Humans plan for the near future to walk economically on uneven terrain.

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 [Formula: see text] , [Formula: see text] 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.

On the rate-limiting dynamics of force development in muscle.

Skeletal muscles produce forces relatively slowly compared with the action potentials that excite them. The dynamics of force production are governed by multiple processes, such as calcium activation, cycling of cross-bridges between myofilaments, and contraction against elastic tissues and the body. These processes have been included piecemeal in some muscle models, but not integrated to reveal which are the most rate limiting. We therefore examined their integrative contributions to force development in two conventional types of muscle models: Hill-type and cross-bridge. We found that no combination of these processes can self-consistently reproduce classic data such as twitch and tetanus. Rather, additional dynamics are needed following calcium activation and facilitating cross-bridge cycling, such as for cooperative myofilament interaction and reconfiguration. We provisionally lump such processes into a simple first-order model of 'force facilitation dynamics' that integrate into a cross-bridge-type muscle model. The proposed model self-consistently reproduces force development for a range of excitations including twitch and tetanus and electromyography-to-force curves. The model's step response reveals relatively small timing contributions of calcium activation (3%), cross-bridge cycling (3%) and contraction (27%) to overall force development of human quadriceps, with the remainder (67%) explained by force facilitation. The same set of model parameters predicts the change in force magnitude (gain) and timing (phase delay) as a function of excitatory firing rate, or as a function of cyclic contraction frequency. Although experiments are necessary to reveal the dynamics of muscle, integrative models are useful for identifying the main rate-limiting processes.

Elastic energy savings and active energy cost in a simple model of running.

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic "Spring-mass" computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

The high energetic cost of rapid force development in muscle.

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.

Soft tissue deformations explain most of the mechanical work variations of human walking.

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.

Determinants of preferred ground clearance during swing phase of human walking.

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 by movement variability, which can influence the average cost actually experienced in practice.

Mechanical and energetic consequences of reduced ankle plantar-flexion in human walking.

The human ankle produces a large burst of 'push-off' mechanical power late in the stance phase of walking, reduction of which leads to considerably poorer energy economy. It is, however, uncertain whether the energetic penalty results from poorer efficiency when the other leg joints substitute for the ankle's push-off work, or from a higher overall demand for work due to some fundamental feature of push-off. Here, we show that greater metabolic energy expenditure is indeed explained by a greater demand for work. This is predicted by a simple model of walking on pendulum-like legs, because proper push-off reduces collision losses from the leading leg. We tested this by experimentally restricting ankle push-off bilaterally in healthy adults (N=8) walking on a treadmill at 1.4 m s(-1), using ankle-foot orthoses with steel cables limiting motion. These produced up to ∼50% reduction in ankle push-off power and work, resulting in up to ∼50% greater net metabolic power expenditure to walk at the same speed. For each 1 J reduction in ankle work, we observed 0.6 J more dissipative collision work by the other leg, 1.3 J more positive work from the leg joints overall, and 3.94 J more metabolic energy expended. Loss of ankle push-off required more positive work elsewhere to maintain walking speed; this additional work was performed by the knee, apparently at reasonably high efficiency. Ankle push-off may contribute to walking economy by reducing dissipative collision losses and thus overall work demand.

Mechanics and energetics of load carriage during human walking.

Although humans clearly expend more energy to walk with an extra load, it is unclear what biomechanical mechanisms contribute to that increase. One possible contribution is the mechanical work performed on the body center of mass (COM), which simple models predict should increase linearly with added mass. The work should be performed primarily by the lower extremity joints, although in unknown distribution, and cost a proportionate amount of metabolic energy. We therefore tested normal adults (N=8) walking at constant speed (1.25 m s(-1)) with varying backpack loads up to 40% of body weight. We measured mechanical work (both performed on the COM and joint work from inverse dynamics), as well as metabolic energy expenditure through respirometry. Both measures of work were found to increase approximately linearly with carried load, with COM work rate increasing by approximately 1.40 W for each 1 kg of additional load. The joints all contributed work, but the greatest increase in positive work was attributable to the ankle during push-off (45-60% of stride time) and the knee in the rebound after collision (12-30% stride). The hip performed increasing amounts of negative work, near the end of stance. Rate of metabolic energy expenditure also increased approximately linearly with load, by approximately 7.6 W for each 1 kg of additional load. The ratio of the increases in work and metabolic cost yielded a relatively constant efficiency of approximately 16%. The metabolic cost not explained by work appeared to be relatively constant with load and did not exhibit a particular trend. Most of the increasing cost for carrying a load appears to be explained by positive mechanical work, especially about the ankle and knee, with both work and metabolic cost increasing nearly linearly with added mass.

The role of series ankle elasticity in bipedal walking.

The elastic stretch-shortening cycle of the Achilles tendon during walking can reduce the active work demands on the plantarflexor muscles in series. However, this does not explain why or when this ankle work, whether by muscle or tendon, needs to be performed during gait. We therefore employ a simple bipedal walking model to investigate how ankle work and series elasticity impact economical locomotion. Our model shows that ankle elasticity can use passive dynamics to aid push-off late in single support, redirecting the body's center-of-mass (COM) motion upward. An appropriately timed, elastic push-off helps to reduce dissipative collision losses at contralateral heelstrike, and therefore the positive work needed to offset those losses and power steady walking. Thus, the model demonstrates how elastic ankle work can reduce the total energetic demands of walking, including work required from more proximal knee and hip muscles. We found that the key requirement for using ankle elasticity to achieve economical gait is the proper ratio of ankle stiffness to foot length. Optimal combination of these parameters ensures proper timing of elastic energy release prior to contralateral heelstrike, and sufficient energy storage to redirect the COM velocity. In fact, there exist parameter combinations that theoretically yield collision-free walking, thus requiring zero active work, albeit with relatively high ankle torques. Ankle elasticity also allows the hip to power economical walking by contributing indirectly to push-off. Whether walking is powered by the ankle or hip, ankle elasticity may aid walking economy by reducing collision losses.

A split-belt instrumented treadmill with uneven terrain.

The biomechanics of walking are far less understood for uneven terrain than flat or even surfaces. This is due in part to a lack of ground reaction force and moment recordings from each leg. These are often obtained with split-belt instrumented treadmills, which are currently incompatible with uneven terrain, making it difficult to perform biomechanics analyses such as inverse dynamics. Here we show how a standard split-belt instrumented treadmill (Bertec, Inc., Columbus, OH) can be modified to accommodate a variety of uneven terrains. The principal design considerations are structural clearance to allow passage of an uneven treadmill belt and fabrication of the terrain. We designed mechanical components with sufficient clearance for terrains up to 0.045 m high, and formed the terrain from uneven strips of polystyrene. Measured ground reaction forces from each leg at typical walking speeds agreed well with an intact benchmark treadmill (minimum interclass cross correlation score = 0.97). The modifications had negligible effect on the treadmill's structural strength. The terrain produced some noise-like vibrations, but at much higher frequencies than fundamental to human locomotion. The uneven terrain treadmill can record many steps of the full complement of ground reaction forces and moments from individual legs.

Mechanical and energetic consequences of rolling foot shape in human walking.

During human walking, the center of pressure under the foot progresses forward smoothly during each step, creating a wheel-like motion between the leg and the ground. This rolling motion might appear to aid walking economy, but the mechanisms that may lead to such a benefit are unclear, as the leg is not literally a wheel. We propose that there is indeed a benefit, but less from rolling than from smoother transitions between pendulum-like stance legs. The velocity of the body center of mass (COM) must be redirected in that transition, and a longer foot reduces the work required for the redirection. Here we develop a dynamic walking model that predicts different effects from altering foot length as opposed to foot radius, and test it by attaching rigid, arc-like foot bottoms to humans walking with fixed ankles. The model suggests that smooth rolling is relatively insensitive to arc radius, whereas work for the step-to-step transition decreases approximately quadratically with foot length. We measured the separate effects of arc-foot length and radius on COM velocity fluctuations, work performed by the legs and metabolic cost. Experimental data (N=8) show that foot length indeed has much greater effect on both the mechanical work of the step-to-step transition (23% variation, P=0.04) and the overall energetic cost of walking (6%, P=0.03) than foot radius (no significant effect, P>0.05). We found the minimum metabolic energy cost for an arc foot length of approximately 29% of leg length, roughly comparable to human foot length. Our results suggest that the foot's apparently wheel-like action derives less benefit from rolling per se than from reduced work to redirect the body COM.

Biomechanics and energetics of walking on uneven terrain.

Walking on uneven terrain is more energetically costly than walking on smooth ground, but the biomechanical factors that contribute to this increase are unknown. To identify possible factors, we constructed an uneven terrain treadmill that allowed us to record biomechanical, electromyographic and metabolic energetics data from human subjects. We hypothesized that walking on uneven terrain would increase step width and length variability, joint mechanical work and muscle co-activation compared with walking on smooth terrain. We tested healthy subjects (N=11) walking at 1.0 m s(-1), and found that, when walking on uneven terrain with up to 2.5 cm variation, subjects decreased their step length by 4% and did not significantly change their step width, while both step length and width variability increased significantly (22 and 36%, respectively; P<0.05). Uneven terrain walking caused a 28 and 62% increase in positive knee and hip work, respectively, and a 26% greater magnitude of negative knee work (0.0106, 0.1078 and 0.0425 J kg(-1), respectively; P<0.05). Mean muscle activity increased in seven muscles in the lower leg and thigh (P<0.05). These changes caused overall net metabolic energy expenditure to increase by 0.73 W kg(-1) (28%; P<0.0001). Much of that increase could be explained by the increased mechanical work observed at the knee and hip. Greater muscle co-activation could also contribute to increased energetic cost but to unknown degree. The findings provide insight into how lower limb muscles are used differently for natural terrain compared with laboratory conditions.

Optimization of energy and time predicts dynamic speeds for human walking.

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual's movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (N=10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.

Humans optimally anticipate and compensate for an uneven step during walking.

The simple task of walking up a sidewalk curb is actually a dynamic prediction task. The curb is a disturbance that could cause a loss of momentum if not anticipated and compensated for. It might be possible to adjust momentum sufficiently to ensure undisturbed time of arrival, but there are infinite possible ways to do so. Much of steady, level gait is determined by energy economy, which should be at least as important with terrain disturbances. It is, however, unknown whether economy also governs walking up a curb, and whether anticipation helps. Here, we show that humans compensate with an anticipatory pattern of forward speed adjustments, predicted by a criterion of minimizing mechanical energy input. The strategy is mechanistically predicted by optimal control for a simple model of bipedal walking dynamics, with each leg's push-off work as input. Optimization predicts a triphasic trajectory of speed (and thus momentum) adjustments, including an anticipatory phase. In experiment, human subjects ascend an artificial curb with the predicted triphasic trajectory, which approximately conserves overall walking speed relative to undisturbed flat ground. The trajectory involves speeding up in a few steps before the curb, losing considerable momentum from ascending it, and then regaining speed in a few steps thereafter. Descending the curb entails a nearly opposite, but still anticipatory, speed fluctuation trajectory, in agreement with model predictions that speed fluctuation amplitudes should scale linearly with curb height. The fluctuation amplitudes also decrease slightly with faster average speeds, also as predicted by model. Humans can reason about the dynamics of walking to plan anticipatory and economical control, even with a sidewalk curb in the way.

TimTrack: A drift-free algorithm for estimating geometric muscle features from ultrasound images.

Ultrasound imaging is valuable for non-invasively estimating fascicle lengths and other features of pennate muscle, especially when performed computationally. Effective analysis techniques to date typically use optic flow to track displacements from image sequences, but are sensitive to integration drift for longer sequences. We here present an alternative algorithm that objectively estimates geometric features of pennate muscle from ultrasound images, without drift sensitivity. The algorithm identifies aponeuroses and estimates fascicle angles to derive fascicle lengths. Length estimates of human vastus lateralis and gastrocnemius fascicles in healthy subjects (N = 9 and N = 17 respectively) compared well (overall root-mean-square difference, RMSD = 0.52 cm) to manual estimates by independent observers (n = 3), with overall coefficient of multiple correlation (CMC) of 0.98. Our tests yielded accuracy (CMC, RMSD) and processing speed similar to or exceeding that of state-of-the-art algorithms. The algorithm requires minimal manual intervention and can optionally extrapolate fascicle lengths that extend beyond the image frame. It thus facilitates automated analysis of ultrasound images without drift.

A biomechanics dataset of healthy human walking at various speeds, step lengths and step widths.

The biomechanics of human walking are well documented for standard conditions such as for self-selected step length and preferred speed. However, humans can and do walk with a variety of other step lengths and speeds during daily living. The variation of biomechanics across gait conditions may be important for describing and determining the mechanics of locomotion. To address this, we present an open biomechanics dataset of steady walking at a broad range of conditions, including 33 experimentally-controlled combinations of speed (0.7-2.0 m·s-1), step length (0.5-1.1 m), and step width (0-0.4 m). The dataset contains ground reaction forces and motions from healthy young adults (N = 10), collected using split-belt instrumented treadmill and motion capture systems respectively. Most trials also include pre-computed inverse dynamics, including 3D joint positions, angles, torques and powers, as well as intersegmental forces. Apart from raw data, we also provide five strides of good quality data without artifacts for each trial, and sample software for visualization and analysis.

An optimality principle for locomotor central pattern generators.

Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands (even in the absence of feedback, termed "fictive locomotion"), and reflex circuits driven by sensory feedback. Each circuit alone serves a clear purpose, and the two together are understood to cooperate during normal locomotion. The difficulty is in explaining their relative balance objectively within a control model, as there are infinite combinations that could produce the same nominal motor pattern. Here we propose that optimization in the presence of uncertainty can explain how the circuits should best be combined for locomotion. The key is to re-interpret the CPG in the context of state estimator-based control: an internal model of the limbs that predicts their state, using sensory feedback to optimally balance competing effects of environmental and sensory uncertainties. We demonstrate use of optimally predicted state to drive a simple model of bipedal, dynamic walking, which thus yields minimal energetic cost of transport and best stability. The internal model may be implemented with neural circuitry compatible with classic CPG models, except with neural parameters determined by optimal estimation principles. Fictive locomotion also emerges, but as a side effect of estimator dynamics rather than an explicit internal rhythm. Uncertainty could be key to shaping CPG behavior and governing optimal use of feedback.

The energetic basis for smooth human arm movements.

The central nervous system plans human reaching movements with stereotypically smooth kinematic trajectories and fairly consistent durations. Smoothness seems to be explained by accuracy as a primary movement objective, whereas duration seems to economize energy expenditure. But the current understanding of energy expenditure does not explain smoothness, so that two aspects of the same movement are governed by seemingly incompatible objectives. Here, we show that smoothness is actually economical, because humans expend more metabolic energy for jerkier motions. The proposed mechanism is an underappreciated cost proportional to the rate of muscle force production, for calcium transport to activate muscle. We experimentally tested that energy cost in humans (N = 10) performing bimanual reaches cyclically. The empirical cost was then demonstrated to predict smooth, discrete reaches, previously attributed to accuracy alone. A mechanistic, physiologically measurable, energy cost may therefore explain both smoothness and duration in terms of economy, and help resolve motor redundancy in reaching movements.

Human walking in the real world: Interactions between terrain type, gait parameters, and energy expenditure.

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.

Extraction of individual muscle mechanical action from endpoint force.

Most motor tasks require the simultaneous coordination of multiple muscles. That coordination is poorly understood in part because there is no noninvasive means of isolating a single muscle's contribution to the resultant endpoint force. The contribution of a single motor unit to isometric tasks can, however, be characterized using the spike-triggered averaging (STA) technique, applied to a single motor unit's spike train. We propose that a technique analogous to STA, which we call electromyogram (EMG)-weighted averaging (EWA), can be applied to surface EMGs to extract muscle mechanical action from the natural endpoint force fluctuations generated during steady isometric contraction. We demonstrate this technique on simultaneous recordings of fingertip force and surface EMG from the first dorsal interosseous (FDI) and extensor indicis (EI) of humans. The EWA direction was approximately the same across a wide range of fingertip force directions, and the average EWA direction was consistent with mechanical action direction of these muscles estimated from cadaveric and imaging data: the EWA directions were 193 +/- 2 degrees for the FDI and 71 +/- 5 degrees for the EI (95% confidence). EWA transient behavior also appears to capture temporal characteristics of muscle force fluctuations with peak force time and general waveform shape similar to that of the associated spike-triggered averages from single motor units. The EWA may provide a means of empirically characterizing the complex transformation between muscle force and endpoint force without the need for invasive electrode recordings or complex anatomical measurements of musculoskeletal geometry.