(Cavagna, Dusman & Margaria, 1968). The amount of energy thus stored

Transcription

1 J. Phy8iol. (1970), 206, pp With 3 text-ftgurem Printed in Great Britain THE SERIES ELASTIC COMPONENT OF FROG GASTROCNEMIUS By GIOVANNI A. CAVAGNA From the Istituto di Fisiologia Umana, Universita di Milano, Milano 20123, Italy (Received 14 April 1969) SUMMARY 1. The force-extension curve of the series elastic elements of the frog gastrocnemius has been determined up to the force attained during stretching by means of the isotonic quick-release method, modified in order to allow the release of the muscle immediately after stretching. 2. The series compliance decreases progressively up to a stress value of about 2 kg/cm2 and then it remains constant up to the maximal values of stress attained (about 10 kg/cm2). 3. The lengthening of the series elastic elements when the stress rises to its full isometric value (POIOIM = 5-2 kg/cm2) is about 3 % of the muscle resting length, lo. The Young's modulus in the linear part of the diagram is 294 kg/cm2. 4. The elastic energy stored up to Po is on average 55 g cm/g; an additional amount of 63 g cm/g is stored during stretching the contracted muscle. INTRODUCTION Elastic energy is stored in the stretched series elastic elements when an active muscle is forcibly stretched by a force greater than the isometric value: much of this energy appears to be utilized as external work when active shortening is allowed to take place immediately after stretching (Cavagna, Dusman & Margaria, 1968). The amount of energy thus stored in the elastic elements needs to be known, together with the chemical break-down and heat production, to reach a complete understanding of the energy transformations taking place in the stretched muscle. The stress-strain curves described in the literature, however, are limited to the maximum isometric force, PO, and no data are available to assess whether the structures under strain exhibit a linear stress-strain relationship at greater forces, or whether they become progressively stiffer, as do most biological materials.

2 258 GIOVANNI A. CA VAGNA In this paper the stress-strain curve of the series elastic elements in the frog gastrocnemius muscle has been determined up to tensions greater than PO. This muscle was chosen for the present study because its anatomical characteristics suggest that it may be a muscle in which elasticity plays a relatively important role. METHODS The load-extension curve was determined up to P0 by means of the isotonic quickrelease technique (Wilkie, 1956) and up to force values greater than P0 by a modification of this method allowing release after stretching. The isotonic lever had a lever ratio of 20: 1, and an equivalent mass of 0 5 g at the point of attachment of the muscle. The load (maximum value about 20 kg) was attached to the lever through a spring in order to reduce its effective inertia. The movement of the lever was recorded by means of a photocell. The force developed by the muscle was measured by means of a transducer built with resistance strain-gauges as described by Wilkie (1949): the transducer was tested up to 1600 g and found to give a linear response within a random error less than 3 %; its time constant was about 1-5 msec. The femur was tightly attached to the transducer and the Achilles tendon was attached to the lever directly in order to reduce the compliance of the connexions: a rather thick silk thread was tied around the tendon at the level where the tendon is attached to the bone, the tendon was then inserted through a hollow at the tip of the lever, leaving the knot above the lever, so that the compliance of only the part of the tendon which usually works in the body was measured. The thread prevented lesion of the tendon by the edge of the lever and, by this connexion, lengthening of the silk thread was avoided. The compliance of the transducer and of the lever, determined in a blank experiment, was mm/g: the total recoil recorded when the force fell abruptly from isometric to isotonic (Fig. 1) was corrected by this factor to obtain the shortening of the series elastic elements of muscle. The frogs (Rana esculenta) were in good condition: their gastrocnemii had an average solid content of about 20 % and developed an average stress, at the length (taken as lo) where the resting force was 5-20 g, of P0ol/M = x 257/0-463 = *15 kg/cm2 (mean and S.E. of mean; n = 20). Stimulation was carried out through the sciatic nerve: stimuli were above maximal. The muscles were immerged in oxygenated Ringer solution: since the temperature of the saline was kept at 0-1 C, a fused tetanus was obtained with 5-10 stimuli/sec. The muscles were released from lo. After a preliminary loadextension curve of the series elastic elements was constructed up to P0, the electromagnetic stop that is used in the isotonic release technique (Wilkie, 1956) was removed and replaced by the device illustrated in Fig. 2. A cam, W, can be turned by hand by means of the bar B, thus pushing the vertical bar V,which supports the lever, upwards against a powerful spring: the contracted muscle is thus forcibly stretched (about 1 mm), and the force reaches a value P' greater than P0. Eventually the discontinuity in the profile of the cam is reached, and the vertical bar is moved suddenly downwards by the recoil of the spring. This action releases the lever, and the force on the muscle falls to the isotonic load chosen. Three records are illustrated in the bottom of Fig. 1: these allow the determination of the changes in length of the series elastic elements for changes of force in a range greater than P0. These changes in length were added to the previously determined extension of the series elastic elements, at the same isotonic load, to obtain the total extension at the force P' > P0. Also in this part of the experiment the muscles were released from the same length near tolo.

3 SERIES ELASTICITY OF GASTROCNEMIUS m-4:~~~~~~~~~~~~~~~~~~~~~~~......t I: 11000l 27,. 24 _. W,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ l o,- r.-. W t 1 -l.,!.:: S!=_ -I T W t Ml-- l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ l h ii E I.._._ 1 :: i.. i _.. _ ~~~~~~~~~~~~~~~~~~~.. Fig. 1. Experimental re swing on te l th. early lengh.cangs. force, r ont right,itgfallsil art to the iso1.tnic lod fo or (b) by stretc.ingthe contracted muscle (three lower tracings). In the 27 [i1> attachdth lepentoftesionis r de to t. lev Lg i -il!' l.... -':0. W!- t- Ti j l- ~~~~~~~~~~~~~~~~~~~~~~~~~~iinduced7by theun-loadedx spring: these, as-it wasunderstoodlater,canbe0 :..: !:.. Jb...,..,... vleatand() duin an ioeri cong0tratrion (fu uppe tracings) j*i ~~~~~~~~~~~~~~~~~~~~~~~005 3 * El26 e y n a r e b bewe spr.in and lever fis pai of recrds obaie whe Time~~~~~~~~~~..... no weghs exep the spin were0 Fig. l. Experimental records showing on the left the early length changesi of0 a frog gastrocnemius (0@442 g, lo = 27 mm, 01 C) which occur when the 27ce...de riht.al abuplytote.soonclod.ro. value attained: (a) during an isometric contraction (four upper tracings).... or (b)by stretching the contracted muscle (three lower tracings). In the... first pair of records, obtained when no weights except the spring were... 26ahdt h eer h aerdvlomn ftnini8d5t h ee hitting~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. stop;.s n of 20mse... perio... tovbain induced bythe unloaded spring: these, as it was understood.later,.can.b eliminated by inserting a rubber band between springlever.~~~~-7r and

4 260 GIOVANNI A. CAVA GNA RESULTS A typical stress-strain curve of the series elastic elements of gastrocnemius is given in Fig. 3 together with the corresponding curves for the frog sartorius (Jewell & Wilkie, 1958; average of curves E, F and G in Fig. 8) and for the gracilis anticus of the rat (Bahler, 1967). The open circles refer to data obtained by releasing the muscle immediately after Fig. 2. The cam (W) can be turned by hand by means of the bar (B). By turning it pushes upward, against the spring (S), the catch (C) ofthe isotonic lever; the contracted muscle, which is attached to the lever, is thus stretched until the step (J) of the wheel reaches the knot (K): the catch is then suddenly accelerated downward by the spring action, thus allowing the muscle to shorten (see Fig. 1). The switch (R) commands the sweep of the oscilloscope just before release. stretching, the filled circles by releasing the muscle in isometric contraction. In all the experiments the series compliance of the gastrocnemius reaches a minimum value at a stress of about 2 kg/cm2 and then it remains

5 SERIES ELASTICITY OF GASTROCNEMIUS 261 constant (the curve of Fig. 3 is straight) for an appreciable range of stress (up to 10 kg/cm2 in one experiment). The stiffness in the straight part of the load-extension curve is, on the average, 20x15 + 0x92 kg/cm (mean and s.e. of mean, n = 20) and the Young's modulus is kg/cm2 (mean and s.e. of mean, n = 20). The elastic energy stored up to P0, 55*20 +2*15 gcm/g (mean and s.e. of mean, n = 20), is about 3-5 times 8 l l l o b 5 L3-0~~~~~ Strain (% of 10) Fig. 3. Typical stress-strain curves of the series elastic component of frog's gastrocnemius (continuous line), of sartorius (interrupted line) (data from Jewell & Wilkie, 1958), and of rat's gracilis anticus (stippled line) (data from Bahler, 1967). The stress is expressed in kg/cm2 of muscle crosssection and the strain as a percentage of muscle resting length 10. greater than for sartorius: this is due to the much greater isometric tension and not to a greater series compliance of gastrocnemius. An additional amount of mechanical energy of g cm/g (mean and s.e. of mean, n = 8) is stored when the force, by stretching, increases by about 60%. DISCUSSION The present results are in agreement with the hypothesis put forward by Hill (1950) that the non-linearity of the stress-strain curve of the series elastic elements is confined to a range of stress in which not all the elastic

6 262 GIOVANNI A. CA VAGNA elements are under tension, but only a variable fraction of them: the decrease of the compliance should be due to a progressive recruiting of elastic elements of different length and not to an intrinsic characteristic of the material. When the force is high enough, as in the present experiments, to put all the elastic elements under tension, the stress-strain curve becomes linear. The range of stress (or strain) necessary to reach the rectilinear part of the curve is much greater in the gastrocnemius than in sartorius (Fig. 3). This finding may be related to the greater length of the tendon of the gastrocnemius and, consequently, the greater spread in length of the individual elastic elements: this would obviously involve a greater range of strain before the recruitment of all the elastic elements is complete. The curve for the gracilis anticus (Bahler, 1967) indicates that the series compliance decreases progressively as the load increases up to P0; a similar behaviour is shown by the cat papillary muscle (Sonnenblick, 1964); the stress of these muscles at P0 is small, 1-5 and 0-6 kg/cm2 respectively, possibly insufficient to stretch all the elastic elements. The author wishes to thank Dr B. Dusman and Mr G. Orlando who projected and constructed the lever. This work was supported by the Italian Council for Research (CNR). REFERENCES BAHLER, A. S. (1967). Series elastic component of mammalian skeletal muscle. Am. J. Physiol. 213, CAVAGNA, G. A., DusMAN, B. & MARGARIA, R. (1968). Positive work done by a previously stretched muscle. J. appl. Physiol. 24, HILL, A. V. (1950). The series elastic component of muscle. Proc. R. Soc. B 137, JEWELL, B. R. & WiTL E, D. R. (1958). An analysis of the mechanical components in frog's striated muscle. J. Phy8iol. 143, SONNENBLICK, E. H. (1964). Series elastic and contractile elements in heart muscle: changes in muscle length. Am. J. Physiol. 207, WILKIIE, D. R. (1949). The relation between force and velocity in human muscle. J. Physiol. 110, WILKIE, D. R. (1956). Measurement of the series elastic component at various times during a single muscle twitch. J. Physiol. 134,