Motor unit firing rates during isometric voluntary contractions performed at different muscle lengths

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.     

Motor unit activation patterns during concentric wrist flexion in humans with different muscle fibre composition

Muscle activity was recorded from the flexor carpi radialis muscle during static and dynamic-concentric wrist flexion in six subjects, who had exhibited large differences in histochemically identified muscle fibre composition. Motor unit recruitment patterns were identified by sampling 310 motor units and counting firing rates in pulses per second (pps). During concentric wrist flexion at 30% of maximal exercise intensity the mean firing rate was 27 (SD 13) pps. This was around twice the value of 12 (SD 5) pps recorded during sustained static contraction at 30% of maximal voluntary contraction, despite a larger absolute force level during the static contraction. A similar pattern of higher firing rates during dynamic exercise was seen when concentric wrist flexion at 60% of maximal exercise intensity [30 (SD 14) pps] was compared with sustained static contraction at 60% of maximal voluntary contraction [19 (SD 8) pps]. The increase in dynamic exercise intensity was accomplished by recruitment of additional motor units rather than by increasing the firing rate as during static contractions. No difference in mean firing rates was found among subjects with different muscle fibre composition, who had previously exhibited marked differences in metabolic response during corresponding dynamic contractions. It was concluded that during submaximal dynamic contractions motor unit firing rate cannot be deduced from observations during static contractions and that muscle fibre composition may play a minor role. Accepted: 5 May 1998     

Motor unit recruitment strategy of knee antagonist muscles in a step-wise, increasing isometric contraction

The purpose of this study was to determine if differences exist between the control strategies of two antagonist thigh muscles during knee flexion and extension muscular coactivation. Surface myoelectric signal (MES) of the quadriceps (rectus femoris) and the hamstrings (semitendinosus) were obtained from both muscles while performing step-wise increasing contractions during flexion and extension with the knee at 1.57 rad of flexion (90 degrees). The median frequency of the power density spectrum, which is related to the average muscle fiber action potential conduction velocity and therefore to motor unit recruitment, was calculated from each MES. The results suggest that, in all the subjects tested, when the muscle acts as antagonist most motor units are recruited up to 50% of the maximal voluntary force, whereas when the muscle acts as antagonist motor units are recruited up to 40% of the maximal voluntary force. The force range past 40–50% of the maximal force is also characterized by differences between the agonist/antagonist.     

Contrast of directional influence upon motor overflow between submaximal and maximal static exertions

This study investigated exertion-dependent motor overflow among healthy adults when they performed isometric tasks with contralateral joints in different task directions. Twenty healthy adults (10 males and 10 females, mean age = 26.2 yrs) were instructed to complete a set of isometric contractions of various force vectors with the shoulder, elbow, and wrist joints, in a total of ten motor tasks at submaximal and maximal intensities (50%, 100% maximal voluntary contractions). The electromyographical activities from eight muscles of the unexercised upper limb were recorded to characterize intensity of motor overflow during sustained isometric contraction. Both occurrence frequency and magnitude of motor overflow in terms of standardized net excitation (SNE) increased with exertion level for all joint movements (P < 0.001). Additionally, the motor overflow magnitude depended strongly on the task direction of maximal isometric contraction (P < 0.05). Motor overflow was particularly augmented by the contralateral isometric contractions where task directions were opposed to gravity. However, such a directional effect upon SNE was not evident during submaximal contraction (P > 0.05). The difference of the net excitation between maximal and submaximal contraction (DNE(100%-50%MVC) data) indicated that the pectoralis major and triceps brachii consistently exhibited a marked recruitment in reaction to change in task direction of isometric contraction. Patterned motor overflow may be physiologically relevant to topological mapping of the ipsilateral pathways and altered effectiveness of use-dependent interhemispherical connectivity. The current observations provide better insight into gain in muscle strength due to contralateral exercise.     

Use of motor cortex stimulation to measure simultaneously the changes in dynamic muscle properties and voluntary activation in human muscles.

Force responses to transcranial magnetic stimulation of motor cortex (TMS) during exercise provide information about voluntary activation and contractile properties of the muscle. Here, TMS-generated twitches and muscle relaxation during the TMS-evoked silent period were measured in fresh, heated, and fatigued muscle. Subjects performed isometric contractions of elbow flexors in two studies. Torque and EMG were recorded from elbow flexor and extensor muscles. One study (n = 6) measured muscle contraction times and relaxation rates during brief maximal and submaximal contractions in fresh and fatigued muscle. Another study (n = 7) aimed to 1) assess the reproducibility of muscle contractile properties during brief voluntary contractions in fresh muscle, 2) validate the technique for contractile properties in passively heated muscle, and 3) apply the technique to study contractile properties during sustained maximal voluntary contractions. In both studies, muscle contractile properties during voluntary contractions were compared with the resting twitch evoked by motor nerve stimulation. Measurement of muscle contractile properties during voluntary contractions is reproducible in fresh muscle and reveals faster and slower muscle relaxation rates in heated and fatigued muscle, respectively. The technique is more sensitive to altered muscle state than the traditional motor nerve resting twitch. Use of TMS during sustained maximal contractions reveals slowing of muscle contraction and relaxation with different time courses and a decline in voluntary activation. Voluntary output from the motor cortex becomes insufficient to maintain complete activation of muscle, although slowing of muscle contraction and relaxation indicates that lower motor unit firing rates are required for fusion of force.     

Myoelectric signal conduction velocity and spectral parameters: influence of force and time

Reports on measurement of muscle fiber conduction velocity in humans are scarce. Inferences on the behavior of conduction velocity have been drawn from the behavior of myoelectric spectral parameters. The present report contains information on conduction velocity and spectral parameters studied at various muscle contraction levels and during and after sustained contractions. The following results have been obtained from measurements on the tibialis anterior muscle. Conduction velocity demonstrated a positive correlation with limb circumference and with muscle force output. Thus we conclude that the diameters of the muscle fibers of high-threshold motor units are, on an average, larger than those of low-threshold motor units. The study of a sustained contraction and on the recovery after such a contraction revealed that conduction velocity consistently decreased during a strong contraction as did various myoelectric spectral parameters. However, the spectral parameters decreased approximately twice as much as did the conduction velocity, and we conclude that factors other than the conduction velocity along the muscle fibers affect the myoelectric signal during a high-level contraction. These other factors appertain to changes in the firing statistics of individual motor units as well as the correlation between the firings of different motor units.     

Fatigue and muscle activation during submaximal elbow flexion in children with cerebral palsy

The purpose of this study was to investigate whether children with cerebral palsy (CP), like typically developing peers, would compensate for muscle fatigue by recruiting additional motor units during a sustained low force contraction until task failure.Twelve children with CP and 17 typically developing peers performed one submaximal isometric elbow flexion contraction until the task could no longer be sustained at on average 25% (range 10–35%) of their maximal voluntary torque. Meanwhile surface electromyography (EMG) was measured from the biceps brachii and triceps brachii, and acceleration variations of the forearm were detected by an accelerometer. Slopes of the change in EMG amplitude and median frequency and accelerometer variation during time normalised to their initial values were calculated.Strength and time to task failure were similar in both groups. Children with CP exhibited a lower increase in EMG amplitude of the biceps brachii and triceps brachii during the course of the sustained elbow flexion task, while there were no significant group differences in median frequency decrease or acceleration variation increase. This indicates that children with CP do not compensate muscle fatigue with recruitment of additional motor units during sustained low force contractions.     

Firing rates of motor units in human vastus lateralis muscle during fatiguing isometric contractions.

We investigated the firing rate of motor units in the vastus lateralis muscle in five healthy young men (mean = 21.4 yr, SD = 0.9) during a sequence of isometric constant-torque contractions repeated to exhaustion. The contractions were sustained at 20% of the maximal voluntary level, measured at the beginning of the test sequence. Electromyographic (EMG) signals were recorded via quadrifilar fine-wire electrodes and subsequently decomposed into their constituent motor unit action potentials to obtain the motor unit firing times. In addition, we measured the whole muscle mechanical properties during the fatigue task using electrical stimulation. The firing rate of motor units first decreased within the first 10-20% of the endurance time of the contractions and then increased. The firing rate increase was accompanied by recruitment of additional motor units as the force output remained constant. The elicited twitch and tetanic torque responses first increased and then decreased. The two processes modulated in a complementary fashion at the same time. Our data suggest that, when the vastus lateralis muscle is activated to maintain a constant torque output, its motoneuron pool receives a net excitatory drive that first decreases to compensate for the short-lived potentiation of the muscle force twitch and then increases to compensate for the diminution of the force twitch. The underlying inverse relationship between the firing rate and the recruitment threshold that has been reported for nonfatigued contractions is maintained. We, therefore, conclude that the central nervous system control of vastus lateralis motor units remains invariant during fatigue in submaximal isometric isotonic contractions.     

Eccentric exercise increases EMG amplitude and force fluctuations during submaximal contractions of elbow flexor muscles.

The purpose of this study was to determine the effect of eccentric exercise on the ability to exert steady submaximal forces with muscles that cross the elbow joint. Eight subjects performed two tasks requiring isometric contraction of the right elbow flexors: a maximum voluntary contraction (MVC) and a constant-force task at four submaximal target forces (5, 20, 35, 50% MVC) while electromyography (EMG) was recorded from elbow flexor and extensor muscles. These tasks were performed before, after, and 24 h after a period of eccentric (fatigue and muscle damage) or concentric exercise (fatigue only). MVC force declined after eccentric exercise (45% decline) and remained depressed 24 h later (24%), whereas the reduced force after concentric exercise (22%) fully recovered the following day. EMG amplitude during the submaximal contractions increased in all elbow flexor muscles after eccentric exercise, with the greatest change in the biceps brachii at low forces (3-4 times larger at 5 and 20% MVC) and in the brachialis muscle at moderate forces (2 times larger at 35 and 50% MVC). Eccentric exercise resulted in a twofold increase in coactivation of the triceps brachii muscle during all submaximal contractions. Force fluctuations were larger after eccentric exercise, particularly at low forces (3-4 times larger at 5% MVC, 2 times larger at 50% MVC), with a twofold increase in physiological tremor at 8-12 Hz. These data indicate that eccentric exercise results in impaired motor control and altered neural drive to elbow flexor muscles, particularly at low forces, suggesting altered motor unit activation after eccentric exercise.     

Ia-afferent input to motoneurons during shortening and lengthening muscle contractions in humans.

The central nervous system employs different strategies to execute specific motor tasks. Because afferent feedback during shortening and lengthening muscle contractions differs, the neural strategy underlying these tasks may be quite distinct. Cortical drive may be adjusted or afferent input regulated. The exact mechanisms are not clear. Here, we examine the control of synaptic transmission across the Ia synapse during shortening and lengthening muscle contractions. Subjects were instructed to maintain isolated activity in a single tibialis anterior (TA) motor unit while muscle length was varied from flexion to extension and back. At a fixed interval after a firing of the active motor unit, a single electrical stimulus was applied to the common peroneal nerve to activate Ia afferents from the TA muscle. We investigated the stimulus-induced change in firing probability of 19 individual low-threshold TA motor units during shortening and lengthening contractions. Any change in firing probability depends on both pre- and postsynaptic mechanisms. In this experiment, motoneuron firing rate was similar during both contraction types. There was no difference in the firing probability between shortening and lengthening contractions (0.23 +/- 0.03 and 0.20 +/- 0.02, respectively). We suggest that there is no contraction type-specific control of Ia input to the motoneurons during shortening and lengthening muscle contractions. Cortical adjustments may have occurred.     

Inhomogeneities in muscle activation reveal motor unit recruitment.

This paper presents a novel method to quantify spatial changes in muscle activation pattern by multi-channel surface electromyography (MCSEMG) in order to investigate motor unit recruitment variation. The method is based on non-uniform distributions of motor units that cause spatial inhomogeneous muscle activation. To evaluate the method, 15 subjects performed three isometric elbow flexion contractions consisting of slow sinusoidal changes in force ranging from 0% to 80% of the maximal voluntary contraction. MCSEMG electrodes were placed in a 10 x 13 grid over the biceps brachii muscle. From all channels, root mean square (RMS) values of bipolar leadings were computed over 0.5 s epochs over the whole recording. Thereafter, correlation coefficients were calculated between the RMS values at one epoch, with the RMS values at another epoch. Results showed consistent spatial changes in the distribution of RMS at different contraction levels up to 80% of maximal voluntary contraction and when comparing increasing and decreasing contractions at the same force level. These findings are reproducible within and between subjects, and in agreement with physiological phenomena and therefore indicate that the spatial inhomogeneities of motor unit properties in the biceps brachii muscle can be used to study changes in motor unit recruitment.     

In vivo assessment of elbow flexor work and activation during stretch-shortening cycle tasks.

The purpose of this study was to use an electromyography (EMG) based muscle model to investigate the performance enhancement of stretch-shortening cycle (SSC) tasks at different elbow flexion-extension velocities. A torque motor was used to oscillate the forearms of seven healthy male subjects (23-40 years) during SSC and non-SSC contractions at four frequencies of movement (.58, 1.5, 2.4 and 3.3Hz) over a range of 105 degrees -162 degrees of elbow extension. The torque was integrated as a function of joint angle to yield the work produced by the elbow flexors. The elbow flexors were transcutaneously stimulated with a voltage equivalent to 60% maximum voluntary isometric contraction torque for 4s at 50Hz. EMG of the elbow flexors and extensors was recorded from the biceps and triceps respectively. The processed EMG was used to drive a Hill based model to predict the torque of the elbow flexors. Results indicate that muscle work increases from non-SSC to SSC trials. Work decreases for SSC and non-SSC trials with increasing velocity. The simulated constant activation muscle model predicted work well for all trials and conditions, indicating muscle model accuracy. The EMG driven model predicted well for all non-SSC trials, but significantly underestimated the work for SSC tasks, suggesting that the contractile component is directly involved in optimising muscle work during SSC tasks.     

Estimation of the muscle fibre semi-length under varying joint positions on the basis of non-invasively extracted motor unit action potentials.

Changes in muscle fibre length and surface electrode position with respect to the muscle fibres affect the amplitude and frequency characteristics of surface electromyography (SEMG) in different ways. Knowledge of changes in muscle fibre length would help towards a better interpretation of the signals. The possibility of estimating the length through SEMG during voluntary contractions was checked in this study. The fibres' semi-length was estimated from the product of the conduction velocity and conduction time during which the wave of excitation propagated from the end-plate region to the ends of the fibres. Short (10 s), moderate (30% of maximum voluntary contraction) isometric contractions were performed by 10 subjects at different elbow joint angles (80-140 degrees in steps of 20 degrees ). Monopolar signals were detected non-invasively, using a two-dimensional electrode array. High spatial resolution EMG and a decomposition technique were utilised to extract single motor unit activities for triggered averaging and to estimate conduction velocity. A significant increase with joint angle was found in conduction time and estimated fibre semi-length. Changes in conduction velocity with joint angle were found to be not significant. The methodology described allows the relative changes in fibres' semi-length to be estimated from SEMG data.     

Does the frequency content of the surface mechanomyographic signal reflect motor unit firing rates? A brief review.

The purpose of this review is to examine the literature that has investigated the potential relationship between mechanomyographic (MMG) frequency and motor unit firing rates. Several different experimental designs/methodologies have been used to address this issue, including: repetitive electrical stimulation, voluntary muscle actions in muscles with different fiber type compositions, fatiguing and non-fatiguing isometric or dynamic muscle actions, and voluntary muscle actions in young versus elderly subjects and healthy individuals versus subjects with a neuromuscular disease(s). Generally speaking, the results from these investigations have suggested that MMG frequency is related to the rate of motor unit activation and the contractile properties (contraction and relaxation times) of the muscle fibers. Other studies, however, have reported that MMG mean power frequency (MPF) does not always follow the expected pattern of firing rate modulation (e.g. motor unit firing rates generally increase with torque during isometric muscle actions, but MMG MPF may remain stable or even decrease). In addition, there are several factors that may affect the frequency content of the MMG signal during a voluntary muscle action (i.e. muscle stiffness, intramuscular fluid pressure, etc.), independent of changes in motor unit firing rates. Despite the potential influences of these factors, most of the evidence has suggested that the frequency domain of the MMG signal contains some information regarding motor unit firing rates. It is likely, however, that this information is qualitative, rather than quantitative in nature, and reflects the global motor unit firing rate, rather than the firing rates of a particular group of motor units.     

Recruitment of single human low-threshold motor units with increasing loads at different muscle lengths.

We investigated the recruitment behaviour of low threshold motor units in flexor digitorum superficialis by altering two biomechanical constraints: the load against which the muscle worked and the initial muscle length. The load was increased using isotonic (low load), loaded dynamic (intermediate load) and isometric (high load) contractions in two studies. The initial muscle position reflected resting muscle length in series A, and a longer length with digit III fully extended in series B. Intramuscular EMG was recorded from 48 single motor units in 10 experiments on five healthy subjects, 21 units in series A and 27 in series B, while subjects performed ramp up, hold and ramp down contractions. Increasing the load on the muscle decreased the force, displacement and firing rate of single motor units at recruitment at shorter muscle lengths (P<0.001, dependent t-test). At longer muscle lengths this recruitment pattern was observed between loaded dynamic and isotonic contractions, but not between isometric and loaded dynamic contractions. Thus, the recruitment properties of single motor units in human flexor digitorum superficialis are sensitive to changes in both imposed external loads and the initial length of the muscle.     

Motor unit activation patterns during isometric, concentric and eccentric actions at different force levels.

Motor unit activation patterns were studied during four different force levels of concentric and eccentric actions. Eight male subjects performed concentric and eccentric forearm flexions with the movement range from 100 degrees to 60 degrees in concentric and from 100 degrees to 140 degrees elbow angle in eccentric actions. The movements were started either from zero preactivation or with isometric preactivation of the force levels of 20, 40, 60 and 80% MVC. The subjects were then instructed to maintain the corresponding relative force levels during the dynamic actions. Intramuscular and surface EMG was recorded from biceps brachii muscle. Altogether 28 motoneuron pools were analyzed using the intramuscular spike-amplitude frequency (ISAF) analysis technique of Moritani et al. The mean spike amplitude was lower and the mean spike frequency higher in the isometric preactivation phase than in the consequent concentric and eccentric actions. When the movements started with isometric preactivation the mean spike amplitude increased significantly (P<0.001) up to 80% in isometric and concentric actions but in eccentric actions the increase continued only up to 60% (P<0.01). The mean spike frequency in isometric preactivation and in concentric action with preactivation was lower only at the 20% force level (P<0.01) as compared to the other force levels while in eccentric action with preactivation the increase between the force levels was significant (P<0.01) up to 60%. When the movement was started without preactivation the mean spike amplitude at 20% and at 40% force level was higher (P<0.01) in eccentric action than in concentric actions. It was concluded that the recruitment threshold may be lower in dynamic as compared to isometric actions. The recruitment of fast motor units may continue to higher force levels in isometric and in concentric as in eccentric actions which, on the other hand, seems to achieve the higher forces by increasing the firing rate of the active units. At the lower force levels mean spike amplitude was higher in eccentric than in concentric actions which might indicate selective activation of fast motor units. This was, however, the case only when the movements were started without isometric preactivation.     

The role of motor unit rate modulation versus recruitment in repeated submaximal voluntary contractions performed by control and spinal cord injured subjects.

The relative roles of motor unit firing rate modulation and recruitment were evaluated when individuals with cervical spinal cord injury (SCI) and able-bodied controls performed a brief (6 s), 50% maximal voluntary contraction (50% MVC; target contraction) of triceps brachii every 10 s until it required maximal effort to achieve the target force. Mean (+/-SD) endurance times for SCI and control subjects were 34+/-26 and 15+/-5 min, respectively, at which point significant reductions in maximal triceps force had occurred. Twitch occlusion analysis in controls indicated that force declines resulted largely from peripheral contractile failure. In SCI subjects, triceps surface EMG and motor unit potential amplitude declined in parallel suggesting failure at axon branch points and/or alterations in muscle membrane properties. The force of low threshold units, measured by spike-triggered averaging, declined in SCI but not control subjects, suggesting that higher threshold units fatigued in controls. Central fatigue was also obvious after SCI. Mean (+/-SD) MVC motor unit firing rates declined significantly with fatigue for control (24.6+/-7.1 to 17.3+/-5.1Hz), but not SCI subjects (25.9+/-12.7 to 20.1+/-9.7Hz). Unit firing rates were unchanged during target contractions for each subject group, but with the MVC rate decreases, units of SCI and control subjects were activated intensely at endurance time (88% and 99% MVC rates, respectively). New unit recruitment also maintained the target contractions although it was limited after SCI because many descending inputs to triceps motoneurons were disrupted. This resulted in sparse EMG, even during MVCs, but allowed the same unit to be recorded throughout. These EMG data showed that both unit recruitment and rate modulation were important for maintaining force during repeated submaximal intermittent contractions of triceps brachii muscles performed by SCI subjects. Similar results were found for control subjects. Muscles weakened by SCI may therefore provide a useful model in which to directly study motor unit rate modulation and recruitment during weak or strong voluntary contractions.     

Experimental muscle pain increases mechanomyographic signal activity during sub-maximal isometric contractions.

This study was designed to investigate the local effect of experimental muscle pain on the MMG and the surface EMG during a range of sub-maximal isometric contractions. Muscle pain was induced by injections of hypertonic saline into the biceps brachii muscle in 12 subjects. Injections of isotonic saline served as a control. Pain intensity and location, MMG and surface EMG from the biceps brachii were assessed during static isometric (0%, 10%, 30%, 50% and, 70% of the maximal voluntary contraction) and ramp isometric (0-50% of the maximal voluntary contraction) elbow flexions. MMG and surface EMG signals were analyzed in the time and frequency domain. Experimentally induced muscle pain induced an increase in root mean square values of the MMG signal while no changes were observed in the surface EMG. Most likely this increase reflects changes in the mechanical contractile properties of the muscle and indicates compensatory mechanisms, i.e. decreased firing rate and increased twitch force to maintain a constant force output in presence of experimental muscle pain. Under well-controlled conditions, MMG recordings may be more sensitive than surface EMG recordings and clinically useful for detecting non-invasively increased muscle mechanical contributions during muscle pain conditions.     

Changes in surface EMG parameters during static and dynamic fatiguing contractions.

The effect of contraction types on muscle fiber conduction velocity (MFCV), median frequency (MDF) and mean amplitude (AMP) of surface electromyography was examined in the vastus lateralis of 19 healthy male adults. The subjects performed knee extension both statically and dynamically until they were exhausted. The static contraction was a sustained isometric extension of the knee at a joint angle of 90 degrees with 50% of the maximum voluntary contraction (MVC) load. The dynamic contraction was a repetitive isotonic extension of the knee between the angles of 90 degrees and 180 degrees with the same 50% MVC load at a frequency of 10 times per minute. MFVC during the static contraction significantly decreased during the exercise (p < 0.01). On the other hand, MFVC during the dynamic contraction did not significantly change throughout the exercise. MDF decreased and AMP increased during both types of contractions (p < 0.01). Because the blood flow within the muscle is maintained during the dynamic contraction by enhanced venous return from the contracting muscle, these results suggested that MFVC is affected by the metabolic state in the muscle and the changes in MDF cannot be explained only by that of MFVC.     

Force-length, torque-angle and EMG-joint angle relationships of the human in vivo biceps brachii

The relationships of EMG and muscle force with elbow joint angle were investigated for muscle modelling purposes. Eight subjects had their arms fixed in an isometric elbow jig where the biceps brachii was electrically stimulated (30 Hz) and also in maximum voluntary contraction (MVC). Biceps EMG and elbow torque transduced at the wrist were recorded at 0.175 rad intervals through 1.75 rad of elbow extension. The results revealed that while the torque-length relationship displayed the classic inverted U pattern in both evoked and MVC conditions, the force-length relationship displayed a monotonically increasing pattern. Analyses of variance of the EMG data showed that there were no significant changes in the EMG amplitudes for the different joint angles during evoked or voluntary contractions. The result also showed that electrical stimulation can effectively isolated the torque-angle and force-length relationships of the biceps brachii and that the myoelectric signal during isometric contraction is uniform regardless of the length of the muscle or the joint angle.