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Experimental validation of the 3-parameter critical power model in cycling

  • Giovanni VinettiEmail author
  • Anna Taboni
  • Paolo Bruseghini
  • Stefano Camelio
  • Matteo D’Elia
  • Nazzareno Fagoni
  • Christian Moia
  • Guido Ferretti
Original Article

Abstract

Purpose

The three-parameter model of critical power (3-p) implies that in the severe exercise intensity domain time to exhaustion (Tlim) decreases hyperbolically with power output starting from the power asymptote (critical power, cr) and reaching 0 s at a finite power limit (0) thanks to a negative time asymptote (k). We aimed to validate 3-p for short Tlim and to test the hypothesis that 0 represents the maximal instantaneous muscular power.

Methods

Ten subjects performed an incremental test and nine constant-power trials to exhaustion on an electronically braked cycle ergometer. All trials were fitted to 3-p by means of non-linear regression, and those with Tlim greater than 2 min also to the 2-parameter model (2-p), obtained constraining k to 0 s. Five vertical squat jumps on a force platform were also performed to determine the single-leg (i.e., halved) maximal instantaneous power.

Results

Tlim ranged from 26 ± 4 s to 15.7 ± 4.9 min. In 3-p, with respect to 2-p, cr was identical (177 ± 26 W), while curvature constant W’ was higher (17.0 ± 4.3 vs 15.9 ± 4.2 kJ, p < 0.01). 3-p-derived 0 was lower than single-leg maximal instantaneous power (1184 ± 265 vs 1554 ± 235 W, p < 0.01).

Conclusions

3-p is a good descriptor of the work capacity above cr up to Tlim as short as 20 s. However, since there is a discrepancy between estimated 0 and measured maximal instantaneous power, a modification of the model has been proposed.

Keywords

Physical work capacity Power–time relationship Non-linear model Hyperbolic model Endurance Anaerobic alactic metabolism 

Abbreviations

[La]max

Capillary blood lactate concentration at the end of the incremental test

[La]peak

Capillary blood lactate concentration at the end of a constant-power trial

2-p

2-parameter critical power model

3-p

3-parameter critical power model

k

Time asymptote of the critical power model

kATP

Time asymptote of the power–time hyperbola provided by the immediately available ATP

Tlim

Time to exhaustion

O2

Oxygen consumption

O2max

Maximal oxygen consumption of the incremental test

O2peak

Peak oxygen consumption of a constant-power trial

Power output

\(\widehat {{\dot {w}}}\)

Maximal instantaneous muscular power

cr

Critical power

0

Power limit of the critical power model as time to exhaustion approaches 0 s

max

Maximal aerobic mechanical power

W’

Energy store component (mechanical)

W+

Mechanical work capacity above the critical power

WATP

Mechanical work above the critical power provided by the immediately available ATP

Notes

Acknowledgements

The authors thank all the volunteers who participated in this study. This work was supported by Grant No. 2015 − 1080 from Cariplo Foundation, and by grants of University of Brescia to Guido Ferretti.

Author contribution statement

GF conceived the hypothesis and the design of the study. GV, AT, SC, MD, NF, and CM performed the experiments. GV, AT, PB, and GF contributed to interpretation of data. GV conducted statistical analysis and wrote the first draft of the manuscript. All authors reviewed the draft and approved the final version of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Molecular and Translational MedicineUniversity of BresciaBresciaItaly
  2. 2.Department of Clinical and Experimental SciencesUniversity of BresciaBresciaItaly
  3. 3.Department of Anesthesiology, Pharmacology and Intensive CareUniversity of GenevaGeneva 4Switzerland

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