ABSTRACT

Center of mass (COM) control has been proposed to serve economy- and stability-related locomotor task objectives. However, given the lack of evidence supporting direct sensing and/or regulation of the COM, it remains unclear whether COM mechanics are prioritized in the control scheme of walking. We posit that peripheral musculoskeletal structures, e.g. muscle, are more realistic control targets than the COM, given their abundance of sensorimotor receptors and ability to influence whole-body energetics. As a first test of this hypothesis, we examined whether conservation of stance-phase joint mechanics is prioritized over COM mechanics in a locomotor task where simultaneous conservation of COM and joint mechanics is not feasible: imposed leg-length asymmetry. Positive joint mechanical cost of transport (work per distance traveled; COTJNT) was maintained at values closer to normal walking than COM mechanical cost of transport (COTCOM; P<0.05, N=15). Furthermore, compared with our measures of COM mechanics (COTCOM, COM displacement), joint-level variables (COTJNT, integrated total support moment) also displayed stronger conservation (less change from normal walking) when the participants' self-selected gait was assessed against other possible gait solutions. We conclude that when walking humans are exposed to an asymmetric leg-length perturbation, control of joint mechanics is prioritized over COM mechanics. Our results suggest that mechanical and metabolic effort is likely regulated via control of peripheral structures and not directly at the level of the COM. Joint mechanics may provide a more accurate representation of the underlying locomotor control targets and may prove advantageous in informing predictive models of human walking.

INTRODUCTION

Limbed terrestrial animals exhibit remarkably conserved center of mass (COM) mechanics during locomotion. Indeed, mammalian (including humans), avian, reptilian and even arthropod species adopt an inverted pendulum-style walking gait, characterized by an exchange between COM gravitational potential energy and kinetic energy (Blickhan and Full, 1987; Cavagna et al., 1977, 1976; Farley and Ko, 1997; Griffin et al., 2004; Griffin and Kram, 2000; Heglund et al., 1982; Rubenson et al., 2004). During faster locomotion, the spring–mass paradigm of running, characterized by in-phase fluctuations of COM gravitational potential energy and kinetic energy, is similarly ubiquitous (Blickhan, 1989; Cavagna et al., 1964; Geyer et al., 2006; Rubenson et al., 2004). Clinically focused studies have also demonstrated conservation of COM mechanics. Despite marked morphological differences, COM mechanical work during walking has been observed to be largely maintained between lower limb amputees walking with a prosthetic limb and able-bodied counterparts (Gitter et al., 1995), as well as between young and old adults (Ortega and Farley, 2007). Moreover, when COM mechanics are perturbed, limb mechanics are rapidly adjusted to restore a normal inverted-pendulum COM trajectory (Hof et al., 2010; Townsend, 1985).

Inverted-pendulum and spring–mass mechanics facilitate a reduction in the mechanical work of the COM and muscles, likely translating to a lower metabolic energy cost of walking (Cavagna et al., 1977; Cavagna and Kaneko, 1977). Accordingly, the stereotypical COM mechanics observed across animal species, including humans, may reflect a COM-level control scheme of legged locomotion aimed at minimizing COM mechanical work and cost of transport (COM work per distance traveled; COTCOM). For example, COM-level control has been observed in a classic series of running and hopping experiments, whereby peripheral limb stiffness is adjusted to account for changes in surface stiffness such that COM mechanics are relatively unaffected (Ferris et al., 1999, 1998; Ferris and Farley, 1997). Yet, despite the apparent COM control observed experimentally and adopted in modeling studies (Grimmer et al., 2008; Hof et al., 2005; Ruina et al., 2005; Srinivasan and Ruina, 2006; Townsend, 1985), it is not well established whether COM mechanics, and more specifically COTCOM, are a priority control target during walking [a ‘target of control’ is defined here as a variable that is sensed (either directly or indirectly) and regulated by the nervous system to achieve a locomotor task goal, e.g. economy].

From a sensorimotor perspective, it remains unclear how COM mechanics are regulated during locomotion (Bruijn and van Dieën, 2018). Integrated sensory input from peripheral structures such as muscles and joints may provide more direct control targets by which locomotor economy can be modulated. These peripheral structures provide well-documented neural sensors in the form of joint receptors, muscle spindles and Golgi tendon organs. Thus, COM mechanics, including COTCOM, may not be the principal control target prioritized for achieving locomotor economy but could instead serve as a sufficient proxy capturing the underlying proprioceptive control of movement in normal steady-state locomotion.

An understanding of COM versus peripheral-level control in locomotion is difficult to derive from the literature because disruptions in COM mechanics and joint/muscle mechanics often occur in parallel (Müller and Blickhan, 2010). Here, we devised an approach to more explicitly dissociate COM mechanical control and what we regard as a first approximation of lower-level peripheral control: joint mechanics. We generated a gait perturbation where simultaneous strong conservation of COM and joint mechanical parameters is not feasible, namely asymmetric leg-length walking. Our primary focus was on parameters affecting locomotor economy [e.g. COTCOM and stance-phase joint mechanical cost of transport (joint work per distance traveled; COTJNT) and joint moments], where deviations from normal walking patterns have been found to increase metabolic cost (Gordon et al., 2009; Massaad et al., 2007). In the case of COM control prioritization, we expected COM mechanics to be more strongly conserved (less affected) between normal and perturbed walking at the expense of joint mechanics. Conversely, if stance-phase joint mechanics better represent the control priority for locomotor economy, they are more likely to maintain patterns more similar to normal walking during leg-length asymmetry perturbation, while COM mechanics will be disrupted. We hypothesized that stance-phase joint mechanics (COTJNT and moments) would be more strongly conserved between normal and perturbed walking than COM mechanics (COTCOM and COM displacement). This hypothesis was motivated by prior work detailing the close association between joint-level mechanics and lower-limb muscle mechanics (Sasaki et al., 2009), and because of the high abundance of motor sensors at a muscle level. Additionally, joint and muscle mechanical behavior appears to be closely related to organismal energetics (Ellerby et al., 2005; Gordon et al., 2009; Selgrade et al., 2017a,b; Umberger and Rubenson, 2011), which further contributed to our hypothesis given the important role of energy minimization as a governing principle of locomotion (Alexander, 1989).

List of abbreviations
     
  • COM

    center of mass

  •  
  • COT

    cost of transport

  •  
  • COTCOM

    center of mass mechanical cost of transport

  •  
  • COTJNT

    joint mechanical cost of transport

  •  
  • iTSM

    integrated total support moment

  •  
  • Wext

    external mechanical work

  •  
  • WJNT

    joint work

MATERIALS AND METHODS

Participants

Healthy adults (N=15: 8 females, 7 males; age 24.4±3.0 years; mass 71.8±11.3 kg; height 1.75±0.05 m; mean±s.d.) were included in this study. Participants were required to have no history of serious lower limb injuries in the past year, and no previously or currently diagnosed balance, stability or coordination diseases, disorders or conditions. They were also required to be within the shoe size range of US 7–11 (8.6±1.2) to accommodate the custom-made platform footwear (described below). Participants provided written informed consent for this study, which was approved by the Human Research Ethics Committee at the University of Western Australia (RA/4/1/7336).

Experimental design

Asymmetric walking was induced by having participants walk with a custom-manufactured ∼90 mm platform shoe on their dominant limb only (equal to 9.7±0.4% of lower limb length). The shoe design is described in detail below. Participant gait mechanics were recorded during continuous walking on a force-plate-instrumented motorized treadmill under four conditions: (1) normal walking in standardized footwear; (2) walking in the asymmetrical footwear using each participant's ‘self-selected’ technique; (3) walking in the asymmetrical footwear using an instructed ‘crouching’ technique (Fig. 1); and (4) walking in the asymmetrical footwear using an instructed ‘vaulting’ technique (described below; Fig. 1).

Fig. 1.

Crouch (left) and vault (right) technique near midstance of the gait cycle.

Fig. 1.

Crouch (left) and vault (right) technique near midstance of the gait cycle.

Comparison between conditions 1 and 2 was used to assess whether COM- or joint-level mechanics are more strongly conserved between normal walking and continuous self-selected walking with an asymmetric leg-length perturbation. (The terms ‘conserved/conservation’ here do not necessitate a total absence of change, but rather we use them to represent the degree to which variables deviate from normal walking.) The leg-length asymmetry intervention was used because it prevents simultaneous strong conservation of COM mechanics and joint mechanics relative to normal walking. A similar divergence in COM and joint work has been reported in symmetrical leg-length crouch walking (Gordon et al., 2009). While we did not specifically test muscle-level control, focusing on the joints allowed us to test a mechanism peripheral to COM mechanics that has direct proprioceptive feedback (Riemann and Lephart, 2002). Furthermore, although joint mechanics do not necessarily mirror muscle mechanics, they are known to be more closely associated with muscle mechanics than the whole-body COM (Sasaki et al., 2009).

Conditions 3 and 4 served as further assessment of whether COM or peripheral mechanics are more strongly conserved during a leg-length asymmetry perturbation. Our rationale was that the self-selected technique will result in stronger conservation of COM or joint mechanical variables compared with other plausible gait solutions if they are a priority control variable and represent the underlying control target. These two imposed conditions also provided the mechanical extremes of possible walking strategies, and thus allowed us to explore the spectrum of possible COM vertical displacement solutions.

It is important to stress that we were primarily concerned with the change between the perturbed and normal walking conditions (conservation of mechanics) rather than the discrete values of mechanical variables. For example, reducing COM displacement as much as possible has been found to be disadvantageous for locomotor economy (Massaad et al., 2007; Ortega and Farley, 2005). The ideal COM displacement might instead reside at some intermediate value (Kuo and Donelan, 2010), with deviations in either direction from this value being sub-optimal (Massaad et al., 2007).

All trials were conducted at 1.3 m s−1, consistent with the average preferred walking speed of previous treadmill studies (Martin et al., 1992; Mohler et al., 2007; Panizzolo et al., 2013; Van Emmerik et al., 2005).

Testing protocol

Limb dominance (12 right, 3 left) was established by asking participants to stand on one leg, with the raised leg deemed dominant (Young et al., 2013). Subsequently, a series of retro-reflective markers were affixed to the participant's trunk and lower limbs in accordance with Besier et al. (2003). Three-dimensional kinematic data were collected using a 10-camera Vicon MX system (250 Hz; Oxford Metrics, Oxford, UK), synchronized to a split-belt (2×6 channel) instrumented treadmill (2000 Hz; Bertec Corporation, Columbus, OH, USA). In standardized footwear, participants completed a 3 min warm-up walk, followed by static and functional trials used to compute a joint coordinate system which included a functional hip joint center and mean helical knee axis (Besier et al., 2003). For this, participants moved their right and left feet (separately) into the following approximate positions whilst maintaining an extended knee: directly anterior (0 deg), 45 deg, 90 deg, 135 deg and directly posterior (180 deg), and completed five consecutive mid-range squats.

First, a 2 min walking trial in normal footwear was completed with the treadmill belt speed set to 1.3 m s−1 (the ‘normal’ condition). The dominant limb shoe (only) was replaced by a ∼90 mm ‘platform’ shoe and the participant began a 3 min exploration period in which they were free to discover their preferred gait pattern under no instruction. A longer familiarization time was intentionally avoided to enable observation of the immediate prioritization response to the perturbation. At the end of the exploration, all participants were deemed, by observation, to have reached a ‘consistent’ technique; that is, displaying no major variation in stride-to-stride technique (e.g. foot strike pattern, vertical movement of the COM). A 2 min trial was collected to assess the self-selected technique when walking in the asymmetrical footwear. Following this, participants completed the two imposed techniques: ‘crouching’ and ‘vaulting’.

For crouching, participants were asked to flex their knee as they walked over the platform shoe so that their peak hip height resembled that of normal walking. For vaulting, participants were asked to vault over the platform shoe, extending their knee as per midstance of normal walking. In this case, they were instructed that their peak hip height relative to their foot should be the same as that during normal walking (i.e. their peak hip height should equal normal walking peak hip height plus the height of the shoe platform). Crouching and vaulting conditions were completed independently, the order of which was reversed for each consecutive participant.

Data processing

Five representative strides from each condition were randomly selected from the recorded data. Marker trajectory and ground reaction force data were low-pass filtered using a zero-lag fourth-order Butterworth filter, with the same cut-off frequency of 15 Hz. Stride events (heel-strike and toe-off) were determined from the vertical ground reaction force. In all computations to follow, we define x, y and z directions as anteroposterior, vertical and mediolateral, respectively.

Computation of COM mechanical variables

We examined two variables across the stride: (1) positive and negative COTCOM, computed as the external COM work (Wext; Eqns 1 and 2), normalized to body mass and distance traveled (J kg−1 m−1), and (2) COM trajectory in the vertical and mediolateral directions (Eqns 7 and 8, respectively). These variables were computed from ground reaction force data. COMCOT was analyzed as opposed to the COM work per step because differences in step frequency may arise between conditions and therefore work per distance will better represent the effect of gait on overall COM work requirements and thus locomotor economy. In computing Wext, the combined limbs method was chosen to quantify the overall resultant COM work, exclusive of individual limb collision costs (Donelan et al., 2002). This method was specifically adopted in order to analyze the overall COM mechanics as opposed to limb-level mechanics. For values of :

formula
(1)
and for values of :
formula
(2)
where Fr is the resultant ground reaction force, vC is the resultant COM velocity, and t1 and t2 are initial and final time boundaries for the stride. The resultant force was computed as the instantaneous sum of the two treadmill force-plate recordings [the force-plate corresponding to the flat shoe limb (f) and the force-plate corresponding to the platform shoe limb (p); Frx=Ffx+Fpx, Fry=Ffy+Fpy and Frz=Ffz+Fpz]. The COM velocities (vCx, vCy and vCz) were computed by integrating the respective components of the combined force recordings and applying integration constants:
formula
(3)
formula
(4)
formula
(5)
where Ff and Fp are the force-plates corresponding to the flat and platform limbs, respectively, with force components denoted by x, y, z. Body mass and gravity (9.81 m s−2) are represented by m and g, respectively, while t1 and t2 are initial and final time boundaries of the stride (heel-strike to heel-strike). Integration constants were set according to Donelan et al. (2002). Briefly, the integration constant for vCx was computed by necessitating the mean vCx over a stride equaled the treadmill velocity and the integration constants for vCy and vCz were computed by necessitating the mean vCy and vCz over a stride equaled zero.
To compute COM displacement (sCx, sCy and sCz), the vCx, vCy and vCz traces were further integrated:
formula
(6)
formula
(7)
formula
(8)
where t1 and t2 are initial and final time boundaries of the stride (heel-strike to heel-strike).

Computation of stance-phase joint mechanical variables

To characterize joint mechanics (ankle, knee and hip), we examined four sets of variables across stance phase: (1) joint angles; (2) net joint and total support moments normalized to body mass, and to body mass and distance traveled per step, respectively (N m kg−1 and N m kg−1 m−1, respectively; Winter, 2009, 1980); (3) instantaneous body mass-specific joint power (W kg−1); and (4) positive and negative COTJNT, computed as joint work (WJNT; Eqns 9 and 10) normalized to body mass and distance traveled (J kg−1 m−1). Joint kinematic and inverse dynamics calculations were performed on both limbs (‘flat’ and ‘platform’) and computed with Vicon Nexus software (Vicon, Oxford Metrics, Oxford, UK). Inertial properties of the foot segment were input, taking into consideration the added mass of the footwear. A combined total value for positive joint work for values of Mω>0, where M represents the joint moment and ω is joint angular velocity, was computed as:
formula
(9)
where values at the ankle, knee and hip are respectively denoted by Af, Kf and Hf for the non-platform shoe (‘flat’) and Ap, Kp and Hp for the platform shoe. t1 and t2 are initial and final time boundaries of the stance phase (heel-strike to toe-off).
The same procedure was applied for total negative joint work for values of Mω<0:
formula
(10)
Supporting body weight has been demonstrated to affect the metabolic cost of locomotion (Kram and Taylor, 1990). The ‘support moment’ represents the total moment required to support the body weight and is composed of the antigravity moments at the individual joints (extension at the hip and knee and plantarflexion at the ankle; Winter, 2009, 1980). The support moment thus serves as a useful cost metric for the overall weight support during gait. The (pre-normalized) integrated net total support moment from each limb was computed and summed to produce a single combined support moment (Eqn 11), which was then normalized to body mass and distance traveled (iTSM; N m kg−1 m−1):
formula
(11)

The non-directional (absolute) percentage change from normal walking was calculated for vertical and mediolateral COM range, positive and negative COTCOM, total positive and negative COTJNT, and the iTSM.

Shoe design

The platform shoe was a modified version of the footwear worn in the normal condition (lightweight, zero heel-to-toe gradient, minimally cushioned with a rubber sole and canvas upper; Volley, Brand Collective, Australia). A block of semi-rigid foam, with a height of approximately 90 mm, was secured to the sole of the platform shoe via adhesive. The foam was crafted to mirror the shape of the sole. However, to increase the base of support and reduce the risk of a fall, 20 mm of additional width was provided at the point of treadmill contact (shoe–ground interface). The height of the foam block as a percentage of dominant limb length (916.2±31.9 mm), ranged from 9.1% to 10.2%. Shoe mass was standardized to ensure equal shoe mass in all four conditions. For the flat shoes, this was achieved by sewing small packages of lead fishing weights to the medial and lateral aspects of the canvas upper.

Statistical analyses

All data were screened for normality. To assess whether COM or joint mechanics were prioritized by our participants, we utilized two approaches. We determined whether significant changes between the four conditions (normal, self-selected, crouch, vault) existed for the collection of COM- and joint-level variables. Analysis of variance (ANOVA; parametric) and Friedman test (non-parametric) repeated-measures statistics were used accordingly, with alpha levels set at 0.05 for all analyses. Significance was followed up with post hoc comparisons; Bonferroni correction (parametric) or Wilcoxon tests (non-parametric) with appropriately adjusted significance (P=0.0125). We tested for differences in temporal parameters using similar ANOVA methods.

Those data that presented with non-normal distributions are indicated in Results with an asterisk; however, where no reference to normality is made, the data have been processed using parametric tests. SPSS 21.0 (Chicago, IL, USA) was used to perform all statistical analyses detailed above.

To further assess how COM and joint mechanical variables changed in the temporal domain between conditions, we performed a cross-correlation analysis (‘xcorr’ in-built function; Matlab 2018a, MathWorks, Natick, MA, USA) on each participant's mean curve for normal versus the asymmetrical conditions (self-selected, crouch and vault). These correlations assess the similarity in the shape of the variable versus time curve but do not consider differences in magnitude. We defined correlations between 1 and 0.8 as very strong, between 0.79 and 0.6 as strong, between 0.59 and 0.4 as moderate, between 0.39 and 0.2 as weak, and between 0.19 and 0 as very weak.

Note that while we present the non-directional percentage difference between the normal condition and the three asymmetrical leg-length conditions (self-selected, crouch, vault), no statistical analyses were run on these data.

RESULTS

Temporal data

Stride rate (non-normally distributed) was assessed for all conditions and presented with an ANOVA main effect. While crouching stride rate (1.00±0.10) exceeded normal stride rate [0.93±0.04; P=0.012*, where the asterisk indicates non-normal distribution of data (see Materials and Methods)], self-selected stride rate (0.95±0.06; P=0.002*) and vaulting stride rate (0.92±0.06; P=0.001*), no other significant differences were present between the four conditions. Stance-phase duration of flat and platform shoe limbs across the four conditions produced an interaction effect. On the flat side, stance-phase duration of normal walking (0.68±0.03 s) exceeded that of the self-selected (0.65±0.04 s; P=0.017) and vault (0.64±0.04 s, P=0.044) conditions, and on the platform side, the crouch stance phase was shorter (0.63±0.05 s) than the stance phase of both the self-selected (0.67±0.05 s; P=0.024) and vault (0.71±0.05 s; P<0.001) techniques. While crouching produced equal stance durations, the platform-limb stance was longer than the flat-limb stance for both the self-selected and vault conditions (P<0.022).

COM mechanics

COM displacement

COM mechanical parameters are displayed in Table 1. A main effect of gait condition was detected for vertical COM displacement. This measure confirmed that our participants generated a range of COM vertical displacements across the self-selected, crouching and vaulting conditions (Fig. 2A). When compared with normal walking (0.05±0.01 m vertical COM displacement), the crouch condition was not significantly different (P>0.999). The self-selected and vault conditions, in contrast, displayed a far greater COM vertical range compared with normal walking (53% and 129% change, respectively; P<0.001). Self-selected asymmetric walking produced a higher COM vertical range than the crouch condition (P=0.009) but a lower range than the vault condition (P<0.001). The mediolateral COM range was also calculated; however, no significant differences were observed between the four conditions (P>0.216; Fig. 2B).

Table 1.

Center of mass and joint mechanical variables

Center of mass and joint mechanical variables
Center of mass and joint mechanical variables
Fig. 2.

Center of mass (COM) vertical and mediolateral displacement over the stride. (A) Vertical displacement; (B) mediolateral displacement. Data begin and end at the normal limb (non-platform shoe) heel-strike. Data are normalized to the center of mass position at initial heel-strike and are presented as means±s.d. (shaded regions) (N=15).

Fig. 2.

Center of mass (COM) vertical and mediolateral displacement over the stride. (A) Vertical displacement; (B) mediolateral displacement. Data begin and end at the normal limb (non-platform shoe) heel-strike. Data are normalized to the center of mass position at initial heel-strike and are presented as means±s.d. (shaded regions) (N=15).

COTCOM

The positive COTCOM (main effect of condition present) was elevated above normal walking during the self-selected condition (P<0.001). The positive COTCOM was also elevated above normal walking in the vaulting condition, but to an even greater extent (P<0.001; Table 1, Fig. 3). Unlike the other two asymmetry conditions, the COTCOM in the crouch condition was not statistically different from that during normal walking (P=0.135). The differences in negative COTCOM exhibited a similar pattern to those of positive COTCOM (non-normally distributed; Table 1, Fig. 3).

Fig. 3.

Non-directional (absolute) percentage change from normal walking for self-selected, crouch and vault conditions. Data (means±s.d., N=15) include: vertical and mediolateral center of mass (COM) range (m), positive and negative center of mass cost of transport (COTCOM; J kg−1 m−1), total positive and negative joint cost of transport (COTJNT; J kg−1 m−1) and integrated net total support moment (iTSM) normalized to body mass and distance traveled (N m kg−1 m−1).

Fig. 3.

Non-directional (absolute) percentage change from normal walking for self-selected, crouch and vault conditions. Data (means±s.d., N=15) include: vertical and mediolateral center of mass (COM) range (m), positive and negative center of mass cost of transport (COTCOM; J kg−1 m−1), total positive and negative joint cost of transport (COTJNT; J kg−1 m−1) and integrated net total support moment (iTSM) normalized to body mass and distance traveled (N m kg−1 m−1).

Joint mechanics

Stance-phase joint kinematic and kinetic gait profiles

Compared with normal walking, crouched walking was characterized by platform-limb flexed hip and knee joint postures throughout stance phase (Fig. 4). The near-isometric behavior of the knee joint was accompanied by an increased net knee extensor moment, deviating considerably from normal gait mechanics (Fig. 5). Conversely, vaulting appeared to utilize platform-limb knee and hip joint extension during the second half of stance phase to increase vertical COM displacement. As would be expected, the resulting kinematic traces in the vaulting stance leg closely mirror those of normal walking (Fig. 4). Furthermore, around the period of double-support, vertical ascent onto the platform shoe is assisted by an earlier onset of flat-limb positive ankle power, coupled with increased platform-limb positive hip power (Fig. 6). The self-selected condition was associated with midrange hip and knee extension relative to the imposed techniques. The large stance-phase knee moment and ankle power associated with crouching and vaulting, respectively, were avoided during the self-selected gait.

Fig. 4.

Joint angles during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15).

Fig. 4.

Joint angles during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15).

Fig. 5.

Net mass-specific joint moments during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15). TSM, total support moment.

Fig. 5.

Net mass-specific joint moments during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15). TSM, total support moment.

Fig. 6.

Net mass-specific joint power during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15).

Fig. 6.

Net mass-specific joint power during stance phase for the flat and platform limb. A normal walking trace is included for comparison. The traces begin at heel-strike and end at toe-off of the respective limb. Data are presented as means±s.d. (shaded regions) (N=15).

Stance-phase COTJNT

Total positive (normally distributed) and negative (non-normally distributed) stance-phase COTJNT is presented in Table 1. Main effects were detected for both measures. Post hoc analyses revealed increases in positive and negative COTJNT in all leg-length asymmetry conditions when compared with values of normal walking (P<0.003). The self-selected technique produced total COTJNT closest to normal walking, with an absolute change of 17% and 31% in positive and negative COTJNT, respectively (Fig. 3). These differences were further exaggerated in the crouch (positive: 20%, negative 44%) and vault (positive: 36%, negative 57%) conditions (Fig. 3). Total positive COTJNT was greater when vaulting than in both the self-selected and crouch trials (P<0.009), which were not significantly different from one another (P=0.959). Total negative COTJNT was lower for the self-selected than for both the crouch and vault techniques (P<0.006*), whilst the two imposed conditions did not vary significantly (P=0.088*).

Work distribution between joints

The distribution of positive and negative COTJNT across the joints throughout stance phase did not differ substantially when walking with the leg-length asymmetry perturbation compared with normal walking (Table 2). In the normal condition, ankle, knee (non-normal distribution) and hip joint positive COTJNT contributions of 35.9±4.1%, 22.9±5.7% and 41.2±4.9% to the total mechanical COT of the limbs (the sum of the COTJNT in each joint from both limbs) were observed, respectively. The ankle, knee and hip (non-normal distribution) joint negative COTJNT accounted for 32.9±8.8%, 43.4±9.2% and 23.7±8.3%, respectively (for the percentage COTJNT contribution in the other conditions, see Table 2). Significance testing revealed the ankle positive COTJNT contribution was greater in the normal condition than in the vault condition (P=0.002). This was the only percentage COTJNT contribution (including both positive and negative values) to deviate significantly from normal walking across all measured joints.

Table 2.

Percentage COTJNT distribution between the ankle, knee and hip joints

Percentage COTJNT distribution between the ankle, knee and hip joints
Percentage COTJNT distribution between the ankle, knee and hip joints
iTSM

Stance-phase support moment parameters are displayed in Table 1. A main effect of gait condition was detected for iTSM. All asymmetrical gaits produced greater iTSM than normal walking (P<0.001), with no significant difference detected between self-selected and vault conditions (P=0.139). Both the self-selected and the vaulting asymmetry techniques, however, displayed significantly (P<0.05) lower iTSM than the crouching condition. The absolute percentage change between the asymmetry conditions and normal walking was 61%, 132% and 49% for the self-selected, crouch and vault conditions, respectively (Fig. 3).

Cross-correlation

Cross-correlations of the normal condition versus each asymmetrical gait condition (self-selected, crouch and vault) are presented in Table 3. COM trajectories produced strong (>0.7) to very strong (>0.8) correlations for each condition. The cross-correlation of most joint variables was also strong to very strong across conditions, but some weak correlations were also exhibited (Table 3). Overall, the strongest correlations existed between normal walking and the self-selected perturbed condition.

Table 3.

Cross-correlation results from COM data, and kinematic and kinetic joint data

Cross-correlation results from COM data, and kinematic and kinetic joint data
Cross-correlation results from COM data, and kinematic and kinetic joint data

DISCUSSION

The current study questioned whether the COM or peripheral structures, in this case joint mechanics, reflect targets of control prioritized by the central nervous system during human walking. This was assessed indirectly by quantifying the efficacy with which COM and joint mechanical costs were conserved (i.e. how much/little they changed relative to normal walking) when humans were exposed to a continuous asymmetrical perturbation in the form of uneven leg-length (footwear heights). Additionally, we imposed two alternative techniques for negotiating the perturbation, namely ‘crouching’ and ‘vaulting’, which spanned the spectrum of possible COM vertical displacement solutions. Our hypothesis that conservation of joint-level mechanics would be stronger than conservation of COM mechanics was supported. During stance phase, the self-selected technique minimized joint-level disturbances compared with those at the COM. This finding indicates objectives other than the literal control of the whole-body COM may be given precedence in the neuromuscular control scheme for economical walking, at least during steady-state locomotion and prior to longer-term motor learning. It must be noted that our findings do not conclusively point to the joints as the specific target of control, nor do we propose there is a direct sensor for COTJNT or overall support moments. Rather, the stronger conservation of joint mechanics observed here is interpreted to reflect a general peripheral-level control scheme for economical locomotion arising from joint and/or muscle feedback.

COM versus peripheral (joint) mechanical conservation

Studies specifically comparing COM- and peripheral-level control are sparse and offer conflicting findings. It has been suggested that variation in joint mechanics is a strategy to conserve higher-level mechanics including whole-limb trajectories and power generation, and COM motion. For example, during postural balance tasks, humans have been observed to regulate COM-related behavior through coordination of lower-level structures including joints and muscles (Nashner, 1977; Nashner and McCollum, 1985; Ting and Macpherson, 2005; Torres-Oviedo et al., 2006). Joint-mediated control of whole-limb mechanics (which are closely linked to COM mechanics) has also been observed both in unperturbed human walking (conserved limb power; Toney and Chang, 2016) and after peripheral nerve injury in walking cats and rodents (conserved limb trajectories; Bauman and Chang, 2013; Chang et al., 2009). Panizzolo et al. (2017) likewise showed that individual joint mechanics (ankle, knee, hip) adapt to various unanticipated terrain disturbances in ways that maintain total positive mechanical work of the lower limb, irrespective of the type of perturbation. Albeit not directly studying walking gait, a pivotal series of running and hopping studies have also shed light on central versus peripheral mechanical conservation. Several groups have shown that humans maintain their COM mechanics by adjusting leg stiffness across various conditions including running speed, hopping frequency and surface stiffness (Chang et al., 2008; Ferris et al., 1998; Ferris and Farley, 1997; Yen et al., 2009).

Taken together, the aforementioned studies indicate the nervous system may prioritize conservation of COM rather than joint-level mechanics. This conclusion is seemingly in contrast with findings of the current study. The previous studies did not, however, directly asses COM- or joint-level costs in the form of mechanical work or COT. This is an important consideration because, as this study shows, even altered joint kinematic and kinetic profiles do not necessarily impair COTJNT (see below for further discussion). It is not clear, therefore, whether the conservation of higher-level mechanics, including the COM, in the previous studies necessarily rules out control of lower-level costs at joints and/or muscles, despite the observed changes in the measured joint mechanics. The current study is arguably less ambiguous with regard to COM- versus joint-level control, in part because it was designed specifically to limit simultaneous strong conservation of COM- and joint-level costs. It is also worth noting that many human subject tests have specific requirements which restrict technique (e.g. hop at a set frequency or set height). These instructions might influence how the subject perceives the task goal and thus might artificially impart conservation of COM- and/or joint-level mechanics. The present study was careful to minimize any instruction in the self-selected condition.

Work on cursorial ground birds which, similarly, do not take instruction on their adopted movement behavior, paints a more complex picture of COM versus joint control strategies. In a comprehensive series of studies on running guinea fowl negotiating both anticipated and unanticipated perturbations, Daley and colleagues provide observations which contradict COM dynamics as the direct target of control (Birn-Jeffery et al., 2014; Daley et al., 2006; Daley and Biewener, 2006). While the authors show that the overall limb-loading magnitude is consistent with spring–mass dynamics, the COM dynamics are not maintained relative to unperturbed gait. This body of work disputes the notion that COM dynamics are strongly conserved, and instead suggests some aspects of limb or joint loading are more likely to be the direct targets of control (Daley et al., 2006; Daley and Biewener, 2006). Full and Koditschek (1999) similarly suggest that any substantial shift in COM behavior from the original ‘template’ indicates that COM mechanics are not a ‘literal control target for the musculoskeletal system’ (Full and Koditschek, 1999). Other experiments provide indirect support for a joint-level control scheme. For example, Kao et al. (2010) showed that unexpected reductions in the ankle joint torque delivered by a powered exoskeleton are accommodated by biological (muscle) moments so that the total moment generation is remarkably similar between perturbed and non-perturbed walking.

The present study indicates that conservation of COM mechanics is not always prioritized during human locomotion, and further challenges the notion that the COM is the principal target of control. There are several lines of evidence suggesting conservation of lower-level peripheral factors, as indicated by joint mechanical costs, are prioritized over conservation of COM costs after induced leg-length asymmetry, as detailed below.

Mechanical COT conservation

First, we demonstrated that positive COTJNT is more strongly conserved (changed less relative to normal walking) than positive COTCOM during a gait perturbation in which simultaneous conservation of both forms of work is not easily achievable. This is especially important considering that minimization of mechanical work, and work-derived metabolic energy predictions, have been an underlying basis for a COM control strategy (Srinivasan, 2010; Srinivasan and Ruina, 2006). The conservation of COTJNT over COTCOM work has a mechanistic explanation if energy cost is, in fact, a locomotor objective. Joint work, unlike COM work, accounts for simultaneous positive and negative work at the joints (Zatsiorsky, 2002), similar to how the individual-limb COM work approach captures simultaneous positive and negative work of the left and right limbs (Donelan et al., 2002). As a result, COTJNT is more strongly associated with muscle mechanical energy (Sasaki et al., 2009) and therefore better captures global (organismal) metabolic energetics compared with COTCOM (Gordon et al., 2009; Umberger and Rubenson, 2011). However, it remains unclear whether the nervous system senses and regulates directly at the level of the joints. While sensory feedback from joints exist, muscle-level targets of control (such as muscle fiber strain, force or activation) might instead dictate the preferred gait solution, with joint work conservation occurring because it is more strongly coupled to muscle function than the COM. The observed conservation of joint mechanics might thus reflect the nervous system optimizing whole-body energy costs based on correlates that are more rapidly sensed than COTJNT (Wong et al., 2017).

It should be noted that minimization of COTCOM does not minimize metabolic energy (Gordon et al., 2009; Massaad et al., 2007; Ortega and Farley, 2005), and therefore we did not expect that COM work should be as low as possible even if it is a target of control. Rather, we would expect that the change in COTCOM between normal and asymmetric walking conditions should be minimal. This is because deviations in COTCOM, both above and below normal walking values, increase the energy cost of walking (Massaad et al., 2007). In contrast, however, our results provide evidence that controlling COTCOM – in particular, avoiding deviations in COTCOM from that of normal walking – is not prioritized during human walking if it degrades other potentially stronger control targets (e.g. joints and/or muscle mechanics).

It is also important to acknowledge that in recent perturbed walking experiments, improved gait symmetry in various biomechanical parameters (e.g. step length) may conserve COM and/or joint mechanics relative to normal walking, but does not necessarily result in energetic optimality (Sánchez et al., 2017). Therefore, it remains possible that COTJNT may have been conserved irrespective of any link to energetic task goals. If this were the case, other joint-level optimality criteria, for example joint stress (Alessandro et al., 2018), might have factored into the observed regulation of gait behavior. Identifying the relative contribution of energetic and mechanical determinants of joint mechanical conservation is challenging but will prove important to further uncover underlying control objectives in human locomotion.

Gait technique selection

Second, only strong conservation of joint mechanical costs was specific to the self-selected gait solution; COTJNT and support moment were minimized in the self-selected condition (Table 1, Fig. 3). This was also reflected to a degree in cross-correlation analyses, which showed the strongest correlation of joint variables between the normal and the self-selected conditions (Table 3). In contrast, stronger conservation of COM costs occurred in the imposed (non-preferred) crouch condition; positive and negative COTCOM, and vertical COM range, were significantly lower in magnitude, and closer to normal walking values, during crouch walking compared with the self-selected asymmetric gait (Table 1, Fig. 3). In fact, unlike the self-selected asymmetric gait, there were no statistical differences in the parameters between normal walking and crouch walking. Similarly, cross-correlations were very strong (>0.8) between normal walking and not only the self-selected condition but also the crouch condition (Table 3; although in general it should be noted that the shape of the COM trajectory appears less impacted by the perturbation than the overall magnitude of COTCOM).

These results offer evidence that direct, purposeful conservation of COM mechanics is not a predictable characteristic of steady-state human gait in which energetic minimization is likely an important objective. Instead, peripheral structures are arguably the more plausible control targets that are sensed and regulated during walking in order to satisfy the task objective of economical gait.

Given the COM displayed a mechanical profile most similar to that of normal walking in the crouch condition, why did participants avoid a crouched gait when selecting their preferred technique? This can be understood when examined in context with joint mechanics. Whilst crouching best maintained COM costs, it was also found to produce an iTSM that deviated substantially from normal walking values (Fig. 3). A crouched gait and the concomitant elevation in iTSM are expected to incur a considerable increase in muscle activation and force, (Abitbol, 1995; Biewener, 1989; Carey and Crompton, 2005; Hicks et al., 2008; Hsu et al., 1993; Perry et al., 1975; Steele et al., 2013, 2010) and, by extension, locomotor energetics (Kram, 2000; Kram and Taylor, 1990; Roberts et al., 1997). Rather than adopting a COM-conserving gait (crouch), subjects instead preferred a gait solution that minimized the increase in both COTJNT and joint moments at the expense of COM mechanics.

Conserved distribution of joint work

Finally, the distribution of work between joints across normal walking and the asymmetric walking conditions provide further evidence that joint mechanics are largely conserved in response to a leg-length asymmetry perturbation. Whereas total positive COTJNT was found to increase in all conditions relative to normal walking, the distribution of positive COTJNT remained largely unchanged between the normal, self-selected and crouch techniques. Only the ankle showed a statistical difference between the normal and vault conditions. In general, decreases in the ankle contribution to positive COTJNT on the platform shoe side were compensated for by increases on the normal shoe side, allowing the ankles to continue to contribute ∼36% to total work.

Are joint kinematics and kinetics both conserved after induced leg-length asymmetry?

It is conceivable that overall support moments and COTJNT are optimally conserved after perturbation, whilst joint kinematics (angles) are altered. Compensation of joint kinematics, for example, has been suggested to be a control strategy by which higher-level gait features, including whole-limb kinematics, are maintained following neuromuscular injury (Bauman and Chang, 2013; Chang et al., 2009). Our analyses of individual joint kinematics, moments and powers provide insight into the extent of joint-level conservation. Similar to Chang et al. (2009), we observed modification of all joint angles during the self-selected gait solution to induced leg-length asymmetry, both for the limb on the platform shoe side and for the limb on the unaltered (flat) shoe side. Unlike joint moments and COTJNT, these joint kinematic modifications were not minimized in the self-selected condition; the smallest deviation in joint angles was observed in the vaulting condition (Fig. 4). Thus, motor redundancy of joint kinematics may aid in the conservation of joint kinetic variables (work and moments). It is important to note, however, that whilst there is clearly a larger offset in joint angle (posture change) in the self-selected gait compared with vaulting, the angular excursions and velocities over the stance phase are greater during vaulting. This can contribute to both the increase in the moments and COTJNT required at the joints during the vaulting gait (Figs 5 and 6). When comparing individual joint moment and power, some deviation is evident during the self-selected gait condition compared with normal walking. Nevertheless, these deviations are smallest overall in the self-selected condition compared with the two imposed conditions (crouching and vaulting), a finding reflected by the stronger cross-reactions of most joint moment and power traces between normal and self-selected conditions. This observation is consistent with the overall smallest effect on COTJNT and net support moments in the self-selected condition.

Is the COM a direct target of control that is sensed?

Several lines of inquiry suggest COM mechanics are a target of neuromuscular control during walking. The view that controlling COM mechanics is important for economical locomotion is often supported by modeling studies, many of which capture salient features of limbed locomotion when using COM mechanical energetics (or metabolic energetics derived from COM mechanics) as their objective function (Alexander, 1980; Ruina et al., 2005; Srinivasan and Ruina, 2006). For instance, in an attempt to determine why humans select walking and running gaits from the myriad of possible biomechanical variations, Srinivasan and Ruina (2006) utilized a basic bipedal pendular model onto which they imposed the goal of minimizing the mechanical COT. This simple model, even when devoid of elastic properties, discovered walking (inverted pendulum) and running (impulsive bouncing) gait solutions at low and high velocities, respectively. Others have proposed that COM control is central to gait stability, which may, in turn, influence locomotor economy (Donelan et al., 2004; Ijmker et al., 2013). Several studies indicate that human limb mechanics are adjusted to maintain a desirable COM kinematic state (Aminiaghdam et al., 2017; Grimmer et al., 2008; Hof et al., 2010, 2005; Townsend, 1985). These COM control schemes, based largely on COM position and velocity, help explain stabilization after perturbations, but also stability during steady-state locomotion (Wang and Srinivasan, 2014).

Under these mechanisms of COM control, the COM state must be either sensed directly or estimated indirectly through other sensory modalities. It is conceivable that the vestibular or visual system, intestinal sensors, proprioceptive feedback or some combination of these provides the necessary sensory input. How plausible these mechanisms are as a sensor for the COM mechanical state has recently been reviewed (Bruijn and van Dieën, 2018), but as the authors point out, whether these sensory modalities are, in fact, mapping COM kinematics and kinetics during gait remains unexplored. Some authors have even proposed that stable steady-state walking can occur in the absence of neural feedback (Garcia et al., 1998; McGeer, 1990).

The current study does not directly test whether the COM mechanical state is sensed. Thus, we cannot definitively discount the COM as a target of control, responsible for the observed mechanical patterns of normal and leg-length asymmetry walking. However, our finding that COM mechanics are not prioritized when they are pitted against joint mechanics provides initial support for a non-COM-based control scheme. Our results are indicative of peripheral control, which we postulate resides at the joint and/or muscle level and suggest that stereotypical COM mechanics may be a derived characteristic. Whether our results generalize to other forms of gait perturbation or normal unperturbed walking is not known. Further experiments that determine more directly whether joint/muscle targets of control indeed dictate observed COM mechanical patterns will prove important for understanding the motor control of walking.

Limitations

This study considers the primary task objective to be energetic cost minimization. Energy minimization is pervasive in steady-state locomotion. However, other task objectives such as stability, musculoskeletal (fatigue/injury avoidance) and psychological (comfort, pain avoidance) factors may also have motivated the self-selected gait mechanics we observed. In the extreme case, the COM may have been the principal control target for a different task objective (e.g. stability) where the self-selected COM mechanics may be the optimally stable solution. This interpretation, however, lacks clear evidence. Although speculative, we also cannot rule out that the preferred gait solution does not reflect any specific task-goal objective (or combination of objectives). This might occur if the preferred gait arises through a feedback-mediated central pattern generator encoding joint mechanics.

No asymmetrical footwear familiarization was provided to participants prior to attending the laboratory and was only minimally provided prior to testing. Limited familiarization allowed us to determine acute control responses, which was our intended objective. However, future work could consider the effect of adaptation to identify shifts in control with training. Finally, a consideration of swing-phase joint mechanics when walking with induced leg-length asymmetry may also provide a more complete understanding of control strategies.

For the current study, we held speed constant in order to compare magnitudes across key variables from each condition, and to present a speed-independent conclusion. It is possible, however, that our COM and joint mechanics were influenced by the experimental speed selected. For example, increased walking speed has been associated with increased vertical and decreased mediolateral COM displacement (Orendurff et al., 2004). An interesting future direction may be to administer the same experiment but allow all conditions to be performed at the subject's preferred walking speed unique to that condition.

Despite these limitations, our finding that conserved joint mechanics are prioritized is consistent with a neuromuscular control scheme of walking defined by targeted control at a peripheral musculoskeletal level rather than the COM.

Conclusions

In summary, COM mechanics serve as a useful metric capturing fundamental features of legged locomotion. However, we propose that the priority for conserving joint mechanics indicates that control targets most likely reside in peripheral musculoskeletal structures as opposed to the COM. We suggest that joint mechanics are a better proxy for the underlying peripheral control of walking. Thus, joint mechanical constraints and/or cost functions may offer advantages over those applied to the COM when modeling human locomotion. The results from this study also have implications for understanding both normal and pathological gait, as well as for bio-inspired robots and wearable technologies (e.g. exoskeletons) where locomotor control is a critical design feature.

Acknowledgements

The authors wish to acknowledge Drs Young-Hui Chang, Monica Daley and Joseph Hamill and two anonymous reviewers for their constructive review and insightful feedback on earlier versions of this manuscript. The authors also wish to acknowledge Dr Suzanne Cox for thoughtful discussions.

Footnotes

Author contributions

Conceptualization: K.A.M., J.R.; Methodology: K.A.M., D.D., J.R.; Formal analysis: K.A.M., J.R.; Investigation: K.A.M., J.R.; Data curation: K.A.M., D.D.; Writing - original draft: K.A.M., J.R.; Writing - review & editing: K.A.M., D.D., J.R.; Supervision: J.R.; Project administration: K.A.M., D.D., J.R.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Data availability

Data from this study are available from the Zenodo repository: doi:10.5281/zenodo.2613075

References

Abitbol
,
M. M.
(
1995
).
Speculation on posture, locomotion, energy consumption, and blood flow in early hominids
.
Gait Posture
3
,
29
-
37
.
Alessandro
,
C.
,
Rellinger
,
B. A.
,
Barroso
,
F. O.
and
Tresch
,
M. C.
(
2018
).
Adaptation after vastus lateralis denervation in rats demonstrates neural regulation of joint stresses and strains
.
eLife
7
,
e38215
.
Alexander
,
R. M. N.
(
1980
).
Optimum walking techniques for quadrupeds and bipeds
.
J. Zool.
192
,
97
-
117
.
Alexander
,
R. M.
(
1989
).
Optimization and gaits in the locomotion of vertebrates
.
Physiol. Rev.
69
,
1199
-
1227
.
Aminiaghdam
,
S.
,
Rode
,
C.
,
Müller
,
R.
and
Blickhan
,
R.
(
2017
).
Increasing trunk flexion transforms human leg function into that of birds despite different leg morphology
.
J. Exp. Biol.
220
,
478
-
486
.
Bauman
,
J. M.
and
Chang
,
Y.-H.
(
2013
).
Rules to limp by: joint compensation conserves limb function after peripheral nerve injury
.
Biol. Lett.
9
,
20130484
.
Besier
,
T. F.
,
Sturnieks
,
D. L.
,
Alderson
,
J. A.
and
Lloyd
,
D. G.
(
2003
).
Repeatability of gait data using a functional hip joint centre and a mean helical knee axis
.
J. Biomech.
36
,
1159
-
1168
.
Biewener
,
A. A.
(
1989
).
Scaling body support in mammals: limb posture and muscle mechanics
.
Science
245
,
45
-
48
.
Birn-Jeffery
,
A. V.
,
Hubicki
,
C. M.
,
Blum
,
Y.
,
Renjewski
,
D.
,
Hurst
,
J. W.
and
Daley
,
M. A.
(
2014
).
Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain
.
J. Exp. Biol.
217
,
3786
-
3796
.
Blickhan
,
R.
(
1989
).
The spring-mass model for running and hopping
.
J. Biomech.
22
,
1217
-
1227
.
Blickhan
,
R.
and
Full
,
R. J.
(
1987
).
Locomotion energetics of the ghost crab: II. Mechanics of the centre of mass during walking and running
.
J. Exp. Biol.
130
,
155
-
174
.
Bruijn
,
S. M.
and
van Dieën
,
J. H.
(
2018
).
Control of human gait stability through foot placement
.
J. R. Soc. Interface
15
,
20170816
.
Carey
,
T. S.
and
Crompton
,
R. H.
(
2005
).
The metabolic costs of ‘bent-hip, bent-knee’ walking in humans
.
J. Hum. Evol.
48
,
25
-
44
.
Cavagna
,
G. A.
and
Kaneko
,
M.
(
1977
).
Mechanical work and efficiency in level walking and running
.
J. Physiol.
268
,
467
-
481
.
Cavagna
,
G. A.
,
Saibene
,
F. P.
and
Margaria
,
R.
(
1964
).
Mechanical work in running
.
J. Appl. Physiol.
19
,
249
-
256
.
Cavagna
,
G. A.
,
Thys
,
H.
and
Zamboni
,
A.
(
1976
).
The sources of external work in level walking and running
.
J. Physiol.
262
,
639
-
657
.
Cavagna
,
G. A.
,
Heglund
,
N. C.
and
Taylor
,
C. R.
(
1977
).
Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure
.
Am. J. Physiol. Integr. Comp. Physiol.
233
,
243
-
261
.
Chang
,
Y.-H.
,
Roiz
,
R. A.
and
Auyang
,
A. G.
(
2008
).
Intralimb compensation strategy depends on the nature of joint perturbation in human hopping
.
J. Biomech.
41
,
1832
-
1839
.
Chang
,
Y.-H.
,
Auyang
,
A. G.
,
Scholz
,
J. P.
and
Nichols
,
T. R.
(
2009
).
Whole limb kinematics are preferentially conserved over individual joint kinematics after peripheral nerve injury
.
J. Exp. Biol.
212
,
3511
-
3521
.
Daley
,
M. A.
and
Biewener
,
A. A.
(
2006
).
Running over rough terrain reveals limb control for intrinsic stability
.
Proc. Natl. Acad. Sci. USA
103
,
15681
-
15686
.
Daley
,
M. A.
,
Usherwood
,
J. R.
,
Felix
,
G.
and
Biewener
,
A. A.
(
2006
).
Running over rough terrain: guinea fowl maintain dynamic stability despite a large unexpected change in substrate height
.
J. Exp. Biol.
209
,
171
-
187
.
Donelan
,
J. M.
,
Kram
,
R.
and
Kuo
,
A. D.
(
2002
).
Simultaneous positive and negative external mechanical work in human walking
.
J. Biomech.
35
,
117
-
124
.
Donelan
,
J. M.
,
Shipman
,
D. W.
,
Kram
,
R.
and
Kuo
,
A. D.
(
2004
).
Mechanical and metabolic requirements for active lateral stabilization in human walking
.
J. Biomech.
37
,
827
-
835
.
Ellerby
,
D. J.
,
Henry
,
H. T.
,
Carr
,
J. A.
,
Buchanan
,
C. I.
and
Marsh
,
R. L.
(
2005
).
Blood flow in guinea fowl Numida meleagris as an indicator of energy expenditure by individual muscles during walking and running
.
J. Physiol.
564
,
631
-
648
.
Farley
,
C. T.
and
Ko
,
T. C.
(
1997
).
Mechanics of locomotion in lizards
.
J. Exp. Biol.
200
,
2188
-
2188
.
Ferris
,
D. P.
and
Farley
,
C. T.
(
1997
).
Interaction of leg stiffness and surface stiffness during human hopping
.
J. Appl. Physiol.
82
,
15
-
22
.
Ferris
,
D. P.
,
Louie
,
M.
and
Farley
,
C. T.
(
1998
).
Running in the real world: adjusting leg stiffness for different surfaces
.
Proc. R. Soc. B
265
,
989
-
994
.
Ferris
,
D. P.
,
Liang
,
K.
and
Farley
,
C. T.
(
1999
).
Runners adjust leg stiffness for their first step on a new running surface
.
J. Biomech.
32
,
787
-
794
.
Full
,
R.
and
Koditschek
,
D. E.
(
1999
).
Templates and anchors: neuromechanical hypotheses of legged locomotion on land
.
J. Exp. Biol.
202
,
3325
-
3332
.
Garcia
,
M.
,
Chatterjee
,
A.
,
Ruina
,
A.
and
Coleman
,
M.
(
1998
).
The simplest walking model: stability, complexity, and scaling
.
J. Biomech. Eng.
120
,
281
-
288
.
Geyer
,
H.
,
Seyfarth
,
A.
and
Blickhan
,
R.
(
2006
).
Compliant leg behaviour explains basic dynamics of walking and running
.
Proc. R. Soc. B
273
,
1861
-
1867
.
Gitter
,
A.
,
Czerniecki
,
J.
and
Weaver
,
K.
(
1995
).
A reassessment of center-of-mass dynamics as a determinate of the metabolic inefficiency of above-knee amputee ambulation
.
Am. J. Phys. Med. Rehabil.
74
,
332
-
338
.
Gordon
,
K. E.
,
Ferris
,
D. P.
and
Kuo
,
A. D.
(
2009
).
Metabolic and mechanical energy costs of reducing vertical center of mass movement during gait
.
Arch. Phys. Med. Rehabil.
90
,
136
-
144
.
Griffin
,
T. M.
and
Kram
,
R.
(
2000
).
Penguin waddling is not wasteful
.
Nature
408
,
929
-
930
.
Griffin
,
T. M.
,
Main
,
R.
and
Farley
,
C.
(
2004
).
Biomechanics of quadrupedal walking: how do four-legged animals achieve inverted pendulum-like movements?
J. Exp. Biol.
207
,
3545
-
3558
.
Grimmer
,
S.
,
Ernst
,
M.
,
Gunther
,
M.
and
Blickhan
,
R.
(
2008
).
Running on uneven ground: leg adjustment to vertical steps and self-stability
.
J. Exp. Biol.
211
,
2989
-
3000
.
Heglund
,
N. C.
,
Fedak
,
M. A.
,
Taylor
,
C. R.
and
Cavagna
,
G. A.
(
1982
).
Energetics and mechanics of terrestrial locomotion IV. Total mechanical energy changes as a function of speed and body size in birds and mammals
.
J. Exp. Biol.
97
,
57
-
66
.
Hicks
,
J. L.
,
Schwartz
,
M. H.
,
Arnold
,
A. S.
and
Delp
,
S. L.
(
2008
).
Crouched postures reduce the capacity of muscles to extend the hip and knee during the single-limb stance phase of gait
.
J. Biomech.
41
,
960
-
967
.
Hof
,
A. L.
,
Gazendam
,
M. G. J.
and
Sinke
,
W. E.
(
2005
).
The condition for dynamic stability
.
J. Biomech.
38
,
1
-
8
.
Hof
,
A. L.
,
Vermerris
,
S. M.
and
Gjaltema
,
W. A.
(
2010
).
Balance responses to lateral perturbations in human treadmill walking
.
J. Exp. Biol.
213
,
2655
-
2664
.
Hsu
,
A.-T.
,
Perry
,
J.
,
Gronley
,
J. K.
and
Hislop
,
H. J.
(
1993
).
Quadriceps force and myoeletric activity during flexed knee stance
.
Clin. Orthop. Relat. Res.
288
,
254
-
262
.
Ijmker
,
T.
,
Houdijk
,
H.
,
Lamoth
,
C. J. C.
,
Beek
,
P. J.
and
van der Woude
,
L. H.
(
2013
).
Energy cost of balance control during walking decreases with external stabilizer stiffness independent of walking speed
.
J. Biomech.
46
,
2109
-
2112
.
Kao
,
P.-C.
,
Lewis
,
C. L.
and
Ferris
,
D. P.
(
2010
).
Joint kinetic response during unexpectedly reduced plantar flexor torque provided by a robotic ankle exoskeleton during walking
.
J. Biomech.
43
,
1401
-
1407
.
Kram
,
R.
(
2000
).
Muscular force or work: what determines the metabolic energy cost of running
.
Exerc. Sport Sci. Rev.
28
,
138
-
143
.
Kram
,
R.
and
Taylor
,
C. R.
(
1990
).
Energetics of running: a new perspective
.
Nature
346
,
265
-
267
.
Kuo
,
A. D.
and
Donelan
,
J. M.
(
2010
).
Dynamic principles of gait and their clinical implications
.
Phys. Ther.
90
,
157
-
174
.
Martin
,
P. E.
,
Rothstein
,
D. E.
and
Larish
,
D. D.
(
1992
).
Effects of age and physical activity status on the speed-aerobic demand relationship of walking
.
J. Appl. Physiol.
73
,
200
-
206
.
Massaad
,
F.
,
Lejeune
,
T. M.
and
Detrembleur
,
C.
(
2007
).
The up and down bobbing of human walking: a compromise between muscle work and efficiency
.
J. Physiol.
582
,
789
-
799
.
McGeer
,
T.
(
1990
).
Passive dynamic walking
.
Int. J. Rob. Res.
9
,
62
-
82
.
Mohler
,
B. J.
,
Thompson
,
W. B.
,
Creem-Regehr
,
S. H.
,
Pick
,
H. L.
and
Warren
,
W. H.
(
2007
).
Visual flow influences gait transition speed and preferred walking speed
.
Exp. Brain Res.
181
,
221
-
228
.
Müller
,
R.
and
Blickhan
,
R.
(
2010
).
Running on uneven ground: leg adjustments to altered ground level
.
Hum. Mov. Sci.
29
,
578
-
589
.
Nashner
,
L. M.
(
1977
).
Fixed patterns of rapid postural responses among leg muscles during stance
.
Exp. Brain Res.
30
,
13
-
24
.
Nashner
,
L. M.
and
McCollum
,
G.
(
1985
).
The organization of human postural movements: a formal basis and experimental synthesis
.
Behav. Brain Sci.
8
,
135
-
150
.
Orendurff
,
M. S.
,
Segal
,
A. D.
,
Klute
,
G. K.
,
Berge
,
J. S.
,
Rohr
,
E. S.
and
Kadel
,
N. J.
(
2004
).
The effect of walking speed on center of mass displacement
.
J. Rehabil. Res. Dev.
41
,
829
.
Ortega
,
J. D.
and
Farley
,
C. T.
(
2007
).
Individual limb work does not explain the greater metabolic cost of walking in elderly adults
.
J. Appl. Physiol.
102
,
2266
-
2273
.
Ortega
,
J. D.
and
Farley
,
C. T.
(
2005
).
Minimizing center of mass vertical movement increases metabolic cost in walking
.
J. Appl. Physiol.
99
,
2099
-
2107
.
Panizzolo
,
F. A.
,
Green
,
D. J.
,
Lloyd
,
D. G.
,
Maiorana
,
A. J.
and
Rubenson
,
J.
(
2013
).
Soleus fascicle length changes are conserved between young and old adults at their preferred walking speed
.
Gait Posture B
38
,
764
-
769
.
Panizzolo
,
F. A.
,
Lee
,
S.
,
Miyatake
,
T.
,
Rossi
,
D. M.
,
Siviy
,
C.
,
Speeckaert
,
J.
,
Galiana
,
I.
and
Walsh
,
C. J.
(
2017
).
Lower limb biomechanical analysis during an unanticipated step on a bump reveals specific adaptations of walking on uneven terrains
.
J. Exp. Biol.
220
,
4169
-
4176
.
Perry
,
J.
,
Antonelli
,
D.
and
Ford
,
W.
(
1975
).
Analysis of knee-joint forces during flexed-knee stance
.
J. Bone Jt. Surg.
57
,
961
-
967
.
Riemann
,
B. L.
and
Lephart
,
S. M.
(
2002
).
The sensorimotor system, part II: the role of proprioception in motor control and functional joint stability
.
J. Athl. Train.
37
,
80
.
Roberts
,
T. J.
,
Marsh
,
R. L.
,
Weyand
,
P. G.
and
Taylor
,
C. R.
(
1997
).
Muscular force in running turkeys: the economy of minimizing work
.
Science
275
,
1113
-
1115
.
Rubenson
,
J.
,
Heliams
,
D. B.
,
Lloyd
,
D. G.
and
Fournier
,
P. A.
(
2004
).
Gait selection in the ostrich: mechanical and metabolic characteristics of walking and running with and without an aerial phase
.
Proc. R. Soc. B
271
,
1091
-
1099
.
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. Theor. Biol.
237
,
170
-
192
.
Sánchez
,
N.
,
Park
,
S.
and
Finley
,
J. M.
(
2017
).
Evidence of energetic optimization during adaptation differs for metabolic, mechanical, and perceptual estimates of energetic cost
.
Sci. Rep.
7
,
7682
.
Sasaki
,
K.
,
Neptune
,
R. R.
and
Kautz
,
S. A.
(
2009
).
The relationships between muscle, external, internal and joint mechanical work during normal walking
.
J. Exp. Biol.
212
,
738
-
744
.
Selgrade
,
B. P.
,
Thajchayapong
,
M.
,
Lee
,
G. E.
,
Toney
,
M. E.
and
Chang
,
Y.-H.
(
2017a
).
Changes in mechanical work during neural adaptation to asymmetric locomotion
.
J. Exp. Biol.
220
,
2993
-
3000
.
Selgrade
,
B. P.
,
Toney
,
M. E.
and
Chang
,
Y.-H.
(
2017b
).
Two biomechanical strategies for locomotor adaptation to split-belt treadmill walking in subjects with and without transtibial amputation
.
J. Biomech.
53
,
136
-
143
.
Srinivasan
,
M.
(
2010
).
Fifteen observations on the structure of energy-minimizing gaits in many simple biped models
.
J. R. Soc. Interface
8
,
74
-
98
.
Srinivasan
,
M.
and
Ruina
,
A.
(
2006
).
Computer optimization of a minimal biped model discovers walking and running
.
Nature
439
,
72
-
75
.
Steele
,
K. M.
,
Seth
,
A.
,
Hicks
,
J. L.
,
Schwartz
,
M. S.
and
Delp
,
S. L.
(
2010
).
Muscle contributions to support and progression during single-limb stance in crouch gait
.
J. Biomech.
43
,
2099
-
2105
.
Steele
,
K. M.
,
Seth
,
A.
,
Hicks
,
J. L.
,
Schwartz
,
M. H.
and
Delp
,
S. L.
(
2013
).
Muscle contributions to vertical and fore-aft accelerations are altered in subjects with crouch gait
.
Gait Posture
38
,
89
-
91
.
Ting
,
L. H.
and
Macpherson
,
J. M.
(
2005
).
A limited set of muscle synergies for force control during a postural task
.
J. Neurophysiol.
93
,
609
-
613
.
Toney
,
M. E.
and
Chang
,
Y.-H.
(
2016
).
The motor and the brake of the trailing leg in human walking: leg force control through ankle modulation and knee covariance
.
Exp. Brain Res.
234
,
3011
-
3023
.
Torres-Oviedo
,
G.
,
Macpherson
,
J. M.
and
Ting
,
L. H.
(
2006
).
Muscle synergy organization is robust across a variety of postural perturbations
.
J. Neurophysiol.
96
,
1530
-
1546
.
Townsend
,
M. A.
(
1985
).
Biped gait stabilization via foot placement
.
J. Biomech.
18
,
21
-
38
.
Umberger
,
B. R.
and
Rubenson
,
J.
(
2011
).
Understanding muscle energetics in locomotion: new modeling and experimental approaches
.
Exerc. Sport Sci. Rev.
39
,
59
-
67
.
Van Emmerik
,
R. E. A.
,
McDermott
,
W. J.
,
Haddad
,
J. M.
and
Van Wegen
,
E. E. H.
(
2005
).
Age-related changes in upper body adaptation to walking speed in human locomotion
.
Gait Posture
22
,
233
-
239
.
Wang
,
Y.
and
Srinivasan
,
M.
(
2014
).
Stepping in the direction of the fall: the next foot placement can be predicted from current upper body state in steady-state walking
.
Biol. Lett.
10
,
20140405
.
Winter
,
D. A.
(
1980
).
Overall principle of lower limb support during stance phase of gait
.
J. Biomech.
13
,
923
-
927
.
Winter
,
D. A.
(
2009
).
Biomechanics and Motor Control of Human Movement
, 4th edn.
John Wiley & Sons
.
Wong
,
J. D.
,
O'Connor
,
S. M.
,
Selinger
,
J. C.
and
Donelan
,
J. M.
(
2017
).
Contribution of blood oxygen and carbon dioxide sensing to the energetic optimization of human walking
.
J. Neurophysiol.
118
,
1425
-
1433
.
Yen
,
J. T.
,
Auyang
,
A. G.
and
Chang
,
Y.-H.
(
2009
).
Joint-level kinetic redundancy is exploited to control limb-level forces during human hopping
.
Exp. Brain Res.
196
,
439
-
451
.
Young
,
P. M.
,
Whitall
,
J.
,
Bair
,
W.-N.
and
Rogers
,
M. W.
(
2013
).
Leg preference associated with protective stepping responses in older adults
.
Clin. Biomech.
28
,
927
-
932
.
Zatsiorsky
,
V. M.
(
2002
).
Kinetics of Human Motion
.
Human Kinetics
.

Competing interests

The authors declare no competing or financial interests.