Acta physiol. scand. 1976. 96. 83-93 From the Laboratory for the Theory of Gymnastics, August Krogh Institute, University of Copenhagen, Denmark

Mechano-Elastic Properties of Human Muscles at Different Temperatures BY


Abstract ASMUSSEN, E., F. BONDE-PETERSEN and K. JBRGENSEN. Mechano-elasticproperties of human muscles at different temperatures. Acta physiol. scand. 1976. 96. 83-93. The effect of changes in the muscle temperature on their ability to store elastic energy was studied by having 5 trained subjects perform maximal vertical jumps on a force platform, with and without counter movement, at muscle temperatures between about 32°C and 37°C. The results showed that the heights of vertical jumps were considerably reduced at lowered temperature, but the gain in heiglir after a counter movement in the form of a jump down from a height of 0.4 m over the force platform, was significantly higher in the cold condition. T o test whether this was due to an increased stiffness of the muscles, experiments with imposed sinusoidal length variations at 14 Hz were performed. Aforce x Alength-L (i.e. stiffness) increased with isometric tension independent of muscle temperature. Experiments in which the rate of tension development and relaxation in voluntary maximal isometric contractions were measured at different muscle temperatures showed that maximal isometric tension changed by less than I X per degree but the rate of tension development and relaxation by 3-57, and 5 % per degree, respectively, in the temperature range studied (30” to 40’). These data may be explained by the hypothesis that the series elastic components of the active muscle are located in the cross-bridges between myosin and actin filaments. The storage of elastic energy would be enhanced if the rate of breaking of these bridges were decreased at lower temperatures. Key words: Elastic energy: muscle stiffness; muscle temperature; rate of tension development and relaxation; vertical jumps

Recently we demonstrated in man that mechanical energy imparted to a muscle while it is actively resisting lengthening, can be stored and reused as elastic energy during a subsequent shortening contraction (Asmussen and Bonde-Petersen 1974). This happens in a vertical jump when the jump is preceded by a countermovement. We assumed that the active muscles behaved as springs, and found that an average of up to 23% of the imparted mechanical energy could be stored as elastic energy and re-used in the subsequent jump. Marey and Derneny (1885) and Cavagna et al. (1971) came to similar conclusions. The nature of the elastic component that allows active muscles to store energy is not fully known, nor is its location. The expressions “parallel-elastic” and “series-elastic” were proposed by Levin and Wyman (1927) to designate the elastic components in parallel with or in series



with the contractile elements in the muscle. The former is usually identified as tendons, intramuscular connective tissue, sarcolemma etc., whereas the latter, in recent literature, has been assumed to be in the cross-bridges that form between myosin and actin filaments during contraction (A. F. Huxley and Simmons 1971, Riiegg 1971, Rack and Westbury 1974, A. F. Huxley 1974). With these possibilities it seemed relevant to study the effect of temperature on the elastic properties, including storage of elastic energy, in human muscles in situ. As a working hypothesis we assumed that lowering of the muscle temperature would increase the stiffness of the visco-elastic components while at the same time decreasing the rate of the chemical processes that underlie the formation and breaking of the cross-bridges.

Methods Muscle reniperarurcs. Variations of muscle temperature were obtained by immersing the subject in cold water, or by active exercise. The muscle temperature was measured by means of a thermo needle (Ellab) inserted into the appropriate muscle to a fixed depth of 25-30 mm. There was a rather steep temperature gradient from the surface inward, especially after cooling. The temperatures measured, therefore, do not represent mean muscle temperatures but are arbitrary values for comparisons between cold and warm muscles. Slorage of elastic energy in the muscles of the legs was estimated from the increase in height of a vertical jump performed in direct continuation of a jump down from a height of 0.40 m, over the height when i t was performed from a semi-squatting position (cf. Asmussen and Bonde-Petersen 1974). The jumps were performed on a force platform (Bonde-Petersen 1975) in connection with an inkwriting recorder at a paper speed of 125 mm x s-'. The registered time, tnlght. between take-off to the jump and touch-down after the jump was used in calculation of h, the height of the jump, according to the formula



vws2 (2g)-' > .


Here, g is the acceleration of gravity (9.81 m 4 s-~) and vpo8 is the velocity at take-off (and touch-down). This velocity is determined from the time spent in moving upwards (or downwards), i tilight, as vpoB= 4 tfllghL g. The height of the jump consequently is h = ( i tilight ?: g)2x (2g)-'= 1.226 (tfIlghJd. When the subject jumps down from an elevation onto the force platform before the actual upwards jump, a certain time, ttotal, is spent in contact with the platform. Part of this time, tneg, is spent in absorbing the energy from the fall down and the rest (ttotal-tneg) in liberating energy for the take-off. The braking movement will take place with a downward velocity that changes from vneg (at first contact with platform) to zero, and the subsequent upward movement, leading to the jump, will have velocity zero at the beginning of the movement and end with velocity=v,,,, as calculated above. The distance covered in the decelerating and accelerating movements, respectively, must be the same; hence from the mean velocities, tnep y 4 vncg(ttotal-tnes) x 4 vpoB.Solving for tnCgone gets tneg = ttotsl

vpos (Vneg+ vpos)-*


In this way the time during which energy is absorbed can be calculated. The rest of the contact time with the platform is used in liberating positive kinetic energy. Muscle sfqfness. An arbitrary expression for the stiffness (Aforce/Alength) of the calf muscles was obtained by imposing sinusoidal length variations of constant amplitude and frequencey on the isometrically contracted muscles, registering the resulting rhythmic variations in force around the mean muscle tensions. For this purpose the subject lay o n his back, his flexed knee pressed against a solid cross-b:am and the ball of his foot lightly tied to a wooden sandal, movably fixed to a ring-shaped strain gauge dynamometer (see Fig. 1). The subject was asked t o press the ball of his foot against the dynamometer by a plantar flexion with a pre-determined force and to keep this constant by watching the hand of the strain gauge meter. The hand was so much damped that it could not follow the rapid sinusoidal oscillations induced by an eccentric driven by a strong motor (see Fig. 2). We found that 14 H z gave good and reproducible force variations with movements of 40 mm peak-to-peak. The length variations at the Achilles tendon must have been



Fig. I . Schematic drawing of set-up for vibrational studies of m.triceps surae. a. wall, floor. 6. supporting frame. c. ring-shaped strain gauge dynamometer. d. wooden sandal, movably attached to r. e. solid cross beam. f. iron lever, movably attached to 6. g. motor and eccentric. about one-third of this, 12-14 mm. Each period, at a maintained constant mean force, lasted 2 to 3 s. Emg mean peak voltage was registered simultaneously by means of skin electrodes over the soleus muscle, both before and during the vibration. Muscle temperatures were measured in the lateral head of the gastrocnemius muscle at a depth of 25 mm. Rare of tension delfoelopment and relaxation.' The speed of these two parameters was measured during maximal voluntary isometric contraction of the elbow flexors, the plantar flexors, and the knee extensorshenceforth called, respectively, biceps br., triceps surae, and quadriceps fem. The registration of the isometric tensions was performed by means of a strain gauge dynamometer with the elbow, ankle, or kneein a standard position. Emg and mean peak voltage were registered simultaneously from double surface electrodes by a Disa electromyograph and an inkwriting recorder (Mingograph) at a paper speed of 250 mm s-I. The maximum mechanical tensions in the cold or warm conditions were expressed as percentages of the maximum isometric tensions at normal temperature o n the same day. Because of the uncertainty of defining the exact beginning and end of the tension development, the rate was expressed as tension increase from 5 t o 90% of maximum over time (Fig. 3). Correspondingly, the speed of relaxation was calculated from the time between 905: and 5:: of maximal tension during relaxation. The rates of tension development and relaxation were expressed as percentages of the controls. In this way all three muscle groups, from three different subjects, could be combined in the same graph with the measured temperature as abscissa (Fig. 6-8).

ustr. 900

Fig. 2. Examples of vibrational force variations at increasing mean tensions in m.triceps surae. Length variations at Achilles tendon: about 12 mm, vibrational frequency 14 Hz, arbitrary force units in jt-strain.






3 00




- 0

1 sec

The experiments in this section were performed by Mr. Finn Andersen as part of his thesis for the cand. scient. degree.



(0.05 - 0.9)P.


I _

Fig. 3. Lower curve: tension development in maximal voluntary isometric contraction of m.triceps surae. Upper curves, iemg (mean peak voltage) and emg. Rate of tension development is taken t o be P0(0.9- 0.05) x t-I where Po is maximal tension and t time in seconds.

50 H r

Subjects were 8 young men, students of physical education, of good health, and well fit for muscular exercise. They did not all serve in all the experiments t o be presented, but each experimental situation was repeated several to many times o n a given subject.

Results Vertical jumps, from a squatting position or in continuation of a jump down from a height of 0.40 m, were performed at different temperatures of the leg muscles. The heights of the jumps, calculated as described under Methods, were plotted against the muscle temperatures, measured in the lateral vastus muscle at a depth of 30 rnm, as shown in Fig. 4 for one of the 5 subjects. It is evident that the height of a vertical jump in both cases is smaller in the cold condition. But it also came out that the gain in height due to the effect of jumping down 0.40 m, was larger both absolutely and relatively in the cold condition. Assuming

Height of jump




0.3 .















, 36





, 39

, LO 'C


Fig. 4. Ordinate: The height of a vertical jump performed from the semisquatting position ( 0 ) .or in continuation of a jump from height 0.40 m ( A ) . Abscissa: Temperature in m.vastus lat. at a depth of 30 mm. Subject M .



TABLE 1. y = a + bx. Subject

After jump down 0.4 m

Squatting jump a






-0.929 -0.854 -0.557 -0.528 -0.531

0.037 0.034 0.024 0.024 0.025

0.938 0.945 0.978 0.907 0.905

-0.668 -0.695 -0.444 -0.258 -0.326

0.030 0.031 0.021 0.018 0.021

0.920 0.945 0.973 0.837 0.894

F. A.


M. B.

Constants in formula y = a + bx, in which y = height of jump in m, and x is muscle temperature in C". r = correlation factor.

the values to lie on straight lines (see Fig. 4), the regression equation for the two kinds of jump was calculated as y = a + bx, where y is the height of the jump, x is the muscle temperature, and a and b are constants. These constants, and the r-values for the correlation, are presented in Table I. If all data from a warm condition (about 37°C) are treated as one series of experiments, and all data from the corresponding cold condition (about 32°C) as another series, average height of the jumps with and without the preceding jump down, can be calculated for each subject. Further, the average gain in height, Ah, after jumping down, over the height obtained in the squatting jump, can be calculated for both series. These data are presented in Table 11. The table shows that in all five subjects the gain in jumping height after a jump down, Ah, was larger with cold muscles than with warm muscles. The average Ah-difference was significant at the 0.01 level, and the individual differences were significant at the 0.1 level in all 5 subjects and at the 0.05 level or better in 4 of the 5 subjects (Table 11). The absorption and storage of energy from the down-jump takes place during the first part of the time spent in contact with the force platform. Its duration, tnEg, can be calculated-as shown under Methods-from formula (2). Of the parameters in the formula vpos is calculated from formula (1) in which h is determined from the appropriate regression equation (Table I) for muscle temperatures 37°C and 32"C, respectively. vnEgis a constant, TABLE 11. Gain in height after jumping down Subject

F. A. S.

M. B.


Cold conditions

Warm conditions

Warm-cold difference


Tkus C"

ih+S.E. m


T&S C"

Ah&S.E. m


37.1 36.5 37.5 37.7 39.6

0.012f0.013 0.037f0.005 0.005+0.003 0.018f0.006 0.017k0.008

II 12 7 9 7

33.1 32.2 33.2 32.9 32.3

0.039f0.006 0.058F0.005 0.020f0.003 0.055 f 0.005 0.052k0.012

0.05 P--0.1 P :c 0.01 P~O.001 P:,of that at the higher temperature. The distance through which the muscles could shorten at takeoff was-as mentioned under Results-identical in the two conditions. A slower development of maximum force consequently leads to less work produced during the positive phase of the jump, even though the time, ttot, is prolonged by about 7 % (Table IV), because the muscles in this time apparently could reach an average tension of only 87 % of that reached in the warm condition. After the jump down from height 0.40 m the muscles are activated to d o negative work. The average tension developed for this purpose was-as follows from the identical tnep (Table Ill) and absorbed kinetic energy-identical in cold and warm conditions. As relaxation takes a longer time in the cold condition (Fig. 8), it will mean that the increased stiffness of the active muscles disappear later and thus will be able to carry more elastic energy over into the positive phase of the jump. This explanation is in good agreement with the experiments in Fig. 7 and 8, and also with the finding that isometric endurance is prolonged at lower temperatures (Clark, Hellon and Lind (1958), Edwards et a/. (1970)). The latter authors also found that the ATP-fluxes, as determined from muscle biopsies of human muscles, were considerably lowered at low muscle temperatures. Our conclusion is that both the generally lower jumping height and the increased ability to carry over energy from a jump down to a subsequent vertical jump can be explained by assuming that the formation and breaking of active cross-bridges in contracting human muscles is considerably delayed at lower temperatures, even though the final maximal tension is only slightly decreased.



References APTER,J. T., Influence of composition on thermal properties of tissues. In Biomechanics. Its foundations andobjecfioes, edited by Y. C. Fung, N. Perrone and M. Anliker, Prentice-Hall, Englewood Cliffs, New Jersey 1972. ASMUSSEN, E. and F. BONDE-PETERSEN, Storage of elastic energy in skeletal muscles in man. Acta physiol. srand. 1974. 91. 385-392. BONDE-PETERSEN, F., A simple force platform. Europ. 1. appl. Physiol. 1975. 34. 51-54. BUCHTHAL, F. and E. KAISER, The rheology of the cross striated muscle fibre with particular reference to isotonic conditions. Dan. Biol. Medd. 21. No. 7. 1951. CAVAGNA, G. A., L. KOMAREK, G. CITTERIO and R. MARGARIA, Power output of previously stretched muscle. In Medicine and Sport, 6, Biomechanics 11, 1971. 159-167. Basel. CLARKE,R . S. J., R. F. HELLONand A. R. LIND,The durations of sustained contractions of the human forearm at different muscle temperatures. J. Physiol. (Land.). 1958. 143. 454473. EDWARDS, R. H. T.,R. C. HARRIS, E. HULTMAN, L. KAIJSER, D. KOH and L.-0. NORDESJO, Energy metabolism during isometric exercise at different temperature of m.quadriceps femoris in man. Acta physiol. srand. 1970. 80. 17-18A. HUXLEY, A. F., Muscular contraction. J. Physiol. (Lond.). 1974. 243. 1 4 3 . HUXLEY, A. F. and R. M. SIMMONS, Mechanical properties of the crossbridges of frog striated muscle. J. Physiol. (Lond.). 1971. 218. 59P-6OP. JOYCE,G. C., P. M. H. RACKand H. F. Ross, The forces generated at the human elbow joint in response to imposed sinusoidal movements of the forearm. J. Physiol. (Land.). 1974. 240. 351-374. The viscous elastic properties of muscle. Pror. roy. Soc. B 1927. 101. 218-243. LEVIN,A. and J. WYMAN, MAREY,M. and M. C. DEMENY, Locomotion hurnaine, mecanisme du saut. C. R. Acad. Sci. (Paris) 1885. 101. 489494. RACK,P. M . H. and D. R. WESTBURY, The short range stiffness of active mammalian muscle and its effect on mechanical properties. J. Physiol. (Land.). 1974. 240. 331-350. RICE, M. H. C., A simple method of measuring joint stiffness in the hand. J. Physiosiul. (Lonil.) 1967. 188. 1-2P. RUEGO,R. E., Mechanochemical energy coupling. In Limiting factors of physical performance, edited by J. Keul, Stuttgart, Georg Thieme Verlag, 1971.

Mechano-elastic properties of human muscles at different temperatures.

The effect of changes in the muscle temperature on their ability to store elastic energy was studied by having 5 trained subjects perform maximal vert...
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