Scientists develop mathematical model to improve performance of elite athletes. GETTY IMAGES

Antoine Le Hyaric, Amandine Aftalion and Brian Hanley are scientists who, according to their published study, are developing a mathematical model that promises to optimise 400m and 1,500m running performance using high-resolution data.

The study 

The aim of this study is to model men's and women's 400 m and 1,500 m championship performances to gain a deeper understanding of the key mechanical and physiological factors affecting running speed and bend running using high-resolution data from live competition. 

The scientists used modelling and simulation to analyse the athletic performances of the European Athletics champions in the 400m metres, such as Matthew Hudson-Smith and world indoor 400m record holder Femke Bol for men and women respectively. 

They also looked at the performances of Norwegian Olympic 1,500 m champion Jakob Ingebrigtsen, and Gaia Sabbatini, the European Athletics U23 women's 1,500m champion.

Tools and techniques 

Using GPS sensors placed under the athletes' jerseys, the researchers accurately tracked each athlete's speed and position, updating their location ten times per second. 

They used chips with IsoLynx technology during the 2022 European Athletics Championships in Munich, Germany, and the 2021 European Athletics U23 Championships in Tallinn, Estonia.

Hudson-Smith in the 400m final at the European Championships in Munich in 2022. GETTY IMAGES
Hudson-Smith in the 400m final at the European Championships in Munich in 2022. GETTY IMAGES

This advanced system, known as the IsoLynx Real-Time Location System (RTLS), uses wireless athlete tags embedded in the or number bibs to collect real-time data during races, such as speed, acceleration, and distance covered.

A mathematical model has been fitted to this speed data for each selected athlete. This model enables predictive simulations and analysis of the impact of various physiological factors on performance.

It predicts important variables such as anaerobic reserve (muscle energy stored for intense, short duration activity when oxygen supply is limited) reserve and peak aerobic value (maximum oxygen consumption during intense exercise). This modelled data can be adjusted to understand the effects of individual variables by changing their values. 

"We wanted to understand what happens at the physiological level during 400 metres, which is a sprint, and 1,500 metres, which is the first endurance race," Amandine Aftalion, one of the researchers involved in the study published in the journal Frontiers in Sports and Active Living, told AFP.

Gaia Sabbatini in U23 Women's 1500m final in Tallinn in 2021. GETTY IMAGES
Gaia Sabbatini in U23 Women's 1500m final in Tallinn in 2021. GETTY IMAGES

How it works?

The main physiological parameters that influence pacing are: the maximum propulsive force per unit of mass, the global friction coefficient, the maximum rate of decrease and increase of propulsive force which is related to motor control, the total anaerobic energy or the maximum accumulated oxygen deficit and the VO2 profile as a function of distance. 

The role of the brain in the movement process, such as motivation, which plays a role in the delay in action. The system is based on Newton's second law of motion (mechanics), on an equation for the variation of neural drive (motor control), and the energy balance, which takes into account the aerobic contribution VO2, the anaerobic contribution, and the power developed by the propulsive force.

Jakob Ingebrigtsen in the 1500m final at the European Championships in Munich in 2022. GETTY IMAGES
Jakob Ingebrigtsen in the 1500m final at the European Championships in Munich in 2022. GETTY IMAGES

This explains why Bol runs more slowly than Hudson-Smith. She has a lower estimated final VO2 (53.2 ml/kg/min vs. 69.6 ml/kg/min) with a slightly higher anaerobic contribution (77.6% vs. 76.0%), which explains her lower absolute drop in speed over the last 100m. 

The data was then analysed by researchers from the French National Centre for Scientific Research (CNRS), who observed its impact on the speed of the champions. 

"Thanks to the quantification of costs and benefits, the model provides immediate access to the best strategy so that the runner 'performs' in an optimised way," the CNRS said in a statement.

Simulated speed for Matthew Hudson-Smith and Femke Bol over 400m at Munich 2022. FRONTIERS
Simulated speed for Matthew Hudson-Smith and Femke Bol over 400m at Munich 2022. FRONTIERS

Conclusions

The study shows that in the 400m, a fast start is essential for oxygen consumption (VO2) reasons and is the best strategy, despite an inevitable slowdown throughout the race. 

In the 1,500m, athletes who can maintain a high VO2 throughout the race maintain a consistently high cruising speed. This requires significant energy from anaerobic resources and limits the potential for a strong acceleration in the sprint finish. Better performance over 1,500 m is associated with a higher fractional use of high VO2. 

The simulations clarified how Ingebrigtsen's ability to quickly reach and maintain maximal oxygen consumption "allows him to run at a faster pace than his competitors throughout the race, even though we see him start less strongly," Aftalion said. 

The model could lead to performance-enhancing software that would allow coaches to "refine the race strategy based on the runner's physiological profile," he concluded.