A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle

We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.     

In vivo moment arm determination using B-mode ultrasonography

The tendon excursion of the tibialis anterior (TA) muscle was measured in vivo using B-mode ultrasonography in seven subjects under three force levels (0, 30 and 60% maximal voluntary contraction, MVC). For each force level, the TA moment arm (m) was determined by calculating the derivative of the tendon excursion relative to the ankle angle (a). A dynamometer controlled the ankle angle while force levels were monitored. The parametric model proposed by Miller and Dennis (1996), m = R sin(a + delta), where R is the largest moment arm and delta represents the offset angle of R from 90 degrees, was used in a least-squares fit of the relationship between moment arm and ankle angle. The R values at 0% MVC were significantly smaller than those at 30 and 60% MVC. The values of calculated moment arm at 0% MVC were not considered adequate estimates of the TA moment arm because of the possible confounding effect of the slackness of the relaxed muscle-tendon unit in more dorsiflexed positions. The moment arm values at 30 and 60% MVC were believed to provide reliable estimates of those of TA since the application of tension probably reduced the effects of the slackness of the muscle-tendon unit and tendon elongation on tendon excursion measurement at these force levels. Since the ultrasonographic technique is an in vivo application of the tendon excursion technique and therefore takes the functional meaning into consideration, it can yield more significant moment arms than other in vivo or cadaver techniques.     

Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults

The generation of muscle-actuated simulations that accurately represent the movement of old adults requires a model that accounts for changes in muscle properties that occur with aging. An objective of this study was to adjust the parameters of Hill-type musculo-tendon models to reflect nominal age-related changes in muscle mechanics that have been reported in the literature. A second objective was to determine whether using the parametric adjustments resulted in simulated dynamic ankle torque behavior similar to that seen in healthy old adults. The primary parameter adjustment involved decreasing maximum isometric muscle forces to account for the loss of muscle mass and specific strength with age. A review of the literature suggested the need for other modest adjustments that account for prolonged muscular deactivation, a reduction in maximum contraction velocity, greater passive muscle stiffness and increased normalized force capacity during lengthening contractions. With age-related changes incorporated, a musculo-tendon model was used to simulate isometric and isokinetic contractions of ankle plantarflexor and dorsiflexor muscles. The model predicted that ankle plantarflexion power output during 120 deg/s shortening contractions would be over 40% lower in old adults compared to healthy young adults. These power losses with age exceed the 30% loss in isometric strength assumed in the model but are comparable to 39-44% reductions in ankle power outputs measured in healthy old adults of approximately 70 years of age. Thus, accounting for age-related changes in muscle properties, other than decreased maximum isometric force, may be particularly important when simulating movements that require substantial power development.     

A new method for measuring passive length-tension properties of human gastrocnemius muscle in vivo

The study of muscle growth and muscle length adaptations requires measurement of passive length-tension properties of individual muscles, but until now such measurements have only been made in animal muscles. We describe a new method for measuring passive length-tension properties of human gastrocnemius muscles in vivo. Passive ankle torque and ankle angle data were obtained as the ankle was rotated through its full range with the knee in a range of positions. To extract gastrocnemius passive length-tension curves from passive torque-angle data it was assumed that passive ankle torque was the sum of torque due to structures which crossed only the ankle joint (this torque was a 6-parameter function of ankle joint angle) and a torque due to the gastrocnemius muscle (a 3-parameter function of knee and ankle angle). Parameter values were estimated with non-linear regression and used to reconstruct passive length-tension curves of the gastrocnemius. The reliability of the method was examined in 11 subjects by comparing three sets of measurements: two on the same day and the other at least a week later. Length-tension curves were reproducible: the average root mean square error was 5.1+/-1.1 N for pairs of measurements taken within a day and 7.3+/-1.2 N for pairs of measurements taken at least a week apart (about 3% and 6% of maximal passive tension, respectively). Length-tension curves were sensitive to mis-specification of moment arms, but changes in length-tension curves were not. The new method enables reliable measurement of passive length-tension properties of human gastrocnemius in vivo, and is likely to be useful for investigation of changes in length-tension curves over time.     

Can Achilles tendon moment arm be predicted from anthropometric measures in pre-pubescent children?

Muscle-tendon moment arm magnitudes are essential variables for accurately calculating muscle forces from joint moments. Their measurement requires specialist knowledge and expensive resources. Research has shown that the patellar tendon moment arm length is related to leg anthropometry in children. Here, we asked whether the Achilles tendon moment arm (MA(AT)) can be accurately predicted in pre-pubescent children from surface anthropometry. Age, standing height, mass, foot length, inter-malleolar ankle width, antero-posterior ankle depth, tibial length, lower leg circumference, and distances from the calcaneus to the distal head of the 1st metatarsal and medial malleolus were determined in 49 pre-pubescent children. MA(AT) was calculated at three different ankle positions (neutral, 10° plantarflexion, and 10° dorsiflexion) by differentiating tendon excursion, measured via ultrasonography, with respect to ankle angle change using seven different differentiation techniques. Backwards stepwise regression analyses were performed to identify predictors of MA(AT.) When all variables were included, the regression analysis accounted for a maximum of 49% of MA(AT) variance at the neutral ankle angle when a third-order polynomial was used to differentiate tendon excursion with respect to ankle angle. For this condition, foot length and the distance between calcaneus and 1st metatarsal were the only significant predictors, accounting for 47% of the variance (p<0.05). The absolute error associated with this regression model was 3.8±4.4 mm, which would result in significant error (mean=14.5%) when estimating muscle forces from joint moments. We conclude that MA(AT) cannot be accurately predicted from anthropometric measures in children.     

Mechanomyogram amplitude vs. isometric ankle plantarflexion torque of human medial gastrocnemius muscle at different ankle joint angles

The purpose of this study was to investigate the influence of changes in ankle joint angle on the mechanomyogram (MMG) amplitude of the human medial gastrocnemius (MG) muscle during voluntary isometric plantarflexion contractions. Ten healthy individuals were asked to perform voluntary isometric contractions at six different contraction intensities (from 10% to 100%) and at three different ankle joint angles (plantarflexion of 26°; plantarflexion of 10°; dorsiflexion of 3°). MMG signals were recorded from the surface over the MG muscle, using a 3-axis accelerometer. The relations between root mean square (RMS) MMG and isometric plantarflexion torque at different ankle joint angles were characterized to evaluate the effects of altered muscle mechanical properties on RMS MMG.We found that the relation between RMS MMG and plantarflexion torque is changed at different ankle joint angles: RMS MMG increases monotonically with increasing the plantarflexion torque but decreases as the ankle joint became dorsiflexed. Moreover, RMS MMG shows a negative correlation with muscle length, with passive torque, and with maximum voluntary torque, which were all changed significantly at different ankle joint angles.Our findings demonstrate the potential effects of changing muscle mechanical properties on muscle vibration amplitude. Future studies are required to explore the major sources of this muscle vibration from the perspective of muscle mechanics and muscle activation level, attributable to changes in the neural command.     

Position dependence of ankle joint dynamics--II. Active mechanics

System identification techniques were used to examine the position dependence of active ankle joint mechanics. Subjects were required to maintain tonic contractions in either the tibialis anterior (TA) or triceps surae (TS) muscles while the ankle was stochastically displaced about different mean angular positions. The dynamic relation between ankle position and torque was determined for each mean position/tonic torque combination; a non-linear minimization technique was used to estimate the three parameters (inertial, viscous and elastic) of a second-order, underdamped system. Whereas the inertial parameter remained essentially invariant across all test conditions, the viscous and elastic (K) parameters became larger as the level of tonic activity increased and as the joint was rotated toward the extremes of the range of motion. The relation between K and torque was linear at all ankle angles. The slope of this relation remained constant at all mean positions during plantarflexor contractions; during dorsiflexor contractions the slope increased as the ankle was rotated from maximum plantarflexion to maximum dorsiflexion. These findings are discussed in terms of: the physiological correlates of ankle mean position, the relative significance of passive and active joint mechanics and contrasts in joint behaviour during active dorsiflexor and plantarflexor contractions.     

Relationship between muscle length and moment arm on EMG activity of human triceps surae muscle.

PURPOSE: The purpose of this experiment was to evaluate the effects of both muscle length and moment arm (MA) on the electromyographic (EMG) and force output of the triceps surae (TS) muscle. RELEVANCE: It is well recognized that changes in muscle length affect both the muscle's force generating capacity as well as its twitch speed. This relationship is well established in animal preparations. Contrary to animal experiments where length can be directly manipulated in isolated muscles, human experiments require that all muscle length changes be secondary to changes in a joint angle. Such experimental manipulations therefore produce changes in not only muscle length, but also in the muscle's MA. The relative effect of muscle length and MA changes on muscle EMG has not been determined in previous experiments. METHODS: This study was executed in two phases. First, using fresh human cadaver lower limbs, data were gathered describing the relationship between knee and ankle angle changes for maintenance of a constant TS muscle length, while its MA at the ankle joint has been changed. In the second phase of the study, results obtained from phase one were applied to 10 healthy adult human subjects to measure the EMG (surface and fine wire) activity of TS at three different conditions: when both length and MA were shortened, when muscle length was decreased given a constant MA and when MA was shortened given a constant muscle length. RESULTS: A significant increase in muscle activity was found as both the length and MA of TS muscle were shortened. A similar pattern of increased muscle activity was observed when the MA was shortened given a constant muscle length. No significant change in TS activity was found when muscle length was shortened, given a constant MA at the ankle joint. CONCLUSIONS: The findings of this study indicate that changes in the Achilles tendon MA predominate over the muscle length variations in determining the level of TS activity when generating plantar flexion torque.     

An ankle-foot orthosis powered by artificial pneumatic muscles

We developed a pneumatically powered orthosis for the human ankle joint. The orthosis consisted of a carbon fiber shell, hinge joint, and two artificial pneumatic muscles. One artificial pneumatic muscle provided plantar flexion torque and the second one provided dorsiflexion torque. Computer software adjusted air pressure in each artificial muscle independently so that artificial muscle force was proportional to rectified low-pass-filtered electromyography (EMG) amplitude (i.e., proportional myoelectric control). Tibialis anterior EMG activated the artificial dorsiflexor and soleus EMG activated the artificial plantar flexor. We collected joint kinematic and artificial muscle force data as one healthy participant walked on a treadmill with the orthosis. Peak plantar flexor torque provided by the orthosis was 70 Nm, and peak dorsiflexor torque provided by the orthosis was 38 Nm. The orthosis could be useful for basic science studies on human locomotion or possibly for gait rehabilitation after neurological injury.     

The influence of stimulation frequency and ankle joint angle on the moment exerted by human dorsiflexor muscles.

The purpose of this study was to investigate the force-frequency relationships and the post-tetanic twitch potentiation as a function of joint angle (i.e. muscle length) in human skeletal muscles under isometric conditions. The dorsiflexor muscles of healthy subjects were stimulated at different ankle joint angles by means of constant frequency bursts at seven submaximal frequencies (50, 33, 25, 20, 16, 12, 8 Hz) with a duration of two seconds. Particular attention has been focused on the stability of recruitment in the range of joint angles examined. The results show that moment-frequency curves of human dorsiflexors change as a function of ankle angle: especially for the lower stimulation frequency range (8, 12, 16, 20 Hz), the normalized moment increases from dorsiflexion to plantar flexion (i.e. with increasing muscle length) resulting in a leftward shift of the normalized moment-frequency curves. Post-tetanic twitch potentiation is shown to be ankle joint dependent as well.     

Human ankle joint stiffness over the full range of muscle activation levels

System identification techniques have been used to track changes in dynamic stiffness of the human ankle joint over a wide range of muscle contraction levels. Subjects lay supine on an experimental table with their left foot encased in a rigid, low-inertia cast which was fixed to an electro-hydraulic actuator operating as a position servo. Subjects generated tonic plantarflexor or dorsiflexor torques of different magnitudes ranging from rest to maximum voluntary contractions (MVC) during repeated presentations of a stochastic ankle angular position perturbation. Compliance impulse response functions (IRF) were determined from every 2.5 s perturbation sequence. The gain (G), natural frequency (omega n), and damping (zeta) parameters of the second-order model providing the best fit to each IRF were determined and used to compute the corresponding inertial (I), viscous (B) and elastic (K) stiffness parameters. The behaviour of these parameters with mean torque was found to follow two simple rules. First, the elastic parameter (K) increased in proportion to mean ankle torque as it was varied from rest to MVC; these changes were considerable involving increases of more than an order of magnitude. Second, the damping parameter (zeta) remained almost invariant over the entire range of contractions despite the dramatic changes in K.     

Inevitable joint angular rotation affects muscle architecture during isometric contraction

The purpose of this study was to quantify the influence of inevitable ankle joint motion during an isometric contraction on the measured change of the gastrocnemius medialis muscle (GM) architecture in vivo during the loading and the unloading phase. Sitting on a dynamometer subjects performed isometric maximal voluntary contractions as well as contractions induced by electrostimulation. Synchronous joint angular motion, plantarflexion moment, foot’s centre of pressure and real-time ultrasonography of muscle architecture changes of the GM were obtained. During the contraction the ankle joint position altered and significantly affected the change in muscle architecture. At maximal tendon force (1094 ± 323 N), the measured fascicle length overestimated the change in fascicle length due to the tendon force by 1.53 cm, while the measured pennation angle overestimated the change in pennation angle due to the tendon force by 5.5°. At the same tendon force the measured fascicle length and pennation angle were significantly different between loading and unloading conditions. After correcting the values for the change in ankle joint angle no differences between the loading and the unloading phase at the same tendon force were found. Concerning the estimation of GM fascicle length–force and pennation angle–force curves during the loading and unloading phase of an isometric contraction, these findings indicate that not accounting for ankle joint motion will produce unreliable results.     

Effects of knee joint angle on the fascicle behavior of the gastrocnemius muscle during eccentric plantar flexions

The present study aimed to clarify the effects of knee joint angle on the behavior of the medial gastrocnemius muscle (MG) fascicles during eccentric plantar flexions. Eight male subjects performed maximal eccentric plantar flexions at two knee positions [fully extended (K0) and 90° flexed (K90)]. The eccentric actions were preceded by static plantar flexion at a 30° plantar flexed position and then the ankle joint was forcibly dorsiflexed to 15° of dorsiflexion with an isokinetic dynamometer at 30°/s and 150°/s. Tendon force was calculated by dividing the plantar flexion torque by the estimated moment arm of the Achilles tendon. The MG fascicle length was determined with ultrasonography. The tendon forces during eccentric plantar flexions were influenced by the knee joint angle, but not by the angular velocity. The MG fascicle lengths were elongated as the ankle was dorsiflexed in K0, but in K90 they were almost constant despite the identical range of ankle joint motion. These results suggested that MG fascicle behavior during eccentric actions was markedly affected by the knee joint angle. The difference in the fascicle behavior between K0 and K90 could be attributed to the non-linear force–length relations and/or to the slackness of tendinous tissues.     

Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb

Measurements of human strength can be important during analyses of physical activities. Such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity. However, the available strength varies substantially with joint position and velocity. When examining dynamic activities, strength measurements should account for these variations. A model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity. The model is based on well-known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb. Isometric, concentric and eccentric maximum voluntary contractions were collected during hip extension, hip flexion, knee extension, knee flexion, ankle plantar flexion and dorsiflexion. Model parameters are reported for each of these exertion directions by gender and age group. This model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques.     

Longer moment arm results in smaller joint moment development, power and work outputs in fast motions

Effects of moment arm length on kinetic outputs of a musculoskeletal system (muscle force development, joint moment development, joint power output and joint work output) were evaluated using computer simulation. A skeletal system of the human ankle joint was constructed: a lower leg segment and a foot segment were connected with a hinge joint. A Hill-type model of the musculus soleus (m. soleus), consisting of a contractile element and a series elastic element, was attached to the skeletal system. The model of the m. soleus was maximally activated, while the ankle joint was plantarflexed/dorsiflexed at a variation of constant angular velocities, simulating isokinetic exercises on a muscle testing machine. Profiles of the kinetic outputs (muscle force development, joint moment development, joint power output and joint work output) were obtained. Thereafter, the location of the insertion of the m. soleus was shifted toward the dorsal/ventral direction by 1cm, which had an effect of lengthening/shortening the moment arm length, respectively. The kinetic outputs of the musculoskeletal system during the simulated isokinetic exercises were evaluated with these longer/shorter moment arm lengths. It was found that longer moment arm resulted in smaller joint moment development, smaller joint power output and smaller joint work output in the larger plantarflexion angular velocity region (>120 degrees/s). This is because larger muscle shortening velocity was required with longer moment arm to achieve a certain joint angular velocity. Larger muscle shortening velocity resulted in smaller muscle force development because of the force-velocity relation of the muscle. It was suggested that this phenomenon should be taken into consideration when investigating the joint moment-joint angle and/or joint moment-joint angular velocity characteristics of experimental data.     

The function of gastrocnemius as a knee flexor at selected knee and ankle angles.

The gastrocnemius has been viewed as an important contributor at the knee joint as a joint flexor and stabilizer across all the knee and ankle joint angles. The purpose of this study was to investigate the influence of knee and ankle joint angles on the knee flexor function of the gastrocnemius. Seventeen participants were tested on a Biodex dynamometer with the gastrocnemius muscle selectively stimulated at a standardized level of electrical current. The results indicated that both ankle and knee joint angle influence the knee joint flexion moment produced by the gastrocnemius. Further analysis revealed that the flexion moment was greatest with the knee joint straight (180 degrees ) across all ankle joint angles. The greatest reduction in knee flexion moment occurred between 180 and 165 degrees of knee angle. No significant difference was observed in the knee flexion moment between 165 degrees and 115 degrees knee flexion, and little knee flexion moment was observed at knee angles of 90 degrees and 75 degrees. The dramatic reduction of moment between 180 degrees and 165 degrees knee angle is possibly due to the change of moment arm while the little moment production during extreme flexion (90 degrees and 75 degrees ) may be due to the reduction of muscle length.     

Characterization of muscle belly elastic properties during passive stretching using transient elastography

Passive muscle stretching can be used in vivo to assess the viscoelastic properties of the entire musculo-articular complex, but does not allow the specific determination of the muscle or tendon viscoelasticity. In this respect, the local muscle hardness (LMH) of the gastrocnemius medialis (GM) belly was measured during a passive ankle stretching of 10 subjects using transient elastography. A Biodex isokinetic dynamometer was used to stretch ankle plantar flexors, to measure ankle angle, and the passive torque developed by the ankle joint in resistance to the stretch. Results show that the LMH increased during the stretching protocol, with an averaged ratio between maximal LMH and minimal LMH of 2.62+/-0.46. Furthermore, LMH-passive torque relationships were nicely fitted using a linear model with mean correlation coefficients (R(2)) of 0.828+/-0.099. A good reproducibility was found for the maximal passive torque (ICC=0.976, SEM=2.9Nm, CV=5.5%) and the y-intercept of the LMH-passive torque relationship (ICC=0.893, SEM=105Pa, CV=7.8%). However, the reproducibility was low for the slope of this relationship (ICC=0.631, SEM=10.35m(-2), CV=60.4%). The y-intercept of the LMH-passive torque relationship was not significantly changed after 10min of static stretching. This result confirms the finding of a previous study indicating that changes in passive torque following static stretching could be explained by an acute increase in muscle length without any changes in musculo-articular intrinsic mechanical properties.     

Knee and ankle joint torque-angle relationships of multi-joint leg extension

The force-length-relation (F-l-r) is an important property of skeletal muscle to characterise its function, whereas for in vivo human muscles, torque-angle relationships (T-a-r) represent the maximum muscular capacity as a function of joint angle. However, since in vivo force/torque-length data is only available for rotational single-joint movements the purpose of the present study was to identify torque-angle-relationships for multi-joint leg extension. Therefore, inverse dynamics served for calculation of ankle and knee joint torques of 18 male subjects when performing maximum voluntary isometric contractions in a seated leg press. Measurements in increments of 10° knee angle from 30° to 100° knee flexion resulted in eight discrete angle configurations of hip, knee and ankle joints. For the knee joint we found an ascending-descending T-a-r with a maximum torque of 289.5° ± 43.3 Nm, which closely matches literature data from rotational knee extension. In comparison to literature we observed a shift of optimum knee angle towards knee extension. In contrast, the T-a-r of the ankle joint vastly differed from relationships obtained for isolated plantar flexion. For the ankle T-a-r derived from multi-joint leg extension subjects operated over different sections of the force-length curve, but the ankle T-a-r derived from isolated joint efforts was over the ascending limb for all subjects. Moreover, mean maximum torque of 234.7 ± 56.6 Nm exceeded maximal strength of isolated plantar flexion (185.7 ± 27.8 Nm). From these findings we conclude that muscle function between isolated and more physiological multi-joint tasks differs. This should be considered for ergonomic and sports optimisation as well as for modelling and simulation of human movement.     

Walking with increased ankle pushoff decreases hip muscle moments

In a simple bipedal walking model, an impulsive push along the trailing limb (similar to ankle plantar flexion) or a torque at the hip can power level walking. This suggests a tradeoff between ankle and hip muscle requirements during human gait. People with anterior hip pain may benefit from walking with increased ankle pushoff if it reduces hip muscle forces. The purpose of our study was to determine if simple instructions to alter ankle pushoff can modify gait dynamics and if resulting changes in ankle pushoff have an effect on hip muscle requirements during gait. We hypothesized that changes in ankle kinetics would be inversely related to hip muscle kinetics. Ten healthy subjects walked on a custom split-belt force-measuring treadmill at 1.25m/s. We recorded ground reaction forces and lower extremity kinematic data to calculate joint angles and internal muscle moments, powers and angular impulses. Subjects walked under three conditions: natural pushoff, decreased pushoff and increased pushoff. For the decreased pushoff condition, subjects were instructed to push less with their feet as they walked. Conversely, for the increased pushoff condition, subjects were instructed to push more with their feet. As predicted, walking with increased ankle pushoff resulted in lower peak hip flexion moment, power and angular impulse as well as lower peak hip extension moment and angular impulse (p<0.05). Our results emphasize the interchange between hip and ankle kinetics in human walking and suggest that increased ankle pushoff during gait may help to compensate for hip muscle weakness or injury and reduce hip joint forces.