Preprint / Version 3

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 of the latter focusing on the steady state.

Methods: We rewrote the mathematical equations in the steady state and tested them on a data set of N = 160 individuals derived from five 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 and cycling do not provide evidence that this relation holds.

Conclusion: Given the current protocols to measure the maximum lactate accumulation rate, the model predictions cannot be considered as quantitative. Its use in individualized performance diagnostics is thus scientifically questionable. Additional model layers and/or more precise methods of measurement may improve the agreement between the model predictions and the data, but require experimental validation.



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2022-01-20 — Updated on 2022-09-09