red meat and iron-enriched grain products, he believes, could be the reason we see high levels of Alzheimer's in countries such as the US and northern Europe.
Dr Estep says that he is not advocating cutting out meat altogether - iron is an important nutrient, particularly for younger women, many of whom are deficient in the mineral because of menstruation. "We should keep it in a range I generally describe as sufficient but low," he says. "I eat a little bit, but not much.
"Individuals are going to vary in how their bodies process iron, so they should have their levels tested rather than using a one-size-fits-all dietary recommendation.
"I certainly wouldn't recommend that anyone with iron-deficient anaemia should avoid meat, or other sources of iron."
Another surprising finding Dr Estep made when studying "Mindspan elite" countries was that their inhabitants ate high levels of carbohydrates - the white, refined carbohydrates we're told to avoid.
"We've been repeatedly told by nutritionists over the years to eat wholegrains such as brown rice and pasta, but I've always known that the Japanese don't eat brown rice; they eat white rice," he says.
"And for the longest-living Mediterraneans, the primary source of energy isn't olive oil - it's actually refined carbohydrates, bread and pasta. They are the very foundations of these cuisines."
Dr Estep says that carbohydrates provide a smooth, steady release of glucose - the best fuel for the brain - and many refined carbs, such as white pasta and traditionally made white bread, have a relatively low glycaemic index and various other benefits for health.
"We think about foods from an overly purist perspective, but nature doesn't necessarily know best."
He warns, though, that bread and pasta in many Western countries is often enriched with iron (in the UK, by law, all white flour must be fortified with iron - this isn't true, though, of bread and pasta made in countries such as Italy).
So could a diet really keep your brain young?
Dr Rosa Sancho, head of research at Alzheimer's Research UK, says iron is an essential building block of red blood cells, and both too much and too little can have a negative effect on health, so balance is key.
"There is mixed evidence for how iron is associated with dementia - some studies have shown being anaemic can increase dementia risk, while others have found iron built up in the brains of people who died with Alzheimer's.
"While there is evidence that a Mediterranean diet is associated with reduced cognitive decline, we don't know for sure that adopting such a diet could prevent dementia.
"The current best evidence for reducing dementia risk is that what is good for the heart is good for the head. Eating a healthy balanced diet, keeping physically and mentally active, not smoking, drinking in moderation, maintaining a healthy weight, and keeping cholesterol and blood pressure in check are all things we can do to reduce our risk."
For years, we've been told that omega-3, from oily fish such as salmon or mackerel, is the best thing to eat for brain health. Dr Estep says: "Fish is important, but you don't need a lot of it. We have this impression that the Mediterraneans eat a huge amount of fish, but the Med is very poor in fish stocks. They do eat it routinely, but only a small amount.
"I eat a small amount every day - a couple of pieces of pickled herring, perhaps.
"Carbs - by which I mean vegetables and grains - are really the base of the Mediterranean and Japanese diet."
Portion size is also crucial to the Mindspan diet: "The Japanese and the Mediterraneans are eating less food, and they're thinner than other developed countries, but the people I interviewed never said they were going hungry.
"The foods they eat give a slow, long-lasting release of energy into the system: one recent study done in Italy found the more pasta you eat, the thinner you are likely to be."
It will be music to the ears of many: according to this leading expert in ageing, pasta, bread and wine are all back on the menu.
Dr Estep's rules for keeping your brain young
Eat at every meal
• Vegetables, including leafy greens, and herbs and pulses.
• A small portion of carbohydrates, such as white rice or pasta, or sourdough breads, such as ciabatta.
• Vinegar and other fermented foods, such as miso and pickled vegetables.
• Coffee or tea. (Drink with meals to inhibit the absorption of iron. Decaffeinated coffee works, too, as does herbal tea.)
• Olive oil and nuts.
Eat a few times a week
• Fish and seafood, particularly smaller, fattier fish such as herring, sardines and anchovies. (If you are vegetarian, choose an omega-3 supplement.)
• Fruits
• Cheese
• Eggs; poultry
• Alcohol (red wine is best, no more than two small glasses a day).
Eat occasionally or never
• Red meat
• Commercial white bread
• Milk and milk products
• Deep-fried food
The Mindspan Diet by Preston Estep is published by Oneworld.
