Hyperbolic Power-duration Relationship Research Articles

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±8.7mLkg-1min-1; peak work rate, 366±40W; and gas exchange threshold, 162±41W) performed three to five constant-load tests to task failure for the determination of CP (246±44W) and W' (18.6±4.1kJ). 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.

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

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. 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. 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. 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.

A Comparison Of Critical Power And Respiratory Compensation Point In COPD: Coincidence Or Equivalence?

Power output at the respiratory compensation point (RCP), measured as the breakpoint in the linear ventilation-carbon dioxide output (V̇E-V̇CO2) relationship during ramp-incremental exercise, is proposed to be equivalent to critical power (CP): the asymptote of the hyperbolic power-duration relationship (P-tLIM). For RCP to be used as a valid index of CP, their values should remain equivalent, even under pulmonary mechanical constraint (e.g., in patients with chronic obstructive pulmonary disease [COPD]). PURPOSE: To determine power output (W) and oxygen uptake (V̇O2) at RCP and CP measured using gold-standard protocols in patients with COPD. METHODS: Ten COPD patients (4 female) volunteered (FEV1 = 41 ± 16% predicted). Power output and V̇O2 at gas exchange threshold (GET) and RCP were measured during ramp-incremental cycle ergometry (5-10 W/min). Critical power was estimated from the asymptote of the hyperbolic P-tLIM relationship from 3-4 constant power exercise tests. Oxygen uptake was measured at 15 and 20 min of a constant power ride at CP. RESULTS: Gas exchange threshold was observed in 9/10 patients and occurred at a V̇O2 of 0.91 ± 0.19 L/min (71 ± 28% V̇O2peak). Respiratory compensation point was identified in 1/10 patients and occurred at a V̇O2 of 1.57 L/min (87% V̇O2peak) versus 1.45 L/min at CP (90 W vs. 67 W, respectively). At intolerance, group mean V̇O2peak was 1.15 ± 0.34 L/min and V̇Epeak was 42.7 ± 20.0 L/min (90 ± 15% of estimated MVV). Ramp-incremental V̇O2peak was not different to that obtained in the 3-4 tests used to characterize the P-tLIM relationship (p = 0.419) and with no differences among tests (p = 0.102; mean V̇O2peak = 1.17 ± 0.32 L/min). Critical power was 37 ± 17 W. In the 9/10 patients who completed the 20 min CP validation ride, V̇O2 reached a steady-state (no difference in values at 15 vs. 20 min; p = 0.47) and was calculated as 1.02 ± 0.27 L/min (90 ± 7 % of ramp-incremental V̇O2peak). CONCLUSIONS: CP was identified in all COPD patients, and the steady-state V̇O2 at CP was sub-maximal. The absence of RCP in 9/10 patients, despite exercise gas-exchange responses consistent with a metabolic acidosis, shows that RCP and CP do not occur at equivalent power output or V̇O2 under conditions of abnormal metabolic, respiratory, and/or ventilatory function. RCP should not be used as a valid surrogate for CP.

Exceeding a "critical" muscle Pi: implications for [Formula: see text] and metabolite slow components, muscle fatigue and the power-duration relationship.

The consequences of the assumption that the additional ATP usage, underlying the slow component of oxygen consumption ([Formula: see text]) and metabolite on-kinetics, starts when cytosolic inorganic phosphate (Pi) exceeds a certain "critical" Pi concentration, and muscle work terminates because of fatigue when Pi exceeds a certain, higher, "peak" Pi concentration are investigated. A previously developed computer model of the myocyte bioenergetic system is used. Simulated time courses of muscle [Formula: see text], cytosolic ADP, pH, PCr and Pi at various ATP usage activities agreed well with experimental data. Computer simulations resulted in a hyperbolic power-duration relationship, with critical power (CP) as an asymptote. CP was increased, and phase II [Formula: see text] on-kinetics was accelerated, by progressive increase in oxygen tension (hyperoxia). Pi is a major factor responsible for the slow component of the [Formula: see text] and metabolite on-kinetics, fatigue-related muscle work termination and hyperbolic power-duration relationship. The successful generation of experimental system properties suggests that the additional ATP usage, underlying the slow component, indeed starts when cytosolic Pi exceeds a "critical" Pi concentration, and muscle work terminates when Pi exceeds a "peak" Pi concentration. The contribution of other factors, such as cytosolic acidification, or glycogen depletion and central fatigue should not be excluded. Thus, a detailed quantitative unifying mechanism underlying various phenomena related to skeletal muscle fatigue and exercise tolerance is offered that was absent in the literature. This mechanism is driven by reciprocal stimulation of Pi increase and additional ATP usage when "critical" Pi is exceeded.

Effects of Prior Upper Body Exercise on the 3-min All-Out Cycling Test in Men.

Prior upper body exercise reduces the curvature constant (W') of the hyperbolic power-duration relationship without affecting critical power. This study tested the hypothesis that prior upper body exercise reduces the work done over the end-test power (WEP; analog of W') during a 3-min all-out cycling test (3MT) without affecting the end-test power (EP; analog of critical power). Ten endurance-trained men (V˙O2max = 62 ± 5 mL·kg·min) performed a 3MT without (CYC) and with (ARM-CYC) prior severe-intensity, intermittent upper body exercise. EP was calculated as the mean power output over the last 30 s of the 3MT, whereas WEP was calculated as the power-time integral above EP. At the start of the 3MT, plasma [La] (1.8 ± 0.4 vs 14.1 ± 3.4 mmol·L) and [H] (42.8 ± 3.1 vs 58.6 ± 5.5 nmol·L) were higher, whereas the strong ion difference (41.4 ± 2.2 vs 30.9 ± 4.6 mmol·L) and [HCO3] (27.0 ± 1.9 vs 16.9 ± 3.2 mmol·L) were lower during ARM-CYC than CYC (P < 0.010). EP was 12% lower during the 3MT of ARM-CYC (298 ± 52 W) than CYC (338 ± 60 W; P < 0.001), whereas WEP was not different (CYC: 12.8 ± 3.3 kJ vs ARM-CYC: 13.5 ± 4.1 kJ, P = 0.312). EP in CYC was positively correlated with the peak [H] (r = 0.78, P = 0008) and negatively correlated with the lowest [HCO3] (r = -0.74, P = 0.015). These results suggest that EP during a 3MT in endurance-trained men is sensitive to fatigue-related ionic perturbation.

Maximal Sustained Isokinetic Power at Exercise Intolerance is not Critical Power.

The asymptote of the hyperbolic power-duration relationship, critical power (CP), demarcates sustainable from non-sustainable exercise. CP is a salient parameter within the theoretical framework determining exercise tolerance. However, measuring CP is time consuming - typically 4 constant-power exercise tests to intolerance, or a 3-min all-out sprint is required.To determine whether 30 s of maximal isokinetic cycling, immediately following the limit of tolerance, approximates CP.Fifteen participants (7 women, 8 men, 23±5 yr, 71±12 kg, V̇O2peak 4.39±1.04 L·min-1; 61±9 mL·kg·min-1) completed 4 constant supra-CP exercise tests to intolerance. Each test was followed immediately by a 30 s maximal isokinetic effort at 80 rpm. Mean isokinetic power was compared to the known CP.Mean±SD CP was 159±47 W (CI95 133, 185 W). Maximal isokinetic power immediately following intolerance was greater (p<0.05) than CP in all but one comparison (181±51 vs. 159±47 W; p>0.07). However, this closest estimation, following the longest duration constant-power test, resulted in 21 W of mean bias and wide limits of agreement (±84 W).Isokinetic power measured immediately following intolerance consistently overestimated critical power. Thus, an adjunct of 30 s maximal isokinetic cycling immediately following the limit of tolerance does not approximate critical power.

Critical power is positively related to skeletal muscle capillarity and type I muscle fibers in endurance-trained 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 morphology is less clear, particularly in endurance-trained individuals, who, relative to their lesser-trained counterparts, possess skeletal muscles that can support high levels of oxygen transport and oxidative capacity, i.e., elevated type I fiber proportion and cross-sectional area (CSA) and capillarity. Fourteen endurance-trained men performed a maximal incremental test to determine peak oxygen uptake (V̇o2peak; 63.2 ± 4.1 ml·min-1·kg-1, mean ± SD) and maximal aerobic power (406 ± 63 W) and three to five constant-load tests to task failure for the determination of CP (303 ± 52 W) and W' (17.0 ± 3.0 kJ). Skeletal muscle biopsies were obtained from the vastus lateralis and analyzed for percent proportion of fiber types, CSA, and indexes of capillarity. CP was positively correlated with the percent proportion ( r = 0.79; P = 0.001) and CSA ( r = 0.73; P = 0.003) of type I fibers, capillary-to-fiber ratio ( r = 0.88; P < 0.001), and capillary contacts around type I fibers ( r = 0.94; P < 0.001) and type II fibers ( r = 0.68; P = 0.008). W' was not correlated with any morphological variables. These data reveal a strong positive association between CP and skeletal muscle capillarity. Our findings support the assertion that CP is an important parameter of aerobic function and offer novel insights into the physiological bases of CP. NEW & NOTEWORTHY This investigation demonstrated very strong positive correlations between critical power and skeletal muscle capillarity, particularly around type I fibers, and type I fiber composition. These correlations were demonstrated in endurance-trained individuals expected to possess well-adapted skeletal muscles, such as high levels of oxygen transport structures and high oxidative capacities, supporting the view that critical power is an important parameter of aerobic function. In contrast, the curvature constant W' was not associated with fiber type composition or capillarity.

Influence of hypoxia on the power-duration relationship during high-intensity exercise.

We investigated the influence of hypoxia on the asymptote (critical power, CP) and the curvature constant (W') of the hyperbolic power-duration relationship, as measured by both conventional and all-out testing procedures. 13 females completed 5 constant-power prediction trials and a 3-min all-out test to estimate CP and W', in both normoxia (N) and moderate hypoxia (H; FiO2=0.13). CP was significantly reduced in hypoxia compared to normoxia when estimated by conventional (H:132±17 vs. N:175±25 W; P<0.001) and all-out methods (H:134±23 vs. N:172±30 W; P<0.01). The W' was not significantly different in hypoxia compared to normoxia when established by conventional (H:12.3±2.7 vs. N:13.2±2.2 kJ) and all-out methods (H:12.0±2.6 vs. N:12.5±1.4 kJ). Estimates of CP and W' obtained with conventional and all-out methods were not significantly different either in normoxia or hypoxia. There was a significant relationship between the % change in CP relative to V̇(O2peak) and the % change in W' in normoxia compared to hypoxia (r=0.83, P<0.001; conventional test). Changes in the W' in hypoxia are related to changes in the CP relative to V̇(O2peak), suggesting that the W' may not be defined simply as an 'anaerobic' energy store.

Influence Of Fiber-specific Muscle Glycogen Depletion On The Parameters Of The 3-min All-out Cycling Test

PURPOSE: The 3 min all-out test has significantly expedited the process of determining the power asymptote (critical power; CP) and the curvature constant (W') of the hyperbolic power-duration relationship for severe intensity exercise. It was hypothesized that selective glycogen depletion of the type I and type II muscle fibres would result in alterations to the CP and W'. Specifically, glycogen depletion of type II muscle fibres was hypothesized to result in a reduction in W' with no appreciable impact upon CP, whereas glycogen depletion of type I muscle fibres was hypothesized to result in a reduction in CP, with no reduction in W'. METHODS: Eight physically active males performed the 3 min all-out cycling test on three occasions: the control condition (C); the day after completing 3-hrs of cycle exercise at 30% VO2max (Type I depletion; T1); and the day after completing 10 x 1-min intervals (5 min rest) at a power output equivalent to 120% VO2max (Type II depletion; T2). The mean power output over the final 30 s of the test was used to estimate the CP; W' was estimated as the power-time integral above end-test power. Data were analyzed using one-way ANOVA. RESULTS: No significant differences were observed between C, T1, or T2, for the estimated CP (225 ± 44, 226 ± 55, 220 ± 46 W respectively) or W' (21.1 ± 2.2, 19.2 ± 4.8, 20.8 ± 3.4 kJ respectively). Blood lactate concentration immediately post the 3 min all-out test was significantly lower following T1 compared to control (9.72 ± 2.32, 8.23 ± 2.31, and 9.44 ± 2.04 mM.L-1 for C, T1 and T2 respectively). CONCLUSIONS: Selective glycogen depletion of either type I or type II muscle fibers had no significant effect on the estimated CP or W'. It is possible that the 3 min all-out test is not of sufficient duration to produce the expected reduction in the CP following T1. The unchanged W' following T2 may be considered surprising, and questions the importance of anaerobic glycolysis to this parameter. Whilst these data are in contrast to our hypotheses, they may have some important implications for the practitioner working in applied sports science. The robustness of the parameters of the 3-min all out cycling test indicates that athletes may complete this test for a valid determination of the CP and W', despite having completed strenuous glycogen-depleting exercise in the preceding 24h.

Influence Of Initial Metabolic Rate On The Parameters Of The 3-min All-out Cycling Test In Men

PURPOSE: It has been established that a single 3 min all-out cycling test can be used to estimate the power asymptote (critical power; CP) and the curvature constant (W[[Unsupported Character - &#900;]]) of the hyperbolic power-duration relationship for severe intensity exercise. The CP represents the highest work rate that does not require the expenditure of the finite work capacity denoted by the W'; the latter is expended at a predictable rate >CP. It was hypothesized that when exercise performed immediately preceding the 3-min all-out test was performed <CP (moderate and heavy exercise), the CP and W' parameters would be unaffected, whereas preceding exercise of different durations >CP (severe exercise) would systematically reduce the W' without affecting the CP. METHODS: Seven physically active male subjects completed 3-min all-out cycling tests in randomized order on 5 occasions: with the test immediately preceded by unloaded cycling (control; C); 6-min moderate (M); 6-min heavy (H); 2-min severe (S2); or 4-min severe (S4) intensity exercise. The CP was estimated from the mean power output over the final 30 s of the test and the W[[Unsupported Character - &#900;]] was estimated as the power-time integral above end-test power. Data were analyzed using one-way ANOVA. RESULTS: There were no significant differences in the estimated CP between C (265 ± 69), M (275 ± 52 W), S2 (274 ± 55 W), or S4 (273 ± 65 W). However, the estimated CP following H (286 ± 66 W) was significantly elevated compared to C (P<0.05). The W[[Unsupported Character - &#900;]] was significantly lower (P<0.05) in S2 (11.5 ± 2.5 kJ) and S4 (8.9 ± 2.2 kJ) than in C (17.3 ± 3.1 kJ), M (17.2 ± 2.4 kJ) and H (15.6 ± 2.3 kJ). CONCLUSION: Consistent with our hypothesis, the W' was significantly reduced by prior severe-intensity exercise with the effect being greater for S4 compared to S2. However, while the CP was not different between the C, M, S2 and S4 conditions, it was significantly increased by preceding H exercise. These results are generally consistent with the predictions of the CP concept. The effects of prior H exercise on the parameters of the power-duration relationship warrant further investigation.

Influence of hyperoxia on muscle metabolic responses and the power–duration relationship during severe‐intensity exercise in humans: a31P magnetic resonance spectroscopy study

Severe-intensity constant-work-rate exercise results in the attainment of maximal oxygen uptake, but the muscle metabolic milieu at the limit of tolerance (T(lim)) for such exercise remains to be elucidated. We hypothesized that T(lim) during severe-intensity exercise would be associated with the attainment of consistently low values of intramuscular phosphocreatine ([PCr]) and pH, as determined using (31)P magnetic resonance spectroscopy, irrespective of the work rate and the inspired O(2) fraction. We also hypothesized that hyperoxia would increase the asymptote of the hyperbolic power-duration relationship (the critical power, CP) without altering the curvature constant (W). Seven subjects (mean +/- s.d., age 30 +/- 9 years) completed four constant-work-rate knee-extension exercise bouts to the limit of tolerance (range, 3-10 min) both in normoxia (N) and in hyperoxia (H; 70% O(2)) inside the bore of 1.5 T superconducting magnet. The [PCr] (approximately 5-10% of resting baseline) and pH (approximately 6.65) at the limit of tolerance during each of the four trials was not significantly different either in normoxia or in hyperoxia. At the same fixed work rate, the overall rate at which [PCr] fell with time was attenuated in hyperoxia (mean response time: N, 59 +/- 20 versus H, 116 +/- 46 s; P < 0.05). The CP was higher (N, 16.1 +/- 2.6 versus H, 18.0 +/- 2.3 W; P < 0.05) and the W was lower (N, 1.92 +/- 0.70 versus H, 1.48 +/- 0.31 kJ; P < 0.05) in hyperoxia compared with normoxia. These data indicate that T(lim) during severe-intensity exercise is associated with the attainment of consistently low values of muscle [PCr] and pH. The CP and W parameters of the power-duration relationship were both sensitive to the inspiration of hyperoxic gas.

Quantifying intervention-related improvements in exercise tolerance

Among the benefits expected to result from a therapeutic intervention in patients with impaired systemic functioning is an increase in exercise tolerance. For this a constant high-intensity work rate has been shown to provide a more sensitive index of improvement than the maximum work rate, or oxygen uptake, on a symptom-limited incremental test. However, the extremely large variability of the improvement in this particular index of tolerance undermines the ability to make general inferences for the underlying functional improvement. We argue that this is a necessary consequence of the particular work rate chosen for the test and the change in the parameters of the subject's hyperbolic power-duration relationship for that form of exercise: its "critical power" and "curvature constant". Without knowledge of these features, any absolute or per cent increase in tolerance time to a single constant-load exercise bout must be interpreted with caution regarding the physiological benefit(s) that have accrued from the intervention.