• Benjamin Rapoport, an MD/PhD student in the Harvard-MIT Division of Health Sciences and Technology, runs in the 2009 Chicago marathon.

    Benjamin Rapoport, an MD/PhD student in the Harvard-MIT Division of Health Sciences and Technology, runs in the 2009 Chicago marathon.

    Photo courtesy of Benjamin Rapoport

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  • Rapoport’s new mathematical model can help marathon runners pick the pace and fueling strategy that will get them to the finish line.

    Rapoport’s new mathematical model can help marathon runners pick the pace and fueling strategy that will get them to the finish line.

    Photo: Patrick Gillooly

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Fueling up for 26.2 miles

Benjamin Rapoport, an MD/PhD student in the Harvard-MIT Division of Health Sciences and Technology, runs in the 2009 Chicago marathon.

HST student develops model that can help marathon runners pace themselves to a strong finish.


Twenty miles into the 2005 New York Marathon, Benjamin Rapoport realized something was wrong. Up to that point, he had been on pace to finish the race in about three hours — his best marathon time yet. But as he entered Manhattan for the last several miles, his legs just didn’t want to keep up the pace.

Rapoport, an MD/PhD student in the Harvard-MIT Division of Health Sciences and Technology, was experiencing a common phenomenon known as “hitting the wall.” Essentially, the body runs out of fuel, forcing the runner to slow down dramatically.

“You feel like you’re not going anywhere,” says Rapoport. “It’s a big psychological letdown, because you feel powerless. You can’t will yourself to run any faster.”

Most marathon runners know they need to consume carbohydrates before and during a race to avoid hitting the wall, but many don’t have a good fueling strategy, says Rapoport. After his experience, he decided to take a rigorous approach to calculating just how much carbohydrate fuel a runner needs to get through 26.2 miles, and what pace that runner can reasonably expect to sustain. The result is a new model, described in the Oct. 21 issue of PLoS Computational Biology, that allows runners to calculate those targets using an estimate of their aerobic capacity.

On the run

Of the hundreds of thousands of people who run a marathon each year, more than 40 percent hit the figurative wall, and 1 to 2 percent drop out before finishing.

“People think hitting the wall is inevitable, but it’s not,” says Rapoport, who has run 18 marathons, including a personal best of two hours and 55 minutes at this year’s Boston Marathon. “In order to avoid it, you need to know what your capabilities are. You need to set a target pace that will get you to the finish without hitting the wall. Once you do that, you need to make sure you appropriately carbo-load.”

During strenuous exercise such as running, the body relies on carbohydrates for most of its energy, even though fat stores are usually much larger. Most of those carbohydrates come from glycogen stored in the liver and in the leg muscles. A small amount of glucose is also present in the blood.

Hitting the wall occurs when those stored carbohydrates are completely depleted, forcing the body to start burning fat. When that happens, the runner’s pace can drop about 30 percent, and ketones, the byproducts of fat metabolism, start building up the body, causing pain and fatigue.

To create his new model, Rapoport identified fundamental physiologic factors that limit performance in endurance runners — aerobic capacity and the ability of the leg muscles to store carbohydrates as glycogen. Aerobic capacity, also known as VO2max, is a measure of how efficiently the muscles can use oxygen during exercise. Oxygen is critical to muscle performance because glucose can only be broken down completely in the presence of oxygen.

The average untrained male has a VO2max of 45 ml/kg/min, but VO2max can be boosted with training, and elite marathoners often have VO2max in excess of 75 ml/kg/min. Measuring exact VO2max requires a treadmill stress test at maximum effort, but it can be estimated by measuring heart rate while running at a constant pace on a treadmill.

Avoiding the wall

Using Rapoport’s model, any runner training for a marathon who estimates his or her VO2max can figure out the pace he or she can sustain without hitting the wall. For example, a man with a VO2max of 60 ml/kg/min could run the race in three hours, 10 minutes, without consuming any carbs during the race.

A VO2max of 60 ml/kg/min is about the highest that most men can attain through training, and 3:10 happens to be a gold standard in marathoning: It’s the time that men ages 18 to 34 must achieve to qualify for the Boston Marathon. For women of the same age, the qualifying time is 3:40, which is also the time that Rapoport’s model predicts for a runner with a VO2max of 52 ml/kg/min, about the highest level than the average woman can attain through training.

The model’s predictions also depend on the runner’s leg muscle mass, because larger muscles can store more glycogen. In the examples above, those finishing times assume that the runner’s leg muscles make up at least 7.5 percent of body mass, which is true of most people. For men, the values range from 14 to 27.5 percent, and in women, they range from 18 to 22.5 percent.

Rapoport’s model also allows runners to calculate how much carbohydrate they need to consume during the race if they want to run a faster pace without hitting the wall. For example, a runner with a VO2max of 50 ml/kg/min who wanted to achieve the 3:10 Boston Marathon qualifying time would need to consume 30 calories of carbohydrate per kilogram of body weight (about 2,090 calories for a 154-pound runner), assuming that his legs make up at least 15 percent of his body mass.

Jake Emmett, professor of kinesiology and sports studies at Eastern Illinois University, says he believes the model could be useful to marathon runners and coaches. “There is a lot of guesswork out there about carbo-loading and about carb intake during a marathon,” he says. “This would at least provide a framework for people to work out a good approximation of how to adapt their diet in the days leading up to a marathon, and what they consume during the race.”

While physiological models like Rapoport’s can help runners plan for their races, Rapoport says that other factors such as mental toughness and racecourse terrain also play important roles in how a runner will perform. One of the most important things a runner should do during a marathon is stick to his or her target pace, Rapoport advises. When runners start out too fast, they burn a higher percentage of carbohydrates, increasing the risk of hitting the wall.

“Once you figure out your target pace, you have to stay at it,” he says. “People sometimes get too excited or change their game plan on the day of the race, and that’s a tactical mistake.”


Topics: Biology, Health sciences and technology, Marathon, Running, Computation

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