A comparison of methods to estimate anaerobic capacity: Accumulated oxygen deficit and W' during constant and all-out work-rate profiles

Anaerobic work capacity in cycling: the effect of computational method

Purpose

To compare the anaerobic work capacity (AnWC, i.e., attributable anaerobic mechanical work) assessed using four different approaches/models applied to time-trial (TT) cycle-ergometry exercise.

Methods

Fifteen male cyclists completed a 7 × 4-min submaximal protocol and a 3-min all-out TT (TTAO). Linear relationships between power output (PO) and submaximal metabolic rate were constructed to estimate TT-specific gross efficiency (GE) and AnWC, using either a measured resting metabolic rate as a Y-intercept (7 + YLIN) or no measured Y-intercept (7-YLIN). In addition, GE of the last submaximal bout (GELAST) was used to estimate AnWC, and critical power (CP) from TTAO (CP3´AO) was used to estimate mechanical work above CP (W’, i.e., “AnWC”).

Results

Average PO during TTAO was 5.43 ± 0.30 and CP was 4.48 ± 0.23 W∙kg−1. The TT-associated GE values were ~ 22.0% for both 7 + YLIN and 7-YLIN and ~ 21.1% for GELAST (both P < 0.001). The AnWC were 269 ± 60, 272 ± 55, 299 ± 61, and 196 ± 52 J∙kg−1 for the 7 + YLIN, 7-YLIN, GELAST, and CP3´AO models, respectively (7 + YLIN and 7-YLIN versus GELAST, both P < 0.001; 7 + YLIN, 7-YLIN, and GELAST versus CP3´AO, all P < 0.01). For the three pair-wise comparisons between 7 + YLIN, 7-YLIN, and GELAST, typical errors in AnWC values ranged from 7 to 11 J∙kg−1, whereas 7 + YLIN, 7-YLIN, and GELAST versus CP3´AO revealed typical errors of 55–59 J∙kg−1.

Conclusion

These findings demonstrate a substantial disagreement in AnWC between CP3´AO and the other models. The 7 + YLIN and 7-YLIN generated 10% lower AnWC values than the GELAST model, whereas 7 + YLIN and 7-YLIN generated similar values of AnWC.

A critical review of critical power

The elegant concept of a hyperbolic relationship between power, velocity, or torque and time to exhaustion has rightfully captivated the imagination and inspired extensive research for over half a century. Theoretically, the relationship's asymptote along the time axis (critical power, velocity, or torque) indicates the exercise intensity that could be maintained for extended durations, or the "heavy-severe exercise boundary". Much more than a critical mass of the extensive accumulated evidence, however, has persistently shown the determined intensity of critical power and its variants as being too high to maintain for extended periods. The extensive scientific research devoted to the topic has almost exclusively centered around its relationships with various endurance parameters and performances, as well as the identification of procedural problems and how to mitigate them. The prevalent underlying premise has been that the observed discrepancies are mainly due to experimental 'noise' and procedural inconsistencies. Consequently, little or no effort has been directed at other perspectives such as trying to elucidate physiological reasons that possibly underly and account for those discrepancies. This review, therefore, will attempt to offer a new such perspective and point out the discrepancies' likely root causes.

Calculation of Critical Speed from Raw Training Data in Recreational Marathon Runners

INTRODUCTION

Critical speed (CS) represents the highest intensity at which a physiological steady state may be reached. The aim of this study was to evaluate whether estimations of CS obtained from raw training data can predict performance and pacing in marathons.

METHODS

We investigated running activities logged into an online fitness platform by >25,000 recreational athletes before big-city marathons. Each activity contained time, distance, and elevation every 100 m. We computed grade-adjusted pacing and the fastest pace recorded for a set of target distances (400, 800, 1000, 1500, 3000, and 5000 m). CS was determined as the slope of the distance-time relationship using all combinations of, at least, three target distances.

RESULTS

The relationship between distance and time was linear, irrespective of the target distances used (pooled mean ± SD: R = 0.9999 ± 0.0001). The estimated values of CS from all models were not different (3.74 ± 0.08 m·s), and all models correlated with marathon performance (R = 0.672 ± 0.036, error = 8.01% ± 0.51%). CS from the model including 400, 800, and 5000 m best predicted performance (R = 0.695, error = 7.67%) and was used in further analysis. Runners completed the marathon at 84.8% ± 13.6% CS, with faster runners competing at speeds closer to CS (93.0% CS for 150 min marathon times vs 78.9% CS for 360 min marathon times). Runners who completed the first half of the marathon at >94% of their CS, and particularly faster than CS, were more likely to slowdown by more than 25% in the second half of race.

CONCLUSION

This study suggests that estimations of CS from raw training data can successfully predict marathon performance and provide useful pacing information.

The Application of Critical Power, the Work Capacity above Critical Power (W'), and its Reconstitution: A Narrative Review of Current Evidence and Implications for Cycling Training Prescription

The two-parameter critical power (CP) model is a robust mathematical interpretation of the power–duration relationship, with CP being the rate associated with the maximal aerobic steady state, and W′ the fixed amount of tolerable work above CP available without any recovery. The aim of this narrative review is to describe the CP concept and the methodologies used to assess it, and to summarize the research applying it to intermittent cycle training techniques. CP and W′ are traditionally assessed using a number of constant work rate cycling tests spread over several days. Alternatively, both the 3-min all-out and ramp all-out protocols provide valid measurements of CP and W′ from a single test, thereby enhancing their suitability to athletes and likely reducing errors associated with the assumptions of the CP model. As CP represents the physiological landmark that is the boundary between heavy and severe intensity domains, it presents several advantages over the de facto arbitrarily defined functional threshold power as the basis for cycle training prescription at intensities up to CP. For intensities above CP, precise prescription is not possible based solely on aerobic measures; however, the addition of the W′ parameter does facilitate the prescription of individualized training intensities and durations within the severe intensity domain. Modelling of W′ reconstitution extends this application, although more research is needed to identify the individual parameters that govern W′ reconstitution rates and their kinetics.

A survey of mathematical models of human performance using power and energy

The ability to predict the systematic decrease of power during physical exertion gives valuable insights into health, performance, and injury. This review surveys the research of power-based models of fatigue and recovery within the area of human performance. Upon a thorough review of available literature, it is observed that the two-parameter critical power model is most popular due to its simplicity. This two-parameter model is a hyperbolic relationship between power and time with critical power as the power-asymptote and the curvature constant denoted by W′. Critical power (CP) is a theoretical power output that can be sustained indefinitely by an individual, and the curvature constant (W′) represents the amount of work that can be done above CP. Different methods and models have been validated to determine CP and W′, most of which are algebraic manipulations of the two-parameter model. The models yield different CP and W′ estimates for the same data depending on the regression fit and rounding off approximations. These estimates, at the subject level, have an inherent day-to-day variability called intra-individual variability (IIV) associated with them, which is not captured by any of the existing methods. This calls for a need for new methods to arrive at the IIV associated with CP and W′. Furthermore, existing models focus on the expenditure of W′ for efforts above CP and do not model its recovery in the sub-CP domain. Thus, there is a need for methods and models that account for (i) the IIV to measure the effectiveness of individual training prescriptions and (ii) the recovery of W′ to aid human performance optimization.

The Critical Power Model as a Potential Tool for Anti-doping

Existing doping detection strategies rely on direct and indirect biochemical measurement methods focused on detecting banned substances, their metabolites, or biomarkers related to their use. However, the goal of doping is to improve performance, and yet evidence from performance data is not considered by these strategies. The emergence of portable sensors for measuring exercise intensities and of player tracking technologies may enable the widespread collection of performance data. How these data should be used for doping detection is an open question. Herein, we review the basis by which performance models could be used for doping detection, followed by critically reviewing the potential of the critical power (CP) model as a prototypical performance model that could be used in this regard. Performance models are mathematical representations of performance data specific to the athlete. Some models feature parameters with physiological interpretations, changes to which may provide clues regarding the specific doping method. The CP model is a simple model of the power-duration curve and features two physiologically interpretable parameters, CP and W′. We argue that the CP model could be useful for doping detection mainly based on the predictable sensitivities of its parameters to ergogenic aids and other performance-enhancing interventions. However, our argument is counterbalanced by the existence of important limitations and unresolved questions that need to be addressed before the model is used for doping detection. We conclude by providing a simple worked example showing how it could be used and propose recommendations for its implementation.