Accounting for Dynamic Changes in the Power-Duration Relationship Improves the Accuracy of W' Balance Modeling.

PURPOSE: This study aimed 1) to examine the accuracy with which W' reconstitution (W' REC ) is estimated by the W' balance (W' BAL ) models after a 3-min all-out cycling test (3MT), 2) to determine the effects of a 3MT on the power-duration relationship, and 3) to assess whether accounting for changes in the power-duration relationship during exercise improved estimates of W' REC . METHODS: The power-duration relationship and the actual and estimated W' REC were determined for 12 data sets extracted from our laboratory database where participants had completed two 3MT separated by 1-min recovery (i.e., control [C-3MT] and fatigued [F-3MT]). RESULTS: Actual W' REC (6.3 ± 1.4 kJ) was significantly overestimated by the W' BAL·ODE (9.8 ± 1.3 kJ; P < 0.001) and the W' BAL·MORTON (16.9 ± 2.6 kJ; P < 0.001) models but was not significantly different to the estimate provided by the W' BAL·INT (7.5 ± 1.5 kJ; P > 0.05) model. End power (EP) was 7% lower in the F-3MT (263 ± 40 W) compared with the C-3MT (282 ± 44 W; P < 0.001), and work done above EP (WEP) was 61% lower in the F-3MT (6.3 ± 1.4 kJ) compared with the C-3MT (16.9 ± 3.2 kJ). The size of the error in the estimated W' REC was correlated with the reduction in WEP for the W' BAL·INT and W' BAL·ODE models (both r > -0.74, P < 0.01) but not the W' BAL·MORTON model ( r = -0.18, P > 0.05). Accounting for the changes in the power-duration relationship improved the accuracy of the W' BAL·ODE and W' BAL·MORTON , but they remained significantly different to actual W' REC . CONCLUSIONS: These findings demonstrate that the power-duration relationship is altered after a 3MT, and accounting for these changes improves the accuracy of the W' BAL·ODE and the W' BAL·MORTON , but not W' BAL·INT models. These results have important implications for the design and use of mathematical models describing the energetics of exercise performance.

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 ([Formula: see text]) 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 ([Formula: see text]) and integral ([Formula: see text]) forms of the [Formula: see text] 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 [Formula: see text] at 2,250 m (P = 0.24). [Formula: see text] returned higher values than [Formula: see text] throughout HIIT (P < 0.001). During HIIT, [Formula: see text] 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, [Formula: see text] 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 [Formula: see text] model in acute hypoxia. This enables the application of [Formula: see text] modelling to training prescription and competition analysis at altitude.

Effect of work and recovery durations on W' reconstitution during intermittent exercise.

PURPOSE: We recently presented an integrating model of the curvature constant of the hyperbolic power-time relationship (W') that permits the calculation of the W' balance (W'BAL) remaining at any time during intermittent exercise. Although a relationship between recovery power and the rate of W' recovery was demonstrated, the effect of the length of work or recovery intervals remains unclear. METHODS: After determining VO2max, critical power, and W', 11 subjects completed six separate exercise tests on a cycle ergometer on different days, and in random order. Tests consisted of a period of intermittent severe-intensity exercise until the subject depleted approximately 50% of their predicted W'BAL, followed by a constant work rate (CWR) exercise bout until exhaustion. Work rates were kept constant between trials; however, either work or recovery durations during intermittent exercise were varied. The actual W' measured during the CWR (W'ACT) was compared with the amount of W' predicted to be available by the W'BAL model. RESULTS: Although some differences between W'BAL and W'ACT were noted, these amounted to only -1.6 ± 1.1 kJ when averaged across all conditions. The W'ACT was linearly correlated with the difference between VO2 at the start of CWR and VO2max (r = 0.79, P < 0.01). CONCLUSIONS: The W'BAL model provided a generally robust prediction of CWR W'. There may exist a physiological optimum formulation of work and recovery intervals such that baseline VO2 can be minimized, leading to an enhancement of subsequent exercise tolerance. These results may have important implications for athletic training and racing.

Validation of a novel intermittent w' model for cycling using field data.

Recently, an adaptation to the critical-power (CP) model was published, which permits the calculation of the balance of the work capacity available above the CP remaining (W'bal) at any time during intermittent exercise. As the model is now in use in both amateur and elite sport, the purpose of this investigation was to assess the validity of the W'bal model in the field. Data were collected from the bicycle power meters of 8 trained triathletes. W'bal was calculated and compared between files where subjects reported becoming prematurely exhausted during training or competition and files where the athletes successfully completed a difficult assigned task or race without becoming exhausted. Calculated W'bal was significantly different between the 2 conditions (P < .0001). The mean W'bal at exhaustion was 0.5 ± 1.3 kJ (95% CI = 0-0.9 kJ), whereas the minimum W'bal in the nonexhausted condition was 3.6 ± 2.0 kJ (95% CI = 2.1-4.0 kJ). Receiver-operator-characteristic (ROC) curve analysis indicated that the W'bal model is useful for identifying the point at which athletes are in danger of becoming exhausted (area under the ROC curve = .914, SE .05, 95% CI .82-1.0, P < .0001). The W'bal model may therefore represent a useful new development in assessing athlete fatigue state during training and racing.

Muscle metabolic responses during high-intensity intermittent exercise measured by (31)P-MRS: relationship to the critical power concept.

We investigated the responses of intramuscular phosphate-linked metabolites and pH (as assessed by (31)P-MRS) during intermittent high-intensity exercise protocols performed with different recovery-interval durations. Following estimation of the parameters of the power-duration relationship, i.e., the critical power (CP) and curvature constant (W'), for severe-intensity constant-power exercise, nine male subjects completed three intermittent exercise protocols to exhaustion where periods of high-intensity constant-power exercise (60 s) were separated by different durations of passive recovery (18 s, 30 s and 48 s). The tolerable duration of exercise was 304 ± 68 s, 516 ± 142 s, and 847 ± 240 s for the 18-s, 30-s, and 48-s recovery protocols, respectively (P < 0.05). The work done >CP (W>CP) was significantly greater for all intermittent protocols compared with the subjects' W', and this difference became progressively greater as recovery-interval duration was increased. The restoration of intramuscular phosphocreatine concentration during recovery was greatest, intermediate, and least for 48 s, 30 s, and 18 s of recovery, respectively (P < 0.05). The W>CP in excess of W' increased with greater durations of recovery, and this was correlated with the mean magnitude of muscle phosphocreatine reconstitution between work intervals (r = 0.61; P < 0.01). The results of this study show that during intermittent high-intensity exercise, recovery intervals allow intramuscular homeostasis to be restored, with the degree of restoration being related to the duration of the recovery interval. Consequently, and consistent with the intermittent CP model, the ability to perform W>CP during intermittent high-intensity exercise and, therefore, exercise tolerance, increases when recovery-interval duration is extended.

Determining anaerobic capacity in sporting activities.

Anaerobic capacity/anaerobically attributable power is an important parameter for athletic performance, not only for short high-intensity activities but also for breakaway efforts and end spurts during endurance events. Unlike aerobic capacity, anaerobic capacity cannot be easily quantified. The 3 most commonly used methodologies to quantify anaerobic capacity are the maximal accumulated oxygen deficit method, the critical power concept, and the gross efficiency method. This review describes these methods, evaluates if they result in similar estimates of anaerobic capacity, and highlights how anaerobic capacity is used during sporting activities. All 3 methods have their own strengths and weaknesses and result in more or less similar estimates of anaerobic capacity but cannot be used interchangeably. The method of choice depends on the research question or practical goal.

Rationale and resources for teaching the mathematical modeling of athletic training and performance.

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.

Beetroot juice and exercise: pharmacodynamic and dose-response relationships.

Dietary supplementation with beetroot juice (BR), containing approximately 5-8 mmol inorganic nitrate (NO3(-)), increases plasma nitrite concentration ([NO2(-)]), reduces blood pressure, and may positively influence the physiological responses to exercise. However, the dose-response relationship between the volume of BR ingested and the physiological effects invoked has not been investigated. In a balanced crossover design, 10 healthy men ingested 70, 140, or 280 ml concentrated BR (containing 4.2, 8.4, and 16.8 mmol NO3(-), respectively) or no supplement to establish the effects of BR on resting plasma [NO3(-)] and [NO2(-)] over 24 h. Subsequently, on six separate occasions, 10 subjects completed moderate-intensity and severe-intensity cycle exercise tests, 2.5 h postingestion of 70, 140, and 280 ml BR or NO3(-)-depleted BR as placebo (PL). Following acute BR ingestion, plasma [NO2(-)] increased in a dose-dependent manner, with the peak changes occurring at approximately 2-3 h. Compared with PL, 70 ml BR did not alter the physiological responses to exercise. However, 140 and 280 ml BR reduced the steady-state oxygen (O2) uptake during moderate-intensity exercise by 1.7% (P = 0.06) and 3.0% (P < 0.05), whereas time-to-task failure was extended by 14% and 12% (both P < 0.05), respectively, compared with PL. The results indicate that whereas plasma [NO2(-)] and the O2 cost of moderate-intensity exercise are altered dose dependently with NO3(-)-rich BR, there is no additional improvement in exercise tolerance after ingesting BR containing 16.8 compared with 8.4 mmol NO3(-). These findings have important implications for the use of BR to enhance cardiovascular health and exercise performance in young adults.

Muscle metabolic determinants of exercise tolerance following exhaustion: relationship to the "critical power".

We tested the hypothesis that muscle high-energy phosphate compounds and metabolites related to the fatigue process would be recovered after exhaustion during recovery exercise performed below but not above critical power (CP) and that these changes would influence the capacity to continue exercise. Eight male subjects completed single-leg, knee-extension exercise to exhaustion (for ∼180 s) on three occasions, followed by a work-rate reduction to severe-intensity exercise, heavy-intensity exercise (CP conditions (at least 10 min and 39 ± 31 s, respectively; P < 0.05). During passive recovery and CP recovery exercise, neither muscle [PCr] nor pH recovered, reaching ∼37% of the initial baseline and 6.6 ± 0.2, respectively. These results indicate that the muscle metabolic dynamics in recovery from exhaustive >CP differ according to whether the recovery exercise is performed below or above the CP. These findings confirm the importance of the CP as an intramuscular metabolic threshold that dictates the accumulation of fatigue-related metabolites and the capacity to tolerate high-intensity exercise.