INTRODUCTION
In sport performance, power is defined by the total work performed relative to time, whereby more work performed in less time is characterized by greater power. Bioenergetics involves studying the underlying chemical processes responsible for mechanical work (^{9} ). Exercise physiology textbooks often apply the steady-state model of bioenergetics to sustained high-intensity power performances. In reality, the steady-state model does not reflect the bioenergetics of high-intensity power accurately (^{12} ).

The steady-state model presumes that the body will meet energy demand aerobically within 2–3 minutes. Specifically, oxygen uptake (V[Combining Dot Above]O_{2} ) will rise and reach a steady state. As early as 1972, however, researchers determined that V[Combining Dot Above]O_{2} does not achieve steady state at higher intensities (^{43} ). Indeed, the time course of V[Combining Dot Above]O_{2} , as it pertains to different exercising intensities, sheds new light on the complex topic of anaerobic capacity and short-term high-intensity power (^{7} ). Moreover, the methods for evaluating physiological parameters contributing to short-term high-intensity power have evolved. The purpose of this article is to discuss new insights of the bioenergetics for short-term high-intensity power, metabolic and mechanical measures of short-term power, and applications for those measurements.

NEW INSIGHTS ON THE BIOENERGETICS OF HIGH-INTENSITY EXERCISE
The bioenergetics of short-term high-intensity exercise can be divided into 3 systems: the phosphocreatine (PCr) system, the fast glycolytic or lactate formation system, and the slow glycolytic or aerobic system. Time ranges of 0–10, 10–30, and beyond 30 seconds are viewed typically for the utilization of PCr, fast glycolytic, and slow glycolytic systems, respectively (^{9} ). These time ranges are in no way appropriate for high-intensity power exercise.

The first primary substrate for muscle adenosine triphosphate (ATP) production is PCr. The steady-state model presumes that PCr utilization is limited approximately to the initial 10 seconds of exercise. For exercise performances beyond 10 seconds, the fast and slow glycolytic pathways are viewed as exclusive mechanisms for supplying ATP (^{9} ). The findings by Jones et al. (^{24} ) indicate that PCr can contribute progressively to ATP production during sustained high-intensity exercise. Their results indicated that PCr was used well beyond 5 and up to 18-minutes of exercise. Such an observation is explained by spatial recruitment and the size principle (^{15} ). The size principle states that when smaller low-threshold motor units fail to meet power demands, larger higher-threshold motor units are recruited.

Housh et al. (^{19} ) determined that constant power output high-intensity exercise evoked greater, time-dependent motor-unit activation in comparison to lower intensities. Progressive recruitment of myofibers would help explain why PCr utilization can occur well beyond 10 seconds during high-intensity exercise. Specifically, an initial motor-unit pool will expend PCr within 10 seconds. Because additional fibers are recruited to meet the constant power output demands, those fibers will supply ATP from PCr, resulting in a small but continual depletion of PCr within the whole muscle over a span of several minutes. Such a view of metabolism is distinct from the notion that the whole muscle expends PCr within the first 10 seconds of a high-intensity bout.

The accumulation of blood lactate during exercise has been viewed as a byproduct associated with hydrogen ion production (^{4} ). However, some lactate yielded by fast glycolysis can be oxidized readily within type I muscle fibers (^{3} ). The prevailing view on lactate production is that hydrogen ions are sequestered rather than accumulated, which serves to increase rather than decrease muscle pH (^{9,36} ). In other words, the acidosis or “burn” associated with fatigue during high-intensity exercise has nothing to do with the formation of lactate (^{3} ). A more likely mechanism for the declining pH during high-intensity exercise is the hydrolysis of ATP (^{36} ), expressed as follows:

where the addition of water (H_{2} O) separates ATP, H^{+} ion accumulation is associated with a declining pH, ADP is adenosine diphosphate, P_{i} is inorganic phosphate, and E represents energy.

Rather than being viewed as a byproduct, lactate is better viewed as an intermediate sugar, produced by fast glycolysis (which yields 2 ATP) that can subsequently enter mitochondria through a monocarboxyl transporter (MCT) and be oxidized in the Krebs' cycle (which yields 36 ATP) (^{29} ). Indeed, endurance athletes can oxidize lactate at a higher percentage of V[Combining Dot Above]O_{2} max because they have more MCT receptors and oxidative enzymes (^{30} ). The lactate threshold is therefore not predicated on the absence or presence of sufficient oxygen supply within muscle (^{5} ). Rather, the accumulation of intramuscular lactate is predicated on the failure of mitochondria to supply ATP at appropriate rates.

The steady-state model presumes that V[Combining Dot Above]O_{2} will reach a constant level within 2–3 minutes of exercise onset. For intensities exceeding the lactate or gas exchange threshold, V[Combining Dot Above]O_{2} exhibits a continual rise termed the V[Combining Dot Above]O_{2} slow component (^{12} ). The slow component emerges between 1.5 and 3 minutes of exercise onset and primarily represents the added oxygen costs associated with recruiting type II muscle fibers (^{7} ). High-intensity power exercise can cause dramatic gains in the V[Combining Dot Above]O_{2} slow component (e.g., in excess of 1 L of added oxygen) (^{34} ), and modeling of bioenergetics indicates that the slow glycolysis contributes more substantially to endeavors that are deemed as “anaerobic.” For example, aerobic metabolism could contribute ∼60–70% of the total energy for sprinting 800 m (∼2 minutes), because of how the V[Combining Dot Above]O_{2} slow component rises during intense exercise.

TRADITIONAL ANAEROBIC CAPACITY TESTING
One of the more popular long-standing tests of anaerobic capacity is the Wingate anaerobic power test. The Wingate test is a 30-second all-out exercise test using a fixed load, typically 7.5–10% body mass (recreational or athletic subject, respectively), whereby flywheel velocity and cycling power are measured relative to time (^{20} ). Most commercial software programs for the Wingate test calculate a peak power (P_{max} ) based on the average of the highest 5-second sampling bin along with a fatigue index of P_{max} relative to the lowest 5-second sampling bin. Concern on the validity of the fatigue index values from the Wingate test has been raised. Specifically, the 30-second duration of the Wingate test has been viewed as too short of a duration to estimate depletion of anaerobic capacity , where 1 group (^{11} ) has reported that 90 seconds (i.e., 3 times the duration of the Wingate test) was insufficient to effectively deplete the anaerobic capacity . Thus, using the fatigue index from the Wingate test to rank-order the anaerobic capacities for a group of athletes is an inaccurate practice.

In the late 1980s, the maximal accumulated oxygen deficit (MAOD) test emerged as an index of anaerobic capacity (^{25} ). The test involved extrapolating expected V[Combining Dot Above]O_{2} demands for a supramaximal bout, or bouts, based on a series of preliminary constant-load submaximal bouts (e.g., 40, 50, and 60% of power evoking V[Combining Dot Above]O_{2} max in a graded exercise test). Subjects were asked to subsequently perform one or more exhaustive supramaximal bouts (^{37} ). Hypothetically, an identical MAOD value would be yielded, regardless of the power output and time to exhaustion (Figure 1 ) (^{40} ). The MOAD method was advocated to distinguish the high-power capacity of untrained, sprint-trained, and endurance-trained subjects (^{14} ).

Figure 1: An example of an individual's maximal accumulated oxygen deficit (MAOD). Where an individual's at a V[Combining Dot Above]O2max of 3.8 L min−1 was 300 W (Wpeak), linear regression from V[Combining Dot Above]O2-power time points (open circles, panel A) were used to calculate supramaximal V[Combining Dot Above]O2 demands, that is, demand at 105% Wpeak (315 W) is 4.0 L min−1 = (315 × 0.0113) + 0.4585 (panel B) and demand at 110% Wpeak (330 W) is 4.2 L min−1 (panel C). The extrapolated accumulated V[Combining Dot Above]O2 demand for 3 minutes at 315 W is 12.0 L and 2 minutes at 330 W is 8.4 L. If accumulated V[Combining Dot Above]O2 at 315 W was 10 L and at 330 W was 6.4 L, the O2 deficit would be equivalent at 2 L (i.e., MAOD = 2 L, a volume of energy met by the anaerobic capacity ). Note that the measured V[Combining Dot Above]O2 during the square-wave bouts at 105 and 110% Wpeak reached the V[Combining Dot Above]O2max of 3.8 L min−1.

The MAOD protocol was attractive, in principle, but failed to gain traction in the sport science community (^{28} ). The shortcomings of the MOAD protocol were as follows: First, energy demand for the MOAD protocol is influenced by the fact that the V[Combining Dot Above]O_{2} -power relationship below and above the gas exchange threshold is not consistent. Thus, the regression equation for estimating V[Combining Dot Above]O_{2} demand for supramaximal bouts is dependent on the number and intensity of bouts (i.e., the more bouts above gas exchange threshold used in the equation would inflate the extrapolated V[Combining Dot Above]O_{2} demand) (^{1} ). Indeed, 1 group reported that a minimum of 10 steady-state bouts are needed to perform the MOAD test validly (^{28} ). Clearly, having to complete 10 steady-state bouts per athlete is a time-consuming task. Second, the time limit for constant-load bouts carried out to exhaustion (T_{lim} ) is an unreliable measurement (^{42} ). Third, the MOAD test yields units of measurement for anaerobic capacity , in absolute values (L) or values relative to body mass (in milliliters per kilogram) that can conceivably rank-order athletes (^{37} ); however, the MOAD metric cannot predict T_{lim} at given power outputs or be used to prescribe exercise. Thus, a mechanical measure of anaerobic capacity is preferred.

MECHANICAL MEASURES OF HIGH-INTENSITY POWER AND CAPACITY
For nearly a century, we have appreciated that the power and the T_{lim} (P-T_{lim} ) relationship is proportional such that fatigue occurs earlier at higher intensities (^{16} ). Monod and Scherrer (^{26} ) are credited as the first to link the P-T_{lim} relationship to a finite limit of stored energy within the muscle (i.e., anaerobic capacity ). The classic method of determining anaerobic capacity and critical power (CP) was to conduct a series of exhaustive bouts at different high-power intensities (^{26,27} ). With power output and T_{lim} data at 3 and preferably 4 different intensities known (^{17} ), CP and the curvature constant abbreviated as W ′ (pronounced W-prime) could be determined. Specifically, the P-T_{lim} relationship was modeled mathematically as a regression of total work (y -axis) and T_{lim} (x -axis) to yield:

where total work is in joules, CP is in watts and represents the slope, T_{lim} is in seconds, and W′ is in joules and represents the y -intercept (Linear-W model). Whipp et al. (^{41} ) introduced a subsequent iteration for the linear model, whereby power output and the inverse of T_{lim} were interpolated to solve the W ′ as the slope and the CP as the y -intercept (Linear-P model). With the Linear-P model, the equation can be expressed as:

The Linear-P model also can be transformed to:

Finally, the T_{lim} for a given power output can be derived using:

Figure 2 provides sample calculations for a representative subject. Take notice that the same power-T_{lim} data points from Figure 1 were used to assist with comparing the MOAD and CP models, respectively. Directions for how to construct the CP model using a Microsoft Excel spreadsheet (Microsoft Corporation, Remond, WA) are published elsewhere (^{31} ).

Figure 2: An example of an individual's power-time limit (P-Tlim) relationship as modeled from the following 4 exhaustive square-wave bouts in the severe exercise domain: 303 W = 300 seconds, 307 W = 240 seconds, 315 W = 180 seconds, and 330 W = 120 seconds (Note: an example data point is shown on each graph). Tlim for each bout is inverted (1/time in seconds) and plotted relative to power (panel A). Linear regression of the data reveals critical power (CP = 285 W, the y-intercept) and anaerobic capacity (W′ = 5,400 joules, the slope). Panel B illustrates the hyperbolic P-Tlim relationship where the y-axis (power) can be solved using power = (W′/Tlim) + CP and the x-axis (Tlim) can be solved using Tlim = 1/[(Power − CP)/W′].

In accordance to Newton's work-energy theorem, the assessment of work, in essence, is a measure of kinetic energy required to complete that work. Thus, W ′ is better viewed as an energy reservoir and work performed at intensities exceeding CP would deplete the W ′ reservoir in a time-dependent manner (^{31} ). Concurrently, exercising above CP evokes a time-dependent rate of metabolite accumulation associated with fatigue (e.g., hydrogen ions) (^{22} ). Indeed, the higher the intensity relative to CP, the more rapid these metabolites accumulate (^{24} ). Such mechanisms explain the hyperbolic nature of the P-T_{lim} relationship (see Figure 2 , right panel).

3-MINUTE ALL-OUT EXERCISE TEST
Some studies (^{6,39} ) have emerged demonstrating that a 3-minute all-out exercise test (3 MT) can predict CP and W′ . The 3 MT is quite similar procedurally to the more familiar 30-second Wingate test (^{20} ); however, the load for the 3 MT is lower (∼3–5% body mass) in comparison to the Wingate test (^{2,8} ). Early attempts of the 90-second all-out exercise duration resulted in inflated estimates of CP (^{11} ); however, 180 seconds was reported as a suitable duration to identify CP, as determined by evaluating V[Combining Dot Above]O_{2} and blood lactate below and above CP (^{6} ). Indeed, the first 150 seconds also was sufficient to estimate the finite capacity for work above CP or W ′ (^{39} ).

Using a prescribed load for resistance (i.e., 3–5% body mass dependent on fitness level) (^{8} ), the subject pedals all-out for a 3-minute duration. Data are subsequently retrieved from the ergometer, and the average power for the last 30 seconds is calculated to arrive at CP. Figure 3 illustrates a representative subject's data from the 3 MT. Take notice of how the values derived from the 3 MT correspond to the traditional method of estimating CP, as shown in Figure 2 .

Figure 3: An example of subject's 3-minute all-out exercise test (3 MT). Notice that all-out power declines and levels out at 285 W, identified by the average power between 150 and 180 seconds, or critical power (CP). The average power for 150 seconds (P150s) was 321 W, or +36 W relative to CP, where +36 W × 150 seconds = 5,400 joules—representing the maximal amount of work above CP that is supported by the anaerobic capacity (W′).

The ability to obtain measures of CP and W ′ from a single all-out exercise test has been projected to advance our understanding of short-term high-intensity power (^{33} ). From a practical standpoint, the 3 MT offers better direction for assessing and prescribing exercise for short-term high-intensity power athletes than methods such as measuring target heart rates or relying on ratings of the perceived exertion. Moreover, findings from our laboratory indicate that 3 MT may be a better method than the “gold standard,” Linear-W or Linear-P techniques, which are more labor- and time-intensive and rely on a series of exhaustive bouts of known variable T_{lim} measures (^{21} ). The 3 MT also removes the debate between which equations to use (i.e., the Linear-W or Linear W-models) because estimates from the 3 MT, using equations 1–4 , are the same.

Our laboratory also validated the 3 MT for running (^{32} ). The athlete simply runs all-out for a period of 3 minutes, and their displacement in relation to time is monitored using global positioning sensor data or video technology. The technique estimates the critical speed and D ′, running analogues to CP and W ′, and T_{lim} estimates can be established for sustaining given running speeds or distances [see reference (^{31} ) for summary of equations]. The 3 MT for running is actually easier to implement because the resistance load (mass and gravitational force) is removed from the computation. Moreover, athletes can be tested in batches and entire teams of athletes can be assessed within a short period of time (e.g., ∼dozen athletes within an hour) (^{32} ).

When applying the CP model using the 3 MT for training purposes, we recommend keeping a few issues in mind. First, the parameter of CP or critical speed has better test-retest reliability, whereas W ′ or D ′ can be quite variable (^{13,21} ). The CP and CV measure can represent a good index of an athlete's maximal steady state (^{22} ). Second, short-term high-intensity power performance is a compilation of W ′ and more importantly the athlete's CP (^{31} ). Thus, the total power measures from the 3 MT (i.e., average power for 150 seconds and average power for 180 seconds) has better test-retest reliability and is a better metric for monitoring improved short-term high-intensity power, than either CP or W ′ individually (^{21} ).

PRACTICAL APPLICATIONS FOR THE CRITICAL POWER MODEL
With a better understanding of the parameters influencing short-term high-intensity power, that is W ′ and CP, we can discuss the utility of the CP model for training different types of athletes. Take for instance a wrestler and a 5,000 m runner. The wrestler should be focusing on W ′ with less regard for CP, using short more intense workouts (e.g., 30 seconds–2 minutes). Conversely, the 5,000 m runner should spend more time training for longer durations to stress both W ′ and CP. Daniels (^{10} ) recommended 2–5 minutes for the interval training of distance runners.

The elegance of the 3 MT is that the test is sensitive for detecting training-induced adaptations in CP (^{38} ). An athlete spending more time training in the extreme domain should expand the anaerobic capacity resulting in an improved all-out power performance along with higher constant-power capacities for shorter durations (i.e., increased W ′). Conversely, the athlete spending more time training in the severe domain will increase CP and either maintain or slightly decrease W ′ (^{35,38} ).

CONCLUSIONS
When exercise is exhaustive, from either all-out effort or constant-load bouts in the severe domain, additional type II muscle fiber recruitment evokes a continual expenditure of PCr (^{23} ), a disproportionate rise in lactate from stored muscle glycogen (^{34} ), and a continual rise of V[Combining Dot Above]O_{2} toward maximum (^{18} ). Training with short-term high-intensity power exercise stresses the energy systems responsible for anaerobic capacity , represented by the mechanical measure W ′; but, such intensities are too short in duration for evoking attainment of V[Combining Dot Above]O_{2} max (^{10} ). Conversely, training between 2 and 5 minutes, in the severe domain, can evoke improvements in CP or the maximal steady state for lactate and V[Combining Dot Above]O_{2} . As such, endurance-trained athletes can oxidize lactate at higher percentages of V[Combining Dot Above]O_{2} max (^{30} ). The 3 MT is recommended to strength and conditioning professionals as an efficient method for measuring and monitoring bioenergetic adaptations to short-term high-intensity power exercise (^{22} ).

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