J. Phyeiol. (1978), 282, pp. 253-261 253 With 5 text-figure8 Printed in Great Britain MEASUREMENTS OF MUSCLE STIFFNESS AND THE MECHANISM OF ELASTIC STORAGE OF ENERGY IN HOPPING KANGAROOS By D. L. MORGAN*, U. PROSKE AND DIANNE WARREN From the Departments of Electrical Engineering and Physiology, Monash University, Clayton, Victoria, Australia (Received 14 December 1977) SUMMARY 1. A kangaroo hopping above a certain speed appears to consume less oxygen than a quadrupedal mammal, of similar weight, running at the same speed (Dawson & Taylor, 1973). This is thought to be achieved by storage of elastic energy in tendons and ligaments. 2. Energy can be stored in a tendon by stretching it, but only if the muscle fibres in series with it are stiff enough to resist most of the length change. We have measured length and tension changes in the contracting gastrocnemius muscle of the wallaby Thylogale during rapid, controlled stretches, and from this determined the amount of movement in muscle fibres and tendon (method of Morgan, 1977). 3. When the muscle was developing close to its maximum isometric tension, up to eight times as much movement occurred in the tendon as in the muscle fibres. This is made possible by the wallaby having a long and compliant tendon. 4. Measurement of work absorption by the muscle with a full length of free tendon and when the tendon had been shortened, showed that with the shortened tendon a larger proportion of movement occurred in the muscle fibres, producing a steep rise in work absorption by the muscle and a consequent increase in energy loss. INTRODUCTION It has been suggested that above a certain speed the kangaroo's hop is a more efficient mode of locomotion, in terms of the energy cost, than that of a quadrupedal mammal running at the same speed (Dawson & Taylor, 1973). This was thought to be achieved by storage of elastic energy in tendons and ligaments. Thus the energy required to propel the animal up from the ground would be provided, in part, by elastic recoil of tendons, such as the Achilles tendon, which had been stretched on landing from the previous hop. Since tendons provide the means of attachment of muscles to skeletal structures, any mechanism based on elastic recoil must include consideration of the elastic properties of muscle fibres as well as of tendon. In a discussion of the proportion of elastic energy stored in muscle and tendon, Alexander & Bennet-Clark (1977) calculated the elastic strain energy of ankle and knee extensor muscles and of the * Present address: Department of Muscle Research, Boston Biomedical Research Institute, 2 Staniford St, Boston, Massachusetts, 2114, U.S.A.
254 D. L. MORGAN, U. PROSKE AND D. WARREN Achilles tendon in a 1 kg Bennett's wallaby and concluded that the tendon could store up to ten times as much energy as the muscle. Their calculations were based on known values of the elasticity of frog semitendinosus (Huxley & Simmons, 1971), and cat soleus muscles (Rack & Westbury, 1974) as well as force platform records and cinematography ofthe wallaby hopping on a treadmill (Alexander & Vernon, 1975). In view of the intuitively appealing notion of a kangaroo bouncing up and down like a rubber ball (cf. Fenn, 193; see also Cavagna & Kaneko, 1977), it seemed worthwhile to attempt to determine directly whether tendons and muscles involved in hopping did in fact behave as elastic structures capable of energy storage over the range they were likely to be stretched during each hop. We have used the medial gastrocnemius muscle of the wallaby Thylogale and have measured, using the method of Morgan (1977), the amounts of movement in tendon and muscle fibres during rapid controlled stretches. It was found that most of an imposed stretch was taken up by the tendon which is thereby able to act as a store of elastic energy. METHODS The animal chosen for experiment because of its size and availability was the red-bellied Pademelon Thylogale billiardieri. Animals were anaesthetized by means of an initial dose, 1 mg/kg wt., of Ketalar (ketamine hydrochloride,parke-davis) followed by inhalation of a mixture of halothane gas (2-4%) and oxygen. The gas mixture was administered at a constant flow rate of 2 ml./min. The muscle selected for study was the medial head of gastrocnemius, which together with other muscles of the triceps sure group is involved in jumping (Alexander & Vernon, 1975). The muscle and tendon were dissected free of surrounding tissue without interference with the muscle's blood supply. The nerve to gastrocnemius was dissected for as long a length as possible and then subdivided into three or four portions. Each portion was stimulated in turn, using the method of distributed stimulation (Rack & Westbury, 1969) to help to achieve smooth tetanic contractions at low levels of force. In spite of this the tension developed during a fused tetanic contraction was often more than the stretching device could withstand. In order to keep the tension within a manageable range (not more than 7N), yet allowing use of a high enough rate of stimulation to obtain a fused contraction, it was necessary to partially paralyze the muscle by I.v. infusion of doses of 5-1 mg Flaxedil (gallamine triethiodide). Previous experiments (Morgan, 1977) had shown that reliable measurements of muscle stiffness can be made using partially paralysed muscles. The muscle's tendon of insertion was exposed right up to the point of attachment to the calcanbum and then freed, with a fragment of bone left attached. A T-shaped bar, was pulled through a slit in the tendon close to the bone and was then screwed into the shaft of the stretching device. By this means the bar pulled on the tendon indirectly via the bone thereby ensuring that no slippage could occur during stretches. In a number of experiments the length of 'free' tendon in series with the muscle was reduced by clamping the tendon at the point where it emerged from the muscle. Here the tendon is arranged as a broad, thin sheet and can be firmly gripped by means of a clamp with finely serrated jaws. The stretching device consisted of a feed-back controlled electromagnetic actuator, which when operating in the controlled position mode had a stiffness in excess of 16 N/m. Tension was measured using a crystal load cell (Kistler model 912) supplemented by a signal derived from the actuator coil current. This system took advantage of the very stiff, fatigue-resistant load cell while eliminating drift usually associated with charge output devices. Muscle length changes were given by the armature position signal, derived from a Shaevitz LVDT transducer (Model 5 MHR) with a 2 khz carrier and synchronous demodulation. Throughout the experiment the animal's body temperature was maintained at 35 'C by means of a servo controlled electric blanket. Skin flaps adjacent to the muscle were lifted tip to form a
ELASTIC STORAGE OF ENERGY IN KANGAROOS pool of paraffin which covered both the muscle and nerve. No attempt was made to maintain the paraffin at body temperature. After an initial period of equilibration the temperature of the pool dropped to 3-33 C and then remained within this range for the remainder of the experiment. RESULTS When actively contracting muscle is stretched, the tension changes recorded during the stretch consist of an initial steep rise in tension, the short-range stiffness (Rack & Westbury, 1974; Flitney & Hirst, 1975) followed by a more gradual change. The short-range stiffness is thought to represent deformation of cross-bridges between actin and myosin filaments of the myofibrils. We have measured the short-range stiffness at a number of levels oftension and derived from this the movement attributable to deformation of cross-bridges plus stretch of the tendon. 255 ] 5 N 4 msec Fig. 1. Tension changes recorded in a partially curarized medial gastrocnemius muscle of the wallaby Thylogale billiardieri when a triangular stretch-release sequence (4 mm amplitude, stretch rate 2 mm/sec) is imposed during the contraction. Tension is shown on the upper trace and length on the lower trace. The bar below the length trace represents the period ofnerve stimulation (distributed stimulation at 3/sec for.5 sec). The experiment consisted of forcibly stretching the contracting muscle and recording length and tension changes during the movement. The movement used was a triangular stretch-release sequence (Fig. 1 lower trace). A typical recording of the tension changes observed in a partially paralyzed preparation is shown in the upper trace of Fig. 1. During the period of stimulation (duration of bar at the bottom of the figure) tension initially rose, and then fell to a more or less steady level depending on the depth of the neuromuscular block. The stretch was applied as soon as a steady tension had been reached. The muscle length at the onset of stretch corresponded to the optimum for a twitch contraction. Although the short-range stiffness is visible in the tension trace of Fig. 1 it becomes much clearer if tension is displayed, not with respect to time but as a function of length. The length-tension figures obtained at several different levels of isometric tension are shown in Fig. 2. The loop at the bottom of the Figure (a), represents the length-tension figure of the unstimulated muscle, showing that very little of the tension changes observed during stretch of active muscle can be attributed to passive properties.
256 D. L. MORGAN, U. PROSKE AND D. WARREN The value of short-range stiffness was determined from the slope of the initial steep tension rise during the stretch. The amplitude of movement chosen was typically about twice that necessary to exceed the limit of the short-range stiffness. The rate of stretch was found not to be important provided the same rate was used throughout a series and provided it was sufficiently rapid (1-2 mm/sec) to show both a clearly identifiable 'corner' in the tension trace and to give stiffness values independent of stretch rate. The recordings in Fig. 2 of length-tension figures at three different levels of isometric tension show that while the limit of the short-range stiffness represented by the 'corner' in the tension trace occurs at much the same point, at the higher tensions the slope of the initial portion of the tension change becomes steeper, that is, the short-range stiffness is greater. 4 N 2 mm Fig. 2. Tension changes as a function of stretch at three different levels of isometric tension. a, unstimulated muscle; b, c, d, progressively higher levels of isometric tension achieved by allowing the muscle to partially recover following curarization. The arrow below each record indicates the 'corner' at the limit of the short-range stiffness. The short-range stiffness measured in these experiments arises from the muscle itself and the tendon in series. Separate stiffness values for muscle and tendon can be obtained by varying the isometric tension and by assuming that the tendon stiffness is constant but that the stiffness of the muscle increases in proportion to tension because more cross-bridges are attached or more fibres are activated (Morgan, 1977). Following Huxley & Simmons (1971), muscle stiffness is equated with that due to the cross-bridges. In practice it is more convenient to use compliance rather than stiffness; if co is the compliance arising from the cross-bridges and ct that of the tendon, then the measured short-range compliance is co + ct. The total and cross-bridge compliances can further be considered in terms of the movement (a) required to reduce the tension (P) to zero, i.e., a = cp and co = cop. Hence a= oo + ctp)
ELASTIC STORAGE OF ENERGY IN KANGAROOS 257 and a plot of a against P should yield a straight line with slope ct and intercept on the a axis of ao. a is defined as the length change which if applied to the compliance ascribable to cross-bridges plus tendon, would reduce the tension to zero. a has therefore units of length. Implicit in the a method is the assumption that the tendon compliance is linear and not exponential over the range of tensions used for measurement. This is supported by the observation that identical ao values are obtained with the full tendon and with the length of tendon reduced by 57% (see below). Furthermore, measurements of the stiffness of isolated segments of tendon showed it to be linear over a wide range of forces. 4 S *Y * @. E 2 1 5 % PO 2 4 6 8 Tension (N) Fig. 3. A plot from a wallaby weighing 6-8 kg of the amount of movement required to reduce the tension to zero if the short-range stiffness continued to act, 'a' (which has its units in millimeters), against isometric tension for a range of different tensions. The regression line drawn through the data had a slope of -4 and was significant (P < -1). The level of tension representing 5% of the maximum isometric tension has been indicated on the abscissa. The dashed line represents the plot of a against per cent maximum tension for a cat soleus muscle (redrawn from Morgan, 1977). The per cent Po value applies to both muscles, the Newton scale only to the wallaby. An example of an a plot is shown in Fig. 3. The values were obtained from a wallaby weighing 6-8 kgm and whose medial gastrocnemius developed (before curarization) a peak tension of 135N. The regression line drawn through the points gives an a value of 1 mm and tendon compliance ct of -4 mm/n. 9 P HY 282
258 D. L. MORGAN, U. PROSKE AND D. WARREN Included in Fig. 3 is the a diagram, appropriately scaled, of a cat soleus muscle (dashed line; data taken from Morgan, 1977). Comparing the two plots shows that both muscles have the same ao value, i.e. the same amount of movement occurs in the cross-bridges but at any one level of tension the amount of movement in the tendon, am-pa, is far greater for the wallaby. A comparison of ao values assumes that the number of sarcomeres, over which the movement is distributed, is the same for both cat and wallaby muscles. Although sarcomere counts were not made, muscle fibre lengths were estimated from muscles fixed at slack length (corresponding to an ankle joint angle of approximately 15 ). The average length, 18 7 + 2O mm is close to the value reported for cat soleus by Rack & Westbury (1969). In three experiments using wallabies (weight 3-3-6-8 kg) in which a diagrams were plotted, the ratio of movement in tendon to that in muscle, extrapolated to P, the maximum isometric tension, gave values ranging from 5 to 8. Thus up to eight times as much movement occurred in the tendon as in the cross-bridges. In a fourth animal which was much younger than the other three (weight 2-2 kgm) ao was again 1 mm but the value of ct was lower, 3 mm/n. This gave a ratio at P of 3-1. Thus in the young animal (which had muscle fibres as long as in adults) although cross-bridge movement was the same as in adults, the tendon appeared to be less compliant. If the muscle and tendon were behaving simply as two springs in series, then any work done in stretching them should re-emerge on shortening. This would produce a completely 'closed' length-tension figure with length and tension changes during release superimposing exactly on those during stretch. If the movement of muscle fibres is restricted to within the range over which the short-range stiffness acts then the muscle does behave much like a stiff spring. However as soon as the short-range length is exceeded, cross-bridges will be broken and the work absorption by the muscle will rise steeply, the amount absorbed being represented by the area contained within the length-tension figure (Rack & Westbury, 1974). We have measured the effect of changing the length of free tendon on the amount of work absorption by the muscle. In Fig. 4 are shown the superimposed lengthtension figures for a series of movements, all beginning from about the same level of isometric tension, but with different amplitudes of movement. The records in A were obtained with the full length of free tendon (79 mm) while in B the tendon had been shortened by 74 mm. In this muscle, muscle fibres lay in series with a total length of 13 mm of tendon, of which 79 mm were 'free'. From stiffness measurements using the shortened tendon a value of ct was obtained which corresponded closely to that predicted for a tendon shortened by 74 mm (57 %). For both sets of recordings, as the amplitude of the movements was increased the area contained within each length-tension figure became progressively larger. However, since the shortened tendon is much stiffer (as was confirmed from the value obtained for ct) here a larger proportion of a movement will occur in the muscle fibres. This can be clearly seen in Fig. 4. In A the short-range stiffness persists for movements up to about 2 mm whereas in B it is little more than 1 mm. Furthermore, the change in slope from short-range stiffness to later compliance is much more sudden in B. The area contained within each loop, the work absorption, has been expressed as a proportion of the work done on the muscle (the area under a figure during stretch)
ELASTIC STORAGE OF ENERGY IN KANGAROOS 259 to give the percent energy loss. A plot of % energy loss against movement amplitude is shown in Fig. 5. This again emphasizes the larger loss with the shortened tendon. Thus for a 2 mm movement the loss with the full tendon is about 25 %, but nearly 5 % with the shortened tendon. A ~~ 7,~ '7, B F>, 2 N ments~~~~~~~~~ Vmm Fig. 4. Length-tension figures at a number of different amplitudes with the full tendon (A) and a shortened tendon (B). In A are shown the length-tension figures for movements of amplitudes -5-5 mm, all commencing from an initial isometric tension of 35 N. In B the tendon was shortened by 74 mm and a series of movements repeated (amplitude -5-3 mm; initial tension 38 N). 9-2
26 D. L. MORGAN, U. PROSKE AND D. WARREN 6 x 4 ) C 2 x X Shortened tendon Full tendon O 1 2 3 4 5 Movement amplitude (mm) Fig. 5. The work absorbed by the muscle, represented by the area contained within each length-tension figure of Fig. 4 has been expressed as a proportion of the work done on the muscle (the total area under each figure during stretch), and called the per cent energy loss. The energy loss is plotted against movement amplitude for the full and shortened tendons. Note that the levels of tension represented here are probably much lower than would be expected during hopping and that at higher levels of tension larger movements with low energy loss would be possible. DISCUSSION The principal aim in the experiments described here was to confirm, by direct measurement, the predictions of Alexander & Bennet-Clark (1977), and thereby provide a firm experimental basis for the elastic recoil hypothesis. Our results show that in the wallaby, stretch of the maximally contracting muscle produces eight times as much movement in the tendon as in the muscle fibres. For cat soleus, on the other hand, stretch displaces muscle fibres and tendon by about the same amount (Morgan, 1977). Furthermore, at maximum tetanic tension the percentage extension of the tendon was twice as great for the wallaby, 4 % (cf. Alexander & Vernon, 1975), as for the cat (2 %). Thus the wallaby tendon is both longer (13 mm compared with 5 mm) and more compliant. Assuming similar values for Young's modulus of tendon in the two animals, the greater compliance of the wallaby tendon means that compared with cat soleus tendon, it has a proportionately smaller cross-sectional area for the size of the muscle which it supports. Considered in terms of precision and speed of limb movement, it is, of course, disadvantageous to have muscles attached to skeletal structures by long, compliant tendons. The onset of a movement is likely to be slow and the subsequent trajectory less accurately controlled. Analysis of limb movements of a wallaby hopping on a treadmill, using high-speed
ELASTIC STORAGE OF ENERGY IN KANGAROOS 261 cinematography (D. Warren, unpublished observations), shows that the ankle joint rotates through about half of its range during hopping and this represents stretch of ankle extensor muscles by 1-15 mm. From the a diagram (Fig. 3), cross-bridge movement without forcible detachment is limited during stretch to only 1 mm, so most of the movement would have to be taken up by the tendon. It was estimated that when the gastrocnemius muscle develops near maximal tension, up to eight times as much movement would occur in the tendon; yet this still gives only a total of 9 mm. However there is not a precise point, at the limit of the short-range stiffness, at which suddenly all cross-bridges are detached with a consequent steep increase in energy loss (otherwise when the short-range elastic limit is exceeded, the tension would fall to zero, see Rack & Westbury, 1974). The forcible detachment of crossbridges is a distributed process and inspection of Fig. 5 for example, shows, that at 35 N of force muscle and tendon can be stretched through 3 mm with a resulting energy loss of only about 4 %. If during hopping the level of tension were as much as four times as high then a similar loss would be incurred by 12 mm of movement. The question that remains is to what extent elastic storage actually helps to conserve energy during hopping. The observations of Dawson & Taylor (1973) suggest that at low speeds hopping is a less efficient mode of locomotion than running in quadrupeds. The advantage of hopping, in terms of the energy cost, emerges when the kangaroo is travelling at speed, and because of the low extra cost, it is able to maintain such speeds for long periods. Financial assistance was provided by a grant from the Australian Research Grants Commission (grant no. 1518). The authors would like to thank Dr C. C. Hunt for help with the manuscript. REFERENCES ALEXANDER, R. McN. & BENNET-CLARK, H. C. (1977). Storage of elastic strain energy in muscle and other tissue. Nature, Lend. 265, 114-117. A=EANDEmR, R.McN. & VE:RNON, A. (1975). The mechanics of hopping by kangaroos (Macropodidae). J. Zool. 177, 265-33. CAVAGNA, G. A. & KANEKO, M. (1977). Mechanical work and efficiency in level walking and running. J. Phy8iol. 268, 467-481. DAwsoN, T. J. & TAYLOR, C. R. (1973). Energetics cost of locomotion in kangaroos. Nature, Lond. 246, 313-314. FENN, W.. (193). Work against gravity and work due to velocity changes in running. Am. J. Physiol. 93, 433-462. FLITNEY, F. W. & HIRST, D. G. (1975). Rapid 'give' of sarcomeres and tension changes during servo-controlled stretches applied to contracting frog's muscle. J. Phyal. 246, 68-69P. HuLEy, A. F. & SIMMONS, R. M. (1971). Mechanical properties of the cross-bridges of frog striated muscle. J. Phyaiol. 218, 59-6P. MORGAN, D. L. (1977). Separation of active and passive components of short-range stiffness of muscle. Am. J. Phyaiol. 232, 45-49. RACK, P. M. H. & WESTBURY, D. R. (1969). The effects of length and stimulus rate on tension in the isometric cat soleus muscle. J. Phyaiol. 24, 443-46. RACK, P. M. H. & WEsTBmuy, D. R. (1974). The short-range stiffness of active mammalian muscle and its effects on mechanical properties. J. Phyajol. 24, 331-35.