Introduction The most common critical power model used in literature was simple hyperbolic model including 2 parameters: critical power (Pc) which would be a fatigueless work rate and anaerobic work capacity (W') which would be a constant amount of work performed over Pc. Depletion of this energy store would cause exercise stopping. Another formulation of the model introduced a third parameter to have a finite limit when time tends to 0 (Pm which would be maximal instantaneous power). This extended model produced lower Pc estimates which would be closer to capacity for sustained exercise (Gaesser et al. 1995, Bull et al. 2000). Simple and extended hyperbolic models included simplifications for the contribution of aerobic and anaerobic energy production. The purpose of this study was to test a new critical power model which could overcome some of these simplifications about exercise energetics. Firstly, this new model took kinetics of aerobic metabolism into account. Secondly, a fraction of energy production was assumed to be supplied by anaerobic metabolism when work rate was greater than critical power. Methods Eleven males subjects (22.9 ± 1.6 years; 179 ± 7 cm; 73.0 ± 8.4 kg; 50.3 ± 3.6 ml/min/kg) performed 1 inclusion ramp test to determinate power at ventilatory threshold (PVT), power at maximal oxygen uptake (MAP) and the maximal power reached during the trial (Ppeak). 5 tests until exhaustion were performed on separate occasions in random order. 4 exercises at fixed work-rate (2 lower and 2 greater than MAP) yielded to duration about 2 to 30 min. 1 exercise at 105% Ppeak was done to measure maximal accumulated oxygen deficit (MAOD). Each test was preceded by a 10-min cycling warm-up at 50% Ppeak. Parameters of the power-duration relationship (P vs T) was fitted by least square method using (1) simple hyperbolic model (NLin-2) in which T= W'/(P-Pc), (2) extended model (NLin-3) in which T= W'/(P-Pc) - W'/(Pm-Pc) and (3) the model proposed in this study (Mod-a). This model included aerobic energy production by taking its kinetics into account trough a time constant fixed at 20 sec. For work rate lower than MAP, anaerobic energy production was assumed to be proportional to the difference between exercise power P and Pc as follows: a .(P - Pc ). For P greater than MAP, anaerobic energy production was assumed to be the difference between P and MAP added to a .(MAP - Pc). The total amount of anaerobic work (W`) was assumed to be the integration of anaerobic contribution over the whole of exercise including deficit due to kinetics of aerobic metabolism. The maximal duration of exercise would correspond to the exhaustion of W`. The 3 parameters Pc, W` and a were fitted according data and MAP was determined from the ramp test. Anaerobic contribution of energy production was computed from a estimate for P equal to PVT, MAP and their median value (Pmedian) as follows: a.(P-Pc)/P. Parameter estimates from the 3 models and MAOD were compared using ANOVA and post hoc test. Results Goodness of fit were R2=0.985 ± 0.023 for NLin-2, 0.995 ± 0.009 from NLin-3 R2=0.998 ± 0.002 for Mod-a. Pc from Mod-a (202 ± 33 W) was not different than Pc from NLin-3 (189 ± 41 W ) and than Pc from NLin-2 (212 ± 29 W). W' from Mod-a (17157 ± 5214 J) was not different than MAOD (14226 ± 2862 J). W' from NLin-2 (30537 ± 9506 J) and W` from NLin-3 (47970 ± 24740 J without 2 out-of range values greater than 100000 J) were significantly greater than MAOD (P<0.001 and P<0.05 respectively) . Only W` from NLin-2 was significantly correlated with MAOD (R =0.80, P <0.01). a estimates was 0.52 ± 0.36 (dimensionless). Discussion/Conclusion Mod-a allowed to fit the power-time relationship at least with the same accuracy than hyperbolic models. Pc from Mod-a was not significantly different from critical power estimated by NLin-2 and NLin-3. W' estimates which could be regarded as an anaerobic capacity overestimated MAOD when using hyperbolic models. On the contrary, Mod-a produced W` estimates not different than MAOD although no significant correlation was observed between both variables. Derivations from a estimates indicated that around 14% of energy production would be supplied by anaerobic metabolism for work-rate at maximal aerobic uptake. This is in keeping with the data of Bangsbo et al. (1990). They estimated from muscle biopsy and blood samples that contribution of anaerobic metabolism would be at least 10% of total energy production at high intensity submaximal exercise. In conclusion, the proposed model could be useful to study exercise energetics although further investigations would be needed to confirm these results.
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