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RESEARCH ARTICLE
Exercise Tolerance Can Be Enhanced through
a Change in Work Rate within the Severe
Intensity Domain: Work above Critical Power
Is Not Constant
Jeanne Dekerle
1
*, Kristopher Mendes de Souza
2
, Ricardo Dantas de Lucas
2
, Luiz
Guilherme Antonacci Guglielmo
2
, Camila Coelho Greco
3
, Benedito Sérgio Denadai
3
1Centre for Sport and Exercise Science and Medicine, University of Brighton, Eastbourne, United Kingdom,
2Physical Effort Laboratory, Sports Center, Federal University of Santa Catarina, Florianópolis, Brazil,
3UNESP, Human Performance Laboratory, Rio Claro, Brazil
*j.dekerle@bton.ac.uk
Abstract
Introduction
The characterization of the hyperbolic power-time (P-t
lim
) relationship using a two-parame-
ter model implies that exercise tolerance above the asymptote (Critical Power; CP), i.e.
within the severe intensity domain, is determined by the curvature (W’) of the relationship.
Purposes
The purposes of this study were (1) to test whether the amount of work above CP (W>CP)
remains constant for varied work rate experiments of high volatility change and (2) to ascer-
tain whether W’determines exercise tolerance within the severe intensity domain.
Methods
Following estimation of CP (208 ±19 W) and W’(21.4 ±4.2 kJ), 14 male participants (age:
26 ±3; peak _
VO2: 3708 ±389 ml.min
-1
) performed two experimental trials where the work
rate was initially set to exhaust 70% of W’in 3 (‘THREE’) or 10 minutes (‘TEN’) before being
subsequently dropped to CP plus 10 W.
Results
W>CP for TEN (104 ±22% W’) and W’were not significantly different (P>0.05) but lower
than W>CP for THREE (119 ±17% W’,P<0.05). For both THREE (r= 0.71, P<0.01) and
TEN (r= 0.64, P<0.01), a significant bivariate correlation was found between W’and t
lim
.
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 1/15
OPEN ACCESS
Citation: Dekerle J, de Souza KM, de Lucas RD,
Guglielmo LGA, Greco CC, Denadai BS (2015)
Exercise Tolerance Can Be Enhanced through a
Change in Work Rate within the Severe Intensity
Domain: Work above Critical Power Is Not Constant.
PLoS ONE 10(9): e0138428. doi:10.1371/journal.
pone.0138428
Editor: Massimo Sacchetti, University of Rome Foro
Italico, ITALY
Received: April 23, 2015
Accepted: August 29, 2015
Published: September 25, 2015
Copyright: © 2015 Dekerle et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.
Data Availability Statement: All relevant data are
within the paper.
Funding: The authors received no specific funding
for this work.
Competing Interests: The authors have declared
that no competing interests exist.
Conclusion
W>CP and t
lim
can be greater than predicted by the P-t
lim
relationship when a decrement in
the work rate of high-volatility is applied. Exercise tolerance can be enhanced through a
change in work rate within the severe intensity domain. W>CP is not constant.
Introduction
In cycle ergometry, the higher the power output (P), the shorter the time to task failure (t
lim
)so
that the P-t
lim
relationship is of a shape of a hyperbole within the severe intensity domain [1,2].
The performance of several exercises performed to task failure allows for an asymptote referred
to as Critical Power (CP) and a curvature constant (W’) to be estimated using a two-parameter
model (Eq 1)[2,3]. One interest in the application of the P-t
lim
relationship would lie in its use-
fulness in predicting t
lim
as long as the work rate requirement is greater than CP (‘P–CP’in Eq
1), i.e. within the severe intensity domain [4]. Indeed, any prediction of t
lim
from the modeling
of the equivalent hyperbolic speed-time relationship in running [5,6]orP-t
lim
relationship in
cycle ergometry [3,7,8] is highly accurate. This relies on and supports the assumptions that while
CP is rate-limited, W’is a fixed or capacity-limited amount of work [4,9–11]. Irrespective of the
work rate requirement above CP, as long as Pexceeds CP, W’is utilized at a rate determined by
the difference between the required Pand CP (‘PCP’in Eq 1) so that at task failure, W’is fully
utilized [4,6,11,12]. A strong determinant of t
lim
in the severe intensity domain (i.e. when
exercising above CP) should therefore be W’although this has never been directly evidenced.
tlim ¼W0
ðPCPÞð1Þ
The most inquisitive design developed to test this hypothesis was that of Fukuba et al. [12]
who manipulated the work rate during exercise performed above CP. Half of W’was to be
expended in the first part of two varied work rate tests (117% and 134% of CP) before an
increase (117% !134%) or decrease (134% !117%) to a new work rate. The latter was to be
maintained till task failure. The total amount of work performed above CP (W>CP) during
these two experimental conditions were not significantly different from W’as estimated from
the modeling of the P-t
lim
relationship leading the authors to conclude that “the work equivalent
of W' is not affected by power output variations during exhausting cycle ergometry, at least in
the Prange of 100–134% of CP.”
Challenges to the work of Fukuba et al. [12] and the use of the P-t
lim
relationship to predict
performance arise when considering the literature on pacing strategies. Indeed, it has been
shown that work production can be maximized, and exercise tolerance consequently enhanced,
through work rate manipulation. This has been evidenced for positive strategies in particular
[or fast-paced pacing [13]] and for performance lying within the severe intensity domain
[14,15]. Some insights into the underlying mechanisms have been proposed: A faster _
VO2
kinetic response and consequently greater mean _
VO2in the early part of a positive exercise,
has been related to improvements in performance lasting from 2 to 5 minutes [14,15]. Such
exercise would enhance the aerobic contribution to the total energy turnover. This aerobic con-
tribution is represented by ‘CP x t
lim’
in the linear equivalent of the hyperbolic P-t
lim
model pre-
sented in Eq 1 (see Eq 2;W: total work done for a given t
lim
). Accumulated oxygen deficit
(AOD) has been found unchanged in a positive vs constant-load strategy [15] suggesting that
the anaerobic contribution to the overall work requirement (W’in the CP model) was
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 2/15
unaffected by the pacing strategy. The different distribution in the utilization of AOD over the
trials was evidenced in the work of Aisbett et al. [15] leading the authors to suggest that the
development of fatigue often associated with the utilization of W’when considering the CP
model [4], could be delayed in positive pacing strategies [15].
W¼W0þCP:tlim ð2Þ
The present study aimed to challenge the application of the CP concept to varied work rate
exercise performed within the severe intensity domain. The present experimental design is less
‘conservative’than that of Fukuba et al. [12]. The experiment has been designed to test two dif-
ferent decrements in the work rate. In both conditions, a greater work rate was to be main-
tained in the first part of the performance trial (Part_1) [12]. This work rate was set to exhaust
70% of W’(as opposed to 50% in Fukuba et al., [13]) in the shortest (3 minutes; condition
THREE) or longest possible times (10 minutes; condition TEN). Some pilot work evidenced
the incapacity for some participants to maintain the work rate required to exhaust 70% of W’
in less than 3 and more than 10 minutes (both extremes when working above CP [4]). The sec-
ond part of the experimental trials was set at CP plus 10 W (Part_2) in order to target the low-
est end of the severe intensity domain, while remaining confidently above CP (>upper limit of
the 95% confidence interval). Based on the CP concept, one would hypothesize that both exer-
cise would cease when the remaining 30% of W’is depleted so that the duration of Part_2 of
the two performance trials do not differ significantly. Because for every second spent at CP
plus 10 W, 30% of W’would be taxed by 10 J for each participant, thus irrespective of their CP
or W’, it was further hypothesized that the greater the W’of the individuals, the greater the
exercise tolerance (or t
lim
) as evidenced by a positive bivariate correlation between W’and the
overall t
lim
.
Methods
Participants
Fourteen active men participating in cycling or triathlon volunteered to take part in this study
(Age: 26 ± 3; weight: 76 ± 7 kg; peak _
VO2: 3708 ± 389 ml.min
-1
). All participants were briefed
as to the benefits and risks of participation and gave their written informed consent to partici-
pate in the study, which was approved by the Tier 1 Ethics Committee of the University of
Brighton, United Kingdom. All were familiarized with the laboratory testing procedures. Par-
ticipants were instructed to arrive at the laboratory at the same time of day, in a rested and
fully hydrated state, at least 3 h postprandial. They were also asked to refrain from caffeine and
alcohol consumption 6 and 24 h before each test, and to avoid strenuous exercise in the 24 h
preceding a test session. All were free of cardiac, metabolic or respiratory diseases.
Equipment
The tests were performed on an electrically-braked cycle (Lode Excalibur Sport, Lode BC, Gro-
ningen, Netherlands). Seat and handlebar heights were kept constant over the sessions for each
participant. The laboratory temperature was set at 20°C with 40–50% relative humidity. Heart
rate was monitored every second using a telemetric heart rate monitor (Accurex +, Polar Elec-
tro Oy, Kempele, Finland). Pulmonary gas exchange was measured continuously using a
breath-by-breath open-circuit system (Cosmed Quark PFTergo, Rome, Italy). Before each test,
the O
2
and CO
2
analysis systems were calibrated using ambient air and a gas of known O
2
and
CO
2
concentration according to the manufacturer’s instructions, while the gas analyzer turbine
flowmeter was calibrated using a 3-l syringe. Respiratory gas exchange variables ( _
VO2,_
VCO2,
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 3/15
_
VE) were corrected to STPD and BTPS, displayed for every breath and then subsequently inter-
polated to provide one value per second. Blood samples were collected from the ear lobe into
microcentrifuge tubes containing 50 μl NaF (1%) for the determination of capillary blood lac-
tate concentration ([La]; YSI 2300 STAT, Yellow Springs, Ohio, EUA).
Experimental design
The participants visited the laboratory for three stages of experimentation. Stage 1 involved the
determination of lactate threshold (LT), peak oxygen uptake (peak _
VO2), and maximal power
output (P
max
) followed by a familiarization to a constant-load test performed to task failure.
Stage 2 consisted of the performance of four to five constant-load tests to task failure to deter-
mine CP and W’. Stage 3 consisted of two randomly assigned condition trials. All tests were
separated by a minimum of 24 h. For all stages, pedaling frequency was kept at 90 ± 5 rpm. Par-
ticipants were instructed to remain seated during each test. The study was completed within
three weeks for all participants.
Stage 1: Determination of LT, peak _
VO2and P
max
The initial power output was 60 to 100 W depending on the fitness level of the participant with
an increase of 20 W every 3 minutes. The incremental test was stopped when the LT was sur-
passed or when [La] rose above 4 mmol.l
-1
. An examination of the [La]–power output relation-
ship was used to determine LT. The highest work rate attained that was not associated with an
elevation in [La] above baseline (resting) levels (less than 1 mmol.l
-1
), as determined by at least
two observers, was designated as the work rate associated with LT [16].
After a rest period of 30 minutes, the participants performed a fast ramp test to exhaustion.
The test began with an initial 5 minutes of cycling at 90% of their previously determined LT
before the work rate increased by 5 W every 12 s (equating to 25 W.min
-1
), to the limit of toler-
ance. End Respiratory Exchange Ratio (RER) and heart rate were systematically above 1.10 and
90% of maximal predicted heart rate, respectively. The breath-by-breath data from each exer-
cise test were filtered manually to remove outlying breaths, defined as breaths ± 3 SD from the
adjacent five breaths. P
max
and peak _
VO2were defined as the highest averaged 15-s power out-
put value, and the highest average 15-s _
VO2value recorded during the incremental test, respec-
tively. A familiarization to the constant-load test was performed following recovery from the
incremental protocol.
Stage 2: Determination of CP and W’
Participants performed a series of four constant-load tests to the limit of tolerance, each at dif-
ferent power outputs (from 75% to 105% of P
max
) chosen to elicit exhaustion in 3 to 15 minutes
[1]. Each test was preceded by 5 minutes of warm-up at 90% of LT, 5 minute of passive rest,
finally followed by 3 minutes of 20 W baseline pedaling. Participants were not informed of the
imposed work rate, their performance times or heart rate. The only variable known to the sub-
jects was their pedaling frequency. For each test, t
lim
was taken as the elapsed time, in seconds,
between the imposed exhaustive work rate and the time at which the participant could no lon-
ger increase their pedaling frequency back to the pre-set level after a fall by 5 rpm for more
than 5 seconds for the second time during the test and despite strong verbal encouragement.
For each participant, the three equivalents of the 2-parameter model were used to fit the
data and estimate CP and W' [17]. An iterative nonlinear regression procedure was used for
the modeling of the hyperbolic P-t
lim
relationship (Microcal Origin 7.5; Northampton, MA,
USA). The CP and W’estimates from the three equations were compared to select the best fit
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 4/15
using the model associated with the lowest standard error for W’(SE-W’). If required, a 5
th
determination trial was performed at a different work rate and entered in the model to bring
the SE of CP and W’below 2 and 10% of CP and W’, respectively. Data from the modeling is
presented in Table 1. The work accumulated above CP (W>CP) was subsequently computed
for each constant-load exercise.
Stage 3: The two condition trials
Once CP and W’were determined, the work rates required for 70% of W’to be taxed in 3 min-
utes [CP + (0.70 x W’)/180] and 10 minutes [CP + (0.70 x W’)/600] were calculated. In the
third stage of testing, participants had to maintain these work rates for the initial part of the
test (Part_1), i.e. for either 3 minutes (condition THREE) or 10 minutes (condition TEN),
before a change in the work rate to CP plus 10 W (Part_2). This new work rate was to be main-
tained to the limit of tolerance. Both tests were preceded by 5 minutes of warm-up at 90% of
LT, 5 minutes of passive rest, finally followed by 3 minutes of 20 W baseline pedaling. For each
test, t
lim
was taken as the elapsed time, in seconds, between the imposed exhaustive work rate
and the time at which the participant could no longer increase their pedaling frequency back to
the pre-set level after a fall by 5 rpm for more than 5 seconds for the second time during the
test and despite strong verbal encouragement. Blood samples were taken at rest and at the end
of Part_1 and Part_2 for the measure of [La]. Part_1 was conducted twice to improve the sig-
nal-to-noise ratio in the _
VO2response. Participants were informed of the test design prior to
the commencement of the exhaustion trials and were therefore expecting the drop in the work
rate between Part_1 and Part_2.
Data analysis
The amount of work accumulated above CP (W>CP) was computed for both Part_1
(W>CP
(1)
) and Par_2 of each trial (W>CP
(2)
) and expressed in both kJ and % of W’. As for the
incremental test, the breath-by-breath data from each exercise test were filtered manually to
remove outlying breaths, defined as breaths ± 3 SD from the adjacent five breaths. The data for
Table 1. Characterization of the P-t
lim
relationship.
Participant Model Number of tests CP (W) SE-CP (W) W’(kJ) SE-W’(kJ)
1P-t
lim-1
5 197 3.9 14.9 1.1
2P-t
lim
4 197 1.3 16.1 0.6
3P-t
lim
4 215 3.2 17.9 1.7
4P-t
lim
4 210 1.5 18.4 1.0
5P-t
lim
4 195 1.4 18.6 0.9
6P-t
lim
4 186 0.9 20.2 0.7
7P-t
lim
4 223 0.8 20.2 0.5
8P-t
lim
4 218 3.3 20.7 1.5
9W-t
lim
4 202 3.0 21.1 1.3
10 P-t
lim
4 221 3.2 25.0 1.7
11 P-t
lim
4 170 4.0 26.6 2.2
12 P-t
lim-1
4 247 3.4 26.7 1.3
13 P-t
lim-1
5 228 1.9 27.8 0.7
14 P-t
lim
4 207 1.7 25.2 0.8
Mean 208 2.4 21.4 1.1
SD 19 1.1 4.2 0.5
doi:10.1371/journal.pone.0138428.t001
Severe Intensity Domain and Exercise Tolerance
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each individual was then interpolated (Microcal Origin 6.0, Northampton, MA, EUA) to pro-
vide 1 s values, and two data sets were time-aligned and averaged. The first 20 s of the data col-
lection post the onset of exercise (i.e., the phase I response) was deleted, and a nonlinear least
squares algorithm was used to fit the data thereafter [16]. A single-exponential model was cho-
sen to characterize the _
VO2responses dynamics following the onset of exercise [14,18], as
described in Eq 3 where _
VO2ðtÞrepresents the absolute _
VO2at a given time t; _
VO2ðbÞrepresents
the mean _
VO2at baseline; A
1
the amplitude, TD the time delay, and τthe time constant of the
_
VO2response. The model fit was initially constrained to the first 60 s of exercise (i.e. 20–60 s).
The window was then lengthened iteratively until the exponential model demonstrated a dis-
cernible departure from the measured response profiles (as judged from visual inspection of a
plot of the residuals of the fit) [19,20]. In addition, a single-exponential model without a time
delay and with a fitting window commencing at t = 0 s (equivalent to the mean response time—
MRT) was used to characterize the kinetics of the overall _
VO2response during the initial part of
the two tests. AOD of the initial part of the test was calculated by subtracting the volume of O
2
actually consumed from the predicted O
2
volume for the total exercise time. The linear _
VO2
Prelationship from the lactate threshold test was used to calculate the latter [15].
_
VO2ðtÞ¼ _
VO2ðbÞþA1ð1etTD=tÞð3Þ
Statistical analysis
Data are reported as mean ± SD unless stated otherwise. All statistical procedures were per-
formed using SPSS (version 20.0, Chicago, USA) with the null hypothesis rejected at an alpha
level of 0.05. The normal distribution (Kolmogorov-Smirnov test) was verified for each set of
data. A two-way ANOVA with repeated measures was performed to identify condition
(THREE and TEN) x time differences. A one-way ANOVA with repeated measures was com-
puted to compare actual (THREE and TEN) and predicted values from the P-t
lim
model. The
compound symmetry, or sphericity, was checked using the Mauchly’s test. When the assump-
tion of sphericity was not met, the significance of F-ratios was adjusted according to the Green-
house–Geisser procedure. Significant differences were followed up using planned pair-wise
comparisons employing the Bonferroni corrected post-hoc test. Relationships were explored
using Pearson’s product-moment or partial correlations. Bland and Altman plots (1986) were
used to determine the bias and limits of agreement between two sets of data when appropriate.
Results
Work rate, t
lim
, and work accumulated above CP (W>CP) for both THREE and TEN are pre-
sented in Table 2. As expected, no significant difference was found between 70% of W’and the
actual W>CP
(1)
for THREE and TEN (F= 2.86, P= 0.11) with strong correlations, low bias
and 95% limits of agreements between 70% of W’and W>CP
(1)
(Table 2).
A significant difference was found between W>CP
(2)
of THREE and TEN and 30% of W’
(F= 7.77, P<0.01). W>CP
(2)
for THREE was significantly greater than both W>CP
(2)
for
TEN (P<0.01) and 30% of W’(Table 2) with no significant difference between the latter two
(P= 1). Significant bivariate correlations were obtained between the three sets of data (THREE
vs TEN for W>CP
(2)
:r= 0.88, P<0.01; 30% of W’vs W>CP
(2)
for THREE: r= 0.68, P<0.01;
30% of W’vs W>CP
(2)
for TEN: r= 0.66, P<0.01). Bias ± 95% limits of agreement when com-
paring 30% of W’to W>CP
(2)
were 64 ± 135% of 30% of W’for THREE and 15 ± 153% of 30%
of W’for TEN (See Table 2 for absolute values). Fig 1 presents mean ± SD alongside individual
values for W>CP accumulated during THREE and TEN, and W’. There was no significant
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 6/15
difference found between W>CP for TEN and W>CP for the constant-load tests (t= 1.60,
P= 0.11). The associated bias ± 95% limits of agreement were 0.4 ± 4.3 kJ or 2 ± 20% of W’.
This bias was not significantly different to zero (t= 1.60, P= 0.11). Absolute bias ± 95% limits
of agreement when comparing W>CP to W’for THREE and TEN are presented in Table 1.
Table 2. Work rate, work done above CP and duration of both parts of the two experimental trials.
Condition THREE TEN
mean ±SD Part_1 Part_2 Overall test Part_1 Part_2 Overall test
Work rate (W) 292 ±28 219 ±20 231 ±19 234 ±22*219 ±20 227 ±18*
Work rate (% of CP) 140 ±8 105 ±1 111 ±2 112 ±2*105 ±1 109 ±2*
Work rate (% of P
max
)91±368±372±373±2*68 ±370±2*
Actual total work done (kJ) 52.5 ±5.0 219 ±97
$
271 ±101
$
140 ±13*132 ±65*272 ±76
Predicted total work done (kJ) 52.5 ±5.2 126 ±31 178 ±36 140 ±13 126 ±31 266 ±43*
Actual W>CP (kJ) 15.0 ±2.7 10.6 ±5.1
$
25.6 ±7.3
$
15.2 ±3.3 7.4 ±5.8*22.6 ±8.4
Predicted W>CP (kJ) 15.0 ±2.9 6.4 ±1.3 21.4 ±4.2 15.0 ±2.9 6.4 ±1.3 21.4 ±4.2
(Bias ±95% limits of agreements (kJ)) (0.0±0.6) (4.2±8.5) (4.2±8.5) (0.5±2.2) (1.0±9.8) (1.5±10.7)
[zero-order correlation coefficient (variance explained)] [.99 (98%)]
&&
[.68 (46%)]
&&
[.83 (86%)]
&&
[.97 (94%)]
&&
[.66 (44%)]
&&
[.90 (81%)]
&&
Actual t
lim
(s) 180 ±0 985 ±393
$
1165 ±393
$
600 ±0 683 ±487*1283 ±487
Predicted t
lim
(s) 642 ±125 822 ±125 642 ±125 1242 ±125
*Significantly different to THREE (P<0.05);
$
Significantly different to predicted by the model (P<0.05);
&&
Significantly correlated (P<0.01)
doi:10.1371/journal.pone.0138428.t002
Fig 1. Mean ±SD alongside individual values for the two sets of W>CP and W’.
doi:10.1371/journal.pone.0138428.g001
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PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 7/15
They were equal to 20 ± 40% of W’for THREE and 7 ± 50% of W’for TEN. The bias for TEN
was not significantly different to zero (t= -1.0, P= 0.34) while a significant difference was
found for THREE (t= -3.61, P<0.01).
Due to technical issues, the mono-exponential modeling of the response _
VO2for Part_1
(Table 3) was only possible on 11 participants. Between-test differences were not significant for
_
VO2ðbÞ(t= 0.92, P= 0.19) but were significant for TD (t= 0.22, P<0.05), τ(t= 4.67, P<0.01),
A
1
(t= 3.65, P<0.01), and absolute _
VO2(i.e., _
VO2ðbÞþA1)(t= 3.65, P<0.01). MRT was also
significantly reduced (t= 2.92, P<0.01) while AOD was significantly smaller for THREE
(t= 4.65, P<0.01). The ability for some participants to produce more work during Part_2 of
THREE (i.e. ‘TEN-THREE’difference in W>CP
(2)
) was not significantly related to the
between-test difference in AOD (r= 0.06, P= 0.86) and the between-test difference in MRT (r
= -0.51, P= 0.11).
A two-way ANOVA with repeated measures revealed a time effect (F= 6.80; P<0.05), but
no test effect (F= 0.35; P= 0.57) or interaction (F= 0.07; P= 0.80) for the [La] values reached
at the end of Part_1 (THREE: 10.4 ± 2.7 mmol.l
-1
; TEN: 10.8 ± 2.0 mmol.l
-1
) and Part_2 of the
two tests (THREE: 11.6 ± 2.7 mmol.l
-1
; TEN: 11.8 ± 2.3 mmol.l
-1
). The change in [La] through-
out Part_2, per second of exercise, was not significantly different between the two tests
(0.08 ± 0.16 mmol.l
-1
.s
-1
vs 0.05 ± 0.07 mmol.l
-1
.s
-1
,t= 5.60, P= 0.59). Similarly, whether
expressed in absolute or relative terms, the mean _
VO2values recorded at the end of Part_1
(THREE: 95 ± 5%; TEN: 95 ± 7% of peak _
VO2) and Part_2 (THREE: 92 ± 5%; TEN: 93 ± 7% of
peak _
VO2) were not significantly different between THREE and TEN (F= 0.05, P= 0.83) but
changed over time (F= 15.2; P<0.01) with no interaction effect (F= 0.25; P= 0.63). For both
experimental conditions, these mean _
VO2values were not significantly different at the end of
Part_1 (P>0.05) but were significantly lower than peak _
VO2at the end of Part_2 (P<0.05).
Individual trends are presented in Fig 2. Cycling efficiency or the _
VO2/ work rate ratio calcu-
lated at the end of Part_1 (THREE: 12.0 ± 0.8 ml.W
-1
.min
-1
; TEN: 15.0 ± 0.7 ml.W
-1
.min
-1
)
and Part_2 (THREE: 15.5 ± 1.0 ml.W
-1
.min
-1
; TEN: 15.7 ± 1.0 ml.W
-1
.min
-1
), was significantly
greater for TEN (F= 183, P<0.01), increased over time (F= 42.5, P<0.01) with a greater
increase during Part_2 of THREE (F= 213, P<0.01).
Table 3. _
V_
O2kinetics parameters for the first part of the two experimental trials.
Variables THREE TEN
_
V_O2ðbÞ(l.min
-1
)0.99 ±0.11 0.97 ±0.15
TD (s) 18.7 ±3.3 15.5 ±5.8*
τ(s) 22.8 ±8.3 30.2 ±8.2*
A
1
(l.min
-1
) 2.35 ±0.45 2.09 ±0.26*
Absolute _
V_O2(l.min
-1
)3.34 ±0.48 3.07 ±0.25
MRT (s) 55 ±12 67 ±13*
AOD (l) 2.41 ±0.67 4.14 ±1.56*
_
V_O2ðbÞ
—mean _
V_O2during the 60-s baseline period; TD—time delay; τ—time constant of _
V_O2kinetics
(defined as the time required to attain 63% of the amplitude); A
1
–amplitude of the _
V_O2response; Absolute
_
V_O2or _
V_O2ðbÞ+A
1
; MRT—Mean Response Time, and; AOD—Accumulated Oxygen Deficit.
*Significantly different to THREE (P<0.05).
doi:10.1371/journal.pone.0138428.t003
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 8/15
Heart rate increased from the end of Part_1 to the end of Part_2 (THREE: 170 ± 13 and
177 ± 11 beats.min
-1
; TEN: 173 ± 14 and 176 ± 12 beats.min
-1
; F = 18.1; P<0.01) with no differ-
ence between the two tests (F = 1.92, P = 0.19) but a greater change depicted for THREE
(F = 5.60, P<0.05). Minute ventilation increased over time (THREE: from 116 ± 14 to 122 ± 13
l.min
-1
; TEN: from 119 ± 19 to 123 ± 17 l.min
-1
;F= 6.40; P<0.05) but with no test difference
(F= 0.62; P= 0.45) or interaction effect (F= 0.19; P= 0.67). This increase over time was the
result of an increased breathing frequency (THREE: from 41.4 ± 12.5 to 51.5 ± 10.4 breaths.
min
-1
; TEN: from 45.0 ± 12.9 to 51.5 ± 11.1 breaths. min
-1
;F= 22.7; P<0.01) despite a slight
decrease in tidal volume (THREE: from 2.94 ± 0.63 to 2.41 ± 0.26 l.breath
-1
; TEN: from
2.76 ± 0.57 l.breath
-1
to 2.44 ± 0.30 l.breath
-1
;F= 12.7; P<0.01). No test-difference was found
for these two physiological variables (P<0.05) but an interaction was depicted for tidal volume
(F= 13.7; P<0.01). The rates of change over time in these physiological variables were not
related to the differences in work produced during THREE and TEN.
Zero-order and partial correlations between the two sets of t
lim
and W’and CP are summa-
rized in Table 4.
Discussion
Exercise tolerance within the severe intensity domain can be enhanced through a variation of
high volatility in the work rate. An initial exercise phase of much greater work rate, 3 minutes
Table 4. Coefficient of correlation (variance explained) for the relationships between t
lim
,W’and CP.
Correlation t
lim
for THREE t
lim
for TEN
W’zero-order 0.71 (50%) ** 0.64 (41) *
W’Partial, controlling for CP 0.67 (45%)*0.65 (42) *
CP zero-order 0.44 (19%)
n.s.
0.75 (56%) **
CP Partial, controlling for W’0.33 (11%)
n.s.
0.76 (58%) **
W’and CP Multiple (forced entry) 0.75 (55%) ** 0.87 (75%) **
doi:10.1371/journal.pone.0138428.t004
Fig 2. Mean _
V_
O2expressed in % of peak _
V_
O2recorded at the end of Part_1 and Part_2 of THREE and
TEN. Group means are presented as open circles with standard deviation bars.
doi:10.1371/journal.pone.0138428.g002
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 9/15
at around 140% before a drop to 105% of CP in the present study, increases the total amount of
work (*49%) predicted from the P-t
lim
relationship. A more conservative work rate decrement
with a smaller difference between the two phases of an exhaustive trial, yet still performed
within the severe intensity domain (10 minutes at around 112% before a decrease to 105% of
CP), leads to the performance predicted from the P-t
lim
modeling. More work above CP than
W’can be produced when a work rate decrement of high volatility is imposed (Fig 1) but this
was not explained by a faster _
VO2kinetic response in the present study. With W’and t
lim
sig-
nificantly correlated for both conditions (Table 4), the present study also demonstrates that W’
can be a stronger determinant of these t
lim
than CP (the case for THREE).
.
Interestingly, a large
proportion of the variance in the t
lim
for THREE remains undetermined.
W>CP was 70 ± 2% for Part_1 and 33 ± 21% of W’for Part_2 of TEN. The latter was not
significantly different to the expected 30% of W’(Table 2 and Fig 1). These results for TEN are
in accordance with the findings of Fukuba et al. [12] who also found exhaustive trials per-
formed within the severe intensity domain to end when W’was fully utilized, even when the
work rate was changing moderately during the exercise. Interestingly, the duration of our trial
was much longer than those of Fukuba et al. [12](*20 vs *6 minutes). From an estimation
of CP and W’using a 3-min all-out test [End Power (EP) and work done above EP (WEP) con-
sidered as surrogates for CP and W’, respectively], Chidnok et al. [11] also found the P-t
lim
model to predict performance of *3 and 12 minutes accurately. WEP was not significantly
different from predicted but with greater Coefficient of Variation (CV; 19–25%) than those
reported for t
lim
(3–8%). In agreement with these findings, in the present study, W>CP
(2)
accu-
mulated during TEN was not significantly different and correlated well with 30% of W’
(Table 2) while the test lasted 1283 s on average, only 41 seconds longer than the prediction
from the model (or 3.2% of t
lim
). Despite this low bias, the 95% limit of agreement was ± 487 s
or one third of the mean t
lim.
CV computed for each individual led to rather large mean and
standard deviation (20 ± 13%) and typical error was 24.7%. A prediction of long t
lim
of varied-
work rate within the severe intensity domain is therefore not as accurate as previously reported
for constant-load tests of shorter duration [5,11]. This could be explained by the loss of accu-
racy in the prediction from the P-t
lim
model as t
lim
increases [5] as well as a possible impact of
the change in work rate during TEN on the overall performance. The bias ± 95% limits of
agreement between W>CP and W’was better for the constant load tests than for TEN, corrob-
orating these findings (Table 2).
As for TEN, Part_1 of THREE was successful in exhausting 70% ± 2% of W’. However,
W>CP
(2),
and therefore overall W>CP, were greater than those predicted by the model
(Table 2; +19% of W’; +4% only for TEN—the more conservative approach). For 12 of the 14
participants, W>CP was greater than the upper limit of the 95% CI associated with the estima-
tion of W’. The participants in the present study could maintain Part_2 of THREE for *6
minutes longer than predicted (Table 2). This improvement in performance differs from the
findings for TEN and previously reported [12], and may challenge the application of the CP
concept to varied work rate exercise, but supports previous results showing that positive pacing
strategies can improve exercise tolerance within the severe intensity domain [14,15,21]. There-
fore, and in disagreement with the previous findings reported by Fukuba et al. [12], W>CP
does not always hold constant when exercising above CP. In agreement, interventions such as
moderate hypoxia [8], heavy-intensity priming exercise [18] or blood flow occlusion [22]have
been shown to increase W’while CP was decreased [8,22] or unchanged [18]. These findings
suggest that W0may be determined by other mechanisms than a finite amount of work, in con-
sistency with emerging evidence [22–24]. Thus, W0may need to be better defined for the
parameter to apply to physiological responses observed during varied work rate exercise.
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 10 / 15
The CP concept is based on a whole-body bioenergetic model [9] with key assumptions
[2,4,25] that can be questioned [see [9] detailed review]. First, the anaerobic component of the
overall energy supply (i.e. W’) is assumed constant. An estimation of ‘true’anaerobic contribu-
tion to exercise is difficult [26] with current questionings of the reliability, accuracy and validity
of AOD (see [27] for a review). With these limitations in mind, previous publications have
reported no change in AOD [15,28,29] despite modifications in the rate of accumulation over a
performance trial when the pacing strategy was manipulated [15]. Interestingly in the present
study, the total volume of O
2
consumed (61–64 l) and work produced were not significantly
different between THREE and TEN leading to an O
2
cost per Joule of *0.24 l.J
-1
for both tests.
This supports previous evidence for a similar anaerobic work capacity to be contributing to the
overall work production, assuming cycling efficiency was kept constant. Secondly, the aerobic
supply is assumed rate-limited in the 2-parameter CP model [2]. This assumption can be ques-
tioned as an increase in the aerobic energy supply has been put forward to explain the better
performances recorded with a positive pacing strategy [14,15,29]: Greater volumes of O
2
con-
sumed and / or faster _
VO2kinetic responses during the first part of fast-paced trials have been
reported [10,14,15,21,30,31]. Part of the difference between W>CP and W’found in the pres-
ent study for THREE could therefore, ‘in true’, be of aerobic nature. The required increase in
CP to equal this difference would only need to be of *3.6 W (i.e. 4.2 kJ over 1165 s). The
increase in CP (+15 W) by self-paced rather than the traditional fixed and pre-imposed work-
rate exercise tests used to model the P-t
lim
relationship supports this explanatory mechanism
[7]. Unfortunately, this is not supported by the present study when analyzing changes in vol-
umes of O
2
or _
VO2kinetic parameters. The third key assumption of the CP model is for cycling
efficiency to be constant within the severe intensity domain, which remains unknown. None of
our physiological measures explain the beneficial effect of the decrement in work rate during
THREE. Of interest, differences in W>CP and W’were computed individually for both tests
and a strong bivariate correlation was obtained (r= 0.83, P<0.01; Fig 3). Participants who per-
formed better than expected for THREE also performed better than expected for TEN. This
would need further exploration.
The previous paragraph discussed the present findings within the original Critical Power
framework [9,25] the scientific community seems to be moving away from [22–24]. The physi-
ological underpinning of W’has been particularly challenged over the past 10 years [24] with
the notion of a fixed energy store [4,9,25] evolving toward a more ‘moldable’work capacity.
Exhaustion has been suggested to occur once accumulations of fatigue-related metabolites
reach critical thresholds within the muscle cells as shown for H
+
and P
i
using
31
P-MRS
[11,32,33]. So any intervention delaying fatigue-related metabolites accumulations should
enhance W’, and exercise tolerance as a consequence. In line with these new view on W’, one
may speculate that one of the ‘priming’effect of the first part of THREE is an increase in blood
flow to type II fibers [24,34]. Oxygen delivery to the muscle cells could facilitate the aerobic
energy turnover (and consequently increase CP) while a better muscular perfusion would also
delay the cellular metabolic instability during the second part of the test [23]. The lack of signif-
icance in the _
VO2
–related variables in the present study, partly because of a lesser efficiency at
the end of part_1 of TEN (*15 ml.min
-1
.W
-1
) when compared to THREE (*12 ml.min
-1
.W
-
1
)[23] could mask dissimilarities in the muscular vascular perfusion between the two experi-
mental tests. In agreement with this assumption is the increase in t
lim
when an imposed work
rate lies within the lower part of the severe intensity domain, i.e. close to CP, similar to the
work rate of the second part of our experimental trials (CP+10 W), following nitrate supple-
mentation [35,36]. The nitrate supplementation resulted in a slight but not statistically signifi-
cant increase in W’(+8.4%) and CP (+1.4%).
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 11 / 15
A more integrative approach to fatigue during exercise of severe intensity would also con-
sider greater volume of oxygen ventilated (*31 l for Part_1 of TEN vs 8 l for Part_1 of
THREE) and possibly reactive oxygen species (ROS) produced during the first part of TEN
[37]. More breaths taken (similar breathing frequencies and minute ventilation at the end of
Part_1 of THREE and TEN while Part_1 was more than 3 times longer for TEN) would lead to
greater respiratory muscle work [38,39]. More mechanical work produced (+ 67%) and conse-
quently heat generated would demand an adequate but straining thermoregulatory response to
keep the muscle cell cool [40]. The repetition of excitation-contraction coupling over time is
also associated with extracellular and intracellular ionic disturbances (ROS, Na
+
,K
+
,Cl
-
,Ca
2+
)
thought to contribute to peripheral fatigue [37,41]. So some elevated but similar metabolic and
cardio-respiratory responses at the end of Part_1 of THREE and TEN could hide a more pro-
nounced development of peripheral and overall fatigue after the first 10 minutes of TEN when
compared to the initial 3 minutes of THREE, even though the same amount of W’was utilized
(70%). Interestingly, heart rate at the end of the first part of THREE (*168 beats.min
-1
) was
slightly lower than that recorded at the end of the first part of TEN (*173 beats.min
-1
), allow-
ing for a greater increase during the second part of this test (+ around 7 vs 3 beats.min
-1
). The
Critical Power framework may offer a reductionist approach for the rather complex integrative
physiological responses underpinning exercise tolerance during whole body exercise [42].
The _
VO2responses during both THREE and TEN demonstrate task failure can occur within
the severe intensity domain without a systematic attainment of peak _
VO2(Fig 2). One may
argue the two tests were not performed till ‘true’exhaustion with a voluntary decision made by
each participant to end the test. It must be noted that these submaximal _
VO2levels at the end
of exercise were observed despite greater (THREE) or similar (TEN) W>CP than expected.
Fig 3. Scatter plots representing the differences between W>CP and W’for THREE against TEN. The
dash line represents the line of identity.
doi:10.1371/journal.pone.0138428.g003
Severe Intensity Domain and Exercise Tolerance
PLOS ONE | DOI:10.1371/journal.pone.0138428 September 25, 2015 12 / 15
Furthermore, the _
VO2values at the end of the first part of both THREE and TEN were not dif-
ferent to peak _
VO2but did decrease thereafter to reach submaximal levels at task failure
(*92–93%). These submaximal _
VO2levels are also in line with previous reports [43–45], i.e.
submaximal _
VO2values as low as *88% of peak _
VO2recorded at the end of exhaustive tests
performed in the lower end of the severe intensity domain [43]. This challenges the physiologi-
cal description of Critical Power as a threshold intensity above which exercise of sufficient
duration will lead to attainment of a peak _
VO2[46].
Three major determinants are traditionally offered to explain aerobic performance of long
duration: (1) cycling efficiency, (2) peak _
VO2, and (3) the ability to maintain a high percentage
of peak _
VO2for a long time [or aerobic endurance, [47,48]. The theoretical framework of the
CP concept offers for W’to govern the capacity for a higher percent of peak _
VO2to be main-
tained for a long time when exercising within the severe intensity domain. Indeed, according to
the CP model, exercise tolerance (i.e. t
lim
) is dictated by the size of W’for any given work rate
above CP (P–CP; Eq 1), so that exercise ends when W’is fully utilized (as evidenced with TEN).
The significant positive relationship between W’and the t
lim
of both THREE and TEN supports
this framework (Table 4). Furthermore, for two tests of similar durations (Table 2), W’becomes
a better determinant of t
lim
than CP for THREE although none of the two variables, even com-
bined (55% of variance explained), explains well exercise tolerance for this condition. The vari-
ance in the t
lim
for TEN is much better shared between W’and CP supporting for the
2-parameter modeling of the P-t
lim
relationship to be challenged by a positive pacing strategy of
high volatility. A negative relationship was reported by Billat et al. [49] between the running
speed associated with peak _
VO2and its associated t
lim
(r= -0.36, P<0.05): The higher the speed,
the shorter the associated t
lim
. The authors mainly discussed aerobic endurance while we
hypothesized for the anaerobic capacity of the runners to potentially explain this result as well.
Conclusion
Exercise tolerance can be enhanced by a positive pacing strategy in the severe intensity domain.
The change in work rate has to be of high volatility with, in the present study, a decrease from
140% to 105% of CP at the third minute of exercise. This led to a *49% increase in the total
amount of work when compared to those predicted from the hyperbolic P-t
lim
relationship.
The work accumulated above CP was greater than W’challenging the application of the CP
concept to varied work rate exercise within the severe intensity domain. Although W’deter-
mines exercise tolerance better than CP in this domain of intensity, work accumulated above
CP can be enhanced with a delay in the accumulation of fatigue-inducing metabolites as one
proposed explanatory mechanism. A more mechanistic approach to the physiological mecha-
nisms underlying the enhancement of exercise tolerance through a change in work rate within
the severe intensity domain is required to investigate the present findings further.
Author Contributions
Conceived and designed the experiments: JD CCG BSD. Performed the experiments: JD KMdS
RDdL LGAG CCG BSD. Analyzed the data: KMdS RDdL LGAG CCG BSD. Contributed
reagents/materials/analysis tools: JD KMdS RDdL LGAG CCG BSD. Wrote the paper: JD CCG
BSD.
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