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.     

Position dependence of ankle joint dynamics--I. Passive mechanics

System identification techniques were used to examine the position dependence of passive ankle joint mechanics. The relaxed ankle was stochastically perturbed about different angles in the range of motion (ROM). The linear dynamic relation between ankle position and torque was identified and modelled as a second-order underdamped system, having inertial (I), viscous (B) and elastic (K) parameters. Mean joint torque changed as the ankle was rotated through the ROM; it was small at mid-range and became much larger toward either extreme. While I remained constant both B and K changed as a function of ankle angle. At the extremes of the ROM, K was much larger than previously assumed and the relation between stiffness and the passive torque generated when the ankle was placed at different mean positions was linear. These results show that large variations in joint mechanics are possible even in the absence of voluntary muscle contraction. Moreover, these changes appear to be related to the torque generated when passive joint structures are stretched.     

Invariance of ankle dynamic stiffness during fatiguing muscle contractions

Our objective was to determine the effect of muscle fatigue on the dynamic stiffness of the human ankle. Four subjects were required to maintain constant-force contractions of tibialis anterior until the required force could no longer be maintained. Repeated pseudo-random displacements of ankle angular position were applied throughout each contraction. The dynamic relation between ankle angular position and ankle torque was identified by determining non-parametric compliance impulse response functions (CIRFs). The CIRFs were redetermined every 2.55s throughout the sustained contractions to provide a quantitative measure of changes in ankle stiffness dynamics. Inspection of these CIRFs revealed little change in shape or magnitude throughout the contractions, despite large increases in tibialis anterior EMG. The dynamics were further quantified by estimating the equivalent joint inertia, viscosity and elasticity associated with each CIRF. As each contraction progressed, the inertial and elastic terms remained constant whereas the viscous term decreased slightly. These findings demonstrate that fatigue of tibialis anterior during sustained constant mean force contractions results in little change in the mechanical dynamics of the human ankle.     

Passive elastic properties of the rat ankle

Passive properties of muscles and tendons, including their elasticity, have been suggested to influence motor control. We examine here the potential role of passive elastic muscle properties at the rat ankle joint, focusing on their potential to specify an equilibrium position of the ankle. We measured the position-dependent passive torques at the rat ankle before and after sequential cuts of flexor (a.k.a. dorsiflexor) and extensor (a.k.a. plantarflexor) ankle muscles. We found that there was a passive equilibrium position of the ankle that shifted systematically with the cuts, demonstrating that the passive torques produced by ankle flexor and extensor muscles work in opposition in order to maintain a stable equilibrium. The mean equilibrium position of the intact rat ankle ranged from 9.3° to 15.7° in extension relative to the orthogonal position, depending on the torque metric. The mean shift in equilibrium position due to severing extensors ranged from 4.4° to 7.7°, and the mean shift due to severing flexors was smaller, ranging from 0.9° to 2.5°. The restoring torques generated by passive elasticity are large enough (approximately 1.5-5 mNm for displacements of 18° from equilibrium) to affect ankle movement during the swing phase of locomotion, and the asymmetry of larger extension vs. flexion torques is consistent with weight support, demonstrating the importance of accounting for passive muscle properties when considering the neural control of movement.     

Contractile properties of human skeletal muscle in childhood and adolescence

Using a combination of single maximal stimuli and maximum voluntary contractions, a comparison has been made of muscle properties in pre- and post-pubertal male subjects. In the dorsiflexor and plantarflexor muscles of the ankle, the twitch and maximum voluntary torques were approximately twice as large in the older subjects; the mean height and mean weight increased by factors of 1.20 and 1.86 respectively. The only other muscle parameter that changed, as a function of age, was the contraction time of the ankle dorsiflexors; the mean value was significantly longer in the older subjects. In the younger subjects, there were already clear differences between the dorsiflexor and plantarflexor muscles, the former developing smaller torques and having shorter contraction and half-relaxation times, greater post-activation potentiation and more susceptibility to fatigue. Even in the youngest subject, motor unit activation was complete in the ankle dorsiflexors; although this was not always true of the plantarflexors, the difference between the two subject groups was not significant.     

Contractile and elastic ankle joint muscular properties in young and older adults

The purpose of this study was to investigate age-related differences in contractile and elastic properties of both dorsi- (DF) and plantarflexor (PF) muscles controlling the ankle joint in young and older adults. Experimental data were collected while twelve young and twelve older male and female participants performed maximal effort isometric and isovelocity contractions on a dynamometer. Equations were fit to the data to give torque-angle (Tθ) and torque-angular velocity (Tω) relations. Muscle series-elasticity was measured during ramped dynamometer contractions using ultrasonography to measure aponeurosis extension as a function of torque; second order polynomials were used to characterize the torque-extension (TΔL) relation. The results showed no age differences in DF maximal torque and none for female PF; however, older males had smaller maximal PF torques compared to young males. In both muscle groups and genders, older adults had decreased concentric force capabilities. Both DF and PF TΔL relations were more nonlinear in the older adults. Older PF, but not DF muscles, were stiffer compared to young. A simple antagonism model suggested age-related differences in Tθ and Tω relations would be magnified if antagonistic torque contributions were included. This assessment of static, dynamic, and elastic joint properties affords a comprehensive view of age-related modifications in muscle function. Although many clinical studies use maximal isometric strength as a marker of functional ability, the results demonstrate that there are also significant age-related modifications in ankle muscle dynamic and elastic properties.     

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.     

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.     

An apparatus to measure in vivo biomechanical behavior of dorsi- and plantarflexors of mouse ankle.

We developed an apparatus to quantify the biomechanical behavior of the dorsi- and plantarflexor muscles of the ankle of an anesthetized mouse. When the dorsi- or plantarflexor muscle group is activated by electrical stimulation of either the peroneal or tibial nerve, the apparatus measures the moment developed about the ankle during isometric, isovelocity shortening, or isovelocity lengthening contractions. Displacements may be performed over the full 105 degrees range of ankle motion with an angular resolution of 0.09 degrees. Bidirectional isovelocity ramps in ankle angle up to 1,100 degrees/s are possible and are equivalent to maximum velocities of 2.3 fiber lengths/s (Lf/s) for the fibers in tibialis anterior muscle and 11.9 Lf/s for those in gastrocnemius muscle. During single contractions of the dorsi- and plantarflexor muscle groups at 37 degrees C and with both knee and ankle joint at 90 degrees neutral position, the isometric tetanic force developed was 1.4 and 3.3 N, power output at 2.2 Lf/s was 3.1 and 5.9 mW, and power absorption at 0.5 Lf/s was 4.9 and 9.0 mW, respectively. These values are in reasonable agreement with data from the same muscle groups tested in situ. We conclude that the apparatus provides valid measurements of force and power of the dorsi- and plantarflexor muscle groups.     

Study of human muscle contraction using electrically evoked twitch responses during passive shortening and lengthening movements

Electrically evoked twitch properties of the human plantarflexor muscles were measured with the muscles at a constant length (static) and during passive shortening and lengthening. A Kin-Com dynamometer system was used to passively move the ankle joint at 0.52 rad s-1 (30 degrees s-1), as well as to record the twitch responses which were elicited by supramaximal electric shocks applied over the tibial nerve in the popliteal fossa. In the lengthening and shortening conditions, twitches were evoked by triggering the shocks so that the twitch response occurred at a similar angular position for all three conditions. The lengthening twitch peak torque was about twice as large as that recorded for the shortening condition. There was, however, no statistical difference in the twitch time course in these three testing conditions. This twofold increase in the peak twitch torque during lengthening, compared to shortening, is much greater than the torque increase reported during eccentric, as compared to concentric maximal voluntary contractions. These findings suggest that a deactivation process of the contractile system occurs during muscle shortening, while in contrast, during passive lengthening a potentiation mechanism is acting, and that both these mechanisms are independent of volitional muscle activation. The present study is the first to demonstrate the possibility of electrically evoked contractions of human muscles during passive lengthening and shortening. We believe that the use of such evoked contractions may be promising for the study of contractile behaviour of human skeletal muscles during eccentric and concentric conditions.     

Contractile changes in opposing muscles of the human ankle joint with aging

The effects of aging on maximal voluntary strength and on the isometric twitch were determined in the ankle dorsiflexor and plantarflexor muscles of 111 healthy men and women aged 20-100 yr. Men were found to be stronger than women at all ages. In both sexes, the average values for maximum voluntary strength of the dorsiflexors and plantarflexors began to decline in the 6th decade. Although the absolute loss of strength was greater for the plantarflexor muscles, the relative losses were similar in the two muscle groups. During maximum voluntary effort, stimulation of motor nerves produced no additional torque in the majority of elderly men and women, indicating that these subjects remained able to utilize their descending motor pathways for optimal muscle activation. Comparisons of muscle compound action potentials, twitch torques, and muscle cross-sectional areas suggested that a decrease in excitable muscle mass was entirely responsible for the lower strength of the elderly. An additional effect of aging was the gradual prolongation of twitch contraction and half-relaxation times throughout the adult life-span.     

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.     

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.     

Motor unit firing patterns of lower leg muscles during isometric plantar flexion with flexed knee joint position

The ankle flexor and extensor muscles are essential for pedal movements associated with car driving. Neuromuscular activation of lower leg muscles is influenced by the posture during a given task, such as the flexed knee joint angle during car driving. This study aimed to investigate the influence of flexion of the knee joint on recruitment threshold-dependent motor unit activity in lower leg muscles during isometric contraction. Twenty healthy participants performed plantar flexor and dorsiflexor isometric ramp contractions at 30 % of the maximal voluntary contraction (MVC) with extended (0°) and flexed (130°) knee joint angles. High-density surface electromyograms were recorded from medial gastrocnemius (MG), soleus (SOL), and tibialis anterior (TA) muscles and decomposed to extract individual motor units. The torque-dependent change (Δpps /Δ%MVC) of the motor unit activity of MG (recruited at 15 %MVC) and SOL (recruited at 5 %MVC) muscles was higher with a flexed compared with an extended knee joint (p < 0.05). The torque-dependent change of TA MU did not different between the knee joint angles. The motor units within certain limited recruitment thresholds recruited to exert plantar flexion torque can be excited to compensate for the loss of MG muscle torque output with a flexed knee joint.     

Behavior of human muscle fascicles during shortening and lengthening contractions in vivo.

The aim of the present study was to investigate the behavior of human muscle fascicles during dynamic contractions. Eight subjects performed maximal isometric dorsiflexion contractions at six ankle joint angles and maximal isokinetic concentric and eccentric contractions at five angular velocities. Tibialis anterior muscle architecture was measured in vivo by use of B-mode ultrasonography. During maximal isometric contraction, fascicle length was shorter and pennation angle larger compared with values at rest (P < 0.01). During isokinetic concentric contractions from 0 to 4.36 rad/s, fascicle length measured at a constant ankle joint angle increased curvilinearly from 49.5 to 69.7 mm (41%; P < 0.01), whereas pennation angle decreased curvilinearly from 14.8 to 9.8 degrees (34%; P < 0.01). During eccentric muscle actions, fascicles contracted quasi-isometrically, independent of angular velocity. The behavior of muscle fascicles during shortening contractions was believed to reflect the degree of stretch applied to the series elastic component, which decreases with increasing contraction velocity. The quasi-isometric behavior of fascicles during eccentric muscle actions suggests that the series elastic component acts as a mechanical buffer during active lengthening.     

Passive muscle mechanical properties of the medial gastrocnemius in young adults with spastic cerebral palsy

Individuals with spastic cerebral palsy (SCP) exhibit restricted joint range of motion and increased joint stiffness due to structural alterations of their muscles. Little is known about which muscle–tendon structures are responsible for these alterations. The aim of this study was to compare the passive mechanics of the ankle joint and medial gastrocnemius (MG) muscle in young adults with SCP and typically developed (TD) individuals. Nine ambulant SCP (17±2 years) and ten TD individuals (18±2 years) participated in the study. Physiological cross sectional area was estimated using freehand 3D ultrasound and found to be 37% lower in the SCP group. An isokinetic dynamometer rotated the ankle through its range while joint torque and ultrasound images of the MG muscle fascicles were simultaneously measured. Mean ankle stiffness was found to be 51% higher and mean MG fascicle strain 47% lower in the SCP group. Increased resistance to passive ankle dorsiflexion in SCP appears to be related to the inability of MG muscle fascicles to elongate with increased force.     

Discharge properties of motor units during steady isometric contractions performed with the dorsiflexor muscles

The purpose of this study was to record the discharge characteristics of tibialis anterior motor units over a range of target forces and to import these data, along with previously reported observations, into a computational model to compare experimental and simulated measures of torque variability during isometric contractions with the dorsiflexor muscles. The discharge characteristics of 44 motor units were quantified during brief isometric contractions at torques that ranged from recruitment threshold to an average of 22 ± 14.4% maximal voluntary contraction (MVC) torque above recruitment threshold. The minimal [range: 5.8-19.8 pulses per second (pps)] and peak (range: 8.6-37.5 pps) discharge rates of motor units were positively related to the recruitment threshold torque (R(2) ≥ 0.266; P < 0.001). The coefficient of variation for interspike interval at recruitment was positively associated with recruitment threshold torque (R(2) = 0.443; P < 0.001) and either decreased exponentially or remained constant as target torque increased above recruitment threshold torque. The variability in the simulated torque did not differ from the experimental values once the recruitment range was set to ～85% MVC torque, and the association between motor twitch contraction times and peak twitch torque was defined as a weak linear association (R(2) = 0.096; P < 0.001). These results indicate that the steadiness of isometric contractions performed with the dorsiflexor muscle depended more on the distributions of mechanical properties than discharge properties across the population of motor units in the tibialis anterior.     

Ankle intrinsic stiffness changes with postural sway

In standing, the human body is inherently unstable and its stabilization requires constant regulation of ankle torque, generated by a combination of ankle intrinsic properties, peripheral reflexes, and central contributions. Ankle intrinsic stiffness, which quantifies the joint intrinsic properties, has been usually assumed constant in standing; however, there is strong evidence that it is highly dependent on the joint torque, which changes significantly with sway in stance. In this study, we examined how ankle intrinsic stiffness changes with postural sway during standing. Ten subjects stood on a standing apparatus, while subjected to pulse perturbations of ankle position. The mean torque of a short period before the start of each pulse was used as a measure of background torque. Responses with similar background torques were grouped together and used to estimate the parameters of an intrinsic stiffness model. Stiffness estimates were normalized to the critical stiffness and the background torque was transformed to the center of pressure location. We found that in most subjects, the normalized stiffness increased linearly with the movement of center of pressure towards the toes, with an average slope of 2.11 ± 0.80 1/m·rad. This modulation of ankle intrinsic stiffness seems functionally appropriate, since the intrinsic stiffness increases quickly, as the center of pressure moves toward the toes and the limits of stability. These large changes of ankle intrinsic stiffness with postural sway must be incorporated in any model of stance control.     

Aging does not affect voluntary activation of the ankle dorsiflexors during isometric, concentric, and eccentric contractions.

This study examines the age-related deficit in force of the ankle dorsiflexors during isometric (Iso), concentric (Con), and eccentric (Ecc) contractions. More specifically, the contribution of neural and muscular mechanisms to the loss of voluntary force was investigated in men and women. The torque produced by the dorsiflexors and the surface electromyogram (EMG) from the tibialis anterior and the soleus were recorded during maximal Iso contractions and during Con and Ecc contractions performed at constant angular velocities (5-100 degrees/s). Central activation was tested by the superimposed electrical stimulation method during maximal voluntary contraction and by computing the ratio between voluntary average EMG and compound muscle action potential (M wave) induced by electrical stimulation (average EMG/M wave). Contractile properties of the dorsiflexor muscles were investigated by recording the mechanical responses to single and paired maximal stimuli. The results showed that the age-related deficit in force (collapsed across genders and velocities) was greater for Iso (20.5%; P < 0.05) and Con (38.6%; P < 0.001) contractions compared with Ecc contractions (6.5%; P > 0.05). When the torque produced during Con and Ecc contractions was expressed relative to the maximal Iso torque, it was significantly reduced in Con contractions and increased in Ecc contractions with aging, with the latter effect being more pronounced for women. In both genders, voluntary activation was not significantly impaired in elderly adults and did not differ from young subjects. Similarly, coactivation was not changed with aging. In contrast, the mechanical responses to single and paired stimuli showed a general slowing of the muscle contractile kinetics with a slightly greater effect in women. It is concluded that the force deficit during Con and Iso contractions of the ankle dorsiflexors in advanced age cannot be explained by impaired voluntary activation or changes in coactivation. Instead, this age-related adaptation and the mechanisms that preserve force in Ecc contractions appeared to be located at the muscular level.     

A parametric model of muscle moment arm as a function of joint angle: Application to the dorsiflexor muscle group in mice

A parametric model was developed to describe the relationship between muscle moment arm and joint angle. The model was applied to the dorsiflexor muscle group in mice, for which the moment arm was determined as a function of ankle angle. The moment arm was calculated from the torque measured about the ankle upon application of a known force along the line of action of the dorsiflexor muscle group. The dependence of the dorsiflexor moment arm on ankle angle was modeled as r=R sin(a+Δ), where r is the moment arm calculated from the measured torque and a is the joint angle. A least-squares curve fit yielded values for R, the maximum moment arm, and Δ, the angle at which the maximum moment arm occurs as offset from 90°. Parametric models were developed for two strains of mice, and no differences were found between the moment arms determined for each strain. Values for the maximum moment arm, R, for the two different strains were 0.99 and 1.14 mm, in agreement with the limited data available from the literature. While in some cases moment arm data may be better fitted by a polynomial, use of the parametric model provides a moment arm relationship with meaningful anatomical constants, allowing for the direct comparison of moment arm characteristics between different strains and species.