The second model, model 2, gave systematically smaller time constants for _p,O2. The _p,O2 for II only ranged between 20 and 39 s for all except subject 3 who, as with _PCr, had a longer time constant of 68 s. The model 2 exponential fit to the data set of subject 1 is shown in Fig. 3B. This function provided a good description of the II response, as it did in all cases.

In order to compare the kinetics of the two variables, we phase-aligned the data. Firstly, the axes for [PCr] were inverted allowing us to compare the [PCr] fall with the _p,O2 increase. In the case of the model 1 fit, the start of exercise functioned as the start of the exponential for both [PCr] and _p,O2. The two responses and their fitting functions for one representative subject are superimposed in Fig. 4A. Even by inspection, it is apparent that the two processes do not follow the same kinetic responses. For the model 2 fit (Fig. 4B), the data set first had to be phase aligned by moving the _p,O2 data set back in time such that the exponential functions began at the same point in time, i.e. 'ignoring' the I data. This phase aligning of the [PCr] and II _p,O2responses to exercise allowed direct comparison of the simultaneously measured pulmonary and intramuscular variables. The two variables clearly follow the same time course. The original [PCr] fall and _p,O2 rise to their new steady-state levels for each subject are shown in Fig. 5A and B. The subsequent superimposition of the kinetic changes of [PCr] and _p,O2 (with the [PCr] axes inverted and the _p,O2 'phase shifted') for all six subjects are shown in Fig. 5C. The two variables appeared to follow the same dynamic response profile in all cases, and it is pertinent to point out that, even in the case of subject 3 who showed such slow _p,O2 kinetics, the time course of [PCr] was not discernibly different.

		View larger version [in this window] [in a new window]
Figure 4. The responses of p,O2 and [PCr] to a step change in work rate of moderate intensity for one subject (subject 1) The responses are superimposed to show the dissimilarity, in the case of A, and similarity, in the case of B, of the kinetic responses of the two variables. A shows the p,O2 () fitted by a model 1 exponential. B shows the p,O2 () phase shifted and fitted by a model 2 exponential. The model 2 fit of p,O2 closely represents the kinetic response of [PCr] () to the exercise (B).

		View larger version [in this window] [in a new window]
Figure 5. The kinetic responses of p,O2 and [PCr] to a constant-load change in work rate in six subjects A shows p,O2 with the II response fitted by a monoexponential. B shows the simultaneously determined [PCr] response. C shows the identity of II p,O2 () and [PCr] () kinetics determined simultaneously during quadriceps exercise. The [PCr] scale has been inverted to facilitate kinetic comparisons. Graphs from top to bottom show data from subjects 1 to 6, respectively.

As shown in Fig. 6A, the time constants for II _p,O2lay very close to the line of identity with _PCr. The error bars describe the 95 % confidence limits of the estimation for the time constant for both variables. This suggested that II _p,O2 closely reflected (i.e. to within 10 %) the kinetics of muscular oxygen utilization (_m,O2) as previously proposed by Barstow et al. (1990) based on their computer modelling and by Grassi et al. (1996) using direct measurements of _m,O2. The '_p,O2 given by model 1, however, systematically lengthened the estimated time constant for _p,O2 with respect to that of [PCr] (Fig. 6B).

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Figure 6. Comparisons of the time constants estimated by model 1 (') and model 2 () with the simultaneously determined PCr A, the time constants () of II p,O2 (model 2) and [PCr] lie within ~10 % of identity. The error bars give the 95 % confidence intervals of the prediction of for each subject. B, the mean response time of p,O2, ' (model 1), systematically overestimates the time constant for the fall in muscle [PCr].

Having determined the [PCr] kinetic response, it was possible to consider the sources of oxidative energy utilized during the transition. The difference in the mean response time for _p,O2 (', reflecting the entire oxygen consumption throughout the transient) and the II time constant (, reflecting muscular O₂ utilization; Grassi et al. 1996) can be used to estimate the change in the oxygen stores, predominantly reflecting the change in muscular venous oxygen content (Cv,O₂). Any reduction in oxygen dissolved in the muscle tissue water or from combination with myoglobin is likely to be minimal. Therefore, because cardiac output () and _p,O2 have a highly linear relationship in the steady state (Grimby et al. 1966; Rowell, 1969; Whipp et al. 1996) and with the assumptions that: (i) _PCr is a surrogate of the time constant of _m,O2 (_m,O2; at these moderate work rates), (ii) _PCr = II _p,O2, and (iii) the muscle blood flow and its distribution in prone exercise are comparable to those for upright cycling exercise, the change in oxygen stores (Whipp & Ward, 1982) can be estimated as:

[O2 stores] = p,O2,ss (' - ).

(5)

The values for the change in oxygen stores are given in Table 2. The values lay between 104 and 328 ml of O₂. The prediction for [O₂ stores] using this relationship would be expected to range from approximately 90 to 180 ml of O₂, considering the work rates performed. Our estimates appear reasonable for the lower work rates but appear to be underestimates at the higher work rates (see Table 2). This is presumably due to the fact that our subjects were performing exercise transitions from rest. The assumption inherent in the equation of Whipp & Ward (1982) is that the relationship between _p,O2 and cardiac output is linear (with a positive intercept). However, this may not be the case when resting values are included. Furthermore, a greater contribution from transient increases in lactate ([La]) at the higher absolute work rates is also possible.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

When measured over the relevant region, the kinetics of the _p,O2 and [PCr] responses lie within the expected equivalence bounds, i.e. ± 10 % (Figs 5C and 6, Table 1). That is, the for _p,O2 during moderate exercise is likely to reflect the average response of a heterogeneous 'pool' of muscle fibres with different contractile and biochemical characteristics (Kushmerick et al. 1992). The determination of the [PCr] fall in a relatively large section (approximately a hemisphere of diameter 5 in) of this exercising muscle (when compared with biopsy techniques, for example) effectively homogenizes the intramuscular response in an analogous sense to that for _m,O2 and _p,O2 measurements. Consequently, _p,O2 can be directly related to the 'homogeneous' [PCr] fall in the muscles performing the exercise. The temporal dissociation of _p,O2 from the intramuscular [PCr] fall, and by implication _m,O2, is a necessary consequence of the size of the intervening venous volume and its blood flow dynamics. Studies by Mahler (1985) have shown a direct proportionality between the kinetics of [PCr] fall and _m,O2 in frog muscle, suggesting that our use of [PCr] as a proxy variable for the kinetics of muscle _O2 is justified, at least at moderate work rates. Furthermore, our results cohere well with those of Grassi et al. (1996) who demonstrated that the of _m,O2 was not significantly different from that of _p,O2 at the same moderate intensity exercise; however, they did not measure [PCr]. It seems reasonable to assume, therefore, that the II _p,O2 response does indeed reflect that of intramuscular [PCr] fall, and by implication that of _m,O2, during the transition from rest to moderate work in humans - at least to the limits of confidence provided by our data. While both McCreary et al. (1996) and Barstow et al. (1994a, b) have also made this point, the small amplitude of the _p,O2 response (100 ml min^-1) in the former, and the different muscle groups operating over different ranges of _p,O2 in the latter (neither making comparisons of simultaneously acquired data), did not make these studies ideal for the purpose of inferring control mechanisms. The present study was designed to exercise a sufficiently large muscle mass to produce large changes in _p,O2,ss and [PCr]_ss and for the two variables to be measured simultaneously (as have Evans et al. (1997) although not with reference to parameter estimation). These are important requirements which enable parameter estimation with the relevant level of confidence (approximately 10 %; as discussed in Whipp et al. 1999). A further confounding influence on the parameter estimation is that of the breath-to-breath noise. This has previously been shown to be part of an uncorrelated Gaussian stochastic process thereby allowing parameter estimation to within known bounds of confidence. By increasing the number of exercise bouts performed, Lamarra et al. (1987) showed that the 95 % confidence limits (K_n) for the estimation of can be increased. The limits of confidence can be described by the equation:

Kn = ^L S0/(nx),

(6)

where x is either [PCr] or _p,O2, assuming that the [PCr] 'noise' is similarly stochastic, as previously described for _p,O2. ^L is a constant depending on the value of the underlying and therefore the number of data points through the early part of the transition. S0 is the standard deviation of the point-to-point fluctuation in the steady state (i.e. -240 to 0 s at rest and approximately 180 to 360 s during exercise). n is the number of independent identical rest-work transitions that have been superimposed to minimize the influence of the stochastic noise process. The K_n for all predictions of _PCr was within the limits of acceptability needed to make comparisons with the kinetic responses of _p,O2.

The biphasic _p,O2 model proposed by Whipp et al. (1982), which has been used in the modelling of the _p,O2 responses in the present study, has important physiological implications, when compared with the more traditional models of Cerretelli & di Prampero (1987), Hill & Lupton (1923) and Whipp (1970). These authors describe the increase in pulmonary _O2 as a simple monoexponential function beginning at the onset of exercise. [PCr] breakdown, and any transient lactate production (as reflected in [La]) (Cerretelli et al. 1979; Scheuermann et al. 1998), provides a buffer to the shortfall of oxygen uptake at the muscle. This traditional model of _p,O2 assumes that the contribution of the O₂ stores to the energy transfer will result in an obligatory slowing of the _p,O2 kinetics relative to that of _m,O2. The time constant for _m,O2 (and by implication [PCr]) is, in this model, obligatorily faster than the time constant of _p,O2, as transient lactate production and a fall in venous oxygen stores causes a dissociation of the pulmonary and muscle _O2. The greater the increment in work rate (i.e. the greater the increment in _p,O2) the more pronounced is this dissociation.

The model of pulmonary oxygen uptake developed by Whipp et al. (1982), however, is based on the demonstration by Krogh & Lindhard (1913) that an initial phase of pulmonary _O2 is induced by the increase in blood flow through the lung (_l). This is followed by a subsequent, usually predominant, phase that is related to that of the muscle oxygen uptake to blood flow ratio (_O2/_m) increase throughout the transient, resulting in a reduction of the muscle venous, and therefore mixed venous, oxygen content. Here the [PCr] change (or some function thereof), directly responsible for the characteristics of _m,O2, will be closely reflected by the II_p,O2kinetics. Thus all three functions should manifest similar kinetics, i.e. to within approximately 10 %, if the predictions of Barstow et al. (1990) are valid under these conditions. The provision of oxygen to the exercising muscle at the onset of exercise seems not to be a limiting factor at this moderate work intensity (Gerbino et al. 1996; Grassi et al. 1998), although Hughson and his associates (Hughson & Morrisey, 1982) have disputed this.

Having identified the relevant parameters and variables for comparison, a further complication is apparent. This is the potential of cardiodynamic 'distortion' of the _m,O2 kinetics on reaching the lung (Barstow et al. 1990). This potential distortion may interfere with the determination of any relationship between _PCr and _p,O2. For example, if at the onset of exercise cardiac output and muscle blood flow increased in precise proportion to _m,O2, then no change in the O₂ content of the venous effluent from the exercising muscle would be evident at any point during the transient. This increase would be immediately reflected in _p,O2 (i.e. entirely dependent). It would therefore be identical to _m,O2. In contrast, if is constrained not to change throughout the transition, the increase in _p,O2 would only occur at a point in time after the onset of exercise, when the 'hypoxic' venous effluent reaches the lung. In this case, there would be an appreciable contribution of the O₂ stores during the transient (see Fig. 2 of Whipp, 1994). The normal situation, where does increase at the onset of exercise (Cummin et al. 1986), may confound any comparison of _p,O2 and _PCr. The fall of [PCr] to a new steady-state level is expected to begin at the onset of exercise, but the blood flow associated with that fall also changes with its own kinetic response to exercise. This degree of the change in blood flow between the muscle and, some time later, the lung will be determined in large part by the kinetics of the increase in . Consequently, if the kinetics of II_p,O2are determined by the kinetics of intramuscular [PCr] fall (or some function thereof), then any estimation of _PCr would be expected to reflect II _p,O2 only to within approximately 10 % (Barstow et al. 1990).

The initial region (I) of the _p,O2 kinetics is dominated by the increase in blood flow at the onset of exercise (Whipp et al. 1982). The extent of the change in oxygen stores (i.e. Cv,O₂, [oxy-myoglobin] and the O₂ equivalent of [La]) during the transient is related to the blood flow kinetics. More rigorously, the extent of the muscle oxygen stores utilization is directly proportional to the mean _O2/_m ratio at the exercising muscle. The immediacy of the fall of [PCr] at the onset of exercise suggests a similarly rapid increase in _m,O2. This is contrary to the findings of Grassi et al. (1996, 1998) who suggest a pure delay dissociating the onset of an increase in _m,O2 from the onset of exercise. However, _m does not increase in the same proportion as _m,O2 (or [PCr] fall), i.e. _O2/_m increases throughout the transient. The consequence of this is that the [PCr] decrement (or some function thereof), muscle oxygen consumption and II pulmonary oxygen uptake can all have approximately the same kinetics despite a fall in the body oxygen stores during the transition. The findings of this study, that II _p,O2 and [PCr] kinetics are identical (to within 10 %), agree with the suggestions of this model. The differences in the necessary inferences between the model suggested by Whipp and colleagues (Whipp et al. 1982) (implying that the responses of [PCr], _m,O2 and II _p,O2will all have the same kinetics at moderate work rates) and those of the models of Hill (1926) and Cerretelli and colleagues (Cerretelli & di Prampero, 1987) (that necessitate different kinetics for these variables) relate directly to the model assumptions.

All subjects in the current study showed a biphasic response in _p,O2 to exercise, as expected. Subjects 1, 2, 4 and 6 all showed an increase in _p,O2 during the I region, as expected, but subjects 3 and 5 appeared to have what would be better described as a pure delay in the _p,O2 response. Subject 3 also had very slow kinetics for _p,O2 and [PCr]; however, _p,O2 and _PCr still agreed to within 10 %. These two factors, slow kinetics and little or no _p,O2 increase during I, combine to create a large O₂ deficit. Furthermore, the I profile is suggestive of a large contribution from the O₂ stores to the energy transfer. The total O₂ deficit of 822 ml is much greater than would be expected for an 30 W increase in work rate, presumably requiring a significant contribution from transient lactate production (Cerretelli et al. 1979). The long delay in _p,O2 for subject 5 gives rise to a large contribution of the O₂ stores to the total O₂ deficit. Using eqn (5), approximately 65 % of the total O₂ deficit appears to be due to the contribution from the O₂ stores, reflecting the 'normal' oxygen uptake kinetics but a relatively long delay from the onset of exercise until the expression of increased muscle O₂ extraction is evident at the lung (i.e. O₂ store contribution to ATP synthesis would be greater). This value for the stored oxygen utilization is plausible considering the work rates and the kinetics of _p,O2.

The results from the present study, that II _p,O2 and _PCr cohere to within 10 %, are in agreement with those suggested by Barstow et al. (1990) from their computer modelling, and also with those of Grassi et al. (1996) who made direct measurements of muscle blood flow and muscle oxygen consumption during exercise. However, the assumptions of the Barstow model were related to upright exercise; we used prone exercise. We know of no data to confirm the model assumptions for this mode of exercise, i.e. the size and constancy of the venous volume and the dynamics of the increases in and _m. The present results demonstrate that '_p,O2, estimated by model 1, systematically overestimates the time constant for _p,O2 or [PCr] due to the influence of the I component on the fitting procedure. Consequently, the conclusion that _p,O2 kinetics are necessarily slower than _m,O2 kinetics is, we believe, incorrect. However, this model 1 time constant, i.e. the mean response time ('_p,O2), is physiologically useful; it can be validly used to establish the magnitude of the O₂ deficit. The difference between and ', therefore, reflects the relative contribution of the O₂ stores and any transient lactate production to ATP synthesis during the non-steady state.

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Acknowledgements

This study was supported by the MRC (UK), grant number G9536012. F. A. H. and J. R. G. are supported by the Cancer Research Campaign. The authors gratefully acknowledge Dr Marion Stubbs for her insightful comments.

Corresponding author

B. J. Whipp: Department of Physiology, St George's Hospital Medical School, Cranmer Terrace, Tooting, London SW17 0RE, UK.

Email: bwhipp{at}sghms.ac.uk

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