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Preprint / Version 2

Simulation of Steady-State Energy Metabolism in Cycling and Running


  • Simon Nolte Institute of Movement and Neurosciences, German Sport University Cologne, Cologne, Germany
  • Oliver Jan Quittmann Institute of Movement and Neurosciences, German Sport University Cologne, Cologne, Germany
  • Volker Meden Institut für Theorie der Statistischen Physik, RWTH Aachen University, Aachen, Germany



performance testing, vo2max, endurance diagnostics, maximum lactate steady-state, lactate metabolism


Purpose: A mathematical model to describe the interplay of distinct metabolic rates during
exercise was developed decades ago. Despite its use in endurance performance diagnostics,
attempts to validate the model’s assumptions and predictions on experimental data are rare.
We here provide a comprehensive study for the steady state.
Methods: We rewrote the mathematical equations in the steady state and tested them on a
data set of N = 101 individuals derived from four studies in cycling and running.
Results: The rewritten equations reveal a unique relationship between the ratio of the
maximum oxygen uptake and the lactate accumulation rate, and the fractional utilization of
oxygen uptake at the maximum lactate steady-state. Experimental data for running do not
provide evidence that this relation holds. For cycling, the experimental evidence is less
devastating but can also not be considered as convincing.
Conclusion: The simulation in its current form is not suitable for a practical use in performance
diagnostics. Additional model layers and/or more precise methods of measurement may
improve the model’s performance, but require experimental validation.


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2022-01-20 — Updated on 2022-09-09