The W' Balance Model: Mathematical and Methodological Considerations

Intensity Matters: Effect of Different Work-Matched Efforts on Subsequent Performance in Cyclists

PURPOSE

To assess the effect of 2 work-matched efforts of different intensities on subsequent performance in well-trained cyclists.

METHODS

The present study followed a randomized controlled crossover design. Twelve competitive junior cyclists volunteered to participate (age, 17 [1] y; maximum oxygen uptake, 71.0 [4.7] mL·kg-1·min-1). The power-duration relationship was assessed through 2-minute, 5-minute, and 12-minute field tests under fresh conditions (control). On subsequent days and following a randomized order, participants repeated the aforementioned tests after 2 training sessions matched for mechanical work (∼15 kJ/kg) of different intensities (ie, a moderate-intensity continuous-training [60%-70% of critical power; CP] session or a session including high-intensity intervals [3-min repetition bouts at 110%-120% of the CP interspersed by 3-min rest periods]).

RESULTS

A significantly lower power output was found in the 2-minute test after the high-intensity training session compared not only with the control condition (-8%, P < .001) but also with the moderate-intensity continuous-training session (-7%, P = .003), with no significant differences between the latter conditions. No significant differences between conditions were found for the remaining tests. As a consequence, the high-intensity training session resulted in significantly lower W' values compared to both the control condition (-27%, P = .001) and the moderate-intensity continuous-training session (-26%, P = .012), with no differences between the 2 latter conditions and with no differences for CP.

CONCLUSION

A session including high-intensity intermittent efforts induces a greater fatigue, particularly in short-duration efforts and W', than a work-matched continuous-training session of moderate intensity.

Running Critical Power and W´: Influence of the Environment, Timing and Time Trial Order

This study aimed to determine the influence of the testing environment (track vs. treadmill), time trial order (long-short vs. short-long), and timing (within-session vs. between-sessions) on the critical power (CP) and work over CP (W´), using the power metric in runners. Fifteen highly trained athletes performed three test sessions composed of two time trials of 9- and 3-min, separated by a 30-min rest period. One session was performed on a track, and two sessions on a treadmill, alternating the order of the time trials. The CP and W´ values determined on the track were significantly greater and lower than on the treadmill, respectively (p<0.001; CP≥89 W; W´≥3.7 kJ). Their degree of agreement was low (SEE CP>5%; W´>10%) and therefore was not interchangeable. There were no performance differences in the timing of the time trials (p=0.320). Lastly, performing the 9-min trial first resulted in a greater power output compared to when executed last (p<0.001; 4.9 W), although this resulted in similar CP and W´ values (Bias<5 and 10%, respectively). In conclusion, it is feasible to test CP and W´ in a single testing session, irrespective of the time trial order, although not interchangeably between track and treadmill.

A dynamic model of the bi-exponential reconstitution and expenditure of W' in trained cyclists

ABSTRACTThe aim of this study was to investigate the effects of different recovery power outputs on the reconstitution of W' and to develop a dynamic bi-exponential model of W' during depletion and reconstitution. Ten trained cyclists (mass 71.7 ± 8.4 kg; V̇O2max 60.0 ± 6.3 ml·kg-1·min-1) completed three incremental ramps (20 W·min-1) to the limit of tolerance on each of six occasions with recovery durations of 30 and 240 s. Recovery power outputs varied between 50 W (LOW); 60% of critical power (CP) (MOD) and 85% of CP (HVY). W' reconstitution was measured following each recovery and fitted to a bi-exponential model. Amplitude and time constant (τ) parameters were then determined via regression analysis accounting for relative intensity and duration to produce a dynamic model of W'. W' reconstitution slowed disproportionately as recovery power output increased (p < 0.001) and increased with recovery duration (p < 0.001). The amplitudes of each recovery component were strongly correlated to W' reconstitution after 240 s at HVY (r = 0.95), whilst τ parameters were found to be related to the fractional difference between recovery power and CP. The predictive capacity of the resultant model was assessed against experimental data with no differences found between predicted and experimental values of W' reconstitution (p > 0.05). The dynamic bi-exponential model of W' accounting for varying recovery intensities closely described W' kinetics in trained cyclists facilitating real-time decisions about pacing and tactics during competition. The model can be customised for individuals from known CP and W' and a single additional test session.HighlightsA dynamic bi-exponential model of W' accounting for both varying power output and duration.Individual customisation of the model can be achieved with a single specific test session.W' reconstitution slows disproportionally with increasing intensity after repeated bouts.

Running Critical Power: A Comparison Of Different Theoretical Models

This study aimed (i) to compare the critical power (CP) and work capacity over CP (W´) values reported by the different CP models available in current analysis software packages (Golden Cheetah and Stryd platform), (ii) to locate the CP values in the power-duration curve (PDC), and (iii) to determine the influence of the CP model used on the W´ balance. Fifteen trained athletes performed four time trials (i. e., 3, 5, 10, 20 minutes) to define their PDC through different CP models: work-time (CPwork), power-1/time (CP1/time), Morton hyperbolic (CPhyp), Stryd platform (CPstryd), and Bioenergetic Golden Cheetah (CPCheetah). Three additional time trials were performed: two to locate the CP values in the PDC (30 and 60 minutes), and one to test the validity of the W' balance model (4 minutes). Significant differences (p<0.001) were reported between models for the estimated parameters (CP, W´). CPcheetah was associated with the power output developed between 10 to 20 minutes, CP1/time, CPstryd CPwork and CPhyp. The W´ reported by the three-parameter CP models overestimated the actual 4 minutes time to exhaustion, with CPwork (0.48 [- 0.19 to 1.16] minutes); and CP1/time (0.40 [- 0.13 to 0.94] minutes) being the only valid models (p≥0.240).

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.

Variability in exercise tolerance and physiological responses to exercise prescribed relative to physiological thresholds and to maximum oxygen uptake

NEW FINDINGS

What is the central question of this study? Does prescribing exercise intensity using physiological thresholds create a more homogeneous exercise stimulus than using traditional intensity anchors? What is the main finding and its importance? Prescribing exercise using physiological thresholds, notably critical power, reduced the variability in exercise tolerance and acute metabolic responses. At higher intensities, approaching or exceeding the transition from heavy to severe intensity exercise, the imprecision of using fixed %V ̇ O 2 max ${\dot V_{{{\rm{O}}_{\rm{2}}}{\rm{max}}}}$  as an intensity anchor becomes amplified.

ABSTRACT

The objective of this study was to determine whether the variability in exercise tolerance and physiological responses is lower when exercise is prescribed relative to physiological thresholds (THR) compared to traditional intensity anchors (TRAD). Ten individuals completed a series of maximal exercise tests and a series of moderate (MOD), heavy (HVY) and severe intensity (HIIT) exercise bouts prescribed using THR intensity anchors (critical power and gas exchange threshold) and TRAD intensity anchors (maximum oxygen uptake;V ̇ O 2 max ${\dot V_{{{\rm{O}}_{\rm{2}}}{\rm{max}}}}$ ). There were no differences in exercise tolerance or acute response variability between MODTHR and MODTRAD . All individuals completed HVYTHR but only 30% completed HVYTRAD . Compared to HVYTHR , where work rates were all below critical power, work rates in HVYTRAD exceeded critical power in 70% of individuals. There was, however, no difference in acute response variability between HVYTHR and HVYTRAD . All individuals completed HIITTHR but only 20% completed HIITTRAD . The variability in peak (F = 0.274) and average (F = 0.318) blood lactate responses was lower in HIITTHR compared to HIITTRAD . The variability in W' depletion (the finite work capacity above critical power) after the final interval bout was lower in HIITTHR compared to HIITTRAD (F = 0.305). Using physiological thresholds to prescribe exercise intensity reduced the heterogeneity in exercise tolerance and physiological responses to exercise spanning the boundary between the heavy and severe intensity domains. To increase the precision of exercise intensity prescription, it is recommended that, where possible, physiological thresholds are used in place ofV ̇ O 2 max ${\dot V_{{{\rm{O}}_{\rm{2}}}{\rm{max}}}}$ .

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.

Competition Between Desired Competitive Result, Tolerable Homeostatic Disturbance, and Psychophysiological Interpretation Determines Pacing Strategy

Scientific interest in pacing goes back >100 years. Contemporary interest, both as a feature of athletic competition and as a window into understanding fatigue, goes back >30 years. Pacing represents the pattern of energy use designed to produce a competitive result while managing fatigue of different origins. Pacing has been studied both against the clock and during head-to-head competition. Several models have been used to explain pacing, including the teleoanticipation model, the central governor model, the anticipatory-feedback-rating of perceived exertion model, the concept of a learned template, the affordance concept, the integrative governor theory, and as an explanation for "falling behind." Early studies, mostly using time-trial exercise, focused on the need to manage homeostatic disturbance. More recent studies, based on head-to-head competition, have focused on an improved understanding of how psychophysiology, beyond the gestalt concept of rating of perceived exertion, can be understood as a mediator of pacing and as an explanation for falling behind. More recent approaches to pacing have focused on the elements of decision making during sport and have expanded the role of psychophysiological responses including sensory-discriminatory, affective-motivational, and cognitive-evaluative dimensions. These approaches have expanded the understanding of variations in pacing, particularly during head-to-head competition.

Critical Power, Work Capacity, and Recovery Characteristics of Team-Pursuit Cyclists

PURPOSE

Leading a 4-km team pursuit (TP) requires high-intensity efforts above critical power (CP) that deplete riders' finite work capacity (W'), whereas riders following in the aerodynamic draft may experience some recovery due to reduced power demands. This study aimed to determine how rider ability and CP and W' measures impact TP performance and the extent to which W' can reconstitute during recovery positions in a TP race.

METHODS

Three TP teams, each consisting of 4 males, completed individual performance tests to determine their CP and W'. Teams were classified based on their performance level as international (INT), national (NAT), or regional (REG). Each team performed a TP on an indoor velodrome (INT: 3:49.9; NAT: 3:56.7; and REG: 4:05.4; min:s). Ergometer-based TP simulations with an open-ended interval to exhaustion were performed to measure individual ability to reconstitute W' at 25 to 100 W below CP.

RESULTS

The INT team possessed higher CP (407 [4] W) than both NAT (381 [13] W) and REG (376 [15] W) (P < .05), whereas W' was similar between teams (INT: 27.2 [2.8] kJ; NAT: 29.3 [2.4] kJ; and REG: 28.8 [1.6] kJ; P > .05). The INT team expended 104% (5%) of their initial W' during the TP and possessed faster rates of recovery than NAT and REG at 25 and 50 W below CP (P < .05).

CONCLUSIONS

The CP and rate of W' reconstitution have a greater impact on TP performance than W' magnitude and can differentiate TP performance level.