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Acute Effects of Reducing Vertical Displacement and Step Frequency on Running Economy

Halvorsen, Kjartan1,2; Eriksson, Martin1; Gullstrand, Lennart3

Journal of Strength and Conditioning Research: August 2012 - Volume 26 - Issue 8 - p 2065–2070
doi: 10.1519/JSC.0b013e318239f87f
Original Research

Halvorsen, K, Eriksson, M, and Gullstrand, L. Acute effects of reducing vertical displacement and step frequency on running economy. J Strength Cond Res 26(8): 2065–2070, 2012—This work studies the immediate effects of altering the vertical displacement of the center of mass (VD) and step frequency (SF) on the metabolic cost of level treadmill running at 16 km·h−1 on 16 male runners. Alterations of VD, SF, and the product VD × SF was induced using a novel feedback system, which presents target and current values to the runner by visual or auditory display. Target values were set to 5 and 10% reductions from individual baseline values. The results were expressed as relative changes from baseline values. Alterations led to an increase in metabolic cost in most cases, measured as V[Combining Dot Above]O2 uptake per minute and kilogram of body mass. Correlations were weak. Still, linear multiple regression revealed a positive coefficient (0.28) for the relationship between VD × SF and V[Combining Dot Above]O2. Separate rank correlation tests showed negative correlation (τ = −0.19) between SF and V[Combining Dot Above]O2 and positive correlation (τ = 0.16) between VD and V[Combining Dot Above]O2. There is a coupling between VD and SF caused by the mechanics of running; hence, isolated reduction of either factor was hard to achieve. The linear model also showed a negative coefficient for the relationship between the height of the center of mass above the ground (CoMh) and V[Combining Dot Above]O2. The effect size was small (multiple R 2 0.07 and 0.12). Still the results indicate that reducing VD × SF by reducing the vertical displacement can have a positive effect on running economy, but a concurrent reduction in CoMh may diminish the positive effect. Midterm and long-term effects of altering the technique should also be studied.

1Division of Medical Engineering, School of Technology and Health, KTH Royal, Institute of Technology, Stockholm, Sweden

2Department of Information Technology, Uppsala University, Uppsala, Sweden

3Elite Sports Centre, Swedish Sports Confederation, Bosön, Lidingö, Sweden

Address correspondence to Kjartan Halvorsen,

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Some studies have found that running economy (RE), defined as oxygen consumed (milliliter per kilogram per minute) while running at a constant speed under steady-state conditions, is a better predictor of distance running performance than maximal oxygen uptake is (4,16). Thus, to better understand and improve running performance, it has become of interest to determine the factors influencing RE. Primarily using cross-sectional study designs, several potentially important factors, including biomechanical ones, have been studied (11). Martin et al. (12) showed that mechanical power estimates accounted for 32% of interindividual differences in RE, and power-related estimates based on the movement of center of mass (CoM) were highly correlated with RE. The vertical displacement of the COM (VD), step frequency (SF), and ground reaction forces are other factors shown to influence the RE (13,18). Williams and Cavanagh (18) reported a tendency toward a reduced VD in a group of elite distance runners compared with that in nonelite distance runners. Heise and Martin (8) found that oxygen consumption correlated with vertical impulse (the time integral of the vertical ground reaction force), and Støren et al. (17) found a similar, positive correlation with the horizontal and vertical peak ground reaction forces.

The VD implies a change in the body's potential energy. This change in potential energy per unit time is obtained by multiplying VD with SF, leading to the expression VD × SF, which expresses the work performed against the gravitational force and which is part of the external mechanical work performed during running. Thus, the primary aim of this study was to test the hypothesis that oxygen consumption while running at a steady state at a constant speed decreases when VD·× SF decreases. We focused on the immediate effects of a reduction in VD × SF in this study. It is suggested that middle- and long-term effects be the subject for further study.

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Experimental Approach to the Problem

To test whether a reduction in VD × SF would improve RE, we recruited well-trained runners whose self-selected VD and SF were manipulated by providing them with real-time feedback. Concurrent information about how much their VD and SF deviated from a target value was presented as automated verbal instructions. The targets were set in relation to their self-selected values. This system has previously been described in Eriksson et al. (5). Here, not all runners were able to attain the target values, but almost all exhibited a change approaching the target value.

In this study, the independent variables were the actual values of VD, SF, and VD × SF obtained by the runner, not the target values. The average height of the CoM measured from the ground was also considered important and included in the set of independent variables. The dependent variable was oxygen uptake.

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Sixteen male runners of mean and (SD) age 28 (5) years, mass 71.7 (5.7) kg, and height 182 (6) cm participated in the study. The subjects included triathletes, orienteerers, and middle- and long-distance runners, each regularly competing at the national level. The subjects were comfortable with running on a treadmill and were accustomed to oxygen uptake measurements.

Written informed consent was obtained from the participants, in accordance with the declaration of Helsinki. The study was approved by the Karolinska Institute regional Research Ethics Committee.

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Running was performed on a treadmill (Rodby Innovision, Vänge, Sweden) with a running surface of 2.5 × 4.5 m, powered by two 5-kW AC motors and with a total mass of 1,700 kg. The surface inclination (0°) was controlled using a digital spirit level. The room temperature was 20°C.

Vertical movement of the CoM was approximated by the vertical movement of the hip (7), which in turn was monitored using a uniaxial position transducer (Mod. 1850-050, Houston Scientific International Inc., Houston, TX, USA). A belt was attached around the pelvic crest of the runner and secured with surgical tape. A thin wire connected the belt and the position transducer, which was attached to the ceiling directly above the runner at a distance of 2.5 m above the running surface. The analog voltage output signal from the position transducer was acquired and sampled on a PC using a 16-bit A/D converter (USB1616FS, Measurement Computing Inc., Norton, MA, USA). Custom-written software computed the height of the CoM above the ground, VD and SF of each step, and the product 2.5 × SF. The latter 3 variables were concurrently transferred to a second PC where they were displayed to the runner as bar plots on a computer screen and as sound. Target values were presented visually as lines intersecting each bar plot. Auditory feedback was provided using a recorded human voice indicating whether the subject was above or below the target level. Sound volume was proportional (up to a maximal level) to the distance of the variables from the target level. The sound was transmitted wirelessly to a set of sound-isolating headphones worn by the participant. The visual feedback was used for initial instructions. Only auditory feedback was used in the actual running trials.

Oxygen uptake (V[Combining Dot Above]O2) was measured using a breath-by-breath gas analyzer (Oxycon Pro, Carefusion GmbH, Hoechberg, Germany) in mixing chamber mode. A rubber oral-nasal face mask with nonrebreathing air inlets (Combitox, Dräger Safety, Lübeck, Germany) was used together with a Radiax nonrebreathing valve and a 1.75-m tube, which led the expired air to the mixing chamber and the analyzing unit.

Lactate blood level was analyzed from microsamples taken from the finger tip using a Biosen C-line device (EKF-Diagnostic, Barleben-Magdeburg, Germany).

After the position transducer was attached, the subject warmed up by running at 12–14 km·h−1 for 5 minutes. The running experiments consisted of seven 5-minute trials at 16 km·h−1 with the concurrent measurement of oxygen uptake and vertical position of the COM. All 7 trials took place during the same session, with sufficient rest (at least 1 minute) between trials. The running speed was chosen to conform with that used in previous studies on runners of a similar capacity. During the first interval, the subject received no feedback. This trial served as a baseline measurement and was used to calculate target levels for the subsequent feedback trials. There were 6 feedback trials, each with different target level: reduced VD, reduced SF, and reduced VD × SF, to 90 and 95% of baseline value, respectively. When either VD or SF was manipulated, feedback on both values was provided, whereas when VD × SF was manipulated, only feedback on this value was given. Each participant would familiarize himself with the feedback system for a period of 5–10 minutes running at 12 km·h−1 before performing the set of feedback trials. The participants were asked to rate their fatigue with respect to (a) their legs and (b) respiration, according to the Borg Rate of Perceived Exertion scale (1) immediately after each 5-minute trial. At the end of the final trial, a fingertip blood sample was taken and analyzed for blood lactate level.

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Statistical Analyses

To obtain baseline values, time averages were computed for the last 3 minutes of the 5-minute baseline trial. For analysis purposes, each 5-minute feedback trial was divided into 4 sections consisting of an initial 2-minute transient phase, for which no further analysis was performed, and three 1-minute intervals. Here, the time averages over each of the 3 minutes for VD, SF, VD × SF, CoMh, and V[Combining Dot Above]O2 uptake were computed. Time averages were normalized to corresponding baseline values.

The relationship between V[Combining Dot Above]O2 and the variables VD, SF, VD × SF, and CoMh was tested in 2 ways: First, using Kendall's rank correlation coefficient τ (10) between V[Combining Dot Above]O2 and each factor separately, and second, using the linear multiple regression models

The use of Kendall's nonparametric rank correlation method is motivated by the fact that several data points were taken from each participant, and hence, they are not independent. The confidence level was set at p = 0.05.

Data processing was implemented in Octave v3.0 (, and statistical analyses were performed using R v2.10 (14).

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Figure 1 shows the baseline values for VD, SF, and V[Combining Dot Above]O2 uptake for all the participants. There is a large span in VD between the individual subjects but a smaller span for SF. The curve VD × SF = a is fitted to the data and overlain in the figure. According to the assumed cost of mechanical power needed to overcome gravity, points on this curve correspond to combinations of VD and SF with equal power demands. These 2 variables are inversely proportional, and the curve is a hyperbola with the lines at VD = 0 and SF = 0 as asymptotes. Note that the line is not a particularly good fit to the data. There is clearly a negative correlation between VD and SF.

Figure 1

Figure 1

Figure 2 shows the effect of altering VD and SF on the metabolic cost of running. All trials except the baseline trial are included. Although different targets were aimed at reducing VD, SF, and VD × SF, the subjects tended to increase VD while reducing SF and vice versa. Notably, most changes resulted in an increase in V[Combining Dot Above]O2 uptake, particularly when the SF was reduced.

Figure 2

Figure 2

Figure 3 shows the change in the CoMh with respect to the baseline. Note that in almost all the feedback trials, the runners tended to reduce the height. The results of the statistical tests are summarized in Table 1.

Figure 3

Figure 3

Table 1

Table 1

The mean blood lactate concentration, measured after the completion of the last trial was 2.5 (SD 1.5) mmol·L−1. Hence, the chosen running speed may be regarded as submaximal and steady state. The RE during the baseline measurement was 51.9 (SD 3.5) ml·kg−1·min−1, which is similar to that previously reported for elite runners (6). The rate of perceived exertion for legs and respiration was moderate (Table 2).

Table 2

Table 2

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An important part of the external work performed during running is expressed by VD × SF, the product of the vertical displacement of the COM and the SF. These variables are logical candidates to manipulate in order to reduce the excess external work performed during running and thus to improve RE.

Manipulation of the self-selected running technique resulted in most cases in a poorer RE, as seen in figure. Typical day-to-day coefficient of variation for steady-state V[Combining Dot Above]O2 measurements at submaximal performance for trained athletes is around 2% (15). This translates to a minimal detectable change (MDC) of

According to this criteria, 1 runner showed a reduction in V[Combining Dot Above]O2 uptake in 2 of the trials, whereas 9 runners showed an increase in V[Combining Dot Above]O2 uptake in all together 22 trials. Six of the runners did not show any changes that fell outside the MDC threshold. These values may have been different for a group of less-trained runners, whose technique is expected to be further from optimal. This is worth looking at further. It is realistic to assume that certain runners, because of their specific running technique, would benefit from deliberately reducing their VD × SF, probably through a reduction in the VD, whereas other runners would not.

Correlations between the dependent and independent variables were weak (Kendall's τ ranged from –0.19 to 0.16), but some relationships were significant. Step frequency and V[Combining Dot Above]O2 uptake were inversely correlated, whereas VD and VD × SF were both positively correlated with the V[Combining Dot Above]O2 uptake. This indicated that a reduction in SF and increase in VD and VD × SF resulted in an increase in the V[Combining Dot Above]O2 uptake. Multiple regression showed a negative relationship between CoMh and V[Combining Dot Above]O2 uptake, indicating that a reduction in CoMh partly explained an increase in the V[Combining Dot Above]O2 uptake. However, the fit of the multiple regression models was poor (multiple R 2 0.07 and 0.12), which implies that the effect size was small: 7 and 12% of, respectively, of the variance explained.

The sign of a positive, but weak, relation between VD × SF and V[Combining Dot Above]O2 supports the hypothesis that decreasing the VD × SF may reduce the V[Combining Dot Above]O2 uptake and hence improve the RE. Both the linear- and the log-linear model showed a significant negative relationship between CoMh and V[Combining Dot Above]O2 uptake. Thus, sinking down from the natural (baseline) height of CoM while running correlated with increased metabolic cost. This suggests that trying to maintain the self-chosen CoMh while reducing VD × SF could be worth investigating further. In the experiments, CoMh was measured but not controlled through feedback to the runner. It is suggested that further testing include feedback on this information as well.

Manipulating SF away from the self-selected one has previously been found to increase oxygen consumption (3,9). Our results are not directly comparable, because VD was manipulated in combination with SF. What is new in this study is the alteration of SF while maintaining VD, and vice versa, and manipulating VD × SF. In the latter case, the runner was free to choose how to change SF and VD to attain the target value. Importantly, the variables VD and SF are expected to covary negatively because of the mechanics of running (2), and this was also observed in the downward trend in figures. The coupling made it difficult for the runners to achieve isolated reductions in either VD or SF alone. Targets were set to impose separate reductions in VD, SF, and VD × SF, respectively, while at the same time maintaining baseline values for the other factors. However, the subjects tended to increase VD when reducing SF and vice versa. When given feedback exclusively on the product VD × SF, many runners chose to increase the SF with respect to the baseline. Although this would in principle increase VD × SF, they were in fact able to reduce their VD sufficiently to attain the target VD × SF value. We made a point of not instructing the runners as to how they should adapt their running techniques, so as not to enforce any specific adaptation.

This study showed mostly negative immediate effects on RE of altering VD × SF. Further studies should look at the effect after a period of deliberate training to reduce VD × SF.

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Practical Applications

It is commonly assumed that, in general, the immediate effect of any alteration of the self-selected running technique on the RE will be negative. In particular, this is expected in a group of well-trained and experienced runners as in this study. We observed 1 runner (out of 16) who significantly improved RE from reducing VD and VD × SF. The other runners showed either no significant change (n = 6) or a decrease (n = 9) in the RE.

It is likely that positive effects require a period of deliberate technique training and that only few runners will show an immediate effect. Some runners might show improvements after some weeks and other runners no positive effect at all from altering their VD and SF. Likely candidates that could benefit are those that show an immediate positive effect and those who run with a larger VD × SF than their peers. This needs to be further studied. The combination of real-time feedback with the measurement of V[Combining Dot Above]O2 uptake may be used as a screening tool to identify such runners.

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This work was funded by the Swedish National Centre for Research in Sports.

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biomechanics; locomotion; energy expenditure; feedback training

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