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.