AdamiA Etal EJAP2013
AdamiA Etal EJAP2013
AdamiA Etal EJAP2013
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ORIGINAL ARTICLE
Received: 24 April 2013 / Accepted: 29 July 2013 / Published online: 15 August 2013
Ó Springer-Verlag Berlin Heidelberg 2013
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Eur J Appl Physiol (2013) 113:2647–2653 2649
Morton’s model
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rffiffiffiffiffiffiffiffiffi
2W0 shortest protocols (15 and 30 s ISRT), during which a
1
T ¼ CP S þ ð5Þ significantly lower HR was reached compared with the two
S
longest tests (180 s ISRT and IIAT). No differences were
If we then multiply Eq. 5 by S, we get: found for the peak [La]b values among the various ISRT.
pffiffiffiffiffiffiffiffiffiffiffi
S T ¼ w_ peak ¼ CP þ 2W0S ð6Þ However, a few peak [La]b values were significantly dif-
pffiffiffi ferent from the peak [La]b of IIAT, for a few low values in
Eq. 6 tells that, if we plot w_ peak as a function of S we ISRT.
pffiffiffiffiffiffiffiffiffi
obtain linear relationships with slope equal to 2W0 and Only the six ISRT w_ peak values were analysed with
y-intercept equal to CP. This equation was tested by using respect to Morton’s model in Fig. 2, where w_ peak was
pffiffiffi
the results of the six ISRT, with S corresponding to the plotted as a function of S (see Eq. 6). From individual
mean ramp slope. linear regression analysis, mean CP turned out equal to
198.08 ± 37.46 W, i.e. 74.2 % of assessed w_ max , and W0
Whipp’s model resulted equal to 16.82 ± 5.69 kJ. The mean value of the
individual regression coefficients was 0.981 ± 0.016. The
A simpler, concurrent model for the analysis of w_ peak was overall regression line on all individual data, reported in
previously proposed by Whipp (1994) for ISRT protocols Fig. 2, is described by the following equation: w_ peak =
pffiffiffi
characterised by discrete ramps with the steps of different 180.95 S ? 198.04; the correlation coefficient is equal to
duration. This model predicted an inverse relationship 0.819, reflecting inter-subject variability.
between w_ peak and step duration, described by a translated On Fig. 3 we reported a theoretical solution of Eq. 8,
equilateral hyperbola of this form: obtained by setting a = W0 (from Fig. 2) and b = w_ max
TS ðw_ peak bÞ ¼ a ð7Þ (from Table 1, IIAT column). The present experimental
data were also reported on the same figure. The equation
where TS is the step duration. According to Whipp (1994), provided by linear regression analysis on the latter data was
constant b is equivalent to w_ max and constant a to the y = 2612x ? 263.5, r = 0.976, indicative of a w_ max of
anaerobic work. Thus, Eq. 7 can be linearized as: 264 W.
a
w_ peak ¼ þ b ð8Þ
TS
Discussion
Statistics
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Table 1 Maximal O2 uptakes and powers, together with associated physiological variables obtained with the seven protocols
15 s 30 s 60 s 90 s 120 s 180 s IIAT
VO
_ 2max ðmL min1 Þ 3,475.8 (±507.8) 3,554.2 (±448.6) 3,538.5 (±438.8) 3,559.7 (±408.1) 3,558.4 (±454.4) 3,503.9 (±484.9) 3,547.1 (±472.8)
w_ peak ðWÞ 428 (±46)* 366 (±46)#,* 320 (±39)#,§,* 297 (±40)#,§,},* 282 (±37)#,§,}, ,* 258 (±35)#,§,}, ,,* w_ max : 267 ð40Þ
V_Emax ðL min1 Þ 129.40 (±26.84) 134.28 (±22.31) 135.16 (±22.76) 134.36 (±24.63) 136.18 (±19.02) 126.21 (±15.06) 134.80 (±15.41)
#,§, #, #,§,} #,§
RERmax 1.30 (±0.09)* 1.25 (±0.05)* 1.19 (±0.05) * 1.18 (±0.07) * 1.13 (±0.06) 1.09 (±0.12) 1.10 (±0.07)
HRmax ðmin1 Þ 181 (±7)* 183 (±7)* 188 (±6)# 187 (±8) 187 (±9) 188 (±7)#,§ 187 (±7)
Peak ½Lab ðmMÞ 11.53 (±2.21)* 12.45 (±1.74) 12.69 (±2.01) 12.06 (±2.22)* 12.25 (±1.73) 11.92 (±2.23) 13.57 (±1.8)
Ramp slope ðW=sÞ 1.67 0.83 0.42 0.28 0.21 0.14 –
VO
_ 2max , maximal oxygen consumption; w_ peak , maximal peak power; w_ max , maximal aerobic mechanical power; V_Emax , maximal expired ventilation; RERmax, maximal respiratory exchange ratio; HRmax,
maximal heart rate; peak[La]b, peak blood lactate concentration
#
Significantly different from 15 s
§
Significantly different from 30 s
}
Significantly different from 60 s
Significantly different from 90 s
Significantly different from 120 s
* Significantly different from IIAT
pffiffiffi
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to Morton’s constant W 0
was calculated on the ensemble of the individual data
angle, as is the case for true ramps (see Fig. 1), but is
assuming y-intercept equal to maximal aerobic power and slope equal
duration. Empty dots: ISRT experimental data. Continuous line:
Fig. 3 ISRT peak powers as a function of the reciprocal of the step
(w_ peak ) is plotted as a function of the square root of the mean ramp
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2652 Eur J Appl Physiol (2013) 113:2647–2653
ramp protocols but its use can be expanded to include all _ 2max (Heubert et al. 2005) than in subjects with
elevated VO
protocols in which there is no interruption between suc- _
low VO2max , as the present ones; and (ii) the CP/w_ max ratio
cessive steps. A further expansion would result from an may vary with aerobic training (Heubert et al. 2003), and
inclusion also of Morton and Billat (2004) model of perhaps, we speculate, may differ according to muscle fibre
intermittent protocols, starting from the consideration that composition. Since CP is strongly related to the so-called
ISRT can be approximated to intermittent tests with anaerobic threshold, a concept widely used in sport
recovery between successive steps equal to 0 s. science, Eq. 10 also explains why intense aerobic training
Recently, Morton (Morton 2011) expanded the original improves both w_ max and the anaerobic threshold, or the
CP model (Monod and Scherrer 1965) to include an anal- _ 2max (di Prampero 1986; Tam
sustainable fraction of VO
ysis of maximal ramp tests by means of a new model. et al. 2012).
Fig. 2 presents a linearized analytical form of that model,
based on Eq. 5. The line’s slope, according to this equa-
pffiffiffiffiffiffiffiffiffi
tion, is equal to 2W0. Morton (2011) stated that W0 cor- Conclusions
responds to the subjects’ anaerobic capacity, yet we think
this is an oversimplification. An analysis of the energy In conclusion, the quantitative analysis illustrated in this
balance at exercise intensity between CP and w_ peak shows study demonstrated that Morton’s model well describes the
that W0 includes at least two terms: (i) the energy derived evolution of w_ peak with any type of ramp, underlying once
from anaerobic lactic energy sources, and (ii) the energy more that its magnitude is protocol-dependent. Moreover, a
provided by the further increase in VO _ 2 at powers above practical consideration emerges: performing a series of
CP. As a consequence, contrary to Morton’s prediction, W0 multiple (minimum three) ISRTs, varying in slope but not
is larger than anaerobic capacity. in power increment, allows the computation of the two
On the other hand, the predictions resulting from other important physiological parameters highlighted in
application of Whipp’s model (Fig. 3), indicated that this study: w_ max and CP. The application of our analysis
(i) the y-intercept of 264 W was indeed very close to the ensures an adequate methodology to correctly determine
measured w_ max that we obtained during the IIAT (267 W, these parameters that are bound to vary together, by the
see Table 1), as predicted by Whipp (1994); whereas (ii) same absolute amount, so that their ratio will result higher
the regression slope a, which corresponded to 2.61 kJ, the higher is VO _ 2max . The simultaneous knowledge of
was about 1/7 of W0. We suggest that the latter discrep- _
VO2max , w_ max , and CP improves our ability of defining
ancy may depend on the different meaning of a and correct training programmes.
W0. Whereas a is the energy from anaerobic sources used
to sustain powers above w_ max , W0 which includes a, is the Acknowledgments The authors thank all the volunteers who par-
energy (aerobic and anaerobic) sustaining all the work ticipated in this study. This research was supported by the Swiss
carried out above CP. We can therefore state that Eqs. 5 National Science Foundation Grant 32003B_127620 to G. Ferretti.
The authors declare that they have no conflict of interest.
and 7 are equally good tools for the description of the
w_ peak attained in ISRT.
The solutions of Eqs. 6 and 8 for w_ peak must be equiv-
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