JOURNALOFN EUROPHYSIOLOGY Vol. 46, No. 2, August 198 1. Printed
in U.S.A.
Comparison of Stiffness of Soleus and Medial Gastrocnemius Muscles in Cats B. WALMSLEY
AND
u. PROSKE
Department of Physiology, Monash University, Clayton, Victoria, Australia 3168
SUMMARY
AND
CONCLUSIONS
I. Tension changes were recorded during stretch of the contracting medial gastrocnemius (MG) and soleus (SOL) muscles in the same hindlimb of cats. 2. The short-range stiffness of both MG and SOL was measured and separated into an active component in muscle fibers and a passive component in the tendon. 3. The active component of the shortrange stiffness was found to be different for the two muscles and the difference could be accounted for in terms of numbers of sarcomeres per muscle fiber. 4. The values of tendon compliance were found to be similar for both muscles despite large differences in the geometrical arrangement of muscle fibers and tendons. 5. With stretches comparable in amplitude to movements during locomotion, total stiffness reached a maximum value not at the peak, as expected, but during the rising phase of a contraction and the tension was largely determined by changes after the region of short-range stiffness had been exceeded. 6. The mechanical properties and geometry of the SOL and MG muscle are discussed with reference to their roles in posture and locomotion. INTRODUCTION
In a previous study (19) the forces produced by medial gastrocnemius (MG) and soleus (SOL) muscles were measured directly by implanted devices in freely moving cats during standing, treadmill locomotion, and jumping. These measurements showed that during normal walking and running most of the recorded tension was contributed 250
0022-3077/8
1 /OOOO-0000$01.25
by SOL. Only at the fastest running speeds and in jumping did the tension in MG become significant. This result was unexpected as slow-twitch muscles like SOL have traditionally been assigned a postural role (e.g., Ref. 3). It suggested that there were other properties of slow-twitch muscles that made them more suitable than fast-twitch muscles for the routine operations in locomotion. In locomotion, limb muscles undergo both stretch and shortening during their periods of activity. A property of muscle that is important in determining the tension while the muscle is undergoing rapid length changes is its stiffness (13, 18). When a contracting muscle is stretched there is an initial steep rise in tension, called the short-range stiffness (18). If the stretch is sufficiently large the short-range stiffness gives way to a more gradual tension change, the transition point being marked by a visible “corner” in the record of tension displayed against length. The measured value of short-range stiffness depends on the isometric tension developed by the muscle prior to stretch, the length of muscle fibers (number of sarcomeres), and the stiffness of the tendon. At low rates of stretch a further factor is the contraction speed of the muscle. However, if the stretch is sufficiently rapid a limiting value of stiffness can be reached (15). Speed of muscle contraction may not only affect the value of short-range stiffness, but during a large movement determines the slope of the subsequent tension change. This is important since during normal locomotion a muscle may be stretched well beyond the limit of the short-range stiffness region. The aim of these experiments was to determine whether mammalian slow and fast muscles showed differences in stiffness, as Copyright
0
198 1 The American
Physiological
Society
STIFFNESS
OF SLOW
do their reptilian and amphibian counterparts (12, 17), and to relate these findings to the muscles’ roles in locomotion. It was found that the short-range stiffness of muscle fibers was quite different for MG and SOL, while the tendon compliance for each muscle was approximately the same. The difference in short-range stiffness could be accounted for entirely by a difference in sarcomere number per muscle fiber for MG and SOL, and was therefore not due to any intrinsic difference between fast and slow muscles. The difference in muscle fiber lengths was also expressed in the shapes of the length-tension curves for the two muscles. With muscle stretches of amplitudes similar to those that occur during locomotion, it was found that total stiffness of the muscle was largely determined by the component of the tension change after the short-range stiffness region had been exceeded. METHODS
IWeasurement of muscle mechanical properties Experiments were performed on four cats, each selected for a weight of 2.5 kg. The animals were induced and maintained on pentobarbital anesthesia. The SOL and MG muscles of the left hindlimb were dissected free of surrounding tissue. The tendons of insertion of plantaris and lateral gastrocnemius muscles were dissected and cut free. The tendons of insertion of MG and SOL were then detached from the calcaneum, along with a portion of that bone. A small hole was drilled in the bone fragment and a stiff wire passed through the hole to connect the muscles to a stretching device. The stretching device consisted of a feedbackcontrolled electromagnetic actuator, which when operated in controlled position mode had a stiffness in excess of lo6 N/m. Tension was measured by means of a pair of semiconductor strain gauges attached to a beryllium copper link in series with the stretching device. The strain gauges were used in a Wheatstone bridge circuit. Muscle length changes were measured with a Shaevitz LVDT transducer (model 500 MHR) built into the stretching device. The animals were fixed on a rigid metal frame by steel pins driven into the pelvis and by pairs of pins in the femur and tibia. The skin of the dissected limb was drawn up to retain a pool of mineral oil that covered the muscles and their nerve supply. The temperature of the leg pool was maintained at 36-38OC bv infrared heat.
AND
FAST
MUSCLES
251
The nerves to MG and SOL were dissected free, cut, and placed on separate bipolar stimulating electrodes so that measurements could be made on each muscle independently. In the case of MG only a portion of the nerve was stimulated so as to limit the amount of tension developed to approximately one-half to one-third of the maximum. Since this represents a rather large proportion, it was not thought that regional inhomogeneities in motor-unit composition (6) influenced the results. Muscle tension was graded by a combination of stimulus frequency and muscle length. Measurements were made only on smooth tetanic contractions.
h4easurements on muscle fibers and tendons The SOL and MG muscles were dissected and fixed in Form01 saline (10% Formalin in physiological saline) at lengths corresponding to 90° knee and ankle joint angles. Following adequate fixation, small bundles of fibers were dissected out and placed on glass slides. Individual fibers were teased apart and covered with a cover slip. Measurements were made of muscle fiber length and the total length of tendon in series with the muscle fiber using a projecting microscope. Average sarcomere length was determined by placing the muscle fibers in the beam from a He-Ne laser (wavelength 632.8 nm) and measuring the distance between the first-order diffraction lines at a known distance from the fiber (12). Measurements were made every 1 mm along the fiber, the average value found, and the mean sarcomere length for the fiber calculated. RESULTS
Measurement of muscle fiber length and tendon length Figure 1 illustrates the geometric arrangement of muscle fibers and tendons in MG and SOL. The two muscles are quite different in structure. MG is a pennate muscle whose muscle fibers are arranged at an angle to its longitudinal axis, whereas SOL contains much longer fibers lying almost parallel to the muscle axis. The distribution of fiber types (fast, fatiguing, FF; fast, fatigue resistant, FR; slow, fatigue resistant, S) within MG is nonuniform (6), with type FF predominating in the dorsal margin of the muscle. Therefore, muscle fiber and tendon measurements were made on three regions of this muscle (dorsal, belly, and ventral regions). No significant differences in sarcomere number or muscle fiber and tendon lengths were
B. WALMSLEY
MG
AND
U. PROSKE
quencies (100 pulses/s for SOL, 200 pulses/ s for MG, for a period of 500 ms) and an interval between stimulus trains chosen such that MG did not progressively fatigue during the measurements. The graphs have been centered at L,, which represents the length corresponding to a maximal isometric tetanus. Peak tensions have been normalized to a value of 1 to facilitate comparison of their shapes. The two curves are very different, with the force in MG decreasing almost twice as rapidly as that for SOL when the two muscles are either shortened or lengthened by a similar amount from L,.
Short-range
--
FIG. 1. Longitudinal sections of the MG and SOL muscles of the cat, drawn to scale, and showing the relationship between muscle fibers and tendons. The diagram to the left of each figure represents a single muscle fiber and its tendinous connections.
found between different regions of the muscle. SOL is composed entirely of type S motor units. Table 1 summarizes the measurements of sarcomere length, muscle fiber length, and tendon length made on two pairs of MG and SOL muscles. The average number of sarcomeres per muscle fiber for MG was found to be about 60% of that for SOL. The length of tendon in series with MG muscle fibers was 50% greater than that for SOL. Length-tension plots were also constructed for MG and SOL, the measurements being made in the same animal. These clearly reflected the differences in sarcomere numbers between the two muscles. Figure 2 shows one such plot. Both muscles were activated at supramaximal stimulus fre-
stiffness of MG and SOL
When an actively contracting muscle is stretched, the initial steep rise in tension, the short-range stiffness, is thought to be due to elastic deformation of existing cross bridges between the actin and myosin filaments of the myofibrils (18). As the muscle tendon is in series with muscle fibers, its compliance will be included in any short-range stiffness measurements made on an intact muscle. Morgan (15) developed a simple method for separating the active (cross bridge) and passive (tendon) components of the short-range stiffness of muscle. The method is based on the measurement of short-range stiffness of the muscle at a number of different levels of isometric tension. If the short-range stiffness of the myofilaments is due to deformation of existing cross bridges without significant breakdown or reformation, then stiffness will be proportional to the number of bridges, and hence to the level of isometric tension, P; i.e., AP/AxB = P/aO, where P is the isometric tension, AP is a small change in the isometric tension, Axg is the associated change in length of the cross bridge array, and cy, is a constant that depends on cross bridge properties and the number of sarcomeres in series. If the tendon is considered as an elastic element of compliance CT, then AX&U? = CT, where AxT is the length change of the tendon. Combining the in-series compliances for the muscle and tendon gives: C = CT + cy,/P, where C is the total compliance. This may be rearranged in the form cy = a, + CrP, where cy = C. P is the amount of shortening required to reduce the tension to zero if the short-range stiffness continued to operate. Thus if a plot of a! vs. l
STIFFNESS TABLE
1.
Measurements
SLOW
AND
Bottom
Soleus
Middle
1
2.3
2.4
2.7
2.5
Sarc no.
2.6 7,7 18
2.6 7,019
2.6 6,701
2.6 7,146
2
7,393
9,905
7,145
8,147
Fiber length, mm
Average of 2
Average
Top
2 1
pm
253
MUSCLES
Gastrocnemius
Sarc length, Pm
Tendon length,
FAST
of muscle jibers Medial
Muscle no.
OF
1
90.5
93.5
91.7
91.9
2
93.3
96.0
96.3
95.2
1
17.4
16.7
18.4
17.5
2
19.2
17.9
18.9
18.7
Piece No. 1
Piece No. 2
2.4
2.55 7,647
93.6
Average
2.4
2.4
2.0 12,223
2.0 1 1,692
2.0 11,958
11,819
12,315
12,067
49.2
47.8
48.5
71.5
73.0
72.3
18.1
28.7
27.9
28.3
23.8
24.8
24.3
Average of 2
2.2 12,013
60.4
26.3
For MG, measurements were made on fiber bundles taken from the top, middle, or bottom region of the muscle. Since SOL is more uniform in composition, only two regions were sampled. The muscles were taken from cats of similar weight (2.5 kg) to those used to obtain the results in Table 2.
P is constructed (an a-diagram), this will give a straight line with intercept cy, and slope CT, enabling the active and passive sources of compliance to be separated. The short-range stiffness was measured at a number of different isometric tensions
by forcibly stretching the contracting muscle with a brief triangular stretch (4 mm amplitude, 400 mm/s). Figure 3 shows the superimposed records of a stretch-release sequence for MG and SOL in the same hindlimb. Muscle tension was plotted against
l
t
MG
0 SOL Lo
1”
1
-
10
”
11
1
’
11
-5 Length
11
11
0 Change
11
1
fi
J
5
(mm)
FIG. 2. Length-tension curves for MG and SOL using tetanic contractions. Stimulus rate for MG, 200 pulses/ s, and for SOL, 100 pulses/s. Tensions developed by each muscle have been normalized to a maximum value of 1 .O to facilitate comparison of shapes of the two curves. Curves are centered around optimum length, L,.
B. WALMSLEY
254
AND
U. PROSKE
-z
IMeasured values of LY,and C,
2.
TABLE
30
Medial Gastrocnemius m
c20 L
Exp No.
.-0 ul c c
10 -
O-
1
0 Length
2 Change
1 4
(mm)
FIG. 3. Measurement of muscle stiffness. The isometrically contracting MG and SOL muscles (developing about 8 N of force) were forcibly stretched and shortened (4 mm amplitude at 400 mm/s). For each muscle, the recorded tension change has been displayed against the length change. At the onset of stretch there is an initial linear steep rise in tension, the short-range stiffness, which in both muscles gives way after about 1 mm of stretch to a more gradual change.
length change and the short-range stiffness is represented by the linear portion of the slope at the start of the stretch. After the short-range stiffness region was exceeded, at about 1 mm stretch, tension in both MG and SOL increased less rapidly as muscle length increased, although the decrease in slope was much less for MG than for SOL. An example of an a-diagram for MG and SOL measured in the same animal is shown in Fig. 4. Regression lines were fitted to the data, giving values of cy, and CT. Table 2 contains pairs of values of cy, and CT for MG and SOL measured in the hindlimbs of four cats of similar weight. The average values for the four experiments were: cy, = 0.39 mm for MG, 0.64 mm for SOL, and CT = 0.06 mm/N for MG, 0.05 mm/N for SOL. Thus, the cy, value for MG was only 60% of that for SOL, while the values of tendon compliance were almost the same for the two muscles.
A4uscle stiffness during largeamplitude stretches SOL and MG produce comparable peak forces during fast treadmill running (15 N peak force, see Fig. 8 of Ref. 19). From the
a0,
Soleus
mm G-,mm/N
I
0.41
0.08
2 3 4 Avg
0.42 0.40 0.34 0.39
0.04 0.04 0.08 0.06
cyo, mm
CT, mm/N
0.53 0.72 0.52 0.79 0.64
0.05 0.03 0.04 0.08 0.05
Values of ac, represent properties of muscle fibers and CT, the tendon compliances for MG and SOL, from the same hindlimb of four cats of similar weight.
CT values, the tendon of SOL was calculated to be stretched by 0.90 mm and the tendon of MG by 0.75 mm at 15 N of force, which 2.0
SOL
i 1.0
’ 2.-
ri’ ur
I
I 0
lb TENSION
Zb (N)
FIG. 4. Plots of cy (see text) against isometric tension over a range of tension for SOL (open circles) and MG (filled circles). Values of ar were obtained from the tension response of the muscle to a brief stretch (4 mm at 400 mm/s, see Fig. 3). Regression lines were fitted to data and have slopes of 0.058 mm/N for SOL and 0.077 mm/N for MG. Intercepts on the ordinate, cyO, are 0.57 mm for SOL and 0.34 mm for MG.
STIFFNESS
OF SLOW
is very little compared with the overall muscle stretch of approximately 5 mm occurring during the yield phase of locomotion. Hence the muscle fibers must be stretched by at least 4 mm, which greatly exceeds the limit of the short-range stiffness. To examine more closely the effects of muscle stretch during locomotion, we used a single muscle twitch and a fused tetanus (representing two extremes of the likely pattern of activation) and transiently stretched the muscle at different times during the contraction. Figure 5A shows the effect of imposing a l-mm stretch at different times during the course of a muscle twitch. Provided the stretch is sufficiently rapid, stiffness of the muscle (not including the tendon) should be proportional to the number of attached cross bridges at the time of stretch. This prediction is borne out by the shortrange stiffness reaching a maximum value at the peak of the twitch. However, during the yield phase of the step cycle in locomotion, SOL is stretched through much
1 2N
1
B
I I I I
1
100 ms
5N
FIG. 5. Tension changes in response to a brief stretch applied at various times during a muscle twitch in SOL. Stretch amplitude 1 mm in A, 5 mm in B. Stretch rate 500 mm/s. For simplicity, tension changes during release phase following stretch have not been shown. Note that tension during stretch reaches a maximum value at the peak of the twitch in A but during the rising phase of the twitch in B.
AND
FAST
MUSCLES
255
50 ms
1ON
50 ms FIG. 6. Tension changes in SOL during stretches (5 mm amplitude at 200 mm/s) applied at different times during a twitch, A, and tetanic contraction, B (stimulus rate, 100 pulses/s). Tension changes during the release phase of movement are not shown.
larger distances (4 mm in walking ( 19) and up to 15 mm during galloping ( 1 1)), and the limit of the short-range stiffness is exceeded at about 1 mm. Figure 5B shows the effect of stretching the muscle through 5 mm at various times during a muscle twitch. During the rising phase of the twitch, the stiffness of the muscle is maintained throughout the stretch. However, at the peak and during the falling phase of the twitch, stiffness decreases considerably after the short-range stiffness region has been exceeded, as seen by a sudden change in slope of the tension record. The stretch rate used to obtain these results was quite rapid (500 mm/s) and such rates are only likely to be approached during galloping ( 11). Figure 6 shows the effect of a stretch at a rate corresponding more closely to that during running in the cat. The same general features are seen, with a decrease in stiffness that is marked by a corner only at the peak and during the falling phase of the twitch. Similar measurements have been made using tetanic contractions (Fig. 6B) and only during the rising phase of the tetanus is muscle stiffness maintained up- to the end of the stretch.
256
B. WALMSLEY
DISCUSSION
Apart from their motor-unit composition (4, 5), MG and SOL differ in a number of respects. The muscle fibers in MG are much shorter, and on average the sarcomere number per muscle fiber is only 60% of that for SOL (RESULTS, Table 1). The cy, value for MG is 60% of the cy,value for SOL, and this difference is therefore entirely accounted for by the difference in sarcomere number per muscle fiber. At low levels of isometric tension the short-range stiffness is dominated by muscle properties, as represented by the value of cy,. This in turn depends on the number of sarcomeres in series. Consequently, at low tensions, MG will have 60% of the compliance of SOL, since the stretch is distributed over a smaller number of sarcomeres. At high tensions the tendon will take up more of the movement and there will be less difference in short-range stiffness between the two muscles. The values of tendon compliance for MG and SOL are approximately the same. Because the MG tendon is much longer than the SOL tendon, this means that the MG tendon has much less compliance per unit length. The most obvious explanation for this is that MG contains many more muscle fibers (4, 7) whose tendons join to form a much thicker, and hence less compliant, free tendon. (The calculated C, value represents the total passive in-series compliance, which includes the free tendon, the intramuscular tendon whose length may be an appreciable fraction of the total tendon length, and other less significant sources of compliance such as the Z lines in the muscle fibers (15). The relative contribution of each of these elements to the CT value is unknown, although experiments in which the tendon has been shortened (15, 16) suggest that the free tendon contributes a major proportion.) Which muscle properties are important during posture? Measurements of tension during standing in cats indicate that SOL contributes a major fraction of the force when compared with MG (19). Both muscles are active over a wide range of lengths, from about 12 mm short of optimal length, L,, to several millimeters greater than L, (11). SOL is better suited to produce the required forces for sev-
AND
U. PROSKE
era1 reasons. First, the longer muscle fibers give SOL a flatter length-tension curve and enable it to maintain tension over more of the observed range of muscle lengths (see also Ref. 14). Second, the motor units of SOL are highly fatigue resistant, allowing them to maintain tension for long periods. Although MG contains approximately 25% type S motor units, quadrupedal standing involves much more force than these could provide (about 4 N in an average muscle), and would require recruitment of a large portion of the FR motor-unit population. This would be disadvantageous as fast-twitch motor units require more energy per unit isometric tension than slow-twitch motor units ( 10, 20). During standing, the position of the limb and, hence, maintenance of constant muscle length, is important. The short-range stiffness of muscle would help to oppose length changes imposed by either external or internal perturbations (e.g., small fluctuations in muscle activity). The fluctuations in muscle length that have been observed to occur during quiet standing are well within the limits of short-range stiffness of both muscles (personal observation). Results obtained from a previous study (19) on cats of similar weight indicate that on average, during standing, SOL produces 12 N and MG produces 5 N of force. From the values of cy, and CT obtained in the RESULTS (Table 2) we can calculate the active &-,/P) and passive (C-r) compliances for the two muscles at these tensions. The passive and active components are equal (0.05 mm/N) for SOL and differ slightly for MG (C, = 0.06 mm/N, a,/P = 0.08 mm/N). This means that in both muscles stretch will cause roughly equal elongation in muscle fibers and in the tendon. The importance of the compliance of the tendon under these conditions is that during an unexpected disturbance it is able to take up half of any imposed displacement, allowing extension of muscle fibers to remain within the limits of the short-range stiffness. Locomotion One of the surprising results to come from previous measurements of tension in soleus during locomotion was that it continued to develop more tension than MG up to the fastest run (19). This was unexpected since
STIFFNESS
OF SLOW
SOL had generally been regarded as a postural muscle. It was proposed at the time that the large, rapidly rising forces recorded in SOL during fast running were achieved by the muscle developing sufficient stiffness. During walking and running, MG and SOL become active about 50 ms before the foot makes contact with the ground (9). On contact, both muscles are transiently stretched (the yield phase) and then shorten. The stretch occurs at a time when muscle activity is at its peak. The muscle is therefore able to meet the stretch with a high value of stiffness to produce a rapid rise in tension. It is of interest that the observed rise and fall in SOL tension is several times faster than that seen during an isometric twitch (Fig. 3 of Ref. 19). Thus, measurements of isometric contraction time may give little or no clue about the tension time course during locomotion. If movements as large as occur during locomotion are used to measure muscle stiffness, two important observations are made. First, total stiffness reaches its largest value not at peak tension but during the rising phase of the contraction, at a time that agrees well with the period in locomotion of maximum activity of the muscle. Second, during such movements, tension changes are no longer dominated by the short-range stiffness but by the subsequent rise in tension. As the short-range stiffness is exceeded, cross bridges between actin and myosin filaments are mechanically broken (rather than enzymatically), reattach to new sites (as these become available on the actin), and are then extended until eventually they too are broken. Thus the tension change beyond the limits of the short-range stiffness is largely determined by rates of formation and breakdown of cross bridges, which had previously been broken by stretch. The observation that total stiffness is largest during the rising phase of a contraction can be most easily explained by assuming that at this time the rate of cross-bridge formation far exceeds that for breakdown. Consequently, any bridges broken by stretch very quickly reform. There is, therefore, no drop in tension at the limit of the short-range stiffness, and tension continues to rise steeply during the subsequent movement. The result is that the tension reached at the end of the stretch
AND
FAST
MUSCLES
257
is much higher than if the stretch had been applied at the peak of the contraction where cross-bridge turnover has begun to slow down. Jumping The importance of the role played by MG in locomotion emerged when tension changes were recorded during jumping. Peak force during the launching phase can be as much as 80 N for MG compared with only about 12 N for SOL (19). From our stiffness measurements we estimate that at these levels of force the MG tendon is stretched about 5 mm while the SOL tendon is stretched only 0.6 mm. After reaching peak force, both muscles rapidly shorten until the animal leaves the ground. The drop in force during the shortening phase is much steeper for SOL. Apart from the obvious explanation that an intrinsically slow muscle like SOL is less able to maintain tension during rapid shortening than a fast muscle (2), it must be remembered that MG spans two joints, the knee and ankle, while SOL acts only at the ankle. During takeoff, extension of the ankle is matched by extension of the knee, which means that MG is shortened at a lower rate than SOL. Probably the most important factor is that most of the shortening in MG occurs in the tendon rather than the muscle fibers. Consequently, the amount and speed of shortening of muscle fibers will be less. These, by virtue of their length-tension and force-velocity characteristics, are therefore able to maintain more tension. This demonstrates another important aspect of tendon compliance, which is the storage of elastic energy (see also Refs. 1, 8, and 16). The elastic energy in the stretched tendon is instantly available to produce force and particularly assists movements in which the muscle undergoes rapid shortening. Design of muscle In Fig. 7 we have tried to summarize the various factors in muscle design, together with their advantages and disadvantages. One point we have intentionally omitted is the number of joints over which a muscle acts. If a muscle is restricted to one joint only, it will be able to provide accurate control of joint angle but may be faced with large length changes during locomotion. The imposed length changes may be less if the
258
B. WALMSLEY
AND U. PROSKE Fatigue resistant; smooth, finely graded contractions; cannot maintain tension during rapid shortening; low energy consumption
Fiber Type Fatigable (FF), fatigue resistant (FR); large rapidly rising forces; able to maintain tension during rapid shortening; energy costly Steep length- tension relation; space saving-greater packing density-more force per unit volume; short-range stiffness limited to small extensions; low shortening speed; energy saving
I
Broad length-tension relation; take up more space- less force per unit volume; short-range stiffness operates over large distances; greater shortening speed; energy costly Transmit more of imposed stretch to muscle; steep length-tension relation and poor forcevelocity characteristics; allows rapid, precisely controlled movements with little delay
Tendon Compliance Slows contraction and delays its onset; smooths out unwanted fluctuations in tension; allows short-range stiffness to act over larger displacements; storage of elastic energy
High
FIG.
7. Design of muscle.
muscle spans several joints but this is achieved at the expense of independence of action. While most of the factors included in Fig. 7 have been stated previously in the paper, some comment is necessary. If a muscle fiber is short, it will develop the same tension as a long fiber but will consume less energy. It will have a lower maximal shortening speed and can be packed in large numbers into the muscle volume. A consequence of the high packing density is that the muscle will be
able to develop large forces. During imposed large-amplitude movements, such a muscle will not be able to maintain its stiffness unless it is attached to a long, compliant tendon, capable of absorbing most of the movement. An advantage of a large number of sarcomeres is that it gives the muscle a high shortening velocity. If the muscle-tendon combination is so designed that it behaves as a simple spring, whether this is achieved by having long muscle fibers or a compliant tendon, the opportunity arises for elastic
STIFFNESS
OF
SLOW
storage of energy. There must, however, be a trade-off between the advantages of elastic storage, the influence of tendon compliance on the speed and accuracy of movements, and the susceptibility of the system to involuntary oscillation.
AND
FAST
MUSCLES
259
Financial assistance was provided by the Australian Research Grants Committee Grant Dl7915101 and from a grant to Professor R. Porter by the National Health and Medical Research Council of Australia.
~
Present address rology Unit, The search, Canberra,
of B. Walmsley: Experimental John Curtin School of Medical ACT, 2601, Australia.
NeuRe-
ACKNOWLEDGMENTS
We thank Dr. D. J. Tracey the manuscript.
for helpful
comments
on
Received 13 August March 1981.
1980; accepted
in final
form
23
REFERENCES R. McN. AND BENNET-CLARK, H. C. Storage of elastic strain energy in muscle and other tissues. Nature London 265: 114-l 17, 1977. BULLER, A. J. The physiology of skeletal muscle. In: Neurophysiology I, edited by C. C. Hunt. Baltimore: Univ. Park, 1975, vol. 3. (Int. Rev. Physiol. Ser .) BULLER, A. J. The mechanisms of postural control in the limbs and trunk. In: jMastication, edited by D. J. Anderson and B. Matthews. Bristol: Wright, 1976, p. 66-71. BURKE, R. E., LEVINE, D. N., SALCMAN, M., AND TSAIRIS, P. Motor units in cat soleus muscle: physiological, histochemical and morphological characteristics. J. Physiol. London 238: 503-5 14, 1974. BURKE, R. E., LEVINE, D. N., TSAIRIS, P., AND ZAJAC, F. E. Physiological types and histochemical profiles in motor units of the cat gastrocnemius. J. Physiol. London 234: 723-748, 1973. BURKE, R. E., STRICK, P. L., KANDA, K., KIM, C. C., AND WALMSLEY, B. Anatomy of medial gastrocnemius and soleus motor nuclei in cat spinal cord. J. Neurophysiol. 40: 667-680, 1977. BURKE, R. E. AND TSAIRIS, P. Anatomy and innervation ratios in motor units of cat gastrocnemius. J. Physiol. London 234: 749-765, 1973. CAVAGNA, G. A., HEGLUND, N. C., ANDTAYLOR, C. R. Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am. J. Physiol. 233 (Regulatory Integrative Comp. Physiol. 3): R243-R261, 1977. ENGBERG, I. AND LUNDBERG, A. An electromyographic analysis of muscular activity in the hindlimb of the cat during unrestrained locomotion. Acta Physiol. Stand. 75: 614-630, 1969. GIBBS, C. L. AND GIBSON, W. R. Energy production of rat soleus muscle. Am. J. Physiol. 223: 864871, 1972. ALEXANDER,
11. GOSLOW, G. E., REINKING, R. M., AND STUART, D. G. Physiological extent, range and rate of muscle stretch for soleus, medial gastrocnemius and tibialis anterior in the cat. Pfluegers Arch. 341: 77-86, 1973. 12. GREGORY, J. E., LUFF, A., MORC;AN, D. L., AND PROSKE, U. The stiffness of amphibian slow and twitch muscle during high speed stretches. Pfluegers Arch. 375: 207-211, 1978. 13. GRILLNER, S. The role of muscle stiffness in meeting the changing postural and locomotor requirements for force development by the ankle extensors. Acta Physiol. Stand. 86: 92- 108, 1972. 14. HENNEMAN, E. AND OLSON, C. B. Relations between structure and function in the design of skeletal muscles. J. Neurophysiol. 28: 58 l-598, 1965. 15. MORGAN, D. L. Separation of active and passive components of short-range stiffness of muscle. Am. J. Physiol. 232 (Cell Physiol. 1): C45-C49, 1977. 16. MORGAN, D. L., PROSKE, U., AND WARREN, D. Measurements of muscle stiffness and the mechanism of elastic storage of energy in hopping kangaroos. J. Physiol. London 282: 253-261, 1978. 17. PROSKE, U. AND RACK, P. M. H. Short-range stiffness of slow fibers and twitch fibers in reptilian muscle. Am. J. Physiol. 23 1: 449453, 1976. 18. RACK, P. M. H. AND WESTBURY, D. R. The shortrange stiffness of active mammalian muscle and its effect on mechanical properties. J. Physiol. London 240: 33 l-350, 1974. 19. WALMSLEY, B., HODGSON, J. A., AND BURKE, R. E. Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. J. Neurophysiol. 41: 1203-l 216, 1978. 20. WENDT, I. R. AND GIBBS, C. L. Energy production of rat extensor digitorum longus muscle. Am. J. Physiol. 224: 1081-1086, 1973.
