Metabolic Power and Oxygen Consumption in Team Sports: A Brief Response to Buchheit et al.

In recent years, advances in GPS technology combined with a better understanding of the energetics of accelerated and decelerated running [5] have made it possible to estimate: i) the time course of the instantaneous metabolic power requirement of any given player in soccer, as well as in other team sports [12], and ii) to infer from this information the time course of the actual O₂ consumption (V̇+O₂), on the basis of some specific assumptions concerning the VO₂ on- and off-responses during metabolic transients (see below and [4]). However, in a recent paper Buchheit et al. compared metabolic power assessment by mean of GPS to direct O₂ uptake measurements via a portable metabolic cart, and on the basis of the data obtained, questioned the validity of metabolic power assessment [1]. The following paragraphs discuss Buchheit et al.’s results [1] in some detail, with the aim of arriving at a clear-cut picture of the overall energy expenditure during any given time period of the match or training session. In essence, this exercise will lend further support to the general validity of metabolic power and O₂ consumption estimate via GPS, albeit within the limits of the underlying data collection technology and physiological assumptions.

In running, as well as in any other form of locomotion, the product of the instantaneous velocity (v, m·s⁻¹) and the corresponding energy cost per unit body mass and distance (C_r, J·kg⁻¹·m⁻¹) yields the instantaneous metabolic power (Ė, W·kg⁻¹) necessary to run at the speed in question:

Ė=v·C_r 1)

As such, Ė is a measure of the overall amount of energy required, per unit of time, to reconstitute the ATP utilized for work performance. We would also like to point out that C_r in equation 1) is the value applying at the very moment at which v is determined. Therefore, whereas during constant speed running, whether on flat terrain or up (down) a constant slope, both C_r and v (and hence Ė) are constant, this is not the case when either the slope of the terrain (and hence the corresponding C_r, e. g., see Margaria [9], Minetti et al. [11]) and/or the speed varies. It should be noted that, in this latter case, the speed changes have a 2-fold effect on the metabolic power: on the one hand, because of the direct role of v in setting Ė, and, on the other hand, because during the acceleration (or deceleration) phase, C_r is increased (or decreased) in direct proportion to the acceleration (deceleration) itself, because of the resulting kinetic energy changes. For a detailed analysis of this matter, the reader is referred to di Prampero et al. [4] [5].

On the contrary, the actual oxygen consumption (V̇+O₂) is a measure of the amount of ATP actually resynthesized at the expense of the oxidative processes. As such, at any given time, V̇+O₂ may be equal, greater or smaller than the metabolic power because the oxidative processes are rather sluggish compared to the rate of change of the work intensity. Indeed, consider as an example a square wave mild aerobic exercise in which case the metabolic power (Ė) is constant from time zero to the end. If this is so, before the attainment of the steady state V̇+O₂<Ė, throughout the steady state V̇+O₂=Ė, whereas in the recovery V̇+O₂>Ė. In addition, during very strenuous exercise bouts of short duration, a common feature in soccer activities, the metabolic power requirement can attain values greatly surpassing the subject’s maximal O₂ consumption (V̇+O₂max). It goes without saying that, in the recovery following a high-intensity bout, the opposite is true.

These considerations show that, at variance with typical “square wave” aerobic exercises of moderate intensity (i. e., below V̇+O₂max), in soccer, as well as in many other team sports, because of the occurrence of several high-intensity bouts of short duration, interspersed among low intensity periods of varied duration, the time course of V̇+O₂ is markedly different than that of metabolic power requirement. Hence, at any given time during a match, or a training drill, in the course of which the intensity (metabolic power) changes randomly (a typical example for one elite soccer player, as obtained by video analysis (Osgnach et al. [12]), is reported in [Fig. 1]), the actual V̇+O₂ can be smaller, equal or greater that the instantaneous power, depending on: i) the time profile of the metabolic power requirement and ii) the subject’s V̇+O₂max.

Fig. 1 Metabolic power requirement (black line) and estimated actual oxygen consumption (V̇ O₂, grey line) during 6 min of an official match.

Furthermore, as discussed in some detail elsewhere (di Prampero et al. [4]), knowledge of the time course of the metabolic power requirement[1] allows one to estimate the corresponding time course of V̇+O₂, assuming a mean time constant of the V̇+O₂ kinetics during metabolic transients, as from literature data, and on the basis of the individual V̇+O₂max. The estimated V̇+O₂ values obtained thus turned out to be essentially equal to the values actually measured in a group of 9 subjects, who performed a series of shuttle runs over 25 m distance in 5 s. Each bout was immediately followed by an equal run in the opposite direction (again 25 m in 5 s). A 20-s interval was interposed between any 2 bouts, and the whole cycle was repeated 10 times (for a total running distance of 500 m). The running speed was continuously monitored by a radar system (Stalker ATS II, TX, USA); the corresponding instantaneous acceleration, energy cost and metabolic power were then calculated by means of the same set of equations as implemented in the GPEXE©[2] system and described in detail elsewhere [4] [5] [12]. The overall actual accumulated VO₂ was than compared to the values obtained by means of a portable metabolic cart (K4, Cosmed, Rome, Italy), allowing us to assess the actual O₂ consumption on a single breath basis.

The data obtained thus are represented for a typical subject in [Fig. 2] which reports the time integral of:

Fig. 2 Overall energy expenditure (J·kg⁻¹) as a function of time (s) as obtained from the time integral of metabolic power requirement (black continuous line), estimated (black dotted line) or directly measured (grey broken line) VO₂ (modified after di Prampero et al. 2015 [4]). For details see text.

• Metabolic power requirement (Ė, black continuous line);

• V̇+O₂ estimated on the basis of a time constant of 20 s at the muscle level (black dotted line);

• Actual measured V̇+O₂ (grey broken line).

Inspection of this fig. shows that:

• Cumulative VO₂ values (estimated or measured) are very close;

• They follow fairly well the time course of the total energy expenditure (i. e., the time integral of the metabolic power requirement);

• The horizontal time difference between the 2 functions (measured or estimated VO₂ and metabolic power) is the time constant of the V̇+O₂ kinetics [6];

• This turns out longer (≈ 35 s) at the measuring site (the upper airways) than that assumed to hold at the muscle level (≈ 20 s); indeed, because of the effects of the O₂ stores depletion (at work onset) and refilling (at work offset) that act as a capacitance in series, V̇+O₂ at the muscle level is faster than measured at the mouth [7];

• The ratio between the overall amount of O₂ consumed above resting and the total distance covered (500 m) is the average energy cost of this type of intermittent exercise, which turns out to be essentially equal to the value estimated using the relevant algorithms (described in reference [5]).

These considerations lend experimental support to the theoretical approach briefly described above and discussed in detail by di Prampero et al. [4]. However, at variance with the data reported in [Fig. 2], Buchheit et al. report in a recent paper a large underestimate of the metabolic power estimated via GPS, as compared to directly measured oxygen consumption [1].

In view of this discrepancy, the aim of the paragraphs that follow is to analyze Buchheit et al.’s data along the same lines briefly outlined above. Indeed, an analysis of Figure 2 of Buchheit et al.’s paper [1] (reproduced for convenience below as [Fig. 3]) highlights some doubtful aspects, as follows:

Fig. 3 This figure is reproduced from Figure 2 of Buchheit et al. 2015 [1]. See text for the meaning of the arrows.

• The measured V̇+O₂ includes the value at rest (about 6.8 ml O₂·kg⁻¹·min⁻¹) and is compared to the corresponding net (above resting) metabolic power (arrow ①);

• At several points in time, the actually measured V̇+O₂ increases markedly, while the simultaneously determined metabolic power remains close to zero for several additional seconds (e. g., at the onset of the section “soccer-specific circuits,” as well as between them) (arrows ②);

• Peak metabolic power values attain about 30 W·kg⁻¹ (i. e., about 85 ml O₂·kg⁻¹·min⁻¹ above resting), thus greatly surpassing the subjects’ V̇+O₂max (arrows ③); as a result, the occurrence of a substantial contribution of anaerobic lactic sources to the overall power requirement is likely, which casts doubt on a direct comparison of actual V̇+O₂ and metabolic power, particularly during recovery after exercise.

Even so, a graphical analysis derived from Buchheit et al. in Figure 2, along the lines reported above, shows that at the end of the investigated time period (500 s), overall cumulated VO₂ was only about 12% less than the overall time integral of the metabolic power. These considerations are reported graphically in [Fig. 4] as follows:

Fig. 4 Upper panel – time course of metabolic power (black continuous line, W·kg⁻¹) and estimated or measured V̇ O₂ (black dotted line and grey broken line, respectively, W·kg⁻¹). Metabolic power and measured V̇ O₂ from original data of Buchheit et al. 2015 [1]. Lower panel – time integral of metabolic power requirement (black continuous line), estimated (black dotted line) or directly measured (grey broken line). For details see text.

• the upper panel reproduces the original data, where, nevertheless, the actual V̇+O₂ (grey broken line) has been corrected for a resting value of 6.8 ml O₂·kg⁻¹·min⁻¹ and is expressed in W·kg⁻¹ to make it directly comparable with the metabolic power (black continuous line);

• the actual cumulated VO₂ was also estimated from the instantaneous metabolic power, as described in our original paper (di Prampero et al. [4]), assuming a time constant of 20 s for the V̇+O₂ kinetics, and without setting any V̇+O₂max ceiling (black dotted line);

• the time integral of the 3 functions is reported in the lower panel which shows that, at the end of the investigated time period, the overall energy expenditure (time integral of the black continuous line) and the overall estimated VO₂ (time integral of the black dotted line) are equal. On the contrary, the time integral of the actually measured net O₂, as reported by Buchheit et al. [1] (grey broken line), is about 12% less.

This difference, albeit small, may be due to the fact that, as mentioned above, whenever the metabolic power exceeds the subject’s V̇+O₂max, a substantial contribution of the anaerobic lactic sources is likely to occur, thus leading to an underestimate of the actually measured V̇+O₂, as compared to the metabolic power requirement.

We are therefore convinced that, if allowance is made for the uncertainties involved in the precise estimate of the individual energy cost of running (see below), and of V̇+O₂max, the approach outlined above yields meaningful results as concerns the time course of the instantaneous metabolic power and the actual V̇+O₂, as well as the corresponding time integrals (i. e., overall energy expenditure and overall cumulated VO₂).

Finally, we would like to point out that the upper panel of [Fig. 4] closely resembles the original (Buchheit et al. [1] Figure 2). However, the comparison between Figure 3 of Buchheit et al. (reproduced for convenience below as [Fig. 5], left panel) with the one derived from our own analysis, [Fig. 4] ([Fig. 5], right panel) leads to a markedly different picture than reported in the original paper. Indeed, the right panel of [Fig. 5] reports the average values of metabolic power (white), estimated (grey) and measured (black) V̇+O₂ during the exercise bouts (C) and in the following recovery periods (R). The right panel of [Fig. 5] thus shows that during the exercise bouts the mean V̇+O₂ (estimated or measured) is substantially less that the corresponding metabolic power. On the contrary, in the following recovery periods the mean V̇+O₂ (estimated or measured) is larger than the simultaneously determined metabolic power. It can be concluded that, as can be expected from textbook physiology, the actual V̇+O₂ kinetics follows the metabolic power requirement with a well-defined time lag and, conversely, that a substantial repayment of the oxygen debt necessarily occurs in recovery after exercise. Thus, for reasons that escape our understanding, the emerging picture is the very opposite than can be gathered from Figure 3 of the original paper (see [Fig. 5], left panel).

Fig. 5 Left panel – mean metabolic power as obtained from GPS (white bars) and mean measured V̇ O₂ (black bars) during soccer-specific circuits and following recovery (reproduced from Figure 3 of Buchheit et al. 2015 [1]). Right panel – mean metabolic power as obtained from GPS (white bars) and mean estimated (grey bars) or measured (black bars) V̇ O₂, as reported in [Fig. 4]. See text for details and calculations.

It must be pointed out that, since the original data were not available to us, the above conclusions were obtained from a graphical analysis of the original Figure 2; as such they should be taken with caution. Even so, the emerging picture yields a more convincing energetic summary of soccer-specific circuits.

In the following section, we discuss the role of the energy cost in setting metabolic power estimates. Indeed, as discussed at length in the original papers [4] [5] [12], to which the reader is referred for further details, the choice of the energy cost for constant speed running (C₀) on flat terrain is pivotal in setting the energy cost of accelerated/decelerated running, and as such the corresponding metabolic power. The net value (above resting) of (C₀, J·kg⁻¹·m⁻¹) ranges from 3.6 as determined on the treadmill by Minetti et al. [11], to 4.32±0.42 on the treadmill and to 4.18±0.34 on the terrain, as determined more recently by Minetti et al. [10] at 11 km·h⁻¹, to 4.39±0.43 (n=65), as determined by Buglione and di Prampero [2] during treadmill running at 10 km·h⁻¹, the great majority of data clustering around a value of 4 J·kg⁻¹·m⁻¹ [8]. So, while it would be advisable to determine C₀ on each subject, it is often convenient to assume a unique value on the order of 4 J·kg⁻¹·m⁻¹.

It should also be pointed out that, apart from the inter-individual variability of C₀, its value depends also on the type of terrain (e. g., artificial vs. natural grass, compact vs. soft surface, etc.), so that once again, the numerical value must be selected with a pinch of salt. Furthermore, it should be stressed that, as mentioned above, C₀ applies to constant speed running on flat terrain, thus neglecting backwards running, running with or without the ball, as well as any sudden changes of direction and/or other soccer-specific actions in vertical direction (e. g., jumps to head the ball, overcome an opponent in a slide tackle, etc.), thus inevitably introducing a certain degree of uncertainty. However, at the present stage, among the clear-cut scientific data available in the literature, none allow one to take into account with reasonable accuracy this state of affairs. As such, rather than relying on dubious corrections and assumptions, we consider it advisable to live with this uncertainty, which is a part of the system’s algorithms.

Another point to be considered when dealing with the energy cost of running is the fact that the equivalence between accelerated/decelerated and uphill/downhill running is based on the data obtained by Minetti et al. [11] in a range of inclines between −0.45 and+0.45. For inclines outside this range, our approach relies on linear extrapolations of Minetti et al.’s data rather than on the authors’ polynomial equation, which clearly cannot be extended beyond the experimental range of observations. Nonetheless, the occurrence of such high values of acceleration/deceleration is rather infrequent in soccer, and this approximation cannot be expected to lead to any substantial errors.

Finally, we would like to point out that, even assuming an ideal scenario that would allow us to determine the actual C₀ of all athletes, the possible individual differences in the economy of accelerated/decelerated running have been neglected. Indeed, the use of one and the same equation for all subjects to estimate the energy cost of accelerated/decelerated running, as derived from Minetti et al. study [11], necessarily implies that all terms of the equation are equal throughout the investigated cohort. Furthermore, this consideration shows that setting a given threshold for all athletes, whether in terms of metabolic power, speed or acceleration, is highly dubious, both as concerns the individual athletic potential (which, however, can be assessed reasonably well in terms of V̇+O₂max) and the corresponding energy cost of running.

It should also be pointed out that the model summarized above is based on several further assumptions briefly reported below; the interested reader is referred to the original papers for further details [4] [5] [12]:

• the overall mass of the runner is condensed in his/her center of mass. This necessarily implies that the energy expenditure due to internal work performance (such as that required for moving the upper and lower limbs in respect to the center of mass) is the same during accelerated running and during uphill running at constant speed up the same equivalent slope (ES);

• assumption i) implies also that the stride frequency of accelerated running, for any given ES value, is equal to that of constant speed (uphill/downhill running) over the corresponding incline;

• for any given ES, the efficiency of metabolic to mechanical energy transformation during accelerated running is equal to that of constant speed running over the corresponding incline. This also implies that the biomechanics of running, in terms of joint angles and torques, etc. is the same in the 2 conditions;

• the calculated ES values are assumed to be in excess of those observed during constant speed running on flat terrain, in which case the runner is leaning slightly forward. This, however, cannot be expected to introduce large errors, since our reference value was the energy cost of constant speed running on flat terrain (C₀);

• as calculated, energy cost and metabolic power do not take into account the energy expenditure against air resistance. This is described by: k·v², where v (m·s⁻¹) is the air velocity, with values of the constant k (J·s²·kg⁻¹·m⁻³) reported in the literature ranging from 0.010 [3] [13] to 0.019 [14]. As such, the effects of air resistance can be easily taken into account, based on the recorded velocity.

In conclusion, we strongly support the general validity of the proposed model, albeit within the limits discussed above. We also would like to stress that the technology for data collection must be appropriately selected: dealing with accelerations, any sampling frequency below 10 Hz is highly questionable. In addition, the filtering of the signal to smooth the accelerations/decelerations of the center of mass in sync with stride frequency must be considered to reduce noise, without losing information. Finally, the often proposed utilization of mechanical quantities obtained by inertial sensors is dubious, because so far no experimental data has convincingly linked the observed mechanical variables with the corresponding time course of energy expenditure during periods of short, high-intensity exercise.

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