A lower duty factor (DF) reflects a greater relative contribution of leg swing versus ground contact time during the running step. Increasing time on the ground has been reported in the scientific literature to both increase and decrease the energy cost (EC) of running, with DF reported to be highly variable in runners. As increasing running speed aligns running kinematics more closely with spring–mass model behaviours and re-use of elastic energy, we compared the centre of mass (COM) displacement and EC between runners with a low (DFlow) and high (DFhigh) duty factor at typical endurance running speeds. Forty well-trained runners were divided in two groups based on their mean DF measured across a range of speeds. EC was measured from 4 min treadmill runs at 10, 12 and 14 km h−1 using indirect calorimetry. Temporal characteristics and COM displacement data of the running step were recorded from 30 s treadmill runs at 10, 12, 14, 16 and 18 km h−1. Across speeds, DFlow exhibited more symmetrical patterns between braking and propulsion phases in terms of time and vertical COM displacement than DFhigh. DFhigh limited global vertical COM displacements in favour of horizontal progression during ground contact. Despite these running kinematics differences, no significant difference in EC was observed between groups. Therefore, both DF strategies seem energetically efficient at endurance running speeds.

The spring–mass model has been used for decades to study the biomechanical characteristics of locomotion (Blickhan, 1989). This model assumes that the body acts as a spring in which the centre of mass (COM) passively bounces on a massless muscle–tendon unit spring, with no energy lost due to the viscosity of structures (Blickhan, 1989). This simplistic model considers the storage and release of elastic energy as an integral component of animal locomotion. This storage and return of energy has been identified as one of the main factors influencing the energetic cost (EC) of running (Moore, 2016). Dalleau et al., 1998 reported an inverse relationship between the cost of running and leg stiffness (as leg stiffness increases, cost of running decreases), and proposed that the re-use of elastic energy is an appropriate model to further understand the inter-individual differences in the cost of running. On this basis, the most economical running strategy would be to decrease the duration of the ground contact phase (tc) due to its inverse relationship with vertical stiffness (Morin et al., 2007). However, vertical stiffness cannot increase indefinitely and is limited to preserve the integrity of the anatomical structures during ground contact (Gollhofer et al., 1984). In addition, the nature of the relationship reported to exist between EC and tc in runners is inconsistent in the scientific literature, with a longer tc also reported as being more economical than a shorter tc by Kram and Taylor (1990). These authors claimed that a long tc allows force to be generated over a longer period, reducing EC. Moreover, for a given step frequency, a decrease in tc would lengthen the duration of the aerial phase (ta) and promote vertical displacement of the COM (Δz), which is known to increase EC (Folland et al., 2017). The relationship between EC and movement pattern is complex.

Running forms should be viewed as a ‘global system’ where relationships exist between biomechanical parameters, as highlighted by the relationship governing tc and footstrike pattern (Di Michele and Merni, 2014). Instead of decreasing tc to minimize EC, one effective strategy could be to increase tc to limit Δz and ta. Such a biomechanical strategy to optimize EC has been proposed recently under the name ‘terrestrial running form’ (Lussiana et al., 2017a), which resembles the grounded locomotive pattern used by some animal species (e.g. quail: Andrada et al., 2013) or the Groucho running style (McMahon et al., 1987). Although Groucho running has been associated with an increased EC by McMahon et al. (1987), individuals were asked to artificially modify their running biomechanics by accentuating leg flexion. Generalizing these results to people who naturally adopt such a running form is not appropriate given that self-selected patterns are often the most economical ones at an individual level as highlighted in a recent review (Moore, 2016). In addition, running biomechanics depend on the environment in which individuals run (Lussiana and Gindre, 2016). For instance, an increase in running speed typically reduces tc and increases ta (Brughelli et al., 2011), while the braking and propulsion times become more symmetrical (Cavagna, 2006, 2010) and align more closely with the spring–mass model as running speed increases. The storage and release of elastic energy could be enhanced at higher running speeds, with a short tc and high ta becoming more efficient (Cavagna et al., 2008a). Indeed, high forces applied on a short tc and an increase of the temporal symmetry of the running step might facilitate isometric muscle contractions, causing the tendons to act as simple springs and favouring elastic energy storage and return (Cavagna, 2006). However, at slower running speeds, the assumptions of quasi-symmetrical ground contact and aerial times underlying the spring–mass model might not apply as readily.

List of symbols and abbreviations
     
  • COM

    centre of mass

  •  
  • DF

    duty factor

  •  
  • DFhigh

    group runners with high duty factor

  •  
  • DFlow

    group runners with low duty factor

  •  
  • EC

    energy cost of running

  •  
  • RER

    respiratory exchange ratio

  •  
  • ta

    duration of the aerial phase

  •  
  • ta+

    duration of the upward displacements of the centre of mass during the aerial phase

  •  
  • ta

    duration of the downward displacements of the centre of mass during the aerial phase

  •  
  • ta+/ta

    ta+ expressed as a percentage of ta+ + ta

  •  
  • tc

    duration of the contact phase

  •  
  • tc+

    duration of the upward displacement of the centre of mass during the contact phase

  •  
  • tc

    duration of the downward displacement of the centre of mass during the contact phase

  •  
  • tc+/tc

    tc+ expressed as a percentage of tc+ + tc

  •  
  • ts

    duration of the leg swing phase

  •  
  • O2

    oxygen consumption

  •  
  • CO2

    carbon dioxide production

  •  
  • Δyc

    forward displacement of the centre of mass during the contact phase

  •  
  • Δz

    global vertical displacement of the centre of mass

  •  
  • Δza

    vertical displacement of the centre of mass during the aerial phase

  •  
  • Δza+

    upward displacement of the centre of mass during the aerial phase

  •  
  • za|

    absolute downward displacement of the centre of mass during the aerial phase

  •  
  • Δzc

    vertical displacement of the centre of mass during the contact phase

  •  
  • Δzc+

    upward displacement of the centre of mass during the contact phase

  •  
  • zc|

    absolute downward displacement of the centre of mass during the contact phase

  •  
  • Δza+za

    Δza+ expressed as a percentage of Δzc+ + |Δza|

  •  
  • Δzc+zc

    Δzc+ expressed as a percentage of Δzc+ + |Δzc|

Considering the behaviour of running mechanics during both tc and the swing phase (ts) provides a better understanding of the global running form compared with when these temporal parameters are taken into account separately. The duty factor (DF) is the ratio of one to the other, with a greater DF reflecting a greater relative contribution of tc and a lesser relative contribution of ts (and therefore ta) to the running step (Minetti, 1998). DF has been reported to be highly variable amongst runners, with values ranging from 0.257 to 0.403 at similar running speeds (Folland et al., 2017). However, DF has not been studied intensively and no relationship between DF and economy has yet been described. Thus, the objective of this study was to investigate the kinematic and energetic values between runners with a high (DFhigh) and low (DFlow) DF at typical endurance running speeds, including measures of COM displacement, temporal symmetry of the running step and EC. As the DFhigh runners exhibit long tc and short ts (and ta), we hypothesized a larger forward COM displacement during ground contact times and a smaller vertical COM displacement during aerial times compared with the DFlow group for a given speed. In addition, having a low DF (short tc) should promote an elastic behaviour; therefore, we hypothesized greater symmetry within contact and aerial phases compared with the DFhigh group. Moreover, a similar EC at endurance running speeds has been observed in runners exhibiting different running forms (Lussiana et al., 2017a). Therefore, despite these differences in running kinematics, we anticipated similar EC values at typical endurance speeds (i.e. 10, 12 and 14 km h−1) between groups.

Participants

Fifty-four trained runners, 33 males (mean±s.d.: age 31±8 years, height 175±6 cm, mass 66±9 kg and weekly running distance 53±15 km) and 21 females (age 32±7 years, height 162±3 cm, mass 52±4 kg and weekly running distance 50±14 km) voluntarily participated in this study. For study inclusion, participants were required to be in good self-reported general health with no current or recent (<3 months) musculoskeletal injuries and to meet a certain level of running performance. More specifically, in the last year, runners were required to have competed in a road race with finishing times of ≤50 min for 10 km, ≤1 h 50 min for 21.1 km or ≤3 h 50 min for 42.2 km. Participants who were, or could be, pregnant were not eligible. The ethical committee of the National Sports Institute of Malaysia approved the study protocol prior to participant recruitment (ISNRP: 26/2015), which was conducted in accordance with international ethical standards (Harriss et al., 2017) and adhered to the Declaration of Helsinki of the World Medical Association.

Experimental procedure

Each participant completed one experimental session in the biomechanics laboratory of the National Sports Institute of Malaysia. Running bouts were always performed in the morning (start of exercise between 07:00 h and 09:00 h), to avoid circadian variance in performance, and under similar environmental conditions (28°C and 74% relative humidity). Participants reported to the laboratory after 10–12 h overnight fast. All participants were advised to avoid strenuous exercise the day before the test. After providing written informed consent, participants ran three laps on a 400 m athletic track at a constant self-selected speed (12.7±1.3 km h−1), which was followed by 2 min at 9 km h−1 on a treadmill (h/p/cosmos mercury®, h/p/cosmos sports & medical gmbh, Nussdorf-Traunstein, Germany) as a warm-up. Participants then completed three 4 min runs at 10, 12 and 14 km h−1 (with 2 min recovery periods between each run) on the treadmill, during which time EC was assessed. Retro-reflective markers were subsequently positioned on individuals (described below) to assess running biomechanics. Each participant then completed five 30 s runs at 10, 12, 14, 16 and 18 km h−1 (with 1 min recovery periods between each run) on the same treadmill, during which time 3D kinematic data were collected. EC and biomechanics were assessed separately, given constraints (e.g. presence of testing equipment that can occlude markers) in measuring the two sets of data simultaneously and to allow assessment of biomechanics at running speeds over steady-state thresholds (16 and 18 km h−1). All participants were familiar with running on a treadmill as part of their usual training programmes and wore their habitual running shoes during testing.

Runners were classified in two groups (DFhigh and DFlow) based on their mean DF recorded from the five 30 s runs at 10, 12, 14, 16 and 18 km h−1. Based on standard sample size calculations, a total of 18 participants per DF group was needed for the purpose of this study (Zar, 1999). Hence, to highlight the presence of different biomechanical running strategies, the statistical analysis focused on the 20 runners with the highest DF and the 20 runners with the lowest DF. Therefore, 14 participants with mid-range DF were excluded from the analysis. These participants were similar in terms of baseline characteristics to the remainder of the group (age, height, mass and running distance, P>0.05). The baseline characteristics of the DFhigh and DFlow groups are given in Table 1 and were similar between groups. As would be anticipated, two-way (DF group × speed) repeated-measures analysis of variance (RM ANOVA) indicated differences in DF between groups at all speeds examined (mean values 0.330±0.018 for DFlow and 0.385±0.028 for DFhigh, P<0.001, Fig. 1). The DF values in our population are in line with those previously reported in the literature at similar running speeds and agree with the proposition that running locomotion DF values should be under 0.500 (Folland et al., 2017; Minetti, 1998). Running speed also affected DF (main effect, P<0.001), with the change in DF with speed being group specific (interaction effect, P=0.003). An increase in speed was associated with a greater decline in DF in the DFhigh than in the DFlow group (Fig. 1).

Table 1.

Participant characteristics for the low (DFlow) and high (DFhigh) duty factor running groups

Participant characteristics for the low (DFlow) and high (DFhigh) duty factor running groups
Participant characteristics for the low (DFlow) and high (DFhigh) duty factor running groups
Fig. 1.

Duty factor (DF) of the two running groups at each running speed. The white circles represent the running group with a low mean duty factor (DFlow). The black circles represent the running group with a high mean duty factor (DFhigh). Values are means±s.d., n=20 per group. *Significant difference (P<0.05) between DF groups as determined by Holm–Šídák post hoc tests.

Fig. 1.

Duty factor (DF) of the two running groups at each running speed. The white circles represent the running group with a low mean duty factor (DFlow). The black circles represent the running group with a high mean duty factor (DFhigh). Values are means±s.d., n=20 per group. *Significant difference (P<0.05) between DF groups as determined by Holm–Šídák post hoc tests.

Physiological parameters

Gas exchange was measured using TrueOne 2400 (ParvoMedics, Sandy, UT, USA) during the three 4 min running bouts. Prior to the runs, the gas analyser was calibrated using ambient air (O2: 20.93% and CO2: 0.03%) and a gas mixture of known concentration (O2: 16.00%, CO2: 4.001%). Volume calibration was performed at different flow rates with a 3 l calibration syringe (5530 series, Hans Rudolph, Shawnee, KS, USA). Oxygen consumption (O2), carbon dioxide production (CO2) and respiratory exchange ratio (RER) values were averaged over the last minute of each 4 min running bout. Steady state was confirmed through visual inspection of the O2 and CO2 curves. RER had to remain below unity during the trials for data to be included in the analysis, otherwise the corresponding data were excluded as they were deemed to not represent a submaximal effort. No trials were excluded on this basis. EC was expressed as the number of kilocalories required per distance covered per body mass (kcal kg−1 km−1). The caloric equivalent of the O2 (kcal l−1) was determined based on the average RER recorded over the last minute (Astrand and Rodahl, 1986; Fletcher et al., 2009). A higher EC cost indicates a less economical running form.

Biomechanical parameters

During the 30 s runs on the treadmill, whole-body 3D kinematic data were collected at 200 Hz using seven infrared Oqus cameras (five Oqus 300+, one Oqus 310+ and one Oqus 311+), Qualisys Track Manager software (version 2.11, build 2902) and the Project Automation Framework Running package (version 4.4) from Qualisys AB (Gothenburg, Sweden). Thirty-five retro-reflective markers of 12 mm diameter were affixed to the skin and shoes of individuals over anatomical landmarks using 3M™ double-sided tape, Hypafix® adhesive non-woven fabric and Mastisol® liquid adhesive following standard guidelines from the Project Automation Framework Running package (Tranberg et al., 2011). The 3D marker data were exported in .c3d format and processed in Visual3D Professional software version 5.02.25 (C-Motion Inc., Germantown, MD, USA). The marker data were interpolated using a third-order polynomial least-square fit algorithm, allowing a maximum of 20 frames for gap filling, and subsequently low-pass filtered at 20 Hz using a fourth-order Butterworth filter. From the marker set, a full-body biomechanical model with six degrees of freedom and 15 rigid segments was constructed. Segments included the head, upper arms, lower arms, hands, thorax, pelvis, thighs, shanks and feet. In Visual3D, segments were treated as geometric objects. Segments were assigned inertial properties and COM locations based on their shape (Hanavan, 1964) and attributed relative mass based on standard regression equations (Dempster, 1955). Whole-body COM location was calculated from the parameters of all 15 segments.

Running events were derived from the kinematic data using similar procedures to those previously reported in the literature (Lussiana et al., 2017b; Maiwald et al., 2009). More explicitly, a mid-foot landmark was generated midway between the heel and toe markers. Footstrike was defined as the instance when the mid-foot landmark reached a local minimal vertical velocity prior to it reaching a peak vertical velocity reflecting the start of swing. Toe-off was defined as the instance when the toe marker attained a peak vertical acceleration before reaching a 7 cm vertical position. ts and tc were defined as the time from toe-off to touch-down and from touch-down to toe-off of the same foot, respectively, and ta as the time from toe-off to touch-down of the opposite foot. Mid-stance and mid-flight events were calculated to divide tc and ta, respectively. Mid-stance was defined as the instance when COM reached its lowest vertical position during tc. Mid-flight was defined as the instance when the COM reached its highest vertical position during ta. All events were verified to ensure correct identification and manually adjusted when required. Values for tc, ta and ts were calculated based on touch-down and toe-off events, and DF was calculated as follows (Minetti, 1998):
formula
(1)
The maximum vertical displacement of the COM during a step (Δz) was calculated as the difference of the COM height between mid-flight and mid-stance events. The vertical and forward displacement of the COM during the contact phase were calculated between touch-down and toe-off events and are represented as Δzc and Δyc, respectively, with Δza representing the vertical displacement of the COM during the aerial phase calculated between toe-off and touch-down events. All values are expressed as a percentage of COM height in static upright stance. The subcomponent of Δzc, i.e. absolute downward and upward displacement of the COM during the contact phase and their respective durations ( and ) were calculated between touch-down and mid-stance events and between mid-stance and toe-off events, respectively. Upward () and absolute downward displacement of the COM during the aerial phase and their respective durations ( and ) were calculated between toe-off and mid-flight events and between mid-flight and touch-down events, respectively. Finally, the total vertical displacement of the COM during a contact or an aerial phase was expressed as follows:
formula
(2)
where i=c or a. The ratios zc and /tc as well as /za and /ta were also calculated to explore upward and downward movement symmetries (Cavagna, 2010). Step symmetry has previously been calculated by Cavagna (2006) using effective contact and aerial times based on vertical ground reaction forces being below and above body weight, respectively, as opposed to the temporal kinematic procedures used in the present study. The difference in computational methods should not affect our results and interpretations as relative and absolute reliability of effective (accelerometer) and visual (video camera) measurements of contact and aerial times have been reported as good (Gindre et al., 2016).

Statistics

As all data were normally distributed on the basis of the Kolmogorov–Smirnov test, parametric statistical methods were employed for data analysis. Descriptive statistics of data are presented as mean±s.d. values. Two-way (DF groups × speed) RM ANOVA employing Holm–Šídák procedures for pair-wise post hoc comparisons were used to investigate whether the EC and the biomechanical parameters differed between DFlow and DFhigh groups, while accounting for the effect of running speed. Statistical significance was set at P<0.05. Statistics were performed using SigmaStat 12 for Windows (Systat Software Inc., San Jose, CA, USA).

EC

There was no main effect of DF on EC across speed (P=0.556, Fig. 2), but a main effect of speed on EC was observed (P=0.022). However, the effect of speed on EC depended on DF group (P=0.025, Fig. 2). EC decreased in the DFlow group with an increase in speed (−2.3±2.6% from 10 to 14 km h–1, P=0.008), but EC did not significantly change in the DFhigh group across speed (1.5±3.8% from 10 to 14 km h–1, P=0.781).

Fig. 2.

Energy cost (EC) of the two running groups at each running speed. The white bars represent the DFlow running group. The black bars represent the DFhigh running group. Values are means±s.d., n=20 per group. *Significant difference (P<0.05) between running speeds as determined by Holm–Šídák post hoc tests.

Fig. 2.

Energy cost (EC) of the two running groups at each running speed. The white bars represent the DFlow running group. The black bars represent the DFhigh running group. Values are means±s.d., n=20 per group. *Significant difference (P<0.05) between running speeds as determined by Holm–Šídák post hoc tests.

COM displacement

There was a significant main effect of DF and speed on Δz and Δyc (Fig. 3), and an interaction effect on Δz. The DFlow group exhibited greater Δz (P=0.047) and lower Δyc (P<0.001) than the DFhigh group at all speeds, whereas increasing speed decreased Δz and increased Δyc in both groups (P<0.001). The interaction effect indicated a greater decrease in Δz in the DFlow group than in the DFhigh group with speed.

Fig. 3.

Displacement of the centre of mass (COM) as function of running speed for the two running groups. (A) Vertical displacement of the COM during the entire running step (Δz). (B) Horizontal displacement of the COM during the contact phase (Δyc). The white circles represent the DFlow running group. The black circles represent the DFhigh running group. Values (means±s.d.) are expressed as a percentage of COM height in static upright stance, n=20 per group. *Significant difference (P<0.05) between DF groups as determined by Holm–Šídák post hoc tests.

Fig. 3.

Displacement of the centre of mass (COM) as function of running speed for the two running groups. (A) Vertical displacement of the COM during the entire running step (Δz). (B) Horizontal displacement of the COM during the contact phase (Δyc). The white circles represent the DFlow running group. The black circles represent the DFhigh running group. Values (means±s.d.) are expressed as a percentage of COM height in static upright stance, n=20 per group. *Significant difference (P<0.05) between DF groups as determined by Holm–Šídák post hoc tests.

All the Δz subcomponents investigated were affected by the increase in speed (Table 2), with being greater in the DFlow than in the DFhigh group (DF main effect, P=0.008; Table 2). Interaction effects between DF groups and speed were observed for , and (all P<0.001). The increase in speed was associated with a greater decrease in (P=0.003) in the DFlow than in the DFhigh group.

Table 2.

Vertical displacement of the centre of mass (COM) during the running step for the DFlow and DFhigh running groups at the different running speeds

Vertical displacement of the centre of mass (COM) during the running step for the DFlow and DFhigh running groups at the different running speeds
Vertical displacement of the centre of mass (COM) during the running step for the DFlow and DFhigh running groups at the different running speeds

Temporal characteristics

There was a significant main effect of DF on all temporal parameters except for (Table 3). The two subcomponents of the contact phase were longer for the DFhigh than for the DFlow group, with a more pronounced difference for (P<0.001) than for (P=0.004). The opposite was observed for ta, with greater values for the DFlow group and a more pronounced difference between groups for (P<0.001) than for . Running speed affected all temporal parameters, with a decrease of tc, and , and an increase of ta, and from 10 to 18 km h−1 (main effect of speed, P<0.001). Interaction effects were observed for most parameters, indicating a more pronounced decrease of tc and , and an increase of ta and with the increase of speed in the DFhigh group (all P≤0.010). remained similar across speed for the DFhigh group but decreased for the DFlow group (P<0.001).

Table 3.

Temporal parameters of the running steps for the DFlow and DFhigh running groups at the different running speeds

Temporal parameters of the running steps for the DFlow and DFhigh running groups at the different running speeds
Temporal parameters of the running steps for the DFlow and DFhigh running groups at the different running speeds

Step symmetry

The DFlow group exhibited more symmetrical upward to downward motion in terms of /tc, /ta and za than the DFhigh group (DF main effect, P≤0.009; Table 4). Running speed affected all four symmetry-related parameters (speed main effect, P<0.001), with all measures becoming more symmetrical with an increase in running speed. The change in symmetry values with speed was more pronounced in DFhigh for /ta and in DFlow for zc (interaction effects, P<0.001 and P=0.003, respectively).

Table 4.

Symmetrical parameters of the runningstepsfor the DFlow and DFhigh running groups at the different running speeds

Symmetrical parameters of the running steps for the DFlow and DFhigh running groups at the different running speeds
Symmetrical parameters of the running steps for the DFlow and DFhigh running groups at the different running speeds

In this study, in accordance with our hypotheses, the DFhigh group demonstrated larger forward displacement of the COM during ground contact (Δyc), smaller vertical displacement of the COM during the aerial phase and less temporal symmetry in terms of contact and aerial phases (/tc and /ta) than the DFlow group. Despite these observations, EC did not appear to be significantly different between these two groups at typical endurance running speeds. The different strategies used to minimize EC between DF groups can be distinguished by simple temporal step measurements.

EC of the DFlow and DFhigh groups was not significantly different between 10 and 14 km h−1. This finding is in contrast with a previous study showing that habitual rearfoot strikers (shorter ta and longer tc) compared with habitual mid-foot strikers (longer ta and shorter tc) had lower EC at 11 and 13 km h−1, but not at 15 km h−1 (Ogueta-Alday et al., 2014). However, in the present study, a speed effect was observed for the DFlow group. Although running biomechanics became more symmetrical in both DF running groups as speed increased, the DFlow group exhibited a greater step symmetry than the DFhigh group, in spite of larger changes in temporal parameters in the DFhigh group. The ratio /tc decreased with increasing speed, becoming closer to 0.5 above 14 km h−1. This decrease could be due to less stretching and shortening of the muscle and greater stretching and shortening of the tendon occurring as muscle force increases with speed. This alteration would lead to greater elastic energy storage and return, and therefore lower EC at high speeds for the DFlow group. Thus, in higher running speed conditions, the speculated increase in the re-use of energy could be a more desirable EC reduction strategy (Lai et al., 2014), reflecting kangaroo species where elastic structures return more energy at higher than at lower speeds (Dawson and Taylor, 1973). In contrast, a decrease of EC could be speculated for the DFhigh group when decreasing speed to values below 10 km h−1 because it would be preferable to limit vertical displacement of the COM and to promote its forward progression. Indeed, the percentage contribution from elastic energy to positive work during running has been shown to decrease when speed is reduced (Lai et al., 2014). Therefore, relying on the re-use of elastic energy to reduce the EC of running might not be the most favourable strategy. It has recently been shown that the vertical COM displacement (during tc or the whole step) explains a large part of the inter-individual difference in EC (27.7% for the amplitude of the pelvis vertical displacement during ground contact) at speeds between 10 and 12 km h−1 (Folland et al., 2017), indicating how this particular metric could be important at slower running speeds. Nevertheless, these findings should be re-examined given that no significant main effect of DF was observed across typical endurance speeds, with no evidence how DF, kinematic parameters and EC values interplay at slower and faster running speeds.

At speeds between 10 and 14 km h−1, the DFlow group ran with similar EC values to those of the DFhigh group with a smaller proportion of time spent on the ground to the detriment of larger vertical oscillation of the COM during the aerial phase. From an elastic energy storage perspective, the stretching of muscle–tendon units needs a certain amount of force to be efficient. At endurance running speeds, the force needed to stretch the muscle–tendon units could be generated via the potential energy from the Δz, and counterbalance the negative effect of a higher vertical displacement during ta on EC. In addition, with a shorter duration of tc, leg stiffness increases as a result of the existence of an inverse relationship between these two quantities (Morin et al., 2007). Therefore, runners belonging to the DFlow group seem to rely on the re-use of elastic energy to a greater extent to reduce EC. In contrast, the DFhigh group appear to minimize EC by reducing vertical displacement, favouring forward displacement (Δyc) of the COM, and demonstrating an asymmetry in the temporal step parameters to the detriment of a longer tc. An increase of tc with particular lengthening of enhances Δyc such that the COM is directed more horizontally than vertically. In addition, as supported by Kram and Taylor (1990), a longer tc allows force to be generated over a longer period, reducing EC. Moreover, the change of these parameters together with the reduction of ta limits the vertical oscillation, especially during the aerial phase, to benefit the horizontal progression. However, as for short tc, a large proportion of the positive work is better explained using the stretch–shortening cycle model and recovery of stored elastic energy (Cavagna, 2009, 2010; Roberts, 2016). There are various biomechanical models used to understand human and mammalian locomotion, all of which have strengths and limitations. In the current paper, the stretch–shortening paradigm was the working model employed.

The existence of asymmetries between the braking and propulsion phases in runners – more precisely, the proportionally longer ground contact time than aerial time (DFhigh group) – mirrors previous observations of a relatively longer than , with lower apparent elastic behaviour in elderly (73.6±5.5 years) than in younger (20.8±1.6 years) runners (Cavagna et al., 2008b). Our findings extend these previous results and indicate that inter-individual differences in the optimization of the spring–mass model during running are not due to age alone, but reflect spontaneous movement patterns. Here, we provide biomechanical evidence to support the proposal that minimizing vertical displacement and work against gravity can be a cost-efficient strategy, despite a lower compliance to the spring–mass model (Fig. 4). Thus, we propose that EC can be minimized through different mechanisms: (1) optimization of the spring–mass model, leading to the re-use of elastic energy (DFlow), and (2) limiting vertical displacement of the COM to promote forward progression (DFhigh). These different minimization strategies can de distinguished by simple temporal step measurements. Some runners further rely more on one mechanism than the other, which is also reflected by some runners having a similar EC despite exhibiting more than twice the vertical displacement of other runners (Folland et al., 2017).

Fig. 4.

Representation of COM displacement while running at 14 km h–1. (A) A runner from the DFlow group. (B) A runner from the DFhigh group. The vertical displacement of the COM during the running step includes a contact phase (tc) and an aerial phase (ta). TD, touch-down; MS, mid-stance; TO, toe-off; MF, mid-flight.

Fig. 4.

Representation of COM displacement while running at 14 km h–1. (A) A runner from the DFlow group. (B) A runner from the DFhigh group. The vertical displacement of the COM during the running step includes a contact phase (tc) and an aerial phase (ta). TD, touch-down; MS, mid-stance; TO, toe-off; MF, mid-flight.

A particular running condition (i.e. speed or distance) can influence the preferred running biomechanics; hence, it is difficult to prove the existence of a single ideal running form. Thus, we encourage running coaches to consider the characteristics of running form at an individual level, as well as the specific race demands in training prescription and preparation. The distinction of running forms can be performed easily as it only requires the measurement of temporal step characteristics. For now, the effect of an acute and chronic change in DF on the EC of runners remains to be tested, although it has been shown that acute changes in self-selected running forms (e.g. a decrease in stride length and vertical oscillation) tend to increase EC (Dallam et al., 2005; Moore, 2016).

Several limitations to this study exist. To start with, there are relatively few studies on DF, making it difficult to know what DF values are typical or how these values are likely to change with confounding variables, such as footwear or running surface. In our study, participants wore their own shoes. To date, the empirical evidence regarding the effect of footwear on EC is conflicting, with some studies indicating an effect (e.g. Hoogkamer et al., 2018) and others indicating no effect (e.g. Cochrum et al., 2017) of footwear on EC when matched for mass. Another limitation is that segment inertial properties in our study were not based on each individual's actual segmental properties. However, the use of standard regression equations is a widespread non-invasive technique that does not require use of expensive magnetic resonance imaging and exposure of individuals to radiation. Finally, the working model is that the re-use of elastic energy reflects spring–mass model mechanics. The impulsive collision model proposed by Ruina et al. (2005) exemplifies how a locomotive pattern can appear elastic without any storage and return of elastic energy, cautioning against reliance on biomechanics alone to infer energy storage and release. That said, Ruina et al.’s (2005) model is very simple and is not suited to understanding how DF affects the cost of running as the model employs an instantaneous impulsive collision (a DF of zero). No calculation on the use of elastic energy was performed in this study given that it would not be representative of the true elastic energy stored in the lower limb in the case of the DFhigh group. Indeed, the formula used to compute elastic energy is correct only within the limits of the spring–mass model, a model which we assume is no longer optimized for the DFhigh group because of the lack of symmetry within the running step.

In summary, runners with a low DF favour short contact times and have a more symmetrical running step. This may be due to less stretching and shortening of the muscle and greater stretching and shortening of the tendon, which would lead to greater re-use of elastic energy and lower EC. Runners with a high DF favour long contact times and reduce work against gravity to promote forward progression to lower EC. Overall, the two running forms (i.e. high and low DF), which can be distinguished by a simple measurement of running step temporal parameters, were here associated with similar EC, suggesting that both strategies can be used efficiently at typical endurance running speeds. These results can impact how running technique and optimal running forms are perceived in diverse environments.

The authors thank Dr Wee Kian Yeo and Dr Chrisopher Martyn Beaven for their help during the design of the study, and Mr Chris Tee Chow Li for assistance during the data collection process. The authors also thank Qualisys AB and C-Motion Inc. for supplying the research team with the necessary hardware and software for data collection and processing. The authors thank all the subjects for their participation. Finally, results for running speeds of 10, 12 and 14 km h−1 in this paper are reproduced from the PhD thesis of Thibault Lussiana (Franche-Comté University, 2016).

Author contributions

Conceptualization: T.L., C.G.; Methodology: T.L., L.M., K.H.-L.; Software: K.H.-L.; Validation: K.H.-L.; Formal analysis: T.L., K.H.-L.; Investigation: T.L., K.H.-L.; Resources: T.L.; Data curation: T.L., K.H.-L.; Writing - original draft: T.L.; Writing - review & editing: A.P., C.G., L.M., K.H.-L.; Supervision: L.M., K.H.-L.; Project administration: L.M.; Funding acquisition: T.L., L.M., K.H.-L.

Funding

This study was financially supported by the Bourgogne Franche-Comté University (France) and the National Sports Institute of Malaysia.

Andrada
,
E.
,
Nyakatura
,
J. A.
,
Bergmann
,
F.
and
Blickhan
,
R.
(
2013
).
Adjustments of global and local hindlimb properties during terrestrial locomotion of the common quail (Coturnix coturnix)
.
J. Exp. Biol.
216
,
3906
-
3916
.
Astrand
,
P. O.
and
Rodahl
,
K.
(
1986
).
Textbook of Work Physiology
.
New York, NY
:
McGraw-Hill Series in Health Ed
.
Blickhan
,
R.
(
1989
).
The spring-mass model for running and hopping
.
J. Biomech.
22
,
1217
-
1227
.
Brughelli
,
M.
,
Cronin
,
J.
and
Chaouachi
,
A.
(
2011
).
Effects of running velocity on running kinetics and kinematics
.
J. Strength Cond. Res.
25
,
933
-
939
.
Cavagna
,
G. A.
(
2006
).
The landing-take-off asymmetry in human running
.
J. Exp. Biol.
209
,
4051
-
4060
.
Cavagna
,
G. A.
(
2009
).
The two asymmetries of the bouncing step
.
Eur. J. Appl. Physiol.
107
,
739
-
742
.
Cavagna
,
G. A.
(
2010
).
Symmetry and asymmetry in bouncing gaits
.
Symmetry
2
,
1270
-
1321
.
Cavagna
,
G. A.
,
Legramandi
,
M. A.
and
Peyré-Tartaruga
,
L.
(
2008a
).
Old men running: mechanical work and elastic bounce
.
Proc. R. Soc. B Biol. Sci.
275
,
411
-
418
.
Cavagna
,
G. A.
,
Legramandi
,
M. A.
and
Peyre-Tartaruga
,
L. A.
(
2008b
).
The landing-take-off asymmetry of human running is enhanced in old age
.
J. Exp. Biol.
211
,
1571
-
1578
.
Cochrum
,
R. G.
,
Connors
,
R. T.
,
Coons
,
J. M.
,
Fuller
,
D. K.
,
Morgan
,
D. W.
and
Caputo
,
J. L.
(
2017
).
Comparison of running economy values while wearing no shoes, minimal shoes, and normal running shoes
.
J. Strength Cond. Res.
31
,
595
-
601
.
Dallam
,
G. M.
,
Wilber
,
R. L.
,
Jadelis
,
K.
,
Fletcher
,
G.
and
Romanov
,
N.
(
2005
).
Effect of a global alteration of running technique on kinematics and economy
.
J. Sports Sci.
23
,
757
-
764
.
Dalleau
,
G.
,
Belli
,
A.
,
Bourdin
,
M.
and
Lacour
,
J.-R.
(
1998
).
The spring-mass model and the energy cost of treadmill running
.
Eur. J. Appl. Physiol. Occup. Physiol.
77
,
257
-
263
.
Dawson
,
T.
and
Taylor
,
C.
(
1973
).
Energetic Cost of Locomotion in Kangaroos
.
Nature
246
,
313
-
314
.
Dempster
,
W.
(
1955
).
Space Requirements of the Seated Operator, Geometrical, Kinematic, and Mechanical Aspects of the Body With Special Reference to the Limbs
.
Wright Air Development Center, Air Research and Development Command, US Air Force.
Di Michele
,
R.
and
Merni
,
F.
(
2014
).
The concurrent effects of strike pattern and ground-contact time on running economy
.
J. Sci. Med. Sport
17
,
414
-
418
.
Fletcher
,
J. R.
,
Esau
,
S. P.
and
MacIntosh
,
B. R.
(
2009
).
Economy of running: beyond the measurement of oxygen uptake
.
J. Appl. Physiol.
107
,
1918
-
1922
.
Folland
,
J.
,
Allen
,
S.
,
Black
,
M.
,
Handsaker
,
J.
and
Forrester
,
S.
(
2017
).
Running Technique is an Important Component of Running Economy and Performance
.
Med. Sci. Sport. Exerc.
49
,
1412
-
1423
.
Gindre
,
C.
,
Lussiana
,
T.
,
Hebert-Losier
,
K.
and
Morin
,
J.-B.
(
2016
).
Reliability and validity of the Myotest® for measuring running stride kinematics
.
J. Sports Sci.
34
,
664
-
670
.
Gollhofer
,
A.
,
Schmidtbleicher
,
D.
and
Dietz
,
V.
(
1984
).
Regulation of muscle stiffness in human locomotion
.
Int J. Sports Med.
5
,
19
-
22
.
Hanavan
,
E.
(
1964
).
A mathematical model of the human body. AMRL-TR
.
Aerosp. Med. Res. Lab.
1
-
149
.
Harriss
,
D.
,
Macsween
,
A.
and
Atkinson
,
G.
(
2017
).
Standards for ethics in sport and exercise science research: 2018 update
.
Int. J. Sports Med.
38
,
1126
-
1131
.
Hoogkamer
,
W.
,
Kipp
,
S.
,
Frank
,
J. H.
,
Farina
,
E. M.
,
Luo
,
G.
and
Kram
,
R.
(
2018
).
A Comparison of the energetic cost of running in marathon racing shoes
.
Sports Med.
48
,
1009
-
1019
.
Kram
,
R.
and
Taylor
,
C. R.
(
1990
).
Energetics of running: a new perspective
.
Nature
346
,
265
-
267
.
Lai
,
A.
,
Schache
,
A. G.
,
Lin
,
Y.-C.
and
Pandy
,
M. G.
(
2014
).
Tendon elastic strain energy in the human ankle plantar-flexors and its role with increased running speed
.
J. Exp. Biol.
217
,
3159
-
3168
.
Lussiana
,
T.
and
Gindre
,
C.
(
2016
).
Feel your stride and find your preferred running speed
.
Biol. Open
5
,
45
-
48
.
Lussiana
,
T.
,
Gindre
,
C.
,
Hébert-Losier
,
K.
,
Sagawa
,
Y.
,
Gimenez
,
P.
and
Mourot
,
L.
(
2017a
).
Similar running economy with different running patterns along the aerial-terrestrial continuum
.
Int J Sport. Physiol. Perform.
12
,
481
-
489
.
Lussiana
,
T.
,
Gindre
,
C.
,
Mourot
,
L.
and
Hébert-Losier
,
K.
(
2017b
).
Do subjective assessments of running patterns reflect objective parameters?
Eur. J. Sport Sci.
17
,
847
-
857
.
Maiwald
,
C.
,
Sterzing
,
T.
,
Mayer
,
T.
and
Milani
,
T.
(
2009
).
Detecting foot-to-ground contact from kinematic data in running
.
Footwear Sci.
1
,
111
-
118
.
McMahon
,
T. A.
,
Valiant
,
G.
and
Frederick
,
E. C.
(
1987
).
Groucho running
.
J. Appl. Physiol.
62
,
2326
-
2337
.
Minetti
,
A. E.
(
1998
).
A model equation for the prediction of mechanical internal work of terrestrial locomotion
.
J. Biomech.
31
,
463
-
468
.
Moore
,
I.
(
2016
).
Is there an economical running technique? A review of modifiable biomechanical factors affecting running economy
.
Sport. Med.
46
,
793
-
807
.
Morin
,
J. B.
,
Samozino
,
P.
,
Zameziati
,
K.
and
Belli
,
A.
(
2007
).
Effects of altered stride frequency and contact time on leg-spring behavior in human running
.
J. Biomech.
40
,
3341
-
3348
.
Ogueta-Alday
,
A.
,
Rodriguez-Marroy
,
J.
and
Garcia-Lopez
,
J.
(
2014
).
Rearfoot striking runners are more economical than midfoot strikers
.
Med. Sci. Sport. Exerc.
46
,
580
-
585
.
Roberts
,
T.
(
2016
).
Contribution of elastic tissues to the mechanics and energetics of muscle function during movement
.
J. Exp. Biol.
219
,
266
-
275
.
Ruina
,
A.
,
Bertram
,
J. E. A.
and
Srinivasan
,
M.
(
2005
).
A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition
.
J. Theo. Biol.
237
,
170
-
192
.
Tranberg
,
R.
,
Saari
,
T.
,
Zügner
,
R.
and
Kärrholm
,
J.
(
2011
).
Simultaneous measurements of knee motion using an optical tracking system and radiostereometric analysis (RSA)
.
Acta Orthop.
82
,
171
-
176
.
Zar
,
J. H.
(
1999
).
Biostatistical Analysis
.
Upper Saddle River, NJ
:
Prentice Hall
.

Competing interests

The authors declare no competing or financial interests.