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Muscle resistance to slow ramp weakly depends on activation level
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Neuroscience Vol. 80, No. 1, pp. 299–306, 1997 IBRO Copyright ? 1997 Published by Elsevier Science Ltd Printed in Great Britain 0306–4522/97 $17.00+0.00 S0306-4522(97)00130-9
MUSCLE RESISTANCE TO SLOW RAMP WEAKLY DEPENDS ON ACTIVATION LEVEL V. S. GURFINKEL,* Y. P. IVANENKO and Y. S. LEVIK Institute for Information Transmission Problems, Russian Academy of Science, Bolshoy Karetny 19, Moscow 101447, Russia Abstract––The mechanical response of human m. flexor pollicis longus to slow (3.2)/s) linear stretch by 5.5) was measured during sustained (45–60 s, 9–13.5 p.p.s.) unfused tetanus evoked by electrical stimulation. The stiffness increased during unfused tetanus. At the late phase of unfused tetanus it was 1.8&0.2 (mean&S.D.) times greater than at the early phase. The sensitivity of the isometric tension level to a short change in a stimulation frequency also increased. At the late phase of unfused tetanus force oscillations increased 1.2&0.2-fold during slow stretch or shortening and immediately reached a smaller amplitude after the cessation of length change. This was probably related to the friction and thixotropy in muscles. Muscle resistance to slow ramp depended only weakly on activation level. In the late phase of unfused tetanus the stiffness per unit force was 1.5&0.4 times greater at 9–13.5 p.p.s. than at 20–25 p.p.s. Thus, the relative value of muscle stiffness was greater for smaller activation levels typical for maintenance of posture. The enhancement of muscle stiffness during sustained unfused tetanus and a weak stiffness dependence on the activation level indicated a non-additivity of processes occurring in active muscle. ? 1997 Published by Elsevier Science Ltd. Key words: skeletal muscle, unfused tetanus, stretch, activation level, human.
Visco-elastic properties of skeletal muscles must be taken into account by the central nervous system when controlling posture and movements. Quick stretches and shortenings of maximally activated muscle fibres are commonly used to study the mechanical properties of skeletal muscles. Small (shortrange) high frequency length changes are often applied to estimate the number of attached crossbridges and their properties.6,9,29 However, it should be noted that slow length changes under relatively low loads are typical for physiological conditions. For example, during human locomotion the timing of muscle activity is about equally distributed between eccentric and concentric modes of contraction, i.e. the stretching of active muscles occurs rather often and with relatively low velocities. The muscle behaviour during slow change of length can also give useful information about cross-bridge kinetics. For instance, at low velocities, the significant deviations of experimental curve from a classic force–velocity law were observed;10 slow length changes can enhance or suppress isometric force.1,11,14,16,3139 These facts are of great interest for a sliding filaments/cross-bridges theory. It is also known that during posture maintenance and a large part of movements muscles develop tension levels that hardly exceed 15% of maximal
force. Low tensions mean that activation levels of muscle fibres are far from maximal. Results obtained at maximal fibre activation cannot be applied without reserve to the situation characterized by permanent oscillations of active state due to the low stimulation rate.4,18,23 For example, the length change can considerably reduce the force level of unfused tetanus (UT) but does not greatly influence the force level of fused tetanus.23 In the present work we studied the stiffness of human skeletal muscle at slow length changes during sustained UT. In addition to the investigation of temporal changes of muscle stiffness at a constant stimulation frequency we also compared muscle stiffness at different activation levels.
*To whom correspondence should be addressed. Abbreviations: EMG, electromyogram; p.p.s., pulse per second; UT, unfused tetanus. 299
EXPERIMENTAL PROCEDURES
Twelve healthy volunteers aged from 20 to 45 years participated in this study. The subject sat in a relaxed posture. Left forearm, hand and fingers were rigidly fixed to a horizontal platform in a pronate position (Fig. 1). We recorded the isometric torque produced by contraction of m. flexor pollicis longus. The end phalanx of the thumb of the left hand was connected to a rigid strain gauge (tensoresistors were glued to a steel beam of a cross section 16#2.5 mm). The stiffness of the strain gauge equalled 2#105 N/m. The measurements of absolute muscle force were difficult because of unknown force arm. So, we expressed the muscle tension in units of absolute readings of strain gauge. Strain gauge signals were fed to a PC computer via an analog-digital converter, sampling frequency being 500/c.
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Fig. 1. Schematic view of the experimental set-up.
To measure muscle stiffness, ramp length changes were applied. The axis of the end phalanx of the thumb was matched with the pivot of the turning plate, which was rotated by 5.5) by an electro-mechanical drive at a constant speed of 3.2)/s. Accordingly, the movement duration was 1.7 s. After 2 s the platform was returned to the initial position with the same velocity (Fig. 2). Thus a whole lengthening-shortening cycle took about 5.5 s. M. flexor pollicis longus is the only flexor of the thumb located in the forearm. It lies beside the flexor profundus in the forearm and is attached to the distal phalanx as is the latter. This muscle, which is unipennate,25 is absent in some primates, this suggests it was acquired comparatively recently in the evolutionary process. The fibre length of human m. flexor pollicis longus equals to about 45 mm.26 Assuming the force arm is equal to about 10 mm, we obtained the total amplitude of the fibre lengthening 5.5)/ 57#10=1 mm. Therefore, the velocity of stretch equalled to approximately 1 mm/1.7 s=0.6 mm/s or 0.6/45=0.013 Lo/s, where Lo is a physiological fibre length. The initial joint angle was approximately in the middle between most flexed and most extended positions. This neutral position was chosen to reduce the impact of passive component on stiffness measurement. In addition, in this angular range the isometric force remained practically constant, as was shown by comparing the twitch force at different joint angles (see Fig. 4C). For most of the subjects, variations of twitch force were negligible (below 5%). The active electrode (about 1 cm diameter) was placed at the corresponding motor point, the other one (6#8 cm) at the dorsal surface of the wrist. A Stimulator ENS-01 with a stabilized current output was controlled by digital output of PC computer. The motor nerve was stimulated by rectangular current pulses (12–18 mA, 1 ms). Greater currents were not used, as they evoked painful sensations during tetanic stimulation. During such stimulation a tetanic tension at 50 pulses per second (p.p.s.) amounted to about 15–25% of maximal voluntary contraction, i.e. only a part of the muscle was activated by the electric current. Under our experimental conditions only direct Mresponse was evoked, as H-reflex is not manifested in passive hand muscles of healthy humans and could appear solely at the background of voluntary activation.40 On the other hand, no detectable electromyogram (EMG) response was generated by the imposed movement when the subject relaxed his thumb.3 The absence of a voluntary interference in muscle activity was proved by a smoothness of a relaxation curve during electrical stimulation.19 Effectiveness of electrical stimulation was different in different subjects. The contribution of the passive component (muscles, ligaments, skin) to the measured stiffness also differed depending on fixation of the second phalanx, thixotropic history.17,20,35 Thus, we selected only those subjects, in which the stiffness of the active muscle was considerably
larger than the passive stiffness. From 12 subjects studied only six were included in the analysis. Unfused tetanus was evoked by a train of 400–600 pulses with a frequency of stimulation in the range of 9–13.5 p.p.s. Overall train duration was 45–60 s. A total of 89 recordings were carried out. To study the dependence of stiffness on force level, the stimulation frequency of UT was increased from 9–13.5 p.p.s. to 20–25 p.p.s. for 8 s (Fig. 2B). We also investigated the influence of short-term increase or decrease of stimulation frequency upon the force of isometric unfused tetanus. Three additional pulses (interpulse interval 20 ms) were inserted into the background stimulus train, or, on the contrary, one interpulse interval was increased to 400 ms (Fig. 5). It is known18,21,27,32 that even after 1 min of contraction the traces of postactivation changes in muscle persist for a long time. So, the period of recovery between two successive UT recordings was no less that 1 h. Except for some cases, the first UT did not differ much from the subsequent ones; so during data analysis we have not differentiated between the first and following tetani. For demonstration of the dependence of muscle visco-elastic properties on ‘‘longterm’’ activation more extensive studies would be necessary. All the data in the text are presented as a mean&S.D.
RESULTS
The characteristics of contractile properties of m. flexor pollicis longus The contractile properties of m. flexor pollicis longus were measured in 12 subjects. These properties had a large intersubject variability which could be explained by large differences in fibre type distribution in human forearm muscles.22 The twitch/tetanus ratio varied from 0.05 to 0.2 for the non-potentiated muscle. Contraction time (Tmax) of initial twitch changed between 48 and 72 ms, and a half-relaxation time-between 34 and 66 ms. The shape of the UT curve also varied. In four subjects with the lowest Tmax (48–54 ms), 9 p.p.s. stimulation rate evoked only a train of twitches rather than tetanus. In these subjects we increased the stimulation frequency to 13.5 p.p.s. to obtain partially fused contraction. In spite of the variability, three phases could be distinguished in the shape of the UT curve (see Fig. 2), differing by a force level and a value of force oscillations. These phases were similar to the ones defined for the human flexor digitorum sublimis muscle.19 At the beginning the muscle developed the force with a relatively small variable component (phase 1). The amplitude of oscillations increased 2–3-fold after 60–100 pulses because of the increase of both a twitch force and a relaxation rate due to a staircase phenomenon (phase 2). Subsequently, after about 200 pulses the relaxation began to slow, force oscillations markedly decreased, a tension level gradually raised 1.5–2.5-fold and reached a maximum by 300–400 pulse (phase 3). During this phase the relaxation is characterized by the appearance of the linear portion,18 this markedly augments the half-relaxation time. The maximal evoked tension, measured as a force of short fused tetanus (1 s, 50 p.p.s.), decreased and at the termination of 400
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Fig. 2. The effect of slow length change in phase 2 and 3 of UT. A) Length changes at constant 9 p.p.s. stimulation rate. B) Length changes applied during temporal increases of stimulation rate to 20 p.p.s. To estimate the force response of passive muscle the length change was also applied before and after muscle stimulation. 1, tension, N; 2, joint angle. Numbers I, II and III denote three phases of UT. Twitches before and after UT and a short-fused tetanus (50 p.p.s., 1 s) were given to assess post-activation changes in muscle and the twitch-tetanus ratio. Both curves (A and B) were obtained on the same subject.
pulse train it was 15–20% lower than at the beginning of UT. Thus, moderate fatigue took place. The change of ‘‘low-frequency’’ stiffness during unfused tetanus Phase 1 of UT is too short to apply slow linear lengthening or shortening. So we confined ourselves to the measurement of muscle resistance to stretch during phases 2 and 3 of UT. These phases differ considerably by the level of force oscillations, by the rate of ATP splitting per unit force13,19 and by the velocity of relaxation.18 For the estimation of the stiffness of active muscle we measured the change of mean force level (the mean force level was calculated as a mean between maximum and minimum of the oscillating force) after
stretch that is a maximal value of force increment (ÄF in Fig. 2). The resistance of passive muscle to stretch was subtracted from this value. For these experiments we selected only those subjects in which the stiffness of active muscle was significantly greater than passive stiffness (six persons out of the initial 12). Experiments have shown that in all subjects the muscle stiffness in phase 3 of UT was 1.8&0.2 times greater than in phase 2 (Table 1). The tension level in phase 3 usually differed from that in phase 2. However, even after normalizing to the force level, the stiffness was 1.6&0.2 times greater in phase 3 than in phase 2. After cessation of stretch the tension immediately began to decrease, however it did not return to the pre-stretch level. This difference between pre- and post-stretch levels was also larger in phase 3 of UT.
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V. S. Gurfinkel et al. Table 1. Muscle resistance to slow ramp phase 2
Subject N.S. O.K. V.S. V.V. Y.I. Y.L. mean
phase 3
ÄFpass
F
ÄF2
F
ÄF3
(ÄF3"ÄFpass)/ (ÄF2"ÄFpass)
0.5&0.4 0.3&0.1 0.4&0.1 0.4&0.1 0.7&0.3 0.7&0.3 0.5&0.2
3.3&2.6 4.9&1.9 7.2&5.3 5.0&4.3 12.9&6.7 3.6&2.5 6.2&3.6
1&0.4 1&0.2 1&0.4 1.0&0.5 2.6&1.0 2.1&0.8 1.4&0.7
4.7&3.6 6.1&1.1 6.8&3.7 8.1&5.8 12.7&6.0 3.4&1.7 7.0&3.2
1.3&0.4 1.6&0.3 1.1&0.4 1.6&0.8 3.7&1.3 2.6&0.9 2.0&1.0
1.9&0.8 1.9&0.6 1.5&0.5 2.2&0.4 1.8&0.6 1.7&0.8 1.8&0.2
ÄFpass, force increment of passive muscle in response to ramp, N; F, force level, N; ÄF2, force increment in phase 2, N; ÄF3, force increment in phase 3, N. As the stretch amplitude was the same, the increment ÄF is directly proportional to muscle stiffness. (ÄF3"ÄFpass)/(ÄF2"ÄFpass), the ratio of active components of force increment in phase 3 and 2.
Fig. 3. Muscle response to slow ramps at different activation levels. Before applying the length change, the muscle was stimulated at 9 p.p.s. for about 45 s. Than two successive lengthening-shortening cycles were applied. During the second one the stimulation rate was increased to 20 p.p.s. Values on X axis denote the time from the beginning of recording. 1, tension, N; 2, joint angle.
The dependence of muscle stiffness on activation level The second phase of UT is characterized by increased force oscillations and, thus, by larger internal displacements. This, in turn, could explain the difference in the stiffness between phases 2 and 3 of UT. For example, relatively large internal displacements and ‘‘gaps’’ in ‘‘active state’’ during phase 2 of UT could reduce to zero some effects related to the history of the contraction,1,7 i.e. to a build up of activation during slow stretch. To test this hypothesis, we changed the force level during tetanus. For this purpose the frequency of stimulation was increased up to 20–25 p.p.s. (Fig. 2B) during stiffness measurement (for 8 s). The level of tetanic force increased accordingly and the oscillatory component of UT practically disappeared. Such experiments have shown that at high activation levels the stiffness in phase 3 was also approximately 1.5-
times higher than in phase 2. We concluded that the change in the muscle state (the increase of crossbridges life, the change in their kinetics) underlies the stiffness augmentation during UT and a decrease of internal displacements or fluctuations of ‘‘active state’’ play a minor role. On the other hand, these experiments revealed an unexpected phenomenon: muscle stiffness did not change in proportion to the activation level (Figs 2, 4). This could also be observed in two successive length changes at different force levels (Fig. 3). On average, the tension at 20–25 p.p.s. and 9–13.5 p.p.s. was equal to 11.5&2.5 N and 5.5&2.4 N, respectively. The force increment at 20–25 p.p.s. and 9–13.5 p.p.s. was equal to 1.7&1.0 N and 1.2&0.7 N, respectively. The enhancement of the stimulation frequency to 20–25 p.p.s. increased the force level during phase 3 by 2.2&0.8-times and the stiffness only by 1.5&0.4-times. As a result, the stiffness per
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never exceeded the resistance of passive muscle. In phase 2 a slight enhancement of variable component could also be observed, however, it was almost negligible at the background of large force oscillations. The influence of short-term increase or decrease of stimulation frequency on tension level The force never returned to the previous level after an increase in stimulation rate (Fig. 2B). Taking into account larger force changes in phase 3 than in phase 2, we supposed that the tension in phase 3 is also more sensitive to the activation history. Indeed, a short-term increase or decrease of stimulation rate markedly influenced the subsequent force level in phase 3 and did not much change the force level in phase 2 (Fig. 5). DISCUSSION
The enhancement of ‘‘low-frequency’’ stiffness during unfused tetanus
Fig. 4. Muscle response to slow ramps at different activation levels. Records (A, B and C) were obtained from the same subject. They were separated by 1 h of rest. Before applying the length change, the muscle was stimulated at 9 p.p.s. for about 45 s, then the activation level was varied by changing the stimulation rate: A) 20 p.p.s.; B) 9 p.p.s.; C) 2 p.p.s. 1, tension, N; 2, joint angle.
unit force was 1.5&0.4-times greater at 9–13.5 p.p.s. than at 20–25 p.p.s. Thus, UT resisted more efficiently than fused tetanus to slowly changing external loads. The changes of force oscillations during linear lengthening and shortening The principal feature of UT is the presence of tension oscillations. We found that the amplitude of these oscillations was modified during imposed slow movements. During length change in phase 3 oscillations increased by a factor of 1.2&0.2 (the range: 1–1.6) and immediately restored after the arrest of motion (Fig. 4B). The recovery time did not exceed 1 interpulse interval of stimulus train. The absolute value of the enhancement of variable component
Our results were obtained under stimulation of a whole muscle in situ. So the question arises: are the observed effects due to change in contractile machinery or are they due to a fatigue in neuromuscular junction or similar phenomena? Data gathered from normal muscles seem to support the fact that the major source of fatigue is within the contractile mechanism and not attributable to the neuromuscular junction.24,38 It should be stressed that the frequencies used in this study were rather low, duration of pulse train never exceeded 60–70 s, and muscular force was far from maximal. Under such conditions pronounced changes in neuromuscular synapses could hardly be expected. Even if there is some fatigue in neuromuscular junction, it will not change the conclusions of our paper because we compared stiffness changes both in absolute values and per force unit, and we found that muscle resistance was enhanced in phase 3 and not decreased. It is also difficult to suggest that the effects observed are totally determined by such factors as a change in force arm during joint excursion, the tendon compliance, the motor units composition. So, we suppose, that the slow stretch of single fibres would show qualitatively the same result. Our experiments confirmed former results obtained on flexors of the elbow joint using the method of damped oscillations.17 Therefore, this phenomenon of stiffness enhancement is of general importance. Relatively large internal displacements and ‘‘gaps’’ in active state during phase 2 of UT could reduce to zero some effects related to the contractile history,1,7 i.e. to the ‘‘activation’’ rise during slow stretch. However, in phase 3 the muscle stiffness was greater than during phase 2 at any activation level irrespective of the value of oscillatory component of UT (Fig. 2B). Thus, the phenomenon of the stiffness
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Fig. 5. The influence of short-term increase (three 20 ms interpulse intervals) and decrease (one 400 ms interval) of stimulation frequency on the tension level in phase 2 and 3 of 9 p.p.s. UT. Ä the difference of average force levels after increase and decrease of stimulation frequency. Twitches and a short-fused tetanus (50 p.p.s., 1 s) were also recorded as in the experiment depicted in Fig. 2.
augmentation during UT is due to the change in the muscle state (the enhancement of life time of crossbridges, the change in their kinetics), but not to the increased force oscillations. The transition to phase 3 of UT is accompanied by a moderate fatigue, since in spite of the rise of tension level in the UT the maximal muscle force fell by about 20%, the relaxation was considerably slowed18 and ATP splitting was diminished.13,19 Seemingly, the increase of stiffness during UT has the same underlying mechanism as an increase of the ‘‘lowfrequency’’ stiffness during moderate fatigue in fused tetanus.9,12,15 The influence of short-term increase or decrease of stimulation frequency on tension level Short-term increase or decrease of stimulation rate markedly influenced the subsequent force level in phase 3 and did not much change the force level in phase 2 (Fig. 5). Possibly, this effect was due to the stretch of a series elastic component and a small change of muscle fibre length during alteration in stimulation rate. In turn, length alterations influence the force in phase 3 more than in phase 2. However, one could not exclude a direct effect of the activation history on the tension level. Possibly, phase 3 of UT
differs from phase 2 not only by the extent of fatigue but by the slower rate of cross-bridges cycling. Force oscillations during linear lengthening and shortening Two possible mechanisms could be suggested for the increase of the oscillatory force component during movement. Joyce et al.23 have observed a pronounced growth of force oscillations in UT of cat soleus muscle during ramp stretch. They explained this effect by a premature cross-bridges detachment and, thus, by increase of oscillations of active cross-bridge number. However, they used greater stretch velocities (11.5 mm/s vs 0.6 mm/s in our experiments). In our case the duration of stretch was about 1.7 s, i.e. 15 cycles of UT at 9 p.p.s. Hence, during one interpulse interval of UT the joint angle changed by 5.5)/ 15=0.37). This corresponded to muscle length change of 0.05 mm assuming the force arm being equal to about 10 mm. The fibre length of m. flexor pollicis longus equals to about 45 mm.25 So, the muscle length change during one interpulse interval of UT was close to 0.1% of the fibre length, i.e. much less than the range of short-range stiffness (about 1%). Hence, the stretch applied should not provoke a considerable cross-bridge detachment. Taking into account a
Muscle resistance to slow ramp
tendon compliance2,34,36 and a redistribution of sarcomeres lengths along the fibre during isometric force development,8 one could suppose that internal displacements during one interpulse interval of UT were much more than 0.1%. Therefore, it seems unlikely that a small ‘‘external’’ length change could increase the variable component of UT up to 1.6 times. Another source of increase of oscillations could be a friction in passive muscles dominating at low stretch velocities.17 Power and Binder33 showed that the force measured when individual motor units are stimulated under isometric conditions is reduced by friction between the active muscle fibres and adjacent passive fibres. The existence of ‘‘dry’’ friction in parallel to the contractile apparatus both between active and passive fibres33 and inside muscle fibres17 should diminish tension oscillations in ‘‘isometric’’ conditions, and the applied slow motion should, in turn, decrease this effect. Moreover, we stimulated only a part of the muscle, so the contribution of the friction of whole muscle and the joint was relatively large. This argument was supported by the fact that the absolute value of the oscillations enhancement never exceeded the resistance of passive muscle and the recovery of the oscillations amplitude took place immediately after the arrest of motion. Friction and thixotropy could also explain the change of a twitch amplitude during slow movement (Fig. 3C). The dependence of muscle stiffness on activation level One of the intriguing results obtained was weak dependence of stiffness on activation level. This result
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can be explained either by a relatively compliant force-independent series elastic component28 or by the non-additivity of processes occurring in active muscle. In the latter case it could be of great interest from the viewpoint of the muscle contraction mechanism.30 For example, a short-range stiffness is approximately proportional to the force level and does not depend on the frequency of stimulation.5,27,37 However, we found that muscle stiffness at slow ramp did not change in proportion to the activation level (Figs 2, 4), that is to the number (density) of cross-bridges (due to their co-operative work, the existence of different cross-bridges populations and so on). This fact contradicts the independence of force generators as demanded by the classic crossbridges/sliding filament theory. However the question of the nature of this phenomenon is still to be clarified.
CONCLUSION
In conclusion, it is worth noting that the relative value (per unit force) of muscle stiffness is greater for smaller activation levels typical for the maintenance of posture. From this point of view UT more efficiently resists to slowly changing external loads than fused tetanus. Acknowledgements—This study was supported by the Russian Foundation for Fundamental Research (grant No. 96-04-48607).
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Abbott B. C. and Aubert X. M. (1952) The force exerted by active striated muscle during and after change of length. J. Physiol. 117, 77–86. Brown T. I. H., Rack P. M. H. and Ross H. F. (1982) Forces generated at the thumb interphalangeal joint during imposed sinusoidal movements. J. Physiol. 332, 69–85. Brown T. I. H., Rack P. M. H. and Ross H. F. (1982) Electromyographic responses to imposed sinusoidal movement of the human thumb. J. Physiol. 332, 87–99. Buschman H. P. J., Elzinga G. and Woledge R. C. (1993) Effect of stimulation frequency on heat and energy output during shortening in single muscle fibers from Xenopus laevis at 20)C. J. Physiol. 473, 82P. Cannon S. C. and Zahalak G. I. (1982) The mechanical behavior of active human skeletal muscle in small oscillations. J. Biomech. 152, 111–121. Colomo F., Lombardi V., Menchetti G. and Piazzesi G. (1989) The recovery of isometric tension after steady lengthening in tetanized fibres isolated from frog muscle. J. Physiol. 415, 130P. Cook C. S. and McDonagh M. J. N. (1993) Shortening force in electrically stimulated human muscle-tendon complex is enhanced by pre-stretch but is independent of pre-stretch velocity. J. Physiol. 473, 90P. Curtin N. A. and Edman K. A. P. (1989) Effects of fatigue and reduced intracellular pH on segment dynamics in ‘‘isometric’’ relaxation of frog muscle fibres. J. Physiol. 413, 159–174. Curtin N. A. and Edman K. A. P. (1994) Force-velocity relation for frog muscle fibres: effects of moderate fatigue and of intracellular acidification. J. Physiol. 4753, 483–494. Edman K. A. P. (1993) Mechanism underlying double-hyperbolic force-velocity relation in vertebrate skeletal muscle. Adv. exp. Med. Biol. 332, 667–676. Edman K. A. P., Caputo C. and Lou F. (1993) Depression of tetanic force induced by loaded shortening of frog muscle fibres. J. Physiol. 466, 535–552. Edman K. A. P. and Lou F. (1990) Changes in force and stiffness induced by fatigue and intracellular acidification in muscle fibres. J. Physiol. 424, 133–149. Edwards R. H. T., Hill A. K. and Jones A. A. (1975) Heat production and chemical changes during isometric contraction of the human quadriceps muscle. J. Physiol. 2512, 303–315. Ettema G. L. and Huijing P. A. (1994) Skeletal muscle stiffness in static and dynamic contractions. J. Biomech. 2711, 1361–1368.
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V. S. Gurfinkel et al. Flitney F. W. and Jones D. A. (1990) Force production during stretch of active, fatigued, isolated mouse soleus. J. Physiol. 473, 55P. Granzier H. L. and Pollack G. H. (1989) Effect of active pre-shortening on isometric and isotonic performance of single frog muscle fibres. J. Physiol. 415, 299–327. Gurfinkel V. S., Ivanenko Y. P. and Levik Y. S. (1990) Unusual mechanical behaviour of skeletal muscle during a slow change in its length. In Contemporary Problems of Biomechanics (eds Chernyi G. G. and Regirer S. A.), pp. 236–256. Mir Publishers/CRC Press, Boca Raton. Gurfinkel V. S., Ivanenko Y. P. and Levik Y. S. (1992) Some properties of linear relaxation in unfused tetanus of human muscle. Physiol. Res. 41, 437–443. Gurfinkel V. S. and Levik Y. S. (1985) Skeletal Muscle: Structure and Function. 147 p., Nauka, Moscow [in Russian]. Hagbarth K. E., Nordin M. and Bongiovanni L. G. (1995) After-effects on stiffness and stretch reflexes of human finger flexor muscles attributed to muscle thixotropy. J. Physiol. 482 Pt1, 215–223. Jami L., Murthy K. S. K., Petit J. and Zytnicki D. (1983) After-effects of repetitive stimulation at low frequency on fast-contracting motor units of cat muscle. J. Physiol. 340, 129–143. Johnson M. A., Polgar D. J., Weightman D. and Appelton D. (1973) Data on the distribution of fibre types in thirty-six human muscles. An autopsy study. J. neurol. Sci. 18, 111–129. Joyce G. C., Rack P. M. H. and Westbury D. R. (1969) The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J. Physiol. 204, 461–474. Kukulka C. G., Russell A. G. and Moore M. A. (1986) Electrical and mechanical changes in human soleus muscle during sustained maximum isometric contractions. Brain Res. 3621, 47–54. Lieber R. L., Jacobson M. D., Fazeli B. M., Abrams R. A. and Botte M. J. (1992) Architecture of selected muscles of the arm and forearm: anatomy and implications for tendon transfer. J. Hand Surg. Am. 175, 787–798. Mangini U. (1960) Flexor policis longus muscle. J. Bone Joint Surg. 42-A, 467–470. Metzger J. M. and Fitts R. H. (1987) Fatigue from high- and low-frequency muscle stimulation: contractile and biochemical alterations. J. appl. Physiol. 625, 2075–2082. Morgan D. L. (1977) Separation of active and passive components of short-range stiffness of muscle. Am. J. Physiol. 2321, C45–C49. Parmiggiani F. and Stein R. B. (1981) Nonlinear summation of contractions in cat muscles. II. Later facilitation and stiffness changes. J. gen. Physiol. 783, 295–311. Pollack G. H. (1988) Cross-bridge theory: do not disturb! J. molec. cell. Cardiol. 20, 563–570. Pollack G. H., Horowitz A., Wussling M. and Trombitas K. (1993) Shortening-induced tension enhancement: implication for length-tension relations. Adv. exp. Med. Biol. 332, 679–688. Powers R. K. and Binder M. D. (1991) Effects of low-frequency stimulation on the tension frequency relations of fast-twitch motor units in the cat. J. Neurophysiol. 66, 905–918. Powers R. K. and Binder M. D. (1991) Summation of motor unit tensions in the tibialis posterior muscle of the cat under isometric and nonisometric conditions. J. Neurophysiol. 666, 1838–1846. Proske U. and Morgan D. L. (1987) Tendon stiffness: methods of measurement and significance for the control of movement. A review. J. Biomech. 20, 75–82. Proske U., Morgan D. L. and Gregory J. E. (1993) Thixotropy in skeletal muscle and in muscle spindles: a review. Prog. Neurobiol. 416, 705–721. Rack P. M. H., Ross H. F., Thilmann A. F. and Walters D. K. W. (1983) Reflex responses at the human ankle: the importance of tendon compliance. J. Physiol. 344, 503–524. Rack P. M. H. and Westbury D. R. (1974) The short range stiffness of active mammalian muscle and its effect on mechanical properties. J. Physiol. 240, 331–350. Siatras T., Poumarat G., Boucher J. P. and Le Flohic J. C. (1994) Normal and paralyzed muscle force and fatigability induced by electrical stimulation. J. manipul. physiol. Ther. 175, 321–328. Suzuki S., Tsuchiya T., Oshimi Y., Takei T. and Sugi H. (1989) Electron microscopic studies on the stretch-induced disordering of the myofilament lattice in tetanized frog skeletal muscle fibers. J. Electron Microsc. 381, 60–63. Tan U. (1989) The Hoffmann reflex from the flexor pollicis longus of the thumb in left-handed subjects: spinal motor asymmetry and supraspinal facilitation to Cattell’s intelligence test. Int. J. Neurosci. 483-4, 255–269. (Accepted 12 March 1997)
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Neuroscience Vol. 80, No. 1, pp. 299–306, 1997 IBRO Copyright ? 1997 Published by Elsevier Science Ltd Printed in Great Britain 0306–4522/97 $17.00+0.00 S0306-4522(97)00130-9
MUSCLE RESISTANCE TO SLOW RAMP WEAKLY DEPENDS ON ACTIVATION LEVEL V. S. GURFINKEL,* Y. P. IVANENKO and Y. S. LEVIK Institute for Information Transmission Problems, Russian Academy of Science, Bolshoy Karetny 19, Moscow 101447, Russia Abstract––The mechanical response of human m. flexor pollicis longus to slow (3.2)/s) linear stretch by 5.5) was measured during sustained (45–60 s, 9–13.5 p.p.s.) unfused tetanus evoked by electrical stimulation. The stiffness increased during unfused tetanus. At the late phase of unfused tetanus it was 1.8&0.2 (mean&S.D.) times greater than at the early phase. The sensitivity of the isometric tension level to a short change in a stimulation frequency also increased. At the late phase of unfused tetanus force oscillations increased 1.2&0.2-fold during slow stretch or shortening and immediately reached a smaller amplitude after the cessation of length change. This was probably related to the friction and thixotropy in muscles. Muscle resistance to slow ramp depended only weakly on activation level. In the late phase of unfused tetanus the stiffness per unit force was 1.5&0.4 times greater at 9–13.5 p.p.s. than at 20–25 p.p.s. Thus, the relative value of muscle stiffness was greater for smaller activation levels typical for maintenance of posture. The enhancement of muscle stiffness during sustained unfused tetanus and a weak stiffness dependence on the activation level indicated a non-additivity of processes occurring in active muscle. ? 1997 Published by Elsevier Science Ltd. Key words: skeletal muscle, unfused tetanus, stretch, activation level, human.
Visco-elastic properties of skeletal muscles must be taken into account by the central nervous system when controlling posture and movements. Quick stretches and shortenings of maximally activated muscle fibres are commonly used to study the mechanical properties of skeletal muscles. Small (shortrange) high frequency length changes are often applied to estimate the number of attached crossbridges and their properties.6,9,29 However, it should be noted that slow length changes under relatively low loads are typical for physiological conditions. For example, during human locomotion the timing of muscle activity is about equally distributed between eccentric and concentric modes of contraction, i.e. the stretching of active muscles occurs rather often and with relatively low velocities. The muscle behaviour during slow change of length can also give useful information about cross-bridge kinetics. For instance, at low velocities, the significant deviations of experimental curve from a classic force–velocity law were observed;10 slow length changes can enhance or suppress isometric force.1,11,14,16,3139 These facts are of great interest for a sliding filaments/cross-bridges theory. It is also known that during posture maintenance and a large part of movements muscles develop tension levels that hardly exceed 15% of maximal
force. Low tensions mean that activation levels of muscle fibres are far from maximal. Results obtained at maximal fibre activation cannot be applied without reserve to the situation characterized by permanent oscillations of active state due to the low stimulation rate.4,18,23 For example, the length change can considerably reduce the force level of unfused tetanus (UT) but does not greatly influence the force level of fused tetanus.23 In the present work we studied the stiffness of human skeletal muscle at slow length changes during sustained UT. In addition to the investigation of temporal changes of muscle stiffness at a constant stimulation frequency we also compared muscle stiffness at different activation levels.
*To whom correspondence should be addressed. Abbreviations: EMG, electromyogram; p.p.s., pulse per second; UT, unfused tetanus. 299
EXPERIMENTAL PROCEDURES
Twelve healthy volunteers aged from 20 to 45 years participated in this study. The subject sat in a relaxed posture. Left forearm, hand and fingers were rigidly fixed to a horizontal platform in a pronate position (Fig. 1). We recorded the isometric torque produced by contraction of m. flexor pollicis longus. The end phalanx of the thumb of the left hand was connected to a rigid strain gauge (tensoresistors were glued to a steel beam of a cross section 16#2.5 mm). The stiffness of the strain gauge equalled 2#105 N/m. The measurements of absolute muscle force were difficult because of unknown force arm. So, we expressed the muscle tension in units of absolute readings of strain gauge. Strain gauge signals were fed to a PC computer via an analog-digital converter, sampling frequency being 500/c.
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Fig. 1. Schematic view of the experimental set-up.
To measure muscle stiffness, ramp length changes were applied. The axis of the end phalanx of the thumb was matched with the pivot of the turning plate, which was rotated by 5.5) by an electro-mechanical drive at a constant speed of 3.2)/s. Accordingly, the movement duration was 1.7 s. After 2 s the platform was returned to the initial position with the same velocity (Fig. 2). Thus a whole lengthening-shortening cycle took about 5.5 s. M. flexor pollicis longus is the only flexor of the thumb located in the forearm. It lies beside the flexor profundus in the forearm and is attached to the distal phalanx as is the latter. This muscle, which is unipennate,25 is absent in some primates, this suggests it was acquired comparatively recently in the evolutionary process. The fibre length of human m. flexor pollicis longus equals to about 45 mm.26 Assuming the force arm is equal to about 10 mm, we obtained the total amplitude of the fibre lengthening 5.5)/ 57#10=1 mm. Therefore, the velocity of stretch equalled to approximately 1 mm/1.7 s=0.6 mm/s or 0.6/45=0.013 Lo/s, where Lo is a physiological fibre length. The initial joint angle was approximately in the middle between most flexed and most extended positions. This neutral position was chosen to reduce the impact of passive component on stiffness measurement. In addition, in this angular range the isometric force remained practically constant, as was shown by comparing the twitch force at different joint angles (see Fig. 4C). For most of the subjects, variations of twitch force were negligible (below 5%). The active electrode (about 1 cm diameter) was placed at the corresponding motor point, the other one (6#8 cm) at the dorsal surface of the wrist. A Stimulator ENS-01 with a stabilized current output was controlled by digital output of PC computer. The motor nerve was stimulated by rectangular current pulses (12–18 mA, 1 ms). Greater currents were not used, as they evoked painful sensations during tetanic stimulation. During such stimulation a tetanic tension at 50 pulses per second (p.p.s.) amounted to about 15–25% of maximal voluntary contraction, i.e. only a part of the muscle was activated by the electric current. Under our experimental conditions only direct Mresponse was evoked, as H-reflex is not manifested in passive hand muscles of healthy humans and could appear solely at the background of voluntary activation.40 On the other hand, no detectable electromyogram (EMG) response was generated by the imposed movement when the subject relaxed his thumb.3 The absence of a voluntary interference in muscle activity was proved by a smoothness of a relaxation curve during electrical stimulation.19 Effectiveness of electrical stimulation was different in different subjects. The contribution of the passive component (muscles, ligaments, skin) to the measured stiffness also differed depending on fixation of the second phalanx, thixotropic history.17,20,35 Thus, we selected only those subjects, in which the stiffness of the active muscle was considerably
larger than the passive stiffness. From 12 subjects studied only six were included in the analysis. Unfused tetanus was evoked by a train of 400–600 pulses with a frequency of stimulation in the range of 9–13.5 p.p.s. Overall train duration was 45–60 s. A total of 89 recordings were carried out. To study the dependence of stiffness on force level, the stimulation frequency of UT was increased from 9–13.5 p.p.s. to 20–25 p.p.s. for 8 s (Fig. 2B). We also investigated the influence of short-term increase or decrease of stimulation frequency upon the force of isometric unfused tetanus. Three additional pulses (interpulse interval 20 ms) were inserted into the background stimulus train, or, on the contrary, one interpulse interval was increased to 400 ms (Fig. 5). It is known18,21,27,32 that even after 1 min of contraction the traces of postactivation changes in muscle persist for a long time. So, the period of recovery between two successive UT recordings was no less that 1 h. Except for some cases, the first UT did not differ much from the subsequent ones; so during data analysis we have not differentiated between the first and following tetani. For demonstration of the dependence of muscle visco-elastic properties on ‘‘longterm’’ activation more extensive studies would be necessary. All the data in the text are presented as a mean&S.D.
RESULTS
The characteristics of contractile properties of m. flexor pollicis longus The contractile properties of m. flexor pollicis longus were measured in 12 subjects. These properties had a large intersubject variability which could be explained by large differences in fibre type distribution in human forearm muscles.22 The twitch/tetanus ratio varied from 0.05 to 0.2 for the non-potentiated muscle. Contraction time (Tmax) of initial twitch changed between 48 and 72 ms, and a half-relaxation time-between 34 and 66 ms. The shape of the UT curve also varied. In four subjects with the lowest Tmax (48–54 ms), 9 p.p.s. stimulation rate evoked only a train of twitches rather than tetanus. In these subjects we increased the stimulation frequency to 13.5 p.p.s. to obtain partially fused contraction. In spite of the variability, three phases could be distinguished in the shape of the UT curve (see Fig. 2), differing by a force level and a value of force oscillations. These phases were similar to the ones defined for the human flexor digitorum sublimis muscle.19 At the beginning the muscle developed the force with a relatively small variable component (phase 1). The amplitude of oscillations increased 2–3-fold after 60–100 pulses because of the increase of both a twitch force and a relaxation rate due to a staircase phenomenon (phase 2). Subsequently, after about 200 pulses the relaxation began to slow, force oscillations markedly decreased, a tension level gradually raised 1.5–2.5-fold and reached a maximum by 300–400 pulse (phase 3). During this phase the relaxation is characterized by the appearance of the linear portion,18 this markedly augments the half-relaxation time. The maximal evoked tension, measured as a force of short fused tetanus (1 s, 50 p.p.s.), decreased and at the termination of 400
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Fig. 2. The effect of slow length change in phase 2 and 3 of UT. A) Length changes at constant 9 p.p.s. stimulation rate. B) Length changes applied during temporal increases of stimulation rate to 20 p.p.s. To estimate the force response of passive muscle the length change was also applied before and after muscle stimulation. 1, tension, N; 2, joint angle. Numbers I, II and III denote three phases of UT. Twitches before and after UT and a short-fused tetanus (50 p.p.s., 1 s) were given to assess post-activation changes in muscle and the twitch-tetanus ratio. Both curves (A and B) were obtained on the same subject.
pulse train it was 15–20% lower than at the beginning of UT. Thus, moderate fatigue took place. The change of ‘‘low-frequency’’ stiffness during unfused tetanus Phase 1 of UT is too short to apply slow linear lengthening or shortening. So we confined ourselves to the measurement of muscle resistance to stretch during phases 2 and 3 of UT. These phases differ considerably by the level of force oscillations, by the rate of ATP splitting per unit force13,19 and by the velocity of relaxation.18 For the estimation of the stiffness of active muscle we measured the change of mean force level (the mean force level was calculated as a mean between maximum and minimum of the oscillating force) after
stretch that is a maximal value of force increment (ÄF in Fig. 2). The resistance of passive muscle to stretch was subtracted from this value. For these experiments we selected only those subjects in which the stiffness of active muscle was significantly greater than passive stiffness (six persons out of the initial 12). Experiments have shown that in all subjects the muscle stiffness in phase 3 of UT was 1.8&0.2 times greater than in phase 2 (Table 1). The tension level in phase 3 usually differed from that in phase 2. However, even after normalizing to the force level, the stiffness was 1.6&0.2 times greater in phase 3 than in phase 2. After cessation of stretch the tension immediately began to decrease, however it did not return to the pre-stretch level. This difference between pre- and post-stretch levels was also larger in phase 3 of UT.
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V. S. Gurfinkel et al. Table 1. Muscle resistance to slow ramp phase 2
Subject N.S. O.K. V.S. V.V. Y.I. Y.L. mean
phase 3
ÄFpass
F
ÄF2
F
ÄF3
(ÄF3"ÄFpass)/ (ÄF2"ÄFpass)
0.5&0.4 0.3&0.1 0.4&0.1 0.4&0.1 0.7&0.3 0.7&0.3 0.5&0.2
3.3&2.6 4.9&1.9 7.2&5.3 5.0&4.3 12.9&6.7 3.6&2.5 6.2&3.6
1&0.4 1&0.2 1&0.4 1.0&0.5 2.6&1.0 2.1&0.8 1.4&0.7
4.7&3.6 6.1&1.1 6.8&3.7 8.1&5.8 12.7&6.0 3.4&1.7 7.0&3.2
1.3&0.4 1.6&0.3 1.1&0.4 1.6&0.8 3.7&1.3 2.6&0.9 2.0&1.0
1.9&0.8 1.9&0.6 1.5&0.5 2.2&0.4 1.8&0.6 1.7&0.8 1.8&0.2
ÄFpass, force increment of passive muscle in response to ramp, N; F, force level, N; ÄF2, force increment in phase 2, N; ÄF3, force increment in phase 3, N. As the stretch amplitude was the same, the increment ÄF is directly proportional to muscle stiffness. (ÄF3"ÄFpass)/(ÄF2"ÄFpass), the ratio of active components of force increment in phase 3 and 2.
Fig. 3. Muscle response to slow ramps at different activation levels. Before applying the length change, the muscle was stimulated at 9 p.p.s. for about 45 s. Than two successive lengthening-shortening cycles were applied. During the second one the stimulation rate was increased to 20 p.p.s. Values on X axis denote the time from the beginning of recording. 1, tension, N; 2, joint angle.
The dependence of muscle stiffness on activation level The second phase of UT is characterized by increased force oscillations and, thus, by larger internal displacements. This, in turn, could explain the difference in the stiffness between phases 2 and 3 of UT. For example, relatively large internal displacements and ‘‘gaps’’ in ‘‘active state’’ during phase 2 of UT could reduce to zero some effects related to the history of the contraction,1,7 i.e. to a build up of activation during slow stretch. To test this hypothesis, we changed the force level during tetanus. For this purpose the frequency of stimulation was increased up to 20–25 p.p.s. (Fig. 2B) during stiffness measurement (for 8 s). The level of tetanic force increased accordingly and the oscillatory component of UT practically disappeared. Such experiments have shown that at high activation levels the stiffness in phase 3 was also approximately 1.5-
times higher than in phase 2. We concluded that the change in the muscle state (the increase of crossbridges life, the change in their kinetics) underlies the stiffness augmentation during UT and a decrease of internal displacements or fluctuations of ‘‘active state’’ play a minor role. On the other hand, these experiments revealed an unexpected phenomenon: muscle stiffness did not change in proportion to the activation level (Figs 2, 4). This could also be observed in two successive length changes at different force levels (Fig. 3). On average, the tension at 20–25 p.p.s. and 9–13.5 p.p.s. was equal to 11.5&2.5 N and 5.5&2.4 N, respectively. The force increment at 20–25 p.p.s. and 9–13.5 p.p.s. was equal to 1.7&1.0 N and 1.2&0.7 N, respectively. The enhancement of the stimulation frequency to 20–25 p.p.s. increased the force level during phase 3 by 2.2&0.8-times and the stiffness only by 1.5&0.4-times. As a result, the stiffness per
Muscle resistance to slow ramp
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never exceeded the resistance of passive muscle. In phase 2 a slight enhancement of variable component could also be observed, however, it was almost negligible at the background of large force oscillations. The influence of short-term increase or decrease of stimulation frequency on tension level The force never returned to the previous level after an increase in stimulation rate (Fig. 2B). Taking into account larger force changes in phase 3 than in phase 2, we supposed that the tension in phase 3 is also more sensitive to the activation history. Indeed, a short-term increase or decrease of stimulation rate markedly influenced the subsequent force level in phase 3 and did not much change the force level in phase 2 (Fig. 5). DISCUSSION
The enhancement of ‘‘low-frequency’’ stiffness during unfused tetanus
Fig. 4. Muscle response to slow ramps at different activation levels. Records (A, B and C) were obtained from the same subject. They were separated by 1 h of rest. Before applying the length change, the muscle was stimulated at 9 p.p.s. for about 45 s, then the activation level was varied by changing the stimulation rate: A) 20 p.p.s.; B) 9 p.p.s.; C) 2 p.p.s. 1, tension, N; 2, joint angle.
unit force was 1.5&0.4-times greater at 9–13.5 p.p.s. than at 20–25 p.p.s. Thus, UT resisted more efficiently than fused tetanus to slowly changing external loads. The changes of force oscillations during linear lengthening and shortening The principal feature of UT is the presence of tension oscillations. We found that the amplitude of these oscillations was modified during imposed slow movements. During length change in phase 3 oscillations increased by a factor of 1.2&0.2 (the range: 1–1.6) and immediately restored after the arrest of motion (Fig. 4B). The recovery time did not exceed 1 interpulse interval of stimulus train. The absolute value of the enhancement of variable component
Our results were obtained under stimulation of a whole muscle in situ. So the question arises: are the observed effects due to change in contractile machinery or are they due to a fatigue in neuromuscular junction or similar phenomena? Data gathered from normal muscles seem to support the fact that the major source of fatigue is within the contractile mechanism and not attributable to the neuromuscular junction.24,38 It should be stressed that the frequencies used in this study were rather low, duration of pulse train never exceeded 60–70 s, and muscular force was far from maximal. Under such conditions pronounced changes in neuromuscular synapses could hardly be expected. Even if there is some fatigue in neuromuscular junction, it will not change the conclusions of our paper because we compared stiffness changes both in absolute values and per force unit, and we found that muscle resistance was enhanced in phase 3 and not decreased. It is also difficult to suggest that the effects observed are totally determined by such factors as a change in force arm during joint excursion, the tendon compliance, the motor units composition. So, we suppose, that the slow stretch of single fibres would show qualitatively the same result. Our experiments confirmed former results obtained on flexors of the elbow joint using the method of damped oscillations.17 Therefore, this phenomenon of stiffness enhancement is of general importance. Relatively large internal displacements and ‘‘gaps’’ in active state during phase 2 of UT could reduce to zero some effects related to the contractile history,1,7 i.e. to the ‘‘activation’’ rise during slow stretch. However, in phase 3 the muscle stiffness was greater than during phase 2 at any activation level irrespective of the value of oscillatory component of UT (Fig. 2B). Thus, the phenomenon of the stiffness
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Fig. 5. The influence of short-term increase (three 20 ms interpulse intervals) and decrease (one 400 ms interval) of stimulation frequency on the tension level in phase 2 and 3 of 9 p.p.s. UT. Ä the difference of average force levels after increase and decrease of stimulation frequency. Twitches and a short-fused tetanus (50 p.p.s., 1 s) were also recorded as in the experiment depicted in Fig. 2.
augmentation during UT is due to the change in the muscle state (the enhancement of life time of crossbridges, the change in their kinetics), but not to the increased force oscillations. The transition to phase 3 of UT is accompanied by a moderate fatigue, since in spite of the rise of tension level in the UT the maximal muscle force fell by about 20%, the relaxation was considerably slowed18 and ATP splitting was diminished.13,19 Seemingly, the increase of stiffness during UT has the same underlying mechanism as an increase of the ‘‘lowfrequency’’ stiffness during moderate fatigue in fused tetanus.9,12,15 The influence of short-term increase or decrease of stimulation frequency on tension level Short-term increase or decrease of stimulation rate markedly influenced the subsequent force level in phase 3 and did not much change the force level in phase 2 (Fig. 5). Possibly, this effect was due to the stretch of a series elastic component and a small change of muscle fibre length during alteration in stimulation rate. In turn, length alterations influence the force in phase 3 more than in phase 2. However, one could not exclude a direct effect of the activation history on the tension level. Possibly, phase 3 of UT
differs from phase 2 not only by the extent of fatigue but by the slower rate of cross-bridges cycling. Force oscillations during linear lengthening and shortening Two possible mechanisms could be suggested for the increase of the oscillatory force component during movement. Joyce et al.23 have observed a pronounced growth of force oscillations in UT of cat soleus muscle during ramp stretch. They explained this effect by a premature cross-bridges detachment and, thus, by increase of oscillations of active cross-bridge number. However, they used greater stretch velocities (11.5 mm/s vs 0.6 mm/s in our experiments). In our case the duration of stretch was about 1.7 s, i.e. 15 cycles of UT at 9 p.p.s. Hence, during one interpulse interval of UT the joint angle changed by 5.5)/ 15=0.37). This corresponded to muscle length change of 0.05 mm assuming the force arm being equal to about 10 mm. The fibre length of m. flexor pollicis longus equals to about 45 mm.25 So, the muscle length change during one interpulse interval of UT was close to 0.1% of the fibre length, i.e. much less than the range of short-range stiffness (about 1%). Hence, the stretch applied should not provoke a considerable cross-bridge detachment. Taking into account a
Muscle resistance to slow ramp
tendon compliance2,34,36 and a redistribution of sarcomeres lengths along the fibre during isometric force development,8 one could suppose that internal displacements during one interpulse interval of UT were much more than 0.1%. Therefore, it seems unlikely that a small ‘‘external’’ length change could increase the variable component of UT up to 1.6 times. Another source of increase of oscillations could be a friction in passive muscles dominating at low stretch velocities.17 Power and Binder33 showed that the force measured when individual motor units are stimulated under isometric conditions is reduced by friction between the active muscle fibres and adjacent passive fibres. The existence of ‘‘dry’’ friction in parallel to the contractile apparatus both between active and passive fibres33 and inside muscle fibres17 should diminish tension oscillations in ‘‘isometric’’ conditions, and the applied slow motion should, in turn, decrease this effect. Moreover, we stimulated only a part of the muscle, so the contribution of the friction of whole muscle and the joint was relatively large. This argument was supported by the fact that the absolute value of the oscillations enhancement never exceeded the resistance of passive muscle and the recovery of the oscillations amplitude took place immediately after the arrest of motion. Friction and thixotropy could also explain the change of a twitch amplitude during slow movement (Fig. 3C). The dependence of muscle stiffness on activation level One of the intriguing results obtained was weak dependence of stiffness on activation level. This result
305
can be explained either by a relatively compliant force-independent series elastic component28 or by the non-additivity of processes occurring in active muscle. In the latter case it could be of great interest from the viewpoint of the muscle contraction mechanism.30 For example, a short-range stiffness is approximately proportional to the force level and does not depend on the frequency of stimulation.5,27,37 However, we found that muscle stiffness at slow ramp did not change in proportion to the activation level (Figs 2, 4), that is to the number (density) of cross-bridges (due to their co-operative work, the existence of different cross-bridges populations and so on). This fact contradicts the independence of force generators as demanded by the classic crossbridges/sliding filament theory. However the question of the nature of this phenomenon is still to be clarified.
CONCLUSION
In conclusion, it is worth noting that the relative value (per unit force) of muscle stiffness is greater for smaller activation levels typical for the maintenance of posture. From this point of view UT more efficiently resists to slowly changing external loads than fused tetanus. Acknowledgements—This study was supported by the Russian Foundation for Fundamental Research (grant No. 96-04-48607).
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