The relationship between power output and endurance: a brief review

Functional Threshold Power Field Test Exceeds Laboratory Performance in Junior Road Cyclists

Vinetti, G, Rossi, H, Bruseghini, P, Corti, M, Ferretti, G, Piva, S, Taboni, A, and Fagoni, N. The functional threshold power field test exceeds laboratory performance in junior road cyclists. J Strength Cond Res 37(9): 1815–1820, 2023—The functional threshold power (FTP) field test is appealing for junior cyclists, but it was never investigated in this age category, and even in adults, there are few data on FTP collected in field conditions. Nine male junior road cyclists (16.9 ± 0.8 years) performed laboratory determination of maximal aerobic power (MAP), 4-mM lactate threshold (P4mM), critical power (CP), and the curvature constant (W ′), plus a field determination of FTP as 95% of the average power output during a 20-minute time trial in an uphill road. The level of significance was set at p < 0.05. Outdoor FTP (269 ± 34 W) was significantly higher than CP (236 ± 24 W) and P4mM (233 ± 23 W). The V ˙ O 2 peak of the field FTP test (66.9 ± 4.4 ml·kg−1·min−1) was significantly higher than the V ˙ O 2 peak assessed in the laboratory (62.7 ± 3.7 ml·kg−1·min−1). Functional threshold power was correlated, in descending order, with MAP (r = 0.95), P4mM (r = 0.94), outdoor and indoor V ˙ O 2 peak (r = 0.93 and 0.93, respectively), CP (r = 0.84), and W ′ (r = 0.66). It follows that in junior road cyclists, the FTP field test was feasible and related primarily to aerobic endurance parameters and secondarily, but notably, to W ′. However, the FTP field test significantly exceeded all laboratory performance tests. When translating laboratory results to outdoor uphill conditions, coaches and sport scientists should consider this discrepancy, which may be particularly enhanced in this cycling age category.

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.

Predictions of the distance running performances of female runners using different tools

This study examined the validity and compared the precision and accuracy of a distance-time linear model (DTLM), a power law and a nomogram to predict the distance running performances of female runners. Official rankings of French women for the 3000-m, 5000-m, and 10,000-m track-running events from 2005 to 2019 were examined. Each performance was predicted from two other performances. Between the actual and predicted performances, only DTLM showed a difference (p < 0.05). The magnitude of the differences in these predicted performances was small if not trivial. All predicted performances were significantly correlated with the actual ones, with a very high correlation coefficient (p < 0.001; r > 0.90), except for DTLM in the 3000-m, which showed a high correlation coefficient (p < 0.001; r > 0.895). Bias and 95% limits of agreement were acceptable because, whatever the method, they were ≤ -3.7 ± 10.8% on the 3000-m, 1.4 ± 4.3% on the 5000-m, and -2.5 ± 7.4% on the 10,000-m. The study confirms the validity of the three methods to predict track-running performance and suggests that the most accurate and precise model was the nomogram followed by the power law, with the DTLM being the least accurate.

Validity of the Training-Load Concept

Training load (TL) is a widely used concept in training prescription and monitoring and is also recognized as as an important tool for avoiding athlete injury, illness, and overtraining. With the widespread adoption of wearable devices, TL metrics are used increasingly by researchers and practitioners worldwide. Conceptually, TL was proposed as a means to quantify a dose of training and used to predict its resulting training effect. However, TL has never been validated as a measure of training dose, and there is a risk that fundamental problems related to its calculation are preventing advances in training prescription and monitoring. Specifically, we highlight recent studies from our research groups where we compare the acute performance decrement measured following a session with its TL metrics. These studies suggest that most TL metrics are not consistent with their notional training dose and that the exercise duration confounds their calculation. These studies also show that total work done is not an appropriate way to compare training interventions that differ in duration and intensity. We encourage scientists and practitioners to critically evaluate the validity of current TL metrics and suggest that new TL metrics need to be developed.

Oxygen Uptake at Critical Speed and Power in Running: Perspectives and Practical Applications

PURPOSE

Intensity domains are recommended when prescribing exercise, and critical power/speed (CP/CS) was designated the "gold standard" when determining maximal metabolic steady state. CS is the running analog of CP for cycle ergometry. However, a CP for running could be useful for controlling intensity when training in any type of condition. Therefore, this study aimed to estimate external, internal, and total CP (CPext, CPint, and CPtot), obtained based on running power calculations, and verified whether they occurred at the same percentage of peak oxygen uptake as the usual CS. Furthermore, this study examined whether selecting strides at the start, half, or end of the exhaustive runs to calculate running power influenced the estimation of the 3 CPs.

METHODS

Thirteen male runners performed a maximal incremental aerobic test and 4 exhaustive runs (90%, 100%, 110%, 120% peak speed) on a treadmill. The estimations of CS and CPs were obtained using a 3-parameter mathematical model fitted using weighted least square.

RESULTS

CS was estimated at 4.3 m/s while the estimates of CPext, CPint, and CPtot were 5.2, 2.6, and 7.8 W/kg, respectively. The corresponding V˙O2 for CS was 82.5 percentage of peak oxygen uptake and 81.3, 79.7, and 80.6 percentage of peak oxygen uptake for CPext, CPint, and CPtot, respectively. No systematic bias was reported when comparing CS and CPext, as well as the 3 different CPs, whereas systematic biases of 2.8% and 1.8% were obtained for the comparison among CS and CPint and CPtot, respectively. Nonetheless, the V˙O2 for CS and CPs were not statistically different (P = .09). Besides, no effect of the time stride selection for CPs as well as their resulting V˙O2 was obtained (P ≥ .44).

CONCLUSIONS

The systematic biases among V˙O2 at CS and CPint and CPtot were not clinically relevant. Therefore, CS and CPs closely represent the same fatigue threshold in running. The knowledge of CP in running might prove to be useful for both athletes and coaches, especially when combined with instantaneous running power. Indeed, this combination might help athletes controlling their targeted training intensity and coaches prescribing a training session in any type of condition.

Critical speed estimated by statistically appropriate fitting procedures

PURPOSE

Intensity domains are recommended when prescribing exercise. The distinction between heavy and severe domains is made by the critical speed (CS), therefore requiring a mathematically accurate estimation of CS. The different model variants (distance versus time, running speed versus time, time versus running speed, and distance versus running speed) are mathematically equivalent. Nevertheless, error minimization along the correct axis is important to estimate CS and the distance that can be run above CS (d'). We hypothesized that comparing statistically appropriate fitting procedures, which minimize the error along the axis corresponding to the properly identified dependent variable, should provide similar estimations of CS and d' but that different estimations should be obtained when comparing statistically appropriate and inappropriate fitting procedure.

METHODS

Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of their peak speed on a treadmill. Several fitting procedures (a combination of a two-parameter model variant and regression analysis: weighted least square) were used to estimate CS and d'.

RESULTS

Systematic biases (P < 0.001) were observed between each pair of fitting procedures for CS and d', even when comparing two statistically appropriate fitting procedures, though negligible, thus corroborating the hypothesis.

CONCLUSION

The differences suggest that a statistically appropriate fitting procedure should be chosen beforehand by the researcher. This is also important for coaches that need to prescribe training sessions to their athletes based on exercise intensity, and their choice should be maintained over the running seasons.

Effect of Mathematical Modeling and Fitting Procedures on the Assessment of Critical Speed and Its Relationship With Aerobic Fitness Parameters

An accurate estimation of critical speed (CS) is important to accurately define the boundary between heavy and severe intensity domains when prescribing exercise. Hence, our aim was to compare CS estimates obtained by statistically appropriate fitting procedures, i.e., regression analyses that correctly consider the dependent variables of the underlying models. A second aim was to determine the correlations between estimated CS and aerobic fitness parameters, i.e., ventilatory threshold, respiratory compensation point, and maximal rate of oxygen uptake. Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of the peak speed of the incremental test on a treadmill. Then, two mathematically equivalent formulations (time as function of running speed and distance as function of running speed) of three different mathematical models (two-parameter, three-parameter, and three-parameter exponential) were employed to estimate CS, the distance that can be run above CS (d'), and if applicable, the maximal instantaneous running speed (s max ). A significant effect of the mathematical model was observed when estimating CS, d', and s max (P < 0.001), but there was no effect of the fitting procedure (P > 0.77). The three-parameter model had the best fit quality (smallest Akaike information criterion) of the CS estimates but the highest 90% confidence intervals and combined standard error of estimates (%SEE). The 90% CI and %SEE were similar when comparing the two fitting procedures for a given model. High and very high correlations were obtained between CS and aerobic fitness parameters for the three different models (r ≥ 0.77) as well as reasonably small SEE (SEE ≤ 6.8%). However, our results showed no further support for selecting the best mathematical model to estimate critical speed. Nonetheless, we suggest coaches choosing a mathematical model beforehand to define intensity domains and maintaining it over the running seasons.

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.

A regression method for the power-duration relationship when both variables are subject to error

PURPOSE

The power-duration relationship has been variously modelled, although duration must be acknowledged as the dependent variable and is supposed to represent the only source of experimental error. However, there are certain situations, namely extremely high power outputs or outdoor field conditions, in which the error in power output measurement may not remain negligible. The geometric mean (GM) regression method deals with the assumption that also the independent variable is subject to a certain amount of experimental error, but has never been utilized in this context.

METHODS

We applied the GM regression method for the two- and three-parameter critical power models and tested it against the usual weighted least square (WLS) procedure with our previous published data.

RESULTS

There were no significant differences between parameter estimates of WLS and GM. Bias and limit of agreements between the two methods were low, while correlation coefficients were high (0.85-1.00).

CONCLUSIONS

GM provided equivalent results with respect to WLS in fitting the critical power model to experimental data and for its conceptual characteristics must be preferred wherever concerns on the precision of P measurement are present, such as for in-field power meters.

Modelling of Running Performances: Comparisons of Power-Law, Hyperbolic, Logarithmic, and Exponential Models in Elite Endurance Runners

Many empirical and descriptive models have been proposed since the beginning of the 20th century. In the present study, the power-law (Kennelly) and logarithmic (Péronnet-Thibault) models were compared with asymptotic models such as 2-parameter hyperbolic models (Hill and Scherrer), 3-parameter hyperbolic model (Morton), and exponential model (Hopkins). These empirical models were compared from the performance of 6 elite endurance runners (P. Nurmi, E. Zatopek, J. Väätäinen, L. Virén, S. Aouita, and H. Gebrselassie) who were world-record holders and/or Olympic winners and/or world or European champions. These elite runners were chosen because they participated several times in international competitions over a large range of distances (1500, 3000, 5000, and 10000 m) and three also participated in a marathon. The parameters of these models were compared and correlated. The less accurate models were the asymptotic 2-parameter hyperbolic models but the most accurate model was the asymptotic 3-parameter hyperbolic model proposed by Morton. The predictions of long-distance performances (maximal running speeds for 30 and 60 min and marathon) by extrapolation of the logarithmic and power-law models were more accurate than the predictions by extrapolation in all the asymptotic models. The overestimations of these long-distance performances by Morton's model were less important than the overestimations by the other asymptotic models.

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.

The relationship between movement speed and duration during soccer matches

The relationship between the time duration of movement (t(dur)) and related maximum possible power output has been studied and modeled under many conditions. Inspired by the so-called power profiles known for discontinuous endurance sports like cycling, and the critical power concept of Monod and Scherrer, the aim of this study was to evaluate the numerical characteristics of the function between maximum horizontal movement velocity (HSpeed) and t(dur) in soccer. To evaluate this relationship, GPS data from 38 healthy soccer players and 82 game participations (≥30 min active playtime) were used to select maximum HSpeed for 21 distinct t(dur) values (between 0.3 s and 2,700 s) based on moving medians with an incremental t(dur) window-size. As a result, the relationship between HSpeed and Log(t(dur)) appeared reproducibly as a sigmoidal decay function, and could be fitted to a five-parameter equation with upper and lower asymptotes, and an inflection point, power and decrease rate. Thus, the first three parameters described individual characteristics if evaluated using mixed-model analysis. This study shows for the first time the general numerical relationship between t(dur) and HSpeed in soccer games. In contrast to former descriptions that have evaluated speed against power, HSpeed against t(dur) always yields a sigmoidal shape with a new upper asymptote. The evaluated curve fit potentially describes the maximum moving speed of individual players during the game, and allows for concise interpretations of the functional state of team sports athletes.

The effects of exercise modality and intensity on energy expenditure and cardiorespiratory response in adults with obesity and treated obstructive sleep apnoea

To inform recommendations for the exercise component of a healthy lifestyle intervention for adults with obesity and treated obstructive sleep apnoea (OSA), we investigated the total energy expenditure (EE) and cardiorespiratory response to weight-supported (cycling) and unsupported (walking) exercise. Individuals with treated OSA and a body mass index (BMI) > 30 kg/m² performed an incremental cardiopulmonary exercise test on a cycle ergometer and a treadmill to determine the peak oxygen uptake [Formula: see text]. Participants subsequently completed two endurance tests on each modality, matched at 80% and 60% of the highest [Formula: see text] determined by the incremental tests, to intolerance. The cardiorespiratory response was measured and total EE was estimated from the [Formula: see text]. Sixteen participants completed all six tests: mean [SD] age 57 [13] years and median [IQ range] BMI 33.3 [30.8-35.3] kg/m². Total EE during treadmill walking was greater than cycling at both high (158 [101] vs. 29 [15] kcal; p < 0.001) and moderate (178 [100] vs. 85 [59] kcal; p = 0.002) intensities, respectively, with similar cardiorespiratory responses and pattern of EE during rest, exercise and recovery. Contrary to current guidelines, walking might be the preferred training modality to achieve the combination of weight loss and increased cardiorespiratory fitness in adults with obesity and treated OSA.

Modelling decremental ramps using 2- and 3-parameter "critical power" models

The "Critical Power" (CP) model of human bioenergetics provides a valuable way to identify both limits of tolerance to exercise and mechanisms that underpin that tolerance. It applies principally to cycling-based exercise, but with suitable adjustments for analogous units it can be applied to other exercise modalities; in particular to incremental ramp exercise. It has not yet been applied to decremental ramps which put heavy early demand on the anaerobic energy supply system. This paper details cycling-based bioenergetics of decremental ramps using 2- and 3-parameter CP models. It derives equations that, for an individual of known CP model parameters, define those combinations of starting intensity and decremental gradient which will or will not lead to exhaustion before ramping to zero; and equations that predict time to exhaustion on those decremental ramps that will. These are further detailed with suitably chosen numerical and graphical illustrations. These equations can be used for parameter estimation from collected data, or to make predictions when parameters are known.

Influence of moderate hypoxia on tolerance to high-intensity exercise

It remains uncertain as how the reduction in systemic oxygen transport limits high-intensity exercise tolerance. 11 participants (5 males; age 35 ± 10 years; peak [Formula: see text] 3.5 ± 0.4 L min(-1)) performed cycle ergometry to the limit of tolerance: (1) a ramp test to determine ventilatory threshold (VT) and peak [Formula: see text]; (2) three to four constant-load tests in order to model the linear P-t (-1) relationship for estimation of intercept (critical power; CP) and slope (AWC). All tests were performed in a random order under moderate hypoxia (FiO(2) = 0.15) and normoxia. The linearity of the P-t (-1) relationship was retained under hypoxia, with a systematic reduction in CP (220 ± 25 W vs. 190 ± 28 W; P < 0.01) but no significant difference in AWC (11.7 ± 5.5 kJ vs. 12.1 ± 4.4 kJ; P > 0.05). However, large individual variations in the change of the latter were observed (-36 to +66%). A significant relationship was found between the % change in CP (r = 0.80, P < 0.01) and both peak [Formula: see text] (CP: r = -0.65, P < 0.05) and VT values recorded under normoxia (CP: r = -0.65, P < 0.05). The present study demonstrates the aerobic nature of the intercept of the P-t (-1) relationship, i.e. CP. However, the extreme within-individual changes in AWC do not support the original assumption that AWC reflects a finite energy store. Lower hypoxia-induced decrements in CP were observed in aerobically fitter participants. This study also demonstrates the greater ability these participants have to exercise at supra-CP but close to CP workloads under moderate hypoxia.

Precision in the prediction of middle distance-running performances using either a nomogram or the modeling of the distance-time relationship

The purpose was to determine the levels of precision in the prediction of middle-distance performances in running using the modeling of the distance-time relationship and a nomogram. Official French running rankings for the men's 3,000; 5,000; and 10,000 m were scrutinized from 1996 to 2007. Only runners who competed over the 3 distances within the same year were included (n = 100). The distance-time relationship was modeled using a linear 2-parameter model from the plot of 2 performances to predict a third one. The nomogram of Mercier was also used to predict 1 performance from the use of the other 2. Actual and predicted performances were significantly different, except for the 5,000- and 10,000-m performances predicted from the nomogram (p > 0.05). Effect sizes (ESs) were lower when the performance was predicted by the nomogram (-0.25 < ES < 0.05) compared with the linear 2-parameter model (-0.99 < ES < 0.47). The predicted performances were significantly correlated to the actual performances (r > 0.46; p < 0.01). The bias ± limits of agreement for the 3,000-; 5,000-; and 10,000-m performances were 1.0 ± 12.8, -0.1 ± 6.9, and 0.1 ± 20.8% and 3.7 ± 15.5, -1.4 ± 6.2, and 2.5 ± 10.6% for prediction from the nomogram and distance-time relationship, respectively. Although the modeling of the distance-time relationship does not enable middle-running performances to be accurately predicted, the precision in the predictions from the nomogram suggests that the nomogram may be used to prescribe adapted training intensities and determine the optimal strategy during the race.

Isoperformance curves: an application in team selection

An isoperformance curve (or surface) defines combinations of two (or more) physiological attributes of individuals such that equal performances for a specified event would be expected of them. Parameters from the two- and three-parameter critical power models are used to illustrate the concept. There are a number of sporting races where teams of individuals compete simultaneously as a unit. Rowing and team pursuit cycling are two well-known examples. Team selection may be difficult if there are more candidates available than places in the team. Based on the assumption that team members should be evenly matched with respect to performance rather than physiological attributes, proximity to a particular isoperformance curve (or surface) may suggest an obvious grouping of individuals. Isoperformance lines also enable identification of an athlete's individual training needs, since the components of the isoperformance lines can be affected by specific training interventions.

Validity of a nomogram to predict long distance running performance

The purpose was to test the validity of a nomogram to predict performance at distances ranging from the 10 km to the marathon. Official running rankings of the French Athletics Federation for the men's 10 km, 20 km, and marathon were scrutinized from 2002 to 2006. Performances of runners who competed in the 3 distances during the same year were noted (n = 330). Predicted performance by the nomogram was obtained for each distance from the performance at 2 other distances. Actual and predicted performances were compared by a Wilcoxon matched pairs test. The magnitude of the difference was assessed by the effect size (ES). Correlation and Bland-Altman plots were used to evaluate the association and the level of agreement between actual and predicted performances. The nomogram overestimated performance at the 10-km distance (13 seconds; p = 0.03) and underestimated performance at the 20-km distance (27 seconds; p < 0.01). The overestimation for the marathon was not significant (85 seconds; p = 0.06). Whatever the distance, ES were trivial (-0.04 < ES < 0.05). Correlations were 0.89 for the 10 km and the marathon and 0.97 for the 20 km. The limits of agreement represented 10.2, 6.1, and 13.2% of the mean of actual and predicted performances in 10 km, 20 km, and marathon, respectively. These results support the validity of the nomogram to predict performance on 10 km, 20 km, and marathon from the performance at 2 other distances. The accuracy of predictions is better when performance is interpolated. Given their validity and accuracy, interpolated predictions of the nomogram may be used to prescribe realistic training intensities during tempo runs, but also to determine the optimal strategy during the race.

Bioenergetic provision of energy for muscular activity

A complex series of metabolic pathways are present in human muscle that break down substrates from nutritional sources to produce energy for different types of muscular activity. However, depending on the activity in which an individual is engaged, the body will make use of different energy systems that have been adapted for the particular activity. More specifically, utilization of bioenergetic substrates depends on the type, intensity, and duration of the exercise. The aerobic oxidative system is used for longer duration activities of low to moderate intensity, the anaerobic glycolytic system is used for short to moderate duration activities of higher intensity, and the high energy phosphagen system is used for short duration activities of high intensity. The efficiency and effectiveness of these pathways can be enhanced through physical activity and training. It is these bioenergetic pathways that are the focus of this review.

The distance – time relationship over a century of running Olympic performances: A limit on the critical speed concept

We analyse the evolution of the slope (critical speed) and the y-intercept (anaerobic distance capacity) of the linear distance-time relationship over a century of Olympic running performances. The distance-time relationship of each Olympic Games (1920-2004) was plotted using the performances in the 800-, 1500- and 5000-m track events. Values for critical speed and anaerobic distance capacity were determined by linear modelling. Mean performances for the 800, 1500 and 5000 m were 104.9 +/- 1.5 s (1.4%), 217.2 +/- 2.8 s (1.3%) and 808.9 +/- 18.4 s (2.3%), respectively. Critical speed improved during the first three-quarters of the twentieth century to reach a plateau in 1984. This is in accordance with the literature (Peronnet & Thibault, 1989) and suggests that "human aerobic endurance" has improved within the century (+13.4%) and tends to stabilize. Anaerobic distance capacity was highly variable over the century (coefficient of variation = 9.4%) and did not show a linear improvement over the years as has previously been suggested (Peronnet & Thibault, 1989). This could be due to an artefact in the application of the two-parameter model to only three Olympic performances. A limitation to the use of this linear mathematical model to fit physiological data may have been demonstrated.

Vmax estimate from three-parameter critical velocity models: validity and impact on 800 m running performance prediction

The purpose of this study was to evaluate the validity of maximal velocity (Vmax) estimated from three-parameter systems models, and to compare the predictive value of two- and three-parameter models for the 800 m. Seventeen trained male subjects (VO2max=66.54+/-7.29 ml min(-1) kg(-1)) performed five randomly ordered constant velocity tests (CVT), a maximal velocity test (mean velocity over the last 10 m portion of a 40 m sprint) and a 800 m time trial (V 800 m). Five systems models (two three-parameter and three two-parameter) were used to compute V max (three-parameter models), critical velocity (CV), anaerobic running capacity (ARC) and V800m from times to exhaustion during CVT. Vmax estimates were significantly lower than (0.19<Bias<0.24 m s(-1)) and poorly associated (0.44<r<0.49) with actual Vmax (8.43+/-0.33 m s(-1)). Critical velocity (CV) alone explained 40-62% of the variance in V800m. Combining CV with other parameters of each model to produce a calculated V800m resulted in a clear improvement of this relationship (0.83<r<0.94). Three-parameter models had a better association (0.93<r<0.94) and a lower bias (0.00<Bias<0.04 m s(-1)) with actual V800 m (5.87+/-0.49 m s(-1)) than two-parameter models (0.83<r<0.91, 0.06<Bias<0.20). If three-parameter models appear to have a better predictive value for short duration events such as the 800 m, the fact the Vmax is not associated with the ability it is supposed to reflect suggests that they are more empirical than systems models.

Estimation of the Parameters of the Relationship Between Power and Time to Exhaustion From a Single Ramp Test

This study aimed to estimate the power/time relationship from a single ramp test (RT) assuming critical power (Pc) from ventilatory threshold (VT) and energy reserve (W') from total work during RT. These estimates from single RT were compared to those from a series of 4 constant power exercises (CPT) and from a series of 4 RT. Only W' from CPT was higher than from the series of RT and from single RT using VT (p <  0.05). Key words: exercise testing, critical power, anaerobic work capacity, cycle ergometry

The critical power and related whole-body bioenergetic models

This paper takes a performance-based approach to review the broad expanse of literature relating to whole-body models of human bioenergetics. It begins with an examination of the critical power model and its assumptions. Although remarkably robust, this model has a number of shortcomings. Attention to these has led to the development of more realistic and more detailed derivatives of the critical power model. The mathematical solutions to and associated behaviour of these models when subjected to imposed "exercise" can be applied as a means of gaining a deeper understanding of the bioenergetics of human exercise performance.

Validity of the two-parameter model in estimating the anaerobic work capacity

The curvature of the power-time (P-t) relationship (W') has been suggested to be constant when exercising above critical power (CP) and to represent the anaerobic work capacity (AWC). The aim of this study was to compare W' to (1) the total amount of work performed above CP (W (90s)') and (2) the AWC, both determined from a 90s all-out fixed cadence test. Fourteen participants (age 30.5 +/- 6.5 years; body mass 67.8 +/- 10.3 kg), following an incremental VO(2max) ramp protocol, performed three constant load exhaustion tests set at 103 +/- 3, 97 +/- 3 and 90 +/- 2% P-VO(2max) to calculate W' from the P-t relationship. Two 90s all-out efforts were also undertaken to determine W (90s)' (power output-time integral above CP) and AWC (power output-time integral above the power output expected from the measured VO(2)). W' (13.6 +/- 1.3 kJ) and W (90s)' (13.9 +/- 1.1 kJ; P = 0.96) were not significantly different but were lower than AWC (15.9 +/- 1.2 kJ) by 24% (P = 0.03) and 17%, respectively (P = 0.04). All these variables were correlated (P < 0.001) but great extents of disagreement were reported (0.2 +/- 6.4 kJ between W' and W (90s)', 2.3 +/- 7.2 kJ between W' and AWC, and 2.1 +/- 4.3 kJ between W (90s)' and AWC). The underestimation of AWC from both W' and W (90s)' can be explained by the aerobic inertia not taking into consideration when determining the two latter variables. The low extents of agreement between W', W (90s)' and AWC mean the terms should not be used interchangeably.

Alternative strategies for exercise critical power estimation in patients with COPD

Exercise critical power (CP) has been shown to represent the highest sustainable work rate (WR) in patients with chronic obstructive pulmonary disease (COPD). Parameter estimation, however, depends on 4 high-intensity tests performed, on different days, to the limit of tolerance (T(lim)). In order to establish a milder protocol that would be more suitable for disabled patients, we contrasted CP derived from 4, 3 and 2 tests (CP4, CP3 and CP2) in 8 males with moderate COPD. In addition, CP was calculated from 2 single-day tests performed on an inverse sequence (CP(2AB) and CP(2BA)): CP values within 5 W from CP4 were assumed as "clinically-acceptable" estimates. We found that [CP4-CP3] and [CP4-CP2] differences were within 5 W in 8 and 6 patients, respectively (95% confidence interval of the differences = -1.3 to 3.5 W and -11.5 to 6.5 W). There was a systematic decline on T(lim) when an exercise bout was performed after a previous test on the same day (P<0.05). Consequently, substantial differences were found between CP4 and any of the CP estimates obtained from single-day tests. In conclusion, clinically-acceptable estimates of CP can be obtained by using 3 or, in most circumstances, 2 constant WR tests in patients with moderate COPD--provided that they are not performed on the same day.

Comparison between maximal power in the power-endurance relationship and maximal instantaneous power

The purpose of this study was to analyze the relevance of introducing the maximal power (P(m)) into a critical-power model. The aims were to compare the P(m) with the instantaneous maximal power (P(max)) and to determine how the P(m) affected other model parameters: the critical power ( P(c)) and a constant amount of work performed over P(c)(W'). Twelve subjects [22.9 (1.6) years, 179 (7) cm, 74.1 (8.9) kg, 49.4 (3.6) ml/min/kg] completed one 15 W/min ramp test to assess their ventilatory threshold (VT), five or six constant-power to exhaustion tests with one to measure the maximal accumulated oxygen deficit (MAOD), and six 5-s all-out friction-loaded tests to measure P(max) at 75 rpm, which was the pedaling frequency during tests. The power and time to exhaustion values were fitted to a 2-parameter hyperbolic model (NLin-2), a 3-parameter hyperbolic model (NLin-3) and a 3-parameter exponential model (EXP). The P(m) values from NLin-3 [760 (702) W] and EXP [431 (106) W] were not significantly correlated with the P(max) at 75 rpm [876 (82) W]. The P(c) value estimated from NLin-3 [186 (47) W] was not significantly correlated with the power at VT [225 (32) W], contrary to other models ( P <0.001). The W' from NLin-2 [25.7 (5.7) kJ] was greater than the MAOD [14.3 (2.7) kJ, P < 0.001] with a significant correlation between them (R = 0.76, P <0.01). For NLin-3, computation of W (P > P c), the amount of work done over P(C), yielded results similar to the W' value from NLin-2: 27.8 (7.4) kJ, which correlated significantly with the MAOD (R = 0.72, P <0.01). In conclusion, the P(m) was not related to the maximal instantaneous power and did not improve the correlations between other model parameters and physiological variables.

Methods to determine aerobic endurance

Physiological testing of elite athletes requires the correct identification and assessment of sports-specific underlying factors. It is now recognised that performance in long-distance events is determined by maximal oxygen uptake (V(2 max)), energy cost of exercise and the maximal fractional utilisation of V(2 max) in any realised performance or as a corollary a set percentage of V(2 max) that could be endured as long as possible. This later ability is defined as endurance, and more precisely aerobic endurance, since V(2 max) sets the upper limit of aerobic pathway. It should be distinguished from endurance ability or endurance performance, which are synonymous with performance in long-distance events. The present review examines methods available in the literature to assess aerobic endurance. They are numerous and can be classified into two categories, namely direct and indirect methods. Direct methods bring together all indices that allow either a complete or a partial representation of the power-duration relationship, while indirect methods revolve around the determination of the so-called anaerobic threshold (AT). With regard to direct methods, performance in a series of tests provides a more complete and presumably more valid description of the power-duration relationship than performance in a single test, even if both approaches are well correlated with each other. However, the question remains open to determine which systems model should be employed among the several available in the literature, and how to use them in the prescription of training intensities. As for indirect methods, there is quantitative accumulation of data supporting the utilisation of the AT to assess aerobic endurance and to prescribe training intensities. However, it appears that: there is no unique intensity corresponding to the AT, since criteria available in the literature provide inconsistent results; and the non-invasive determination of the AT using ventilatory and heart rate data instead of blood lactate concentration ([La(-)](b)) is not valid. Added to the fact that the AT may not represent the optimal training intensity for elite athletes, it raises doubt on the usefulness of this theory without questioning, however, the usefulness of the whole [La(-)](b)-power curve to assess aerobic endurance and predict performance in long-distance events.

Maximal endurance time at VO2max

INTRODUCTION

There has been significant recent interest in the minimal running velocity which elicits VO2max. There also exists a maximal velocity, beyond which the subject becomes exhausted before VO2max is reached. Between these limits, there must be some velocity that permits maximum endurance at VO2max, and this parameter has also been of recent interest. This study was undertaken to model the system and investigate these parameters.

METHODS

We model the bioenergetic process based on a two-component (aerobic and anaerobic) energy system, a two-component (fast and slow) oxygen uptake system, and a linear control system for maximal attainable velocity resulting from declining anaerobic reserves as exercise proceeds. Ten male subjects each undertook four trials in random order, running until exhaustion at velocities corresponding to 90, 100, 120, and 140% of the minimum velocity estimated as being required to elicit their individual VO2max.

RESULTS

The model development produces a skewed curve for endurance time at VO2max, with a single maximum. This curve has been successfully fitted to endurance data collected from all 10 subjects (R2 = 0.821, P < 0.001). For this group of subjects, the maximal endurance time at VO2max can be achieved running at a pace corresponding to 88% of the minimal velocity, which elicits VO2max as measured in an incremental running test. Average maximal endurance at VO2max is predicted to be 603 s in a total endurance time of 1024 s at this velocity.

CONCLUSION

Endurance time at VO2max can be realistically modeled by a curve, which permits estimation of several parameters of interest; such as the minimal running velocity sufficient to elicit VO2max, and that velocity for which endurance at VO2max is the longest.

Simulated front crawl swimming performance related to critical speed and critical power

PURPOSE

Competitive pool swimming events range in distance from 50 to 1500 m. Given the difference in performance times (+/- 23-1000 s), the contribution of the aerobic and anaerobic energy systems changes considerably with race distance. In training practice the regression line between swimming distance and time (Distance = critical velocity x time + anaerobic swimming capacity) is used to determine the individual capacity of the aerobic and anaerobic metabolic pathways. Although there is confidence that critical velocity and anaerobic swimming capacity are fitness measures that separate aerobic and anaerobic components, a firm theoretical basis for the interpretation of these results does not exist. The purpose of this study was to evaluate the critical power concept and anaerobic swimming capacity as measures of the aerobic and anaerobic capacity using a modeling approach.

METHODS

A systems model was developed that relates the mechanics and energetics involved in front crawl swimming performance. From actual swimming flume measurements, the time dependent aerobic and anaerobic energy release was modeled. Data derived from the literature were used to relate the energy cost of front crawl swimming to swimming velocity. A balance should exist between the energy cost to swim a distance in a certain time and the concomitant aerobic and anaerobic energy release. The ensuing model was used to predict performance times over a range of distances (50-1500 m) and to calculate the regression line between swimming distance and time.

RESULTS AND CONCLUSIONS

Using a sensitivity analysis, it was demonstrated that the critical velocity is indicative for the capacity of the aerobic energy system. Estimates of the anaerobic swimming capacity, however, were influenced by variations in both anaerobic and aerobic energy release. Therefore, it was concluded that the anaerobic swimming capacity does not provide a reliable estimate of the anaerobic capacity.

Alternative forms of the critical power test for ramp exercise

The critical power test provides estimates of two important parameters characterizing work performance; anaerobic work capacity (AWC) and critical power (CP). The CP concept has recently been adapted to a test procedure involving ramp exercise. Just as the constant power format of the CP test can be expressed in several mathematically equivalent forms, so too can the ramp format. This communication illustrates these forms and tests the various AWC and CP estimates so obtained. It is found that three of the four forms provide equivalent estimates for both AWC and CP. It is concluded that provided either endurance time or total work performed is taken as the dependent variable, researchers can expect consistent estimates for both AWC and CP.