Accounting for Dynamic Changes in the Power-Duration Relationship Improves the Accuracy of W' Balance Modeling

Purpose: This study aimed 1) to examine the accuracy with which W ' reconstitution (W '(REC)) is estimated by the W ' balance (W '(BAL)) models after a 3-min all-out cycling test (3MT), 2) to determine the effects of a 3MT on the power-duration relationship, and 3) to assess whether accounting for changes in the power-duration relationship during exercise improved estimates of W '(REC). Methods: The power-duration relationship and the actual and estimated W '(REC) were determined for 12 data sets extracted from our laboratory database where participants had completed two 3MT separated by 1-min recovery (i.e., control [C-3MT] and fatigued [F-3MT]). Results: Actual W '(REC) (6.3 +/- 1.4 kJ) was significantly overestimated by the W '(BALmiddotODE) (9.8 +/- 1.3 kJ; P < 0.001) and the W '(BALmiddotMORTON) (16.9 +/- 2.6 kJ; P < 0.001) models but was not significantly different to the estimate provided by the (W ' BALmiddotINT) (7.5 +/- 1.5 kJ; P > 0.05) model. End power (EP) was 7% lower in the F-3MT (263 +/- 40 W) compared with the C-3MT (282 +/- 44 W; P < 0.001), and work done above EP (WEP) was 61% lower in the F-3MT (6.3 +/- 1.4 kJ) compared with the C-3MT (16.9 +/- 3.2 kJ). The size of the error in the estimated (W ' REC) was correlated with the reduction in WEP for the W '(BALmiddotINT) and W '(BALmiddotODE) models (both r > -0.74, P < 0.01) but not the W '(BALmiddotMORTON) model (r = -0.18, P > 0.05). Accounting for the changes in the power-duration relationship improved the accuracy of the W '(BALmiddotODE) and W '(BALmiddotMORTON), but they remained significantly different to actual W '(REC). Conclusions: These findings demonstrate that the power-duration relationship is altered after a 3MT, and accounting for these changes improves the accuracy of the W '(BALmiddotODE) and the W '(BALmiddotMORTON), but not W '(BALmiddotINT) models. These results have important implications for the design and use of mathematical models describing the energetics of exercise performance.

Automated summary

The purpose of this study was to examine the accuracy of different W ' balance models in estimating W '(REC) after a 3-minute all-out cycling test (3MT), determine the effects of the 3MT on the power-duration relationship, and assess whether accounting for changes in this relationship improved estimates of W '(REC). The actual W '(REC) was overestimated by some models, but accounting for changes in the power-duration relationship improved their accuracy. These findings have important implications for mathematical models of exercise performance.