With adults, and to an extent children, the nature of the kinetic response has been identified to depend upon the relative exercise intensity set. At the onset of moderate intensity exercise (below the anaerobic threshold (TAN, (Wasserman et al., 1994)), a cardiodynamic phase (phase 1) which is independent of oxygen uptake at the muscle (Qo₂) is followed by an observable exponential rise in VO₂ (phase 2) towards a steady state (phase 3), and an oxygen (O₂) cost relative to work rate in adults (and probably children) of approximately 10mLO₂·min^-1·W^-1. When the exercise intensity is above and TAN below critical power (CP, (Moritani, 1981)), in the heavy intensity domain, the steady-state in VO₂ is delayed, and an additional slow component of VO₂ causes an eventual and elevated steady-state, and an elevation in the oxygen cost of exercise (Poole et al., 1988). Above CP, in the very heavy intensity domain, VO₂ continues to rise almost linearly, and the slow component causes the eventual attainment of peak VO₂. In severe intensity exercise, where the projected VO₂ is greater than peak , the response is truncated with the rapid attainment of peak VO₂ within minutes (Whipp and Mahler, 1980).

The rise in VO₂ during phase 2 is thought to be a linear function of exercise intensity, certainly within the moderate domain. That is, the magnitude of the response is proportional to the stimulus, but the rate change is constant across exercise intensities. It is the rate of this change that is of considerable interest, since the more rapid is the rise to steady state, the smaller is the O₂ deficit, and the less is the drain on exhaustible sources. The mechanism (s) controlling this response have been an issue of some contention, although the literature suggests that it is primarily governed by the muscles' potential for O₂ utilisation, with a number of additional contributory factors involved (Tschakovsky and Hughson, 1999). With exercise intensities above TAN, although the exponential nature of phase 2 is maintained, the influence of exercise intensity upon the rate change within the heavy and very heavy domains is not confirmed. Although there is conflicting evidence (Burnley et al., 2000, Tschakovsky and Hughson, 1999) it is possible that at these higher exercise intensities, O₂ delivery may play a greater contributory role in the adaptation of VO₂ (Grassi et al., 2000). The source of the additional O₂ cost of exercise in phase 3 at intensities above TAN (i.e. the slow component) remains equivocal, but has clear implications regarding efficiency. Current consensus refutes a causative link with lactate production (Poole et al., 1991, Womack et al., 1995), and favours a dependence upon fibre type distribution and recruitment (Barstow et al., 1996, Gaesser and Poole, 1996, Poole et al., 1994) with a range of possible contributory factors (Gaesser and Poole, 1996).

The aim of quantifying the VO₂ kinetic response is to evaluate the speed and the magnitude of the response, which more often than not is to a square wave transition in exerciseintensity during either cycle or treadmill ergometry. This may be achieved using non-linear regression and iterative fitting procedures, and fitting a specified model to the available data as best as possible by choosing the line of best fit that reduces the residual error (within the remits of the specified model). In order to achieve this, the following is necessary; a) The relative exercise intensity must be known so that b) the basic pattern of the response may be predicted and an appropriate model may be applied to data that must c) have high temporal resolution in order to apply any given model with d) a signal-to-noise ratio which is sufficiently good to achieve confidence in response parameters. Each of these requirements will be discussed below.

a) Since the amplitude and pattern of the VO₂ kinetic response differs according to the exercise intensity domain, making valid intra-and inter-study comparisons requires that subjects are exercising at the same exercise intensity relative to the domain demarcators TAN (moderate intensity) and CP (heavy intensity). However, in order to study the response to moderate intensity exercise, a number of studies with children have set exercise intensities relative to peak VO₂ alone or have enforced a single exercise intensity across individuals (see Table 1). This is problematic since TAN has been shown in children to vary considerably as to the percentage of peak VO₂ at which it occurs, not least due to the method by which TAN is detected and the method's reproducibility, reliability and validity. More appropriately, setting the exercise intensity as a percentage TAN of provides some assurance that subjects are at least within the same intensity domain, which due to the linearity of the response, is sufficient in order to make valid comparisons.

The kinetic response to exercise intensities above TAN with children has rarely been studied within carefully defined exercise intensity domains. The majority of studies have assessed the response to maximal and supramaximal exercise intensities and few studies have attempted to assess the existence or magnitude of the slow component of VO₂ with children (Table 2). This is most likely because the assessment of the threshold of heavy intensity exercise, CP, is especially demanding in terms of both subject effort and testing time and only once to the authors' knowledge has assessment been attempted and reported with children (Fawkner and Armstrong, 2002a). As a result, investigators intending to explore the response to heavy intensity exercise have set exercise intensities as a percentage of the difference between TAN and peak VO₂. With 12 year old children, 40% of the differences (40% D) is considered to lie below CP (Fawkner and Armstrong, 2002a) and fall within the heavy intensity domain.

b) A number of models have been proposed to represent the pattern of the kinetic response, both generically and within well-defined exercise intensity domains. Originally, it was considered that the speed of the response to any exercise intensity could be assessed by measuring the time it took to reach half of the peak exercise VO₂ achieved during the exercise test (the t½, see Table 1 and 2). This method however fails to observe the exponential nature of the response, and subsequently the time constant (τ), which represents the time taken to achieve 63% of the change in VO₂from baseline to steady state (DVO₂) has been used in its place and is solved using model 1 (see Appendix).

This model allows a monoexponential to be fit to data from the onset of exercise (i.e. when time = 0), and the time constant is usually referred to as the mean response time (MRT). However, as has been identified above, the phase 1 response that lasts 10-20 seconds is independent of , Qo₂ which only becomes evident at the mouth after the muscle - lung transit delay. Therefore there is a delay in time before VO₂ is representative of the exponential increase in Qo₂. In order to account for this, a delay term may be included in the model (model 2, see Appendix), and phase 1 data eliminated from the modelling process. Although the MRT does not necessarily allow for the accurate determination of the Qo₂ kinetics, it does provide a useful parameter with which to assess the O₂ deficit in the moderate intensity domain, which is the product of the increase in VO₂ during the transition (DVO₂) and the MRT.

As is clearly identifiable from Table 1, a number of different models have been used to analyse the response to moderate intensity exercise with children, and the effect this has on response parameters is most evident when a number of the models are applied to the same data set (Fawkner and Armstrong, 2002b). This study, which addressed the use of different modelling techniques with children, confirmed that as with adults, the response to moderate intensity exercise is best described using a single exponential and delay term following phase 1 (model 2, see Appendix).

The situation becomes more complex when dealing with heavy intensity exercise. The true nature of the response, specifically the slow component, is not entirely understood. Despite this, some authors have chosen to model the slow component as an additional exponential (model 3, see Appendix) suggesting that it represents a delayed and slowly emerging component rather than one that emerges in synchrony with the initial phase 2 primary component. Thus the model includes two exponentials each with an independent delay term and two amplitudes which represent the amplitude of the primary and slow component. With this model, the secondary delay (δ₂) has been interpreted as the time of the onset of the slow component. Other authors have chosen to model the slow component as a linear term (model 4, see Appendix), which has some justification at exercise intensities above CP since at these intensities VO₂ rises rapidly towards peak VO₂.

Despite the wide spread use of these models (with adults and to an extent children), unlike the primary phase 2 component, modelling the slow component with either an exponential or a linear term does not have any confirmed physiological rationale. In fact, attempts to combine models of both the primary and slow component in the one model can negate the accuracy with which the primary time constant and amplitude are estimated (see below). This concern is paramount when a model is forced to fit a data set for which the basic pattern of response does not comply. In the case of fitting a double exponential, this is frequently the case if there is either no clear slow component, or its rise more closely resembles a linear function than an exponential one (see Table 3 and Figure 1, step change 3 for an example).

As a result, more recently, authors are adopting the process of attempting to objectively identify the onset of the slow component, model the data of the primary component independently and report the amplitude of the slow component with respect to the end exercise VO₂ (Fawkner and Armstrong, 2004a;, 2004c, Rossiter et al., 2002). Until a model with sound physiological basis with which to paramaterise the slow component is identified, it is suggested that this is the model of choice (Fawkner and Armstrong, 2004b).

In severe intensity exercise the slow component of VO₂ does not have time to develop (although investigators must be assured that the exercise intensity is severe enough such that this is the case), and the mono-exponentiality of the response is therefore not distorted (Whipp and Özyener, 1998), and can be modelled as such (model 2, see Appendix). However, only a few early studies have attempted to investigate the kinetic responseto severe intensity exercise with children, and they have adopted more simple methods (see Table 2) to characterise the response. This is possibly due to the poor temporal resolution of the data collected which would have prevented more complex model parameterisation (see below).

c) Early studies with children examining the VO₂ kinetic response to exercise relied on traditional mixing chamber systems, where by measures of mixed expired samples were drawn off mixing chambers with measurement intervals of typically 15 to 30s (Tables 1 and 2). However, in order to be able to accurately capture the dynamic response of VO₂ to the onset of exercise, gas and respiratory data must be collected with a much higher temporal resolution, i.e. on a breath-by-breath basis. Online metabolic carts have come a long way since the pioneering work of Beaver et al., 1973, and although the combination of mass spectrometry and turbine flow meters is possibly still the ultimate tool for assessing true 'breath- by- breath' responses at the mouth, most commercially available metabolic carts with rapidly responding and carbon dioxide analysers now have the facility to generate breath-by-breath data. Despite this, as is clear from tables 1 and 2, there are still few studies that have employed these techniques with children.

d) One of the disadvantages of assessing gas and ventilatory variables on a breath-by-breath basis is that the response data reflect not only the true physiological signal of interest, but also breath-by-breath fluctuations in breathing patterns. Unfortunately for the paediatric exercise physiologist, the magnitude of these fluctuations (the noise) seems to be larger during exercise than it is with adults (Potter et al., 1999). Since the signal (VO₂amplitude in this case) is also smaller for children, the resulting signal-to-noise ratio is often so poor that fitting complex mathematical models requires serious consideration if the investigator is to be at all confident that the model fit is a true reflection of the physiological signal. This is particularly so when models involve a number of parameters, all of which are interdependent (such as models 3 - 5, see Table 3 and Figure 1, and see Appendix). It is also a serious issue when dealing with clinical populations, whose tolerance of exercise stresses may be restricted such that the stimulus must be low and thus the response signal is disproportionately small.

There are two main procedures that the investigator might carry out to improve confidence in their reported response parameters; reducing the signal-to-noise ratio and reporting the 95% confidence intervals of the response parameters.

The latter of these procedures is now relatively simple to achieve, as many iterative fitting programmes also return the 95% confidence intervals for the response parameters. Ideally, a confidence interval of no more than ± 5s for the primary τ, and ± 5% for the primary amplitude should be achieved. Reducing the signal-to-noise ratio to achieve this can however place a substantial practical demand upon the study design. By carrying out a number of repeat transitions, time aligning and averaging the responses, the magnitude of the noise may be reduced, whilst theoretically the signal remains unaltered (see Lamarra et al, 1987) for an in depth explanation of this). So, whilst a single transition does not allow suitable confidence in estimating response parameters, averaging a series of data sets may do so (see table 3 and figure 1 for an example). The number of transitions that are required to achieve suitable confidence is directly proportional to the amount of data being fit, the variability of the data and the magnitude of the signal, and thus will vary from one individual to another. With children's data which are inherently noisy, as many as 10 transitions at moderate intensity might be required. At heavier intensities, fewer transitions are required because the signal is greater.

For practical purposes, if the investigator is interested in modelling the response to a step change at moderate intensity, s/he may estimate the number of repeat transitions required to achieve a given 95% confidence interval using the following equation (Lamarra et al., 1987). For this, only the amplitude and standard deviation of the steady state Vo₂ following a single transition are required (equation 1)

Equation 1

where n is the number of transitions required; L is a constant dependent upon the underlying time constant, and the amount of data available for fitting; VO₂ (sd) is the standard deviation of breath-by-breath fluctuations in VO₂; DVO₂ (ss) is the steady-state amplitude of VO₂ above the baseline; and Kn is the confidence interval.

This technique has proved useful when investigating the VO₂ kinetic response in children (Fawkner et al., 2002) but might be especially effective when dealing with young children with cardiorespiratory or metabolic disorders. In these instances, a number of repeat bouts of exercise might be particularly demanding and practically difficult to achieve, yet may also be meaningless if the responses are still too noisy after averaging for use (Potter and Unnithan, 2005). For example, a recent study examining VO₂ kinetics in cystic fibrosis patients (mean age 15.8 ± 6.1 years) had to exclude six of the 24 patients due to noise magnitude, despite averaging up to four transitions (Hebestreit et al., 2005).

Unfortunately, few investigators to date have incorporated either of these procedures, and where they may have averaged a number of transitions together in order to reduce the signal-to-noise ratio, this is relatively meaningless unless confidence intervals are also provided (Tables 1 and 2).