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.     

Muscle contributions to whole-body sagittal plane angular momentum during walking

Walking is a complex dynamic task that requires the regulation of whole-body angular momentum to maintain dynamic balance while performing walking subtasks such as propelling the body forward and accelerating the leg into swing. In human walking, the primary mechanism to regulate angular momentum is muscle force generation. Muscles accelerate body segments and generate ground reaction forces that alter angular momentum about the body’s center-of-mass to restore and maintain dynamic stability. In addition, gravity contributes to whole-body angular momentum through its contribution to the ground reaction forces. The purpose of this study was to generate a muscle-actuated forward dynamics simulation of normal walking to quantify how individual muscles and gravity contribute to whole-body angular momentum in the sagittal plane. In early stance, the uniarticular hip and knee extensors (GMAX and VAS), biarticular hamstrings (HAM) and ankle dorsiflexors (TA) generated backward angular momentum while the ankle plantar flexors (SOL and GAS) generated forward momentum. In late stance, SOL and GAS were the primary contributors and generated angular momentum in opposite directions. SOL generated primarily forward angular momentum while GAS generated backward angular momentum. The difference between muscles was due to their relative contributions to the horizontal and vertical ground reaction forces. Gravity contributed to the body’s angular momentum in early stance and to a lesser extent in late stance, which was counteracted primarily by the plantar flexors. These results may provide insight into balance and movement disorders and provide a basis for developing locomotor therapies that target specific muscle groups.     

Pattern of anterior cruciate ligament force in normal walking

The goal of this study was to calculate and explain the pattern of anterior cruciate ligament (ACL) loading during normal level walking. Knee-ligament forces were obtained by a two-step procedure. First, a three-dimensional (3D) model of the whole body was used together with dynamic optimization theory to calculate body-segmental motions, ground reaction forces, and leg-muscle forces for one cycle of gait. Joint angles, ground reaction forces, and muscle forces obtained from the gait simulation were then input into a musculoskeletal model of the lower limb that incorporated a 3D model of the knee. The relative positions of the femur, tibia, and patella and the forces induced in the knee ligaments were found by solving a static equilibrium problem at each instant during the simulated gait cycle. The model simulation predicted that the ACL bears load throughout stance. Peak force in the ACL (303 N) occurred at the beginning of single-leg stance (i.e., contralateral toe off). The pattern of ACL force was explained by the shear forces acting at the knee. The balance of muscle forces, ground reaction forces, and joint contact forces applied to the leg determined the magnitude and direction of the total shear force acting at the knee. The ACL was loaded whenever the total shear force pointed anteriorly. In early stance, the anterior shear force from the patellar tendon dominated the total shear force applied to the leg, and so maximum force was transmitted to the ACL at this time. ACL force was small in late stance because the anterior shear forces supplied by the patellar tendon, gastrocnemius, and tibiofemoral contact were nearly balanced by the posterior component of the ground reaction.     

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.     

Hip joint contact force in the emu (Dromaius novaehollandiae) during normal level walking

The emu is a large, (bipedal) flightless bird that potentially can be used to study various orthopaedic disorders in which load protection of the experimental limb is a limitation of quadrupedal models. An anatomy-based analysis of normal emu walking gait was undertaken to determine hip contact forces for comparison with human data. Kinematic and kinetic data captured for two laboratory-habituated emus were used to drive the model. Muscle attachment data were obtained by dissection, and bony geometries were obtained by CT scan. Inverse dynamics calculations at all major lower-limb joints were used in conjunction with optimization of muscle forces to determine hip contact forces. Like human walking gait, emu ground reaction forces showed a bimodal distribution over the course of the stance phase. Two-bird averaged maximum hip contact force was approximately 5.5 times body weight, directed nominally axially along the femur. This value is only modestly larger than optimization-based hip contact forces reported in literature for humans. The interspecies similarity in hip contact forces makes the emu a biomechanically attractive animal in which to model loading-dependent human orthopaedic hip disorders.     

Contributions of individual muscles to hip joint contact force in normal walking

The human hip joint withstands high contact forces during daily activity and is therefore susceptible to injury and structural deterioration over time. Knowledge of muscle-force contributions to hip joint loading may assist in the development of strategies to prevent and manage conditions such as osteoarthritis, femoro-acetabular impingement and fracture. The main aim of this study was to determine the contributions of individual muscles to hip contact force in normal walking. Muscle contributions to hip contact force were calculated based on a previously published dynamic optimization solution for normal walking, which provided the time histories of joint motion, ground reaction forces, and muscle forces during the stance and swing phases of gait. The force developed by each muscle plus its contribution to the ground reaction force were used to determine the muscle’s contribution to hip contact force. Muscles were the major contributors to hip contact force, with gravitational and centrifugal forces combined contributing less than 5% of the total contact force. Four muscles that span the hip – gluteus medius, gluteus maximus, iliopsoas, and hamstrings – contributed most significantly to the three components of the hip contact force and hip contact impulse (integral of hip contact force over time). Three muscles that do not span the hip – vasti, soleus, and gastrocnemius – also contributed substantially to hip joint loading. These results provide additional insight into lower-limb muscle function during walking and may also be relevant to studies of cartilage degeneration and bone remodelling at the hip.     

An actuated dissipative spring-mass walking model: Predicting human-like ground reaction forces and the effects of model parameters

Simple models are widely used to understand the mechanics of human walking. The optimization-based minimal biped model and spring-loaded-inverted-pendulum (SLIP) model are two popular models that can achieve human-like walking patterns. However, ground reaction forces (GRF) from these two models still deviate from experimental data. In this paper, we proposed an actuated dissipative spring-mass model by integrating these two models to realize more human-like GRF patterns. We first explored the function of stiffness, damping, and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and GRF profiles. The stiffness and objective weight affect the number and size of peaks in the vertical GRF and stance time. The damping changes the relative size of the peaks but has little influence on stance time. Based on these observations, these parameters were manually tuned at three different speeds to approach experimentally measured vertical GRF and the highest correlation coefficient can reach 0.983. These results indicate that the stiffness, damping, and proper objective functions are all important factors in achieving human-like motion for this simple walking model. These findings can facilitate the understanding of human walking dynamics and may be applied in future biped models.     

Modelling torque generation by the mero-carpopodite joint of the american lobster and the snow crab

The torque generated by a rotating joint comprises the useful force exerted by the joint on the external environment, and both the magnitude and distribution of torque through the step cycle during walking are important variables in understanding the mechanics of walking. The mechanics of the American lobster (Homarus americanus) and snow crab (Chionoecetes opilio) during walking were modelled to examine the relative roles of flexor versus extensor apodeme-muscle complexes, investigate which legs of these decapods likely contribute the greatest to locomotion, determine scaling effects of torque generation, and assess the relative roles of various model variables on torque production. Force generated along the length of the apodeme by the muscle was modelled based on apodeme surface area, muscle stress, and muscle fibre pinnation angle. Torque was then calculated from this estimated force and the corresponding moment arm. The flexor apodeme-muscle complex is calculated to generate consistently greater forces than the extensor, and generally this results in flexor torque being larger than extensor, though the snow crab does illustrate the opposite in two of its legs. This greater torque generation in flexion suggests that, in addition to the pushing of the trailing legs, the pulling action of the leading legs may play a significant role, at least during lateral walking. Leg 4 of both species appears to generate greater torques and thus provide the greatest forces for locomotion. Torque generation as a function of body size shows a second order response due to the increase in apodeme surface area. The pinnation angle of the muscle fibre is found to be insignificant in force generation, apodeme surface area (representing muscle cross sectional area) likely plays the most influential role in total force production, and moment arm controls the distribution of this force through the step cycle. Muscle stress remain a largely unknown quantity however, and may significantly affect both magnitude and distribution through step cycle of forces, and thus torque. Despite the uncertainty associated with the muscle stress parameter, the modelled results fit well with previously published force measurements.     

Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking.

Walking is a motor task requiring coordination of many muscles. Previous biomechanical studies, based primarily on analyses of the net ankle moment during stance, have concluded different functional roles for the plantar flexors. We hypothesize that some of the disparities in interpretation arise because of the effects of the uniarticular and biarticular muscles that comprise the plantar flexor group have not been separated. Furthermore, we believe that an accurate determination of muscle function requires quantification of the contributions of individual plantar flexor muscles to the energetics of individual body segments. In this study, we examined the individual contributions of the ankle plantar flexors (gastrocnemius (GAS); soleus (SOL)) to the body segment energetics using a musculoskeletal model and optimization framework to generate a forward dynamics simulation of normal walking at 1.5 m/s. At any instant in the gait cycle, the contribution of a muscle to support and forward progression was defined by its contribution to trunk vertical and horizontal acceleration, respectively, and its contribution to swing initiation by the mechanical energy it delivers to the leg in pre-swing (i.e., double-leg stance prior to toe-off). GAS and SOL were both found to provide trunk support during single-leg stance and pre-swing. In early single-leg stance, undergoing eccentric and isometric activity, they accelerate the trunk vertically but decelerate forward trunk progression. In mid single-leg stance, while isometric, GAS delivers energy to the leg while SOL decelerates it, and SOL delivers energy to the trunk while GAS decelerates it. In late single-leg stance through pre-swing, though GAS and SOL both undergo concentric activity and accelerate the trunk forward while decelerating the downward motion of the trunk (i.e., providing forward progression and support), they execute different energetic functions. The energy produced from SOL accelerates the trunk forward, whereas GAS delivers almost all its energy to accelerate the leg to initiate swing. Although GAS and SOL maintain or accelerate forward motion in mid single-leg stance through pre-swing, other muscles acting at the beginning of stance contribute comparably to forward progression. In summary, throughout single-leg stance both SOL and GAS provide vertical support, in mid single-leg stance SOL and GAS have opposite energetic effects on the leg and trunk to ensure support and forward progression of both the leg and trunk, and in pre-swing only GAS contributes to swing initiation.     

Muscle coordination of mediolateral balance in normal walking

The aim of this study was to describe and explain how individual muscles control mediolateral balance during normal walking. Biomechanical modeling and experimental gait data were used to quantify individual muscle contributions to the mediolateral acceleration of the center of mass during the stance phase. We tested the hypothesis that the hip, knee, and ankle extensors, which act primarily in the sagittal plane and contribute significantly to vertical support and forward progression, also accelerate the center of mass in the mediolateral direction. Kinematic, force plate, and muscle EMG data were recorded simultaneously for five healthy subjects who walked at their preferred speeds. The body was modeled as a 10-segment, 23 degree-of-freedom skeleton, actuated by 54 muscles. Joint moments obtained from inverse dynamics were decomposed into muscle forces by solving an optimization problem that minimized the sum of the squares of the muscle activations. Muscles contributed significantly to the mediolateral acceleration of the center of mass throughout stance. Muscles that generated both support and forward progression (vasti, soleus, and gastrocnemius) also accelerated the center of mass laterally, in concert with the hip adductors and the plantarflexor everters. Gravity accelerated the center of mass laterally for most of the stance phase. The hip abductors, anterior and posterior gluteus medius, and, to a much lesser extent, the plantarflexor inverters, actively controlled balance by accelerating the center of mass medially.     

Comparison of in vivo measured loads in knee,hip and spinal implants during level walking

Walking is a task that we seek to understand because it is the most relevant human locomotion. Walking causes complex loading patterns and high load magnitudes within the human body. This work summarizes partially published load data collected in earlier in vivo measurement studies on 9 patients with telemeterized knee endoprostheses, 10 with hip endoprostheses and 5 with vertebral body replacements. Moreover, for the 19 endoprosthesis patients, additional simultaneously measured and previously unreported ground reaction forces are presented.The ground reaction force and the implant forces in the knee and hip exhibited a double peak during each step. The maxima of the ground reaction forces ranged from 100% to 126% bodyweight. In comparison, the greatest implant forces in the hip (249% bodyweight) and knee (271% bodyweight) were much greater. The mean peak force measured in the vertebral body replacement was 39% bodyweight and occurred at different time points of the stance phase.We concluded that walking leads to high load magnitudes in the knee and hip, whereas the forces in the vertebral body replacement remained relatively low. This indicates that the first peak force was greater in the hip than in the knee joint while this was reversed for the second peak force. The forces in the spinal implant were considerably lower than in the knee and hip joints.     

Muscular contributions to hip and knee extension during the single limb stance phase of normal gait: a framework for investigating the causes of crouch gait

Crouch gait, a troublesome movement abnormality among persons with cerebral palsy, is characterized by excessive flexion of the hips and knees during stance. Treatment of crouch gait is challenging, at present, because the factors that contribute to hip and knee extension during normal gait are not well understood, and because the potential of individual muscles to produce flexion or extension of the joints during stance is unknown. This study analyzed a three-dimensional, muscle-actuated dynamic simulation of walking to quantify the angular accelerations of the hip and knee induced by muscles during normal gait, and to rank the potential of the muscles to alter motions of these joints. Examination of the muscle actions during single limb stance showed that the gluteus maximus, vasti, and soleus make substantial contributions to hip and knee extension during normal gait. Per unit force, the gluteus maximus had greater potential than the vasti to accelerate the knee toward extension. These data suggest that weak hip extensors, knee extensors, or ankle plantar flexors may contribute to crouch gait, and strengthening these muscles--particularly gluteus maximus--may improve hip and knee extension. Abnormal forces generated by the iliopsoas or adductors may also contribute to crouch gait, as our analysis showed that these muscles have the potential to accelerate the hip and knee toward flexion. This work emphasizes the need to consider how muscular forces contribute to multijoint movements when attempting to identify the causes of abnormal gait.     

Contributions of muscles to mediolateral ground reaction force over a range of walking speeds

Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.     

Estimating Youth Locomotion Ground Reaction Forces Using an Accelerometer-Based Activity Monitor

To address a variety of questions pertaining to the interactions between physical activity, musculoskeletal loading and musculoskeletal health/injury/adaptation, simple methods are needed to quantify, outside a laboratory setting, the forces acting on the human body during daily activities. The purpose of this study was to develop a statistically based model to estimate peak vertical ground reaction force (pVGRF) during youth gait. 20 girls (10.9±0.9 years) and 15 boys (12.5±0.6 years) wore a Biotrainer AM over their right hip. Six walking and six running trials were completed after a standard warm-up. Average AM intensity (g) and pVGRF (N) during stance were determined. Repeated measures mixed effects regression models to estimate pVGRF from Biotrainer activity monitor acceleration in youth (girls 10–12, boys 12–14 years) while walking and running were developed. Log transformed pVGRF had a statistically significant relationship with activity monitor acceleration, centered mass, sex (girl), type of locomotion (run), and locomotion type-acceleration interaction controlling for subject as a random effect. A generalized regression model without subject specific random effects was also developed. The average absolute differences between the actual and predicted pVGRF were 5.2% (1.6% standard deviation) and 9% (4.2% standard deviation) using the mixed and generalized models, respectively. The results of this study support the use of estimating pVGRF from hip acceleration using a mixed model regression equation.     

Men and women adopt similar walking mechanics and muscle activation patterns during load carriage

Although numerous studies have investigated the effects of load carriage on gait mechanics, most have been conducted on active military men. It remains unknown whether men and women adapt differently to carrying load. The purpose of this study was to compare the effects of load carriage on gait mechanics, muscle activation patterns, and metabolic cost between men and women walking at their preferred, unloaded walking speed. We measured whole body motion, ground reaction forces, muscle activity, and metabolic cost from 17 men and 12 women. Subjects completed four walking trials on an instrumented treadmill, each five minutes in duration, while carrying no load or an additional 10%, 20%, or 30% of body weight. Women were shorter (p<0.01), had lower body mass (p=0.01), and had lower fat-free mass (p=0.02) compared to men. No significant differences between men and women were observed for any measured gait parameter or muscle activation pattern. As load increased, so did net metabolic cost, the duration of stance phase, peak stance phase hip, knee, and ankle flexion angles, and all peak joint extension moments. The increase in the peak vertical ground reaction force was less than the carried load (e.g. ground force increased approximately 6% with each 10% increase in load). Integrated muscle activity of the soleus, medial gastrocnemius, lateral hamstrings, vastus medialis, vastus lateralis, and rectus femoris increased with load. We conclude that, despite differences in anthropometry, men and women adopt similar gait adaptations when carrying load, adjusted as a percentage of body weight.     

Influence of muscle activity on the forces in the femur: An in vivo study

Experiments were performed on two patients with custom-made instrumented massive proximal femoral prostheses implanted after tumour resection. In vivo axial forces transmitted along the prostheses were telemetered during level walking, single- and double-leg stance, and isometric exercises of the hip muscles. These activities varied the lever arms available to the external loads: minimum for double-leg stance and maximum for hip isometric exercises. Kinematic, force plate, EMG and telemetered force data were recorded simultaneously. The force magnification ration (FMR; the ratio of the telemetered axial force to the external force) was calculated. The FMRs ranged from 1.3 (during double-leg stance) to 29.8 (during abductors test), indicating that a major part of the axial force in the long bones is a response to muscle activity, the strength of which depends on the lever arms available to the external loads. From these results, it was shown that the bulk of the bending moment along limbs is transmitted by a combination of tensile forces in muscles and compressive forces in bones, so moments transmitted by the bones are smaller than the limb moments. It was concluded that appropriate simulation of muscle forces is important in experimental or theoretical studies of load transmission along bones.     

Foot modeling affects ankle sagittal plane kinematics during jump-landing

The foot-ankle complex is a key-element to mitigate impact forces during jump-landing activities. Biomechanical studies commonly model the foot as a single-segment, which can provide different ankle kinematics compared to a multi-segmented model. Also, it can neglect intersegmental kinematics of the foot-ankle joints, such as the hindfoot-tibia, forefoot-hindfoot, and hallux-forefoot joints, that are used during jump-landing activities. The purpose of this short communication was to compare ankle kinematics between a three- and single-segmented foot models, during forward and lateral single-leg jump-landings. Marker trajectories and synchronized ground reaction forces of 30 participants were collected using motion capture and a force plate, during multidirectional single-leg jump-landings. Ankle kinematics were computed using a three- (hindfoot-tibia) and a single-segmented (ankle) foot models, at initial contact (IC), peak vertical ground reaction force (PvGRF) and peak knee flexion (PKF). Repeated measures ANOVAs were conducted (p < 0.05). The findings of this study showed that during lateral and forward jump-landing directions, the three-segmented foot model exhibited lower hindfoot-tibia dorsiflexion angles (PvGRF and PKF, p < 0.001) and excursions (sagittal: p < 0.001; frontal: p < 0.05) during the weightbearing acceptance phase than the single-segmented model. Overall, the two foot models provided distinctive sagittal ankle kinematics, with lower magnitudes in the hindfoot-tibia of the three-segmented foot. Furthermore, the three-segmented foot model may provide additional and representative kinematic data of the ankle and foot joints, to better comprehend its function, particularly in populations whose foot-ankle complex plays an important role (e.g., dancers).     

A new parametric approach for modeling hip forces during gait

An analytical parametric model was developed to estimate the natural biological variations in muscle forces and their effect on the hip forces subject only to physiological constraints and not predefined optimization criterion. Force predictions are based on the joint kinematics and kinetics of each subject, a previously published muscle model, and physiological constraints on the muscle force distributions. The model was used to determine the hip contact forces throughout the stance phase of gait of a subject with a total hip replacement (THR). The parametrically modeled peak hip force without antagonistic muscle activity varied from 2.7 to 3.2 Body Weights (mean 2.9 Body Weights), which agreed well with published in vivo measurements from instrumented THRs in other subjects. For every 10% increase in antagonistic activity, the mean peak hip force increased by 0.2 Body Weights. The parametric model allows one to examine the effect of specific muscle weaknesses or increased antagonistic muscle activity on the hip forces. The model also provides a tool for studying the effect of gait adaptations on hip forces, as predictions are based on each individual's gait data. Differences in peak forces between subjects can then be evaluated relative to the uncertainty in not knowing the precise muscle force distributions.     

Initiation of walk and tiptoe of a planar nine-link biped

A nine-link planar biped model is studied. Its nonlinear differential equations are derived. Constraints due to the connections of the links and the contact between the model and the ground are analyzed, and forces of constraint are specified as functions of the state and inputs. With large external forces acting on the model, connection constraints are maintained by the ligaments and other soft tissue structures. It is shown that ligamentious structures contribute to the stability of the system and help maintain the integrity of the joint. By using linear feedback control, the nine-link model is stabilized around the vertical stance. The stable motion of the system in the vicinity of the vertical is studied by computer simulation of walking and tiptoe gaits.