Development and field validation of an omni-domain power-duration model

Modelling human endurance: power laws vs critical power

The power-duration relationship describes the time to exhaustion for exercise at different intensities. It is believed to be a "fundamental bioenergetic property of living systems" that this relationship is hyperbolic. Indeed, the hyperbolic (a.k.a. critical-power) model which formalises this belief is the dominant tool for describing and predicting high-intensity exercise performance, e.g. in cycling, running, rowing or swimming. However, the hyperbolic model is now the focus of a heated debate in the literature because it unrealistically represents efforts that are short (< 2 min) or long (> 15 min). We contribute to this debate by demonstrating that the power-duration relationship is more adequately represented by an alternative, power-law model. In particular, we show that the often-observed good fit of the hyperbolic model between 2 and 15 min should not be taken as proof that the power-duration relationship is hyperbolic. Rather, in this range, a hyperbolic function just happens to approximate a power law fairly well. We also prove mathematical results which suggest that the power-law model is a safer tool for pace selection than the hyperbolic model and that the former more naturally models fatigue than the latter.

Modeling the Power-Duration Relationship in Professional Cyclists During the Giro d'Italia

ABSTRACT

Vinetti, G, Pollastri, L, Lanfranconi, F, Bruseghini, P, Taboni, A, and Ferretti, G. Modeling the power-duration relationship in professional cyclists during the Giro d'Italia. J Strength Cond Res 37(4): 866-871, 2023-Multistage road bicycle races allow the assessment of maximal mean power output (MMP) over a wide spectrum of durations. By modeling the resulting power-duration relationship, the critical power ( CP ) and the curvature constant ( W' ) can be calculated and, in the 3-parameter (3-p) model, also the maximal instantaneous power ( P0 ). Our aim is to test the 3-p model for the first time in this context and to compare it with the 2-parameter (2-p) model. A team of 9 male professional cyclists participated in the 2014 Giro d'Italia with a crank-based power meter. The maximal mean power output between 10 seconds and 10 minutes were fitted with 3-p, whereas those between 1 and 10 minutes with the 2- model. The level of significance was set at p < 0.05. 3-p yielded CP 357 ± 29 W, W' 13.3 ± 4.2 kJ, and P0 1,330 ± 251 W with a SEE of 10 ± 5 W, 3.0 ± 1.7 kJ, and 507 ± 528 W, respectively. 2-p yielded a CP and W' slightly higher (+4 ± 2 W) and lower (-2.3 ± 1.1 kJ), respectively ( p < 0.001 for both). Model predictions were within ±10 W of the 20-minute MMP of time-trial stages. In conclusion, during a single multistage racing event, the 3-p model accurately described the power-duration relationship over a wider MMP range without physiologically relevant differences in CP with respect to 2-p, potentially offering a noninvasive tool to evaluate competitive cyclists at the peak of training.

Can Popular High-Intensity Interval Training (HIIT) Models Lead to Impossible Training Sessions?

High-Intensity Interval Training (HIIT) is a time-efficient training method suggested to improve health and fitness for the clinical population, healthy subjects, and athletes. Many parameters can impact the difficulty of HIIT sessions. This study aims to highlight and explain, through logical deductions, some limitations of the Skiba and Coggan models, widely used to prescribe HIIT sessions in cycling. We simulated 6198 different HIIT training sessions leading to exhaustion, according to the Skiba and Coggan-Modified (modification of the Coggan model with the introduction of an exhaustion criterion) models, for three fictitious athlete profiles (Time-Trialist, All-Rounder, Sprinter). The simulation revealed impossible sessions (i.e., requiring athletes to surpass their maximal power output over the exercise interval duration), characterized by a few short exercise intervals, performed in the severe and extreme intensity domains, alternating with long recovery bouts. The fraction of impossible sessions depends on the athlete profile and ranges between 4.4 and 22.9% for the Skiba model and 0.6 and 3.2% for the Coggan-Modified model. For practitioners using these HIIT models, this study highlights the importance of understanding these models’ inherent limitations and mathematical assumptions to draw adequate conclusions from their use to prescribe HIIT sessions.

Power profiling and the power-duration relationship in cycling: a narrative review

Emerging trends in technological innovations, data analysis and practical applications have facilitated the measurement of cycling power output in the field, leading to improvements in training prescription, performance testing and race analysis. This review aimed to critically reflect on power profiling strategies in association with the power-duration relationship in cycling, to provide an updated view for applied researchers and practitioners. The authors elaborate on measuring power output followed by an outline of the methodological approaches to power profiling. Moreover, the deriving a power-duration relationship section presents existing concepts of power-duration models alongside exercise intensity domains. Combining laboratory and field testing discusses how traditional laboratory and field testing can be combined to inform and individualize the power profiling approach. Deriving the parameters of power-duration modelling suggests how these measures can be obtained from laboratory and field testing, including criteria for ensuring a high ecological validity (e.g. rider specialization, race demands). It is recommended that field testing should always be conducted in accordance with pre-established guidelines from the existing literature (e.g. set number of prediction trials, inter-trial recovery, road gradient and data analysis). It is also recommended to avoid single effort prediction trials, such as functional threshold power. Power-duration parameter estimates can be derived from the 2 parameter linear or non-linear critical power model: P(t) = W′/t + CP (W′—work capacity above CP; t—time). Structured field testing should be included to obtain an accurate fingerprint of a cyclist’s power profile.

The W' Balance Model: Mathematical and Methodological Considerations

Since its publication in 2012, the W' balance model has become an important tool in the scientific armamentarium for understanding and predicting human physiology and performance during high-intensity intermittent exercise. Indeed, publications featuring the model are accumulating, and it has been adapted for popular use both in desktop computer software and on wrist-worn devices. Despite the model's intuitive appeal, it has achieved mixed results thus far, in part due to a lack of clarity in its basis and calculation. Purpose: This review examines the theoretical basis, assumptions, calculation methods, and the strengths and limitations of the integral and differential forms of the W' balance model. In particular, the authors emphasize that the formulations are based on distinct assumptions about the depletion and reconstitution of W' during intermittent exercise; understanding the distinctions between the 2 forms will enable practitioners to correctly implement the models and interpret their results. The authors then discuss foundational issues affecting the validity and utility of the model, followed by evaluating potential modifications and suggesting avenues for further research. Conclusions: The W' balance model has served as a valuable conceptual and computational tool. Improved versions may better predict performance and further advance the physiology of high-intensity intermittent exercise.