A slow V̇_O2 on-response allows comfortable adoption of aerobically unaffordable walking and running speeds on short stair ascents

Locomotion on flat ground is not very expensive: for example, walking costs about 2 ‘metabolic’ J to move 1 kg of body mass (M, kg) a (horizontal) distance of 1 m (at a speed of about 1.2 m s⁻¹; see Fig. 1). In contrast, uphill gaits require an increase in the potential energy of the body at each stride. For instance, an incline of +57% (about 30 deg), for which the ratio between the height gain (Δh) and the distance travelled on the gradient (Δd) is 0.5, is associated with an extra cost of about 20 metabolic J kg⁻¹ m⁻¹. In fact, the difference in gravitational potential energy (in ‘mechanical’ J) is MgΔh (or Mg0.5Δd, where g is acceleration due to gravity), and when expressed in (‘mechanical’) J kg⁻¹ m⁻¹ it reduces to 0.5g. The ‘metabolic’ cost is then calculated as ‘mechanical’ cost divided by muscle efficiency of positive work (0.5g/0.25=20). Such a gradient was chosen not just for illustrative purposes but because it represents the average steepness of most stairs in a residential building.

Gradient locomotion has been widely studied in the past (since Margaria, 1938) and the metabolic cost of walking and running has been measured for several inclines and speeds. Fig. 1 shows that level walking reports the lowest cost at a speed of 1.2 m s⁻¹, while at +53% gradient the cost is much higher (about 22 J kg⁻¹ m⁻¹, as expected from the previous paragraph) and displays a minimum at a speed of 0.45 m s⁻¹. In such a graph it is convenient to get additional information on the metabolic effort of each locomotor condition (gait, gradient, speed) by their spatial contiguity with iso-metabolic power hyperbolas [metabolic power (W kg⁻¹)=metabolic cost×speed]. These curves are labelled as fractions of the maximum aerobic power (for a subject with 15 W kg⁻¹ or a V̇_O2,max of about 44 ml O₂ kg⁻¹ min⁻¹): the grey area above 100% is where aerobic metabolism alone is no longer sufficient to sustain the exercise. The first remark here is that to ascend on a gradient corresponding to ‘average’ stairs requires a threefold amount of metabolic power versus level walking (both at the respective optimal speeds). The predicted ascent speed in order to maintain the same metabolic power (say, the same heart rate and ventilation) as level walking is obtained at the intersection between the relevant iso-power hyperbola (i.e. 25%) and the thick curve of metabolic cost of walking at a +53% gradient, resulting in a value of 0.13 m s⁻¹. Actually, such a low speed is never observed in (even sedentary) healthy subjects, who instead tend to choose the 3 times faster, metabolically optimal speed of 0.45 m s⁻¹ (see also Results). Now we are facing apparently conflicting results: although the spontaneous ascent speed is chosen according to minimization of the cost of transport, a criterion pervasively adopted across species (Alexander, 1989), why not to select a speed that would require a metabolic power much lower than 75%, the last being commonly associated with a higher perceived effort (prolonged tachycardia, tachypnoea, etc.)? The same question applies to running: Fig. 1 shows that level running (at a slow speed, namely 2.2 m s⁻¹) is associated with a metabolic power close to 70% of the aerobic limit, but on a +53% steep incline running at half that speed (the spontaneous ascent speed, see Results) implies a remarkable contribution of anaerobic metabolism (225%, more than twice the aerobic maximum power). So, why do we sometimes run up short flights of stairs (on every other step)?

The above considerations are based on data collected during locomotion on inclined paths/treadmills, about which biomechanical and metabolic research has been quite prolific in the past 90 years (Margaria, 1938; Minetti et al., 1993, 1994, 2002; Giovanelli et al., 2006). Climbing stairs, the ancient man-made alternative to moving on an inclined path, unfortunately has not received the same attention from the scientific community (Lehrmann and Engelmann, 1933; Kamon, 1970). It is expected, though, that the same rationale and physical constraints originating and guiding the present study pertain to both climbing types.

In addition, the quoted metabolic cost of walking and running uphill at very steep gradients has been measured (Minetti et al., 2002) in athletes with a maximum aerobic power much higher than the average value for the same general population cohort. Although that feature gave them enough time to reach a steady-state metabolism, we see no reason why the measured metabolic cost would not apply to the whole population.

Finally, exercise duration is very important here as it potentially affects the locomotion puzzle (above) independently from the maximum aerobic power level: all of us intuitively know that when the stairs to be climbed are made of hundreds of steps, the spontaneous choice reduces to just a very slow (and surely aerobic) walking ascent.

In summary, because of the need to increase body gravitational potential energy, ascending the same short flight of stairs requires almost the same mechanical work (and therefore the same metabolic energy) whether we are walking or running (on every other step), while the mechanical power (and therefore the metabolic power) is expected to be much higher when the task is achieved in a shorter time, as in walking up at high (albeit optimal) speeds or running. The reasons behind our spontaneous choice in terms of gait/speed combination for climbing a short flight of stairs probably reside in such a comprehensive approach to the puzzle: do humans decide to ascend faster just because they are often in a hurry?

In this study, using flights of stairs at two different heights, we aimed: (1) to assess the spontaneous ascent speed with the two gaits, (2) to quantify all the determinants of the total mechanical work, and (3) to measure metabolism kinetics during these tasks and also during the recovery period, from which the maximum metabolic power (V̇_O2,peak) and the total metabolic energy spent in these (often interchangeable) conditions could be obtained.

Twenty-four non-athlete subjects (15 men and 9 women; age men: 30.0±10.2 years, women: 30.0±6.5 years; body mass men: 75.6±6.7 kg, women: 59.2±7.3 kg; height men: 1.77±0.04 m, women: 1.63±0.06 m, means±s.d.) gave their written informed consent for the experimental procedure. The study was approved by the Ethics Committee of the University of Milan. Participants were free of any musculoskeletal, bone and joint, or cardiac and pulmonary diseases and were not taking any medication. Several restrictions were imposed on the volunteers: no food intake 3–4 h before and no stimulants (coffee, tea) or intense physical activity 12 h before the experimental protocol (Cooke, 1996).

Subjects participated in four experiments in a randomized sequence: walking up one flight of stairs (1FOS) at spontaneous speed (on all the steps), running up 1FOS at spontaneous speed (on every other step), walking up two flight of stairs (2FOS) at spontaneous speed (on all the steps), running up 2FOS at spontaneous speed (on every other step). Each experiment started with 10 min rest while sitting on a chair, with the goal of minimizing the effects of any previous physical activity and/or emotional conditioning. Subjects, who were unaware of the time passing, were instructed to relax as much as possible and to promptly start climbing at the experimenter's command. Biological variables were continuously sampled during the pre-exercise rest for 5 min, during the climbing effort and at rest post-exercise (excess post-exercise oxygen consumption, EPOC) for another 5 min while sitting on another chair located at the end of the ascent. The height of the stairs was 2.57 m and 4.81 m, the overall distance covered (the diagonal displacement plus the distance to leave and reach the two chairs) was 5.93 m and 10.63 m, and the total number of steps was 16 and 30 for 1FOS and 2FOS, respectively. The measured stairs gradient was 53%.

Oxygen uptake (V̇_O2, ml O₂ min⁻¹) and expiratory ventilation (V̇_E, l min⁻¹) at rest and during exercise were measured using a portable open-circuit metabograph. Expired air was analysed breath by breath using a COSMED K4b2 portable monitor (Rome, Italy), while single-beat heart rate (f_H) was measured using a POLAR S810i portable monitor (Kajaani, Finland). Before each experimental session, the metabograph was calibrated with ambient air and with a known gas mixture. The turbine flowmeter was calibrated using a 3 l syringe at the beginning of the test protocol. Response delay calibration was performed according to the manufacturer's instructions.

In addition, subjects' initial acceleration and duty factor (D), i.e. the fraction of the stride period at which one foot is in contact with the ground, during walking and running were measured by means of a high-speed (210 Hz) camera (Casio EX-FH20, Tokyo, Japan). Reflective markers were placed on the great trochanter and on the edge of each stair step. The video camera was positioned to face the subject's left side, at a distance of 3 m and a halogen lamp was used to illuminate the reflective markers. The acceleration of the great trochanter, a surrogate of the body centre of mass, and its duration were calculated by performing a frame-by-frame analysis of motion (iMovie, Apple Inc.).

The above procedures were applied to the total expiratory volume (V_E,totalnet) and total net number of heart beats (HB_totalnet). Oxygen-related variables were expressed per kg of body mass. Total V_O2 values (Eqn 1) were converted to metabolic cost of transport (C_met, the energy needed to move 1 kg of body mass along 1 m, J kg⁻¹ m⁻¹) assuming an energy equivalent of 20.9 kJ l⁻¹ O₂ (corresponding to a non-proteic respiratory exchange ratio of 0.96) and divided by the relevant distance covered. Peak values for V̇_O2, V̇_E and f_H were measured, and peak net values ⁠, and were calculated as the difference between peak and basal values.

Average vertical (⁠⁠) and diagonal (⁠⁠) speed were obtained as the ratio between the height or diagonal displacement, respectively, and ascent time (for both 1FOS and 2FOS).

For the 2FOS, W_turn was also calculated. The metabolic work needed to execute the turn has been estimated according to Minetti et al. (2011) as 283.1 ml O₂ kg⁻¹ km⁻¹, where subjects moved in circles of about 1 m radius. W_turn was obtained by assuming a muscular efficiency of 0.25 and half a circumference distance per turn, and expressed as J kg⁻¹ turn⁻¹.

Average mechanical power (⁠⁠, W) was calculated as the ratio between W_mech and exercise time. Mechanical cost of transport (C_mech) was calculated by dividing W_mech by body mass and the relevant displacement, either vertical (Δh, C_mech,vert) or diagonal (L_diag, C_mech.diag). Metabolic cost of transport (C_met) is also presented relative to those two displacements (C_met.vert and C_met.diag, respectively). Ascent efficiency (Eff) was obtained as the ratio between C_mech and C_met.

The ratio between running and walking for 1FOS and 2FOS was calculated for ⁠, ⁠, ⁠, ⁠, C_mech and C_met.

Descriptive statistics were used, with the data presented as means±s.d. A Shapiro–Wilk's test was used to verify the normality of the data distribution. A paired two-tailed Student's t-test was used in order to compare, for each variable, the different conditions (2FOS versus 1FOS, running versus walking). One-sample t-test was used to compare the ratio of pooled running/walking data with the reference value 1. An alpha level of 0.05 was adopted for all statistical tests, which were performed using SPSS software (version 15.0).

Mean values of diagonal and vertical speed, cardio-respiratory variables and heart rate are shown in Table 1. There were no significant differences between 1FOS and 2FOS, indicating that these variables are independent of the number of flights of stairs.

Components of total mechanical work are presented in Fig. 2. ⁠, C_mech and C_met for 1FOS and 2FOS (Table 2) were significantly higher during running compared with walking. No significant difference in Eff between walking and running was found in 1FOS, though significantly higher values for walking were found in 2FOS (Table 2).

The ratio between running and walking values of ⁠, ⁠, ⁠, \widehat{f}_H,net, C_mech and C_met, separately during 1FOS and 2FOS is reported in Fig. 3A. Pooled (1FOS and 2FOS) running/walking ratios for each variable are shown in Fig. 3B. According to the statistical analyses, all variables were significantly higher than 1.

This investigation reports that when people freely move on a short height of stairs, they walk at 0.47 m s⁻¹ and/or run (on every other step) at 1.1 m s⁻¹, irrespective of FOS number. Despite the two different gaits and ascent speeds, and thus mechanical power needed (running/walking≈+250%), cardiorespiratory and metabolic parameters increased only slightly when running (running/walking≈+25%; see Fig. 3B). Ascending 1FOS or 2FOS made no difference to the results (Fig. 3A), allowing us to conclude that the combination of slow cardio-respiratory–metabolic kinetics and very short exercise duration makes the two gaits almost interchangeable for stairs up to about 5 m height (at a gradient close to 53%). This is well illustrated in Fig. 4, where V̇_O2 kinetics are very similar in walking and running at each ascent level. A more comprehensive picture of the difference between mechanical and metabolic power of the gaits in the same ascent condition (1FOS) is shown in Fig. 5 for a representative subject. Although the metabolic equivalent of mechanical power of ascent by walking and running (vertical rectangles in Fig. 5) is very different between the two (running/walking≈+250%) and both of them exceed the maximum aerobic power (dash–dot horizontal line in Fig. 5), the measured time course of metabolic power is almost identical for the two gaits (black and grey dots in Fig. 5), showing peaks of the order of 1/4 to 1/5 of V̇_O2,max. Thus, ascending a short flight of stairs by walking on every step or running on every other step, in both cases at spontaneous speed, makes no difference in terms of the metabolic power (and hence perceived effort) involved during and after the end of exercise.

In summary, the overall mechanical cost of transport associated with stair ascent in our experimental protocol is higher than expected from the mere gravitational component because of the internal work and acceleration, which are even higher in running. Acceleration in particularly would be an almost negligible component in a long-lasting stair ascent, but becomes substantial when the exercise duration is short (5–13 s).

The rather unorthodox estimate of the effects on oxygen consumption of a very short-lasting exercise, as obtained by sampling it during the subsequent 5 min recovery period raises the question about the reliability of what we termed a ‘micro V_O2’ approach in capturing the entire metabolic event. With respect to traditional and consolidated metabolic assessment based on 1–2 min, steady-state high O₂ consumption, the sampling rate during both the very short exercise and EPOC, together with the challenged metabograph response during long-lasting recovery at near-basal rate (low signal to noise ratio) could affect the reliability of the present data. The assumption here was that most of the required metabolic energy for such a short exercise comes from phosphocreatine (PCr) and that 5 min of recovery would suffice to replenish its stores. To check for consistency, the average of absolute 2FOS/1FOS ratios (while pooling gaits) and running/walking ratios (while pooling FOS data) were calculated both for C_mech and C_met. The mean absolute difference of FOS ratios was only 5% and 9% for C_mech and C_met, respectively, while that for the gait ratios was 17% and 32%, respectively. This indicates that the costs are slightly affected by the number of FOS, as should be expected, while they more strongly depend on the chosen gait, with running being both mechanically and metabolically more expensive. Consistency is also supported by efficiency results, which ranges in the four conditions from 14% to 17%. When pooling 1FOS and 2FOS data, efficiency ranges from 14% to 16%; by considering that at a gradient of 53% the monotonically ascending path of the body centre of mass implies (i) the presence only of positive work (Margaria, 1938; Minetti et al., 1993, 1994) and (ii) the precluded elastic energy-saving paradigm of running (Minetti et al., 1994), the almost invariant efficiency is not a surprise.

Although these results, in relative terms, support the consistency of micro V_O2 experiments across different conditions, the low value of efficiency in absolute terms (with respect to muscle efficiency; Woledge et al., 1985) suggests potential bias, particularly in the metabolic assessment of exercise. To investigate the amount and the reasons for such a discrepancy, a comprehensive review of the literature reporting the metabolic cost of human ascent on a treadmill or laddermill at a similar gradient and speed to that used in this study was carried out (see Table 3). Average C_met of these investigations (where only Halder et al., 2018, has been excluded because of a much steeper gradient) was 22.0±2.5 J kg⁻¹ m⁻¹ for walking and 26.1±2.9 J kg⁻¹ m⁻¹ for running upstairs. Differently from level locomotion, where running C_met is almost double walking values (+100%; e.g. Saibene and Minetti, 2003), running cost on treadmills at a staircase gradient seems to be just +18% higher. C_met obtained in the present study was +53% and +70% more expensive for walking and running, respectively, than values in the literature and running here was +32% costlier than walking. The reasons for these discrepancies are to be found in the mechanical and metabolic characteristics of the experimental protocol and analysis, which deviate from the customary constant speed ascent and long-lasting steady-state acquisition of metabolic data.

Apart from the additional cost of acceleration and of turning (in 2FOS only), we can speculate that, differently from walking economy that seems to benefit from moving at a +53% gradient on steps (rather than on the inclined treadmill surface; see Table 3), running on every other step could involve a greater vertical excursion of the body centre of mass trajectory to ensure the step rise is cleared before each landing. This could partially explain the +32% increase in C_met in running with respect to walking (when compared with +18% of the literature), as obtained in this study. So far, no investigation has been published on the mechanics and energetics of staircase running at +53% gradient. However, even after removing from our results the metabolic equivalent of accelerative work (estimated by Eqn 5 or by a recent model for shuttle running; Minetti and Pavei, 2018), only 5% and 30% of the excess cost is reduced in ascent by walking and running, respectively.

The remarkable difference in (absolute) C_met values found here (with respect to the literature) is possibly due to the micro V_O2 experiment, where the metabolic effect of a very short mechanical event is sampled within a much wider time frame including the preceding rest and successive recovery period, with the aim of investigating through metabolic comparison the spontaneous gait choice when ascending stairs. The next four paragraphs discuss aspects of such an experimental protocol that should be considered.

V̇_O2 on-phase, lasting much longer than the exercise duration, is an early truncated ramp leading to the metabolic steady state (V̇_O2,ss) for that exercise intensity that is never reached, while V̇_O2 off-phase could represent the last part of a recovery kinetic from the same V̇_O2,ss; differently from traditional gait economy studies, here metabolic cost of transport has been evaluated from a curve made of the on- and off-V̇_O2 transient, rather than from just steady-state values; as depicted in Fig. 4, V̇_O2 on-kinetics continue to increase beyond the end of exercise, when the subject is recovering seated on the chair, for 40–50 s, after which off-kinetics begins (similar to fig. 4 in di Prampero et al., 1973, where the authors in an ancillary experiment adopted a protocol similar to the present study). This is a clear example of a ‘pulse work rate’ (Hughson et al., 1988; Rossiter, 2011) where oxygen consumption continues to increase presumably in order to rebuild the energy sources utilized during the exercise (PCr, myoglobin) (Hughson et al., 1988) and/or due to the limb-to-lung delay (Rossiter, 2011). Short stair climbing, even at preferred walking and running speed can be seen as an example of daily-life pulse exercise.

It is known that metabographs are reliable for steady-state V̇_O2 measurements, while some inaccuracy is expected for the V̇_O2 transient, as processing algorithms only rarely take into account pulmonary oxygen stores (Aliverti et al., 2009); this could partially be responsible, within consistent results, of the higher costs.

A biphasic V̇_O2 on-response, classically observed at the pulmonary level (Linnarsson, 1974), has recently been found at the level of the single fibre (Wüst et al., 2013), where the first phase has been attributed to mitochondrial calcium-dependent activation that precedes ADP feedback in controlling the metabolic transient. Such an activation phase (not affecting the off-transient) is likely to be the determinant of the asymmetry/imbalance between the on-phase oxygen deficit and the EPOC described in that study (Wüst et al., 2013). The 30–40% lower oxygen deficit reported for low and intermediate oxidative muscle fibres (Wüst et al., 2013) is the basis for a related higher metabolic cost from the V̇_O2 on-phase, and thus for the overestimation found in the present experiments. The present set-up also suffers for the lack of a long-lasting steady-state condition (see Fig. 4) contributing, with its strong signal, to make a more weighted integral of the V̇_O2 time course, and thus to converge towards a more realistic cost.

The decreasing portion of V̇_O2 off-kinetics could incorporate determinants of the overall O₂ debt other than just the one devoted to replenishment of PCr stores: (1) lactate accumulation could occur in the case of local PCr stores decreasing below a given threshold, and (2) entropy could increase as a result of a change in temperature and in the biochemical homeostasis inside all involved muscles. To dissipate any doubt about the contribution of lactate to the O₂ debt payment during exercise recovery, an ancillary experiment with serial blood samples was set up, regarding one subject running up 2FOS at spontaneous speed. Net lactate production was found to be negligible, at 0.6 mmol l⁻¹. However, although determinant (2) is assumed to be small because of the shortness of the exercise, as witnessed by the extinction at rest level in less than 5 min of the second part of biphasic V̇_O2 decay, its ‘weight’ is not negligible. It is expected that by removing that component from the integral leading to the metabolic cost calculation, the final estimation would be in line with previous costs of transport (Table 3). According to the aims of this investigation, namely the mechanically/metabolically based understanding of gait choice interchangeability during short stair ascent, we did not remove the slow component of the recovery decay from the computation of the metabolic cost of transport because we consider the complete restoration of initial conditions (PCr resynthesis and homeostasis) an integral part of that choice.

In summary, moving up 1–2 flights of stairs (up to 4.8 m vertically at a gradient of +53%) by running (on every other step) or by walking (on all the steps) is viable at almost no cardio-respiratory discomfort. Despite a predicted metabolism approaching V̇_O2,max for walking and more than doubling it for running, both reflecting the required mechanical power as measured in this study, the two gait/speed combinations can be adopted (almost interchangeably) in daily life because the slow V̇_O2 on-response and the very short duration of such tasks limit the exercise V̇_O2,peak to values well below V̇_O2,max. V̇_O2 measurements extended to a few minutes after the end of a few seconds of exercise (micro V_O2 experiments) led to consistent (but probably inaccurate) efficiency and metabolic cost values for the two gaits that reliably parallel the expected (and assessed) mechanical constraints. Further development of this investigation includes the extension of the experimental protocol to higher climbing distances on stairs, where additional burdens in exercise V̇_O2,peak level and more substantial differences in the metabolic response of walking or running could change the spontaneous speed and the interchangeability of the two gaits.