Benjamin I. Rapoport, a student in the Harvard-MIT Division of Health Sciences and Technology, has developed a new model that allows marathon runners to calculate fueling requirements based upon their aerobic capacity and target pace.

Rapoport, the author of the paper that details the research, said that he sought to provide a tool that distance runners can use to prepare for and run a successful race.

Many marathon runners tend to run the beginning of a race too quickly, depleting their carbohydrate reserves and leading to the experience of “hitting the wall,” when the body begins to burn fat in the absence of carbohydrates. Not only is the experience painful, but it forces a runner to slow his or her pace considerably, according to Rapoport.

The model, published last week in PLoS Computational Biology, allows runners to calculate how much fuel they need to consume before a race to sustain their target pace without “hitting the wall.”

“No one before had properly quantified how much fuel you need [to sustain a given pace],” Rapoport said. “My goal was to generate a mathematical model to figure out how the body works as an engine.”

He has launched an online endurance calculator that uses his model for individuals to calculate their own fueling requirements given a target pace.

The model uses aerobic capacity, or VO2max, to calculate fueling requirements. VO2max is a measure of how much oxygen the body can transport to the muscles and use during aerobic exercise.

Although the energetics are different for each sport, the principles of aerobic exercise are the same, according to Rapoport. As a result, he said that his model could be extended to other athletes like triathletes, hikers, and swimmers, whose forms of exercise are mostly aerobic.

He also said that other factors—including the levels of fluid electrolytes such as sodium and potassium—also affect aerobic performance. Rapoport said that he hopes to conduct further research to quantify these parameters.

Rapoport started his research six years ago, when he missed a Medical School class to run the Boston Marathon. To make up for his absence, Rapoport was asked to deliver a talk to the class about the physiology of endurance running. Rapoport has given this lecture every year since.

“It is a beautiful thing to confront your limits,” Rapoport said about endurance running. “I hope that this model will help people to get as close to those limits as possible.”