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HIGHLIGHTED TOPICS
Neural Control of Movement
Neuromuscular Research Center, Department of Biology of Physical Activity, University of Jyväskylä, FIN-40100 Jyväskylä, Finland
Submitted 16 September 2003 ; accepted in final form 5 February 2004
| ABSTRACT |
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muscle stretch; reflex; muscle adaptation
According to Taylor et al. (37), the mechanical changes of the muscle-tendon unit are time and history dependent because of the viscoelastic nature of the tissue. Two different responses in this regard have been suggested. The first is stress relaxation (27, 38), which is purely mechanical in nature and is mainly responsible for the reduced passive tension of the muscletendon unit over time. The second response is called plastic deformation, which means reorientation of the supporting connective and soft tissue-supporting tissue into more parallel arrays (34). This response is suggested to be more time dependent of the maintained tissue strain.
The increased compliance of the muscle-tendon unit may also influence neural activation patterns because of neural feedback responses (10). Avela et al. (1) demonstrated a clear reduction (84.8%) in the stretch-reflex peak-to-peak amplitude after 1 h of repeated fast passive muscle stretching. This reduction was related to a significant reduction in the passive stretch-resisting force of the muscle. Therefore, Avela et al. suggested that the origin of the reduced reflex sensitivity could be a reduction in the activity of the large-diameter afferents, resulting from the reduced mechanical sensitivity of the muscle spindles to repeated stretch.
The purpose of the following study was to seek more direct evidence for interaction between mechanical changes of the muscle-tendon unit and reduced reflex sensitivity after repeated and prolonged passive muscle stretching. Because skeletal muscle consists of three components (muscle fibers, aponeurosis, and free tendon) and each of them exhibits different material behavior, ultrasonography was used to differentiate the length changes of each component. It is also well known that the fast passive stretch of the muscle induces a stretch reflex through facilitation of the
-motoneuron pool. Hoffmann (H) reflexes were, therefore, recorded after several stretching ramps at the beginning and end of the stretching protocol to evaluate the possible modulation (state of excitability) of the motoneuronal pool induced by the stretching protocol. Consequently, the possible interaction between changes in reflex sensitivity and mechanical responses of the muscle could be taken as evidence of the mechanical origin of the reduced reflex sensitivity. This information could be relevant also during active fatigue tasks, since simultaneous reduction in the passive stretch-resisting force and reflex sensitivity have been observed after different types of active stretch-shortening cycle exercises (2, 3).
| METHODS |
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Experimental protocol. All eight subjects underwent a repeated passive stretching (RPS) of the calf muscles (1) twice, and each RPS lasted for 1 h. A minimum of 2 wk was allowed to elapse between the two RPS exercises to ensure full recovery from the first exercise. In both stretching sessions, the subjects were instructed not to resist the mechanical stretching of the calf muscles. Both RPS exercises and all the measurements included in this study were performed on the ankle ergometer. The whole experimental protocol is summarized in Fig. 1.
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In the first RPS exercise (RPS1), pre- and posttest measurements included several measurements in the following order: 1) maximal voluntary isometric plantar flexion torque (MVC) at 90° ankle joint angle, 2) muscle contractions of 10 and 50% of MVC at 90° ankle joint angle, 3) mechanical response of the relaxed plantar flexor muscles to double supramaximal electrical impulse (passive double twitch), and 4) MVC with superimposed double electrical impulse (28). The two latter measurements were done at ankle joint angles of 80, 90, and 115° to construct a torque-fascicle length (Lfasc) relationship. Ultrasonography was used during the isometric tests and at the beginning and end of the stretching protocol to calculate the Lfasc changes. No electromyogram (EMG) measurements were done in the first RPS exercise.
In the second RPS exercise (RPS2), which was performed at least 2 wk later, all isometric measurements were done at 90° ankle joint ankle. Passive double twitch and MVC with superimposed double twitch were again measured to test the repeatability of the two RPS exercises. The other pre- and posttests in the RPS2 included the measurements of the maximal M-wave and H-reflex responses. In these measurements, at least 30 s were allowed to elapse between MVCs and H-reflex recordings to avoid the problem of postcontraction depression of the H reflex (39). In addition, H reflexes and passive-stretch reflexes were measured during the RPS2 exercise for 10 stretching ramps at the beginning and end of exercise.
Stretch model. Both 1-h RPS exercises were induced by repeated dynamic stretching of the calf muscles, performed by an ankle ergometer similar to that of Gollhofer and Schmidtbleicher (16) and used in our laboratory's earlier studies on stretch-reflex sensitivity during stretch-shortening cycle fatigue (2, 30, 32). In all experimental conditions, the subjects sat in the ergometer chair. The foot was mounted on the rotation platform so that the rotation axes of the ankle joint and the motor-driven platform coincided. The torque around the rotational axis of the motor was measured by a piezoelectric crystal transducer (Kistler), and the angular movement of the ankle joint with respect to plane of the ergometer was monitored by a linear potentiometer. The initial ankle position was 90°, and the knee angle was fixed at 120°. The stretching amplitude corresponded to 10° dorsiflexion of the ankle joint with an average velocity of 200°/s (Fig. 2). The waveform of the stretching signal was trapezoidal, and the frequency of these stretches was 1.5 cycles/s.
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Stretch- and H-reflex measurements. The stretch reflexes were measured with the same mechanical stimulation as used in RPS. Ten consecutive stretch reflexes were averaged, and peak-to-peak amplitudes of the EMG responses were analyzed together with latency times, torques, and displacements of the ankle joint (for details, see Ref. 30). Torque analyses were divided into two different time periods. An average plantar flexion torque was analyzed for the first 40 ms of the stretch, before the torque increases due to the stretch reflex could take place. This torque was defined as a passive stretch-resisting torque of the muscle (PsrT) (1). In addition, an average torque was also measured for the time period of 5080 ms after the onset of stretch. This torque corresponds to the torque output of the short-latency, stretch-reflex response and was therefore defined as a reflex torque (for other details, see Refs. 30, 32).
To evaluate the possible modulation of the
-motoneuron pool induced by the RPS exercise, H reflexes were recorded during the pre- and posttests and also during different phases of the second RPS exercise. After preparing the skin, stimulation electrodes (pregelified Ag-AgCl electrodes, type 4560, Niko Surgical) were positioned for H-reflex and M-wave (muscle compound action potential) testing. The leg cathode (1.5 x 1.5 cm) was placed over the tibial nerve in the popliteal fossa, and the anode (5 x 8 cm) was placed superior to the patella. Because standing position facilitates the H reflex, the position of the stimulation electrodes was tested first in the upright stance and then checked in the experimental position to ensure constant recording conditions. The electrical stimulus used for the H-reflex and M-wave recording was rectangular, and a single-mode signal with a pulse duration of 1 ms (frequency of 0.2 Hz) was delivered from a signal generator of the evoked potential measuring system (MEB-5304K, Nihon Kohden, Tokyo, Japan). In addition, all responses were amplified (bandwidth 10 Hz to 1 kHz), stored, and analyzed by the same system. The intensity of the stimulus was set in every testing unit to elicit maximal H response and M response. The reflex excitability was calculated according to the method used by Garland and McComas (14). Maximal H-reflex peak-to-peak amplitudes were expressed in relation to the maximal M-wave peak-to-peak amplitudes. Theoretically the H-to-M ratios, so determined, should not have been affected by any changes in the peripheral excitability of the muscle fibers.
H reflexes were also recorded during 10 stretching ramps (Fig. 2) selected for the beginning and end of the RPS2 exercise. It is essential that stimulus strength remains invariant between recording sessions, because the size of the H reflex depends heavily on the stimulus intensity. Therefore, when repeated H-reflex measurements are performed, stimulation intensity should be related to the size of the maximal M wave (usually 1030%) to ensure that the same number of motor axons are recruited in each trial (e.g., Ref. 35). In the present experiment, the target amplitude for the M wave was 25% of the maximal M wave (8), which was measured in an earlier ramp. An average of three highest H responses was used as a final result. Low variability in H-reflex peak-to-peak amplitude between the measurements performed at the beginning and at the end of the RPS2 exercise (8.2 and 7.7%, respectively) indicated comparable recording conditions.
While stretch and H reflexes were measured at the beginning of the RPS2 exercise, the first 10 stretching ramps were disregarded to avoid the effect of muscle thixotropy. In addition, background EMG activity was monitored throughout all reflex measurements on an oscilloscope to ensure that it was silent. This precaution was important in the present experiment because muscle activation is known to affect the excitability of the H reflex (39).
Torque measurements and activation-level calculations. In both RPS exercises and in each condition, three MVCs were performed before the RPS exercise. This was repeated only once immediately after the exercise to avoid premature recovery during the posttests. All MVC measurements were done with the twitch interpolation method (28). For passive double twitch, one trial was performed in each condition.
Passive and superimposed double twitches were both induced by supramaximal nerve stimuli with a frequency of 100 Hz, and the duration of each pulse was 1 ms. In both cases, stimulation electrode was applied identically to the one used in H-reflex testing. In the superimposed stimulation, the stimulus intensity was set
25% higher than that of the maximal M wave to ensure maximal response in every testing condition. In addition, in twitch interpolation, special care was taken to ensure that the double twitch was applied during MVC.
The following parameters were analyzed from the passive double-twitch recordings: maximum twitch torque, time to peak torque, total duration of the twitch, and half relaxation time.
The central activation level (AL) during MVC was calculated according to the following formula (36)
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All MVC values were analyzed trial by trial. In addition, in RPS2 exercise, the integrated EMG was divided by the integration time (500 ms) to obtain an average EMG.
EMG instrumentation. The recording electrodes for the H reflexes, M waves, stretch reflexes, and EMGs associated with MVC were bipolar surface electrodes (Beckman miniature skin electrodes 650437) fixed at a constant center-to-center interelectrode distance of 20 mm. The electrodes were placed
6 cm above the superior aspect of the calcaneus on the soleus (Sol) muscle and between the center of the innervation zone and distal end of the lateral head of the gastrocnemius (Ga) muscle. EMG signals were transferred telemetrically, amplified by a FM-microvolt amplifier (Glonner Electronic, Munich, Germany), and finally transferred through an analog-to-digital converter (analog-to-digital sampling frequency was 13 kHz, depending on the signal) to a microcomputer or, in a case of H-reflex testing, to a Nihon Kohden measuring system.
Fascicle and tendon length measurements with ultrasonography. Length of the medial Ga (MG) fascicle was calculated on the basis of ultrasonographic measurements before, during, and after RPS1. With the subjects seated on the ankle ergometer, an ultrasound probe (40 mm, 7.5 MHz, B-mode, Aloka SSD-2000 with scanning frequency of 42 Hz) was firmly attached to the muscle belly of the MG muscle. The real-time images were captured on videotape at 50 Hz. Fascicle interfaces appeared as light stripes in the ultrasound image. One of these stripes was chosen for analysis, and its length was tracked throughout the movement. A parallelogram model (Fig. 3A) was used when images were digitized and analyzed with Motus software (Peak Performance Technologies). For three subjects, the entire fascicle was not fully visible within the image area during passive muscle conditions. In those cases, the total Lfasc was calculated according to Finni et al. (9). When the aponeuroses were not in parallel, the angle between them was subtracted from pennation angle to make the calculation possible (Fig. 3A). Length changes in the tendinous tissue (tendon and aponeurosis) were calculated according to Fukunaga et al. (12) (Fig. 3B).
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The model of Hawkins and Hull (18) was used to estimate the length changes in the muscle-tendon unit. This model requires information about joint angles. For the ankle joint angle, this was obtained by using a potentiometer of the ankle ergometer. The knee angle was kept constant (120°). Information of the MTU length changes was needed for the tendon length calculations.
To compensate for the low scanning frequency of the ultrasonography, 10 consecutive stretch cycles were averaged. For this purpose, manually triggered electrical signal was used to synchronize the video and analog data. In MVC, the Lfasc changes for the zero torque and maximal torque were analyzed as an average of 50 data points.
Ultrasonography has been widely used in studying muscle function and tendinous tissue behavior in isometric and isokinetic movements (e.g., Refs. 11, 19). Many researchers have reported good reliability and repeatability of the method (e.g., Refs. 24, 29). In addition, the error due to the linear extrapolation of Lfasc has been investigated in our laboratory. Finni et al. (9) and Ishikawa et al. (23), respectively, reported it to be 27 and 4.55.9% for vastus lateralis muscle. For the MG muscle, however, the error is considerably smaller than in vastus lateralis muscle because a greater proportion of the total Lfasc could be visualized. Due to these reasons, the reliability of the Lfasc calculations was not tested in this experiment nor discussed in this paper.
Statistical analysis. Mean and standard deviation values were calculated for the various parameters in all the different tests. Pearson's correlation coefficients were calculated to reveal significant relationships between selected parameters. Because the whole data showed normality in every case, Student's t-test for paired samples was used to determine differences between two parameters. The statistical significances for MVC and ALs between different RPS experiments were determined according to multivariate ANOVA. When a significant F ratio occurred for the main effects, profile analysis was carried out by multivariate ANOVA to locate the source of the difference. Level of significance in all tests was set to P < 0.05, P < 0.01, and P < 0.001.
| RESULTS |
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The cause of the impairment in MVC could have been due to reduction in AL, but no exercise session-induced reduction was observed in this parameter. AL values at 90° ankle joint angle were the same before and after 1 h of RPS1 (97.9 ± 2.0 and 97.7 ± 2.5%, respectively). Similar results were obtained for the other two MVC measurement angles (range of change was from 97.2 to 98.5%).
Because MVC was measured at three different ankle angles of 80, 90, and 115°, this gave the possibility to use the simultaneously measured MG Lfasc to construct the torque-Lfasc relationship. These relationships have been drawn in Fig. 5, which shows that the overall shift was downward and to the right during RPS1. The Lfasc increased more during 1-h stretching at shorter Lfasc [90 and 115° ankle joint angles: from 2.54 ± 0.62 to 2.85 ± 0.90 cm (P < 0.05) and from 2.34 ± 0.84 to 2.49 ± 0.97 cm (P < 0.05), respectively]. In RPS1, the Lfasc were also calculated for four different ALs at 90° ankle joint angle (Fig. 6). During zero activation, the fascicles became shorter by 0.30 ± 0.13 cm (P < 0.05) after RPS. At maximal activation, the length changes were to the opposite direction by 0.24 ± 0.09 cm (P < 0.05). Figure 6 also shows the respective changes for the tendon length calculations. Because the ankle joint displacements were constant and the model of Fukunaga et al. (12) merely subtracts the Lfasc changes from that of the tendomuscular unit, the tendon length changes were the same but to the opposite direction from those of the Lfasc changes.
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Double supramaximal electrical stimulus applied to the passive muscle before and after RPS at 90° ankle joint angle revealed impaired responses. This was shown by a 16.8 ± 16.8% (P < 0.01) reduction in the maximum twitch torque and by a 14.0 ± 8.7% increase in the total duration of the twitch. In addition, time to peak torque and half-relaxation time were lengthened by 15.1 ± 7.7% (P < 0.001) and 19.7 ± 11.9% (P < 0.01), respectively.
The maximal H-reflex amplitude decreased by 29.1 ± 22.1% (P < 0.01) immediately after RPS2. This reduction was not associated with any changes in the maximal M wave, indicating that there was no failure in neuromuscular transmission. Therefore, the changes in the maximal H reflex resulted in a reduced maximal H-to-M ratio (mean decline 29.2 ± 20.4%, P < 0.01), suggesting impaired excitation of the
-motoneuron pool.
Measurements during passive stretching. EMG responses of the stretch reflexes showed a dramatic peak-to-peak reduction at a very end of RPS (Fig. 7). These reductions were 41.0 ± 37.3% (P < 0.05) and 27.5 ± 25.2% (P < 0.05) for the Ga and Sol muscles, respectively. PsrT showed very similar changes during RPS stimulation. The immediate post-RPS reduction was 11.2 ± 8.2% (P < 0.05). In addition, the changes in the PsrT were significantly related to changes in MVC, to Lfasc changes during MVC, and to the stretch-reflex amplitude changes (Fig. 8). There was also a very clear drop in the reflex torque immediately after RPS (31.7 ± 17.9%, P < 0.05). Thus a moderate relationship existed between reflex torque and PsrT (R = 0.63; P = not significant).
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Figure 9A shows average recordings of the Lfasc changes for the whole subject group. This figure represents one passive stretch cycle (average of 10 cycles) at the beginning and end of RPS1. In addition, Fig. 9B shows clearly that the fascicles became shorter throughout the passive stretch cycle (P < 0.05) at the end of RPS1. This result is very similar to the one in the isometric condition with relaxed muscle at 90° ankle joint angle (Fig. 5). During the stretch cycle, the measured H reflex was reduced from 3.6 ± 0.3 mV (beginning of the stretching session) to 1.9 ± 0.1 mV (P < 0.01) (end of session). Figure 7 presents the H-reflex signals of one representative subject measured at the beginning and end of the RPS1.
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| DISCUSSION |
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Additional explanation could be sought from possible alterations in the force-length relationship of the muscle-tendon unit induced by modifying contribution of the length changes of its different components. In a passive muscle-tendon system, this elongation can be facilitated by stress relaxation and/or plastic deformation. Stress relaxation is viscoelastic in nature, and according to Taylor et al. (37) it occurs primarily in the connective tissue. Stress relaxation is indicated by a descending passive torque over time for a given stretched muscle length (38). Contribution of the stress relaxation is difficult to estimate in a cyclic RPS protocol. In addition, in the present experiment, the time course of the behavior of the PsrT was not followed during the RPS. However, our laboratory's previous experiment (1) with identical protocol showed that 50% of the total reduction in the PsrT was achieved already 15 min after the beginning of the RPS. This implies that stress relaxation may indeed play a role also in a cyclic passive-stretching protocol, especially during the early part of it.
Usually, plastic deformation (creep) is related to maintained tissue strain, which causes a reorientation of the supporting connective tissue to more-ordered arrays (34). In our laboratory's earlier experiment (1), one-third of the reduction in the PsrT took place during the latter part of the 1-h RPS. In addition, a clear drop in the passive torque was seen during the plateau phase of the cyclic RPS exercise at the end of the present experiment. Therefore, it could be suggested that plastic deformation seems to depend on the total tissue strain regardless of the mode of stretching.
In the present experiment, torque-Lfasc and torque-tendon length relationships were calculated for different ALs. After RPS, the Lfasc was shorter during low torques and longer during high torques compared with the ones measured before RPS exercise. Because of the tendon model and the isometric nature of the contraction, the tendon length changes were exactly the opposite. These results indicate altered tendomuscular material properties. As discussed above, stress relaxation and plastic deformation occur mainly on connective tissue (34, 37). Therefore, it could be suggested that the major changes in the tendomuscular material properties that could affect the torque-Lfasc relationship take place somewhere in the aponeurosis-tendon system. This is supported also by the finding of Herbert et al. (20) that, for the relaxed tibialis anterior and Ga muscles, more than one-half of the total change in muscle-tendon length was taken up by stretch of tendon. It should be noted that their tendon model was not able to separate the length changes of the aponeurosis from that of the outer tendon. In addition, Lieber et al. (25) found in a frog semitendinosus muscle that aponeurosis strain during contraction was significantly below that measured during passive loading. Therefore, they suggested that aponeurosis actually changes its intrinsic properties during muscle contraction. Huijing and Ettema (21) also reported similar differences in aponeurosis properties between passively and actively loaded muscle. Unfortunately, in the present experiment, the tendon model was unable to differentiate the behavior of the aponeurosis and the tendon. However, crossing of the present torque-tendon length and torque-Lfasc curves with different ALs before and after RPS could be a result of material modification of the aponeurosis due to passive stretching.
If the previous suggestion holds true and RPS induces a slack in aponeurosis, this could also lead to impaired torque production. Garfin et al. (13) reported a relationship between muscle stiffness and contractile performance. They found that surgical small release of fascia resulted in a 15% reduction in force production due to lower compartment pressure during contraction. Therefore, as suggested by Fowles et al. (10), plastic deformation could decrease fascia stiffness to a point that could result in reduced force production. The fact that, in the present study, PsrT had a rather high relationship with MVC and Lfasc changes measured during MVC could also support this suggestion.
In addition, the reported length changes could place muscle fascicles to a less optimal portion of the torque-Lfasc curve and result in reduced MVC. In the present experiment, the torque-Lfasc curve was also measured during MVC at three different ankle joint angles (Fig. 5). Pre- and post-RPS measurements gave indication of the rightward shift in this curve. Fowles et al. (10) reported a similar finding in a twitch torque-joint angle relation after passive stretch of the human plantar flexors. If this rightward shift means that the fascicles are replaced at a length corresponding to a descending limb of the torque-length relationship, this would obviously result in a reduced maximal torque production.
Altered torque-Lfasc characteristics may also influence the neural activation patterns. For example Fowles et al. (10) found a significant reduction in motor unit activation and EMG after 13 passive maximal stretches (30 min of time under stretch) of the human plantar flexors. In the present study, activation level was calculated during all MVCs. In contrast to the experiment of Fowles et al. (10), our results showed that motor unit activation was not a limiting factor for the maximal torque production after the RPS exercise. These contradictory results can be explained by the differences in the passive-stretching protocols. In our experiment, RPS was cyclic and the stretch amplitude corresponded to only 10° dorsiflexion of the ankle joint, which was much less than to one used by Fowles et al. Therefore, it seems that the level of neural modification induced by passive stretching depends on the total strain of the muscle-tendon complex induced by the protocol.
Despite the fact that no changes in the activation level were observed in the present experiment, a clear reduction in maximal H-to-M ratio was observed after RPS. This result indicates that some neural modification has indeed taken place. In addition, because there was a 14% increase in the total twitch duration, slowing of the excitation-contraction coupling could be suggested. Therefore, it would be tempting to use the concept of muscle wisdom (5) to explain these parallel changes in neural input and muscle mechanics.
In any case, it is puzzling why the neural modifications were so clear after passive stretching in the present experiment. To explore these possible mechanisms, stretch and H reflexes were measured during RPS exercise. However, in the interpretation of these reflexes, the mechanisms of postactivation depression will not be discussed, since in the present beginning-end comparison this effect should be systematic in both and, therefore, in regard to the reflex modulation of the RPS exercise, insignificant.
The underlying mechanisms for the reflex modification pose a challenging question because several aspects should be considered. It is known that the supraspinal influences on the H reflex are very strong (33). This was tested in our previous experiment with RPS (1) by using the contralateral leg as a control leg. The assumption was that, in a case of supraspinal modulation, similar changes in H reflex should be observed in both legs. However, this was not the case. The effect of Ib afferents can also be excluded because, first of all, they are known to be very sensitive during active contraction but much less sensitive to passive stretches (6), and second Guissard et al. (17) showed that, in a case of small amplitude stretching (10° of dorsiflexion), the premotoneuronal mechanisms are mainly involved. In a case of mechanoreceptors of the skin and joint capsule, it has been shown that ischemia with induced blockage of these afferents did not change the Sol stretch and H reflexes (22). In addition, presynaptic inhibition induced by group III and IV muscle afferents (4) is not a very likely candidate, because these afferents are known to be operative in a presence of metabolic fatigue and/or muscle damage. However, to the best of our knowledge, no data has conclusively shown that such a small amplitude passive stretching of the muscle could induce either of these.
Because the above-mentioned mechanisms did not seem to be ideal for the reflex modification during RPS, proprioceptive feedback should be taken into consideration. In our laboratory's previous RPS experiment (1), it was suggested that the most likely explanation for the depressed H reflex is a reduction in the excitatory drive from the Ia afferents onto the
-motoneurons. In addition, we proposed that the origin for this reduction could be a decreased resting discharge of the muscle spindles because of the increased compliance of the muscle. This assumption was made on the basis of the reduction in PsrT. Our present experiment verifies this result. However, because there was shortening in the passive Lfasc after the RPS exercise, this increased compliance seems to take place somewhere in the aponeurosis-tendon system, as discussed earlier. In addition, the above-mentioned hypothesis seems to be valid for two reasons. First, there was a high correlation between PsrT and the stretch-reflex response of the Sol muscle (Fig. 8). Second, the H reflex, measured at the end of the stretching ramp, showed an
50% reduction at the end of RPS exercise. These results could be interpreted so that the increased compliance of the muscle results in a reduced mechanical response of the muscle spindle leading to disfacilitation of the
-motoneuron pool.
In summary, repeated and prolonged passive muscle stretching impairs both electrically and voluntarily induced muscle contractions. This impairment was mainly related to modification of the torque-Lfasc relationship due to altered material behavior of the aponeurosis-tendon system. In addition, altered material properties seem to affect proprioceptive feedback and, therefore, the motor unit activation in proportion to the contractile failure. Similar changes in muscle mechanics and parameters related to neural behaviour have also been observed during SSC type of muscle fatigue (2, 31). Therefore, it would be interesting to examine the corresponding mechanisms also during active conditions by applying the present methodology.
| FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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