The critical power and related whole-body bioenergetic models

Wearable heart rate sensing and critical power-based whole-body fatigue monitoring in the field

Whole-body fatigue (WBF) presents a concerning risk to construction workers, which can impact function and ultimately lead to accidents and diminished productivity. This study proposes a new WBF monitoring technique by applying the Critical Power (CP) model, a bioenergetic model, with a wrist-worn heart rate sensor. The authors modified the CP model to calculate WBF from the percentage of heart rate reserve (%HRR) and generated a personalized model via WBF perception surveys. Data were collected for two days from 33 workers at four construction sites. The results showed that the proposed technique can monitor field workers' perceived WBF with a mean absolute error of 12.8% and Spearman correlation coefficient of 0.83. This study, therefore, demonstrates the viability of wearable WBF monitoring on construction sites to support programs aimed at improving workplace safety and productivity.

Critical Power and Maximal Lactate Steady State in Cycling: "Watts" the Difference?

From a physiological perspective, the delineation between steady-state and non-steady-state exercise, also referred to as the maximal metabolic steady state, holds paramount importance for evaluating athletic performance and designing and monitoring training programs. The critical power and the maximal lactate steady state are two widely used indices to estimate this threshold, yet previous studies consistently reported significant discrepancies between their associated power outputs. These findings have fueled the debate regarding the interchangeability of critical power and the maximal lactate steady state in practice. This paper reviews the methodological intricacies intrinsic to the determination of these thresholds, and elucidates how inappropriate determination methods and methodological inconsistencies between studies have contributed to the documented differences in the literature. Through a critical examination of relevant literature and by integration of our laboratory data, we demonstrate that differences between critical power and the maximal lactate steady state may be reconciled to only a few Watts when applying appropriate and strict determination criteria, so that both indices may be used to estimate the maximal metabolic steady-state threshold in practice. To this end, we have defined a set of good practice guidelines to assist scientists and coaches in obtaining the most valid critical power and maximal lactate steady state estimates.

Characterizing the Exponential Profile of W' Recovery Following Partial Depletion

PURPOSE

The aim of this study was to characterize W' recovery kinetics in response to a partial W' depletion. We hypothesized that W' recovery following a partial depletion would be better described by a biexponential than by a monoexponential model.

METHODS

Nine healthy men performed a ramp incremental exercise test, three to five constant load trials to determine critical power and W', and 10 experimental trials to quantify W' depletion. Each experimental trial consisted of two constant load work bouts (WB1 and WB2) interspersed by a recovery interval. WB1 was designed to evoke a 25% or 75% W' depletion (DEP 25% and DEP 75% ). Subsequently, participants recovered for 30, 60, 120, 300, or 600 s and then performed WB2 to exhaustion to calculate the observed W' recovery (W' OBS ). W' OBS data were fitted using monoexponential and biexponential models, both with a variable and with a fixed model amplitude. Root mean square error and Akaike information criterion (AIC c ) were calculated to evaluate the models' goodness-of-fit.

RESULTS

The biexponential model fits were associated with overall lower root mean square error values (0.4% to 5.0%) when compared with the monoexponential models (2.9% to 8.0%). However, ΔAIC c resulted in negative values (-15.5 and -23.3) for the model fits where the amplitude was kept free, thereby favoring the use of a monoexponential model for both depletion conditions. For the model fits where the amplitude was fixed at 100%, ΔAIC c was negative for DEP 25% (-15.0) but positive for DEP 75% (11.2). W' OBS values were strongly correlated between both depletion conditions ( r = 0.92) and positively associated with V̇O 2peak , critical power, and gas exchange threshold ( r = 0.67 to 0.77).

CONCLUSIONS

The present study results did not provide evidence in favor of a biexponential modeling technique to characterize W' recovery following a partial depletion. Moreover, we demonstrated that fixed time constants were insufficient to model W' recovery across different depletion levels, and that W' recovery was positively associated with aerobic fitness. These findings underline the importance of employing variable and individualized time constants in future predictive W' models.

Energetics of sinusoidal exercise below and across critical power and the effects of fatigue

PURPOSE

Previous studies investigating sinusoidal exercise were not devoted to an analysis of its energetics and of the effects of fatigue. We aimed to determine the contribution of aerobic and anaerobic lactic metabolism to the energy balance and investigate the fatigue effects on the cardiorespiratory and metabolic responses to sinusoidal protocols, across and below critical power (CP).

METHODS

Eight males (26.6 ± 6.2 years; 75.6 ± 8.7 kg; maximum oxygen uptake 52.8 ± 7.9 ml·min-1·kg-1; CP 218 ± 13 W) underwent exhausting sinusoidal cycloergometric exercises, with sinusoid midpoint (MP) at CP (CPex) and 50 W below CP (CP-50ex). Sinusoid amplitude (AMP) and period were 50 W and 4 min, respectively. MP, AMP, and time-delay (tD) between mechanical and metabolic signals of expiratory ventilation (V ˙ E ), oxygen uptake (V ˙ O 2 ), and heart rate ( f H ) were assessed sinusoid-by-sinusoid. Blood lactate ([La-]) and rate of perceived exertion (RPE) were determined at each sinusoid.

RESULTS

V ˙ O 2 AMP was 304 ± 11 and 488 ± 36 ml·min-1 in CPex and CP-50ex, respectively. Asymmetries between rising and declining sinusoid phases occurred in CPex (36.1 ± 7.7 vs. 41.4 ± 9.7 s forV ˙ O 2 tD up and tD down, respectively; P < 0.01), with unchanged tDs.V ˙ O 2 MP and RPE increased progressively during CPex. [La-] increased by 2.1 mM in CPex but remained stable during CP-50ex. Anaerobic contribution was larger in CPex than CP-50ex.

CONCLUSION

The lower aerobic component during CPex than CP-50ex associated with lactate accumulation explained lowerV ˙ O 2 AMP in CPex. The asymmetries in CPex suggest progressive decline of muscle phosphocreatine concentration, leading to fatigue, as witnessed by RPE.

Skeletal muscle mitochondrial correlates of critical power and W' in healthy active individuals

The asymptote (critical power; CP) and curvature constant (W') of the hyperbolic power-duration relationship can predict performance within the severe-intensity exercise domain. However, the extent to which these parameters relate to skeletal muscle mitochondrial content and respiratory function is not known. Fifteen males (peak O2 uptake, 52.2 ± 8.7 mL kg-1 min-1; peak work rate, 366 ± 40 W; and gas exchange threshold, 162 ± 41 W) performed three to five constant-load tests to task failure for the determination of CP (246 ± 44 W) and W' (18.6 ± 4.1 kJ). Skeletal muscle biopsies were obtained from the vastus lateralis to determine citrate synthase (CS) activity, as a marker of mitochondrial content, and the ADP-stimulated respiration (P) and maximal electron transfer (E) through mitochondrial complexes (C) I-IV. The CP was positively correlated with CS activity (absolute CP, r = 0.881, P < 0.001; relative CP, r = 0.751, P = 0.001). The W' was not correlated with CS activity (P > 0.05). Relative CP was positively correlated with mass-corrected CI + IIE (r = 0.659, P = 0.038), with absolute CP being inversely correlated with CS activity-corrected CIVE (r = -0.701, P = 0.024). Relative W' was positively correlated with CS activity-corrected CI + IIP (r = 0.713, P = 0.021) and the phosphorylation control ratio (r = 0.661, P = 0.038). There were no further correlations between CP or W' and mitochondrial respiratory variables. These findings support the assertion that skeletal muscle mitochondrial oxidative capacity is positively associated with CP and that this relationship is strongly determined by mitochondrial content.

Acute alcohol ingestion decreases the work done above the end-test power during a 3-min all-out cycling exercise

INTRODUCTION

Alcohol ingestion influences metabolism during a subsequent exercise session, as evidenced by increased blood lactate concentration during fixed-intensity exercise. Therefore, augmented blood concentrations of alcohol may interfere with the anaerobic metabolism during high-intensity, short-duration exercise bout, thereby leading to impaired athletic performance.

OBJECTIVE

This study investigated whether the acute ingestion of alcohol as ethanol modulates performance parameters derived from the power-duration relationship in a 3-min all-out cycling test that allows for identifying the power output related to heavy and severe exercise intensities.

METHODS

Twenty-four recreationally active cyclists (16 men and 8 women) ingested a beverage containing either 0.4 g ethanol.kg-1 body mass (EtOH) or a placebo (PLA) solution. Thirty minutes following ingestion, they completed a 3-min all-out test to measure power output and determine the end-test power (EP) and the work done above EP (WEP).

RESULTS

Alcohol ingestion decreased WEP by 16% (EtOH: 5.6 ± 2.5 kJ vs. PLA: 6.7 ± 2.4 kJ; P = .003) but did not change EP (EtOH: 211 ± 44 W vs. PLA: 212 ± 44 W; P = .671). The alcohol-mediated effect in WEP was not influenced when controlling for participants' sex or accuracy in identifying the beverage ingested.

CONCLUSION

Our data indicate that alcohol ingestion impaired the anaerobic work capacity, as evidenced by the reduction in WEP during the 3-min all-out test. Moreover, the ability to exercise at an intensity above the heavy domain may be decreased after ingestion of a moderate alcohol dose.

Modelling the optimization of world-class 400 m and 1,500 m running performances using high-resolution data

The 400 m and 1,500 m are track events that rely on different but important contributions from both the aerobic and anaerobic energy systems. The purpose of this study is to model men's and women's 400 m and 1,500 m championship performances to gain a deeper understanding of the key mechanical and physiological factors affecting running speed and bend running using high-resolution data from live competition (10 Hz). To investigate World-class athletes' instantaneous speeds, propulsive forces and aerobic and anaerobic energy, we model and simulate the performances of the men's and women's European Athletics 400 m champions, Matthew Hudson-Smith and Femke Bol, as well as the men's European Athletics 1,500 m champion, Jakob Ingebrigtsen, and the women's European Athletics U23 1,500 m champion, Gaia Sabbatini. The simulations show that a fast start is essential in both the 400 m and 1,500 m because of the need for fast oxygen kinetics, with peak running speeds occurring within the first ∼50 m in both events. Subsequently, 400 m athletes slow continually from this maximum speed to the finish, and a total anaerobic contribution of ∼77% is found for both male and female champions. The key to faster 400 m racing is to reduce the decrease in velocity: this comes from both a high VO2 and a high anaerobic contribution. Ingebrigtsen's winning tactic in the European 1,500 m final is to adopt a very fast cruising pace from 300 m onwards that is possible because he is able to maintain a high VO2 value until the end of the race and has a large anaerobic contribution. He has fast VO2 kinetics that does not require as fast a start as his opponents, but then he speeds up in the last two laps, without a fast sprint finish. The comparison between Sabbatini's slower and quicker races (∼8 s difference) shows that it is the improvement of aerobic metabolism that has the greatest effect on 1,500 m performance. Coaches should note in particular that the all-out pacing nature of the 400 m requires the prioritization of anaerobic energy system development, and those who coach the 1,500 m should note the differing energy contributions between even-paced races and championship racing.

Individualized physiology-based digital twin model for sports performance prediction: a reinterpretation of the Margaria-Morton model

Performance in many racing sports depends on the ability of the athletes to produce and maintain the highest possible work i.e., the highest power for the duration of the race. To model this energy production in an individualized way, an adaptation and a reinterpretation (including a physiological meaning of parameters) of the three-component Margaria-Morton model were performed. The model is applied to the muscles involved in a given task. The introduction of physiological meanings was possible thanks to the measurement of physiological characteristics for a given athlete. A method for creating a digital twin was therefore proposed and applied for national-level cyclists. The twins thus created were validated by comparison with field performance, experimental observations, and literature data. Simulations of record times and 3-minute all-out tests were consistent with experimental data. Considering the literature, the model provided good estimates of the time course of muscle metabolite concentrations (e.g., lactate and phosphocreatine). It also simulated the behavior of oxygen kinetics at exercise onset and during recovery. This methodology has a wide range of applications, including prediction and optimization of the performance of individually modeled athletes.

Metabolic cost and mechanical work of walking in a virtual reality emulator

PURPOSE

The purpose of this study was to investigate the metabolic cost (C), mechanical work, and kinematics of walking on a multidirectional treadmill designed for locomotion in virtual reality.

METHODS

Ten participants (5 females, body mass 67.2 ± 8.1 kg, height 1.71 ± 0.07 m, age 23.6 ± 1.9 years, mean ± SD) walked on a Virtuix Omni multidirectional treadmill at four imposed stride frequencies: 0.70, 0.85, 1.00, and 1.15 Hz. A portable metabolic system measured oxygen uptake, enabling calculation of C and the metabolic equivalent of task (MET). Gait kinematics and external, internal, and total mechanical work (WTOT) were calculated by an optoelectronic system. Efficiency was calculated either as WTOT/C or by summing WTOT to the work against sliding frictions. Results were compared with normal walking, running, and skipping.

RESULTS

C was higher for walking on the multidirectional treadmill than for normal walking, running, and skipping, and decreased with speed (best-fit equation: C = 20.2-27.5·speed + 15.8·speed2); the average MET was 4.6 ± 1.4. Mechanical work was higher at lower speeds, but similar to that of normal walking at higher speeds, with lower pendular energy recovery and efficiency; differences in efficiency were explained by the additional work against sliding frictions. At paired speeds, participants showed a more forward-leaned trunk and higher ankle dorsiflexion, stride frequency, and duty factor than normal walking.

CONCLUSION

Walking on a multidirectional treadmill requires a higher metabolic cost and different mechanical work and kinematics than normal walking. This raises questions on its use for gait rehabilitation but highlights its potential for high-intensity exercise and physical activity promotion.

Mathematical modeling of exercise fatigability in the severe domain: A unifying integrative framework in isokinetic condition

Muscle fatigue is the decay in the ability of muscles to generate force, and results from neural and metabolic perturbations. This article presents an integrative mathematical model that describes the decrease in maximal force capacity (i.e. fatigue) over exercises performed at intensities above the critical force Fc (i.e. severe domain). The model unifies the previous Critical Power Model and All-Out Model and can be applied to any exercise described by a changing force F over time. The assumptions of the model are (i) isokinetic conditions, an intensity domain of Fc Collapse

Key Words

• All-out
• Anaerobic capacities
• Critical power
• Endurance
• Exercise fatigability
• Fatigue
• Maximal force capacity
• Muscular capacities
• Power-time relationship
• Time to exhaustion

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MESH Headings

• Exercise/physiology
• Muscle Fatigue
• Muscles/physiology
• Models, Theoretical
• Muscle, Skeletal/physiology

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Grants Collapse

Affiliation(s)

M Bowen Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France.
P Samozino Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France
M Vonderscher Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France
D Dutykh Mathematics Department, Khalifa University of Science and Technology, PO Box 127788, Abu Dhabi, United Arab Emirates; Causal Dynamics Pty Ltd, WA 6009, Perth, Australia
B Morel Laboratoire Interuniversitaire de Biologie de la Motricité LIBM, EA 7424, Savoie Mont Blanc University, F-7300, Chambéry, France

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Critical power, W' and W' reconstitution in women and men

PURPOSE

The aim of this study was to compare critical power (CP) and work capacity W', and W' reconstitution (W'REC) following repeated maximal exercise between women and men.

METHODS

Twelve women ([Formula: see text]O2PEAK: 2.53 ± 0.37 L·min-1) and 12 men ([Formula: see text]O2PEAK: 4.26 ± 0.30 L·min-1) performed a minimum of 3 constant workload tests, to determine CP and W', and 1 maximal exercise repetition test with three work bouts (WB) to failure, to quantify W'REC during 2 recovery periods, i.e., W'REC1 and W'REC2. An independent samples t test was used to compare CP and W' values between women and men, and a repeated-measures ANOVA was used to compare W'REC as fraction of W' expended during the first WB, absolute W'REC, and normalized to lean body mass (LBM).

RESULTS

CP normalized to LBM was not different between women and men, respectively, 3.7 ± 0.5 vs. 4.1 ± 0.4 W·kgLBM-1, while W' normalized to LBM was lower in women 256 ± 29 vs. 305 ± 45 J·kgLBM-1. Fractional W'REC1 was higher in women than in men, respectively, 74.0 ± 12.0% vs. 56.8 ± 9.5%. Women reconstituted less W' than men in absolute terms (8.7 ± 1.2 vs. 10.9 ± 2.0 kJ) during W'REC1, while normalized to LBM no difference was observed between women and men (174 ± 23 vs. 167 ± 31 J·kgLBM-1). W'REC2 was lower than W'REC1 both in women and men.

CONCLUSION

Sex differences in W'REC (absolute women < men; fractional women > men) are eliminated when LBM is accounted for. Prediction models of W'REC might benefit from including LBM as a biological variable in the equation. This study confirms the occurrence of a slowing of W'REC during repeated maximal exercise.

A Single, Multimodal Exercise Tolerance Test Can Assess Combat Readiness in Army-ROTC Cadets: A Brief Report

The Army Combat Fitness Test (ACFT) is a multi-event assessment battery designed to determine the combat readiness of U.S. Army personnel. However, for Reserve Officers' Training Corps (ROTC) programs the logistical demands of collegiate life make repeated administration of the ACFT challenging. The present study sought to design and evaluate a single, multimodal exercise tolerance test (METT) capable of serving as a time-efficient proxy measure of combat readiness.

METHODS

Using a formal instrument design process, we constructed the METT to mimic the demands of the ACFT and assessed its reliability, validity, and responsiveness.

RESULTS

The METT demonstrates minimal measurement error (i.e., a 2% coefficient of variation), concurrent validity with the ACFT (R2 = 0.327, F = 10.67, p < 0.001), the ability to classify cadets who may be at-risk for failing the ACFT (X2 = 8.16, p = 0.017, sensitivity = 0.878, specificity = 0.667), and appropriate change following a training intervention (5.69 ± 8.9%).

CONCLUSIONS

The METT has the potential to provide a means to monitor progress, identify areas for improvement, and guide informed decision-making regarding individualization of cadet combat training plans.

Critical Velocity, Maximal Lactate Steady State, and Muscle MCT1 and MCT4 after Exhaustive Running in Mice

Although the critical velocity (CV) protocol has been used to determine the aerobic capacity in rodents, there is a lack of studies that compare CV with maximal lactate steady state intensity (iMLSS) in mice. As a consequence, their physiological and molecular responses after exercise until exhaustion at CV intensity remain unclear. Thus, we aimed to compare and correlate CV with iMLSS in running mice, following different mathematical models for CV estimation. We also evaluated their physiological responses and muscle MCT1 and MCT4 after running until exhaustion at CV. Thirty C57BL/6J mice were divided into two groups (exercised-E and control-C). Group E was submitted to a CV protocol (4 days), using linear (lin1 and lin2) and hyperbolic (hyp) mathematical models to determine the distance, velocity, and time to exhaustion (tlim) of each predictive CV trial, followed by an MLSS protocol. After a running effort until exhaustion at CV intensity, the mice were immediately euthanized, while group C was euthanized at rest. No differences were observed between iMLSS (21.1 ± 1.1 m.min-1) and CV estimated by lin1 (21.0 ± 0.9 m.min-1, p = 0.415), lin2 (21.3 ± 0.9 m.min-1, p = 0.209), and hyp (20.6 ± 0.9 m.min-1, p = 0.914). According to the results, CV was significantly correlated with iMLSS. After running until exhaustion at CV (tlim = 28.4 ± 8,29 min), group E showed lower concentrations of hepatic and gluteal glycogen than group C, but no difference in the content of MCT1 (p = 0.933) and MCT4 (p = 0.123) in soleus muscle. Significant correlations were not found between MCT1 and MCT4 and tlim at CV intensity. Our results reinforce that CV is a valid and non-invasive protocol to estimate the maximal aerobic capacity in mice and that the content of MCT1 and MCT4 was not decisive in determining the tlim at CV, at least when measured immediately after the running effort.

Can we predict long-duration running power output? A matter of selecting the appropriate predicting trials and empirical model

When facing a long-distance race, athletes and practitioners could develop an efficient pacing strategy and training paces if an accurate performance estimate of the target distance is achieved. Therefore, this study aims to determine the validity of different empirical models (i.e. critical power [CP], Power law and Peronnet) to predict long-duration power output (i.e. 60 min) when using two or three time trial configurations. In a 5-week training period, fifteen highly trained athletes performed nine-time trials (i.e. 1, 2, 3, 4, 5, 10, 20, 30, and 60 min) in a randomized order. Their power-duration curves were defined through the work-time (CPwork), power-1/time (CP1/time), two-parameter hyperbolic (CP2hyp), three-parameter hyperbolic (CP3hyp) CP models using different two- and three-time trial configurations. The undisclosed proprietary CP models of the Stryd (CPstryd) and Golden Cheetah training software (CPcheetah) were also computed as well as the non-asymptotic Power law and Peronnet models. These were extrapolated to the 60-min power output and compared to the actual performance. The shortest valid configuration (95% confidence interval < 12 W) for CPwork and CP1/time was 3-30 min (Bias: 8.3 [4.9 to 11.7] W), for CPstryd was 10-30 min (Bias: 4.2 [- 1.0 to 9.4] W), for CP2hyp, CP3hyp and CPcheetah was 3-5-30 min (Bias < 5.7 W), for Power law was 1-3-10 min (- 1.0 [- 11.9 to 9.9] W), and for Peronnet was 4-20 min (- 3.0 [- 10.2 to 4.3] W). All the empirical models provided valid estimates when the two or three predicting trial configurations selected attended each model fitting needs.

Critical Power and Respiratory Compensation Point Are Not Equivalent in Patients with COPD

INTRODUCTION

Several studies report that pulmonary oxygen uptake (V̇O 2 ) at the respiratory compensation point (RCP) is equivalent to the V̇O 2 at critical power (CP), suggesting that the variables can be used interchangeably to demarcate the threshold between heavy and severe intensity domains. However, if RCP is a valid surrogate for CP, their values should correspond even when assessed in patients with chronic obstructive pulmonary disease (COPD) in whom the "normal" mechanisms linking CP and RCP are impeded. The aim of this study was to compare V̇O 2 at CP with V̇O 2 at RCP in patients with COPD.

METHODS

Twenty-two COPD patients (14 male/8 female; forced expiratory volume in 1 s, 46% ± 17% pred) performed ramp-incremental cycle ergometry to intolerance (5-10 W·min -1 ) for the determination of gas exchange threshold (GET) and RCP. CP was calculated from the asymptote of the hyperbolic power-duration relationship from 3-5 constant-power exercise tests to intolerance. CP was validated with a 20-min constant-power ride.

RESULTS

GET was identified in 20 of 22 patients at a V̇O 2 of 0.93 ± 0.18 L·min -1 (75% ± 13% V̇O 2peak ), whereas RCP was identified in just 3 of 22 patients at a V̇O 2 of 1.40 ± 0.39 L·min -1 (85% ± 2% V̇O 2peak ). All patients completed constant-power trials with no difference in peak physiological responses relative to ramp-incremental exercise ( P > 0.05). CP was 46 ± 22 W, which elicited a V̇O 2 of 1.04 ± 0.29 L·min -1 (90% ± 9% V̇O 2peak ) during the validation ride. The difference in V̇O 2 at 15 and 20 min of the validation ride was 0.00 ± 0.04 L, which was not different from a hypothesized mean of 0 ( P = 0.856), thereby indicating a V̇O 2 steady state.

CONCLUSIONS

In COPD patients, who present with cardiopulmonary and/or respiratory-mechanical dysfunction, CP can be determined in the absence of RCP. Accordingly, CP and RCP are not equivalent in this group.

Optimally controlling nutrition and propulsion force in a long distance running race

Introduction

Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies.

Methods

We formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem.

Results

As the goal of an optimal control model is to determine the optimal strategy, comparing our results against real data presents a challenge; however, in comparing our results to the world record for the marathon, our results differed by 0.4%, 31 seconds. Per each additional gel consumed, the runner is able to run 0.5 to 0.7 kilometers further in the same amount of time, resulting in a 7.75% increase in taking five 100 calorie gels vs no nutrition.

Discussion

Our results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero, by consuming in-race nutrition. While this model does not take all factors into account, we consider it a building block for future models, considering our novel energy representation, and in-race nutrition.

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.

Effect of varying recovery intensities on power outputs during severe intensity intervals in trained cyclists during the Covid-19 pandemic

Purpose

The study aimed to investigate the effects of different recovery intensities on the power outputs of repeated severe intensity intervals and the implications for W' reconstitution in trained cyclists.

Methods

Eighteen trained cyclists (FTP 258.0 ± 42.7 W; weekly training 8.6 ± 1.7 h∙week-1) familiar with interval training, use of the Zwift® platform throughout the Covid-19 pandemic, and previously established FTP (95% of mean power output from a 20-min test), performed 5 × 3-min severe intensity efforts interspersed with 2-min recoveries. Recovery intensities were: 50 W (LOW), 50% of functional threshold power (MOD), and self-selected power output (SELF).

Results

Whilst power outputs declined as the session progressed, mean power outputs during the severe intervals across the conditions were not different to each other (LOW 300.1 ± 48.1 W; MOD: 296.9 ± 50.4 W; SELF: 298.8 ± 53.3 W) despite the different recovery conditions. Mean power outputs of the self-selected recovery periods were 121.7 ± 26.2 W. However, intensity varied during the self-selected recovery periods, with values in the last 15 s being greater than the first 15 s (p < 0.001) and decreasing throughout the session (128.7 ± 25.4 W to 113.9 ± 29.3 W).

Conclusion

Reducing recovery intensities below 50% of FTP failed to enhance subsequent severe intensity intervals, suggesting that a lower limit for optimal W' reconstitution had been reached. As self-selected recoveries were seen to adapt to maintain the severe intensity power output as the session progressed, adopting such a strategy might be preferential for interval training sessions.

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.

Anaerobic work capacity in cycling: the effect of computational method

Purpose

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

Methods

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

Results

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

Conclusion

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

Animal Models of Exercise From Rodents to Pythons

Acute and chronic animal models of exercise are commonly used in research. Acute exercise testing is used, often in combination with genetic, pharmacological, or other manipulations, to study the impact of these manipulations on the cardiovascular response to exercise and to detect impairments or improvements in cardiovascular function that may not be evident at rest. Chronic exercise conditioning models are used to study the cardiac phenotypic response to regular exercise training and as a platform for discovery of novel pathways mediating cardiovascular benefits conferred by exercise conditioning that could be exploited therapeutically. The cardiovascular benefits of exercise are well established, and, frequently, molecular manipulations that mimic the pathway changes induced by exercise recapitulate at least some of its benefits. This review discusses approaches for assessing cardiovascular function during an acute exercise challenge in rodents, as well as practical and conceptual considerations in the use of common rodent exercise conditioning models. The case for studying feeding in the Burmese python as a model for exercise-like physiological adaptation is also explored.

A critical review of critical power

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

A Fitness-Fatigue Model of Performance in Peripheral Artery Disease: Predicted and Measured Effects of a Pain-Free Exercise Program

Banister impulse-response (IR) model estimates the performance in response to the training impulses (TRIMPs). In 100 patients with peripheral artery disease (PAD), we tested by an IR model the predictability of the effects of a 6-month structured home-based exercise program. The daily TRIMPs obtained from prescribed walking speed, relative intensity and time of exercise determined the fitness-fatigue components of performance. The estimated performance values, calculated from the baseline 6-min and pain-free walking distance (6MWD and PFWD, respectively) were compared with values measured at visits through regression models. Interval pain-free walking at controlled speed prescribed during circa-monthly hospital visits (5 ± 1) was safely performed at home with good adherence (92% of scheduled sessions, 144 ± 25 km walked in 50 ± 8 training hours). The mean TRIMP rose throughout the program from 276 to 601 a.u. The measured 6MWD and PFWD values increased (+33 m and +121 m, respectively) showing a good fit with those estimated by the IR model (6MWD: R² 0.81; PFWD: R² 0.68) and very good correspondence (correlation coefficients: 0.91 to 0.95), without sex differences. The decay of performance without training was estimated at 18 ± 3 weeks. In PAD, an IR model predicted the walking performance following a pain-free exercise program. IR models may contribute to design and verify personalized training programs.

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.

Over 55 years of critical power: Fact or artifact?

This report aims to generate an evidence-based debate of the Critical Power (CP), or its analogous Critical Speed (CS), concept. Race times of top Spanish runners were utilized to calculate CS based on three (1500-m to 5000-m; CS_1.5-5km ) and four (1500-m to 10000-m; CS_1.5-10km ) distance performances. Male running world records from 1000 to 5000-m (CS_1-5km ), 1000 to 10,000-m (CS_1-10km ), 1000-m to half marathon (CS_{1km-half marathon} ), and 1000-m to marathon (CS_1km-marathon ) distance races were also utilized for CS calculations. CS_1.5-5km (19.62 km h^-1 ) and CS_1.5-10km (18.68 km h^-1 ) were different (p < 0.01), but both approached the average race speed of the longest distance chosen in the model, and were remarkably homogeneous among subjects (97% ±1% and 98% ±1%, respectively). Similar results were obtained using the world records. CS values progressively declined, until reaching a CS_1km-marathon value of 20.77 km h^-1 (10% lower than CS_1-5km ). Each CS value approached the average speed of the longest distance chosen in the model (96.4%-99.8%). A power function better fitted the speed-time relationship compared with the standardized hyperbolic function. However, the horizontal asymptote of a power function is zero. This better approaches the classical definition of CP: the power output that can be maintained almost indefinitely without exhaustion. Beyond any sophisticated mathematical calculation, CS corresponds to 95%-99% of the average speed of the longest distance chosen as an exercise trial. CP could be considered a mathematical artifact rather than an important endurance performance marker. In such a case, the consideration of CP as a physiological "gold-standard" should be reevaluated.

Validity and Reliability of Hydraulic-Analogy Bioenergetic Models in Sprint Roller Skiing

Purpose: To develop a method for individual parameter estimation of four hydraulic-analogy bioenergetic models and to assess the validity and reliability of these models' prediction of aerobic and anaerobic metabolic utilization during sprint roller-skiing. Methods: Eleven elite cross-country skiers performed two treadmill roller-skiing time trials on a course consisting of three flat sections interspersed by two uphill sections. Aerobic and anaerobic metabolic rate contributions, external power output, and gross efficiency were determined. Two versions each (fixed or free maximal aerobic metabolic rate) of a two-tank hydraulic-analogy bioenergetic model (2TM-fixed and 2TM-free) and a more complex three-tank model (3TM-fixed and 3TM-free) were programmed into MATLAB. The aerobic metabolic rate (MR _ae ) and the accumulated anaerobic energy expenditure (E _an,acc ) from the first time trial (STT1) together with a gray-box model in MATLAB, were used to estimate the bioenergetic model parameters. Validity was assessed by simulation of each bioenergetic model using the estimated parameters from STT1 and the total metabolic rate (MR _tot ) in the second time trial (STT2). Results: The validity and reliability of the parameter estimation method based on STT1 revealed valid and reliable overall results for all the four models vs. measurement data with the 2TM-free model being the most valid. Mean differences in model-vs.-measured MR _ae ranged between -0.005 and 0.016 kW with typical errors between 0.002 and 0.009 kW. Mean differences in E _an,acc at STT termination ranged between -4.3 and 0.5 kJ and typical errors were between 0.6 and 2.1 kJ. The root mean square error (RMSE) for 2TM-free on the instantaneous STT1 data was 0.05 kW for MR _ae and 0.61 kJ for E _an,acc , which was lower than the other three models (all P < 0.05). Compared to the results in STT1, the validity and reliability of each individually adapted bioenergetic model was worse during STT2 with models underpredicting MR _ae and overpredicting E _an,acc vs. measurement data (all P < 0.05). Moreover, the 2TM-free had the lowest RMSEs during STT2. Conclusion: The 2TM-free provided the highest validity and reliability in MR _ae and E _an,acc for both the parameter estimation in STT1 and the model validity and reliability evaluation in the succeeding STT2.

Biomechanical Response of the Lower Extremity to Running-Induced Acute Fatigue: A Systematic Review

Objective: To investigate (i) typical protocols used in research on biomechanical response to running-induced fatigue, (ii) the effect of sport-induced acute fatigue on the biomechanics of running and functional tests, and (iii) the consistency of analyzed parameter trends across different protocols.

Methods: Scopus, Web of Science, Pubmed, and IEEE databases were searched using terms identified with the Population, Interest and Context (PiCo) framework. Studies were screened following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines and appraised using the methodological index for non-randomized studies MINORS scale. Only experimental studies with at least 10 participants, which evaluated fatigue during and immediately after the fatiguing run were included. Each study was summarized to record information about the protocol and parameter trends. Summary trends were computed for each parameter based on the results found in individual studies.

Results: Of the 68 included studies, most were based on in-lab (77.9%) protocols, endpoint measurements (75%), stationary measurement systems (76.5%), and treadmill environment (54.4%) for running. From the 42 parameters identified in response to acute fatigue, flight time, contact time, knee flexion angle at initial contact, trunk flexion angle, peak tibial acceleration, CoP velocity during balance test showed an increasing behavior and cadence, vertical stiffness, knee extension force during MVC, maximum vertical ground reaction forces, and CMJ height showed a decreasing trend across different fatigue protocols.

Conclusion: This review presents evidence that running-induced acute fatigue influences almost all the included biomechanical parameters, with crucial influence from the exercise intensity and the testing environment. Results indicate an important gap in literature caused by the lack of field studies with continuous measurement during outdoor running activities. To address this gap, we propose recommendations for the use of wearable inertial sensors.

Anaerobic Speed/Power Reserve and Sport Performance: Scientific Basis, Current Applications and Future Directions

Many individual and team sport events require extended periods of exercise above the speed or power associated with maximal oxygen uptake (i.e., maximal aerobic speed/power, MAS/MAP). In the absence of valid and reliable measures of anaerobic metabolism, the anaerobic speed/power reserve (ASR/APR) concept, defined as the difference between an athlete's MAS/MAP and their maximal sprinting speed (MSS)/peak power (MPP), advances our understanding of athlete tolerance to high speed/power efforts in this range. When exercising at speeds above MAS/MAP, what likely matters most, irrespective of athlete profile or locomotor mode, is the proportion of the ASR/APR used, rather than the more commonly used reference to percent MAS/MAP. The locomotor construct of ASR/APR offers numerous underexplored opportunities. In particular, how differences in underlying athlete profiles (e.g., fiber typology) impact the training response for different 'speed', 'endurance' or 'hybrid' profiles is now emerging. Such an individualized approach to athlete training may be necessary to avoid 'maladaptive' or 'non-responses'. As a starting point for coaches and practitioners, we recommend upfront locomotor profiling to guide training content at both the macro (understanding athlete profile variability and training model selection, e.g., annual periodization) and micro levels (weekly daily planning of individual workouts, e.g., short vs long intervals vs repeated sprint training and recovery time between workouts). More specifically, we argue that high-intensity interval training formats should be tailored to the locomotor profile accordingly. New focus and appreciation for the ASR/APR is required to individualize training appropriately so as to maximize athlete preparation for elite competition.

W' reconstitution rate at different intensities above critical torque: the role of muscle size and maximal strength

NEW FINDINGS

What is the central question of this study? Do muscle size, maximal force and exercise intensity influence the recovery time constant for the finite impulse above critical torque (τ_IET' )? What is the main finding and its importance? Muscle size and maximal strength have different influences on the parameters of the hyperbolic torque-time to task failure relationship. Greater muscle size and maximal strength, as well as exercise at an intensity of 60% MVC, prolong τ_IET' during intermittent isometric exercise.

ABSTRACT

Muscle perfusion and O₂ delivery limitations through muscle force generation appear to play a major role in defining the hyperbolic torque-time to task failure (T_lim ) relationship. Therefore, we aimed to determine the influence of muscle size and maximal strength on the recovery time constant for the finite impulse above critical torque (τ_IET' ). Ten men participated in the study and performed intermittent isometric tests until task-failure (T_lim ) for the knee-extensors (KE) (35% and 60% maximal voluntary contraction (MVC)) and plantar flexors (PF) (60% MVC). The τ_IET' was determined for each of these T_lim tests using the IET'_BAL model. The IET' (9738 ± 3080 vs. 2959 ± 1289 N m s) and end-test torque (ET)(84.5 ± 7.1 vs. 74.3 ± 12.7 N m) were significantly lower for PF compared to KE (P < 0.05). Exercise tolerance (T_lim ) was significantly longer for PF (239 ± 81 s) than KE (150 ± 55 s) at 60% MVC, and significantly longer for KE at 35% MVC (641 ± 158 s) than 60% MVC. The τ_IET' was significantly faster at 35% MVC (641 ± 177 s) than 60% MVC (1840 ± 354 s) for KE, both of which were significantly slower than PF at 60% MVC (317 ± 102 s). This study showed that τ_IET' during intermittent isometric exercise is slower with greater muscle size and maximal strength.

Maximal muscular power: lessons from sprint cycling

Maximal muscular power production is of fundamental importance to human functional capacity and feats of performance. Here, we present a synthesis of literature pertaining to physiological systems that limit maximal muscular power during cyclic actions characteristic of locomotor behaviours, and how they adapt to training. Maximal, cyclic muscular power is known to be the main determinant of sprint cycling performance, and therefore we present this synthesis in the context of sprint cycling. Cyclical power is interactively constrained by force-velocity properties (i.e. maximum force and maximum shortening velocity), activation-relaxation kinetics and muscle coordination across the continuum of cycle frequencies, with the relative influence of each factor being frequency dependent. Muscle cross-sectional area and fibre composition appear to be the most prominent properties influencing maximal muscular power and the power-frequency relationship. Due to the role of muscle fibre composition in determining maximum shortening velocity and activation-relaxation kinetics, it remains unclear how improvable these properties are with training. Increases in maximal muscular power may therefore arise primarily from improvements in maximum force production and neuromuscular coordination via appropriate training. Because maximal efforts may need to be sustained for ~15-60 s within sprint cycling competition, the ability to attenuate fatigue-related power loss is also critical to performance. Within this context, the fatigued state is characterised by impairments in force-velocity properties and activation-relaxation kinetics. A suppression and leftward shift of the power-frequency relationship is subsequently observed. It is not clear if rates of power loss can be improved with training, even in the presence adaptations associated with fatigue-resistance. Increasing maximum power may be most efficacious for improving sustained power during brief maximal efforts, although the inclusion of sprint interval training likely remains beneficial. Therefore, evidence from sprint cycling indicates that brief maximal muscular power production under cyclical conditions can be readily improved via appropriate training, with direct implications for sprint cycling as well as other athletic and health-related pursuits.

Peak Running Velocity or Critical Speed Under Field Conditions: Which Best Predicts 5-km Running Performance in Recreational Runners?

This study aimed to examine which variable, between the peak running velocity determined on the track field (V_{peak_TF}) and critical speed (CS), is the best predictor of the 5-km running performance in recreational runners. Twenty-five males performed three tests to determine the V_{peak_TF}, CS, and 5-km running performance on the track field, with a minimal interval of 48 h between each test. The V_{peak_TF} protocol started with a velocity of 8 km⋅h^–1, followed by an increase of 1 km⋅h^–1 every 3 min until volitional exhaustion, which was controlled by sound signals, with cones at every 25 m indicating when the participants were required to pass the cone’s position to maintain the required velocity. The participants performed three time trials (TTs) (1: 2,600 m; 2: 1,800 m; and 3: 1,000 m) on the same day, with a 30-min rest period to determine the CS through the combinations of three (CS₁,₂,₃) and two TTs (CS₁,₂, CS₁,₃, and CS₂,₃). The 5-km running performance time was recorded to determine the test duration, and the mean velocity (MV) was calculated. There was a significant difference observed between the V_{peak_TF} and the MV 5-km running performance. However, no differences were found between the CS values and the MV 5-km running performance. A correlation was observed between the V_{peak_TF} (R = −0.90), CS₁,₂,₃ (R = −0.95), CS₁,₃ (R = −0.95), and the 5-km running performance time. Linear regression indicated that the V_{peak_TF} (R² = 0.82), CS₁,₂,₃ (R² = 0.90), and CS₁,₃ (R² = 0.90) significantly predicted the 5-km running performance time. The CS results showed a higher predictive power for the 5-km running performance, slightly better than the V_{peak_TF}. Also, CS₁,₂,₃ and the CS₁,₃ presented the highest predictive power for the 5-km running performance of recreational runners.

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.

W' Reconstitution Accelerates More with Decreasing Intensity in the Heavy- versus the Moderate-Intensity Domain

INTRODUCTION

The purpose of this study was to investigate the effect of the recovery intensity domain on W' reconstitution. We used the W'BAL model as a framework and tested its predictive capabilities (W'PRED) across the different intensity domains.

METHODS

Twelve young men (51.7 ± 5.9 mL·kg-1·min-1) completed a ramp incremental test, three to five constant power output (PO) tests to determine critical power (CP) and W', and minimally two trials to verify the maximal lactate (La-) steady state. During four experimental trials, subjects performed two work bouts (WB1 and WB2) at P6 (i.e., PO that predicts exhaustion within 6 min) separated by a recovery interval at CP-10 W, Δgas exchange threshold (GET)-CP, GET, and 50% GET, respectively. WB1 was designed to deplete 75% W', and the recovery time varied to replenish 50% W'. WB2 was performed to exhaustion (W'ACT). W'PRED was compared with W'ACT to evaluate the accuracy of the W'BAL model. Excess postexercise oxygen consumption was calculated as the difference between the measured and the predicted oxygen uptake during recovery.

RESULTS

W'ACT averaged 49% ± 24%, 69% ± 24%, 81% ± 28%, and 93% ± 21% for CP-10 W, ΔGET-CP, GET, and 50% GET, respectively (P = 0.002). W'PRED overestimated W'ACT in CP-10 W (34% ± 32%, P = 0.004) and underestimated W'ACT in 50% GET (24% ± 28%, P = 0.013). Excess postexercise oxygen consumption was lowest in CP-10 W (P < 0.01) and higher in GET compared with ΔGET-CP (P = 0.01).

CONCLUSION

We demonstrated that W'PRED overestimated and underestimated W'ACT in the heavy- and moderate-intensity domain, respectively. Therefore, the practical applicability of a single recovery time constant, which only relies on the difference between the recovery PO and the CP, is questionable.

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.

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

INTRODUCTION

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

METHODS

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

RESULTS

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

CONCLUSION

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

Modeling the depletion and reconstitution of W': Effects of prior exercise on cycling tolerance

Thirteen healthy male subjects (age 28 ± 7 years) performed tests for critical power and W' determination and two square-wave high-intensity exercises until exhaustion either with prior very-heavy intensity cycling (EXP) or without (CON). Prior exercise bout induced a depletion of 60 % of W'. After 10 min of recovery, W' reconstitution was not fully achieved (∼ 92 %). Time to exhaustion and Δ blood lactate concentration were significantly lower in EXP compared to CON (595 ± 118 s vs. 683 ± 148 s; 3.5 ± 1.2 mmol.L^-1 vs. 8.8 ± 2.3 mmol.L^-1; p < 0.05, respectively). Oxygen uptake (VO₂) and heart rate were significantly higher in EXP, during the first 150 s of exercise (p < 0.05). The carbon dioxide production kinetics was significantly slower in EXP (mean response time = 87.8 ± 17.8 s vs. 73.7 ± 16.6 s in CON; p < 0.05). Thus, prior exercise impairs high-intensity cycling performance which can partly be explained by physiological disturbances linked to W' depletion.

Mechanical Power in Endurance Running: A Scoping Review on Sensors for Power Output Estimation during Running

Mechanical power may act as a key indicator for physiological and mechanical changes during running. In this scoping review, we examine the current evidences about the use of power output (PW) during endurance running and the different commercially available wearable sensors to assess PW. The Boolean phrases endurance OR submaximal NOT sprint AND running OR runner AND power OR power meter, were searched in PubMed, MEDLINE, and SCOPUS. Nineteen studies were finally selected for analysis. The current evidence about critical power and both power-time and power-duration relationships in running allow to provide coaches and practitioners a new promising setting for PW quantification with the use of wearable sensors. Some studies have assessed the validity and reliability of different available wearables for both kinematics parameters and PW when running but running power meters need further research before a definitive conclusion regarding its validity and reliability.

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.

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

Purpose: To validate and compare a novel model based on the critical power (CP) concept that describes the entire domain of maximal mean power (MMP) data from cyclists.Methods: An omni-domain power-duration (OmPD) model was derived whereby the rate of W' expenditure is bound by maximum sprint power and the power at prolonged durations declines from CP log-linearly. The three-parameter CP (3CP) and exponential (Exp) models were likewise extended with the log-linear decay function (Om3CP and OmExp). Each model bounds W' using a different nonconstant function, W'eff (effective W'). Models were fit to MMP data from nine cyclists who also completed four time-trials (TTs).Results: The OmPD and Om3CP residuals (4 ± 1%) were smaller than the OmExp residuals (6 ± 2%; P < 0.001). W'eff predicted by the OmPD model was stable between 120-1,800 s, whereas it varied for the Om3CP and OmExp models. TT prediction errors were not different between models (7 ± 5%, 8 ± 5%, 7 ± 6%; P = 0.914).Conclusion: The OmPD offers similar or superior goodness-of-fit and better theoretical properties compared to the other models, such that it best extends the CP concept to short-sprint and prolonged-endurance performance.

Time to exhaustion during cycling is not well predicted by critical power calculations

Three to 5 cycling tests to exhaustion allow prediction of time to exhaustion (TTE) at power output based on calculation of critical power (CP). We aimed to determine the accuracy of CP predictions of TTE at power outputs habitually endured by cyclists. Fourteen endurance-trained male cyclists underwent 4 randomized cycle-ergometer TTE tests at power outputs eliciting (i) mean Wingate anaerobic test (WAnT_mean), (ii) maximal oxygen consumption, (iii) respiratory compensation threshold (VT₂), and (iv) maximal lactate steady state (MLSS). Tests were conducted in duplicate with coefficient of variation of 5%-9%. Power outputs were 710 ± 63 W for WAnT_mean, 366 ± 26 W for maximal oxygen consumption, 302 ± 31 W for VT₂ and 247 ± 20 W for MLSS. Corresponding TTE were 00:29 ± 00:06, 03:23 ± 00:45, 11:29 ± 05:07, and 76:05 ± 13:53 min:s, respectively. Power output associated with CP was only 2% lower than MLSS (242 ± 19 vs. 247 ± 20 W; P < 0.001). The CP predictions overestimated TTE at WAnT_mean (00:24 ± 00:10 mm:ss) and MLSS (04:41 ± 11:47 min:s), underestimated TTE at VT₂ (-04:18 ± 03:20 mm:ss; P < 0.05), and correctly predicted TTE at maximal oxygen consumption. In summary, CP accurately predicts MLSS power output and TTE at maximal oxygen consumption. However, it should not be used to estimate time to exhaustion in trained cyclists at higher or lower power outputs (e.g., sprints and 40-km time trials). Novelty CP calculation enables to predict TTE at any cycling power output. We tested those predictions against measured TTE in a wide range of cycling power outputs. CP appropriately predicted TTE at maximal oxygen consumption intensity but err at higher and lower cycling power outputs.

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

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

Establishing the V̇o2 versus constant-work-rate relationship from ramp-incremental exercise: simple strategies for an unsolved problem

The dissociation between constant work rate of O₂ uptake (V̇o₂) and ramp V̇o₂ at a given work rate might be mitigated during slowly increasing ramp protocols. This study characterized the V̇o₂ dynamics in response to five different ramp protocols and constant-work-rate trials at the maximal metabolic steady state (MMSS) to characterize 1) the V̇o₂ gain (G) in the moderate, heavy, and severe domains, 2) the mean response time of V̇o₂ (MRT), and 3) the work rates at lactate threshold (LT) and respiratory compensation point (RCP). Eleven young individuals performed five ramp tests (5, 10, 15, 25, and 30 W/min), four to five time-to-exhaustions for critical power estimation, and two to three constant-work-rate trials for confirmation of the work rate at MMSS. G was greatest during the slowest ramp and progressively decreased with increasing ramp slopes (from ~12 to ~8 ml·min^-1·W^-1, P < 0.05). The MRT was smallest during the slowest ramp slopes and progressively increased with faster ramp slopes (1 ± 1, 2 ± 1, 5 ± 3, and 10 ± 4, 15 ± 6 W, P < 0.05). After "left shifting" the ramp V̇o₂ by the MRT, the work rate at LT was constant regardless of the ramp slope (~150 W, P > 0.05). The work rate at MMSS was 215 ± 55 W and was similar and highly correlated with the work rate at RCP during the 5 W/min ramp (P > 0.05, r = 0.99; Lin's concordance coefficient = 0.99; bias = -3 W; root mean square error = 6 W). Findings showed that the dynamics of V̇o₂ (i.e., G) during ramp exercise explain the apparent dichotomy existing with constant-work-rate exercise. When these dynamics are appropriately "resolved", LT is constant regardless of the ramp slope of choice, and RCP and MMSS display minimal variations between each other.NEW & NOTEWORTHY This study demonstrates that the dynamics of V̇o₂ during ramp-incremental exercise are dependent on the characteristics of the increments in work rate, such that during slow-incrementing ramp protocols the magnitude of the dissociation between ramp V̇o₂ and constant V̇o₂ at a given work rate is reduced. Accurately accounting for these dynamics ensures correct characterizations of the V̇o₂ kinetics at ramp onset and allows appropriate comparisons between ramp and constant-work-rate exercise-derived indexes of exercise intensity.

Dynamics of the power-duration relationship during prolonged endurance exercise and influence of carbohydrate ingestion

We tested the hypotheses that the parameters of the power-duration relationship, estimated as the end-test power (EP) and work done above EP (WEP) during a 3-min all-out exercise test (3MT), would be reduced progressively after 40 min, 80 min, and 2 h of heavy-intensity cycling and that carbohydrate (CHO) ingestion would attenuate the reduction in EP and WEP. Sixteen participants completed a 3MT without prior exercise (control), immediately after 40 min, 80 min, and 2 h of heavy-intensity exercise while consuming a placebo beverage, and also after 2 h of heavy-intensity exercise while consuming a CHO supplement (60 g/h CHO). There was no difference in EP measured without prior exercise (260 ± 37 W) compared with EP after 40 min (268 ± 39 W) or 80 min (260 ± 40 W) of heavy-intensity exercise; however, after 2 h EP was 9% lower compared with control (236 ± 47 W; P < 0.05). There was no difference in WEP measured without prior exercise (17.9 ± 3.3 kJ) compared with after 40 min of heavy-intensity exercise (16.1 ± 3.3 kJ), but WEP was lower (P < 0.05) than control after 80 min (14.7 ± 2.9 kJ) and 2 h (13.8 ± 2.7 kJ). Compared with placebo, CHO ingestion negated the reduction of EP following 2 h of heavy-intensity exercise (254 ± 49 W) but had no effect on WEP (13.5 ± 3.4 kJ). These results reveal a different time course for the deterioration of EP and WEP during prolonged endurance exercise and indicate that EP is sensitive to CHO availability.NEW & NOTEWORTHY The parameters of the power-duration relationship [critical power (CP) and the curvature constant (W')] have typically been considered to be static. Here we report the time course for reductions in CP and W', as estimated with the 3-min all-out cycle test, during 2 h of heavy-intensity exercise. We also show that carbohydrate ingestion during exercise preserves CP, but not W', without altering muscle glycogen depletion. These results provide new mechanistic and practical insight into the power-duration curve and its relationship to exercise-related fatigue development.

The maximal metabolic steady state: redefining the 'gold standard'

The maximal lactate steady state (MLSS) and the critical power (CP) are two widely used indices of the highest oxidative metabolic rate that can be sustained during continuous exercise and are often considered to be synonymous. However, while perhaps having similarities in principle, methodological differences in the assessment of these parameters typically result in MLSS occurring at a somewhat lower power output or running speed and exercise at CP being sustainable for no more than approximately 20-30 min. This has led to the view that CP overestimates the 'actual' maximal metabolic steady state and that MLSS should be considered the 'gold standard' metric for the evaluation of endurance exercise capacity. In this article we will present evidence consistent with the contrary conclusion: i.e., that (1) as presently defined, MLSS naturally underestimates the actual maximal metabolic steady state; and (2) CP alone represents the boundary between discrete exercise intensity domains within which the dynamic cardiorespiratory and muscle metabolic responses to exercise differ profoundly. While both MLSS and CP may have relevance for athletic training and performance, we urge that the distinction between the two concepts/metrics be better appreciated and that comparisons between MLSS and CP, undertaken in the mistaken belief that they are theoretically synonymous, is discontinued. CP represents the genuine boundary separating exercise in which physiological homeostasis can be maintained from exercise in which it cannot, and should be considered the gold standard when the goal is to determine the maximal metabolic steady state.

The Reliability of 4-Minute and 20-Minute Time Trials and Their Relationships to Functional Threshold Power in Trained Cyclists

PURPOSE

The mean power output (MPO) from a 60-min time trial (TT)-also known as functional threshold power, or FTP-is a standard measure of cycling performance; however, shorter performance tests are desirable to reduce the burden of performance testing. The authors sought to determine the reliability of 4- and 20-min TTs and the extent to which these short TTs were associated with 60-min MPO.

METHODS

Trained male cyclists (n = 8; age = 25 [5] y; VO2max = 71 [5] mL/kg/min) performed two 4-min TTs, two 20-min TTs, and one 60-min TT. Critical power (CP) was estimated from 4- and 20-min TTs. The typical error of the mean (TEM) and intraclass correlation coefficient (ICC) were calculated to assess reliability, and R2 values were calculated to assess relationships with 60-min MPO.

RESULTS

Pairs of 4-min TTs (mean: 417 [SD: 45] W vs 412 [49] W, P = .25; TEM = 8.1 W; ICC = .98), 20-min TTs (342 [36] W vs 344 [33] W, P = .41; TEM = 4.6 W; ICC = .99), and CP estimates (323 [35] W vs 328 [32] W, P = .25; TEM = 6.5; ICC = .98) were reliable. The 4-min MPO (R2 = .95), 20-min MPO (R2 = .92), estimated CP (R2 = .82), and combination of the 4- and 20-min MPO (adjusted R2 = .98) were strongly associated with the 60-min MPO (309 [26] W).

CONCLUSION

The 4- and 20-min TTs appear useful for assessing performance in trained, if not elite, cyclists.

The combined effect of sprint interval training and postexercise blood flow restriction on critical power, capillary growth, and mitochondrial proteins in trained cyclists

Sprint interval training (SIT) combined with postexercise blood flow restriction (BFR) is a novel method to increase maximal oxygen uptake (V̇o2max) in trained individuals and also provides a potent acute stimulus for angiogenesis and mitochondrial biogenesis. The efficacy to enhance endurance performance, however, has yet to be demonstrated. Trained male cyclists ( n = 21) (V̇o2max: 62.8 ± 3.7 ml·min−1·kg−1) undertook 4 wk of SIT (repeated 30-s maximal sprints) either alone (CON; n = 10) or with postexercise BFR ( n = 11). Before and after training V̇o2max, critical power (CP) and curvature constant ( Wʹ) were determined and muscle biopsies obtained for determination of skeletal muscle capillarity and mitochondrial protein content. CP increased ( P = 0.001) by a similar extent following CON (287 ± 39 W to 297 ± 43 W) and BFR (296 ± 40 W to 306 ± 36 W). V̇o2max increased following BFR by 5.9% ( P = 0.02) but was unchanged after CON ( P = 0.56). All markers of skeletal muscle capillarity and mitochondrial protein content were unchanged following either training intervention. In conclusion, 4 wk of SIT increased CP; however, this was not enhanced further with BFR. SIT was not sufficient to elicit changes in skeletal muscle capillarity and mitochondrial protein content with or without BFR. However, we further demonstrate the potency of combining BFR with SIT to enhance V̇o2max in trained individuals.

NEW & NOTEWORTHY This investigation has demonstrated that 4 wk of sprint interval training (SIT) increased critical power in trained individuals; however, postexercise blood flow restriction (BFR) did not enhance this further. SIT, with or without BFR, did not induce any changes in skeletal muscle capillarity or mitochondrial protein content in our trained population. We do, however, confirm previous findings that SIT combined with BFR is a potent stimulus to enhance maximal oxygen uptake.