Effect of a steady-state exercise on maximal anaerobic power in man

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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Mechanical and metabolic power in accelerated running-Part II: team sports

PURPOSE

This manuscript is devoted to discuss the interplay between velocity and acceleration in setting metabolic and mechanical power in team sports.

METHODS

To this aim, an essential step is to assess the individual Acceleration-Speed Profile (ASP) by appropriately analysing training sessions or matches. This allows one to estimate maximal mechanical and metabolic power, including that for running at constant speed, and hence to determine individual thresholds thereof.

RESULTS

Several approaches are described and the results, as obtained from 38 official matches of one team (Italian Serie B, season 2020-2021), are reported and discussed. The number of events in which the external mechanical power exceeded 80% of that estimated from the subject's ASP ([Formula: see text]) was 1.61 times larger than the number of accelerations above 2.5 m s-2 ([Formula: see text]). The difference was largest for midfielders and smallest for attackers (2.30 and 1.36 times, respectively) due to (i) a higher starting velocity for midfielders and (ii) a higher external peak power for attackers in performing [Formula: see text]. From the energetic perspective, the duration and the corresponding metabolic power of high-demanding phases ([Formula: see text]) were essentially constant (6 s and 22 W  kg-1, respectively) from the beginning to the end of the match, even if their number decreased from 28 in the first to 21 in the last 15-min period, as a consequence of the increased recovery time between [Formula: see text] from 26 s in the first to 37 s in the last 15-min period.

CONCLUSION

These data underline the flaws of acceleration counting above fixed thresholds.

A century of exercise physiology: key concepts on coupling respiratory oxygen flow to muscle energy demand during exercise

After a short historical account, and a discussion of Hill and Meyerhof’s theory of the energetics of muscular exercise, we analyse steady-state rest and exercise as the condition wherein coupling of respiration to metabolism is most perfect. The quantitative relationships show that the homeostatic equilibrium, centred around arterial pH of 7.4 and arterial carbon dioxide partial pressure of 40 mmHg, is attained when the ratio of alveolar ventilation to carbon dioxide flow (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$\end{document}V˙A/V˙RCO2) is − 21.6. Several combinations, exploited during exercise, of pertinent respiratory variables are compatible with this equilibrium, allowing adjustment of oxygen flow to oxygen demand without its alteration. During exercise transients, the balance is broken, but the coupling of respiration to metabolism is preserved when, as during moderate exercise, the respiratory system responds faster than the metabolic pathways. At higher exercise intensities, early blood lactate accumulation suggests that the coupling of respiration to metabolism is transiently broken, to be re-established when, at steady state, blood lactate stabilizes at higher levels than resting. In the severe exercise domain, coupling cannot be re-established, so that anaerobic lactic metabolism also contributes to sustain energy demand, lactate concentration goes up and arterial pH falls continuously. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{V}}_{A}/{\dot{V}}_{R}{CO}_{2}$$\end{document}V˙A/V˙RCO2 decreases below − 21.6, because of ensuing hyperventilation, while lactate keeps being accumulated, so that exercise is rapidly interrupted. The most extreme rupture of the homeostatic equilibrium occurs during breath-holding, because oxygen flow from ambient air to mitochondria is interrupted. No coupling at all is possible between respiration and metabolism in this case.

Warm up II: performance changes following active warm up and how to structure the warm up

While warm up is considered to be essential for optimum performance, there is little scientific evidence supporting its effectiveness in many situations. As a result, warm-up procedures are usually based on the trial and error experience of the athlete or coach, rather than on scientific study. Summarising the findings of the many warm-up studies conducted over the years is difficult. Many of the earlier studies were poorly controlled, contained few study participants and often omitted statistical analyses. Furthermore, over the years, warm up protocols consisting of different types (e.g. active, passive, specific) and structures (e.g. varied intensity, duration and recovery) have been used. Finally, while many studies have investigated the physiological responses to warm up, relatively few studies have reported changes in performance following warm up. The first part of this review critically analyses reported changes in performance following various active warm-up protocols. While there is a scarcity of well-controlled studies with large subject numbers and appropriate statistical analyses, a number of conclusions can be drawn regarding the effects of active warm up on performance. Active warm up tends to result in slightly larger improvements in short-term performance (<10 seconds) than those achieved by passive heating alone. However, short-term performance may be impaired if the warm-up protocol is too intense or does not allow sufficient recovery, and results in a decreased availability of high-energy phosphates before commencing the task. Active warm up appears to improve both long-term (>/=5 minutes) and intermediate performance (>10 seconds, but <5 minutes) if it allows the athlete to begin the subsequent task in a relatively non-fatigued state, but with an elevated baseline oxygen consumption (VO(2)). While active warm up has been reported to improve endurance performance, it may have a detrimental effect on endurance performance if it causes a significant increase in thermoregulatory strain. The addition of a brief, task-specific burst of activity has been reported to provide further ergogenic benefits for some tasks. By manipulating intensity, duration and recovery, many different warm-up protocols may be able to achieve similar physiological and performance changes. Finally, passive warm-up techniques may be important to supplement or maintain temperature increases produced by an active warm up, especially if there is an unavoidable delay between the warm up and the task and/or the weather is cold. Further research is required to investigate the role of warm up in different environmental conditions, especially for endurance events where a critical core temperature may limit performance.

Effect of hyperoxia on aerobic and anaerobic performances and muscle metabolism during maximal cycling exercise

The hyperoxia-improved tolerance to maximal aerobic performance was studied in relation to exercising muscle metabolic state. Five students were submitted to four different tests on a cycle ergometer, each being conducted under normoxia and hyperoxia (60% FiO2) on separate days: Test 1, a progressive exercise until exhaustion to determine the maximal work load (Wmax) which was unchanged by hyperoxia; Test 2, an exercise at Wmax (287 +/- 12 W) until exhaustion to determine the performance time (texh) which was elevated by 38% under hyperoxia but exhaustion occurred at the same arterial proton and lactate concentrations; Test 3 (S-Exercise test) consisted of cycling at Wmax for 90% normoxic-texh (4.8 +/- 0.5 min under both O2 conditions) then followed by a 10-s sprint bout during which the total work output (Wtot) was determined; Wtot was elevated by 15% when exercising under hyperoxia; Test 4 (M-Exercise test) consisted also of cycling at Wmax for 4.8 +/- 0.5 min with blood and muscle samples taken at rest and at the end of the exercise to compare the level of different metabolites. During hyperoxic M-Exercise test, glycogen was twice more depleted whereas glucose-6-phosphate and lactate were less accumulated when compared with normoxia. No significant differences were observed for pyruvate, phosphocreatine and muscle/blood lactate ratio between the two conditions. Conversely to normoxia, levels of ATP, ADP and total NADH were maintained at their resting level under 60% FiO2. These data lead us to suppose a higher oxidation rate for pyruvate and NADH in mitochondria, thereby lowering the metabolic acidosis and allowing a better functioning of the glycolytic and contractile processes to delay the time to exhaustion.

Effects of prolonged cycle ergometer exercise on maximal muscle power and oxygen uptake in humans

The mechanical power (Wtot, W.kg-1) developed during ten revolutions of all-out periods of cycle ergometer exercise (4-9 s) was measured every 5-6 min in six subjects from rest or from a baseline of constant aerobic exercise [50%-80% of maximal oxygen uptake (VO2max)] of 20-40 min duration. The oxygen uptake [VO2 (W.kg-1, 1 ml O2 = 20.9 J)] and venous blood lactate concentration ([la]b, mM) were also measured every 15 s and 2 min, respectively. During the first all-out period, Wtot decreased linearly with the intensity of the priming exercise (Wtot = 11.9-0.25.VO2). After the first all-out period (t greater than 5-6 min), and if the exercise intensity was less than 60% VO2max, Wtot, VO2 and [la]b remained constant until the end of the exercise. For exercise intensities greater than 60% VO2max, VO2 and [la]b showed continuous upward drifts and Wtot continued decreasing. Under these conditions, the rate of decrease of Wtot was linearly related to the rate of increase of VO2 [(dWtot/dt) (W.kg-1 x s-1) = 5.0 x 10(-5) -0.20.(VO2/dt) (W.kg-1 x s-1)] and this was linearly related to the rate of increase of [la]b [(dVO2/dt) (W.kg-1 x s-1) = 2.3 x 10(-4) + 5.9 x 10(-5).(d[la]b/dt) (mM.s-1)].(ABSTRACT TRUNCATED AT 250 WORDS)

Modelling human power and endurance

A generalised three component hydraulic model has been proposed to represent the human bioenergetic processes relating internal energy stores to performance during exercise, and into recovery. Further development of the model allows testable predictions to be made. In particular in this paper I examine certain hypotheses of chemical fuel shortage as a subgroup of the potential causes of fatigue, and their implications for maximal power and for endurance. The assumption that the limitation to sustainable power is direct proportionality to the glycogen store remaining, appears the most feasible. Based on this assumption, equations for the decline in maximum attainable power over time, the endurance at fixed workrates and the endurance at incremental tests (as a function of the increment slope) are obtained. Using published data for fit males, the maximum exertable power declines after about 6 s at 972 W to very low levels after about 2 min. For constant powers selected between 208 and 927 W, endurance declines from ad infinitum to only 6 s. Endurance at VO2max is predicted to be about 9 min. For incremental exercise tests of slope ranging from 30 W/min to 60 W/min, endurance lessens from 14 to 9 min. In these tests the anaerobic threshold is reached in times between 6 and 3 min. Although the power at termination of a test increases with incremental slope, terminal oxygen consumption is effectively constant. Almost all these model predictions are observed to correspond well with published experimental findings. These results suggest that the model can be used to represent an adequate overview of the operation of the human bioenergetic system.

A simple model to link hemodynamics, fatigue and endurance in static work

This paper combines assumptions on blood flow changes during static work, on fatigue resulting from a shortage of chemical fuel, and on energy supply and demand considerations, to construct a systems model for endurance time in the maintenance of isometric muscle tension. All these quantitative assumptions are based on published experimental findings. The model is applied to published data on isometric endurance and a fit yielding R2 = 0.98 obtained on a composite data set.

On a model of human bioenergetics. II. Maximal power and endurance

The properties of a proposed three component hydraulic model of human bioenergetics are examined in respect of the maximum exertable power and the endurance time for given workloads. An equation expressing the decline in maximal effort during an "all-out" exercise is derived, from which a VO2 time equation can be deduced. In addition a workload versus endurance time equation can be obtained, enabling the prediction of time to exhaustion. The resulting equations are illustrated graphically by means of a numerical example. Model predictions, when compared with experimental results, reveal discrepancies which confirm the rejection of the model, as was suggested in an earlier paper.

Energy sources and mechanical efficiency of anaerobic work in dog gastrocnemius

Thermally isolated dog gastrocnemii were stimulated to exhaustion by rhythmic isotonic tetani of 0.2s duration (30 min-1) in complete occlusion of blood flow. Total enthalpy change, H = heat + work, work output, w, (kJ . kg-1) and average mechanical efficiency over the working period, n = w/H, were determined from deep muscle temperature increase and amount of shortening, and lactate produced, La, (mol . kg-1) from washout curves, respectively. Under these conditions H is the sum of the enthalpies due to a) alactic sources (Hal), i.e., net approximately P depletion and muscle O2 stores utilization, and b) formation: H = Hal + "delta HLa" . La. Thus, as "delta HLa", the molar enthalpy of La formation, amounts to 76 kJ . mol-1, Hal could be calculated. It was observed that: i) n ranged from 0.2-0.5 and was higher the lower H, this inverse relationship being essentially due to the dependence of n on Hal as described by: Hal = Ho . 10-kn + a (where Ho = 9.3, k = 3.7 and a = 0.15), and ii) the shortening speed of the first few tetani (vi, mm . s-1), was directly related to Hal as described by: vi = 63.3 + 30.7 Hal. Hal is essentially proportional to the approximately P content of resting muscle. These findings suggest therefore that the efficiency of contraction and the shortening speed are both affected by the approximately P concentration, the efficiency increasing, and the speed decreasing with decreasing approximately P.

Alactic capacity and power: reliability and interpretation

The purpose of this investigation was to determine test-retest reliability for measuring maximal values of alactic capacity (ALCmax) and alactic power (ALPmax). For this, 31 men and 13 women each completed two ALCmax and ALPmax tests. Test-retest correlation coefficients for ALCmax and ALPmax values were 0.78 and 0.90, respectively. In addition, for both variables no significant differences were found between test no. 1 and test no. 2. Mean ALCmax values of 429 and 317 J . kg-1, as well as mean ALPmax values of 3.79 and 3.08 W . kg-1 were found for the men and women, respectively. Both ALCmax and ALPmax values were lower (p less than 0.05) for women than men. However, for the capacity power ratio (ALCmax . ALPmax-1) no difference was found between men and women. A correlation coefficient of r = 0.61 was found between mean values for ALCmax and ALPmax . ALCmax values were discussed as being related to skeletal muscle phosphagen concentrations, and ALPmax values were discussed as being related to phosphagen splitting rate. The observed sex differences were suggested to reflect a greater percent body fat in women than men.

The effect of external loading upon power output in stair climbing

Previous studies have examined man's ability to produce external power output during maximal repetitive work cycles of short duration. It appears, however, that there were methodological limitations which would inherently mask man's true capacities. Consequently, we examined the effect of variable external loads upon external power output as measured by running upstairs. Fourteen male subjects (16-31 years of age) who regularly participated in competitive sports performed maximal stair step tests under five experimental loading conditions (no external load, 10.1, 19.2, 24.2, and 29.2 kg). Significant increases (P < 0.05) in external power output were found. External power output increased from a mean of 15.9 W x kg-1 +/- 1.0 (unloaded condition) to 18.5 W x kg-1 +/- 1.5 (external load of 29.2 kg). This is the first modern investigation demonstrating that external loads effect external power output as measured by this technique.

The effects of intermittent warm-up on 7-9 year-old boys

Twelve boys, 7-9 years old, who, by use of questionnaires, were found to be ignorant of the concept of "warm-up", performed maximal aerobic and anaerobic tasks 4 min after completing a 15 min intermittent warm-up (WU) (30 sec treadmill run, 30 sec pause). The WU required some 60% of the individual's VO2max, and raised rectal temp. by 0.52 +/- 0.19 degrees C. The aerobic criterion task (CT) was a one-stage bicycle ride at a load predetermined to exhaust the subject after 4 min. The anaerobic CT was a 30 sec all-out ride against resistance of 35 gm/kg BW. Subjects also performed both CT's without any WU. VO2max (aerobic CT), HRmax, as well as total mechanical work output achieved during the aerobic CT, were significantly higher with WU, compared with the non-WU sessions. During the anaerobic CT total revolutions, total power output, as well as peak HR, were significantly higher following WU. It is suggested that the benefits of intermittent WU, as used in this study in young children, can be attributed to physiological rather than psychological mechanisms.