A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45–7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.     

A model of human muscle energy expenditure

A model of muscle energy expenditure was developed for predicting thermal, as well as mechanical energy liberation during simulated muscle contractions. The model was designed to yield energy (heat and work) rate predictions appropriate for human skeletal muscle contracting at normal body temperature. The basic form of the present model is similar to many previous models of muscle energy expenditure, but parameter values were based almost entirely on mammalian muscle data, with preference given to human data where possible. Nonlinear phenomena associated with submaximal activation were also incorporated. The muscle energy model was evaluated at varying levels of complexity, ranging from simulated contractions of isolated muscle, to simulations of whole body locomotion. In all cases, acceptable agreement was found between simulated and experimental energy liberation. The present model should be useful in future studies of the energetics of human movement using forward dynamic computer simulation.     

A Model of Human Muscle Energy Expenditure

A model of muscle energy expenditure was developed for predicting thermal, as well as mechanical energy liberation during simulated muscle contractions. The model was designed to yield energy (heat and work) rate predictions appropriate for human skeletal muscle contracting at normal body temperature. The basic form of the present model is similar to many previous models of muscle energy expenditure, but parameter values were based almost entirely on mammalian muscle data, with preference given to human data where possible. Nonlinear phenomena associated with submaximal activation were also incorporated. The muscle energy model was evaluated at varying levels of complexity, ranging from simulated contractions of isolated muscle, to simulations of whole body locomotion. In all cases, acceptable agreement was found between simulated and experimental energy liberation. The present model should be useful in future studies of the energetics of human movement using forward dynamic computer simulation.     

Dynamic optimization of human walking

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by slimming five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.     

Performance criteria for generating predictive optimal control simulations of bicycle pedaling

The purpose of this study was to identify one or more performance-based criteria that may be used to generate predictive optimal control simulations of submaximal pedaling. Two-legged pedaling simulations were generated based on minimizing muscle activation, muscle stress, metabolic energy, time derivative of muscle force, and minimizing metabolic energy while pedaling smoothly. The simulations based on minimizing muscle activation and muscle stress most closely matched experimental pedaling data, with the activation criterion better matching experimental muscle activation timing. We conclude that predictive simulations of submaximal pedaling may be generated using a cost function based on minimizing muscle activation.     

Modeling and optimal control of an energy-storing prosthetic knee

Advanced prosthetic knees for transfemoral amputees are currently based on controlled damper mechanisms. Such devices require little energy to operate, but can only produce negative or zero joint power, while normal knee joint function requires alternative phases of positive and negative work. The inability to generate positive work may limit the user's functional capabilities, may cause undesirable adaptive behavior, and may contribute to excessive metabolic energy cost for locomotion. In order to overcome these problems, we present a novel concept for an energy-storing prosthetic knee, consisting of a rotary hydraulic actuator, two valves, and a spring-loaded hydraulic accumulator. In this paper, performance of the proposed device will be assessed by computational modeling and by simulation of functional activities. A computational model of the hydraulic system was developed, with methods to obtain optimal valve control patterns for any given activity. The objective function for optimal control was based on tracking of joint angles, tracking of joint moments, and the energy cost of operating the valves. Optimal control solutions were obtained, based on data collected from three subjects during walking, running, and a sit-stand-sit cycle. Optimal control simulations showed that the proposed device allows near-normal knee function during all three activities, provided that the accumulator stiffness was tuned to each activity. When the energy storage mechanism was turned off in the simulations, the system functioned as a controlled damper device and optimal control results were similar to literature data on human performance with such devices. When the accumulator stiffness was tuned to walking, simulated performance for the other activities was sub-optimal but still better than with a controlled damper. We conclude that the energy-storing knee concept is valid for the three activities studied, that modeling and optimal control can assist the design process, and that further studies using human subjects are justified.     

The energetic cost of walking: a comparison of predictive methods

Background

The energy that animals devote to locomotion has been of intense interest to biologists for decades and two basic methodologies have emerged to predict locomotor energy expenditure: those based on metabolic and those based on mechanical energy. Metabolic energy approaches share the perspective that prediction of locomotor energy expenditure should be based on statistically significant proxies of metabolic function, while mechanical energy approaches, which derive from many different perspectives, focus on quantifying the energy of movement. Some controversy exists as to which mechanical perspective is “best”, but from first principles all mechanical methods should be equivalent if the inputs to the simulation are of similar quality. Our goals in this paper are 1) to establish the degree to which the various methods of calculating mechanical energy are correlated, and 2) to investigate to what degree the prediction methods explain the variation in energy expenditure.

Methodology/Principal Findings

We use modern humans as the model organism in this experiment because their data are readily attainable, but the methodology is appropriate for use in other species. Volumetric oxygen consumption and kinematic and kinetic data were collected on 8 adults while walking at their self-selected slow, normal and fast velocities. Using hierarchical statistical modeling via ordinary least squares and maximum likelihood techniques, the predictive ability of several metabolic and mechanical approaches were assessed. We found that all approaches are correlated and that the mechanical approaches explain similar amounts of the variation in metabolic energy expenditure. Most methods predict the variation within an individual well, but are poor at accounting for variation between individuals.

Conclusion

Our results indicate that the choice of predictive method is dependent on the question(s) of interest and the data available for use as inputs. Although we used modern humans as our model organism, these results can be extended to other species.     

Neuromusculoskeletal computer modeling and simulation of upright, straight-legged, bipedal locomotion of Australopithecus afarensis (A.L. 288-1)

The skeleton of Australopithecus afarensis (A.L. 288-1, better known as "Lucy") is by far the most complete record of locomotor morphology of early hominids currently available. Even though researchers agree that the postcranial skeleton of Lucy shows morphological features indicative of bipedality, only a few studies have investigated Lucy's bipedal locomotion itself. Lucy's energy expenditure during locomotion has been the topic of much speculation, but has not been investigated, except for several estimates derived from experimental data collected on other animals. To gain further insights into how Lucy may have walked, we generated a full three-dimensional (3D) reconstruction and forward-dynamic simulation of upright bipedal locomotion of this ancient human ancestor. Laser-scanned 3D bone geometries were combined with state-of-the-art neuromusculoskeletal modeling and simulation techniques from computational biomechanics. A detailed full 3D neuromusculoskeletal model was developed that encompassed all major bones, joints (10), and muscles (52) of the lower extremity. A model of muscle force and heat production was used to actuate the musculoskeletal system, and to estimate total energy expenditure during locomotion. Neural activation profiles for each of the 52 muscles that produced a single step of locomotion, while at the same time minimizing the energy consumed per meter traveled, were searched through numerical optimization. The numerical optimization resulted in smooth locomotor kinematics, and the predicted energy expenditure was appropriate for upright bipedal walking in an individual of Lucy's body size.     

Muscle mechanical advantage of human walking and running: implications for energy cost.

Muscular forces generated during locomotion depend on an animal's speed, gait, and size and underlie the energy demand to power locomotion. Changes in limb posture affect muscle forces by altering the mechanical advantage of the ground reaction force (R) and therefore the effective mechanical advantage (EMA = r/R, where r is the muscle mechanical advantage) for muscle force production. We used inverse dynamics based on force plate and kinematic recordings of humans as they walked and ran at steady speeds to examine how changes in muscle EMA affect muscle force-generating requirements at these gaits. We found a 68% decrease in knee extensor EMA when humans changed gait from a walk to a run compared with an 18% increase in hip extensor EMA and a 23% increase in ankle extensor EMA. Whereas the knee joint was extended (154-176 degrees) during much of the support phase of walking, its flexed position (134-164 degrees) during running resulted in a 5.2-fold increase in quadriceps impulse (time-integrated force during stance) needed to support body weight on the ground. This increase was associated with a 4.9-fold increase in the ground reaction force moment about the knee. In contrast, extensor impulse decreased 37% (P < 0.05) at the hip and did not change at the ankle when subjects switched from a walk to a run. We conclude that the decrease in limb mechanical advantage (mean limb extensor EMA) and increase in knee extensor impulse during running likely contribute to the higher metabolic cost of transport in running than in walking. The low mechanical advantage in running humans may also explain previous observations of a greater metabolic cost of transport for running humans compared with trotting and galloping quadrupeds of similar size.     

Using computed muscle control to generate forward dynamic simulations of human walking from experimental data

The objective of this study was to develop an efficient methodology for generating muscle-actuated simulations of human walking that closely reproduce experimental measures of kinematics and ground reaction forces. We first introduce a residual elimination algorithm (REA) to compute pelvis and low back kinematic trajectories that ensure consistency between whole-body dynamics and measured ground reactions. We then use a computed muscle control (CMC) algorithm to vary muscle excitations to track experimental joint kinematics within a forward dynamic simulation. CMC explicitly accounts for delays in muscle force production resulting from activation and contraction dynamics while using a general static optimization framework to resolve muscle redundancy. CMC was used to compute muscle excitation patterns that drove a 21-degrees-of-freedom, 92 muscle model to track experimental gait data of 10 healthy young adults. Simulated joint kinematics closely tracked experimental quantities (mean root-mean-squared errors generally less than 1 degrees), and the time histories of muscle activations were similar to electromyographic recordings. A simulation of a half-cycle of gait could be generated using approximately 30 min of computer processing time. The speed and accuracy of REA and CMC make it practical to generate subject-specific simulations of gait.     

A three-dimensional whole-body model to predict human walking on level ground

Predictive simulation of human walking has great potential in clinical motion analysis and rehabilitation engineering assessment, but large computational cost and reliance on measurement data to provide initial guess have limited its wide use. We developed a computationally efficient model combining optimization and inverse dynamics to predict three-dimensional whole-body motions and forces during human walking without relying on measurement data. Using the model, we explored two different optimization objectives, mechanical energy expenditure and the time integral of normalized joint torque. Of the two criteria, the sum of the time integrals of the normalized joint torques produced a more realistic walking gait. The reason for this difference is that most of the mechanical energy expenditure is in the sagittal plane (based on measurement data) and this leads to difficulty in prediction in the other two planes. We conclude that mechanical energy may only account for part of the complex performance criteria driving human walking in three dimensions.

     

Effects of suppressing arm swing on kinematics, kinetics, and energetics of human walking

Human walking is characterized by pronounced arm movement, yet computer simulation models of walking usually lump the mass of the arms with the head and torso. The implications of this simplification have not been thoroughly documented in the literature. Thus, the purpose of this study was to establish the dependence of several biomechanical and energetic variables on suppressing arm swing (AS) in walking. Eight healthy adult subjects walked with and without normal AS, with speed and stride frequency/length matched between trials. Metabolic data were collected during walking on a treadmill, while kinematic and kinetic data were collected during overground walking. Gross and net energy expenditure were significantly higher during walking without AS, with the mean differences being less than 10%. Joint angles, angular velocities, and ground reaction forces were nearly identical for walking with and without AS. Most joint moments and powers were also similar between AS conditions; however, some kinetic variables (e.g., knee joint power) exhibited larger differences, primarily during the stance phase. The variable that differed most between walking with and without AS was the free vertical moment between the foot and ground. In summary, most variables differed by less than 10% and were highly correlated (r0.90) between walking with and without normal AS. Thus, researchers may be justified in using walking models without articulated arms. However, a few variables exhibited larger differences, which might be of relevance based on the specific research question being addressed.     

Energetic output of subadult polar bears (Ursus maritimus): resting, disturbance and locomotion.

1. Indirect calorimetry was used to determine metabolic rates in subadult polar bears at rest after human-controlled disturbance and at four rates of locomotion. 2. Disturbance factors that do not result in locomotion would only have a significant effect on energy expenditure if they occurred over an extended period of time. 3. Human disturbance resulting in locomotion would have a relatively high energetic cost to individual animals. 4. Polar bears may require a relatively high energetic output to initiate walking.     

In vivo behaviour of human muscle tendon during walking

In the present study we investigated in vivo length changes in the fascicles and tendon of the human gastrocnemius medialis (GM) muscle during walking. The experimental protocol involved real-time ultrasound scanning of the GM muscle, recording of the electrical activity of the muscle, measurement of knee- and ankle-joint rotations, and measurement of ground reaction forces in six men during walking at 3 km h(-1) on a treadmill. Fascicular lengths were measured from the sonographs recorded. Musculotendon complex length changes were estimated from anatomical and joint kinematic data. Tendon length changes were obtained combining the musculotendon complex and fascicular length-change data. The fascicles followed a different length-change pattern from those of the musculotendon complex and tendon throughout the step cycle. Two important features emerged: (i) the muscle contracted near-isometrically in the stance phase, with the fascicles operating at ca. 50 mm; and (ii) the tendon stretched by ca. 7 mm during single support, and recoiled in push-off. The behaviour of the muscle in our experiment indicates consumption of minimal metabolic energy for eliciting the contractile forces required to support and displace the body. On the other hand, the spring-like behaviour of the tendon indicates storage and release of elastic-strain energy. Either of the two mechanisms would favour locomotor economy     

The metabolic and mechanical costs of step time asymmetry in walking

Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg⁻¹) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg⁻¹), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.     

Biomechanical analysis of primate bipedal walking by computer simulation

A computer simulation technique was applied to make clear the mechanical characteristics of primate bipedal walking. A primate body and the walking mechanism were modeled mathematically with a set of dynamic equations. Using a digital computer, the following were calculated from these equations by substituting measured displacements and morphological data of each segment of the primate: the acceleration, joint angle, center of gravity, foot force, joint moment, muscular force, transmitted force at the joint, electric activity of the muscle, generated power by the leg and energy expenditure in walking.The model was evaluated by comparing some of the calculated results with the experimental results such as foot force and electromyographic data, and improved in order to obtain the agreement between them.The level bipedal walking of man, chimpanzee and Japanese monkey and several types of synthesized walking were analyzed from the viewpoint of biomechanics.It is concluded that the bipedal walking of chimpanzee is nearer to that of man than to that of the Japanese monkey because of its propulsive mechanism, but it requires large muscular force for supporting the body weight.     

Individual muscle contributions to the axial knee joint contact force during normal walking

Muscles are significant contributors to the high joint forces developed in the knee during human walking. Not only do muscles contribute to the knee joint forces by acting to compress the joint, but they also develop joint forces indirectly through their contributions to the ground reaction forces via dynamic coupling. Thus, muscles can have significant contributions to forces at joints they do not span. However, few studies have investigated how the major lower-limb muscles contribute to the knee joint contact forces during walking. The goal of this study was to use a muscle-actuated forward dynamics simulation of walking to identify how individual muscles contribute to the axial tibio-femoral joint force. The simulation results showed that the vastii muscles are the primary contributors to the axial joint force in early stance while the gastrocnemius is the primary contributor in late stance. The tibio-femoral joint force generated by these muscles was at times greater than the muscle forces themselves. Muscles that do not cross the knee joint (e.g., the gluteus maximus and soleus) also have significant contributions to the tibio-femoral joint force through their contributions to the ground reaction forces. Further, small changes in walking kinematics (e.g., knee flexion angle) can have a significant effect on the magnitude of the knee joint forces. Thus, altering walking mechanics and muscle coordination patterns to utilize muscle groups that perform the same biomechanical function, yet contribute less to the knee joint forces may be an effective way to reduce knee joint loading during walking.     

An Experimental Analysis of Overcoming Obstacle in Human Walking

In this paper, an experimental analysis of overcoming obstacle in human walking is carried out by means of a motion capture system. In the experiment, the lower body of an adult human is divided into seven segments, and three markers are pasted to each segment with the aim to obtain moving trajectory and to calculate joint variation during walking. Moreover, kinematic data in terms of displacement, velocity and acceleration are acquired as well. In addition, ground reaction forces are measured using force sensors. Based on the experimental results, features of overcoming obstacle in human walking are ana- lyzed. Experimental results show that the reason which leads to smooth walking can be identified as that the human has slight movement in the vertical direction during walking; the reason that human locomotion uses gravity effectively can be identified as that feet rotate around the toe joints during toe-off phase aiming at using gravitational potential energy to provide propulsion for swing phase. Furthermore, both normal walking gait and obstacle overcoming gait are characterized in a form that can provide necessary knowledge and useful databases for the implementation of motion planning and gait planning towards overcoming obstacle for humanoid robots.     

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.