The Kinetics of the Work Capacity Above Critical Power

Abstract

The critical power (CP) model includes two constants: the CP and the W′ [P = W′ / t) + CP]. The W′ is the finite work capacity available above CP. Power output above CP results in depletion of the W′; complete depletion of the W′ results in exhaustion. It is possible to model the charge and discharge of the W′ during intermittent exercise using a novel integrating model (the W′BAL model), and to generate a function describing a curvilinear relationship between time constants of reconstitution of the W′ in terms of the difference between recovery power and CP (DCP) (r2 = 0.77). The depletion of the W′ as predicted by the W′BAL model during intermittent exercise is linearly related to the rise in V ̇O_2 above exercise baseline (r2 = 0.82 – 0.96).

During intermittent exercise, the W′BAL model is generally robust with respect to the length of work and recovery interval, yielding a mean under-prediction of the W′BAL of only -1.6 ±1.1 kJ. The amount of W′ remaining after a period of intermittent exercise correlates with the difference between the subject’s V ̇O_2 at that time (V ̇O_2START) and V ̇O_2PEAK (DVO2) (r = 0.79, p < 0.01). Moreover, the W′BAL model also performs well in the field, permitting accurate estimation of the point at which an athlete becomes exhausted during hard training or competition (mean W′BAL at exhaustion = 0.5 ± 1.3 kJ (95% CI = 0 – 0.9 kJ). The W′BAL model meets the mathematical criteria of an excellent diagnostic test for exhaustion (area under ROC curve = 0.91).

31P magnetic resonance spectroscopy during single leg extensor exercise revealed a correlation between the recovery of the W′BAL model and recovery of creatine phosphate ([PCr]) after a bout of exhaustive single leg extensor exercise (r = 0.99, p < 0.01). The W′BAL model also accurately predicted recovery of the W′ in this setting (r = 0.97, p < 0.05). However, a complete understanding of the relationship between the depletion and recovery of [PCr] and the depletion and recovery of the W′ remains elusive. Muscle carnosine content is curvilinearly related to the rate of W′BAL recovery, with higher muscle carnosine associated with faster recovery, with implications for muscle buffering capacity and calcium handling.

The W′BAL model may be recast in the form of a differential equation, permitting definition of the time constant of recovery of the W′BAL in terms of the subject’s known W′ and the DCP. This permits the scaling of the model to different muscle groups or exercise modalities. Moreover, modifications to this mathematical form may help explain some of the variability noted in the model in earlier studies, suggesting novel avenues of research. However, the present formulation of the W′BAL model is mathematically robust and represents an important addition to the scientific armamentarium, which may aid the understanding the physiology of human performance.