Articles in PresS. J Appl Physiol (February 19, 2009). doi:10.1152/japplphysiol.00158.2009
Point: Counterpoint “The kinetics of oxygen uptake
during muscular exercise do / do not manifest timedelayed phases.”
Point: The kinetics of oxygen uptake during muscular exercise do
manifest time-delayed phases
Author: Brian J. Whipp
Authors: James Robert Stirling & Maria Zakynthinaki
Copyright © 2009 by the American Physiological Society.
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Counterpoint: The kinetics of oxygen uptake during muscular exercise
do not manifest time-delayed phases
2
"The kinetics of oxygen uptake during muscular exercise
do manifest time-delayed phases"
Brian J Whipp
Human Bio-Energetics Research Centre,
Crickhowell, Powys, NP8 1AT, U.K.
Modeling a physiological system’s response to a stressor, such as
characterization
of
its
transient
response
profile:
adequacy
and
appropriateness are not synonymous. The model constituents should be
reflective of the system’s physiological features, with implications both
for its control mechanisms and providing testable hypotheses for their
confirmation or not.
& O ) has been demonstrated to be
As muscle oxygen consumption ( Q
2
under the dominant feedback control of enzymatic processes linked to
high-energy phosphate utilization (6, 11, 27), exponentiality inheres in
its response to a change in work rate (WR) (13), most simply for
moderate-intensity exercise. And so it has been demonstrated to be, both
inferentially by the intra-muscular phosphocreatine profile (19) and from
& M ) and its arterio-venous O2
direct determination of muscle blood flow ( Q
content difference (7) - despite the formidable difficulties of directly
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muscular exercise, demands more than a mathematically-adequate
3
demonstrating this with precision, among which is the muscle-effluent
& M changes (1) and the likely-small
delay to the sampling site varying as Q
quantitative consequence of the Fick equation not being rigorous in the
non-steady state.
But there is no such a priori expectation for the rate at which pulmonary
& O ) increases during exercise. For the muscle, a flow
oxygen uptake ( V
2
small storage effect as its PO2 increases - unless the muscle is already
& P ) has a reduced O2 content
flow-limited. In contrast, the lung inflow ( Q
( CvO2 ); this is raised to arterial level during the pulmonary-capillary
& O 2 increase even if CvO2
transit, necessitating a flow-dependent V
& O 2 profile during
remains constant (10). This is clearly evident in the V
the transient of a step-increase in WR, especially from rest (23; Fig 1,
upper panel).
Subsequently, however, the influence of the decreasing muscle-venous
O2 content results in a decrease in CvO2 at a time dependent on the
& O 2 response therefore
vascular transit delay between the sites. The V
& P and that of CvO2 into, what is termed, its
conflates the influence of Q
phase I and its subsequent and dominant first-order component (at all
but very low WRs (21)) of the non-steady-state response (phase II) to the
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& O except for the extremelyincrease alone will not, of itself, increase Q
2
4
steady state (phase III). It is therefore hard to see how the assertion that
& O 2 kinetics has a delayed component during moderate exercise can be
V
seriously challenged.
But the concern under consideration is more related to whether, for
& O 2 response has a subsequent component
higher-intensity exercise, the V
of delayed origin superimposed upon a fundamental first-order kinetic
not, is there compelling contradictory evidence? The presence of a slow
phase of delayed onset is often evident even by inspection (4, 16; Fig. 1,
middle panel). In other cases, its onset is most clearly established by a
“simple” mono-exponential characterization of the entire transient being
no longer justifiable. The ‘best-fit’ characterization of the response
requires an additional component, the onset of which (its ‘delay’) merges
onto the still-rising phase of the fundamental (5, 14) typically after oneand-a-half to two-and-a-half minutes (although see 12)) with an
amplitude that correlates highly with the proportion of type 2 fibers (3, 9).
& O 2 ‘slow’ component, as typically characterized (for discussion, see
This V
Whipp and Rossiter (22)), can be of considerable relative amplitude and
large time constant (e.g. 5, 14, 25). One might expect the presence of a
component of such magnitude throughout the transient to distort the
phase II mono-exponentiality – it doesn’t seem to ((4, 14, 26)! And so, if
the component is neither apparent nor discernible as a statistically-
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response. The simplest answer is that ‘there certainly seems to be’! And if
5
justifiable component throughout the entire phase II, at least by best-fit
multi-exponential summing, then one seems compelled either to accept
the conclusion that it is not there or the less-than-satisfying conclusion
that it is there but can’t be seen! Furthermore, that the slow phase is a
different component of the response is suggested by the demonstration
that a sufficiently-recent bout of high-intensity priming exercise can
reduce its magnitude with no discernible effect on the fundamental
& O 2 response expressed without delay, including
components of the V
those of ventilatory and cardiac work. But the dominant component of
the slow phase originates in the locomotor muscles (18, 22); it is this
which is at issue.
Considerations of superposition also prove to be instructive. If instead of
& O 2 response to a constant WR one considers
considering the profile of V
its response to a constant rate-of-change of WR (an incremental ramp),
then the expected lagged-linear response, with a slope equal to that of
the steady-state requirement, is evident throughout the moderateintensity domain (24; Fig. 1, lower panel). However, for ramp durations of
8-12 minutes (and in some cases even longer), this behavior is also
maintained throughout the heavy- and very heavy-intensity domains (Fig.
1, lower panel). It is as if the slow phase of the kinetics is not, or is not
yet, contributory. The response to more-prolonged ramps (8) or small-
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component (5, 17). Of course, there are additional non-locomotor
6
step increments (25, 29), however, remains consistent with first-order
kinetics throughout the moderate-intensity range but one for which the
response profile backs away from simple linearity at higher intensities as if a delayed component is now supplementing the underlying process
only in the heavy- and very heavy-intensity domains.
But, if we also
consider the response to a decremental ramp, instituted immediately
from a step to the highest WR achieved on the incremental ramp, then an
& O 2 response increases to a value appreciably greater than “expected” for
V
the particular WR, based on the incremental ramp kinetics, and which
subsequently decreases with a markedly steeper slope - as if the high WR
fiber-type recruitment profile utilizes units with high energy-cost of force
production.
And so, the issue is not simply a mathematical quibble over fitting
strategies
but
one
with
significant
physiological
implications.
A
& O 2 response kinetics that does not
characterization of the high-intensity V
consider a delay in the slow phase onset necessitates the process to be
established from the onset rather than one subsequently resulting from
the contractile-energetic consequence(s) of fatigue, mediated for example
by mechanisms linked to a sufficient increase of intra-cellular inorganic
& O 2 response profile,
phosphate – a close kinetic correlate of the V
including its slow phase (20). Maintaining force production would
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entirely different response is evident (Fig 1, lower panel). In this case the
7
necessitate additional motor units to be recruited or/and a decrease in
the contractile efficiency of the operational pool (1), i.e. that will not be
manifest until this fatigue begins to be expressed, at some time after
exercise onset. The current literature addressing this issue provides
evidence that is both confirmatory and contradictory (e.g. (16, 28) and
see also Poole and Jones for discussion (17)) – we await decisive
resolution.
shallow-contoured sigmoidal component, for example, operates throughout
the high-intensity transient, there seems to be no sufficient justification to
rule it in. But the debate under consideration is useful, as it is
“…imperative to be absolutely clear that one’s equations make strict and
accurate sense. However, it is equally important not to be insensitive to
‘things going on behind the scenes’ which may ultimately lead to deeper
insights.” (15).
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In conclusion, while we cannot definitively rule out the possibility that a
8
REFERENCES
Bangsbo J, Krustrup P, Gonzalez-Alonso J, Boushel R, Saltin B.
Muscle oxygen kinetics at onset of intense dynamic exercise in
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R899-R906, 2000.
2.
Bangsbo J, Krustrup P, Gonzalez-Alonso J, Saltin B. ATP
production and efficiency of human skeletal muscle during intense
exercise: effect of previous exercise. Am J Physiol Endocrinol Metab
280: E956-E964, 2001.
3.
Barstow TJ, Jones AM, Nguyen PH, Casaburi R. Influence of
muscle fibre type and pedal frequency on oxygen uptake kinetics of
heavy exercise. J Appl Physiol, 81: 1642-1650, 1996.
4.
Barstow TJ, Molé PA. Linear and non-linear characteristics of
oxygen uptake kinetics during heavy exercise. J Appl Physiol 71:
2099-2106, 1991.
5.
Burnley M, Doust JH, Ball D, Jones AM. Effects of prior heavy
& O 2 kinetics during heavy exercise are related to
exercise on V
changes in muscle activity. J Appl Physiol 93: 167–174, 2002.
6.
Chance B, Williams CM. Respiratory enzymes in oxidative
phosphorylation. I. Kinetics of oxygen utilisation. J Biol Chem 217:
383-393, 1955.
7.
Grassi B, Poole DC, Richardson RS, Knight DR, Erickson BK,
Wagner PD. Muscle O2 uptake kinetics in humans: implications for
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8.
Hansen JE, Sue DY, Oren A, Wasserman K. Relation of oxygen
uptake to work rate in normal men and men with circulatory
disorders. Am J Cardiol 59: 669-674, 1987.
9.
Jones A, Pringle JS, Carter H. Influence of muscle fibre type and
& O 2 kinetics. In: Oxygen Uptake Kinetics
motor unit recruitment on V
in Health and Disease, edited by Jones AM, Poole DC. London:
Routledge, 2005, p. 261-293.
10. Krogh A, Lindhard J. The regulation of respiration and circulation
during the initial stages of muscular work. J Physiol 47: 112-136,
1913.
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1.
9
11. Kushmerick MJ, Conley KE. Energetics of muscle contraction: the
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12. Linnarsson D. Dynamics of pulmonary gas exchange and heart rate
changes at the start and end of exercise. Acta Physiol Scand (suppl)
415: 1-68, 1974.
13. Mahler M. First order kinetics of muscle oxygen consumption, and
& O and phosphorylcreatine level.
equivalent proportionality between Q
2
Implications for the control of respiration. J Gen Physiol 86: 135-165,
1985.
15. Penrose R. The Road To Reality. London: Jonathan Cape, 2004, p.
79.
16. Perrey S, Betik A, Candau R, Rouillon JD, Hughson RL.
Comparison of oxygen uptake kinetics during concentric and
eccentric cycle exercise. J Appl Physiol 91:2135-2142, 2001.
17. Poole DC, Jones AM. Towards an understanding of the mechanistic
& O 2 kinetics. In: Oxygen Uptake Kinetics in Health and
bases of V
Disease, edited by Jones AM, Poole DC. London: Routledge, 2005, p.
294-328.
18. Poole DC, Schaffartzik W, Knight DR, Derion T, Kennedy B, Guy
HJ, Prediletto R, Wagner PD. Contribution of exercising legs to the
slow component of oxygen uptake kinetics in humans. J Appl Physiol
71: 1245-1253, 1991.
19. Rossiter HB, Ward SA, Doyle VL, Howe FA, Griffiths JR, Whipp
BJ. Inferences from O2 uptake with respect to intramuscular [PCr]
kinetics during moderate exercise in humans. J Physiol 518: 921932, 1999.
20. Rossiter HB, Ward SA, Kowalchuk JM, Howe FA, Griffiths JR,
Whipp BJ. Dynamic asymmetry of phosphocreatine concentration
and O2 uptake between the on- and off-transients of moderate- and
high-intensity exercise in humans. J Physiol 541: 991-1002, 2002.
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14. Özyener F, Rossiter HB, Ward SA, Whipp BJ. Influence of exercise
intensity on symmetry of the on- and off-transient kinetics of
pulmonary oxygen uptake. J Physiol 533: 891-902, 2001
10
21. Sietsema KE, Daly JA, Wasserman K. Early dynamics of oxygen
uptake and heart rate as affected by exercise work rate. J Appl
Physiol 67: 2535-2541, 1989.
22. Whipp BJ, Rossiter HB. The kinetics of oxygen uptake:
physiological inferences from the parameters. In: Oxygen Uptake
Kinetics in Health and Disease, edited by Jones AM, Poole DC.
London: Routledge, 2005, p. 64-94.
23. Whipp BJ, Ward SA, Lamarra N, Davis JA, Wasserman K.
Parameters of ventilatory and gas exchange dynamics during
exercise. J Appl Physiol 52: 1506-1513, 1982.
25. Whipp BJ, Mahler M. Dynamics of gas exchange during exercise In:
Pulmonary Gas Exchange, vol. II. Edited by West JB. New York:
Academic Press, p. 33-96, 1980.
26. Wilkerson DP, Koppo K, Barstow TJ, Jones AM. Effect of work
rate on the functional 'gain' of Phase II pulmonary O2 uptake
response to exercise. Respir Physiol Neurobiol 142: 211-223, 2004.
27. Wilson DF. Factors affecting the rate and energetics of
mitochondrial oxidative phosphorylation. Med Sci Sports Exerc 26:
37-43, 1994.
28. Zoladz JA, Gladden B, Hogan MC, Niecarz Z, Grassi B. Progressive
recruitment of muscle fibers is not necessary for the slow
& O 2 kinetics. J Appl Phyiol 105: 575-580, 2007.
component of V
29. Zoladz JA, Rademaker AC, Sargeant AJ. Non-linear relationship
between O2 uptake and power output at high intensities of exercise
in humans. J Physiol 488: 211-217, 1995.
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24. Whipp, BJ, Ward SA, Paterson DA. Dynamic asymmetries of
ventilation and pulmonary gas exchange during on- and offtransients of heavy exercise in humans. In: Control of Breathing and
Its Modeling Perspective. Edited by Honda Y, Miyamoto Y, Konno K,
Widdicombe JG. New York: Plenum Press, 1992, p. 237-243.
11
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12
&O )
Fig 1. Upper panel: time course of the pulmonary O2 uptake ( V
2
response
from
rest
to
a
constant
moderate-intensity
work
rate
demonstrating the phases of the response (from ref 23).
Middle panel: as for upper panel, except the work rate is of heavy
intensity (from ref 4)
& O 2 response to an incremental (x) and
Bottom panel: time course of the V
a step-decremental (o) ramp, (modified, by the addition of the steadyDownloaded from http://jap.physiology.org/ by 10.220.33.6 on June 14, 2017
state relationship (solid symbols), from ref 24).
13
COUNTERPOINT: THE KINETICS OF OXYGEN UPTAKE DURING
MUSCULAR EXERCISE DO NOT MANIFEST TIME-DELAYED PHASES
Authors:
Stirling James Robert1
Zakynthinaki Maria1,2
1- Faculty of physical activity and sport sciences. Technical University of Madrid
2- Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM (Spain)
Contact information:
James Robert Stirling: Faculty of physical activity and sport sciences. Technical
University of Madrid, Avd. Martin Fierro s/n, 28040 Madrid, Spain. Email:
[email protected]
Zakynthinaki Maria: Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM,
c/Serrano 121, 28006 Madrid, Spain. Email: [email protected]
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(Spain)
14
The existence of time delayed phases (1) is not supported by oxygen uptake kinetics data.
Despite many attempts for a number of years, no convincing physiological mechanism
for such behavior has been proven to exist. The reason is that these time delayed phases
are a figment of the incorrect treatment of the data and the overly simple curve fitting of
the, usually, averaged data. The reported problems regarding high levels of uncertainty in
TD2 or insufficient clarity in the drop in the pulmonary gas exchange ratio, R, defining
TD1 are due to trying to fit time delayed phases to data with no such features. Due to the
Breath-by-breath recordings exhibit spontaneous fluctuations (18). A number of different
algorithms with different assumptions are therefore used to estimate the breath-by-breath
V&O2 , resulting in notable differences observable throughout the whole on/off transient,
most extremely so in the initial response (16). These algorithms can also effect the 3phase curve parameters estimates (9, 13). Breath-by-breath variability may have
biological significance (5) as nonlinear systems such as those governing the respiratory
and circulatory functions can produce signals which look like random noise but are in
fact not stochastic (3, 11, 14, 15, 21). Therefore part of what is attributed to noise can
contain inherent features and vital information (30). For example in both constant and
free-paced 10,000 m runs the V&O2 (and HR) has a scaling exponent above 0.5, the value
for white noise (4).
Noise reduction is commonly achieved via ensemble averaging the responses of multiple
supposedly identical exercise bouts (17). This is only justified when the noise is Gaussian
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poor data handling and curve fitting the time constants are also physiologically irrelevant.
15
and stochastic (26) and the basic response pattern of each bout is identical, which in
general is not the case (2, 20). To support this procedure (17, 20) are often quoted as
showing that the noise is white. These papers however do not provide sufficient proof of
the noise’s whiteness for the whole on/off transient at any intensity, as only the steady
states at rest or during the last 2 minutes (120s is a very short sample size) of non-slow
component data are analyzed. In contrast more modern studies show that some breath-bybreath algorithms produce data with non-white noise (4, 7, 9) hence averaging several
values on repeated testing days it is debatable whether ensemble averaging is an accurate
method (2). Parameter variability is also reported, especially in the time constants (19).
Differences between bouts, when ensemble averaged, can produce features not found in
the raw un-averaged time series for a single bout of exercise (30). Therefore a model
which is fit to the features of averaged data is not necessarily a good model of the raw unaveraged data of a single exercise bout (in which features such as time delayed phases
cannot be observed due to the high frequency signal oscillations (5, 23)). A curve without
time delayed phases (22, 23, 24, 25, 28, 29, 30) can fit the data perfectly well. If the data
for a single bout of exercise is instead filtered using a low-pass filter or a moving average
with sufficient high n (30) or a more sophisticated nonlinear curve smoothing techniques
(15) then the curve obtained will provide the basic response pattern for that bout of
exercise. The basic response pattern is what should be modeled, not the average, which in
general is a different curve (30).
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repetitions can be methodologically unjustified (9). Also due to variation in parameter
16
The phase 1/2 components are intertwined complicating the TD1 interpretation (26). In
theory the start of phase 2 (i.e. TD1) should be triggered by a fall in the pulmonary gas
exchange ratio (R= V&CO2 / V&O2 ) however “this decrease is often not sufficiently clear for
this purpose and a value of at least 20s is commonly used” (26). Many researchers try to
improve the phase-2 fit by constraining the fitting window to start some time after the
exercise onset (26). As there exists a high degree of interdependency in the parameters
(16), arbitrarily cutting data affects all the parameter values. As a result tau2 will be
the phase-1 and slow component, the best fit to the data can result in un-physiologically
large values of the amplitude and/or time constant (16). It is debatable therefore whether
the exponential is a good model for these phases (8, 12, 26). The determination of both
the phase-2 asymptote and TD2 is highly uncertain and via dependency, this can
dramatically effect the parameters values and confidence, possibly causing an
unacceptable reduction in the tau2 confidence (26).
Slow kinetics can easily be observed to exist by inspection, what is not certain however is
the existence of a time delayed slow component, nor has a physiological mechanisms
been proven (26). Slow kinetics emerge from the background noise after a time period
however crucially this does not imply the existence of a time delayed phase (26). The
slow phase gain profile and time constant(s?) also remain to be determined (26). A stepwise increment in oxygen demand after a time delay TD2 has recently been recognized to
be unrealistic and an n-phase curve has been proposed instead (2, 26 , 27). In a more
powerful approach however (28) numerically estimate the time dependency of the
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dependent on the amount of data removed, making it of limited use physiologically. For
17
oxygen demand from the on/off transient kinetics. Mathematically speaking the n-phase
curve (2, 27) refers to the way a smooth function is approximated using first principles of
infinitesimal calculus (30). A more rigorous model therefore would consist of a smooth
function (23, 25).
A single exponential rise for phase-2 has been argued against as almost identical curves
can be produced using very different assumptions based on numerous compartments with
amplitudes (6, 27). Hence doubts exist regarding the phase-2 parameters physiological
relevance. Regarding all the 3/n phase curves the number of parameters used is large as
their values depend on the exercise intensity. Ideally in a good model these parameters
should be far fewer and remain constant for all exercise intensities, hence characterizing
the individual (23, 25).
In conclusion, just because a curve has good statistical fit it doesn’t mean that this is
significant if the curve is not constructed from physiologically proven principles. For
example fitting straight lines point to point would result in a perfect fit having no
physiological significance. Marginal statistical improvement in the fit (i.e. by adding time
delays) of an arbitrary curve also have no significance, baring in mind the spread of the
raw data in a single bout of exercise. Finally as time delays cannot be seen with any sort
of clarity in raw data from a single response, and bearing in mind all of the
methodological problems previously discussed and the lack of a proven physiological
mechanism, we have no reason to believe such features exist. To quote (10) (see also (9))
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either a range of tau values and the same amplitudes or the same tau but different
18
“data reporting modifications of the gas exchange parameters in several conditions and
after different experimental manipulations, should be taken with a pinch of salt.”
GRANTS
Supported by the programs Ramon-y-Cajal 2004 and I3 2006, MICINN, Spain.
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28) Zakynthinaki MS, Stirling JR. Stochastic optimization for the calculation of the
time dependency of the physiological demand during exercise and recovery. Comp Phys
Commun 179(12): 888-894, 2008.
29) Zakynthinaki MS, Stirling JR. Stochastic optimization for modeling
physiological time series: application to the heart rate response to exercise. Comp Phys
Commun 176(2): 98-108, 2007.
30) Zakynthinaki MS, Stirling JR, Sillero M, Sampedro J, Refoyo I. Obtaining the
basic response pattern of physiological time series data: a comparison of methods
[Online]. Mat2, Universitat Autonoma de Barcelona.
http://mat.uab.cat/matmat/PDFv2007/v2007n08.pdf [2007].
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by Jones AM, Poole DC. Oxon: Routledge, 2005.
22
Rebuttal to: “Counterpoint: The kinetics of oxygen uptake
during muscular exercise do not manifest time-delayed
phases”
Brian J Whipp
Human Bio-Energetics Research Centre,
Crickhowell, Powys, NP8 1AT, U.K.
I expected the Stirling-Zakinthinaki “Counterpoint” (2) to provide
alternative physiological explanations for the discernibly-different oxygen
Some of their points seem warranted: the lack of justification for an
exponential phase (φ) 1 fit, and the “slow-phase” exponential fit reflecting
a process with a single time-constant (τ) and gain. But so many of their
assertions demand challenge. For example, they state that the problems
regarding the decrease of ‘R’ as an indicator of, what they term TD2, “are
due to trying to fit time delayed phases with no such features”. Well,
there are such features! The φ1-φ2 transition often coincides with a
time-delayed transient R decrease (4); where not, it is not that the
delayed component is not there but that it is “smeared” by increased
perfusion from other regions and/or transient hyperventilation. Its
presence is physiologically justified: the transient alkalosis (1, 3),
resulting from proton trapping as [phosphocreatine] decreases, retains
CO2 intramuscularly. When the φ1-φ2 transition cannot be clearly
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& O ) kinetics at different exercise intensities.
uptake ( V
2
23
determined from R, a portion of the φ1 response should not be allowed to
influence the φ2-τ estimation: this is a physiological control parameter
not a parameter of convenience (6), as are the φ1 and slow-component
τ’s. Deleting a portion of the early response slightly greater than the real
delay may influence the confidence of the φ2-τ estimation; deleting too
little will affect its value – a greater concern.
individual response, i.e. including breath-by-breath variability, will
necessarily yield “a different curve” (2) from that after appropriate
ensemble-averaging (c.f. 5, Figs 1, 2). We do not dispute that such
“noise”
contains
physiologically-relevant
features,
including
those
consequent to pleural pressure variations associated with tidal volume
& O response
changes. This yields a “cardio-dynamically mediated” V
2
superimposed upon the underlying kinetics; there is no equivalent in the
muscle kinetics!
We, among others, have proposed physiological equivalents to the
estimated intensity-dependent response parameters. That these should
“remain constant for all exercise intensities” (2) seems unjustified – the
physiology doesn’t! Furthermore, the authors neglect to note that our
suggested alternative (6) to the common slow-phase characterization was
cited as just one of the alternate means of producing such a response.
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Also, we disagree with their assertion that parameter estimation from an
24
That its physiological mechanism(s) have not been elucidated does not
justify assertions that it is not there.
Would that Stirling and Zakinthinaki had informed us how their nodelay(s) model might be mediated physiologically.
REFERENCES
Rossiter HB, Ward SA, Kowalchuk JM, Howe FA, Griffiths JR,
Whipp BJ. Dynamic asymmetry of phosphocreatine concentration and
O2 uptake between the on- and off-transients of moderate- and highintensity exercise in humans. J Physiol 541: 991-1002, 2002.
2.
Stirling JS, Zakinthinaki M. Counterpoint: the kinetics of oxygen
uptake during muscular exercise do not manifest time-delayed phases. J
Appl Physiol (in press).
3.
Wasserman K, Stringer W, Casaburi R, Zhang YY. Mechanism of
exercise hyperkalemia: an alternate hypothesis. J Appl Physiol 83: 631–
643, 1997.
4.
Whipp BJ, Ward SA. Cardiopulmonary coupling during exercise. J
Exp Biol 100: 175-193, 1982.
5.
Whipp BJ, Ward SA, Lamarra N, Davis JA, Wasserman K.
Parameters of ventilatory and gas exchange dynamics during exercise. J
Appl Physiol 52: 1506-1513, 1982.
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1.
25
6.
Whipp BJ, Ward SA, Rossiter HB. Pulmonary O2 uptake during
exercise: conflating muscular and cardiovascular responses. Med Sci
Sports Exerc 37: 1574-1585, 2005.
Rebuttal to: “Point: The kinetics of oxygen uptake during
muscular exercise do manifest time-delayed phases”
Authors:
Zakynthinaki Maria1,2
3- Faculty of physical activity and sport sciences. Technical University of Madrid
(Spain)
4- Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM (Spain)
This is not a “mathematical quibble over fitting strategies” (8), it is a description of
serious errors in the 3/n phase approach with major physiological implications, as a
search for non-existent error induced features, will obviously be fruitless (10). The
delayed component during moderate exercise and the evidence for a time delayed slow
component have been seriously challenged (5).
That a “mono-exponential characterization of the entire transient is no longer
justifiable”(8) is insufficient proof of the need for an additional time delayed phase. It is
incorrect that not implementing a delayed slow component “necessitates the process to be
established from the onset” as is the expectance of a distortion to “the phase-2 monoexponentially”(8) by a substantial slow component. These problems are all due to the 3/nphase curve fitting procedure, other physiologically relevant functions (7, 6) have been
perfectly fit.
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Stirling James Robert1
26
That a “priming exercise can reduce the slow components magnitude with no discernible
effect on the fundamental component” (8) doesn’t suggest a different component’s
existence. It only shows the effect on the subsequent kinetics of a change in the initial
conditions of the human system.
Figure 1 top/middle panel (8) doesn’t present raw un-averaged data and hence is
unsuitable for drawing physiological implications (5). The phase-1 is misleading due to
the superposition of the model curve; the spread and amount of raw-un-averaged data
points in this region cannot be seen (numerous counter examples exist 2, 4, 6). Slow
connection between a delayed slow component and the “backing away from the simple
linearity at higher intensities” (8) is not trivial or obvious, physiologically or
mathematically, as the effect of forcing a system with a square wave or a ramp is
different.
These physiological processes are obviously time dependent (1, 3) with certain features
becoming apparent or emerging from the high frequency oscillations with time. However
to use time delayed phases is an extremely strong condition to impose, as the
nonexistence of a phase before the time delay and its sudden switching on needs a
concrete proof. Such features need to be clearly observable in raw un-averaged data from
a single bout of exercise (which is not the case) and suitable physiological mechanisms
needs to be found which are true time delayed phases and not just processes becoming
apparent after a period of time (which has not been done).
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kinetics are easily observable, however a time delayed phase is not apparent (9). The
27
REFERENCES
1) Glass L, Mackey MC. From Clocks to Chaos. The Rhythms of Life. New Jersey:
Princeton University Press 1988, p.1-34.
2) Giménez P, Busso T. Implications of breath-by-breath oxygen uptake
determination on kinetics assessment during exercise. Resp Phys Neurobiol 162:
238-241, 2008.
3) Kaplan D, Glass L. Understanding Nonlinear Dynamics. New York: Springer
4) Koga S, Shiojiri T, Kondo N. Measuring V&O2 kinetics. In: Oxygen uptake
kinetics in sport, exercise and medicine, edited by Jones AM, Poole DC. Oxon:
Routledge, 2005.
5) Stirling JR, Zakynthinaki MS. CounterPoint: The kinetics of oxygen uptake
during muscular exercise do not manifest time-delayed phases. J Appl Physiol.
6) Stirling JR, Zakynthinaki MS, Billat VL. Modeling and Analysis of the Effect of
Training on V&O2 Kinetics and Anaerobic Capacity. Bull Math Biol 70(5): 134870, 2008.
7) Stirling JR, Zakynthinaki MS, Saltin B. A model of oxygen uptake kinetics in
response to exercise: Including a means of calculating oxygen
demand/deficit/debt. Bull Math Biol 67(5): 989-1015, 2005.
8) Whipp BJ. Point: The kinetics of oxygen uptake during muscular exercise do
manifest time-delayed phases. J Appl Physiol.
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1995, p.147-278.
28
9) Whipp BJ, Rossiter HB. The kinetics of oxygen uptake, Physiological inferences
from the parameters. In: Oxygen uptake kinetics in sport, exercise and
medicine, edited by Jones AM, Poole DC. Oxon: Routledge, 2005.
10) Zakynthinaki MS, Stirling JR, Sillero M, Sampedro J, Refoyo I. Obtaining the basic
response pattern of physiological time series data: a comparison of methods
[Online]. Mat2, Universitat Autonoma de Barcelona.
http://mat.uab.cat/matmat/PDFv2007/v2007n08.pdf [2007].
Downloaded from http://jap.physiology.org/ by 10.220.33.6 on June 14, 2017
Downloaded from http://jap.physiology.org/ by 10.220.33.6 on June 14, 2017