Understanding metabolic power

Aug 5, 2015 | ACADEMY

“Is the Metabolic Power really understood?”
An interview with Professor di Prampero to explain some topics about this approach

Often the meaning of metabolic power and oxygen consumption are misinterpreted: can we refresh these concepts?


The product of the instantaneous velocity (v, m⋅s⁻¹) and the corresponding energy cost per unit body mass and distance (Cr, J⋅kg⁻¹⋅m⁻¹), as obtained from the acceleration (and hence the equivalent slope), yields the instantaneous metabolic power (Ė, W⋅kg⁻¹) necessary to run at the speed in question:

Ė = v ⋅ Cr

As such, metabolic power is a measure of the overall amount of energy required, per unit of time, to reconstitute the ATP utilized for work performance. On the contrary, the actual oxygen consumption (V̇O₂), at any given time may be equal, greater, or smaller than the metabolic power itself.


  1. the oxidative processes are rather sluggish as compared to the rate of change of the work intensity, in so far as they adapt to the required metabolic power following an exponential process, the time constant of which is on the order of 20 s;
  2. during very strenuous exercise of short duration, a common feature in soccer activities, the metabolic power requirement can attain values greatly surpassing the subject’s maximal O₂ consumption (V̇O₂max).

So they could be different depending on the intensities change…

These considerations show that, at variance with typical “square wave” aerobic exercises in which case, after about 3 minutes, actual V̇O₂ and metabolic power coincide, the characteristics of soccer, as well as of many other team sports, are such that, in the great majority of instances, the time course of V̇O₂ is markedly different than that of metabolic power requirement. Hence, at any given time during an exercise in the course of which the intensity (metabolic power) changes randomly (Figure 1), the actual V̇O₂ can be smaller, equal or greater than the instantaneous power, depending on:

  1. the time profile of the metabolic power requirement;
  2. the subject’s V̇O₂max.

Figure 1: metabolic power requirement (red) and estimated aerobic power (V̇O₂, blue) during 6 minutes of an official match.

Therefore, the oxygen consumption varies according to the instantaneous energy demands (i.e. Metabolic Power)…

As discussed in some detail elsewhere (di Prampero, Botter, Osgnach, 2015), knowledge of the time course of the metabolic power requirement allows one to estimate the corresponding time course of V̇O₂, assuming a mean time constant of the V̇O₂ kinetics during metabolic transients, as from literature data, and on the basis of the individual V̇O₂max. The so obtained estimated V̇O₂ values turned out to be essentially equal to the actually measured ones 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 seconds interval was interposed between any two 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, 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 ©. The overall actual cumulated VO₂, obtained as described in detail in the paper, was then compared to the values obtained by means of a portable metabolic cart wore by the subject (K4, Cosmed, Rome, Italy), allowing us to assess the actual O₂ consumption on a single breath basis.

The so obtained data are represented for a typical subject in Figure 2 which reports the time integral of:

  1. metabolic power requirement (red line);
  2. V̇O₂ estimated on the basis of a time constant of 20 s at the muscle level (blue line);
  3. actually measured V̇O₂ (green line).

figura-2 Figure 2: overall energy expenditure (J⋅kg⁻¹) as a function of time (s) as obtained from the time integral of metabolic power requirement (red), estimated (blue) or directly measured (green) V̇O₂. For details see text.

Things seem going pretty well…

Inspection of this figure shows that:

  1. cumulated VO₂ values (estimated or measured) are very close;
  2. they follow fairly well the time course of the total energy expenditure (i.e. of the time integral of the metabolic power requirement);
  3. the horizontal time difference between the two functions (measured or estimated VO₂, and metabolic power) is the time constant of the V̇O₂ kinetics;
  4. this turns out longer (≈ 35 s) at the measuring site (the upper airways) than that assumed to hold at the muscle level (≈ 20 s);
  5. the ratio between the overall amount of O₂ consumed above resting and the total distance covered (500 meters) is the average energy cost of this type of intermittent exercise which turns out to be essentially equal to the value estimated from the appropriate algorithms.

In a recent paper published on Int J Sports Med, Buchheit et at. report a large underestimate of the metabolic power calculation via GPS as compared to the actual oxygen consumption measures: what is your opinion about it?

The previous excursus lends experimental support to the theoretical approach briefly described above and discussed in detail by di Prampero et al. (2015); even if the recent paper by Buchheit et al. (2015) seems to report contradictory data. It must be pointed out, however, that an analysis of Figure 2 of this paper (reproduced for convenience below as Figure 3) highlights some doubtful aspects, as follows:

  1. the measured V̇O₂ start from a rest value of about 5 ml O₂⋅kg⁻¹⋅min⁻¹ and is compared to the corresponding metabolic power that does not include the resting expenditure (orange arrow);
  2. at several points in time, the actually measured V̇O₂ 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) (red arrows);
  3. 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’ V̇O₂max (green arrows); hence the occurrence of a substantial contribution of anaerobic lactic sources to the overall power requirement is likely, thus rendering a direct comparison of actual V̇O₂ and metabolic power rather suspicious, particularly so during recovery after exercise.

figura-3 Figure 3: This figure is reproduced from Figure 2 of Buchheit et al. paper. See text for the meaning of the coloured arrows.

Is there anything else that could help us in understanding these topics?

Even so, a graphical analysis derived from Buchheit et al. Figure 3, along the lines of the above-reported Figure 1, shows that at the end of the 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 Figure 4, as follows:

  1. the upper panel reproduces the original data, where, however, the actual V̇O₂ (green) is expressed in W⋅kg⁻¹ to make it directly comparable with the metabolic  power (red);
  2. the actual cumulated VO₂ was also estimated as described in our original paper (di Prampero et al., 2015), assuming a time constant of 20 s for the V̇O₂ kinetics, and without setting any V̇O₂max ceiling (blue);
  3. the time integral of the three 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 red line) and the overall estimated V̇O₂ (time integral of the blue line) are equal. On the contrary, the time integral of the actually measured V̇O₂, as reported by Buchheit et al. (green line), is about 12 % less;
  4. as mentioned above, this difference, albeit small, may be due to the fact that, at several instances, i.e. whenever the metabolic power exceeds the subjects’ V̇O₂max, substantial lactate production is likely to occur.

gpexe metabolic power explained Figure 4: upper panel – time course of metabolic power (red, W⋅kg⁻¹) and estimated or measured V̇O₂ (blue and red, respectively, W⋅kg⁻¹). Metabolic power and measured V̇O2 as from Buchheit et al. original data. Lower panel – time integral of metabolic power requirement (red), estimated (blue) or directly measured (green). For details see text.

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), of V̇O₂max, and of the necessary correction for the resting V̇O₂, the approach outlined above yields meaningful results as concerns the time course of the instantaneous metabolic power and of the actual V̇O₂ and of 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 Figure 4 closely resembles the original (Buchheit at al., Figure 2). However, the comparison between the next figure of Buchheit et al. paper (Figure 5, left panel) with the one derived from our Figure 4 (Figure 5, right panel) leads to a markedly different picture than reported in the original paper. Indeed, the right panel of Figure 5 reports the average values of metabolic power (white), estimated (grey) and measured (black) V̇O₂ and shows that:

  1. during the exercise bouts (C) the mean V̇O₂ (estimated or measured) is substantially less than the corresponding energy requirement per unit of time;
  2. in the following recovery periods (R) the mean V̇O₂ (estimated or measured) is larger than the simultaneously determined metabolic power.

This shows that, as can be expected from textbook physiology, the actual V̇O₂ kinetics follows the 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, even if the above data were obtained from a graphical analysis of the original Figure 2, and as such, they should be taken with caution, the emerging picture yields a more convincing energetic summary of soccer-specific circuits.

metabolic power Figure 5: left panel – mean metabolic power as obtained from GPS (white bars) and mean measured V̇O₂ (black bars) during soccer-specific circuits and following recovery (reproduced from Figure 3 of Buchheit et al. paper). Right panel – mean metabolic power as obtained from GPS (white bars) and mean estimated (grey bars) or measured V̇O2 (black bars). See text for details and calculations.

…But each player is different, especially in the economy of movement on the pitch: how does the energy cost affect metabolic power estimates?

The additional point to be considered is the choice of the energy cost for constant speed running (C₀) on flat terrain. Its net value (above resting) (J⋅kg⁻¹⋅m⁻¹) ranges from 3,6 as determined on the treadmill by Minetti et al. (2002), 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. (2012) at 11 km⋅h⁻¹, to 4.39 ± 0.43 (n = 65), as determined by Buglione and di Prampero (2013) during treadmill running at 10 km⋅h⁻¹, the great majority of data clustering around a value of 4 J⋅kg⁻¹⋅m⁻¹ (Lacour and Bourdin, 2015). Thus, whereas on the one side it would be advisable to determine C₀ on each subject, on the other, 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, its numerical value must be selected with a pinch of salt. Furthermore, it should also 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, 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 deem it advisable to live with this uncertainty, inevitably built in the system’s algorithms.

…And what happens when the player accelerates at his maximum?

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. (2002) 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, obviously enough, can not be extended beyond the experimental range of observations. However, the occurrence of such high values of acceleration/deceleration is rather infrequent so that this approximation cannot be expected to lead to any substantial errors.

However, the limits of metabolic power assessment must be known: can we analyse them together?

The model summarized above is based on several additional assumptions briefly reported below, the interested reader is referred to the original papers for further details (di Prampero et al. 2005; Osgnach et al., 2010; di Prampero et al., 2015):

  1. the overall mass of the runner is condensed in his/her centre 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 centre of mass) is the same during accelerated running and during uphill running at constant speed up the same equivalent slope;
  2. assumption i) implies also that the stride frequency of accelerated running is equal to that of constant speed running over the corresponding incline (ES);
  3. 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 two conditions;
  4. 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 lining slightly forward. This, however, cannot be expected to introduce large errors, since our reference value was the measured energy cost of constant speed running on flat terrain (C₀);
  5. as calculated, energy cost and metabolic power do not take into account the energy expenditure against the air resistance. This is described by: k⋅v², where v (m⋅s⁻¹) is the air velocity, the values of the constant k (J⋅s²⋅kg⁻¹⋅m⁻³) reported in the literature ranging from 0.010 (Pugh, 1970, di Prampero, 1986) to 0.019 (Tam et al., 2012). As such, the effects of air resistance can be easily taken into account, based on the recorded velocity.

We discussed the calculations, advantages and limits of the approach. Did we forget the other side of the coin?

Concerning the model, we strongly support its general validity, albeit within the limits discussed above. We also would like to stress that the technology for data collection must be appropriately selected: since we deal with accelerations, any sampling frequency below 10 Hz is highly questionable. In addition, also the filtering of the signal to smooth the accelerations/decelerations of the centre of mass synchronous with the stride frequency must be considered in order to reduce the noise, without losing information. Finally, the often proposed utilization of mechanical quantities obtained by inertial sensors is dubious, because of the absence, so far, of any convincing experimental data linking the observed mechanical variables with the corresponding energy expenditure.


  1. Buchheit M, Manouvrier C, Cassirame J, Morin JB (2015). Monitoring locomotor load in soccer: is metabolic power, powerful? Int J Sports Med, in press.
  2. Buglione A, Prampero PE (di) (2013). The energy cost of shuttle running. Eur J Appl Physiol 113:1535-1543.
  3. Lacour JR, Bourdin M (2015). Factors affecting the energy cost of level running at submaximal speed. Eur J Appl Physiol 115:651-653.
  4. Minetti AE, Gaudino P, Seminati E, Cazzola D (2012). The cost of transport of human running is not affected, as in walking, by wide acceleration/deceleration cycles. J Appl Physiol 114:498-503.
  5. Minetti AE, Moia C, Roi GS, Susta D, Ferretti, G (2002). Energy cost of walking and running at extreme uphill and downhill slopes. J Appl Physiol 93:1039-1046.
  6. Osgnach C, Poser S, Bernardini R, Rinaldo R, Prampero PE (di) (2010). Energy cost and metabolic power in elite soccer: a new match analysis approach. Med Sci Sports Exerc 42:170-178.
  7. Prampero PE (di) (1986). The energy cost of human locomotion on land and in water. Int J Sports Med 7:55-72.
  8. Prampero PE (di), Botter A, Osgnach C (2015). The energy cost of sprint running and the role of metabolic power in setting top performances. Eur J Appl Physiol 115:451-469.
  9. Prampero PE (di), Fusi S, Sepulcri L, Morin JB, Belli A, Antonutto G (2005). Sprint running: a new energetic approach. J Exp Biol 208:2809-2816.
  10. Pugh LGCE (1970) Oxygen intake in track and treadmill running with observations on the effect of air resistance. J Physiol Lond 207:823-835.
    Tam E, Rossi H, Moia C, Berardelli C, Rosa G, Capelli C, Ferretti, G (2012). Energetics of running in top-level marathon runners from Kenya. Eur J Appl Physiol 112:3797-3806.
Author: Cristian Osgnach
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