A Mathematical Challenge to Obesity

By CLAUDIA DREIFUS

Carson C. Chow deploys mathematics to solve the everyday problems of real life. As an investigator at the National Institute of Diabetes and Digestive and Kidney Diseases, he tries to figure out why 1 in 3 Americans are obese.

We spoke at the recent annual meeting of the American Association for the Advancement of Science, where Dr. Chow, 49, gave a presentation on “Illuminating the Obesity Epidemic With Mathematics,” and then later by telephone; a condensed and edited version of the interviews follows.

You are an M.I.T.-trained mathematician and physicist. How did you come to work on obesity?

In 2004, while on the faculty of the math department at the University of Pittsburgh, I married. My wife is a Johns Hopkins ophthalmologist, and she would not move. So I began looking for work in the Beltway area. Through the grapevine, I heard that the N.I.D.D.K., a branch of the National Institutes of Health, was building up its mathematics laboratory to study obesity. At the time, I knew almost nothing of obesity.

I didn’t even know what a calorie was. I quickly read every scientific paper I could get my hands on.

I could see the facts on the epidemic were quite astounding. Between 1975 and 2005, the average weight of Americans had increased by about 20 pounds. Since the 1970s, the national obesity rate had jumped from around 20 percent to over 30 percent.

The interesting question posed to me when I was hired was, “Why is this happening?”

Why would mathematics have the answer?

Because to do this experimentally would take years. You could find out much more quickly if you did the math.

Now, prior to my coming on staff, the institute had hired a mathematical physiologist, Kevin Hall. Kevin developed a model that could predict how your body composition changed in response to what you ate. He created a math model of a human being and then plugged in all the variables — height, weight, food intake, exercise. The model could predict what a person will weigh, given their body size and what they take in.

However, the model was complicated: hundreds of equations. Kevin and I began working together to boil it down to one simple equation. That’s what applied mathematicians do. We make things simple. Once we had it, the slimmed-down equation proved to be a useful platform for answering a host of questions.

What new information did your equation render?

That the conventional wisdom of 3,500 calories less is what it takes to lose a pound of weight is wrong. The body changes as you lose. Interestingly, we also found that the fatter you get, the easier it is to gain weight. An extra 10 calories a day puts more weight onto an obese person than on a thinner one.

Also, there’s a time constant that’s an important factor in weight loss. That’s because if you reduce your caloric intake, after a while, your body reaches equilibrium. It actually takes about three years for a dieter to reach their new “steady state.” Our model predicts that if you eat 100 calories fewer a day, in three years you will, on average, lose 10 pounds — if you don’t cheat.

Another finding: Huge variations in your daily food intake will not cause variations in weight, as long as your average food intake over a year is about the same. This is because a person’s body will respond slowly to the food intake.

Did you ever solve the question posed to you when you were first hired — what caused the obesity epidemic?

We think so. And it’s something very simple, very obvious, something that few want to hear: The epidemic was caused by the overproduction of food in the United States.

Beginning in the 1970s, there was a change in national agricultural policy. Instead of the government paying farmers not to engage in full production, as was the practice, they were encouraged to grow as much food as they could. At the same time, technological changes and the “green revolution” made our farms much more productive. The price of food plummeted, while the number of calories available to the average American grew by about 1,000 a day.

Well, what do people do when there is extra food around? They eat it! This, of course, is a tremendously controversial idea. However, the model shows that increase in food more than explains the increase in weight.

In the 1950s, when I was growing up, people rarely ate out. Today, Americans dine out — with these large restaurant portions and oil-saturated foods — about five times a week.

Right. Society has changed a lot. With such a huge food supply, food marketing got better and restaurants got cheaper. The low cost of food fueled the growth of the fast-food industry. If food were expensive, you couldn’t have fast food.

People think that the epidemic has to be caused by genetics or that physical activity has gone down. Yet levels of physical activity have not really changed in the past 30 years. As for the genetic argument, yes, there are people who are genetically disposed to obesity, but if they live in societies where there isn’t a lot of food, they don’t get obese. For them, and for us, it’s supply that’s the issue.

Interestingly, we saw that Americans are wasting food at a progressively increasing rate. If Americans were to eat all the food that’s available, we’d be even more obese.

Any practical advice from your number crunching?

One of the things the numbers have shown us is that weight change, up or down, takes a very, very long time. All diets work. But the reaction time is really slow: on the order of a year.

People don’t wait long enough to see what they are going to stabilize at. So if you drop weight and return to your old eating habits, the time it takes to crawl back to your old weight is something like three years. To help people understand this better, we’ve posted an interactive version of our model at bwsimulator.niddk.nih.gov. People can plug in their information and learn how much they’ll need to reduce their intake and increase their activity to lose. It will also give them a rough sense of how much time it will take to reach the goal. Applied mathematics in action!

What can Americans do to stem the obesity epidemic?

One thing I have concluded, and this is just a personal view, is that we should stop marketing food to children. I think childhood obesity is a major problem. And when you’re obese, it’s not like we can suddenly cut your food off and you’ll go back to not being obese. You’ve been programmed to eat more. It’s a hardship to eat less. Michelle Obama’s initiative is helpful. And childhood obesity rates seem to be stabilizing in the developed world, at least. The obesity epidemic may have peaked because of the recession. It’s made food more expensive.

You said earlier that nobody wants to hear your message. Why?

I think the food industry doesn’t want to know it. And ordinary people don’t particularly want to hear this, either. It’s so easy for someone to go out and eat 6,000 calories a day. There’s no magic bullet on this. You simply have to cut calories and be vigilant for the rest of your life.