Optimal pacing and carbohydrate intake strategies for ultramarathons

The purpose of this research is to determine the pacing and nutrition strategies which minimize completion time and carbohydrate intake for athletes competing in ultramarathon races.

We present the formulation of a two-phase optimization model. The first-phase mixed-integer nonlinear program (MINLP) determines the minimum completion time subject to the altitude, terrain, and distance of the race, as well as the mass and cardiovascular fitness of the athlete. The second-phase MINLP determines the minimum carbohydrate intake required for the athlete to achieve the completion time prescribed by the first-phase subject to the flow of carbohydrates through the stomach, liver, and muscles. Consequently, the second-phase model provides the optimal pacing and nutrition strategies for a particular athlete for each kilometer of a particular race.

We validate model results for a wide range of athlete parameters by comparing completion times to those reported for two case-study events. We also compare the kilometer-by-kilometer pacing and nutrition strategies prescribed by the model to those of a particular athlete. In all cases, the model results closely match those witnessed in the actual events.

We have developed a baseline metabolic model that provides athletes prescriptive guidance regarding optimal pacing and carbohydrate intake strategies prior to competing in ultramarathon races. Given the highly variable topographical characteristics common to many ultramarathon courses and the potential inexperience of many athletes with such courses, our model provides valuable insight to competitors who might otherwise fail to complete the event due to exhaustion or carbohydrate depletion.