Simulation of Steady-State Energy Metabolism in Cycling and Running
DOI:
https://doi.org/10.51224/SRXIV.110Keywords:
performance testing, vo2max, endurance diagnostics, maximum lactate steady-state, lactate metabolismAbstract
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.
Metrics
References
Adam, J., Öhmichen, M., Öhmichen, E., Rother, J., Müller, U. M., Hauser, T., & Schulz, H. (2015).
Reliability of the calculated maximal lactate steady state in amateur cyclists. Biology of
Sport, 32(2), 97–102. https://doi.org/10.5604/20831862.1134311
Barstow, T. J., Buchthal, S. D., Zanconato, S., & Cooper, D. M. (1994). Changes in potential
controllers of human skeletal muscle respiration during incremental calf exercise.
Journal of Applied Physiology (Bethesda, Md. : 1985), 77(5), 2169–2176.
https://doi.org/10.1152/jappl.1994.77.5.2169
Bassett, D. R., & Howley, E. T. (2000). Limiting factors for maximum oxygen uptake and
determinants of endurance performance. Medicine and Science in Sports and Exercise,
(1), 70–84. https://doi.org/10.1097/00005768-200001000-00012
Bateman, H. (1910). Solution of a system of differential equations occurring in the theory of
radioactive transformations. Proc. Cambridge Phil. Soc., 15, 423–427.
Beneke, R. (2003). Methodological aspects of maximal lactate steady state-implications for
performance testing. European Journal of Applied Physiology, 89(1), 95–99.
https://doi.org/10.1007/s00421-002-0783-1
Beneke, R., Hütler, M., Jung, M., & Leithäuser, R. M. (2005). Modeling the blood lactate kinetics
at maximal short-term exercise conditions in children, adolescents, and adults. Journal
of Applied Physiology (Bethesda, Md. : 1985), 99(2), 499–504.
https://doi.org/10.1152/japplphysiol.00062.2005
Chance, B., & Williams, G. R. (1955). Respiratory enzymes in oxidative phosphorylation. I.
Kinetics of oxygen utilization. The Journal of Biological Chemistry, 217(1), 383–393.
Donovan, C. M., & Brooks, G. A. (1983). Endurance training affects lactate clearance, not lactate
production. The American Journal of Physiology, 244(1), E83-92.
https://doi.org/10.1152/ajpendo.1983.244.1.E83
Donovan, C. M., & Pagliassotti, M. J. (1990). Enhanced efficiency of lactate removal after
endurance training. Journal of Applied Physiology (Bethesda, Md. : 1985), 68(3), 1053–
https://doi.org/10.1152/jappl.1990.68.3.1053
Dyson, F. (2004). A meeting with Enrico Fermi. Nature, 427(6972), 297.
https://doi.org/10.1038/427297a
Faude, O., Kindermann, W., & Meyer, T. (2009). Lactate threshold concepts: How valid are they?
Sports Medicine (Auckland, N.Z.), 39(6), 469–490. https://doi.org/10.2165/00007256-
-00003
Gladden, L. B. (2000). Muscle as a consumer of lactate. Medicine and Science in Sports and
Exercise, 32(4), 764–771. https://doi.org/10.1097/00005768-200004000-00008
Hauser, T. (2013). Untersuchungen zur Validität und Praktikabilität des mathematisch bestimmten
maximalen Laktat-steady-states bei radergometrischen Belastungen. TU-Chemnitz,
Chemnitz.
Hauser, T., Adam, J., & Schulz, H. (2014). Comparison of calculated and experimental power in
maximal lactate-steady state during cycling. Theoretical Biology & Medical Modelling,
:25. https://doi.org/10.1186/1742-4682-11-25
Holloszy, J. O., & Coyle, E. F. (1984). Adaptations of skeletal muscle to endurance exercise and
their metabolic consequences. Journal of Applied Physiology: Respiratory, Environmental
and Exercise Physiology, 56(4), 831–838. https://doi.org/10.1152/jappl.1984.56.4.831
Hommel, J., Öhmichen, S., Rudolph, U. M., Hauser, T., & Schulz, H. (2019). Effects of six-week
sprint interval or endurance training on calculated power in maximal lactate steady
state. Biology of Sport, 36(1), 47–54. https://doi.org/10.5114/biolsport.2018.78906
Howley, E. T., Bassett, D. R., & Welch, H. G. (1995). Criteria for maximal oxygen uptake: Review
and commentary. Medicine and Science in Sports and Exercise, 27(9), 1292–1301.
Katch, V. L., Sady, S. S., & Freedson, P. (1982). Biological variability in maximum aerobic power.
Medicine and Science in Sports and Exercise, 14(1), 21–25.
https://doi.org/10.1249/00005768-198201000-00004
Mader, A. (1984). Eine Theorie zur Berechnung der Dynamik und des steady state von
Phosphorylierungszustand und Stoffwechselaktivität der Muskelzelle als Folge des
Energiebedarfs [Habilitation]. Deutsche Sporthochschule Köln, Köln.
Mader, A. (1994). Modellbildung und Simulation biologischer Prozesse am Menschen - Ein
neues Instrument für Therorieentwicklung und Interpretation experimenteller Befunde.
In A. Mader & H. Allmer (Eds.), Brennpunkte der Sportwissenschaft: 8 (2).
Brennpunktthema: Computersimulation: Möglichkeiten zur Theoriebildung und
Ergebnisinterpretation (pp. 95–101). Academia-Verlag.
Mader, A. (2003). Glycolysis and oxidative phosphorylation as a function of cytosolic
phosphorylation state and power output of the muscle cell. European Journal of Applied
Physiology, 88(4-5), 317–338. https://doi.org/10.1007/s00421-002-0676-3
Mader, A., & Heck, H. (1986). A theory of the metabolic origin of "anaerobic threshold".
International Journal of Sports Medicine, 7 Suppl 1, 45–65.
Mader, A., & Heck, H. (1991). Möglichkeiten und Aufgaben in der Forschung und Praxis der
Humanleistungsphysiologie. Spectrum der Sportwissenschaften, 3(2), 5–54.
Millet, G. P., Vleck, V. E., & Bentley, D. J. (2009). Physiological differences between cycling and
running: Lessons from triathletes. Sports Medicine (Auckland, N.Z.), 39(3), 179–206.
https://doi.org/10.2165/00007256-200939030-00002
Phillips, S. M., Green, H. J., Tarnopolsky, M. A., & Grant, S. M. (1995). Increased clearance of
lactate after short-term training in men. Journal of Applied Physiology (Bethesda, Md. :
, 79(6), 1862–1869. https://doi.org/10.1152/jappl.1995.79.6.1862
Quittmann, O. J., Abel, T., Zeller, S., Foitschik, T., & Strüder, H. K. (2018). Lactate kinetics in
handcycling under various exercise modalities and their relationship to performance
measures in able-bodied participants. European Journal of Applied Physiology, 118(7),
–1505. https://doi.org/10.1007/s00421-018-3879-y
Quittmann, O. J., Appelhans, D., Abel, T., & Strüder, H. K. (2020). Evaluation of a sport-specific
field test to determine maximal lactate accumulation rate and sprint performance
parameters in running. Journal of Science and Medicine in Sport, 23(1), 27–34.
https://doi.org/10.1016/j.jsams.2019.08.013
Quittmann, O. J., Foitschik, T., Vafa, R., Freitag, F., Spearmann, N., Nolte, S., & Abel, T. (unpubl. b).
Augmenting the metabolic profile in endurance running by maximal lactate
accumulation rate.
Quittmann, O. J., Schwarz, Y. M., Mester, J., Foitschik, T., Abel, T., & Strüder, H. K. (2020). Maximal
Lactate Accumulation Rate in All-out Exercise Differs between Cycling and Running.
International Journal of Sports Medicine. Advance online publication.
https://doi.org/10.1055/a-1273-7589
Quittmann, O. J., Schwarz, Y. M., Nolte, S., Fuchs, M., Gehlert, G., Slowig, Y., Schiffer, A.,
Foitschik, T., & Abel, T. (unpubl. a). Relationship between physiological parameters and
time trial performance over 1, 2 and 3 km in trained runners.
Sahlin, K. (2014). Muscle energetics during explosive activities and potential effects of nutrition
and training. Sports Medicine (Auckland, N.Z.), 44 Suppl 2, S167-73.
https://doi.org/10.1007/s40279-014-0256-9
Sjödin, B., Jacobs, I., & Svedenhag, J. (1982). Changes in onset of blood lactate accumulation
(OBLA) and muscle enzymes after training at OBLA. European Journal of Applied
Physiology and Occupational Physiology, 49(1), 45–57.
https://doi.org/10.1007/BF00428962
van Hall, G. (2010). Lactate kinetics in human tissues at rest and during exercise. Acta
Physiologica (Oxford, England), 199(4), 499–508. https://doi.org/10.1111/j.1748-
2010.02122.x
Veech, R. L., Lawson, J. W., Cornell, N. W., & Krebs, H. A. (1979). Cytosolic phosphorylation
potential. The Journal of Biological Chemistry, 254(14), 6538–6547.
Vickers, R. (2003). Measurement Error in Maximal Oxygen Uptake Tests. Naval Health Research
Center.
Weber, S. (2003). Berechnung leistungsbestimmender Parameter der metabolischen Aktivität auf
zellulärer Ebene mittels fahrradergometrischer Untersuchungen [Diplomarbeit]. Deutsche
Sporthochschule Köln, Köln.
Downloads
Posted
Versions
- 2022-09-09 (3)
- 2022-09-09 (2)
- 2022-01-20 (1)
License
Copyright (c) 2022 Simon Nolte, Oliver Jan Quittmann, Volker Meden
This work is licensed under a Creative Commons Attribution 4.0 International License.
