Modeling Intermittent Cycling Performance in
Hypoxia Using the Critical Power Concept
SAMANTHA SHEARMAN1, DAN DWYER1, PHILIP SKIBA2, and NATHAN TOWNSEND1,3
1
Centre for Exercise & Sport Science, Deakin University, Geelong, AUSTRALIA; 2Department of Sports Medicine, Advocate
Lutheran General Hospital, Park Ridge, IL; and 3Athlete Health and Performance Centre, Aspetar Orthopaedic and Sports
Medicine Hospital, Doha, QATAR
ABSTRACT
SHEARMAN, S., D. DWYER, P. SKIBA, and N. TOWNSEND. Modeling Intermittent Cycling Performance in Hypoxia Using the
Critical Power Concept. Med. Sci. Sports Exerc., Vol. 48, No. 3, pp. 527–535, 2016. Purpose: This study investigated the efficacy of an
intermittent critical power (CP) model, termed the ‘‘work-balance’’ (W ¶BAL) model, during high-intensity exercise in hypoxia (HYPO).
Methods: Eleven trained male cyclists (mean T SD age, 27 T 6.6 yr; V̇O2peak, 4.79 T 0.56 LIminj1) completed a maximal ramp test and a
3-min ‘‘all-out’’ test to determine CP and work performed above CP (W ¶). On another day, an intermittent exercise test to task failure was
performed. All procedures were performed in normoxia (NORM) and HYPO (FiO2 , 0.155) in a single-blind, randomized, and counterbalanced experimental design. The W ¶BAL model was used to calculate the minimum W ¶ (W ¶BALmin) achieved during the intermittent test.
The W ¶BALmin in HYPO was also calculated using CP + W ¶ derived in NORM (N + H). Results: In HYPO, there was an 18% decrease in
V̇O2peak (4.79 T 0.56 vs 3.93 T 0.47 LIminj1; P G 0.001) and a 9% decrease in CP (347 T 45 vs 316 T 46 W; P G 0.001). No significant
change for W ¶ occurred (13.4 T 3.9 vs 13.7 T 4.9 kJ; P = 0.69; NORM vs HYPO). The change in V̇O2peak was significantly correlated with
the change in CP (r = 0.72; P = 0.01). There was no difference between NORM and HYPO for W ¶BALmin (1.1 T 0.9 kJ vs 1.2 T 0.6 kJ). The
N + H analysis grossly overestimated W ¶BALmin (7.8 T 3.4 kJ) compared with HYPO (P G 0.001). Conclusion: The W ¶BAL model produced
similar results in HYPO and NORM, but only when model parameters were determined under the same environmental conditions as the
performance task. Application of the W ¶BAL model at altitude requires a modification of the model or that CP and W ¶ are measured at
altitude. Key Words: ALTITUDE, WORK-BALANCE, HIGH-INTENSITY, FATIGUE
D
Address for Correspondence: Nathan E. Townsend, Ph.D., Athlete Health
and Performance Research Center, Aspetar Orthopaedic and Sports Medicine Hospital, Doha, Qatar; E-mail: [email protected].
Submitted for publication April 2015.
Accepted for publication September 2015.
0195-9131/16/4803-0527/0
MEDICINE & SCIENCE IN SPORTS & EXERCISE!
Copyright " 2015 by the American College of Sports Medicine
DOI: 10.1249/MSS.0000000000000794
527
Copyright © 2016 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
APPLIED SCIENCES
Variable intensity exercise consisting of high-intensity
work bouts interspersed with periods of recovery is common
in the sporting world, particularly road cycling and team
sports (4,16). Intermittent high-intensity exercise imposes an
additional challenge for the CP model, since W ¶ replenishes
during periods spent at power output below CP, delaying the
point of task failure compared with constant load exercise (17).
In 2004, Morton and Billat (31) demonstrated the application
of an intermittent CP model to asses distance covered during
interval training in a group of middle distance runners. Subsequently, this intermittent CP model was tested during cycling
exercise, where the rate of W ¶ reconstitution was found to be
dependent on recovery exercise intensity (13). Morton and
Billat_s intermittent CP model assumes a linear recovery of W ¶,
yet it was recently observed that this occurs exponentially (17).
Subsequently, Skiba et al. (34) developed a continuous integral
equation including an exponential term, to calculate the balance of W ¶ remaining at any point during intermittent exercise.
A detailed description of the mathematical framework of the
model is presented by those authors (34). Briefly, the model,
termed the ‘‘work-balance’’ (W ¶BAL) model, includes the following assumptions: 1) expenditure of W ¶ occurs when the
power output exceeds CP, 2) reconstitution of the W ¶ occurs
when the power output falls below CP, and 3) the reconstitution of W ¶ follows a predictable monoexponential time course.
uring constant load exercise in the severe intensity
domain, there is a curvilinear relationship between
exercise intensity and time to exhaustion. The critical power (CP) concept is a mathematical framework, which
describes this relationship using two key input parameters referred to as CP and work performed above CP (W ¶) (29). The
CP is thought to represent the maximal sustainable aerobic
energy contribution, whereas W ¶ represents an additional fixed
capacity, a nonsustainable energy contribution that is drawn
upon when the power output rises above CP (25). Therefore,
during constant load exercise performed above CP, the point
of task failure theoretically corresponds with the complete
depletion of W ¶.
The W ¶BAL model proposed takes the form of a continuous
integral equation as follows:
t
jðtjuÞ
TW ¶
W ¶BAL ¼ W ¶ j X0 W ¶ exp e
du
½1%
where W ¶exp is the amount of W ¶ presently expended, and
(tju) is equal to the time in seconds, where the athlete is
recovering below CP. The time constant for the reconstitution
of W ¶ (TW ¶) is a function of the difference between the recovery power and the individual_s CP (DCP) according to the
following equation (34):
TW ¶ ¼ 546 eðj0:01 DCP Þ þ 316
½2%
The W ¶BAL model has been validated empirically by examining the effect of recovery power (34) and work-to-rest ratios
(37) on the reconstitution of W ¶. Furthermore, the W ¶BAL
model was shown to exhibit good sensitivity to distinguish
instances of volitional exhaustion from difficult but nonfatiguing efforts during training and racing (35). These results
indicate that the W ¶BAL model has practical use for describing
the limit of tolerance to high-intensity intermittent exercise in
normoxia (NORM). For the model to be applicable at altitude
though, the effect of hypoxia (HYPO) requires investigation.
Hypoxia has been shown to reduce CP during constant load
exercise (15,30,33); hence, it is likely the validity of the
W ¶BAL model in HYPO will be challenged if input parameters
are not also determined in HYPO. To date, though, no study
has examined the W ¶BAL model under hypoxic conditions.
Therefore, the primary aim of this study was to investigate
the effect of HYPO on the efficacy of the W ¶BAL model
during high-intensity intermittent exercise. We hypothesized
that the W ¶BAL model would remain valid under hypoxic
conditions, so long as estimation of the model input parameters and performance during an intermittent exercise task
are conducted under the same inspired oxygen concentration.
Given that CP is generally accepted to be an index of aerobic
energy supply (25), we also hypothesized that diminished
oxygen transport, as determined by V̇O2peak, would be related
to the decline in CP in HYPO.
METHODS
Participants and recruitment. Eleven well-trained
male cyclists (mean T SD age, 27 T 6.6 yr; height, 179 T
7.5 cm; body mass, 78.0 T 7.1 kg) volunteered to participate
in this study, which was approved by the Deakin University
Human Research Ethics Committee. Participant inclusion was
based on age (18–35 yr), training history (2-yr minimum cycling training history, 7-hIwkj1 minimum average training),
and health status (free from injury or illness). Informed consent was obtained after explanation of the experimental procedures, associated risks, and potential benefits.
Experimental overview. The participants attended
Deakin University exercise physiology laboratory on five
occasions within a 3-wk period. Participants were instructed
to avoid strenuous exercise 24 h before each testing session
528
Official Journal of the American College of Sports Medicine
and to abstain from caffeine and alcohol on the day of testing. After a familiarization trial, two separate test sessions
(day 1 and day 2) were each completed twice; once in
NORM and again in normobaric HYPO (FiO2 of ~0.155).
The experimental design was single-blind, randomized, and
counterbalanced. All exercise tests were performed on an
electronically braked cycles ergometer (Lode Excalibur Sport,
Groningen, The Netherlands) inside a temperature-controlled
(20-C) simulated altitude room. For the HYPO test sessions,
normobaric HYPO was created via nitrogen dilution using a
hypoxic generator (ATS-HP unit, Altitude Training Systems,
Sydney, Australia). The test procedures for day 1 began with a
10-min warm-up inside the altitude chamber to allow for
equilibrium of body O2 stores (3) followed by a ramp incremental test to determine ventilatory threshold 1 (VT1), VT2,
and V̇O2peak. Then, after a 30-min recovery period (14), a
3-min ‘‘all out’’ test (3AOT) was performed to estimate CP
and W ¶ (40). On day 2, a high-intensity intermittent exercise
test was performed to the limit of tolerance.
Incremental ramp test. The incremental ramp test commenced with 3-min cycling at 20 W followed by a continuous
increasing work rate of 30 WIminj1 until task failure, defined
as the inability to remain within 10 rpm of preferred cadence.
Breath-by-breath oxygen consumption (V̇O2), carbon dioxide
production (VCO2), and expired ventilation (V̇E), were measured using a Metalyzer 3B CPET system (Cortex Biophysik,
Leipzig, Germany). Heart rate (HR) was measured using an
HR monitor (RS800CX, Polar, Finland), and oxyhemoglobin
saturation (SpO2) was recorded continuously at 1 Hz via pulse
oximetry (Nellcor Bedside Respiratory Monitor, Covidien,
Mansfield, MA, USA). The metabolic cart was calibrated immediately before each test with two commercially prepared gas
mixtures (reference: O2, 20.90%; CO2, 0.03%; physiological:
O2, 15.95%; CO2, 4.00%). Ventilation was measured using a
Triple V turbine ventilometer (Cortex Biophysik), calibrated
using a 3-L precision syringe (Hans Rudolph, Inc., Kansas
City, KS, USA).
Breath-by-breath V̇O2 data were initially filtered to remove aberrant data points due to swallowing, coughing, or
sighing (greater than four standard deviation points from
the mean) (32), then converted to 10-s bin averages for the
estimation of VT1 and VT2. Ventilatory threshold 1 was
estimated from multiple standard criteria including 1) the Vslope method, breakpoint in VCO2/V̇O2 against time, 2) an
increase in V̇E/V̇O2 with no increase in V̇E/VCO2, and 3) an
increase in end-tidal oxygen tension (PETO2) without a
corresponding fall in end-tidal carbon dioxide tension
(PETCO2) (5). Ventilatory threshold 2 was determined via
identification of 1) the first disproportionate increase in V̇E
versus VCO2, 2) a second nonlinear increase in V̇E/V̇O2,
and 3) a fall in PETCO2 (5). V̇O2peak was defined as the
highest V̇O2 measurement recorded over a 30-s interval. All
other measured cardiorespiratory variables were averaged
over the same 30-s interval as V̇O2peak. Peak power output
(PPO) was recorded as the maximal power in watts attained
at termination of the ramp protocol.
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Three-minute all-out test (3AOT). The 3AOT began
with 3 min of baseline pedaling at 20 W followed by a 3-min
all-out maximal sprint effort. The linear factor in the sprint
phase was calculated so that at preferred cadence, power
output corresponded to the midpoint between VT1 and PPO
(50% delta) (12). During the last 5 s of the baseline period,
subjects were instructed to increase cadence to approximately 110 to 120 rpm and thereafter maintain cadence as
high as possible for the entire 3-min sprint phase. Subjects
were specifically instructed not to pace during the sprint
phase, and strong verbal encouragement was provided to
obtain maximal effort. Evidence suggests a conservative
pacing strategy is adopted during maximal all-out exercise
when knowledge of the test end point is denied (10,21);
therefore, we provided test duration feedback every 15 s.
Mean power output during the final 30 s of the test was
calculated and is referred to as end power (EP) (40). During
both pilot and experimental testing, we observed multiple
instances where EP was slightly greater than the minimum
30-s moving average power. Previous research indicates the
EP may overestimate CP determined via the two-parameter
nonlinear model (8,9,28). Thus, to avoid any potential overestimation of CP, we also determined the minimum 30-s
moving average power output, which is expressed as CP in
the ‘‘Results’’ and ‘‘Discussion’’ sections. Works performed
above EP (W ¶EP) and above CP (W ¶) during the 3AOT were
determined from the power-time integral above EP and CP,
respectively. During the 3AOT, V̇O2peak was defined as the
highest value measured over a 30-s interval at any point in the
test. Rating of perceived exertion (RPE) was recorded upon
completion of the test using Borg_s category ratio scale (11).
Intermittent test. The intermittent test commenced
with 3 min of baseline pedaling at 20 W, followed by repeat
60-s work intervals, and 30-s recovery periods until task
failure. The 60-s work intervals were performed at a power
output predicted to produce task failure during constant load
exercise in 4 min (P4) according to the two-parameter CP
model as follows:
P4 ¼ ðW ¶=tdesired Þ þ CP
½6%
MODELING W ¶ IN HYPOXIA
RESULTS
Incremental ramp test. Two-way ANOVA results
from the incremental ramp test are presented in Table 1.
There was a significant main effect of condition for work
rate (W) (F1,10 = 54.1; P G 0.001), V̇O2 (LIminj1) (F1,10 =
155.0; P G 0.001), V̇O2 (mLIkgj1Iminj1) (F1,10 = 127.6;
P G 0.001), and SpO2 (F1,10 = 84.5; P G 0.001). Post hoc
analysis revealed a reduction in V̇O2 (LIminj1) by 18% at
V̇O2peak and VT2 (P G 0.001), and 15% at VT1 (P G 0.001)
in HYPO. There were significant decreases (P G 0.001) in
PPO (8%), power at VT2 (10%), and power at VT1 (11%),
and SpO2 was significantly lower at all points during the
incremental test in HYPO (P G 0.001). There were strong
correlations between NORM and HYPO for V̇O2peak (r =
0.88, P G 0.001), PPO (r = 0.94, P G 0.001), and power at
VT2 (r = 0.87, P G 0.001).
Three-minute all-out test (3AOT). The results from
the 3AOT test are presented in Table 2. Critical power was
reduced by 9% in HYPO (P G 0.001), and V̇O2peak (LIminj1)
declined by 20% (P G 0.001). Mean W ¶ remained unchanged
between conditions (P = 0.69). The mean difference (95%
confidence limits) in W ¶ between NORM and HYPO was
j0.7 (j2.3 to 0.9 kJ). Total work completed was significantly lower in HYPO (P G 0.001), which thus reflects the
lower CP. V̇O2peak in the 3AOT was not different from
V̇O2peak in the ramp incremental test for either NORM (P =
0.73) or HYPO (P = 0.27). In NORM, 9 of 11 subjects produced a higher EP compared to CP (range, 1–17 W), whereas
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529
APPLIED SCIENCES
where P4 is the power output and tdesired is the desired time
to task failure (in this case, 240 s). This workload was
chosen for ease of comparison to previous studies (13,34)
and is mathematically identical to the power output predicted to result in task failure in 6 min (P6) plus 50% P6 j
CP. All recovery intervals were conducted at 20 W, and time
to fatigue was recorded to the nearest second. Equation 1
was used to calculate W ¶BAL remaining at the point of task
failure (W ¶BALtf). On occasion, we noted lower W ¶BAL values
after the final completed work interval compared with the
moment of actual task failure. Therefore, the minimum W ¶BAL
(W ¶BALmin) was also calculated to avoid misrepresenting the
lowest W ¶BAL value that subjects could attain near the point of
task failure. The time constant for reconstitution of W ¶ (TW ¶)
was calculated using equation 2 (34). Additionally, W ¶BAL in
HYPO was calculated using CP parameter estimates derived
from the 3AOT in NORM. This analysis condition is referred
to as N + H and was conducted to examine the magnitude of
error in the W ¶BAL model introduced by using CP + W ¶ derived
in NORM, but in the scenario where a cyclist trains at simulated or natural altitude.
Statistical analysis. Statistical analysis was completed
on all data using the Statistical Package for Social Sciences
(SPSS), version 22.0 (SPSS Inc., Champaign, IL). Normality of the data was checked using the Shapiro-Wilk test, with
P G 0.05 indicating nonnormality. Comparisons between
NORM and HYPO for dependent variables were analyzed
using paired sample t-tests. For measures of W ¶BAL, a oneway, repeated-measures ANOVA was used to search for a
significant main effect of condition (NORM, HYPO, and N +
H) with a Bonferroni correction applied for post hoc analysis
of differences. For variables measured during the ramp incremental test a two-way (time ' condition), ANOVA was
used to identify differences between NORM and HYPO at
three time points (VT1, VT2, and V̇O2peak) for power output,
and four time points (baseline, VT1, VT2, and V̇O2peak) for
all other dependent variables. Post hoc pairwise comparisons
between conditions were conducted using least significant
difference correction. The Pearson product–moment correlation coefficient was used to examine relationships between
variables. All variables are reported as mean T SD, with
statistical significance set at P G 0.05.
TABLE 1. Incremental ramp test results.
BASE
NORM
Power, W
V̇O2, LIminj1
V̇O2, mLIkgj1Iminj1
V̇E, LIminj1
HR, bpm
SpO2, %
HYPO
Power, W
V̇O2, LIminj1
V̇O2, mLIkgj1Iminj1
V̇E, LIminj1
HR, bpm
SpO2, %
VT1
VT2
V̇O2peak
20 T
0.95 T
12.2 T
26.5 T
85.6 T
99 T
0
0.08
1.1
2.9
9.4
1
171
2.61
33.5
60.9
129.1
98.4
T 28
T 0.32
T 3.8
T 8.8
T 8.6
T 1.3
325
4.12
52.9
117.9
165.5
95.7
T 37
T 0.42
T 3.9
T 19.0
T 9.6
T 2.0
433
4.79
61.5
183.2
185.4
93.8
T 46
T 0.56
T 5.7
T 29.7
T 9.2
T 1.5
20 T
0.88 T
11.4 T
25.5 T
87.0 T
93.6 T
0
0.12*
1.3*
3.6
6.9
2.7*
152
2.22
28.4
62.2
127.3
89.4
T 24*
T 0.30*
T 3.1*
T 9.8
T 11.0
T 6.2*
292
3.36
43.0
117.4
164.3
85.1
T 41*
T 0.41*
T 3.8*
T 20.0
T 15.1
T 5.2*
399
3.93
50.4
176.5
181.4
83.8
T 43*
T 0.47*
T 5.7*
T 25.3
T 9.8
T 4.0*
Data are presented as mean T SD.
Power (W) at V̇O2peak refers to peak incremental test power output. All other variables are 30-s averages temporally aligned with V̇O2peak. See ‘ Methods’’ text for details.
*Significantly different from NORM (P G 0.05).
in HYPO, only 3 of 11 subjects produced a higher EP than
CP (range, 8–13 W). Correlational analysis is presented on
the CP results only. There was a strong correlation between
CP measured in NORM and HYPO (r = 0.87, P G 0.001;
Fig. 1A), and W ¶ measured in NORM and HYPO (r = 0.85,
P G 0.001; Fig. 1B). Critical power and power at VT2 were
not significantly different in either NORM (P = 0.89) or
HYPO (P = 0.12); however, these variables were not significantly correlated either (NORM, P = 0.08; HYPO; P = 0.14).
Critical power was correlated with ramp V̇O2peak (LIminj1)
in both NORM (r = 0.67, P = 0.002; Fig. 2A) and HYPO (r =
0.71, P = 0.001; Fig. 2B). Additionally, $CP was correlated
with both $PPO (r = 0.72, P = 0.01) and ramp $V̇O2peak
(LIminj1) (r = 0.52, P = 0.01; Fig. 2C). RPE for the 3AOT
was 10.0 T 0.0 for both NORM and HYPO.
Intermittent test and W ¶BAL. An example of individual W ¶BAL model data for a single subject is presented in
Figure 3. Table 3 presents mean W ¶BAL model results calculated from both EP and CP. Additionally, the minimum
W ¶BAL (W ¶BALmin) is reported along with W ¶BAL at the moment of task failure (W ¶BALtf). In both NORM and HYPO,
all values of W ¶BAL calculated were significantly greater
than a criterion value of 0 kJ (P G 0.01). There was a significant main effect of condition on both W ¶BALmin (F2,30 =
39.1; P G 0.001), and W ¶BALtf (F2,30 = 36.7; P G 0.001).
Post hoc analysis revealed no significant differences for any
estimate of W ¶BAL between NORM and HYPO, whereas
TABLE 2. Three-minute ‘ all-out’’ test results.
NORM
V̇O2peak, LIminj1
V̇O2peak, mLIkgj1Iminj1
EP, W
W ¶EP, kJ
CP
W¶
Worktot, kJ
HRpeak, bpm
SpO2, %
4.83 T
62.7 T
353 T
12.6 T
347 T
13.4 T
76 T
179.2 T
92.9 T
0.57
7.3
46
4.1
45**
3.9***
8.7
7.2
2.7
HYPO
3.85 T
49.6 T
319 T
13.3 T
316 T
13.7 T
70 T
179 T
81.5 T
0.48*
6.7*
49*
5.3
46*
4.9
7.6*
7.2
4.2*
Data are presented as mean T SD.
*Significantly different from NORM (P G 0.05).
**Significantly different from EP (P G 0.05).
***Significantly different from W ¶EP (P G 0.05).
530
Official Journal of the American College of Sports Medicine
the N + H analysis condition led to a large overestimation
of W ¶BAL for all model combinations compared to either
NORM or HYPO (P G 0.001; Table 3). In NORM only, both
W ¶BALtf (P G 0.01) and W ¶BALmin (P G 0.05) were significantly lower when CP + W ¶ were used in the W ¶BAL model
compared with EP + W ¶EP.
Relative to a suggested W ¶BAL ‘‘fatigue threshold’’ of 1.5
kJ (9), we observed W ¶BALmin drop to below 1.5 kJ in 9 of 11
instances in NORM and 8 from 11 in HYPO, when using CP
as the model parameter. For W ¶BALtf, this decreased to 7 of 11
and 6 of 11 in NORM and HYPO, respectively. When EP
was used, only 5 of 11 (NORM) and 6 of 11 (HYPO) cases
fell below 1.5 kJ for W ¶BALmin, whereas for W ¶BALtf, the
numbers were 4 of 11 (NORM) and 6 of 11 (HYPO). For
W ¶BALtf using EP model inputs, the 95% confidence limits
were 1.4 to 2.6 kJ in NORM, which thus represented the least
accurate W ¶BAL model results.
The mean time constant for the reconstitution of W ¶ (TW ¶)
was significantly longer in HYPO (P G 0.001), and time to
task failure was significantly shorter in HYPO compared to
NORM (P G 0.05). RPE within 1–3 min of task failure was
near maximal but not significantly different between NORM
(9.7 T 0.4) and HYPO (9.3 T 0.6) (P 9 1.00).
DISCUSSION
The effect of HYPO on CP has previously been examined
in only a few studies (15,30,33), whereas this is the first
study to investigate the W ¶BAL model under hypoxic conditions. The principal finding of this study was that no difference in calculated W ¶BAL at task failure occurred in
HYPO compared with NORM. This suggests the W ¶BAL
model can be successfully applied in HYPO for the purposes
of performance monitoring. It is important to note that W ¶BAL
model parameters were derived under the same environmental conditions as the intermittent task was performed. However, when CP + W ¶ were derived in NORM and W ¶BAL was
calculated during exercise in HYPO, less than 50% depletion
of W ¶ occurred at task failure. The marked overestimation of
W ¶BAL in this case demonstrates the essential requirement to
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the power rises above CP, 2) reconstitution of W ¶ commences
immediately when the power drops below CP, and 3) the
depletion and reconstitution of W ¶ follows a predictable exponential time course (34). The W ¶BAL model was subsequently validated in NORM using an intermittent exercise
FIGURE 1—A, Linear regression between CP in NORM (W) and CP
in HYPO (W). B, Linear regression between W ¶ in NORM (kJ) and W ¶
in HYPO (kJ). Curved dotted lines represent 95% confidence intervals,
and the thin gray diagonal line is the line of identity.
MODELING W ¶ IN HYPOXIA
FIGURE 2—Linear regression between CP (W) and ramp test V̇O2peak
(LIminj1) in NORM (A) and HYPO (B) conditions. C, Linear regression between $CP (W) and ramp test $V̇O2peak (LIminj1), where $ refers to NORMjHYPO. Dotted lines indicate 95% confidence intervals.
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531
APPLIED SCIENCES
measure CP + W ¶ under appropriate environmental conditions.
We observed a significant 9% decrease in CP in HYPO
compared with NORM, but no change in W ¶. Furthermore,
there was a significant correlation between $V̇O2peak in
HYPO and $CP. These results are consistent with the broader
concept that CP is an index of aerobic metabolism (25,31).
The CP concept identifies CP as being a rate, not a capacitylimited variable (25); thus, the value of CP itself reveals little
information about tolerance to high-intensity intermittent
exercise, which may continue until task failure. However,
since the value of W ¶ is capacity limited, then its value
theoretically reflects the limit of tolerance to exercise
performed above CP. In the present study, we estimated CP +
W ¶ via the 3AOT in both NORM and HYPO and used these
variables as parameter inputs in the W ¶BAL model. This
model, introduced in 2012 by Skiba et al. (34), is an extension
of an earlier intermittent CP model proposed by Morton et al.
(31) and was designed to calculate the remaining W ¶ at any
point during variable intensity exercise based on the following assumptions: 1) W ¶ begins to deplete immediately when
may be related to the choice of time constant used in the
model. We calculated TW ¶ from equation 2, which itself
represents data fitted on only seven healthy males (34),
rather than determining it individually, which was beyond
the scope of this study. Alternatively, since TW ¶ is a function
of the CP estimate, any overestimation in CP would have led
to a faster time constant for the recovery of W ¶BAL, in turn
slightly overestimating the true value of W ¶BAL during intermittent high-intensity exercise. Discussion of the validity
and reliability of the 3AOT is contained within the ‘‘Methodological considerations’’ section.
Confirming the validity of the W ¶BAL in NORM was an
essential prerequisite for testing its efficacy under hypoxic
conditions. Hypoxia is known to modulate muscle blood
flow during exercise (27), and Skiba et al, (37) reported a
significant underprediction of modeled W ¶BAL during intermittent activity with short recovery durations, citing a postexercise hyperemic effect, especially in trained subjects, as a
possible explanation (39). Additionally, there is evidence
that HYPO can magnify central fatigue (19), and in the case
of severe HYPO, this effect occurs independently of altered
afferent feedback and peripheral muscle fatigue (2). Thus,
there was no guarantee the W ¶BAL model should behave
identically in HYPO as demonstrated for NORM. The results of the present study though, clearly indicate no significant effect of HYPO (FiO2 , 0.155, or , 2450 m) on W ¶BAL
during high-intensity intermittent exercise. Similar to
NORM, 8 of 11 subjects were able to deplete W ¶BALmin to
below 1.5 kJ in the HYPO condition, whereas RPE values
remained near maximal.
Two key aspects of the experimental design seem to underpin our main findings. First, we estimated the W ¶BAL
model parameters CP + W ¶ in both NORM and HYPO; and
second, the work intervals in the intermittent test were
performed at the same relative intensity in both conditions.
Results of the 3AOT revealed a significant 9% decline in CP
in HYPO, whereas no change occurred for W ¶. Several
previous studies have examined the effect of HYPO on CP
(15,30,33). Our results are consistent with those of Dekerle
et al. (15) who reported a 14% decrease in CP without any
change in W ¶ at a similar FiO2 used in the present study.
Similarly, Moritani et al. (30) reported a large decrease in
CP and no change in W ¶ in two subjects exercising at an
FIGURE 3—Modeled W ¶BAL depletion and reconstitution for a representative subject in NORM, HYPO (FiO2 , 0.155), and in HYPO using
NORM-derived model inputs (N + H). Light gray bars indicate work
and recovery intervals. P4 indicates the power output predicted to result in exhaustion in 4 min. Note that the recovery power output (20 W)
remained the same across each condition.
task, which depleted approximately 50% of the W ¶, followed
immediately by a 4-min maximal effort (37). During the final
4-min effort, these authors reported a mean difference between modeled W ¶BAL and actual W ¶ expended of less than
2 kJ across a variety of work to rest ratio conditions. This
corresponds well with results from the intermittent task in the
present study in which we observed mean W ¶BAL in the range
of 1.1 to 2.0 kJ at, or near, task failure. However, in comparison to a criterion W ¶BAL value of 0 kJ, we found significantly greater W ¶BAL remaining at task failure; hence,
subjects were unable to reduce W ¶BAL to 0 kJ despite the
finding that RPE was at or near maximal in all cases.
The concept of a W ¶BAL fatigue threshold was recently
investigated using a receiver–operator characteristic analysis
(35). It was demonstrated that optimal sensitivity/specificity
to distinguish between exhaustion and nonexhaustion could
be achieved by using a threshold value of 1.5 kJ (35), thus
representing a range between 0 and 1.5 kJ in which volitional fatigue is likely to occur. Since 9 of 11 subjects in the
present study depleted W ¶BALmin below 1.5 kJ, our data
provide further support for the use of the W ¶BAL model under normoxic conditions. The question of why our subject
cohort was unable to achieve values of W ¶BAL closer to zero
TABLE 3. W ¶BAL model results for the intermittent test.
HYPO
EP
Timetf, s
Worktot, kJ
TW ¶, s
W ¶BALtf, kJ
W ¶BALmin, kJ
Worktot 9 CP, kJ
1057
286.8
337
2.0
1.7
35.0
T 261
T 69.1
T9
T 0.9
T 0.9***
T 14.5
CP
339
1.5
1.1
39.0
–
–
T 9**
T 0.9**
T 0.9**,***
T 13.9**
EP
860 T
219.0 T
347 T
1.5 T
1.3 T
32.8 T
N+H
CP
173*
50.5*
12*
0.8
0.8
17.4
–
–
346 T
1.4 T
1.2 T
34.2 T
12*
0.7
0.6
15.8
EP
CP
–
–
–
8.4 T 3.2****
8.3 T 3.2****
12.2 T 9.1****
–
–
–
7.9 T 3.4**,****
7.8 T 3.4**,****
15.5 T 9.1**,****
Data are presented as mean T SD.
*Significantly different from NORM (P G 0.01).
**Significantly different from EP (P G 0.05).
***Significantly different from W ¶BALtf (P G 0.05).
****Significantly different from HYPO (P G 0.001).
532
Official Journal of the American College of Sports Medicine
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MODELING W ¶ IN HYPOXIA
the valid application of the W ¶BAL model, both in NORM
and under conditions of variable FiO2.
Although Worktot 9 CP in the intermittent test was not
significantly different in HYPO, there was however, a trend
toward a decrease (P = 0.08). Since W ¶BAL was not different
between conditions, this finding seems to be a consequence
of significantly decreased Timetf in HYPO (860 T 173 s)
compared with NORM (1057 T 261 s). The shorter Timetf in
HYPO can be explained by the inverse correlation between
TW ¶ and DCP (equation 2), since recovery power remained
20 W in each condition, whereas CP decreased in HYPO.
Hence, although the same relative work intensity was used
for both conditions, reconstitution of W ¶BAL would have
been slower in HYPO. The availability of high-energy
phosphates, in particular PCr, is considered to play an important role in intermittent high-intensity exercise (18) and
has been proposed to contribute to the value of W ¶ (25,26).
The recovery of PCr is an indicator of skeletal muscle oxidative metabolism, thus after a bout of exercise, the recovery
of PCr is slower in HYPO (22) and in untrained compared
with endurance trained subjects (38). A recent study reported a strong correlation between modeled W ¶BAL and the
fractional amount of PCr able to be expended in a second
exhaustive exercise bout (36). The authors suggested that
recovery of W ¶ may be related to the muscle ‘‘oxidative reserve.’’ Collectively, these studies indicate that the oxidative
capacity of skeletal muscle sets an upper limit on the rate of
recovery from high-intensity exercise. In line with our
findings, we suggest that when the O2 supply is limited, this
reduces the CP, which decreases the oxidative reserve of the
muscle. Therefore, whereas exercise at equivalent relative
intensity above CP in NORM and HYPO induces little or no
difference to the depletion of W ¶, the lower oxidative reserve
during recovery in HYPO significantly slows reconstitution
of W ¶, thereby affecting the overall duration that highintensity intermittent exercise can be sustained.
Methodological considerations. In the simulated N +
H condition, we found a large difference in the calculated
value of W ¶BAL compared with either NORM or HYPO. In
this scenario, CP was overestimated, whereas W ¶ remained
approximately the same. Since this affects the time constant
of W ¶BAL depletion and reconstitution, if CP is overestimated, this will lead to W ¶BAL values higher than expected,
highlighting the importance of determining CP accurately.
The 3AOT has been validated against the linear 1/time CP
model, using a mixture of recreationally active subjects and
endurance trained cyclists and runners (40). These authors
reported strong correlations between both EP and CP (r =
0.99) and W ¶EP and W ¶ (r = 0.84), whereas the standard error
for the estimation of CP from EP was 6 W. Standard error
for estimation of W ¶ from W ¶EP was 2.8 kJ (40). Elsewhere,
typical error for the estimation of CP and W ¶ has been
reported as 15 W and 2864 J, respectively (24). Despite
strong correlations with parameter estimates from traditional
CP test methods (25), it should be noted that error associated with testing CP + W ¶ via the 3AOT may contribute
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533
APPLIED SCIENCES
FiO2 of ,0.09. In a study by Parker-Simpson et al. (33),
a ,22% decrease in EP derived from a 3AOT was reported.
This study used a lower FiO2 compared to the present investigation (0.13 vs 0.155) and only female participants who
may be more prone to exercise-induced arterial hypoxemia at
altitude (20). Collectively, these results confirm the validity
of the 3AOT test as a measure of aerobic capacity, and that
CP is reduced in HYPO, whereas W ¶ is not.
By determining CP + W ¶ in HYPO, we were able to calculate a workload from equation 6 that predicted task failure
in 4 min in both NORM and HYPO (P4). Since no change in
W ¶ occurred between NORM and HYPO, the power output
for the intermittent work intervals in HYPO was an equivalent magnitude above CP as for NORM. As a result, in the
intermittent test Worktot 9 CP was not significantly different
between NORM and HYPO (Table 3). Our finding that estimates of W ¶, W ¶BAL, and Worktot 9 CP were not different
in NORM and HYPO during equal relative intensity exercise,
is consistent with the emerging hypotheses that a) W ¶, and by
extension W ¶BAL, are related to development of peripheral
muscle fatigue such as progressive depletion of high-energy
phosphates, failure of excitation-contraction coupling, and
accumulation of fatigue inducing metabolites (25) and b) the
magnitude of peripheral fatigue is a regulated variable that
remains approximately the same at the point of task failure
under a variety of conditions including moderate HYPO (2),
hyperoxia (1), and when neuromuscular electrical stimulation
was used to create differing levels of ‘‘prefatigue’’ (23).
Further evidence in support of the notion that CP is an
index of aerobic energy provision was found in the present
study. We observed strong correlations between V̇O2peak
and CP in both NORM and HYPO (Figs. 2A and 2B, respectively). Additionally, V̇O2peak declined by 19% in
HYPO, and this change was significantly correlated to the
change in CP (Fig. 2C). During high-intensity whole-body
exercise in HYPO, numerous studies have reported exaggerated peripheral locomotor muscle fatigue (1,2) compared
with NORM; thus, it might be expected that depletion of
W ¶BAL in the intermittent test should have occurred more
rapidly in HYPO and hence Worktot 9 CP would be markedly reduced. As discussed previously though, we used a
work rate that required approximately the same energy demand above CP in both conditions, whereas the studies
reporting exaggerated peripheral locomotor muscle fatigue
in HYPO used the same absolute intensity, which therefore
represents a different relative workload (1,2). By calculating
W ¶BAL in HYPO using model parameters derived in NORM,
this simulated the effect of decreasing the intensity relative
to CP (the N + H condition). Subsequently, W ¶BALtf, and
W ¶BALmin for the N + H condition were markedly higher
than both NORM and HYPO, whereas Worktot 9 CP was
well below. This finding is similar to observations that peripheral fatigue is delayed or attenuated in HYPO (1) and
highlights the interaction between CP and development of
fatigue during high-intensity intermittent exercise. We
therefore consider accurate determination of CP essential to
to uncertainty in modeled values of W ¶BAL during intermittent exercise.
Several studies have found CP determined in the 3AOT to
overestimate CP from the 2-parameter nonlinear model
(8,9,28), particularly in well-trained endurance athletes (28).
These studies did not use identical methods though to those
of Vanhatalo et al. (40). In the present study, we followed
the original methodology (40) precisely except for one difference; we chose to provide duration feedback to our subjects throughout the 3AOT, whereas they did not, in order to
prevent pacing. However, recent research has shown that
when knowledge of the end point is denied during repeated
all-out cycling sprints (10) and maximal voluntary contractions (21), then subjects adopt a more conservative pacing
approach rather than giving full maximal efforts. Second,
there is evidence that indicates pacing may occur for any
all-out sprint duration lasting longer than 15 s (41). Therefore, regardless of whether duration feedback is provided or
not, there is potential for pacing to occur in an all-out test
lasting 3 min. In particular, without duration feedback, a
more conservative pacing approach might be adopted. To
reduce the likelihood of conservative pacing, we suggest
that feedback duration could be provided. A consequence of
this though, is that subjects may achieve a short-term increase in power, known as an ‘‘end spurt’’ (6), upon nearing
completion of the test. Without exception, all subjects in the
present study reported an RPE of 10 following the 3AOT in
both conditions. Furthermore, when queried more intensively, all subjects stated they did not pace the effort and
attempted to maximize cadence at all times during the test.
Nevertheless, in 9 of 11 tests in NORM and 3 of 11 in
HYPO, the EP was higher than CP; hence, mean EP was
significantly higher than CP in NORM. Rejecting these performances on grounds of invalidity carries negative connotations for the practical application of the 3AOT. Given that
several studies have reported high values for CP via the 3AOT
compared with a nonlinear model (7,9,28), and in the present
investigation, we found W ¶BAL was significantly greater (in
NORM) when the EP values were used as opposed to CP;
then, it would seem justified to determine both EP and CP
from the minimum 30-s moving average. This has the advantage of allowing investigators to integrate the entire area
above the 30-s moving average, thus apportioning the work
done above this value to the W ¶. Future research should focus
on the rigorous testing of this modification.
Lastly, we chose to calculate both W ¶BALtf and W ¶BALmin
during the intermittent test, since there were multiple instances where the recovery of W ¶BAL preceding the final
exercise interval exceeded depletion of remaining W ¶BAL in
final, incomplete interval. In these cases, W ¶BALmin was
lower than W ¶BALtf; and in NORM, this led to a significantly
higher mean W ¶BALtf compared with W ¶BALmin. In summary,
without including both the minimum 30-s moving average
CP estimate and W ¶BALmin analysis, the potential to falsely
overestimate W ¶BAL at task failure existed in NORM, given
that W ¶BALtf using EP was 2.0 T 0.9 kJ (95% CI, 1.4–2.6 kJ),
which is almost entirely above the field validated fatigue
threshold W ¶BAL value of 1.5 kJ (35).
Summary and conclusions. In the present study, we
examined the effect of HYPO on the W ¶BAL model during a
high-intensity intermittent exercise task. We found no difference in estimates of W ¶BAL between NORM and HYPO;
therefore, we conclude that the W ¶BAL model remains valid
under hypoxic conditions and can be successfully applied to
real-world scenarios such as competition and training at altitude. However, owing to the key assumptions of the W ¶BAL
model, it is particularly sensitive to the estimate of CP used,
since any error in this parameter will alter both relative intensity during work bouts above CP, and the oxidative reserve during recovery periods below CP. Together, these
errors will create a mismatch between the actual development of fatigue and modeled W ¶BAL. Hypoxia induces a
marked reduction in CP; therefore, if exercise is performed
at altitude, then sea level estimates of CP will lead to
grossly overestimated values of W ¶BAL. Successful application of the W ¶BAL model necessitates measurement of CP
at the same ambient oxygen concentration, or a mathematical modification to correct for altered oxygen concentration or altitude.
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 have no conflicts of interest
to report.
SS, DD, and NT acknowledge the contribution of David Gleadon
who provided technical support before and during this project.
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APPLIED SCIENCES
MODELING W ¶ IN HYPOXIA
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