The energetic cost of human walking as a function of uneven terrain amplitude

Hosseini-Yazdi S.S., Kuo A.D.

Jessup L.N., Kelly L.A., Cresswell A.G., Lichtwark G.A.

The cost of walking and running on uneven terrain is not directly explained by external mechanical work. Whilst metabolic cost of transport increases linearly with gradient at uphill and downhill gradients exceeding 15%, at shallower gradients the relationship is non-linear, with the minimum cost occurring at ~10% downhill grade. Given these non-linear relationships between grade and metabolic cost, we projected a significant difference in the total metabolic cost of two walking conditions that required the same total external mechanical work be performed over the same total period of time; in one condition time was spent walking to gradients that were fixed at +10.5% and -10.5% and in the other condition time was spent walking to gradients that varied from 0 to +21% and from -21 to 0%. We compared these two conditions experimentally, using an approach to quantify non-steady-state oxidative energy expenditure. In line with our projection, the 'variable' grade condition resulted in an 8.3 ± 2.2% higher total cumulative oxidative energy expenditure (J⋅kg-1) compared to the 'fixed' grade condition (p < 0.001). Future work should aim to apply our approach across different gradients, speeds and forms of locomotion; especially those that might provide insight into how humans optimise locomotion on variable grade routes.

Darici O., Kuo A.

Humans experience small fluctuations in their gait when walking on uneven terrain. The fluctuations deviate from the steady, energy-minimizing pattern for level walking and have no obvious organization. But humans often look ahead when they walk, and could potentially plan anticipatory fluctuations for the terrain. Such planning is only sensible if it serves some an objective purpose, such as maintaining constant speed or reducing energy expenditure, that is also attainable within finite planning capacity. Here, we show that humans do plan and perform optimal control strategies on uneven terrain. Rather than maintaining constant speed, they make purposeful, anticipatory speed adjustments that are consistent with minimizing energy expenditure. A simple optimal control model predicts economical speed fluctuations that agree well with experiments with humans (N = 12) walking on seven different terrain profiles (correlated with model  ρ = 0.55 ± 0.11  , P < 0.05 all terrains). Participants made repeatable speed fluctuations starting about six to eight steps ahead of each terrain feature (up to ±7.5 cm height difference each step, up to 16 consecutive features). Nearer features matter more, because energy is dissipated with each succeeding step’s collision with ground, preventing momentum from persisting indefinitely. A finite horizon of continuous look-ahead and motor working space thus suffice to practically optimize for any length of terrain. Humans reason about walking in the near future to plan complex optimal control sequences.

Downey R.J., Richer N., Gupta R., Liu C., Pliner E.M., Roy A., Hwang J., Clark D.J., Hass C.J., Manini T.M., Seidler R.D., Ferris D.P.

We developed a method for altering terrain unevenness on a treadmill to study gait kinematics. Terrain consisted of rigid polyurethane disks (12.7 cm diameter, 1.3–3.8 cm tall) which attached to the treadmill belt using hook-and-loop fasteners. Here, we tested four terrain unevenness conditions: Flat, Low, Medium, and High. The main objective was to test the hypothesis that increasing the unevenness of the terrain would result in greater gait kinematic variability. Seventeen younger adults (age 20–40 years), 25 higher-functioning older adults (age 65+ years), and 29 lower-functioning older adults (age 65+ years, Short Physical Performance Battery score < 10) participated. We customized the treadmill speed to each participant’s walking ability, keeping the speed constant across all four terrain conditions. Participants completed two 3-minute walking trials per condition. Using an inertial measurement unit placed over the sacrum and pressure sensors in the shoes, we calculated the stride-to-stride variability in step duration and sacral excursion (coefficient of variation; standard deviation expressed as percentage of the mean). Participants also self-reported their perceived stability for each condition. Terrain was a significant predictor of step duration variability, which roughly doubled from Flat to High terrain for all participant groups: younger adults (Flat 4.0%, High 8.2%), higher-functioning older adults (Flat 5.0%, High 8.9%), lower-functioning older adults (Flat 7.0%, High 14.1%). Similarly, all groups exhibited significant increases in sacral excursion variability for the Medium and High uneven terrain conditions, compared to Flat. Participants were also significantly more likely to report feeling less stable walking over all three uneven terrain conditions compared to Flat. These findings support the hypothesis that altering terrain unevenness on a treadmill will increase gait kinematic variability and reduce perceived stability in younger and older adults.

Ahuja S., Franz J.R.

Our aim was to quantify the role of metabolic energy cost in governing neuromuscular adaptation to prolonged exposure to optical flow walking balance perturbations in young adults. We hypothesized that metabolic cost would increase at the onset of balance perturbations in a manner consistent with wider and shorter steps and increased step-to-step variability. We also hypothesized that metabolic cost would decrease with prolonged exposure in a manner consistent with a return of step width and step length to values seen during normal, unperturbed walking. Healthy young adults (n = 18) walked on a treadmill while viewing a virtual hallway. Optical flow balance perturbations were introduced over a 10-minute interval during a 20-minute walking bout while measuring step kinematics and metabolic energy cost. For all outcome measures, we computed average values during the following four time periods of interest: Pre (minutes 3–5), Early Perturbation (minutes 5–7), Late Perturbation (minutes 13–15), and Post (minutes 18–20). A repeated-measures ANOVA tested for main effects of time, following by post-hoc pairwise comparisons. With the onset of perturbations, participants walked with 3% shorter, 17% wider, and 53–73% more variable steps. These changes were accompanied by a significant 12% increase in net metabolic power compared to walking normally. With prolonged exposure to perturbations, step width and step length tended toward values seen during normal, unperturbed walking – changes accompanied by a 5% reduction in metabolic power (p-values≤0.05). Our study reveals that the adoption of generalized anticipatory control at the onset of optical flow balance perturbations and the subsequent shift to task-specific reactive control following prolonged exposure have meaningful metabolic consequences. Moreover, our findings suggest that metabolic energy cost may shape the strategies we use to adapt walking balance in response to perturbations. • Measured the metabolic cost of walking with prolonged exposure to perturbations. • Initial response to perturbations exacted a 12% metabolic penalty. • Prolonged exposure to perturbations reduced metabolic cost by 5%. • Metabolic changes likely explained by shift from anticipatory to reactive control. • Metabolic cost may shape the strategies used for walking balance control.

van der Zee T.J., Kuo A.D.

ABSTRACT Humans perform mechanical work during walking, some by leg joints actuated by muscles, and some by passive, dissipative soft tissues. Dissipative losses must be restored by active muscle work, potentially in amounts sufficient to cost substantial metabolic energy. The most dissipative, and therefore costly, walking conditions might be predictable from the pendulum-like dynamics of the legs. If this behavior is systematic, it may also predict the work distribution between active joints and passive soft tissues. We therefore tested whether the overall negative work of walking, and the fraction owing to soft tissue dissipation, are both predictable by a simple dynamic walking model across a wide range of conditions. The model predicts whole-body negative work from the leading leg's impact with the ground (termed the collision), to increase with the squared product of walking speed and step length. We experimentally tested this in humans (N=9) walking in 26 different combinations of speed (0.7–2.0 m s−1) and step length (0.5–1.1 m), with recorded motions and ground reaction forces. Whole-body negative collision work increased as predicted (R2=0.73), with a consistent fraction of approximately 63% (R2=0.88) owing to soft tissues. Soft tissue dissipation consistently accounted for approximately 56% of the variation in total whole-body negative work, across a wide range of speed and step length combinations. During typical walking, active work to restore dissipative losses could account for 31% of the net metabolic cost. Soft tissue dissipation, not included in most biomechanical studies, explains most of the variation in negative work of walking, and could account for a substantial fraction of the metabolic cost.

van der Zee T.J., Kuo A.D.

ABSTRACT Muscles consume metabolic energy for active movement, particularly when performing mechanical work or producing force. Less appreciated is the cost for activating muscle quickly, which adds considerably to the overall cost of cyclic force production. However, the cost magnitude relative to the cost of mechanical work, which features in many movements, is unknown. We therefore tested whether fast activation is costly compared with performing work or producing isometric force. We hypothesized that metabolic cost would increase with a proposed measure termed force rate (rate of increase in muscle force) in cyclic tasks, separate from mechanical work or average force level. We tested humans (N=9) producing cyclic knee extension torque against an isometric dynamometer (torque 22 N m, cyclic waveform frequencies 0.5–2.5 Hz), while also quantifying quadriceps muscle force and work against series elasticity (with ultrasonography), along with metabolic rate through respirometry. Net metabolic rate increased by more than four-fold (10.5 to 46.8 W) with waveform frequency. At high frequencies, the hypothesized force-rate cost accounted for nearly half (40%) of energy expenditure. This exceeded the cost for average force (17%) and was comparable to the cost for shortening work (43%). The force-rate cost is explained by additional active calcium transport necessary for producing forces at increasing waveform frequencies, owing to rate-limiting dynamics of force production. The force-rate cost could contribute substantially to the overall cost of movements that require cyclic muscle activation, such as locomotion.

Kowalsky D.B., Rebula J.R., Ojeda L.V., Adamczyk P.G., Kuo A.D.

Humans often traverse real-world environments with a variety of surface irregularities and inconsistencies, which can disrupt steady gait and require additional effort. Such effects have, however, scarcely been demonstrated quantitatively, because few laboratory biomechanical measures apply outdoors. Walking can nevertheless be quantified by other means. In particular, the foot’s trajectory in space can be reconstructed from foot-mounted inertial measurement units (IMUs), to yield measures of stride and associated variabilities. But it remains unknown whether such measures are related to metabolic energy expenditure. We therefore quantified the effect of five different outdoor terrains on foot motion (from IMUs) and net metabolic rate (from oxygen consumption) in healthy adults (N = 10; walking at 1.25 m/s). Energy expenditure increased significantly (P < 0.05) in the order Sidewalk, Dirt, Gravel, Grass, and Woodchips, with Woodchips about 27% costlier than Sidewalk. Terrain type also affected measures, particularly stride variability and virtual foot clearance (swing foot’s lowest height above consecutive footfalls). In combination, such measures can also roughly predict metabolic cost (adjusted R2 = 0.52, partial least squares regression), and even discriminate between terrain types (10% reclassification error). Body-worn sensors can characterize how uneven terrain affects gait, gait variability, and metabolic cost in the real world.

Voloshina A.S., Kuo A.D., Ferris D.P., Remy C.D.

AbstractHuman walking on uneven terrain is energetically more expensive than on flat, even ground. This is in part due to increases in, and redistribution of positive work among lower limb joints. To improve understanding of the mechanical adaptations, we performed analytical and computational analyses of simple mechanical models walking over uneven terrain comprised of alternating up and down steps of equal height. We simulated dynamic walking models using trailing leg push-off and/or hip torque to power gait, and quantified the compensatory work costs vs. terrain height. We also examined the effect of swing leg dynamics by including and excluding them from the model. We found that greater work, increasing approximately quadratically with uneven terrain height variations, was necessary to maintain a prescribed average forward speed. Greatest economy was achieved by modulating precisely-timed push-offs for each step height. Least economy was achieved with hip power, which did not require as precise timing. This compares well with observations of humans on uneven terrain, showing similar near-normal push-off but with more variable step timing, and considerably more hip work. These analyses suggest how mechanical work and timing could be adjusted to compensate for real world environments.

Darici O., Temeltas H., Kuo A.D.

Humans and other walking bipeds often encounter and compensate for uneven terrain. They might, for example, regulate the body’s momentum when stepping on stones to cross a stream. We examined what to do and how far to look, as a simple optimal control problem, where forward momentum is controlled to compensate for a step change in terrain height, and steady gait regained with no loss of time relative to nominal walking. We modeled planar, human-like walking with pendulum-like legs, and found the most economical control to be quite stereotypical. It starts by gaining momentum several footfalls ahead of an upward step, in anticipation of the momentum lost atop that step, and then ends with another speed-up to regain momentum thereafter. A similar pattern can be scaled to a variety of conditions, including both upward or downward steps, yet allow for considerably reduced overall energy and peak power demands, compared to compensation without anticipation. We define a “persistence time” metric from the transient decay response after a disturbance, to describe how momentum is retained between steps, and how far ahead a disturbance should be planned for. Anticipatory control of momentum can help to economically negotiate uneven terrain.

Mahaki M., Bruijn S.M., van Dieën J.H.

It is still unclear how humans control mediolateral (ML) stability in walking and even more so for running. Here, foot placement strategy as a main mechanism to control ML stability was compared between walking and running. Moreover, to verify the role of foot placement as a means to control ML stability in both modes of locomotion, this study investigated the effect of external lateral stabilization on foot placement control. Ten young adults participated in this study. Kinematic data of the trunk (T6) and feet were recorded during walking and running on a treadmill in normal and stabilized conditions. Correlation between ML trunk CoM state and subsequent ML foot placement, step width, and step width variability were assessed. Paired t-tests (either SPM1d or normal) were used to compare aforementioned parameters between normal walking and running. Two-way repeated measures ANOVAs (either SPM1d or normal) were used to test for effects of walking vs. running and of normal vs. stabilized condition. We found a stronger correlation between ML trunk CoM state and ML foot placement and significantly higher step width variability in walking than in running. The correlation between ML trunk CoM state and ML foot placement, step width, and step width variability were significantly decreased by external lateral stabilization in walking and running, and this reduction was stronger in walking than in running. We conclude that ML foot placement is coordinated to ML trunk CoM state to stabilize both walking and running and this coordination is stronger in walking than in running.

Darici O., Temeltas H., Kuo A.D.

Bipedal locomotion may occur over imperfect surfaces with bumps or other features that disrupt steady gait. An unexpected bump in the road is generally expected to slow down most types of locomotion. On wheels, speed may be regained quite readily with “cruise control” performed in continuous time. But legged locomotion is less straightforward, because the stance leg may be under-actuated, and the continuous-time dynamics are periodically disrupted by discrete ground contact events. Those events may also afford good control opportunities, albeit subject to the delay between discrete opportunities. The regulation of walking speed should ideally use these opportunities to compensate for lost time, and with good economy if possible. However, the appropriate control strategy is unknown. Here we present how to restore speed and make up for time lost going over a bump in the road, through discrete, once-per-step control. We use a simple dynamic walking model to determine the optimal sequence of control actions—pushing off from the leg at the end of each stance phase—for fast response or best economy. A two-step, deadbeat sequence is the fastest possible response, and reasonably economical. Slower responses over more steps are more economical overall, but a bigger difference is that they demand considerably less peak power. A simple, reactive control strategy can thus compensate for an unexpected bump, with explicit trade-offs in time and work. Control of legged locomotion is not as straightforward as with wheels, but discrete control actions also allow for effective and economical reactions to imperfect terrain.

Wu A.R., Kuo A.D.

During each step of human walking, the swing foot passes close to the ground with a small but (usually) non-zero clearance. The foot can occasionally scuff against the ground, with some risk of stumbling or tripping. The risk might be mitigated simply by lifting the foot higher, but presumably at increased effort, of unknown amount. Perhaps the normally preferred ground clearance is a trade-off between competing costs, one for lifting the foot higher, and one for scuffing it. We tested this by measuring the metabolic energy cost of lifting and scuffing the foot, treating these apparently dissimilar behaviors as part of a single continuum, where scuffing is a form of negative foot lift. We measured young, healthy adults (N=9) lifting or scuffing the foot by various amounts mid-swing during treadmill walking, and observed substantial costs, each well capable of doubling the net metabolic rate for normal walking (gross cost minus that for standing). In relative terms, the cost for scuffing increased over twice as steeply as that for lifting. That relative difference means that the expected value of cost, which takes into account movement variability, occurs at a non-zero mean clearance, approximately matching the preferred clearance we observed. Energy cost alone is only a lower bound on the overall disadvantages of inadvertent ground contact, but it is sufficient to show how human behavior may be determined not only by the separate costs of different trade-offs, but also movement variability, which can influence the average cost actually experienced in practice.

Ojeda L.V., Rebula J.R., Kuo A.D., Adamczyk P.G.

Walking is not always a free and unencumbered task. Everyday activities such as walking in pairs, in groups, or on structured walkways can limit the acceptable gait patterns, leading to motor behavior that differs from that observed in more self-selected gait. Such different contexts may lead to gait performance different than observed in typical laboratory experiments, for example, during treadmill walking. We sought to systematically measure the impact of such task constraints by comparing gait parameters and their variability during walking in different conditions over-ground, and on a treadmill. We reconstructed foot motion from foot-mounted inertial sensors, and characterized forward, lateral and angular foot placement while subjects walked over-ground in a straight hallway and on a treadmill. Over-ground walking was performed in three variations: with no constraints (self-selected, SS); while deliberately varying walking speed (self-varied, SV); and while following a toy pace car programmed to vary speed (externally-varied, EV). We expected that these conditions would exhibit a statistically similar relationship between stride length and speed, and between stride length and stride period. We also expected treadmill walking (TM) would differ in two ways: first, that variability in stride length and stride period would conform to a constant-speed constraint opposite in slope from the normal relationship; and second, that stride length would decrease, leading to combinations of stride length and speed not observed in over-ground conditions. Results showed that all over-ground conditions used similar stride length-speed relationships, and that variability in treadmill walking conformed to a constant-speed constraint line, as expected. Decreased stride length was observed in both TM and EV conditions, suggesting adaptations due to heightened awareness or to prepare for unexpected changes or problems. We also evaluated stride variability in constrained and unconstrained tasks. We observed that in treadmill walking, lateral variability decreased while forward variability increased, and the normally-observed correlation between wider foot placement and external foot rotation was eliminated. Preferred stride parameters and their variability appear significantly influenced by the context and constraints of the walking task.

Wang Y., Srinivasan M.

During human walking, perturbations to the upper body can be partly corrected by placing the foot appropriately on the next step. Here, we infer aspects of such foot placement dynamics using step-to-step variability over hundreds of steps of steady-state walking data. In particular, we infer dependence of the ‘next’ foot position on upper body state at different phases during the ‘current’ step. We show that a linear function of the hip position and velocity state (approximating the body center of mass state) during mid-stance explains over 80% of the next lateral foot position variance, consistent with (but not proving) lateral stabilization using foot placement. This linear function implies that a rightward pelvic deviation during a left stance results in a larger step width and smaller step length than average on the next foot placement. The absolute position on the treadmill does not add significant information about the next foot relative to current stance foot over that already available in the pelvis position and velocity. Such walking dynamics inference with steady-state data may allow diagnostics of stability and inform biomimetic exoskeleton or robot design.

Hosseini-Yazdi S., Bertram J.E.