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1.
This study aimed at examining the effects of joint angle and age on the maximal voluntary contraction (MVC) torque, for the agonist and antagonist muscle groups around the ankle, i.e., the dorsi- and plantar-flexors. To this aim, neural and muscular factors were investigated in two groups of healthy men: 11 young (mean age, 24 years) and 18 older (mean age, 78 years). Plantar-flexion (PF) and dorsiflexion (DF) isometric MVC torques were measured in three different ankle joint angles and surface electromyographic activities of the triceps surae and of the tibialis anterior muscles were recorded. The main findings were that the DF-to-PF MVC torque ratio varied with joint angle and age, indicating that aging affected at different rates the two muscle groups: this ratio was always higher in older adults because of the PF strength decline with aging. Furthermore, the DF MVC torque-angle relationship appeared to be especially explained by neural factors, whereas the relationship in PF seemed to be mainly due to muscular parameters. These relationships would not be a discriminating factor between the two age groups. As a consequence, measurements at one ankle joint angle, whatever the angle, are thus enough to examine the differences within age groups and to perform a rapid assessment of the imbalance at the ankle joint.  相似文献   

2.
The purpose of this study was to test the hypotheses that, under isovelocity conditions, older compared with young humans would 1). be slower to reach target velocity and 2). exhibit a downward shift in the torque-velocity and power-velocity relationships in the ankle dorsiflexor and knee extensor muscles. We studied 12 young (26 +/- 5 yr, 6 men/6 women) and 12 older (72 +/- 6 yr, 6 men/6 women) healthy adults during maximal voluntary concentric contractions at preset target velocities (dorsiflexion: 0-240 degrees /s; knee extension: 0-400 degrees /s) using an isokinetic dynamometer. The time to target velocity was longer in older subjects in the dorsiflexors and knee extensors (both P 相似文献   

3.
Many studies have reported strength gains in older adults following high-intensity resistance training. However, the muscle contraction types examined have been primarily isometric (static) or concentric (CONC; shortening). Less is known about how eccentric (ECC) strength in older adults responds to training or about the efficacy of ECC contractions as training stimuli in these subjects, even though muscle contractions of this type are performed in most training regimens and daily physical activities. In this study, 15 physically active, healthy older women [68 (5) years; mean (SD)] completed an 8-week resistance training program of two sessions per week. Training consisted of three sets of eight repetitions of CONC ankle plantar flexion (PF) and ECC dorsiflexion (DF), at greater than 80% of the initial peak torque, in a standing position only. Subjects were tested in standing and supine positions for: (1) strength over a range of 10° DF to 20° PF for both CONC and ECC; DF and PF (2) passive resistive torque of the plantar flexors at 6°/s; and (3) DF and PF rate of torque development. All strength testing and training was done at 30°/s. Significant increases (P < 0.01) were found for both CONC DF (↑30%) and ECC DF (↑17%) peak torque in the standing position. No significant changes occurred for DF strength as measured with the subjects in the supine position, PF strength in either position, passive resistive torque, or rate of torque development. In summary, strength gains occurred only in the dorsiflexors, which were trained using ECC contractions. Improvements in DF strength were specific to the position of training, which has implications for the transferability of strength gains to functional tasks such as maintaining gait. Accepted: 17 January 1997  相似文献   

4.
Individuals with spastic cerebral palsy (CP) typically experience muscle weakness. The mechanisms responsible for muscle weakness in spastic CP are complex and may be influenced by the intrinsic mechanical properties of the muscle and tendon. The purpose of this study was to investigate the medial gastrocnemius (MG) muscle fascicle active torque-length and Achilles tendon properties in young adults with spastic CP. Nine relatively high functioning young adults with spastic CP (GMFCS I, 17±2 years) and 10 typically developing individuals (18±2 years) participated in the study. Active MG torque-length and Achilles tendon properties were assessed under controlled conditions on a dynamometer. EMG was recorded from leg muscles and ultrasound was used to measure MG fascicle length and Achilles tendon length during maximal isometric contractions at five ankle angles throughout the available range of motion and during passive rotations imposed by the dynamometer. Compared to the typically developing group, the spastic CP group had 33% lower active ankle plantarflexion torque across the available range of ankle joint motion, partially explained by 37% smaller MG muscle and 4% greater antagonistic co-contraction. The Achilles tendon slack length was also 10% longer in the spastic CP group. This study confirms young adults with mild spastic CP have altered muscle–tendon mechanical properties. The adaptation of a longer Achilles tendon may facilitate a greater storage and recovery of elastic energy and partially compensate for decreased force and work production by the small muscles of the triceps surae during activities such as locomotion.  相似文献   

5.
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.  相似文献   

6.
It has been suggested that the effects of old age on the ability to resist fatigue may be task dependent. To test one aspect of this hypothesis, we compared the neuromuscular responses of nine young (26 +/- 4 yr, mean +/- SD) and nine older (72 +/- 4 yr) healthy, relatively sedentary men to intermittent isometric (3 min, 5 s contract/5 s rest) and dynamic (90 at 90 degrees /s) maximum voluntary contractions (MVC) of the ankle dorsiflexor muscles. To assess the mechanisms of fatigue (defined as the ratio of postexercise MVC to preexercise MVC), we also measured isometric central activation ratios (CAR), tetanic torque, contractile properties, and compound muscle action potentials before and immediately after exercise. Because dynamic contractions are more neurally complex and metabolically demanding than isometric contractions, we expected an age-related fatigue resistance observed during isometric exercise to be absent during dynamic exercise. In contrast, older men (O) fatigued less than young (Y) during both isometric (O = 0.77 +/- 0.07, Y = 0.66 +/- 0.02, mean +/- SE; P < 0.01) and dynamic (O = 0.45 +/- 0.07, Y = 0.27 +/- 0.02; P = 0.04) contractions (ratio of postexercise to preexercise MVC), with no evidence of peripheral activation failure in either group. We observed no obvious limitations in central activation in either group, as assessed using isometric CAR methods, after both isometric and dynamic contractions. Preexercise half-time of tetanic torque relaxation, which was longer in O compared with Y, was linearly associated with fatigue resistance during both protocols (r = 0.62 and 0.66, P < or = 0.004, n = 18). These results suggest that relative fatigue resistance is enhanced in older adults during both isometric and isokinetic contractions and that age-related changes in fatigue may be due largely to differences within the muscle itself.  相似文献   

7.
The aim of this study was to investigate the association between the rate of torque development and maximal motor unit discharge frequency in young and elderly adults as they performed rapid submaximal contractions with the ankle dorsiflexors. Recordings were obtained of the torque exerted by the dorsiflexors during the isometric contractions and the surface and intramuscular electromyograms (EMGs) from the tibialis anterior. The maximal rate of torque development and integrated EMG (percentage of total EMG burst) at peak rate of torque development during fast contractions were lower in elderly than young adults by 48% (P < 0.05) and 16.5% (P < 0.05), respectively. The young adults, but not the elderly adults, exhibited a positive association (r2 = 0.33; P < 0.01) between the integrated EMG computed up to the peak rate of torque development and the maximal rate of torque development achieved during the fast contractions. These age-related changes during fast voluntary contractions were accompanied by a decline (P < 0.001) in motor unit discharge frequency (19, 28, and 34% for first 3 interspike intervals, respectively) and in the percentage of units (45%; P < 0.05) that exhibited double discharges (doublets) at brief intervals (<5 ms). Because aging decreased the maximal rate of torque development of fast voluntary contractions to a greater extent ( approximately 10%) than that of an electrically evoked twitch, collectively the results indicate that the age-related decline in maximal motor unit discharge frequency likely limit, in addition to the slowing of muscle contractile properties, the performance of fast voluntary contractions.  相似文献   

8.
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.  相似文献   

9.
A recorded muscular torque at one joint is a resultant torque corresponding to the participation of both agonist and antagonist muscles. This study aimed to examine the effect of aging on the mechanical contributions of both plantar- and dorsi-flexors to the resultant maximal voluntary contraction (MVC) torques exerted at the ankle joint, in dorsi-flexion (DF) and plantar-flexion (PF). The estimation of isometric agonist and antagonist torques by means of an EMG biofeedback technique was made with nine young (mean age 24 years) and nine older (mean age 80 years) men. While there was a non-significant age-related decline in the measured resultant DF MVC torque (?15%; p = 0.06), there was a clear decrease in the estimated agonist MVC torque exerted by the dorsi-flexors (?39%; p = 0.001). The DF-to-PF resultant MVC torque ratio was significantly lower in young than in older men (0.25 vs. 0.31; p = 0.006), whereas the DF-to-PF agonist MVC torque ratio was no longer different between the two populations (0.38 vs. 0.35; p > 0.05). Thus, agonist MVC torques in PF and DF would be similarly affected by aging, which could not be deduced when only resultant torques were examined.  相似文献   

10.
During voluntary contractions, the skeletal muscle of healthy older adults often fatigues less than that of young adults, a result that has been explained by relatively greater reliance on muscle oxidative metabolism in the elderly. Our aim was to investigate whether this age-related fatigue resistance was eliminated when oxidative metabolism was minimized via ischemia induced by cuff (220 mmHg). We hypothesized that 1) older men (n = 12) would fatigue less than young men (n = 12) during free-flow (FF) contractions; 2) both groups would fatigue similarly during ischemia; and 3) reperfusion would reestablish the fatigue resistance of the old. Subjects performed 6 min of intermittent, maximal voluntary isometric contractions of the ankle dorsiflexors under FF and ischemia-reperfusion (IR) conditions. Ischemia was maintained for the first 3 min of contractions, followed by rapid cuff deflation and reperfusion for 3 additional minutes of contractions. Central activation, peripheral activation, and muscle contractile properties were measured at 3 and 6 min of contractions. Older men fatigued less than young men during FF (P 相似文献   

11.
Stretch of an activated muscle causes a transient increase in force during the stretch and a sustained, residual force enhancement (RFE) after the stretch. The purpose of this study was to determine whether RFE is present in human muscles under physiologically relevant conditions (i.e., when stretches were applied within the working range of large postural leg muscles and under submaximal voluntary activation). Submaximal voluntary plantar flexion (PF(v)) and dorsiflexion (DF(v)) activation was maintained by providing direct visual feedback of the EMG from soleus or tibialis anterior, respectively. RFE was also examined during electrical stimulation of the plantar flexion muscles (PF(s)). Constant-velocity stretches (15 degrees /s) were applied through a range of motion of 15 degrees using a custom-built ankle torque motor. The muscles remained active throughout the stretch and for at least 10 s after the stretch. In all three activation conditions, the stable joint torque measured 9-10 s after the stretch was greater than the isometric joint torque at the final joint angle. When expressed as a percentage of the isometric torque, RFE values were 7, 13, and 12% for PF(v), PF(s), DF(v), respectively. These findings indicate that RFE is a characteristic of human skeletal muscle and can be observed during submaximal (25%) voluntary activation when stretches are applied on the ascending limb of the force-length curve. Although the underlying mechanisms are unclear, it appears that sarcomere popping and passive force enhancement are insufficient to explain the presence of RFE in these experiments.  相似文献   

12.
Strength training counteracts motor performance losses during bed rest.   总被引:4,自引:0,他引:4  
The purpose of the study was to determine the effect of bed rest with or without strength training on torque fluctuations and activation strategy of the muscles. Twelve young men participated in a 20-day bed rest study. Subjects were divided into a non-training group (BRCon) and a strength-training group (BRTr). The training comprised dynamic calf-raise and leg-press exercises. Before and after bed rest, subjects performed maximal contractions and steady submaximal isometric contractions of the ankle extensor muscles and of the knee extensor muscles (2.5-10% of maximal torque). Maximal torque decreased for both the ankle extensors (9%, P < 0.05) and knee extensors (16%, P < 0.05) in BRCon but not in BRTr. For the ankle extensors, the coefficient of variation (CV) for torque increased in both groups (P < 0.05), with a greater amount (P < 0.05) in BRCon (88%) compared with BRTr (41%). For the knee extensors, an increase in the CV for torque was observed only in BRCon (22%). The increase in the CV for torque in BRCon accompanied the greater changes in electromyogram amplitude of medial gastrocnemius (122%) and vastus lateralis (59%) compared with BRTr (P < 0.05). The results indicate that fluctuations in torque during submaximal contractions of the extensor muscles in the leg increase after bed rest and that strength training counteracted the decline in performance. The response varied across muscle groups. Alterations in muscle activation may lead to an increase in fluctuations in motor output after bed rest.  相似文献   

13.
During maximal contractions, the sum of forces exerted by homonymous muscles unilaterally is typically higher than the sum of forces exerted by the same muscles bilaterally. However, the underlying mechanism(s) of this phenomenon, which is known as the bilateral strength deficit, remain equivocal. One potential factor that has received minimal attention is the contribution of body adjustments to bilateral and unilateral force production. The purpose of this study was to evaluate the plantar-flexors in an innovative dynamometer that permitted the influence of torque from body adjustments to be adapted. Participants were identically positioned between two setup configurations where torques generated from body adjustments were included within the net ankle torque (locked-unit) or independent of the ankle (open-unit). Twenty healthy adult males performed unilateral and bilateral maximal voluntary isometric plantar-flexion contractions using the dynamometer in the open and locked-unit mechanical configurations. While there was a significant bilateral strength deficit in the locked-unit (p = 0.01), it was not evident in the open-unit (p = 0.07). In the locked-unit, unilateral torque was greater than in the open-unit (p<0.001) and this was due to an additional torque from the body since the electromyographic activity of the agonist muscles did not differ between the two setups (p>0.05). This study revealed that the mechanical configuration of the dynamometer and then the body adjustments caused the observation of a bilateral strength deficit.  相似文献   

14.
Despite an age-related loss of voluntary isometric and concentric strength, muscle strength is well maintained during lengthening muscle actions (i.e., eccentric strength) in old age. Additionally, in younger adults during lengthening of an activated skeletal muscle, the force level observed following the stretch is greater than the isometric force at the same muscle length. This feature is termed residual force enhancement (RFE) and is believed to be a combination of active and passive components of the contractile apparatus. The purpose of this study was to provide an initial assessment of RFE in older adults and utilize aging as a muscle model to explore RFE in a system in which isometric force production is compromised, but structural mechanisms of eccentric strength are well-maintained. Therefore, we hypothesised that older adults will experience greater RFE compared with young adults. Following a reference maximal voluntary isometric contraction (MVC) of the dorsiflexors in 10 young (26.1±2.7y) and 10 old (76.0±6.5y) men, an active stretch was performed at 15°/s over a 30° ankle joint excursion ending at the same muscle length as the reference MVCs (40° of plantar flexion). Any additional torque compared with the reference MVC therefore represented RFE. In older men RFE was ∼2.5 times greater compared to young. The passive component of force enhancement contributed ∼37% and ∼20% to total force enhancement, in old and young respectively. The positive association (R 2 = 0.57) between maintained eccentric strength in old age and RFE indicates age-related mechanisms responsible for the maintenance of eccentric strength likely contributed to the observed elevated RFE. Additionally, as indicated by the greater passive force enhancement, these mechanisms may be related to increased muscle series elastic stiffness in old age.  相似文献   

15.
Antagonist coactivation is the simultaneous activation of agonist and antagonist muscles during a motor task. Age-related changes in coactivation may contribute to observed differences in muscle performance between children and adults. Our aim was to systematically summarize age-related differences in antagonist muscle coactivation during multi-joint dynamic and single-joint isometric and isokinetic contractions. Electronic databases were searched for peer-reviewed studies comparing coactivation in upper or lower extremity muscles between healthy children and adolescents/young adults. Of the 1083 studies initially identified, 25 met eligibility criteria. Thirteen studies examined multi-joint dynamic movements, 10 single-joint isometric contractions, and 2 single-joint isokinetic contractions. Of the studies investigating multi-joint dynamic contractions, 83% (11/13 studies) reported at least one significant age-related difference: In 84% (9/11 studies) coactivation was higher in children, whereas 16% (2/11 studies) reported higher coactivation in adults. Among single-joint contractions, only 25% (3/12 studies) reported significantly higher coactivation in children. Fifty six percent of studies examined females, with no clear sex-related differences. Child-adult differences in coactivation appear to be more prevalent during multi-joint dynamic contractions, where generally, coactivation is higher in children. When examining child–adult differences in muscle function, it is important to consider potential age-related differences in coactivation, specifically during multi-joint dynamic contractions.  相似文献   

16.
The purpose of the work was to determine whether the age-related muscle weakness diminishes older adults’ ability to use mechanisms responsible for maintaining dynamic stability after forward falls. Nine older and nine younger adults participated in this study. To analyse the capacities of the leg-extensor muscle–tendon units, all subjects performed isometric maximal voluntary plantarflexion and knee extension contractions on a dynamometer. The elongation of the gastrocnemius medialis and the vastus lateralis tendon and aponeuroses during isometric contraction was examined by ultrasonography. Recovery behaviour was determined after a sudden fall from two forward-inclined lean angles. Compared to older adults, younger adults had higher muscle strength and tendon stiffness. Younger adults created a higher margin of stability compared to older, independent of perturbation intensity. The main mechanism improving the margin of dynamic stability was the increase of the base of support. The results, further, demonstrated that the locomotion strategy employed before touchdown affects the stability of the stance phase and that muscle strength and tendon stiffness contributed significantly to stability control. We concluded that, to reduce the risk of falls, older individuals may benefit from muscle–tendon unit strengthening programs as well as from interventions exercising the mechanisms responsible for dynamic stability.  相似文献   

17.
The extents to which decreased muscle size or activation are responsible for the decrease in strength commonly observed with aging remain unclear. Our purpose was to compare muscle isometric strength [maximum voluntary contraction (MVC)], cross-sectional area (CSA), specific strength (MVC/CSA), and voluntary activation in the ankle dorsiflexor muscles of 24 young (32 +/- 1 yr) and 24 elderly (72 +/- 1 yr) healthy men and women of similar physical activity level. Three measures of voluntary muscle activation were used: the central activation ratio [MVC/(MVC + superimposed force)], the maximal rate of voluntary isometric force development, and foot tap speed. Men had higher MVC and CSA than did women. Young men had higher MVC compared with elderly men [262 +/- 19 (SE) vs. 197 +/- 22 N, respectively], whereas MVC was similar in young and elderly women (136 +/- 15 vs. 149 +/- 16 N, respectively). CSA was greater in young compared with elderly subjects. There was no age-related impairment of specific strength, central activation ratio, or the rate of voluntary force development. Foot tap speed was reduced in elderly (34 +/- 1 taps/10 s) compared with young subjects (47 +/- 1 taps/10 s). These results suggest that isometric specific strength and the ability to fully and rapidly activate the dorsiflexor muscles during a single isometric contraction were unimpaired by aging. However, there was an age-related deficit in the ability to perform rapid repetitive dynamic contractions.  相似文献   

18.
This paper uses a EMG-driven Hill-type muscle model to estimate individual muscle forces of the triceps surae in isometric plantar flexion contractions. A uniform group of 20 young physical-active adult males was instructed to follow a specific contraction protocol with low (20%MVC) and medium-high (60%MVC) contractions, separated by relaxing intervals. The torque calculated by summing the individual muscle forces multiplied by the respective moment arms was compared to the torque measured by a dynamometer. Musculoskeletal parameters from the literature were used. Then, three different “correction factors” or bias have been applied on some of the muscle model parameters. These factors were based on anthropometric and dynamometric measurements: moment arm scaled by bimalleolar diameter, tendon slack length by leg length and optimal force by the maximum torque. Model torque agreement with dynamometer was recalculated with the parameter scales. It was observed that the relative torque estimation error decreased slightly but significantly when all factors were applied simultaneously (12.92±4.94% without scaling to 10.12±1.73%), which resulted mainly from the correction of the maximal muscle force parameter.  相似文献   

19.
Previous studies have suggested that older adults may be more resistant to muscular fatigue than young adults. We sought to determine whether motor unit firing rate might be a factor that determines the response to fatiguing exercise in young and older subjects. Motor unit recordings and muscular forces were obtained from the tibialis anterior (TA) muscle of 11 young and 8 older individuals. Maximal voluntary force was first measured during maximal-effort dorsiflexion contractions. Each subject then performed a series of 15 maximal isometric contractions, with each contraction lasting 30 s. A 10-s rest period separated the fatiguing contractions. As a result of the fatiguing exercise, both subject groups demonstrated a significant loss in maximal force. The force decline was less in the older adults (20.4%) than in the young adults (33.8%). As expected, prior to muscle fatigue, maximal firing rates in the TA muscle were greater in the young (28.1 ± 5.8 imp/s) than in the older adults (22.3 ± 4.8 imp/s). The decrease in motor unit firing rate with fatigue was also greater in the young adults (34.9%), than in the older adults (22.0%). These results suggest that the greater fatigue-resistance exhibited by older individuals might be explained by the fact that the decline in motor unit firing rate during fatigue is greater in young persons than it is in older adults.  相似文献   

20.
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.  相似文献   

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