Mathematical Model for Carb Loading

Runners rely on carbohydrates stored primarily as glycogens in the liver and leg muscles for energy during a race. When these glycogens run out, the body starts burning fat instead. This slows the runner considerably and also causes ketones to build up in the body causing fatigue and pain.

Harvard and MIT MD and Ph.D. student Benjamin Rapoport, himself a marathon runner, developed an algorithm designed to maximize carbohydrates within the body and limit fat burning. His model is based on two factors – aerobic capacity and the ability of leg muscles to store glycogens.

Aerobic capacity is important because the body needs oxygen to properly break down the stored carbohydrates into usable energy. An exact measurement of this factor requires a full stress test, but a good estimate can be made based on heart rate while running at a constant pace on a treadmill. This estimated aerobic capacity can then be used to calculate the fastest pace the runner can safely maintain in a race without eating additional carbs and without hitting the wall.

Aerobic capacity is measured in milliliters per kilograms per minute. Most men can attain a maximum capacity of 60 mL/kg/min with training which corresponds to a 3:10 marathon time using Rapoport’s calculations. This happens to be the required qualifying time for the Boston Marathon for men age 18-34. Similarly, most women can achieve a capacity of 52 mL/kg/min corresponding to a 3:40 marathon time, the required qualifying time for women age 18-34 in the Boston Marathon. Runners can also use Rapoport’s model to calculate how much carbohydrate they need to consume to maintain a specific pace given their running heart rate (aerobic capacity measurement) and an estimate of how much of their body mass is in their legs.

TFOT has previously reported on other sports medicine and sports technology advances including the Nike+ Sportsband which monitors vital statistics and tracks activity during workouts and athletic performances, the Xtenec shoelaces designed to help shoes mold exactly to the wearer’s foot and eliminate the need to readjust the laces in the middle of longer runs, and the Mercury Skate which reduces vibrations of inline skates and thus reduces skater fatigue and stress on skater joints.

Read more about Rapoport’s model for maximizing carbohydrates and limiting fat burning during marathons in this MIT press release or this Harvard University news article. You can also read Rapoport’s paper in the PLOS Computational Biology journal.