Mechanical work accounts for most of the energetic cost in human running.

The metabolic cost of human running is not well explained, in part because the amount of work performed actively by muscles is largely unknown. Series elastic tissues such as tendon can save energy by performing work passively, but there are few direct measurements of the active versus passive contributions to work in running. There are, however, indirect biomechanical measures that can help estimate the relative contributions to overall metabolic cost. We developed a simple cost estimate for muscle work in humans running (N = 8) at moderate speeds (2.2-4.6 m/s) based on measured joint mechanics and passive dissipation from soft tissue deformations. We found that even if 50% of the work observed at the lower extremity joints is performed passively, active muscle work still accounts for 76% of the net energetic cost. Up to 24% of this cost compensates for the energy lost in soft tissue deformations. The estimated cost of active work may be adjusted based on assumptions of multi-articular energy transfer, elasticity, and muscle efficiency, but even conservative assumptions yield active work costs of at least 60%. Passive elasticity can reduce the active work of running, but muscle work still explains most of the overall energetic cost.

Stepping onto the unknown: reflexes of the foot and ankle while stepping with perturbed perceptions of terrain.

Unanticipated variations in terrain can destabilize the body. The foot is the primary interface with the ground and we know that cutaneous reflexes provide important sensory feedback. However, little is known about the contribution of stretch reflexes from the muscles within the foot to upright stability. We used intramuscular electromyography measurements of the foot muscles flexor digitorum brevis (FDB) and abductor hallucis (AH) to show for the first time how their short-latency stretch reflex response (SLR) may play an important role in responding to stepping perturbations. The SLR of FDB and AH was highest for downwards steps and lowest for upwards steps, with the response amplitude for level and compliant steps in between. When the type of terrain was unknown or unexpected to the participant, the SLR of AH and the ankle muscle soleus tended to decrease. We found significant relationships between the contact kinematics and forces of the leg and the SLR, but a person's expectation still had significant effects even after accounting for these relationships. Motor control models of short-latency body stabilization should not only include local muscle dynamics, but also predictions of terrain based on higher level information such as from vision or memory.

A shared neural integrator for human posture control.

Control of standing posture requires fusion of multiple inputs including visual, vestibular, somatosensory, and other sensors, each having distinct dynamics. The semicircular canals, for example, have a unique high-pass filter response to angular velocity, quickly sensing a step change in head rotational velocity followed by a decay. To stabilize gaze direction despite this decay, the central nervous system supplies a neural "velocity storage" integrator, a filter that extends the angular velocity signal. Similar filtering might contribute temporal dynamics to posture control, as suggested by some state estimation models. However, such filtering has not been tested explicitly. We propose that posture control indeed entails a neural integrator for sensory inputs, and we test its behavior with classic sensory perturbations: a rotating optokinetic stimulus to the visual system and a galvanic vestibular stimulus to the vestibular system. A simple model illustrates how these two inputs and body tilt sensors might produce a postural tilt response in the frontal plane. The model integrates these signals through a direct weighted sum of inputs, with or without an indirect pathway containing a neural integrator. Comparison with experimental data from healthy adult subjects (N = 16) reveals that the direct weighting model alone is insufficient to explain resulting postural transients, as measured by lateral tilt of the trunk. In contrast, the neural integrator, shared by sensory signals, produces the dynamics of both optokinetic and galvanic vestibular responses. These results suggest that posture control may involve both direct and indirect pathways, which filter sensory signals and make them compatible for sensory fusion.NEW & NOTEWORTHY Control of standing posture requires fusion of multiple inputs including visual, vestibular, somatosensory, and other sensors, each having distinct dynamics. We propose that postural control also entails a shared neural integrator. To test this theory, we perturbed standing subjects with classic sensory stimuli (optokinetic and galvanic vestibular stimulation) and found that our proposed shared filter reproduces the dynamics of subjects' postural responses.

Soft tissues store and return mechanical energy in human running.

During human running, softer parts of the body may deform under load and dissipate mechanical energy. Although tissues such as the heel pad have been characterized individually, the aggregate work performed by all soft tissues during running is unknown. We therefore estimated the work performed by soft tissues (N=8 healthy adults) at running speeds ranging 2-5 m s(-1), computed as the difference between joint work performed on rigid segments, and whole-body estimates of work performed on the (non-rigid) body center of mass (COM) and peripheral to the COM. Soft tissues performed aggregate negative work, with magnitude increasing linearly with speed. The amount was about -19 J per stance phase at a nominal 3 m s(-1), accounting for more than 25% of stance phase negative work performed by the entire body. Fluctuations in soft tissue mechanical power over time resembled a damped oscillation starting at ground contact, with peak negative power comparable to that for the knee joint (about -500 W). Even the positive work from soft tissue rebound was significant, about 13 J per stance phase (about 17% of the positive work of the entire body). Assuming that the net dissipative work is offset by an equal amount of active, positive muscle work performed at 25% efficiency, soft tissue dissipation could account for about 29% of the net metabolic expenditure for running at 5 m s(-1). During running, soft tissue deformations dissipate mechanical energy that must be offset by active muscle work at non-negligible metabolic cost.

Elastic coupling of limb joints enables faster bipedal walking.

The passive dynamics of bipedal limbs alone are sufficient to produce a walking motion, without need for control. Humans augment these dynamics with muscles, actively coordinated to produce stable and economical walking. Present robots using passive dynamics walk much slower, perhaps because they lack elastic muscles that couple the joints. Elastic properties are well known to enhance running gaits, but their effect on walking has yet to be explored. Here we use a computational model of dynamic walking to show that elastic joint coupling can help to coordinate faster walking. In walking powered by trailing leg push-off, the model's speed is normally limited by a swing leg that moves too slowly to avoid stumbling. A uni-articular spring about the knee allows faster but uneconomical walking. A combination of uni-articular hip and knee springs can speed the legs for improved speed and economy, but not without the swing foot scuffing the ground. Bi-articular springs coupling the hips and knees can yield high economy and good ground clearance similar to humans. An important parameter is the knee-to-hip moment arm that greatly affects the existence and stability of gaits, and when selected appropriately can allow for a wide range of speeds. Elastic joint coupling may contribute to the economy and stability of human gait.

Biomechanical energy harvesting: generating electricity during walking with minimal user effort.

We have developed a biomechanical energy harvester that generates electricity during human walking with little extra effort. Unlike conventional human-powered generators that use positive muscle work, our technology assists muscles in performing negative work, analogous to regenerative braking in hybrid cars, where energy normally dissipated during braking drives a generator instead. The energy harvester mounts at the knee and selectively engages power generation at the end of the swing phase, thus assisting deceleration of the joint. Test subjects walking with one device on each leg produced an average of 5 watts of electricity, which is about 10 times that of shoe-mounted devices. The cost of harvesting-the additional metabolic power required to produce 1 watt of electricity-is less than one-eighth of that for conventional human power generation. Producing substantial electricity with little extra effort makes this method well-suited for charging powered prosthetic limbs and other portable medical devices.

The effect of lateral stabilization on walking in young and old adults.

We tested how lateral stability affects gait as a function of age. A simple computational model suggests that walking is laterally unstable and that age-related decreases in motor and sensory function may be treated as noise-like perturbations to the body. Step width variability may be affected by active control of foot placement subject to noise. We hypothesized that age-related deficits may lead to increased step width variability. A possible compensation would be to walk with wider steps to reduce the lateral instability. The addition of external stabilization, through elastic cords acting laterally on the body during treadmill walking, would be expected to yield reduced step width variability and/or reduced average step width. We measured step width, its variability (defined as standard deviation), and metabolic energy expenditure in eight adult human subjects aged less than 30 years (Young) and ten subjects aged at least 65 years (Old). Subjects walked with and without external stabilization, each at a self-selected step width as well as a prescribed step width of zero. In normal walking, Old subjects preferred 41% wider steps than Young, and expended 26% more net energy (P < 0.05). External stabilization caused both groups to prefer 58% narrower steps. In the prescribed zero step width condition, Old subjects walked with 52% more step width variability and at 20% higher energetic cost. External stabilization resulted in reduced step width variability and 16% decreased energetic cost. Although there was no significant statistical interaction between age group and stabilization, Old and Young subjects walked with similar energetic costs in the stabilized, prescribed step width condition. Age-related changes appear to affect lateral balance, and the resulting compensations explain much of the increased energetic cost of walking in older adults.

Mechanical and metabolic requirements for active lateral stabilization in human walking.

Walking appears to be passively unstable in the lateral direction, requiring active feedback control for stability. The central nervous system may control stability by adjusting medio-lateral foot placement, but potentially with a metabolic cost. This cost increases with narrow steps and may affect the preferred step width. We hypothesized that external stabilization of the body would reduce the active control needed, thereby decreasing metabolic cost and preferred step width. To test these hypotheses, we provided external lateral stabilization, using springs pulling bilaterally from the waist, to human subjects walking on a force treadmill at 1.25 m/s. Ten subjects walked, with and without stabilization, at a prescribed step width of zero and also at their preferred step width. We measured metabolic cost using indirect calorimetry, and step width from force treadmill data. We found that at the prescribed zero step width, external stabilization resulted in a 33% decrease in step width variability (root-mean-square) and a 9.2% decrease in metabolic cost. In the preferred step width conditions, external stabilization caused subjects to prefer a 47% narrower step width, with a 32% decrease in step width variability and a 5.7% decrease in metabolic cost. These results suggest that (a). human walking requires active lateral stabilization, (b). body lateral motion is partially stabilized via medio-lateral foot placement, (c). active stabilization exacts a modest metabolic cost, and (d). humans avoid narrow step widths because they are less stable.

Contributions of altered sensation and feedback responses to changes in coordination of postural control due to aging.

We used multivariate kinematics and joint torque measurements during dynamic posturography to determine the relative contributions of changes in overall control gain, relative weighting of sensors, and noise-like effects on posture control in the elderly. Our results show that sway coordination and amplitude both change with age, but that changes in overall feedback gains do not explain these differences. We propose that increased sway of elderly subjects in platform sway-referenced conditions is due to sensory noise or decreased ability to detect small motions of the platform, while increased sway during visual sway-referencing is due to re-weighting of the various sensors.

Mechanical and metabolic determinants of the preferred step width in human walking.

We studied the selection of preferred step width in human walking by measuring mechanical and metabolic costs as a function of experimentally manipulated step width (0.00-0.45L, as a fraction of leg length L). We estimated mechanical costs from individual limb external mechanical work and metabolic costs using open circuit respirometry. The mechanical and metabolic costs both increased substantially (54 and 45%, respectively) for widths greater than the preferred value (0.15-0.45L) and with step width squared (R(2) = 0.91 and 0.83, respectively). As predicted by a three-dimensional model of walking mechanics, the increases in these costs appear to be a result of the mechanical work required for redirecting the centre of mass velocity during the transition between single stance phases (step-to-step transition costs). The metabolic cost for steps narrower than preferred (0.10-0.00L) increased by 8%, which was probably as a result of the added cost of moving the swing leg laterally in order to avoid the stance leg (lateral limb swing cost). Trade-offs between the step-to-step transition and lateral limb swing costs resulted in a minimum metabolic cost at a step width of 0.12L, which is not significantly different from foot width (0.11L) or the preferred step width (0.13L). Humans appear to prefer a step width that minimizes metabolic cost.

A simple model of bipedal walking predicts the preferred speed-step length relationship.

We used a simple model of passive dynamic walking, with the addition of active powering on level ground, to study the preferred relationship between speed and step length in humans. We tested several hypothetical metabolic costs, with one component proportional to the mechanical work associated with pushing off with the stance leg at toe-off, and another component associated with several possible costs of forcing oscillations of the swing leg. For this second component, a cost based on the amount of force needed to oscillate the leg divided by the time duration of that force predicts the preferred speed-step length relationship much better than other costs, such as the amount of mechanical work done in swinging the leg. The cost of force/time models the need to recruit fast muscle fibers for large forces at short durations. The actual mechanical work performed by muscles on the swing leg appears to be of relatively less importance, although it appears to be minimized by the use of short bursts of muscle activity in near-isometric conditions. The combined minimization of toe-off mechanical work and force divided by time predicts the preferred speed-step length relationship.

Active control of lateral balance in human walking.

We measured variability of foot placement during gait to test whether lateral balance must be actively controlled against dynamic instability. The hypothesis was developed using a simple dynamical model that can walk down a slight incline with a periodic gait resembling that of humans. This gait is entirely passive except that it requires active control for a single unstable mode, confined mainly to lateral motion. An especially efficient means of controlling this instability is to adjust lateral foot placement. We hypothesized that similar active feedback control is performed by humans, with fore-aft dynamics stabilized either passively or by very low-level control. The model predicts that uncertainty within the active feedback loop should result in variability in foot placement that is larger laterally than fore-aft. In addition, loss of sensory information such as by closing the eyes should result in larger increases in lateral variability. The control model also predicts a slight coupling between step width and length. We tested 15 young normal human subjects and found that lateral variability was 79% larger than fore-aft variability with eyes open, and a larger increase in lateral variability (53% vs. 21%) with eyes closed, consistent with the model's predictions. We also found that the coupling between lateral and fore-aft foot placements was consistent with a value of 0.13 predicted by the control model. Our results imply that humans may harness passive dynamic properties of the limbs in the sagittal plane, but must provide significant active control in order to stabilize lateral motion.

EquiTest modification with shank and hip angle measurements: differences with age among normal subjects.

The Sensory Organization Test protocol of the EquiTest system (NeuroCom International, Clackamas Oregon) tests utilization of visual, vestibular, and proprioceptive sensors by manipulating the accuracy of visual and/or somatosensory inputs during quiet stance. In the standard Sensory Organization Test, both manipulation of sensory input (sway-referencing) and assessment of postural sway are based on ground reaction forces measured from a forceplate. The purpose of our investigation was to examine the use of kinematic measurements to provide a more direct feedback signal for sway-referencing and for assessment of sway. We compared three methods of sway-referencing: the standard EquiTest method based on ground reaction torque, kinematic feedback based on servo-controlling to shank motion, and a more complex kinematic feedback based on servo-controlling to follow position of the center of mass (COM) as calculated from a two-link biomechanical model. Fifty-one normal subjects (ages 20-79) performed the randomized protocol. When using either shank or COM angle for sway-referencing feedback as compared to the standard EquiTest protocol, the Equilibrium Quotient and Strategy Score assessments were decreased for all age groups in the platform sway-referenced conditions (SOT 4, 5, 6). For all groups of subjects, there were significant differences in one or more of the kinematic sway measures of shank, hip, or COM angle when using either of the alternative sway-referencing parameters as compared to the standard EquiTest protocol. The increased sensitivities arising from use of kinematics had the effect of amplifying differences with age. For sway-referencing, the direct kinematic feedback may enhance ability to reduce proprioceptive information by servo-controlling more closely to actual ankle motion. For assessment, kinematics measurements can potentially increase sensitivity for detection of balance disorders, because it may be possible to discriminate between body sway and acceleration and to determine the phase relationship between ankle and hip motion.

Multivariate changes in coordination of postural control following spaceflight.

Postural and gait instabilities in astronauts returning from spaceflight are thought to result from in-flight adaptation of central nervous system processing of sensory inputs from the vestibular, proprioceptive, and visual systems. We hypothesized that reorganization of posture control relying on these multiple inputs would result in not only greater amounts of sway, but also changes in interjoint coordination. We tested this hypothesis by examining the multivariate characteristics of postural sway and comparing the postural control gain used for maintenance of upright stance during the altered sensory conditions of the Sensory Organization Test (EquiTest, Neurocom Intl.). We used the covariance of hip and ankle kinematics as a measure of joint motion and interjoint coordination, and then utilized discriminant analysis to further examine these characteristics in a group of 10 first-time astronauts. In five of the six conditions, the most important difference was an increased relative utilization of the hip strategy, which would not be evident using conventional balance measures such as peak or root-mean-square sway. This finding was supported by indications of increased hip torque gains relative to lower extremity and neck motion in at least four conditions (p < 0.05). In contrast, ankle torque gains to these motions did not appear to change. These results suggest that after spaceflight, astronauts exhibit significant multivariate changes in multijoint coordination, of which increased sway is only one component. These changes are consistent with reweighting of vestibular inputs and changes in control strategy in a multivariable control system.

Effect of altered sensory conditions on multivariate descriptors of human postural sway.

Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

A least-squares estimation approach to improving the precision of inverse dynamics computations.

A least-squares approach to computing inverse dynamics is proposed. The method utilizes equations of motion for a multi-segment body, incorporating terms for ground reaction forces and torques. The resulting system is overdetermined at each point in time, because kinematic and force measurements outnumber unknown torques, and may be solved using weighted least squares to yield estimates of the joint torques and joint angular accelerations that best match measured data. An error analysis makes it possible to predict error magnitudes for both conventional and least-squares methods. A modification of the method also makes it possible to reject constant biases such as those arising from misalignment of force plate and kinematic measurement reference frames. A benchmark case is presented, which demonstrates reductions in joint torque errors on the order of 30 percent compared to the conventional Newton-Euler method, for a wide range of noise levels on measured data. The advantages over the Newton-Euler method include making best use of all available measurements, ability to function when less than a full complement of ground reaction forces is measured, suppression of residual torques acting on the top-most body segment, and the rejection of constant biases in data.

Optimization-based differential kinematic modeling exhibits a velocity-control strategy for dynamic posture determination in seated reaching movements.

We proposed a velocity control strategy for dynamic posture determination that underlay an optimization-based differential inverse kinematics (ODIK) approach for modeling three-dimensional (3-D) seated reaching movements. In this modeling approach, a four-segment seven-DOF linkage is employed to represent the torso and right arm. Kinematic redundancy is resolved efficiently in the velocity domain via a weighted pseudoinverse. Weights assigned to individual DOF describe their relative movement contribution in response to an instantaneous postural change. Different schemes of posing constraints on the weighting parameters, by which various motion apportionment strategies are modeled, can be hypothesized and evaluated against empirical measurements. A numerical optimization procedure based on simulated annealing estimate the weighting parameter values such that the predicted movement best fits the measurement. We applied this approach to modeling 72 seated reaching movements of three distinctive types performed by six subjects. Results indicated that most of the movements were accurately modeled (time-averaged RMSE < 5 degrees) with a simple time-invariant four-weight scheme which represents a time-constant, inter-joint motion apportionment strategy. Modeling error could be further reduced by using less constrained schemes, but notably only for the ones that were relatively poorly modeled with a time-invariant four-weight scheme. The fact that the current modeling approach was able to closely reproduce measured movements and do so in a computationally advantageous way lends support to the proposed velocity control strategy.

An optimal control model for analyzing human postural balance.

The question posed in this study is whether optimal control and state estimation can explain selection of control strategies used by humans, in response to small perturbations to stable upright balance. To answer this question, a human sensorimotor control model, compatible with previous work by others, was assembled. This model incorporates linearized equations and full-state feedback with provision for state estimation. A form of gain-scheduling is employed to account for nonlinearities caused by control and biomechanical constraints. By decoupling the mechanics and transforming the controls into the space of experimentally observed strategies, the model is made amenable to the study of a number of possible control objectives. The objectives studied include cost functions on the state deviations, so as to control the center of mass, provide a stable platform for the head, or maintain upright stance, along with a cost function on control effort. Also studied was the effect of time delay on the stability of controls produced using various control strategies. An objective function weighting excursion of the center of mass and deviations from the upright stable position, while taking advantage of fast modes of the system, as dictated by inertial parameters and musculoskeletal geometry, produces a control that reasonably matches experimental data. Given estimates of sensor performance, the model is also suited for prediction of uncertainty in the response.

A biomechanical analysis of muscle strength as a limiting factor in standing posture.

We developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture. The method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize, geometrically, how constraints internal and external to the body affect movement. We developed an algorithm to calculate the set of all feasible accelerations (i.e., the 'feasible acceleration set', or FAS) that muscles can induce. For the ankle, knee, and hip joints in the sagittal plane, this set is a polyhedron in three dimensions. Using the volume of the FAS as an indicator of overall mobility, we found that strengthening muscles on the posterior side (as opposed to the anterior) of the body would cause greater increases in mobility. Employing the experimental observations of others, we also found that acceleration constraints greatly reduce the range of feasible accelerations. We then defined a set of four basic acceleration vectors which, when used in various combinations, can produce the repertoire of postural movements. We used linear programming to find the maximum magnitudes of these vectors, and the sensitivity of these magnitudes to muscle strength, thereby delineating those muscles which, if strengthened, would cause the greatest increase in the body's ability to generate the basic acceleration vectors. For our particular model, those muscle groups were found to be hamstrings, tibialis anterior, rectus femoris, and gastrocnemius. These muscle groups would be of great importance in cases involving severely reduced muscle strength. This methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling.

Human standing posture: multi-joint movement strategies based on biomechanical constraints.

We developed a theoretical framework for studying coordination strategies in standing posture. The framework consists of a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize, geometrically, how constraints internal and external to the body affect movement. The set of all feasible accelerations (i.e., the "feasible acceleration set" or FAS) that muscles can induce at positions near upright were calculated. We found that musculoskeletal mechanics dictate that independent control of joints is relatively difficult to achieve. When muscle activations are constrained so the knees stay straight, to approximate the typical postural response to perturbation, the corresponding subset of the feasible acceleration set greatly favors a combination of ankle and hip movement in the ratio 1:3 (called the "hip strategy"). Independent control of these two joints remains difficult to achieve. When near the boundary of instability, the orientation and shape of this subset show that the movement strategy necessary to maintain stability, without taking a step, is quite restricted. Hypothesizing that regulation of center-of-mass position is crucial to maintaining balance, we examined the feasible set of center-of-mass accelerations. When the knees must be kept straight, the acceleration of the center of mass is severely limited vertically, but not horizontally. We also found that the "ankle strategy", involving rotation about the ankles only, requires more muscle activation than the "hip strategy" for a given amount of horizontal acceleration. Our model therefore predicts that the hip strategy is most effective at controlling the center of mass with minimal muscle activation ("neural effort").