Parker Simpson & Kordi - 2016 - Comparison of Critical Power and wprime derived from two or three maximal tests- Ahead of Print

“Comparison of Critical Power and W Derived from Two or Three Maximal Tests” by Parker Simpson L, Kordi M

International Journal of Sports Physiology and Performance

© 2016 Human Kinetics, Inc.

Note. This article will be published in a forthcoming issue of the

International Journal of Sports Physiology and Performance. The article

appears here in its accepted, peer-reviewed form, as it was provided by

the submitting author. It has not been copyedited, proofread, or

formatted by the publisher.

Section: Original Investigation

Article Title: Comparison of Critical Power and W Derived from Two or Three Maximal Tests

Authors: Len Parker Simpson1, 2 and Mehdi Kordi1, 3

Affiliations: 1English Institute of Sport, Manchester, UK. 2University of Kent, UK. 3Northumbria University, UK.

Journal: International Journal of Sports Physiology and Performance

Acceptance Date: October 21, 2016

©2016 Human Kinetics, Inc.

DOI: http://dx.doi.org/10.1123/ijspp.2016-0371

http://dx.doi.org/10.1123/ijspp.2016-0371




Title: Comparison of Critical Power and W Derived from Two or Three Maximal Tests.

Submission Type: Original Investigation

Authors & Affiliations

Len Parker Simpson 1, 2.; 1English Institute of Sport, Manchester, UK, 2University of Kent, UK.

Mehdi Kordi 1, 3; 1English Institute of Sport, Manchester, UK, 3Northumbria University, UK.

Corresponding Author:

Dr Len Parker Simpson

English Institute of Sport

MIHP 299 Alan Turing Way

Manchester, UK

M11 3BS

T: +44 (0)7714 564 367

e: [email protected]

Running Head: Measuring CP & W′ in the Applied Setting

Abstract Word Count: 198

Text Only Word Count: 3370

Number of Figures: 5

Number of Tables: 0

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mailto:[email protected]?subject=




ABSTRACT

PURPOSE: Typically, accessing the asymptote (Critical Power; CP) and curvature constant

(W) parameters of the hyperbolic power-duration relationship requires multiple constant-power,

exhaustive exercise trials, spread over several visits. However, more recently single-visit

protocols and personal power meters have been used. We investigated the practicality of using a

two-trial, single-visit protocol in providing reliable CP & W estimates. METHODS: 8 trained

cyclists underwent 3- and 12-min maximal exercise trials in a single session to derive (2-trial)

CP & W estimates. On a separate occasion a 5-min trial was performed providing a third trial to

calculate (3-trial) CP & W. RESULTS: There were no differences in CP (283 ± 66 vs. 282 ± 65

W) or W′ (18.72 ± 6.21 vs. 18.27 ± 6.29 kJ) obtained from either the 2-trial or 3-trial methods

respectively. Following two familiarisation sessions (completing a 3- & 12-min trial on both

occasions), both CP and W remained reliable over additional, separate measurements.

CONCLUSIONS: The present study demonstrates that following two familiarisation sessions,

reliable CP & W parameters can be obtained from trained cyclists using only two maximal

exercise trials. These results offer practitioners a practical, time-efficient solution for

incorporating power-duration testing into applied athlete support.

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INTRODUCTION

The hyperbolic power-duration relationship is a fundamental characteristic of human

physiology at both the muscle- 1,2 and whole body-level 3–5. The hyperbolic relationship has

an asymptote, termed ‘Critical Power’ (CP) which represents an inherent characteristic of the

sustainable aerobic capabilities of the body 5. The curvature constant of the hyperbola, termed

W′, represents a fixed quantity of work which may be completed at exercise intensities above CP

5. The CP thus demarcates distinct exercise-intensity domains; below CP (heavy-intensity

domain) physiological homeostasis is attained 4,6 above CP (severe-intensity domain) is

driven toward its maximum 4 and multiple metabolites project inexorably toward their nadirs, at

which point, exhaustion ensues 6,7.

The power-duration relationship parameters, CP & W′, provide a full picture of

mechanical performance capability of an athlete. Once CP & W′ are known, mechanical exercise

performance capability can be accurately determined 8–10. Both the CP and W′ can alter with

exercise training 11–14. Changes in either or both the CP and/or W′ help explain changes in

mechanical performance capability observed in other mechanical assessments (e.g. ramp test

performance etc.). Thus, CP & W′ offer the coach, athlete and practitioner greater physiological

insight into training-induced changes in performance capabilities than other commonly used

assessment methods such as a ramp test, step-incremental sub-maximal test, maximal lactate

steady state assessment or functional threshold power tests. However, most alternative

assessments to the CP assessment require less than ~ 90 min of an athlete’s time, whereas the CP

assessment has been more drawn-out.

The traditional method of assessing CP & W′ requires a cyclist to perform multiple (3 to

5), exhaustive, constant-power exercise trials of varying intensity over a number of days 3,4. The

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advent of a single, 3-min all-out test helped expedite the estimation of CP & W′ 15 but still

required specific, expensive laboratory equipment. More recently, there has been increasing

interest in obtaining the power-duration relationship of athletes and doing so in a more practical

manner 10,16,17. Karsten et al. have previously reported valid CP estimates using a 3-trial (trials

separated by 30 min recoveries) method conducted outdoors on bicycles fitted with power meters

17. An approach akin to this would be an attractive option to athletes and coaches due to the

ostensibly higher ecological validity of the results. Furthermore, it should help eliminate any

additional error in the CP & W′ parameter estimates brought about through testing on one power

meter yet training and racing on another.

Strictly, two maximal or exhaustive exercise trials only are required to obtain CP & W′

estimates. However, when using only two trials, the linear relationship between work done and

time (or power and time-1) will be ‘perfect’ (R2 = 1.00). In this scenario, any change (under-

performance) in either of the two trials will have a large effect on the CP & W′ parameter

estimates 18. Once a third trial is introduced, it is possible to assess the goodness of fit of the

linear relationship and determine the error in both the CP & W′ estimates. While this additional

information is of interest to the practitioner and coach, it is unlikely to appeal to the athlete who

has to perform an additional maximal effort. Thus, if reliable CP & W′ estimates were

obtainable from just two trials, this may promote the inclusion of power-duration testing.

Elite athletes often follow demanding racing and training schedules. Integrating objective

assessment of an athlete’s physiological condition and capabilities can be a perennial challenge

for coaches and practitioners. Providing a scientifically valid and time efficient assessment

method, which provides athlete and coach with insightful information, could allow for more

frequent assessment of these parameters. A power-duration assessment requires only a power

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meter and a stopwatch 18,19. With the addition of a stationary trainer, the assessment can be

conducted anywhere, anytime with laboratory-style reproducible conditions. Using a series of

self-paced, fixed-duration time trials (TT) where the objective is to average the highest power

output possible for a given duration, CP & W′ can be obtained over a number of days 10 or within

a single session 17. Although previously it has been demonstrated that CP & W′ estimates derived

from multiple trials conducted on the same day are not different to the multiple-day protocol, the

duration of rest between trials was 3-hours 20. A 3-h recovery window between trials would make

a 1-day protocol difficult to implement within the applied field. However, Karsten et al.

successfully employed just a 30-min recovery window between all three trials on a single day 17.

A 30-min recovery window is likely to enable the full ‘replenishment’ of W′ based on the W′

reconstitution time course 21. An option for 30-min recovery windows would instantly become

more attractive for athletes as the full assessment could be completed within ~ 90-

min. Furthermore, in elite athletes who maintain a persistent high-level of performance, the

reproducibility of exercise tasks is likely to be very high 22. If this were the case, it would

mitigate the issues with an underperformance in one (or both) trial(s) when employing only two

trials in characterising the power-duration relationship.

The purpose of the present study was to determine the effects of using a 2-trial or 3-trial

protocol on both CP & W′. Additionally, we wanted to determine the number of familiarisation

sessions required before consistent CP & W parameters were obtained. We hypothesized that in

well-familiarized participants, the addition of a third trial would add no practical difference to

the CP and W′ parameters derived from the 2-trial protocol.

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METHODS

Participants.

Eight (7 male and 1 female) healthy, trained cyclists (mean ± SD: age 31 ± 4 yrs; body

mass 68.5 ± 10.0 kg; height 1.79 ± 0.13 m) gave written informed consent to participate in the

study, which was approved by the University of Kent ethics committee. All participants were

competitive amateur road cyclists, at least ‘Category 2’ standard, with a minimum weekly

training volume of 14-h. Before testing, participants were informed of the protocol and the

potential risks associated with the study. Participants were instructed to arrive for each testing

session at the same time of day (+/- 2-h), 3-h post prandial, and to have refrained from

exhaustive exercise for 24-h.

Study Design.

During each test occasion, participants each used their own road racing bicycle fitted with

a power meter (PowerTap G3 wheel; CycleOps, Madison, USA) attached to a custom-made, air-

resisted stationary trainer (United Kingdom Sport Institute). The trainer’s resistance unit was

secured against the rear wheel with a spring-mounted mechanism ensuring resistance on the rear

wheel was consistent for all participants and all trials. Before beginning each trial, the power

meter had its zero-offset manually checked in accordance with the manufacturer’s instructions.

Participants self-selected pedal cadences and gear ratios, and were free to change these during

the tests. For the peak power output tests participants were allowed to change gear ratios between

efforts but not during an effort. Participants visited the laboratory on five separate occasions.

Each visit was separated by at least 1-d and no more than 7-d. All testing sessions were

completed within five weeks and conducted during the racing season.

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All participants completed three supervised familiarization sessions in the laboratory that

were identical to the first experimental testing session (Figure 1). Each visit began with the

participant(s) performing a 20-min self-selected warm up prior to the experimental trials. Data

from the 20-min warm up period was not recorded, but following the warm-up, the zero-offset of

the power meter was re-set.

Experimental Protocol 1

Experimental protocol 1 consisted of (i) peak power output (PPO) assessment, (ii) 3-min

TT and (iii) 12-min TT, conducted in that order. At least 5-min of passive and/or active rest was

prescribed between finishing the PPO assessments and the 3-min TT. Following the 3-min TT, a

40-min passive and/or active recovery window was prescribed; permitting a 30-min window for

W reconstitution plus an additional 10 minutes for re-warm-up. This order was chosen so that

the 3-min TT trial was not compromised due to the prior performance of an exhaustive exercise

bout. As both central and peripheral muscle fatigue will likely contribute to the highest average

power output achieved in a 12-min TT 23, prior performance of an exhaustive exercise bout

would have a relatively smaller effect on the 12-min trial outcome.

Experimental Protocol 2

Experimental protocol 2 consisted of only (i) 5-min TT.

Peak Power Output (PPO)

Participants completed three ~ 5-s repeat efforts to determine PPO, interspersed with a 3-

min active recovery period. Each effort began when participants reached 90 rpm in their selected

gear. At that point, a maximal effort was initiated and maintained for ~ 5-s. Participants were

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instructed to accelerate as hard and as fast as possible in a seated position. PPO was taken as the

highest 1-s value recorded across the three PPO efforts.

Fixed-duration time trials (TT)

TT efforts began from a rolling start. Participants were instructed to increase their power

output in the 10- to 15-s period prior to the start of the effort. The participants were instructed to

average the highest power they could for the duration (3- 5- or 12-min) of the trial and to finish

the trial with nothing more to give (“empty the tank”). It was explained that a power profile

resembling a ‘square-wave’ was preferable. Gear choice, and thus cadence were freely adaptable

throughout each trial to help achieve this. Participants had access to elapsed and remaining time

feedback throughout each trial as well as real-time power output and cadence feedback.

3-min TT

Participants were offered a guide power output to not exceed at the beginning of the 3-

min TT. This guide was issued to help avoid a power profile resembling an ‘all-out’ pacing

strategy.

12-min TT

The 12-min TT posed the highest ‘risk’ to invalidating the CP & W′ estimates. If, at any

point throughout the 12-min TT, power output fell below a participants CP (unknown until

completion of the 12-min TT) the parameter estimates would be incorrect 24. Thus to help

provide a guide power output with which to begin the 12-min TT, a conservative estimation for

W′ (typically ~ 11.0 kJ) was subtracted from the total work done within the 3-min TT. The result

was divided by the duration of the 3-min trial (180 s) to provide a conservative estimate

(overestimation) of CP. This value (± 10 W) was suggested as a starting intensity for the 12-min

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TT. After ~ 1-3 min of the 12-min TT, participants were free to adjust the intensity to enable

them to maximise the average power achievable.

5-min TT

The 5-min TT power guideline was simply to not exceed the average power achieved

during the 3-min TT at the start of the trial.

Data Capture and Analysis

Throughout all exercise trials, power output and cadence were recorded every second

using an ANT+ wireless cycle computer (Garmin Edge 500, Garmin International, Kansas,

USA). Data were downloaded into desktop software (Golden Cheetah training software,

goldencheetah.org) where the highest 1-s, 3-, 5-, and 12-min power output windows were found.

These data were extracted and subsequently analysed in spreadsheet software (Excel, Microsoft

Corporation, Redmond, WA) to calculate CP & W′ estimates using both the linear work-time and

linear power-time-1 models (equation 1).

P = (W′/t) + CP [Eq. 1]

The linear model providing the best fit (highest R2) and least standard error of the

estimate (SEE) was used to provide the CP & W′ parameters. The same linear model providing

the least error was also used for the two-trial method (3- and 12-min trials only).

Statistical Analysis

All data were analysed using SPSS statistical software (IBM SPSS Inc., Chicago, IL.). A

one-way repeated measures ANOVA was employed to check for differences in CP & W′

estimates in the 2-trial method between familiarisation and experimental protocol 1. Where a

significant difference was discovered, post-hoc tests were conducted (with Bonferroni

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adjustment applied to the alpha level) to confirm where differences occurred between group

means. A paired sample t-test was used to compare the CP & W′ obtained from the 2-trial and 3-

trial methods. Pearson product moment correlation analysis was used to provide an indication of

the strength of any relationship between the 3-trial and 2-trial values for CP and W′. All data are

reported as mean ± SD unless otherwise stated.

RESULTS

3-trial and 2-trial CP (Figure 2) and W’ (Figure 3) values were significantly correlated

(R2 = 0.999; P <0.01 and R2 = 0.973; P<0.01, respectively). There were no differences in either

the CP (283 ± 66 W vs. 282 ± 65 W; t= 0.012; P = 0.990) nor W′ (18.72 ± 6.21 kJ vs. 18.27 ±

6.29 kJ; t = 0.145; P = 0.886) obtained from either the 2-trial or 3-trial methods

respectively. The SEE for CP and W’ (3-trial model) was 1.25 W (0.44%) and 1.11 kJ (5.8%),

respectively.

CP derived from familiarisation sessions 1 (272 ± 58 W, P = 0.011) and 2 (274 W ± 51

W, P = 0.028) were significantly different to CP from experimental protocol 1 (288 ± 63 W).

However, from familiarisation session 3 onward, CP remained unchanged compared with that

obtained from experimental protocol 1 (Figure 4). W′ remained consistent across all

familiarisation sessions and experimental protocol 1 (Figure 5).

DISCUSSION

The primary findings of the present study are; (i) in accordance with our hypothesis, the

addition of a third trial when calculating CP and W’ does not significantly nor meaningfully alter

the power-duration parameter estimates and (ii) following two familiarisation sessions, CP and

W′ estimates remain consistent.

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Previously a number of others have assessed the test-retest reliability of CP & W′ 11,20,25,26

reporting retest increases in CP of between 3.4 to 6% and changes in W′ ranging from -1.8 to

11.1%. However, in each of these cases, the methodology employed differed to the present

study, in that in all previous cases a cycle ergometer has been used and a fixed power output

imposed until exhaustion was reached. Recently, Black et al. (2015) demonstrated a difference in

CP & W′ estimates obtained from constant-power exhaustive trials and self-paced (fixed quantity

of work done) ‘time trials’. When self-pacing trials were used, CP was 7% higher than CP

derived from constant-power exhaustive trials. However, W′ was 12% (non-significant) lower

when derived from the time trial efforts. Black et al. (2015) found that when self-paced trials

were performed, they were completed in a significantly shorter time than their equivalent

constant-power exhaustive trials. These are important considerations for the longitudinal support

of athletes, where repeat measurements will be taken over years. Fixing the power output

(exhaustive) or work done to be completed (self-paced) have the potential to vary considerably in

trial duration as an athlete matures and improves. This is important as Bishop et al (1998) have

clearly shown the effect of trial duration on CP & W′ parameter estimates. When trial durations

become shorter, CP estimates artificially inflate and W′ estimates reduce. The opposite is true

when trial durations lengthen. For this reason, fixing the duration of trials used in the

determination of CP & W′, especially in applied, longitudinal athlete support, seems most

appropriate.

The trial durations chosen for the present study (3- and 12-min for the shortest and

longest trials and 5-min for the middle trial) were selected for a number of reasons. The shortest

duration of exercise permitting the attainment of max and ostensibly the complete

‘expenditure’ of W′ is ~ 150 s 27. Thus, we selected 3 min as the shortest trial duration to permit

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an additional 30 s to help accommodate participants with perhaps slower oxygen uptake

kinetics. The difference between the shortest and longest trials was also an important

consideration. While Housh et al (1990) recommended that shortest and longest trials be

separated by at least 5-min, it is a common recommendation within the literature that trial

durations span 1- to 10- min 28,29. This provides a 9-min difference between shortest and longest

trial. Given that the shortest duration chosen was 3-min in the present study, to uphold a 9-min

difference between shortest and longest trials necessitated a long trial of 12-min duration. This

too satisfied the suggestion of Bishop et al (1998) that as trial duration extends, other factors

(e.g. motivation, temperature etc.) may detract from exercise performance. Theoretically the

additional ‘middle-duration’ trial could be any duration between 3- and 12-min and would fall

along the linear work-time (or power-time-1) regression. Since the 3- and 12-min trials total 15

min of effort required from an athlete, and given that elsewhere in the ‘scientific’ support of

cyclists a 20-min functional threshold power test 30 is commonplace, a 5-min middle-duration

trial was selected to equal the total time commitment of the functional threshold test.

Characterising the power-duration relationship offers many advantages over the common

alternatives. Most notably once CP and W′ are known, it is possible to accurately predict

exercise performance over a range of durations 9,10 and with different exercise tasks (ramp-

incremental 8, intermittent intervals 9). In addition, obtaining these physiologically underpinned

parameters (CP & W′) requires only a power meter and a stopwatch. No invasive or intrusive

measurements are needed and from an athlete support perspective, where teams or squads of

athletes often follow a similar training and racing schedule, multiple athletes can be ‘assessed’

simultaneously. In the absence of multiple ergometers (and other equipment), it is not possible to

conduct alternative assessments (e.g. ramp-incremental test, step-incremental sub maximal test,

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maximum lactate steady state) in this manner. While alternative assessments have their

physiological merits, they all lack the mechanical performance insight offered by the CP

concept. Additionally, and similarly to Karsten et al. (2014), assessing CP & W′ using a self-

paced, fixed-duration method does not require the additional visit and test mandated by

numerous other assessment procedures; the ramp-incremental max test. The self-pacing of the

discrete trials eliminates the requirement to set exercise intensities relative to an individual’s

metabolic or mechanical parameters. Again, this is an important consideration when attempting

to ensure consistent monitoring can be incorporated into longitudinal athlete support, as is the

number of familiarisation sessions required to elicit reliable CP & W parameters.

The present study shows that in trained cyclists, previously unfamiliar with fixed-

duration, self-paced TTs, two familiarisation sessions were necessary before CP estimates

became reproducible. This is something to consider when assessing athletes for the first (and

second) time using this method. However, the relative stability of the W estimates, even from

familiarisation trial 1, could prove extremely useful. Arguably, W is an important parameter for

success in endurance events which last between ~ 2 and 8 min. The ability to gain insight into an

athlete’s W from the first power-duration assessment could be useful for talent ID purposes, or

for guiding athletes toward certain sporting disciplines.

PRACTICAL APPLICATIONS

The power-duration parameters, CP & W′, have great practical importance across many

aspects within cycling and other endurance sports.

1. Fundamentally, CP demarcates distinct physiological intensity domains, and thus is an

important parameter for both setting training ‘zones’ and monitoring training intensity

distribution.

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2. The W′ is an important parameter which dictates exercise capacity across a range of

durations. To enhance performance over shorter durations (~ < 6 min), attempting to

enlarge the W′ could be a viable option.

3. When supporting/monitoring athletes over time (months to years), fixing the duration of

the trials used in the determination of CP & W′ becomes important to limit alterations in

either parameter simply due to trial duration.

4. The combination of CP & W′ enables real-world performance to be modelled or

simulated. It is therefore possible to predict the required changes in either CP or W to

elicit the performance change desired.

5. The method(s) presented here provide athletes, coaches and practitioners simple,

applicable tools with which power-duration monitoring can be incorporated into training

programmes.

CONCLUSIONS

The present study offers a method to assess a cycling-trained individual’s power-duration

relationship requiring only two discrete exercise trials of 3- and 12-min duration. Following only

two familiarisation sessions, each consisting of a 3- and 12-min TT, CP & W′ estimates

remained reliable thereafter and did not differ when compared to CP & W′ derived from the 3-

trial protocol. Combined, these results offer practitioners a viable, single-visit protocol to obtain

CP & W′ estimates from trained athletes.

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ACKNOWLEDGEMENTS

The authors would like to thank the riders for their time and participation in this study as well as

Professor Louis Passfield and Dr Chris Fullerton for reviewing the manuscript.

CONFLICTS OF INTEREST

The authors of this manuscript have no conflicts of interest to declare.

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Figure 1. A schematic of the lab sessions. Familiarization sessions 1, 2 and 3 and Experimental

session 1 were identical. Each session included three peak power output efforts, a 3-min TT and

a 12-min TT. Experimental session 2 was a 5-min TT.

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Figure 2. Correlation between 3-trial and t-trial Critical Power (CP).

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Figure 3. Correlation between 3-trial and 2-trial W’.

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Figure 4. Mean power output for the 3-min and 12-min TT as well as the Critical Power between

all three familiarization sessions (Fam 1, 2 and 3) and the experimental session (Exp 1); *denotes

significant difference from Exp 1.

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Figure 5. W’ and peak power output (PPO) of all familiarization (Fam 1, 2 and 3) and

Experimental (Exp) sessions.

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Parker Simpson & Kordi - 2016 - Comparison of Critical Power and wprime derived from two or three maximal tests- Ahead of Print