A Minimal Physiological Model for Human Running Performance
Thorsten Emig (LPTMS, Université Paris-Sud)
Measurements of physiological variables during exercise and performance evaluations and predictions are important for a fundamental understanding of physiological processes, training and assessment of athletes, and beyond sport in the study of complex physiological response related to aging, muscular structure and cardiovascular health. Models for human running performances of various complexities and underlying principles have been proposed, often employing a combination of data for world record performances and concepts that are not always based on simple principles of human physiology. We present a novel, minimal model for human running performance that follows from a self-consistency relation for the time dependent power output during racing events. The model has a total of four parameters that are not fixed a priori and characterize individual physiological profiles for a runner. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles. Various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m and to the Marathon are excellently described by our model, with mean absolute errors of (often much) less than 1%. Physiological parameters of our model, as obtained from records and individual runners, are consistent with existing laboratory measurements. The computed maximal power output that can be sustained for a given time describes well existing experimental data for the time to exhaustion dependence of supramaximal oxygen consumption in the anaerobic regime. Our model is used to define and estimate endurance for both the aerobically and anaerobically dominated performances. As an application of our model, we derive personalized training speeds for prescribed duration and intensity. Our findings could be a basis for plethora of further studies including assessment of performance dependence on age, altitude, muscular structure, specialization of athlete, racing strategies, and optimal dosing of recreational exercise.