Modeling Intermittent Cycling Performance in Hypoxia Using the Critical Power Concept

Effects of acute simulated altitude on the maximal lactate steady state in humans

We sought to determine the effects of acute simulated altitude on the maximal lactate steady state (MLSS) and physiological responses to cycling at and 10 W above the MLSS-associated power output (PO) (MLSSp and MLSSp+10, respectively). Eleven (4 females) participants (means [SD]; 28 [4] yr; V̇o2max: 54.3 [6.9] mL·kg-1·min-1) acclimatized to ∼1,100 m performed 30-min constant PO trials in simulated altitudes of 0 m sea level (SL), 1,111 m mild altitude (MILD), and 2,222 m moderate altitude (MOD). MLSSp, defined as the highest PO with stable (<1 mM change) blood lactate concentration ([BLa]) between 10 and 30 min, was significantly lower in MOD (209 [54] W) compared with SL (230 [56] W; P < 0.001) and MILD (225 [58] W; P = 0.001), but MILD and SL were not different (P = 0.12). V̇o2 and V̇co2 decreased at higher simulated altitudes due to lower POs (P < 0.05), but other end-exercise physiological responses (e.g., [BLa], ventilation [V̇e], heart rate [HR]) were not different between conditions at MLSSp or MLSSp + 10 (P > 0.05). At the same absolute intensity (MLSSp for MILD), [BLa], HR, and V̇E and all perceptual variables were exacerbated in MOD compared with SL and MILD (P < 0.05). Maximum voluntary contraction, voluntary activation, and potentiated twitch forces were exacerbated at MLSSp + 10 relative to MLSSp within conditions (P < 0.05); however, condition did not affect performance fatiguability at the same relative or absolute intensity (P > 0.05). As MLSSp decreased in hypoxia, adjustments in PO are needed to ensure the same relative intensity across altitudes, but common indices of exercise intensity may facilitate exercise prescription and monitoring in hypoxia.NEW & NOTEWORTHY This study demonstrates the power output and metabolic rate associated with the maximal lactate steady-state (MLSS) decline in response to simulated altitude; however, common indices of exercise intensity remained unchanged when cycling was performed at the work rate associated with MLSS at each simulated altitude. These results support previous studies that investigated the effects of hypoxia on alternative measures of the critical intensity of exercise and will inform exercise prescription/monitoring across altitudes.

A model for calculating the mechanical demands of overground running

An energy-based approach to quantifying the mechanical demands of overground, constant velocity and/or intermittent running patterns is presented. Total mechanical work done (Wtotal) is determined from the sum of the four sub components: work done to accelerate the centre of mass horizontally (Whor), vertically (Wvert), to overcome air resistance (Wair) and to swing the limbs (Wlimbs). These components are determined from established relationships between running velocity and running kinematics; and the application of work-energy theorem. The model was applied to constant velocity running (2-9 m/s), a hard acceleration event and a hard deceleration event. The estimated Wtotal and each sub component were presented as mechanical demand (work per unit distance) and power (work per unit time), for each running pattern. The analyses demonstrate the model is able to produce estimates that: 1) are principally determined by the absolute running velocity and/or acceleration; and 2) can be attributed to different mechanical demands given the nature of the running bout. Notably, the proposed model is responsive to varied running patterns, producing data that are consistent with established human locomotion theory; demonstrating sound construct validity. Notwithstanding several assumptions, the model may be applied to quantify overground running demands on flat surfaces.

Modeling the expenditure and reconstitution of distance above critical speed during two swimming interval training sessions

In swimming, the speed-time relationship provides the critical speed (CS) and the maximum distance that can be performed above CS (D′). During intermittent severe intensity exercise, a complete D′ depletion coincides with task failure, while a sub-CS intensity is required for D′ reconstitution. Therefore, determining the balance D′ remaining at any time during intermittent exercise (D'_BAL) could improve training prescription. This study aimed to 1) test the D'_BAL model for swimming; 2) determine an equation to estimate the time constant of the reconstitution of D' (τD′); and 3) verify if τD′ is constant during two interval training sessions with the same work intensity and duration and recovery intensity, but different recovery duration. Thirteen swimmers determined CS and D′ and performed two high-intensity interval sessions at a constant speed, with repetitions fixed at 50 m. The duration of passive recovery was based on the work/relief ratio of 2:1 (T2:1) and 4:1 (T4:1). There was a high variability between sessions for τD' (coefficient of variation of 306%). When τD′ determined for T2:1 was applied in T4:1 and vice versa, the D'_BAL model was inconsistent to predict the time to exhaustion (coefficient of variation of 29 and 28%). No linear or nonlinear relationships were found between τD′ and CS, possibly due to the high within-subject variability of τD'. These findings suggest that τD′ is not constant during two high-intensity interval sessions with the same recovery intensity. Therefore, the current D'_BAL model was inconsistent to track D′ responses for swimming sessions tested herein.

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.

New Horizons in Carbohydrate Research and Application for Endurance Athletes

The importance of carbohydrate as a fuel source for exercise and athletic performance is well established. Equally well developed are dietary carbohydrate intake guidelines for endurance athletes seeking to optimize their performance. This narrative review provides a contemporary perspective on research into the role of, and application of, carbohydrate in the diet of endurance athletes. The review discusses how recommendations could become increasingly refined and what future research would further our understanding of how to optimize dietary carbohydrate intake to positively impact endurance performance. High carbohydrate availability for prolonged intense exercise and competition performance remains a priority. Recent advances have been made on the recommended type and quantity of carbohydrates to be ingested before, during and after intense exercise bouts. Whilst reducing carbohydrate availability around selected exercise bouts to augment metabolic adaptations to training is now widely recommended, a contemporary view of the so-called train-low approach based on the totality of the current evidence suggests limited utility for enhancing performance benefits from training. Nonetheless, such studies have focused importance on periodizing carbohydrate intake based on, among other factors, the goal and demand of training or competition. This calls for a much more personalized approach to carbohydrate recommendations that could be further supported through future research and technological innovation (e.g., continuous glucose monitoring). Despite more than a century of investigations into carbohydrate nutrition, exercise metabolism and endurance performance, there are numerous new important discoveries, both from an applied and mechanistic perspective, on the horizon.

Bi-exponential modelling of [Formula: see text] reconstitution kinetics in trained cyclists

PURPOSE

The aim of this study was to investigate the individual [Formula: see text] reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe [Formula: see text] reconstitution.

METHODS

Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; [Formula: see text] 58.6 ± 7.1 mL kg min^-1) completed three incremental ramps (20 W min^-1) to the limit of tolerance with varying recovery durations (15-360 s) on 5-9 occasions. [Formula: see text] reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R² and bias-corrected Akaike information criterion (AICc).

RESULTS

A bi-exponential model outperformed the mono-exponential model of [Formula: see text] reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR² = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)_FC = 21.5 s; τ_SC = 388 s. Following the second recovery, W' reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τ_SC to 716 s with τ_FC unchanged. Individual bi-exponential models also fit well (adjR² = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)_FC = 22.0 ± 11.8 s; (τ)_SC = 377 ± 100 s; second recovery: (τ)_FC = 16.3.0 ± 6.6 s; (τ)_SC = 549 ± 226 s).

CONCLUSIONS

W' reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W' reconstitution confined to an increase in the time constant of the slow component.

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.

Using Field Based Data to Model Sprint Track Cycling Performance

Cycling performance models are used to study rider and sport characteristics to better understand performance determinants and optimise competition outcomes. Performance requirements cover the demands of competition a cyclist may encounter, whilst rider attributes are physical, technical and psychological characteristics contributing to performance. Several current models of endurance-cycling enhance understanding of performance in road cycling and track endurance, relying on a supply and demand perspective. However, they have yet to be developed for sprint-cycling, with current athlete preparation, instead relying on measures of peak-power, speed and strength to assess performance and guide training. Peak-power models do not adequately explain the demands of actual competition in events over 15-60 s, let alone, in World-Championship sprint cycling events comprising several rounds to medal finals. Whilst there are no descriptive studies of track-sprint cycling events, we present data from physiological interventions using track cycling and repeated sprint exercise research in multiple sports, to elucidate the demands of performance requiring several maximal sprints over a competition. This review will show physiological and power meter data, illustrating the role of all energy pathways in sprint performance. This understanding highlights the need to focus on the capacity required for a given race and over an event, and therefore the recovery needed for each subsequent race, within and between races, and how optimal pacing can be used to enhance performance. We propose a shift in sprint-cyclist preparation away from training just for peak power, to a more comprehensive model of the actual event demands.

Effects of Normobaric Hypoxia on Matched-severe Exercise and Power-duration Relationship

We investigated the effects of hypoxia on matched-severe intensity exercise and on the parameters of the power-duration relationship. Fifteen trained subjects performed in both normoxia and normobaric hypoxia (F_iO₂=0.13, ~3000 m) a maximal incremental test, a 3 min all-out test (3AOT) and a transition from rest to an exercise performed to exhaustion (T_lim) at the same relative intensity (80%∆). Respiratory and pulmonary gas-exchange variables were continuously measured (K5, Cosmed, Italy). T_lim test's V̇O₂ kinetics was calculated using a two-component exponential model. V̇O₂max (44.1±5.1 vs. 58.7±6.4 ml.kg^-1.min^-1, p<0.001) was decreased in hypoxia. In T_lim, time-to-exhaustion sustained was similar (454±130 vs. 484±169 s) despite that V̇O₂ kinetics was slower (_τ1: 31.1±5.8 vs. 21.6±4.7 s, p<0.001) and the amplitude of the V̇O₂ slow component lower (12.4±5.4 vs. 20.2±5.7 ml.kg^-1.min^-1, p<0.05) in hypoxia. CP was reduced (225±35 vs. 270±49 W, p<0.001) but W' was unchanged (11.3±2.9 vs. 11.4±2.7 kJ) in hypoxia. The changes in CP/V̇O₂max were positively correlated with changes in W' (r = 0.58, p<0.05). The lower oxygen availability had an impact on aerobic related physiological parameters, but exercise tolerance is similar between hypoxia and normoxia when the relative intensity is matched despite a slower V̇O₂ kinetics in hypoxia.

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.

Minimal Effects of Moderate Normobaric Hypoxia on the Upper Body Work-Time Relationship in Recreationally Active Women

Background: Sex-based differences in metabolism and morphological characteristics may result in unique exercise responses during periods of limited oxygen availability. Purpose: To evaluate the effects of moderate normobaric hypoxia on the parameters of the work-time relationship during upper body exercise in women. Materials and Methods: Thirteen recreationally active women (age: 22.7 ± 2.6 years; height: 167 ± 8.6 cm; weight: 66.4 ± 9.7 kg; body fat: 27.6% ± 5% body fat) completed a maximal graded exercise test in both normobaric hypoxia (H; fraction of inspired oxygen (F_iO₂) = 0.14) and normoxia (N; F_iO₂ = 0.20) on an arm ergometer to determine peak oxygen uptake (VO₂peak) and peak power output (PPO). Each participant completed four constant, work rate, arm-cranking time-to-exhaustion tests at 90%-120% PPO in both environmental conditions. Linear regression was used to estimate critical power (CP) and anaerobic capacity (W') through the work-time relationship during the constant work rate tests. Paired sample t-tests compared mean differences between VO₂peak, PPO, CP, and W' between conditions (normoxia vs. hypoxia). Two-way (condition × intensity) repeated measures analysis of variance (ANOVA) was used to compare total work (TW) and time to exhaustion. Results: Hypoxia significantly reduced VO₂peak (N: 1.73 ± 0.31 L·minute^-1 vs. H: 1.62 ± 0.27 L·minute^-1, p = 0.008), but had no effects on PPO (N: 78.08 ± 14.51 W vs. H: 75.38 ± 13.46 W, p = 0.09), CP (N: 57.44 ± 18.89 W vs. H: 56.01 ± 12.36 W, p = 0.55), and W' (N: 4.81 ± 1.01 kJ vs. H: 4.56 ± 0.91 kJ, p = 0.51). No significant condition × intensity interactions were noted for TW or time to exhaustion (p > 0.05). Conclusions: Moderate normobaric hypoxia significantly reduced VO₂peak, but had minimal effects on CP and W' using the work-time model in women.

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.

Prediction of Critical Power and W' in Hypoxia: Application to Work-Balance Modelling

Purpose: Develop a prediction equation for critical power (CP) and work above CP (W′) in hypoxia for use in the work-balance (WBAL′) model.

Methods: Nine trained male cyclists completed cycling time trials (TT; 12, 7, and 3 min) to determine CP and W′ at five altitudes (250, 1,250, 2,250, 3,250, and 4,250 m). Least squares regression was used to predict CP and W′ at altitude. A high-intensity intermittent test (HIIT) was performed at 250 and 2,250 m. Actual and predicted CP and W′ were used to compute W′ during HIIT using differential (WBALdiff′) and integral (WBALint′) forms of the WBAL′ model.

Results: CP decreased at altitude (P < 0.001) as described by 3rd order polynomial function (R² = 0.99). W′ decreased at 4,250 m only (P < 0.001). A double-linear function characterized the effect of altitude on W′ (R² = 0.99). There was no significant effect of parameter input (actual vs. predicted CP and W′) on modelled WBAL′ at 2,250 m (P = 0.24). WBALdiff′ returned higher values than WBALint′ throughout HIIT (P < 0.001). During HIIT, WBALdiff′ was not different to 0 kJ at completion, at 250 m (0.7 ± 2.0 kJ; P = 0.33) and 2,250 m (−1.3 ± 3.5 kJ; P = 0.30). However, WBALint′ was lower than 0 kJ at 250 m (−0.9 ± 1.3 kJ; P = 0.058) and 2,250 m (−2.8 ± 2.8 kJ; P = 0.02).

Conclusion: The altitude prediction equations for CP and W′ developed in this study are suitable for use with the WBAL′ model in acute hypoxia. This enables the application of WBAL′ modelling to training prescription and competition analysis at altitude.

Determinants of curvature constant (W') of the power duration relationship under normoxia and hypoxia: the effect of pre-exercise alkalosis

Purpose

This study investigated the effect of induced alkalosis on the curvature constant (W’) of the power-duration relationship under normoxic and hypoxic conditions.

Methods

Eleven trained cyclists (mean ± SD) Age: 32 ± 7.2 years; body mass (bm): 77.0 ± 9.2 kg; VO_2peak: 59.2 ± 6.8 ml·kg⁻¹·min⁻¹ completed seven laboratory visits which involved the determination of individual time to peak alkalosis following sodium bicarbonate (NaHCO₃) ingestion, an environment specific ramp test (e.g. normoxia and hypoxia) and four x 3 min critical power (CP) tests under different experimental conditions. Participants completed four trials: alkalosis normoxia (ALN); placebo normoxia (PLN); alkalosis hypoxia (ALH); and placebo hypoxia (PLH). Pre-exercise administration of 0.3 g.kg⁻¹ BM of NaHCO₃ was used to induce alkalosis. Environmental conditions were set at either normobaric hypoxia (FiO₂: 14.5%) or normoxia (FiO₂: 20.93%).

Results

An increase in W’ was observed with pre-exercise alkalosis under both normoxic (PLN: 15.1 ± 6.2 kJ vs. ALN: 17.4 ± 5.1 kJ; P = 0.006) and hypoxic conditions (ALN: 15.2 ± 4.9 kJ vs. ALN: 17.9 ± 5.2 kJ; P < 0.001). Pre-exercise alkalosis resulted in a larger reduction in bicarbonate ion (HCO₃⁻) concentrations during exercise in both environmental conditions (p < 0.001) and a greater blood lactate accumulation under hypoxia (P = 0.012).

Conclusion

Pre-exercise alkalosis substantially increased W’ and, therefore, may determine tolerance to exercise above CP under normoxic and hypoxic conditions. This may be due to NaHCO₃ increasing HCO₃⁻ buffering capacity to delay exercise-induced acidosis, which may, therefore, enhance anaerobic energy contribution.