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Effect of Work and Recovery Durations on W′ Reconstitution during Intermittent Exercise


Medicine & Science in Sports & Exercise: July 2014 - Volume 46 - Issue 7 - p 1433–1440
doi: 10.1249/MSS.0000000000000226
Applied Sciences

Purpose We recently presented an integrating model of the curvature constant of the hyperbolic power–time relationship (W′) that permits the calculation of the W′ balance (WBAL) remaining at any time during intermittent exercise. Although a relationship between recovery power and the rate of W′ recovery was demonstrated, the effect of the length of work or recovery intervals remains unclear.

Methods After determining V˙O2max, critical power, and W′, 11 subjects completed six separate exercise tests on a cycle ergometer on different days, and in random order. Tests consisted of a period of intermittent severe-intensity exercise until the subject depleted approximately 50% of their predicted WBAL, followed by a constant work rate (CWR) exercise bout until exhaustion. Work rates were kept constant between trials; however, either work or recovery durations during intermittent exercise were varied. The actual W′ measured during the CWR (WACT) was compared with the amount of W′ predicted to be available by the WBAL model.

Results Although some differences between WBAL and WACT were noted, these amounted to only −1.6 ± 1.1 kJ when averaged across all conditions. The WACT was linearly correlated with the difference between V˙O2 at the start of CWR and V˙O2max (r = 0.79, P < 0.01).

Conclusions The WBAL model provided a generally robust prediction of CWR W′. There may exist a physiological optimum formulation of work and recovery intervals such that baseline V˙O2 can be minimized, leading to an enhancement of subsequent exercise tolerance. These results may have important implications for athletic training and racing.

1Sport and Health Sciences, College of Life and Environmental Sciences, St. Luke’s Campus, University of Exeter, Exeter, Devon, UNITED KINGDOM; and 2Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, CANADA

Address for correspondence: Andrew M. Jones, Ph.D., Sport and Health Sciences, College of Life and Environmental Sciences, St. Luke’s Campus, University of Exeter, Heavitree Road, Exeter, Devon EX1 2LU, United Kingdom; E-mail:

Submitted for publication October 2013.

Accepted for publication November 2013.

The critical power (CP) concept has profound implications for the modeling of human performance (14,16). It consists of two parameters: the CP and the W′. The CP represents a power output below which it is possible to maintain steady-state exercise and above which the time to exhaustion becomes highly predictable. The W′ represents a finite amount of energy available for work performed in excess of the CP:



where T lim is the time to exhaustion at any power (P) in excess of the CP. Although several limitations of this formulation have been noted (14), the model is useful in that it represents a robust mathematical representation of human performance.

The depletion and reconstitution of the W′ during exercise is of paramount interest to athletes. For example, the balance of W′ remaining (WBAL) at any point in a race necessarily determines the frequency, duration, and intensity of surges above CP an athlete may make to escape a competitor, or to close a gap (13). Recently, Skiba et al. (22) presented a novel integrating model of the W′ that permits the calculation of the WBAL at any time t during intermittent exercise.



In this formulation, Wexp is equal to the expended W′, (tu) is equal to the time in seconds between segments of the exercise session that resulted in a depletion of W′, and τ W is the time constant of the reconstitution of the W′. Thus, the WBAL at any point during a training session or race is the difference between the known W′ and the total W′ expended before time t in the exercise session, which is being recharged exponentially when power falls below CP (22).

It is assumed that the W′ recovers with an exponential time course during intermittent large muscle mass exercise (equation 2) (11,22). Moreover, τ W seems to vary as a curvilinear function of the difference (D CP) between recovery P and the CP, suggesting a highly organized underlying control process (22):



where the numerical constants are arbitrary parameters fit to the previously reported data set; in particular, 316 W seems to represent an asymptote beyond which a larger D CP does not further speed recovery. This recovery schema may be conceptualized in several ways. Noodhof et al. (20) recently offered the example of a vessel of water (W′), which may be filled by a tap (aerobic metabolism) and emptied by a drain of variable size (supra-CP work rate). In such a case, the rate of refill would be curvilinearly related to the difference between the fill rate and the drain rate.

A robust model of the depletion and reconstitution of the W′ provides an opportunity to test how different performance scenarios may affect W′ kinetics. Given the importance of the W′ as a performance indicator, this might have valuable real-world applications for athletes. In particular, investigating whether (and how) different work and recovery intervals alter the τ W will be important in refining the intermittent model of W′ presented previously (22) with consequent practical applications for athletic training and the tactics used by athletes during competition.

Thus far, there have been no attempts to study the effects of intermittent protocols as conditioning or “priming” exercise on subsequent exercise energetics. This question is of considerable importance from a performance perspective, as foot and bicycle races often involve a series of surges in pace before a final, protracted effort in the finale. Indeed, road and track cyclists are often observed to limit the length of a “pull” while leading a group of riders, preferring to divide the work among the group. As there have been some data suggesting a linkage between the W′ and the V˙O2 “slow component” (V˙O2SC) (22,27), it is possible that there exists a physiologically optimum formulation of intermittent exercise, which may minimize the development of the V˙O2SC and thus permit an increase in time to exhaustion.

The primary purpose of this investigation was to test the robustness of the WBAL model using a variety of work and recovery durations during intermittent exercise performed before an exhaustive constant work rate (CWR) exercise bout. We hypothesized that the WBAL model would accurately predict the W′ remaining and therefore available for use during this subsequent bout of CWR exercise. We also hypothesized that there would be a positive relationship between the difference between the V˙O2 immediately preceding the start of the CWR bout and the V˙O2peak (

) and the W′ remaining for CWR exercise.

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Five healthy males (mean ± SD: age = 27.4 ± 6 yr, height = 1.84 ± 0.08 m, body mass = 85.2 ± 18 kg) and six healthy females (mean ± SD: age = 25.2 ± 1.6 yr, height = 1.67 ± 0.12 m, body mass = 65.3 ± 12.7 kg) volunteered to participate in this study. The subjects were recreational athletes but were not highly trained. All subjects were familiar with laboratory exercise testing procedures. The study was approved by the University of Exeter Research Ethics Committee. After the experimental procedures, associated risks, and potential benefits of the study protocol had been explained to the subjects, they were required to give their written informed consent to participate. Subjects were instructed to arrive at the laboratory in a rested and fully hydrated state, at least 3 h postprandial. They were also asked to avoid strenuous exercise in the 24 h preceding each testing session and to refrain from caffeine and alcohol for 3 h before each test. All tests were performed at the same time of day (±2 h) at sea level in an air-conditioned laboratory at 20°C. At least 48 h separated each test, with the main experiment being completed within a 2-wk period.

All testing was carried out using the same Lode Excalibur Sport (Lode, Groningen NL). The gas exchange threshold and the maximum oxygen uptake (V˙O2max) were estimated for each subject from data collected during a standard ramp incremental protocol (30 W·min−1). After an advance familiarization trial, the subject’s CP and W′ were estimated using a 3-min all-out test as previously described (24). The CP was taken as the mean power output for the final 30 s of the test, and the W′ was estimated as the power–time integral above the CP (21).

In each of six subsequent visits, the subjects performed intermittent exercise, followed by a CWR exercise bout until exhaustion (Fig. 1). For ease of comparison with previous work from our laboratory (9,22), the work rates for both the “on” interval of the intermittent exercise and the CWR portion of each trial (P EXP) were calculated as that predicted to result in exhaustion in 6 min (P 6; equation 1) + 50% of the difference between P 6 and the CP. The “off” or recovery intervals were performed at 20 W in all cases, again in keeping with previous publications (9,22). The ergometer was set for the fastest possible change in load, which is reported by the manufacturer to be nearly instantaneous, and which we observed to be less than 0.5 s during testing.



The pattern of the intermittent work was different in each of the six visits, with the duration of either the work intervals or the recovery intervals being manipulated. In three of the trials, the work interval duration was varied (60, 40, or 20 s) while maintaining a recovery interval of 30 s (trials 60–30, 40–30, and 20–30, respectively). In the other three trials, a work interval duration of 20 s was maintained, followed by a recovery interval duration of 20, 10, or 5 s (trials 20–20, 20–10, and 20–5, respectively). In each case, the intermittent exercise portion of the protocol was designed to result in an approximately 50% depletion of the W′ by using equation 3 (22).

The CWR portion of each trial began immediately after the final recovery interval (Fig. 1) and was continued until the subject’s cadence fell by more than 5 rpm below the subject’s self-selected cadence despite vigorous verbal encouragement (T lim). All subjects completed all trials in a randomized order. After the completion of the main protocol, subjects returned to the laboratory to complete another 3-min all-out test to determine any potential training effect.

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V˙O2 data collection and modeling

During all sessions, pulmonary gas exchange was measured breath by breath (Jaeger Oxycon Pro, Hoechberg, Germany) with subjects wearing a nose clip and breathing through a low dead space (90 mL), low resistance (0.75 mm Hg·L−1·s−1 at 15 L·s−1) mouthpiece and impeller turbine assembly (Jaeger Triple V). The analyzer was calibrated before each test with gases of known concentration, and the turbine volume transducer was calibrated using a 3-L syringe (Hans Rudolph, Kansas, MO). V˙O2, carbon dioxide output, and minute ventilation were calculated using standard formulae (1).

The breath-by-breath V˙O2 data collected during exercise testing were reviewed to exclude errant breaths resulting from sighing, coughing, or swallowing. Values lying >4 SD from the local mean were removed. The remaining data were subsequently linearly interpolated to provide second-by-second values. V˙O2start was defined as the mean V˙O2 calculated for the 30 s immediately preceding the CWR bout. V˙O2peak was defined as the mean V˙O2 calculated for the final 30 s of exercise in each CWR bout.

was calculated as the difference between V˙O2start and V˙O2peak.

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The power data from all sessions were fit to equation 2. τW was varied by an iterative process until the WBAL at the time CWR began was equal to the amount of W′ actually measured to be available during the CWR portion of the trial (WACT). WACT was calculated as the sum of the work performed in excess of the CP, assuming a constant CP. WBAL and WACT, as well as the predicted and actual T lim were compared using repeated-measures ANOVA (SPSS ver. 20; IBM Corporation, Armonk, NY). Repeated-measures ANOVA was also used to compare any differences in V˙O2start between trials. The Pearson product moment correlation coefficient was used to test the relationship between the

and the WACT. Paired-samples t-test were used to compare the CP, W′, and maximum 30-s V˙O2 measured during the 3-min all-out test before and after the main experiment. Statistical significance was accepted at the P = 0.05 level, and data are reported as group mean ± SD.

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Variable work interval trials

The group mean τ W fell considerably (i.e., the kinetics were faster) as the work interval duration was reduced from 60 to 40 to 20 s (conditions 60–30, 40–30, and 20–30; Table 1 and Fig. 2), indicating that subjects recovered more quickly than predicted as work duration was shortened. This led to a relative underprediction of T lim and WACT (Table 1 and Fig. 3). The difference between WBAL and WACT was not significant in the 60–30 or 40–30 bout but reached significance in the 20–30 bout (P < 0.01). The relationship between the work interval duration and the WACT underprediction was linear (r = 0.99, P < 0.05). The comparison of the predicted and measured T lim yielded a significant difference in both the 40–30 and the 20–30 conditions (P < 0.01; Table 1).







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Variable recovery interval trials

Decreasing the recovery interval duration from 30 to 20 s resulted in an additional reduction of the τ W (Table 1 and Fig. 2), indicating a faster than expected recovery. This resulted in a relative underprediction of WACT (Table 1 and Fig. 3). The differences between WBAL and WACT were statistically significant in the 20–20 (P < 0.01) and 20–10 bouts (P < 0.01). There was no significant difference between WBAL and WACT in the 20–5 bout. A similar pattern was noted for the comparison of the predicted and measured T lim (Table 1). These underpredictions were also statistically different from one another in several cases (Table 1).

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V˙O2 analysis

Group mean V˙O2 data are presented in Figures 4a–4d. A “sawtooth” pattern for V˙O2 during work and recovery was evident in the 60–30 and 40–30 conditions but was lost in the 20–30 condition, where the trace resembled a slow curvilinear rise in V˙O2. There was a significant difference between the V˙O2start recorded in the 60–30, 40–30, and 20–30 trials (P < 0.05), with a trend toward a linear fall in V˙O2start as the work interval was reduced from 60 to 20 s (r = 0.99, P = 0.07; Fig. 4a). There was no significant difference between trials in the V˙O2peak recorded.



The group mean pattern of the work and recovery interval V˙O2 resembled a slow curvilinear rise in the 20–20, 20–10, and 20–5 trials (Figs. 4c and 4d). There was a significant difference in V˙O2start between the 20–30 and the 20–10 and 20–5 trials (P < 0.05) (Table 1). There was also a significant difference between the V˙O2start for the 20–10 and 20–5 trials. The V˙O2start for the 20–5 trial was significantly greater than all of the other trials. Overall, there was a linear increase in V˙O2start as the recovery interval was decreased from 30 to 5 s (r = 0.99, P < 0.01). There was no significant difference between the V˙O2peak recorded in any of the trials (Table 1). The

was significantly correlated with the W′ remaining in the CWR (r = 0.79, P < 0.01; Fig. 5).



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Changes in CP

There was a group mean increase in CP of 18 W ± 20 W and a group mean reduction in the W′ of 0.6 ± 0.6 kJ during the study. The change in CP was statistically significant (P < 0.05), whereas the change in W′ was not. There was an inverse correlation between the change in CP and the change in W′ (r = 0.89, P < 0.01). The group mean peak V˙O2 measured during the 3-min all-out test increased by 260 ± 223 mL·min−1 (P < 0.01). When the sessions were arranged in order of execution, no significant differences were found in the peak V˙O2 between most cases. However, a solitary significant difference of approximately 2% was noted between the fourth and the sixth sessions (3416 ± 916 vs 3488 ± 969 mL·min 1, P < 0.05).

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Our goal was to test the predictive ability of the WBAL model in a variety of conditions and to examine the relationship between V˙O2 and W′. We report three novel results in this investigation. First, we expected to find a predictable WACT, regardless of the way the intermittent work or recovery durations were prescribed. This was not the case. Rather, a larger than expected WACT was observed as work interval duration was reduced (trials 60–30, 40–30, and 20–30; Fig. 2). Second, reducing recovery duration from 30 to 20 s also resulted in an underprediction of the WACT, although this difference was small in absolute terms (<2 kJ). Third, there was a positive correlation between the

and the W′ available for CWR exercise. The findings of the study have important implications for both training prescription and performance management during competition.

These observations can be interpreted in multiple ways with respect to the WBAL model. One possibility is that intermittent exercise reduces the τ W , speeding the recovery of the W′ during intermittent exercise (Fig. 2). Priming exercise has previously been reported to increase the CP (18), and it is known that the CP and the τ W are correlated (22). Consideration of equation 3 indicates that a larger D CP would result in a faster τ W , irrespective of whether that larger D CP was the result of a lower recovery power or a higher CP. It is therefore possible that prior intermittent exercise increased the CP and the D CP and hence permitted a more complete recovery of the W′ before CWR exercise began.

It has been reported that exercise above CP (where W′ would be used) is associated with disproportionally increased perfusion of Type II muscle fibers (10). Recent work also indicates that the CP can be increased in hyperoxia (26). These results suggest that fiber-specific improvements in O2 delivery may result in enhanced exercise tolerance. It is possible that intermittent exercise positively affects the CP through a mechanism similar to postexercise hyperemia (23). That is, as exercise moves from, for example, 300 W down to 20 W during a short recovery interval, muscle perfusion may remain higher on average than might be the case with a longer recovery interval. The net result would be muscle that remains better oxygenated (supporting PCr resynthesis) and well “flushed” (removing accumulating, fatigue-related metabolites) due to a higher net blood flow. This might be expected to result in a faster recovery of the W′.

Previous reports indicating that heavy-intensity priming exercise results in an increase in apparent W′ during subsequent exercise (8,15) suggest that our results could also be explained by an increased W′. In the present study, the mean power output for the intermittent portion of the majority of the trials fell within the heavy exercise domain. The preceding intermittent exercise may therefore have functioned to prime the muscle (i.e., raise the W′) before the CWR bout (8,15). The apparent priming effect on the W′ seemed to increase as the ratio of work to rest decreased from 2 (trial 60–30) to 0.67 (trial 20–30) (Fig. 3). This may suggest that intermittent exercise protocols resulting in a lower mean power output within the heavy domain might provide an effective priming stimulus.

An explanation invoking priming becomes troublesome in the context of the variable recovery duration data, however. These data indicate that the estimated W′ available for CWR exercise increased in the face of a constant work interval duration as the recovery duration was reduced from 30 to 10 s (trials 20–30 and 20–10, work–recovery ratio varying from 0.67 to 2) (Table 1). The observed W′ during the CWR portion of the trial did not approach the predicted value until the recovery duration was reduced to 5 s and the work–recovery ratio became 4 (Fig. 3). However, it is apparent that the W′ does not simply represent an “energy store” but is also related to the depletion of substrates or accumulation of metabolites to some critical limiting values (11,12,14,16,21). It is possible that relatively longer work intervals may result in a greater accumulation of metabolites implicated in fatigue (i.e., [Pi], [H+], and [Ca2+]) and/or a greater depletion of substrates (i.e., [PCr], [ATP], and [glycogen]), thereby reducing the apparent W′ remaining. This reasoning may be supported by a comparison between trial 60–30 and trial 20–10 (Table 1). Despite having an equal work–recovery ratio and an identical mean P during the intermittent portion of the trial, the 20–10 protocol resulted in a considerably larger WACT as compared with the 60–30 condition. Thus, the intermittent protocol used here may represent a fundamentally different priming stimulus compared with CWR exercise followed by a long recovery. Interestingly, both of the existing studies indicating an increase in W′ with priming exposed the subjects to both active recovery (20 W cycling) and several minutes of passive rest before the subsequent work bout (8,15). There have been reports that [PCr] recovery may exhibit an overshoot to a level greater than resting baseline in the period after exercise cessation (17,19). An increased W′ may be, at least in part, a consequence of that overshoot.

The linear relationship between

and the W′ available for CWR exercise represents an extension of previous results correlating the amplitude of the V˙O2SC and the absolute size of the W′ (27) and the modeled discharge of the W′ and the V˙O2SC (22). A previous study also reported significant correlations between indices of anaerobic exercise performance and the amplitude of the V˙O2SC (2). The present results suggest that the lower the V˙O2start, the more capacity there is for subsequent fatiguing work (Fig. 5). This increased “muscle reserve” may reflect effects on fiber recruitment and/or metabolite concentrations. It may therefore be conceptually helpful to consider these factors in the context of a multicompartment model of the W′ previously proposed (22). In such a scenario, the CP and the W′ remain constant. However, separate “compartments” (notionally similar to Type I and Type II fiber populations) are assumed to make discrete individual contributions to the macroscopic W′ and possess differing time constants of W′ reconstitution, owing to differences in fiber-specific aerobic and anaerobic capacity. The faster-recovering compartment might tend to contribute more to the overall work capacity during intermittent exercise and therefore potentially lead to an extended T lim during subsequent CWR.

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Overall model performance

The group mean τW in the 60–30 trial (403 s; Fig. 2) is in good agreement with that derived for the WBAL model previously (377 s) using the same work and recovery durations (22). Considering the mean across all conditions, the model as applied to the present data tended to underpredict time to exhaustion by approximately 27 s and underpredict the W′ remaining for CWR by approximately 1.6 kJ (Table 1). Thus, while the model remains reasonably robust over a wide variety of conditions, it may be refined to account more specifically for work and recovery durations during intermittent exercise.

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During the 2-wk intervention period, CP improved in nine subjects and decreased in two. The group mean CP increased by approximately 9%, in keeping with other studies that have described the efficacy of high-intensity interval training on various physiological parameters (5–7). The changes in W′ represented almost a mirror image of the CP, increasing in three subjects and decreasing in the remainder, with the difference not achieving statistical significance, consistent with Vanhatalo et al. (25). Moreover, the peak V˙O2 measured in the 3-min all-out test increased by 8% during the experimental testing. It is possible that the training effect observed on CP may complicate the interpretation of the W′ recovery data. However, the randomized order of the sessions would be expected to obviate an order effect. We note that the subjects who showed the smallest increase in CP (in particular the subject who improved by only 1 W) showed τ W and W′ underprediction profiles closest to the group mean values depicted in Figures 1 and 2. Moreover, when placed in order of execution, no significant differences were noted between the peak V˙O2 values recorded during the intermittent protocols, except the fourth and the sixth experimental sessions, which showed a difference of approximately 2%. Collectively, this suggests that the randomization was successful in equally distributing any effect of the (likely unavoidable) improvements in fitness during the study, such that our results chiefly reflect differences in work and recovery duration between the intermittent exercise protocols used.

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Practical implications

Whether through an increase in absolute W′ or an increase in CP, there seems to be a clear advantage to subsequent exercise performance in limiting work duration during intermittent severe intensity cycling exercise. There may also exist an optimum recovery duration, but more work will be required to fully elucidate this. On the basis of the present data, it would seem that limiting the work interval to 20 s or less and maintaining a recovery interval of between 20 and 10 s would be most advantageous. These results are useful to coaches and the athletes they counsel. As cycling races are often decided by rapid accelerations in the final kilometers, the athlete who best preserves their W′ until the last possible moment has a distinct advantage. These results are also important with respect to training prescription. For example, it is now common coaching practice to use “microinterval” protocols (e.g., 15–15 s or 30–30 s [3,4]) interchangeably with more traditional interval work because these microinterval protocols seem less taxing to the athlete. The present results lend credence to these reports. However, our results also suggest that there may be more complex physiology at work than is assumed by many sports practitioners who may think of work and rest intervals purely in terms of accumulated work. Therefore, it may be advisable that athletes continue to be counseled to train in ways most applicable to the way they intend to race. Finally, although the group mean τ W in the present study closely corresponds with previous reports (11,22), we have found subjects who seem to recover their W′ considerably faster. For example, subject 9 (CP = 366 W, τ W = 104 s in the 60–30 condition) had a calculated τ W more than 200 s faster than the apparent asymptote of equation 3. It may therefore be advisable to develop a “personalized” predictive function for the estimation of τ W for well-trained athletes.

In conclusion, these results indicate that reductions in work interval duration during intermittent exercise result in a greater-than-expected improvement in subsequent severe-domain CWR performance. These results also indicate that, in the setting of sufficiently short work duration, reductions in recovery duration can also yield subsequent CWR performance in excess of model predictions. Finally, there is a positive relationship between

and the amount of W′ available for subsequent CWR exercise, such that optimizing intermittent exercise to minimize fatigue during subsequent exercise may be linked to minimizing V˙O2. The mechanisms responsible for these phenomena remain unclear but may relate to possible priming effects of intermittent exercise on W′ and/or CP with consequent effects on the rate of W′ reconstitution.

This research was not supported by external funding.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

The authors declare no conflict of interest.

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