New Math Model to Enhance Elite Athletes Performance

Running is one of the most popular and competitive sports in the world, but what are the secrets behind the success of elite athletes? A team of researchers from France and the UK has developed a groundbreaking mathematical model that precisely demonstrates the impact of physiological and psychological factors on running performance. The findings, published in the journal Frontiers in Sports and Active Living on March 5th, 2024, offer valuable insights for optimizing training regimens.

Data from champions

The researchers analyzed extremely precise data from the performances of elite athletes such as Matthew Hudson-Smith (400m), Femke Bol (400m), Jakob Ingebrigtsen (1500m), and Gaia Sabbatini (1500m) at major European championships. Thanks to new technology of GPS sensors placed under athletes’ jerseys, they were able to trace with precision the speeds of each athlete, with their position indicated ten times per second.

A novel mathematical model

The researchers used this data to construct an optimal control problem that accounts for finishing time, effort, and energy expenditure. This is an innovative mathematical approach that aims to find the best possible solution for a given objective. Remarkably, this is the first such model to incorporate the variability of motor control – the role of the brain in producing movement – adding an extra layer of precision to the simulations. The model grants access to physiological parameters like oxygen consumption (VO2) and energy expenditure during a race, allowing researchers to quantify costs and benefits and determine the best strategy for optimal performance.

Optimal strategies for 400m and 1500m races

Among the findings, the study highlights the importance of a quick start in the first 50 meters due to the need for rapid oxygen kinetics, as well as the need to reduce velocity decrease in a 400m race. Additionally, the scientists demonstrated that improving aerobic metabolism (oxygen uptake) and the ability to maintain VO2 are crucial factors for success in 1500m races. The simulations notably explained the performance of middle distance runner Ingebrigtsen by his ability to quickly reach his maximum oxygen consumption (VO2), and to maintain it throughout the race. A particularity which allows the Olympic champion “to run at a greater pace than his competitors throughout the race, even though we see him start less strongly,” explained Amandine Aftalion, co-author of the study.

A powerful tool for enhancing training strategies

The development of this groundbreaking mathematical model represents a significant advancement in studying physiological parameter variations during championship races, where in vivo measurements are often impossible to obtain. By combining cutting-edge mathematics with elite athletic data, this research offers a powerful tool for enhancing training strategies and unlocking the full potential of top-tier runners.

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