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1.
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   

2.
During lengthening of an activated skeletal muscle, the force maintained following the stretch is greater than the isometric force at the same muscle length. This is termed residual force enhancement (RFE), but it is unknown how muscle damage following repeated eccentric contractions affects RFE. Using the dorsiflexors, we hypothesised muscle damage will impair the force generating sarcomeric structures leading to a reduction in RFE. Following reference maximal voluntary isometric contractions (MVC) in 8 young men (26.5±2.8y) a stretch was performed at 30°/s over a 30° ankle excursion ending at the same muscle length as the reference MVCs (30° plantar flexion). Surface electromyography (EMG) of the tibialis anterior and soleus muscles was recorded during all tasks. The damage protocol involved 4 sets of 25 isokinetic (30°/s) lengthening contractions. The same measures were collected at baseline and immediately post lengthening contractions, and for up to 10min recovery. Following the lengthening contraction task, there was a 30.3±6.4% decrease in eccentric torque (P<0.05) and 36.2±9.7% decrease in MVC (P<0.05) compared to baseline. Voluntary activation using twitch interpolation and RMS EMG amplitude of the tibialis anterior remained near maximal without increased coactivation for MVC. Contrary to our hypothesis, RFE increased (~100-250%) following muscle damage (P<0.05). It appears stretch provided a mechanical strategy for enhanced muscle function compared to isometric actions succeeding damage. Thus, active force of cross-bridges is decreased because of impaired excitation-contraction coupling but force generated during stretch remains intact because force contribution from stretched sarcomeric structures is less impaired.  相似文献   

3.
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.  相似文献   

4.
Following active muscle lengthening, steady-state isometric force is elevated compared with an isometric contraction without prior lengthening for the same muscle length and activation level. This property of muscle contraction is known as residual force enhancement (RFE). Here, we aimed to determine whether neural factors may mask some of the mechanical benefits of RFE on plantar flexion torque production. Inherent to lengthening contractions is an increase in cortical and spinal-mediated inhibition, while knee flexion places the medial gastrocnemius at a neuromechanical disadvantage. Neuromuscular properties of the plantar flexors were investigated with a Humac Norm dynamometer in 10 males (∼27 years) with a flexed (90°) and extended (180°) knee and with or without calcaneal tendon vibration (frequency range: 80–110 Hz). There was no effect for vibration (p > 0.05), but there was an effect for knee angle (p < 0.05) such that there was a 2 fold increase in RFE with the knee flexed compared with extended. During submaximal torque matching, following active lengthening there was an activation reduction (electromyography; EMG) of 7.2 and 4.7% with the knee flexed and extended, respectively for soleus as compared with the reference isometric contraction, but no difference for the medial gastrocnemius. Despite attempting to excite Ia input onto the plantar flexor motor neuron pool, vibration had no influence on RFE. Surprisingly, RFE was elevated more for the knee flexed than extended, which was possibly owing to the activation differences across the disparate muscles of the triceps surae during the plantar flexion task.  相似文献   

5.
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   

6.
The purpose of this study was to evaluate whether and how isometric multijoint leg extension strength can be used to assess athletes' muscular capability within the scope of strength diagnosis. External reaction forces (Fext) and kinematics were measured (n = 18) during maximal isometric contractions in a seated leg press at 8 distinct joint angle configurations ranging from 30 to 100° knee flexion. In addition, muscle activation of rectus femoris, vastus medialis, biceps femoris c.l., gastrocnemius medialis, and tibialis anterior was obtained using surface electromyography (EMG). Joint torques for hip, knee, and ankle joints were computed by inverse dynamics. The results showed that unilateral Fext decreased significantly from 3,369 ± 575 N at 30° knee flexion to 1,015 ± 152 N at 100° knee flexion. Despite maximum voluntary effort, excitation of all muscles as measured by EMG root mean square changed with knee flexion angles. Moreover, correlations showed that above-average Fext at low knee flexion is not necessarily associated with above-average Fext at great knee flexion and vice versa. Similarly, it is not possible to deduce high joint torques from high Fext just as above-average joint torques in 1 joint do not signify above-average torques in another joint. From these findings, it is concluded that an evaluation of muscular capability by means of Fext as measured for multijoint leg extension is strongly limited. As practical recommendation, we suggest analyzing multijoint leg extension strength at 3 distinct knee flexion angles or at discipline-specific joint angles. In addition, a careful evaluation of muscular capacity based on measured Fext can be done for knee flexion angles ≥ 80°. For further and detailed analysis of single muscle groups, the use of inverse dynamic modeling is recommended.  相似文献   

7.
The purpose of this study was to determine in vivo moment arm lengths (MAs) of three elbow flexors at rest and during low- and relatively high-intensity contractions, and to examine the contraction intensity dependence of MAs at different joint positions. At 50°, 80° and 110° of elbow flexion, MAs of the biceps brachii, brachialis and brachioradialis were measured in 10 young men using sagittal images of the right arm obtained by magnetic resonance imaging, at rest and during 20% and 60% of isometric maximal voluntary elbow flexion. In most conditions, MAs increased with isometric contractions, which is presumably due to the contraction-induced thickening of the muscles. This phenomenon was especially evident in the flexed elbow positions. The influence of the contraction intensities on the increases in MAs varied across the muscles. These results suggest that in vivo measurements of each elbow flexor MA during contractions are essential to properly examine the effects on the interrelationships between elbow flexion torque and individual muscle forces.  相似文献   

8.
It is thought that the magnitude of residual force enhancement (RFE) is not affected by stretch velocity. However, the range of stretch velocities studied in previous investigations has been limited to slow and moderate velocities. High velocities of muscle stretching are associated with a loss of force and incomplete cross-bridge attachment to actin, thus creating a unique set of eccentric conditions referred to as slippage. The purpose of this study was to extend the relationship between stretch velocity and RFE to high velocities. We hypothesized that slippage at high velocities might affect RFE. We stretched cat soleus muscles for 4 mm to the plateau of the force-length relationship at speeds of 2, 4, 8, 16, 32, 64 mm/s to induce RFE, and slippage for the fastest condition. For each RFE test, a corresponding isometric reference test was conducted. Residual force enhancement was quantified as the relative increase in isometric steady state force between the experimental stretch and the isometric reference tests. Residual force enhancement was similar for all stretch speeds, as expected, with the exception of the fastest speed (64 mm/s), which was associated with slippage and no significant RFE. These results suggest that if stretch speeds are too fast, and are associated with slippage, RFE is abolished. We conclude from these findings that proper cross-bridge engagement is required during eccentric muscle action to produce RFE.  相似文献   

9.
This study compared the steadiness of submaximal contractions with the knee extensor muscles in young and old adults. Twenty young and twenty old subjects underwent assessment of isometric maximum voluntary contraction (MVC), one-repetition maximum (1-RM) strength, and steadiness during isometric, concentric, and eccentric contractions with the knee extensor muscles. The old adults displayed 33% lower MVC force and a 41% lower 1-RM load. The coefficient of variation for force was significantly greater for the old adults during isometric contractions at 2, 5, and 10% of MVC but not at 50% MVC. The decline in steadiness at low forces experienced by the men was marginally greater than that experienced by the women. The steadiness of concentric and eccentric contractions was similar in young and old adults at 5, 10, and 50% of 1-RM load. Old subjects exhibited greater coactivation of an antagonist muscle compared with young subjects during the submaximal isometric and anisometric contractions. These results indicate that, whereas the ability to exert steady submaximal forces with the knee extensor muscles was reduced in old adults, fluctuations in knee joint angle during slow movements were similar for young and old adults.  相似文献   

10.
The objectives were to examine knee angle-, and gender-specific knee extensor torque output and quadriceps femoris (QF) muscle recruitment during maximal effort, voluntary contractions. Fourteen young adult men and 15 young adult women performed three isometric maximal voluntary contractions (MVC), in a random order, with the knee at 0 degrees (terminal extension), 10 degrees, 30 degrees, 50 degrees, 70 degrees, and 90 degrees flexion. Knee extensor peak torque (PT), and average torque (AT) were expressed in absolute (N m), relative (N m kg(-1)) and allometric-modeled (N m kg(-n)) units. Vastus medialis (VM), vastus lateralis (VL), and rectus femoris (RF) muscle EMG signals were full-wave rectified and integrated over the middle 3 s of each contraction, averaged over the three trials at each knee angle, and normalized to the activity recorded at 0 degrees. Muscle recruitment efficiency was calculated as the ratio of the normalized EMG of each muscle to the allometric-modeled average torque (normalized to the values at 0 degrees flexion), and expressed as a percent. Men generated significantly greater knee extensor PT and AT than women in absolute, relative and allometric-modeled units. Absolute and relative PT and AT were significantly highest at 70 degrees, while allometric-modeled values were observed to increase significantly across knee joint angles 10-90 degrees. VM EMG was significantly greater than the VL and RF muscles across all angles, and followed a similar pattern to absolute knee extensor torque. Recruitment efficiency improved across knee joint angles 10-90 degrees and was highest for the VL muscle. VM recruitment efficiency improved more than the VL and RF muscles across 70-90 degrees flexion. The findings demonstrate angle-, and gender-specific responses of knee extensor torque to maximal-effort contractions, while superficial QF muscle recruitment was most efficient at 90 degrees, and less dependent on gender.  相似文献   

11.
The purpose of this study was to examine the effect of different muscle contraction modes and intensities on patellar tendon moment arm length (d(PT)). Five men performed isokinetic concentric, eccentric and passive knee extensions at an angular velocity of 60 deg/s and six men performed gradually increasing to maximum effort isometric muscle contractions at 90( composite function) and 20( composite function) of knee flexion. During the tests, lateral X-ray fluoroscopy imaging was used to scan the knee joint. The d(PT) differences between the passive state and the isokinetic concentric and extension were quantified at 15( composite function) intervals of knee joint flexion angle. Furthermore, the changes of the d(PT) as a function of the isometric muscle contraction intensities were determined during the isometric knee extension at 90( composite function) and 20( composite function) of knee joint flexion. Muscle contraction-induced changes in knee joint flexion angle during the isometric muscle contraction were also taken into account for the d(PT) measurements. During the two isometric knee extensions, d(PT) increased from rest to maximum voluntary muscle contraction (MVC) by 14-15%. However, when changes in knee joint flexion angle induced by the muscle contraction were taken into account, d(PT) during MVC increased by 6-26% compared with rest. Moreover, d(PT) increased during concentric and eccentric knee extension by 3-15%, depending on knee flexion angle, compared with passive knee extension. These findings have important implications for estimating musculoskeletal loads using modelling under static and dynamic conditions.  相似文献   

12.
Hamstring strain rehabilitation programs with an eccentric bias are effective but have a low adherence rate. Post-stretch isometric (PS-ISO) contractions which incorporate a highly controlled eccentric contraction followed by an isometric contraction resulting in elevated torque during following stretch, compared with isometric contractions at the same joint angle. This study measured torque, activation and musculotendinous unit behaviour of the hamstrings during PS-ISO contractions of maximal and submaximal levels using two stretch amplitudes. Ten male participants (24.6 years ± 2.22 years) completed maximal and submaximal baseline isometric contractions at 90°, 120° and 150° knee flexion and PS-ISO contractions of maximal and submaximal intensity initiated at 90° and 120° incorporating active stretch of 30° and 60° at 60°·s−1. Torque and muscle activation of the knee flexors were simultaneously recorded. Musculotendinous unit behaviour of the biceps femoris long head was recorded via ultrasound during all PS-ISO contractions. Compared with baseline, torque was 8% and 39% greater in the maximal and submaximal PS-ISO conditions respectively with no change in muscle activation. The biceps femoris long head muscle lengthened during all PS-ISO contractions. PS-ISO contractions may be beneficial where the effects of highly controlled eccentric contractions and elevated isometric torque are desired, such as hamstring rehabilitation.  相似文献   

13.
Although activity of the rectus femoris (RF) differs from that of the other synergists in quadriceps femoris muscle group during physical activities in humans, it has been suggested that the activation pattern of the vastus intermedius (VI) is similar to that of the RF. The purpose of present study was to examine activation of the VI during isometric hip flexion. Ten healthy men performed isometric hip flexion contractions at 25%, 50%, 75%, and 100% of maximal voluntary contraction at hip joint angles of 90°, 110° and 130°. Surface electromyography (EMG) was used to record activity of the four quadriceps femoris muscles and EMG signals were root mean square processed and normalized to EMG amplitude during an isometric knee extension with maximal voluntary contraction. The normalized EMG was significantly higher for the VI than for the vastus medialis during hip flexion at 100% of maximal voluntary contraction at hip joint angles of 110° and 130° (P < 0.05). The onset of VI activation was 230–240 ms later than the onset of RF activation during hip flexion at each hip joint angle, which was significantly later than during knee extension at 100% of maximal voluntary contraction (P < 0.05). These results suggest that the VI is activated later than the RF during hip flexion. Activity of the VI during hip flexion might contribute to stabilize the knee joint as an antagonist and might help to smooth knee joint motion, such as in the transition from hip flexion to knee extension during walking, running and pedaling.  相似文献   

14.
Maximal and submaximal activation level of the right knee-extensor muscle group were studied during isometric and slow isokinetic muscular contractions in eight male subjects. The activation level was quantified by means of the twitch interpolation technique. A single electrical impulse was delivered, whatever the contraction mode, on the femoral nerve at a constant 50 degrees knee flexion (0 degrees = full extension). Concentric, eccentric (both at 20 degrees /s velocity), and isometric voluntary activation levels were then calculated. The mean activation levels during maximal eccentric and maximal concentric contractions were 88.3 and 89.7%, respectively, and were significantly lower (P < 0.05) with respect to maximal isometric contractions (95.2%). The relationship between voluntary activation levels and submaximal torques was linearly fitted (P < 0.01): comparison of slopes indicated lower activation levels during submaximal eccentric compared with isometric or concentric contractions. It is concluded that reduced neural drive is present during 20 degrees /s maximal concentric and both maximal and submaximal eccentric contractions. These results indicate a voluntary activation dependency on both tension levels and type of muscular actions in the human knee-extensor muscle group.  相似文献   

15.
Stretch of activated muscles leads to enhanced forces compared to isometric contractions at the same muscle length and the same level of activation. This so-called residual force enhancement (RFE) is thought to be a property of all muscles and preparations. However, observations concerning the existence, amount and duration of RFE are inconsistent, especially for voluntary activated large human muscles. Therefore, physiological relevance for daily activity is still questionable and the purpose of this study was to examine whether RFE is present in voluntary sub-maximal activated quadriceps femoris (QF). Seated in a rotational dynamometer with EMG attached to superficial parts of QF, 30 subjects performed isometric and isometric-eccentric-isometric contractions (20° stretch, ω = 60° s−1) at 30% and 60% of maximum voluntary activation (MVA) and contraction (MVC). To account for the complexity of the multi-headed QF, a compensation model based on physiological cross-sectional area and individual EMG-torque relations was used to interpret EMG data. For both levels of intensity and both feedback control strategies, ANOVA identified significant RFE (at the same level of activation) and reduced activation (at the same level of torque). Against expectations, RFE was independent of the level of activation.  相似文献   

16.
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   

17.
Following active lengthening of muscle, force reaches an isometric steady state above that which would be achieved for a purely isometric contraction at the same muscle length. This fundamental property of muscle, termed “residual force enhancement (RFE),” cannot be predicted by the force-length relationship, and is unexplained by the cross-bridge theory of muscle contraction. Recently, we showed that older adults experience higher RFE than young for the ankle dorsiflexors primarily owing to a greater reliance on passive force enhancement (PFE) and similar RFE for the knee extensors but a greater contribution of PFE to total RFE. Natural adult aging may prove a useful model in exploring mechanisms of RFE which may reside in the dissipation of force transients following stretch. A post-hoc analysis was conducted on previously described RFE experiments in young (~26 years) and old (~77 years) men for the dorsiflexors and knee extensors to fit the force following stretch with a biexponential decay. In both muscle groups the decay half-life of the first exponential was two times slower in the older compared with young men. There were significant associations between PFE and the decay in force, suggesting a greater “non-active” contribution to total RFE across muscles in older compared with young men. The greater “non-active” component of RFE in older adults could be due to structural age-related changes causing increased muscle stiffness during and following stretch.  相似文献   

18.
The current investigation examined the effect of various types of background muscle contractions on the short-latency stretch reflex (SLR) elicited from the soleus muscle while subjects were in a sitting position. A stretch was applied to the calf muscles while they performed an isometric (pre-ISO), shortening (pre-SHO) and lengthening contraction (pre-LEN) with several pre-contraction levels. The ankle was at a 90 degrees tibio-tarsal joint angle when the perturbation was applied. Subjects developed and maintained a given pre-load level, which was maintained at various percentages of the maximum voluntary isometric plantar flexion torque. This was performed at 80 degrees in pre-SHO, 90 degrees in pre-ISO and 100 degrees in pre-LEN for about 2s before the contractions. The SLRs in trials with 0, 35 and 50% of the maximum voluntary contraction torque level were compared among the three conditions. The main results were as follows. (1) Pre-ISO and pre-SHO showed an equal SLR area and a different SLR waveform in the active muscle. (2) Pre-LEN showed the smallest SLR area of three conditions in the active muscle. (3) Pre-LEN showed shorter SLR latencies than the other conditions. (4) Pre-SHO showed a longer SLR latency in the relaxed muscle than in the active muscle. (5) The SLR area was larger in the active muscle than in the relaxed muscle. These findings demonstrate that the muscle contraction type and the pre-contraction level before a stretch perturbation have a considerable influence on the latency, the area and the waveform of the SLR. In particular, the equal area and the different waveforms of the SLR between pre-ISO and pre-SHO were a unique finding in the present study. They might result from differences in muscle spindle sensitivity and afferent input from various receptors induced by the present motor task.  相似文献   

19.
The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.  相似文献   

20.
Firing rates of motor units and surface EMG were measured from the triceps brachii muscles of able-bodied subjects during brief submaximal and maximal isometric voluntary contractions made at 5 elbow joint angles that covered the entire physiological range of muscle lengths. Muscle activation at the longest, midlength, and shortest muscle lengths, measured by twitch occlusion, averaged 98%, 97%, and 93% respectively, with each subject able to achieve complete activation during some contractions. As expected, the strongest contractions were recorded at 90 degrees of elbow flexion. Mean motor unit firing rates and surface EMG increased with contraction intensity at each muscle length. For any given absolute contraction intensity, motor unit firing rates varied when muscle length was changed. However, mean motor unit firing rates were independent of muscle length when contractions were compared with the intensity of the maximal voluntary contraction (MVC) achieved at each joint angle.  相似文献   

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