Human Movement North-Holland

301

Science 3 (1984) 301-336

AN ALTERNATIVE VIEW OF THE CONCEPT OF UTILISATION OF ELASTIC ENERGY IN HUMAN MOVEMENT G.J. van INGEN

SCHENAU

Free University of Amsterdam,

*

The Netherlands

Van Ingen Schenau, G.J., 1984. An alternative view of the concept of utilisation of elastic energy in human movement. Human Movement Science 3, 301-336. It is widely accepted that the series elastic component (SEC) of muscles and tendons plays an important role in dynamic human movements. Many experiments seem to show that during a pm-stretch movement energy can be stored in the SEC which is reused during the subsequent concentric contraction. Mechanical calculations were performed to calculate the capacity for muscles and tendons to store elastic energy. The storage of elastic energy in muscle tissue appears to be negligible. In tendons some energy can be stored but the total elastic capacity of the tendons of the lower extremities appears far too small to explain reported advantages of a pre-stretch during jumping and running. Based on literature concerning chemical change and enthalpy production during experiments on isolated muscles, a model is proposed which can explain the advantages of a preliminary counter movement on force and work output during the subsequent concentric contraction. The main advantage of a pre-stretch, as seen in movements like jumping, throwing and running, seems to be to prevent a waste of cross bridges at the onset of a contraction in taking up the slack of the muscle. The model can explain why the mechanical efficiency in running can be much higher than in cycling. A muscle which is stretched prior to concentric contraction can do more work at the same metabolic cost when compared with a concentric contraction without pre-stretch.

1. Introduction The literature shows a consensus of opinion about the significance of the series elastic component (SEC) of muscles in dynamic human and animal movements. From experiments on isolated muscles as well as from complex human movements much evidence is derived in favour of * The author wishes to express his appreciation to the reviewers of Human Movement Science for their comments on a preceding manuscript and to Drs. A. de Haan, Dr. A.P. Hollander, Dr. P.A. Huijing, Prof. Dr. R.H. Rozendal and Dr. Ir. R.D. Woittiez for many fruitful discussions and critical reading of the manuscript. Author’s address: G.J. van Ingen Schenau, Dept. of Functional Anatomy, IFLO, P.O. Box 7161, 1081 BT Amsterdam. The Netherlands. 0167-9457/84/$3.00

0 1984, Elsevier Science Publishers

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the hypothesis that SEC plays an important role which is more or less comparable to the performance of a spring. Since the SEC can be stretched by an external force, it is possible to store elastic energy in the SEC which can be re-utilised in a subsequent phase of the contraction. Though the results of the majority of the experiments of this type indeed seem to be explained quite satisfactorily with this SEC concept, a confrontation of results from experiments in isolated muscles, tendons or muscle fibres with studies concerning storage of elastic energy in complex movements leads to a number of discrepancies. Moreover, relatively simple mechanical calculations of elastic energy on the basis of the relationship between force on the muscle and stretch of the muscle show that many assumptions of the total amount of stored elastic energy cannot hold. The fact that the concept of the SEC acting as a conservative spring can provide proper qualitative explanations for many results derived in biomechanical and in physiological experiments, might explain why no alternative hypotheses have been developed. Recent studies on the mechanics and energetics of the contractile machinery of muscles however provide evidence that the significance of elastic behaviour of muscles in complex movements is trivial and that other explanations can explain reality more adequately. The purpose of this paper is to present an alternative hypothesis with respect to the effect of a pre-stretch on the mechanical and energetical performance of muscle contraction. The paper is subdivided into the following sections: _ Section 2 presents an overview concerning major studies which seem to provide evidence for the existence and significance of the SEC; _ In section 3 some arguments against the significance of SEC are developed; _ Section 4 presents the alternative hypothesis; ~ In section 5 this alternative hypothesis is applied to shed new light on a number of experiments described in the literature.

2. Evidence in favour of muscle elasticity 2.1. Isolated muscles and muscle fibres The concept of the SEC of a muscle was introduced extensive review of his own work (Hill 1970) many

by Hill. In his experiments are

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presented which show that muscles possess compliance. The results of quick release and quick stretch experiments as well as the fact that it takes time (the rise time) for the muscle to develop force at the onset of a contraction or after a quick release are all explained by the elastic properties of the muscle. The rise time, for example, can be reduced by applying a suitable stretch during the early stages of a contraction (Hill 1970: ch. 5). Moreover, the mean sarcomere length shows a considerable shortening during the rise time of an isometric contraction. It simply seems to take time to stretch the SEC (Hill 1970; Alexander and Goldspink 1977; Komi 1979). Evidence for storage of elastic energy is also deduced from the fact that starting from a certain (isometric) force a muscle can always do some external work during a subsequent isotonic contraction even at its maximal contraction velocity (Hill 1970: ch. 6). Isolated fibres also show compliance in quick release experiments (Edman 1979; Alexander and Goldspink 1977; Huxley and Simmons 1970, 1971; Huxley 1974). Isolated muscles can do more work during concentric contraction when they are stretched previously (eccentric contraction; Cavagna et al. 1968; Cavagna and Citterio 1974) and maximal force is higher after a pre-stretch than when no pre-stretch is applied (Hill 1970; Abbott et al. 1952; Abbott and Aubert 1952; Curtin and Woledge 1979a). Muscles can even shorten against loads higher than the maximal isometric force when the concentric contraction is preceded by an eccentric contraction (Cavagna and Citterio 1974). This last phenomenon cannot entirely be explained by muscle compliance (since the force of the contractile element is equal to the force in the SEC). In these cases it is assumed that stretching an active muscle also increases the capability of the contractile element to deliver force and to do work (Hill 1970; Cavagna 1978). The fashionable word for this effect is “potentiating” of the muscle (Hill 1970: ch. 5). No studies, however, have explained the nature of this potentiation satisfactorily. Nevertheless, many experiments concerning the compliance of muscles and muscle fibres simply prove that muscles possess elasticity. The same can be stated about the tendons lying in series with the muscles (Benedict et al. 1968; Welsch et al. 1971; Stucke 1950; Arnold 1974; Blanton and Biggs 1970). 2.2. Stiffness In muscles, muscle groups or entire limbs involving several muscle groups stiffness is defined as the quotient of a (small) change in force

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(or moment) and the corresponding change in length, position or angle. Compliance is the inverse of this quotient. Since stiffness seems to increase at increasing force levels, the stiffness or compliance is usually measured as a function of the force level, Many different experiments have been performed to measure different types of stiffness. Hill (1970) used external extra compliance to calculate the internal muscle compliance. This method was applied to knee flexion-extension experiments by Shorten (1984). Vincken (1983) used small disturbances in lower arm movements. Many authors calculated stiffness by means of natural frequencies, frequency-response measurements and external force-displacement of centre of gravity measurements in jumping, hopping or running (Bach et al. 1983; Cavagna 1970; Luhtanen and Komi 1980; Greene and McMahon 1979; McMahon and Greene 1979; Cannon and Zahalak 1982; Melvill Jones and Watt 1971; Vigreux et al. 1980; Cnockaert et al. 1978). The results show a wide range of (normalised) stiffness from about 100 Nm/kg up to 100,000 Nm/kg. Even in the same muscle group differences between eccentric and concentric phases of a factor 237 are reported (30,000 Nm/kg and 129 Nm/kg, respectively; Luhtanen and Komi 1980). Although a number of authors explicitly speak of apparent stiffness or even reflex-stiffness (indicating an influence of motor control on stiffness), many of these experiments can be properly described with the theory concerning mass-spring systems (including a significant role of muscle and tendon elasticity). 2.3. Running, hopping and jumping The effect of a so-called stretch-shortening contraction cycle in complex movements where one or more joints are involved is widely known. External forces and work output can be increased when a movement is preceded by a counter movement. Particularly in explosive movements like jumping and throwing the significance of such counter movements is beyond dispute. With particular reference to Cavagna’s experiments on isolated muscles (Cavagna et al. 1968), the extra jumping height during a vertical jump with a preliminary counter movement when compared with a squat jump from a semi-squatting position, is generally explained by the storage and re-utilisation of elastic energy in the counter movement jump (Asmussen and Bonde Petersen 1974a; Steben and Steben 1981; Bosco and Komi 1979a; Komi and Bosco 1978; Bosco et al. 1981; Bosco et al. 1982b). The extra jumping height and the

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elastic capacity seems to be dependent on sex (Komi and Bosco 1978), training (Luhtanen and Komi 1979), age (Bosco and Komi 1980), fibre type (Viitasalo and Bosco 1982) and maximal flexion angle (Bosco et al. 1981). To explain these phenomena it is perhaps not surprising that these authors assume that SEC is mainly located in the muscles (Bosco et al. 1981; Bosco et al. 1982b). Arm movements show comparable results as found for the vertical jump (Bober et al. 1980; Cnockaert et al. 1978). Alexander showed that animals also store and re-use considerable amounts of elastic energy (Alexander and Goldspink 1977; Alexander and Vernon 1975b; Alexander 1974). Alexander argues (on the basis of material properties) that SEC is mainly located in tendons and not in muscles, both in animals as well as humans (Alexander and Bennet Clark 1977; Alexander and Vernon 1975a). Evidence for the concept of storage and re-utilisation of elastic energy is also deduced from studies of the mechanics and energetics of running. Given a certain maximal mechanical efficiency (see next paragraph) the (high) external power in running cannot be explained on the basis of oxygen consumption measurements both in humans (Cavagna et al. 1964; Ito et al. 1983; Luhtanen and Komi 1978; Cavagna and Kaneko 1977; Alexander 1975; Cavagna et al. 1971; Williams and Cavanagh 1983; Pierrynowski et al. 1980, 1981) and in animals (Heglund et al. 1982; Taylor and Heglund 1982; Alexander and Goldspink 1977). It should be noted that large animals (including humans) seem to use relatively more elastic energy during locomotion than small animals (Taylor and Heglund 1982; Boyne et al. 1981). This is concluded from the fact that all animals need about the same amount of external power per kilogram body weight at one particular speed but that the cost of metabolic energy per kilogram is larger in smaller animals. 2.4. Mechanical

efficiency

Elastic components can store elastic potential energy when they are stretched by an external force. In different types of movements a change of the energy state of the centre of gravity of the entire body or of the separate limbs can be observed. The SEC can help to conserve energy in one part of the movement and release this energy in another part. Without this re-utilisation of energy all mechanical work resulting in external work and in an increase of the energy state of the limbs

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would have to originate from the contractile elements and all negative work on eccentric contracting muscles would be converted into heat. In running, the work per step (about 200 J) and step frequency result in an external power of about 600 Watts or more (Alexander 1975; Williams and Cavanagh 1983; Luhtanen and Komi 1978) which cannot be explained by the energy requirements of the runner if a mechanical efficiency (e,) of 25% is assumed. Most studies on running show that this e,, defined as the quotient of external power and the free energy of the original food stuff (glycogen or fat; Astrand and Rodahl 1977) should lie between 40% and 80% (Ito et al. 1983; Pierrynowski et al. 1981; Cavagna and Kaneko 1977; Williams and Cavanagh 1983; Cavagna et al. 1964; Cavagna 1978). All authors indicate that this can only be explained by storage and re-utilisation of energy in the SEC of the leg extensor muscles during stance phase. Kinetic as well as potential energy of the body centre of gravity both decrease in the eccentric phase and energy is assumed to be stored in the leg extensor muscles. During push off at least part of this elastic energy is used to assist plantar flexion and knee extension. Hof et al. (1983) show that such an economic conservation of energy is also likely in the plantar flexors during walking. The hypothesis of storage and re-utilisation of elastic energy is also used to explain the difference in mechanical efficiency found in knee bending experiments with and without rebound (Thys et al. 1972; Asmussen and Bonde Petersen 1974a), and between running and cycling against horizontal or vertical external forces (Asmussen and Bonde Petersen 1974a; Zacks 1973; Lloyd and Zacks 1972). The high apparent efficiencies (see Gaesser and Brooks 1975, for definitions) of running against external forces (up to 69%; Pugh 1971) are often explained by the same type of re-utilisation of elastic energy as is seen in normal running. Since cycling does not show an active eccentric phase in the leg extensor muscles such a conservation of energy is not possible in that type of locomotion. Literature concerning the maximal possible e, in isolated muscles seems to show no values of e,, higher than about 30% (Stainsby et al. 1980). The mechanical efficiency of a muscle is equal to the product of two parts: (1) the phosphorylative

coupling

efficiency

free energy conserved as ATP eP = free energy of oxidised foodstuff

ep

G.J. uan Ingen Schenau / Elastic energy

(2) the contraction coupling efficiency e, external work ec = free energy conserved as ATP The first ( ep) is assumed to have a value of about 60% while e, is estimated to be about 50% (Whipp and Wasserman 1969; Astrand and Rodahl 1977; Stainsby et al. 1980). So it seems reasonable to assume that the overall e, in complex movements cannot exceed 20-25% (Heglund et al. 1982; Lloyd and Zacks 1972; Alexander 1975; Cavagna 1978) since many muscles contract but not all of them will be involved in doing external work. A mechanical efficiency of running of about 50% thus seems to prove that at least 50% of all external power has to originate from elastic energy which previously was stored in the leg extensor muscles.

3. Arguments against the significance of the SEC 3.1. Mechanical principles Work done by a body is equal to the force F delivered by that body multiplied by the displacement (/) of the point of application of that (external) force according to Al

A=

J F dl, 0

where A equals the external work and AZ the total displacement. This equation is also valid for a muscle in series with tendons with an initial length I,, and a final length I, = I, - Al. Apart from the parallel elastic elements the work done by the muscle can originate from the contractile element (CE), the series elastic element (SEC) or both. The force F however is always the same in the CE and the SEC (only accelerated masses can change a force in a chain of different elements in series with each other). Eq. (1) shows that a muscle and tendon can only do work if force is exerted on the environment and if the distance between origin and insertion decreases. On the other hand the environment can only do

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work on a muscle if the muscle is stretched (Al) under the influence of a force F. So eq. (I) can also describe the work on the muscle done by the environment. This work done by the environment is also referred to as negative work done by the muscle (Al in (1) is negative). If negative work is done by the CE this work is converted into heat. If however the length of CE remains constant (or even shortens, see Hof et al. 1983), the work done on the muscle and tendon can be stored as elastic energy in the SEC. Whatever occurs inside the muscle or tendon, one statement is always true: the muscle cannot re-use elastic energy which was not previously stored in the muscle as negative work according to eq. (1). All other energy during concentric contraction has to be delivered by the CE. This simple statement is a valuable tool for judging the capacity for muscles and tendons to store elastic energy. From the above (section 2.1) one can conclude that it seems beyond dispute that muscles and tendons contain elastic elements. The remaining question however is: how much? All studies concerning the nature of tendon or muscle compliance show that the compliance decreases at increasing muscle force. The amount of work which can be stored in an element which is stretched over a distance As under the influence of a force F is equal to the area bounded by the force-stretch curve (F=f(s)) and S = As (fig. 1). Though many different relations between F and s are reported, most of those curves can be approximated quite adequately by a power curve F = klsn

where k, and n are constants. equals E =

J0

(2)

(n ’ 0, The energy

which can be stored

Asklsn ds = --&k,Asn+‘.

At s = As, F = F, (the force at stretch As). Substituting (2) and (2) in (3) yields: E=

then

--&F,~s.

So, dependent

on n the maximal amount

these values in

(4) of elastic energy which can be

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stored in the SEC is simply a function of the stretch and force at that stretch. If the relation between F and s shows discontinuities for example as a result of an increasing number of active motor units at higher forces (more parallel cross bridges) eq. (4) overestimates the actual amount of stored energy. The exponential relation for the SEC of human calf muscles (and tendon) used by Hof et al. (1983) can be very closely (r = 0.9999) approximated by eq. (2) if n = 2 is substituted. In this paper we will use this value to estimate the capacity of the elastic tissues of muscles and tendons. At small (stretch) distances eqs. (2), (3) and (4) can also be applied for the moment-angular displacement relationships at a joint. With n = 2 thus the following equations approximate the moment-stretch relationship and the stored elastic energy: M,,, = k,Aq=,

(5)

E = +M,,,Arp,

(6)

where AT equals the angular displacement which is necessary to stretch the SEC of the involved muscle(s) and tendon(s) and M,,, the moment needed to achieve that stretch. Since the order of magnitude of muscle forces, maximal stretch distances and torques are fairly well known,

F

m

___-_------

F ds

Fig. 1. The amount of energy which can be stored in an elastic element lies under the force (F)-displacement (s) curve F = f(s).

is equal to the area which

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these equations can help to test the significance of the stored elastic energy. If, for example, these equations are applied to running, the assumptions with respect to the total amount of elastic energy cannot hold. If a maximal mechanical efficiency of 25% is assumed, in each step about 100 J of positive work has to originate from re-utilisation of elastic energy (see section 2.4). Since the hip joint does not show a flexion-extension cycle, the re-utilisation of elastic energy can only take place in the knee extensor muscles and plantar flexors (Ito et al. 1983; Alexander and Bennet Clark 1977; Elftman 1940). Knee flexion and dorsiflexion in running are limited to 15-20” and 20-30” approximately while the maximal moments in both joints are about 150-200 Nm (Alexander and Vernon 1975a; Winter 1983; Elftman 1940, Alexander 1975; Luhtanen and Komi 1978; see also section 2.3). Even if all maximal values are substituted and even if we assume that the entire knee flexion and dorsiflexion is used for storage of elastic energy (then the CE remains constant or shortens) not more than 56 J of elastic energy can be stored. It must be noted that positive work done by the CE also requires a combination of moment and angular displacement. So under the assumptions made in this example the CE cannot contribute to positive work during knee extension. The total knee extension is necessary to release the elastic energy. Later it will be argued that on the basis of muscle and tendon properties this 56 J is still overestimated. A second example might provide more convincing evidence for the points made in this section. Shorten (1984) calculated the compliance of the knee extensor muscles according to a method described by Hill (see section 2.2). With this relation he calculated that per step 66 J of energy is stored in the knee extensor muscles during treadmill running. According to eq. (6) such a storage would require a knee flexion of about 55”-75” at a maximal moment of 150-200 Nm. Such flexion angles never occur during running. Even if an (unrealistic) value of n = 1 is substituted, unrealistic flexion angles would be required to explain such an amount of elastic energy. 3.2. Muscle elasticity As stated above, muscles contain elastic elements. The question is to what extent this elasticity can play a significant role in dynamic human movements. The elastic capacity of a muscle can be estimated if the maximal possible stretch of a muscle, according to eq. (4) is known.

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One of the methods used to estimate this maximal stretch is quick release of a maximally stimulated muscle. If the release is performed in a shorter time than the cross bridge re-attachment time the force will fall to zero as soon as the release distance is larger than the maximal stretch of the elastic elements. The largest stretch found in the literature is 7% of muscle resting length reported by Bahler (1967). This value was calculated by means of (complicated) extrapolation methods. From the more directly derived data reported by Cavagna and Citterio (1974) a maximal stretch of 2% can be calculated. Stienen et al. (1978) mention a maximal stretch of 11-15 nm/half sarcomere in the frog. Taking 2 pm as resting sarcomere length this means a total stretch of l-1.5%. Comparable results can be deduced from experiments on isolated muscle fibres. By manipulating the degree of overlap between the actin and myosin filaments, Huxley showed that muscle elasticity is mainly located within the cross bridges (Huxley and Simmons 1970, 1971; Huxley 1974). The total stretch (including a damped component of SEC) in those experiments was 12 nm/half sarcomere (l-1.5% of fibre resting length). Apart from the limited capacity for storage of significant amounts of elastic energy based on these stretch data, these results have severe consequences for a number of studies mentioned in section 2. If muscle elasticity is mainly located within the cross bridges, elastic energy can only be stored in muscles if the cross bridges remain attached. As stated by Alexander and Goldspink (1977) the elastic energy is lost as heat as soon as the cross bridges detach. This was probably the reason for Bosco et al. (1981) to introduce the term “coupling time” as the time when the muscle remains the same length. This coupling time should be shorter than the cross bridge cycle time to prevent cross bridge detachment. It would however be interesting to know how energy can be stored in a muscle without changing the length of the muscle according to eq. (4) or (6). If a muscle or muscle fibre cannot be stretched more than one or two percent (Stienen et al. 1978; Huxley 1974; Edman 1979; Alexander and Goldspink 1977) the total amount of elastic energy can be estimated with the help of eq. (4). At a total muscle length of for example 20 cm and an extreme force of 4000 N, the maximal amount of stored energy equals 5 J. The force taken for this calculation is slightly below the maximal force which can be delivered by the m. triceps surae. The maximal force (4700 N) predicted by Woittiez et al. (1984) lies in the range of tensile strength reported for the Achilles tendon (Benedict et al. 1968; Stucke 1950). Due to the

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viscous properties of part of the cross bridge elasticity (Huxley and Simmons 1971) only a part of this 5 J can be re-utilised. The results of this calculation of the elastic capacity of muscles agrees with the value of 5 Joule per kilogram muscle mass mentioned by Alexander and Bennet Clark (1977). These authors conclude that the role of muscle elasticity in mammalian running is trivial. It can be concluded that muscle strain energy can be neglected with respect to the maximal work which can be done by the CE (> 400 J/kg; Alexander and Bennet Clark 1977). It must be noted that during submaximal exercises both work done by the CE as well as the storage of elastic energy will be lower due to lower muscle forces. Since muscles cannot store a significant amount of elastic energy, the only tissues for such a storage are the tendons. This however is a passive element which means that it is rather unrealistic to assume that the elastic capacity is strongly related to muscle fibre types as reported by Viitasalo and Bosco (1982), or fatigue (Boulanger et al. 1979; Vigreux et al. 1980). 3.3. Tendon elasticity The mechanical properties of unembalmed human tendons are fairly well known (Benedict et al. 1968; Stiicke 1950; Arnold 1974; Blanton and Biggs 1970). For the Achilles tendon, maximal tensile strengths of 4000-6000 N are reported, at relative stretch distances of 5-8%. Tendons are stronger and stiffer at increasing strain rates (Welsh et al. 1971; Arnold 1974). For the same maximal force this means that less storage of elastic energy can occur at higher strain rates. To estimate the ultimate amount of elastic energy to be stored the lower limits of the forces and stretches mentioned above: 4000 N and 5% stretch will be used. The longest tendons in the leg are in series with the triceps surae. To estimate an effective tendon length for all tendons together it is assumed that each muscle fibre is in series with a tendon fibre whose length is equal to the mean distance between origin and insertion, minus the mean fibre length. On the basis of physiological cross section, the m. soleus and the m. gastrocnemius each account for 50% of the total force. Therefore the mean tendon fibre length of the fibres of the heads of the m. gastrocnemius and the fibres of the m. soleus is taken as effective tendon length for the entire triceps surae. The data were derived from Woittiez et al. (1984) and Huijing (unpublished

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results). This calculation results in an effective length of 26 cm. With these data a maximal stretch of 1.3 cm can be calculated. The corresponding angle of dorsiflexion then equals 16”. The maximal amount of stored energy equals 17 J. The stretch of 1.3 cm is somewhat lower than the values of 1.8 cm reported by Alexander and Bennet Clark (1977). The amount of stored energy is only about half of the value mentioned by these authors. The difference might be related to a different calculation method. Alexander and Bennet Clark used the weight of the tendon and compared this weight with an amount of energy which can be stored per kilogram tendon tissue. It is unclear to what extent that method accounts for the influence of the geometry of the tendon (thick and short or thin and long), while the present calculation used data which were actually measured on unembalmed Achilles tendons. Moreover from their formulae it can be concluded that Alexander and Bennet Clark used a linear stress-strain relation which does not agree with actual stress-strain experiments (Stucke 1950; Arnold 1974; Abrahams 1967). Since the tendons of the leg extensor muscles are shorter than the tendons of the triceps surae it can be concluded that it is unlikely that the total amount of elastic energy in the upper and lower leg muscles and tendons will exceed the 30-40 J during running or jumping. Finally it must be noted that according to Arnold (1974) the Achilles tendon shows viscous properties. His figures show that a considerable amount of stored energy will be converted into heat (the stress strain curve is, at release, more concave upwards than during stretch). Arnold (1974) argues that these viscous properties of tendons might be advantageous in damping vibrations. It can be concluded that tendon elasticity will play some minor role in dynamic human movements. The significance of this elasticity seems to be less pronounced than in jumping of a dog (Alexander 1974) or hopping by kangaroos (Alexander and Vernon 1975b). 3.4. Heat measurements and rise time Apart from the calculations made above, there are other arguments against the concept of storage of elastic energy in muscle tissue. The major part of the entire change in enthalpy liberated during the chemical reactions, which are involved in muscular contraction, is heat. With sensitive thermopile experiments the instantaneous heat production during muscular contraction (for review see: Woledge 1971) can be

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measured. Such experiments can provide insight into the mechanics and energetics of muscular contraction, particularly if these experiments are combined with the measurements of chemical change. During the first tenths of a second a muscle shows a tremendous heat production, usually referred to as activation heat. After this initial phase the heat production falls to a stable value during a continuing isometric contraction (Woledge 1971; Goldspink 1978; Alexander and Goldspink 1977). The activation heat seems, at least in part, to be dependent on the acto-myosin system (Woledge 1971). If the rise time (the time needed to develop force) is related to the stretching of the SEC of a muscle (Hill 1970; Alexander and Goldspink 1977; Komi 1979) it is amazing that so much energy is liberated as heat in this phase since the energy which is stored in the SEC cannot be liberated as heat until the relaxation phase. Although Hill (1970) reports an increase of heat during quick release (the thermo-elastic heat; Hill 1970: ch. VI), Curtin and Woledge (1979a) also report an increased rate of heat production during a forcible stretch of a stimulated muscle. During stretch the heat production appears to be three times larger than during isometric contraction and equal to the negative work done by the muscle (Curtin and Woledge 1979a). It might be expected, however, that this negative work would be stored in the SEC, at least in part. During relaxation of these stretched muscles no extra heat is liberated in comparison to the relaxation heat of the muscles which were not stretched (Curtin and Woledge 1979a). Thus, it can be concluded, that heat measurements do not provide any evidence for the storage of elastic energy. With respect to the rise time of a muscle contraction Huxley and Simmons (1971) showed that this rise time is also present if no shortening of the sarcomeres occurs. They conclude that the time course of tension rise appears to correspond simply to an increasing number of attached cross bridges. Even in situations where the sarcomeres shorten during the onset of a contraction this conclusion seems correct since the SEC of a muscle fibre is believed to be located within the cross bridges. The attachment and detachment of cross bridges can only be applied to store energy in tissue which are in series with the cross bridges but not to store energy in the cross bridges themselves, since that energy is lost as soon as the cross bridges detach. Laser beam diffraction shows that the mean sarcomere length is shortened considerably even during the onset of an isometric contraction of a muscle or muscle fibre without tendon (Alexander and Goldspink 1977) while the maximal step length

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of an attached cross bridge is assumed not to exceed 12-15 nm (Curtin et al. 1974; Homsher et al. 1981). It seems likely that during the first tenths of a second of an isometric contraction the sarcomeres have to shorten to take up some type of slack in the muscle. The majority of the internal work done in taking up this slack however will be lost as heat, since muscle elasticity can be neglected (see section 3.2). 3.5. Stiffness In the light of the calculations made with respect to muscle and tendon elasticity many results of studies on in vivo stiffness measurements cannot be explained by elastic elements of the muscles since most of the series elasticity appears to be located in (passive) tendons and not in (active) muscles. At about the same force levels differences in stiffness of a factor 237 (Luhtanen and Komi 1980) between the concentric and eccentric phase of the same muscle group cannot be explained by differences in stiffness of the involved tendons. The only explanation can be that the relations between force and displacement in those experiments is strongly influenced by the neuro-muscular control system. This may be the reason why a number of authors speak of reflex stiffness or apparent stiffness (Greene and McMahon 1979; Vincken 1983). Melvill Jones and Watt (1971) showed that running and hopping are controlled by a predetermined pattern of neuro-muscular activity and that the most comfortable frequency in those movements might be determined by a stretch reflex. Vincken (1983) showed that the control of stiffness is simply a part of the motor program for a movement. Since the force displacement relationship appears to be only slightly affected by actual muscle and tendon elasticity, calculations of storage of elastic energy on the basis of such relationships as reported by Luhtanen and Komi (1980) seem to make no sense. 3.6. Mechanical

stiffness

If the calculation of maximal tendon and muscle elasticity made above is correct then either the calculation of external power or the proposed maximal mechanical efficiency (e,) for running has to be wrong. Williams and Cavanagh (1983) discuss the influence of many assumptions made by several authors concerning efficiency of negative work, exchange of energy between the limbs and the amount of elastic energy

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during running on the predicted external power and e,. Dependent on those assumptions, e, varies between 31 and 197% and the external power between 273 and 1775 Watts. The authors show that both extremes are unlikely, if not, impossible. If the increase of potential kinetic and rotational energy of the limbs during push off in running are calculated it seems beyond dispute that such an increase in energy can only be delivered by the contractile element or the elastic elements or both. No other energy sources are available. Even if only this amount of work is taken as work per step and no energy cost is incorporated for negative work, still a mechanical efficiency of about 50% has to be assumed to explain the power output in running both for men as well as for large animals (Taylor and Heglund 1982; Pierrynowski et al. 1981; Cavagna and Kaneko 1977), if no storage and re-utilisation of elastic energy occurs. With the estimated maximal storage of elastic energy of 30-40 J per step made above a mechanical efficiency during running of at least 40% is needed to explain the external power. Such a value has never been reported in the literature for the gross efficiency of the conversion of metabolic to mechanical energy. Many authors however argue that for the efficiency of muscular work the gross efficiency should not be taken but, rather, the apparent (or work) efficiency. This efficiency is derived by dividing the external work during cycling or running against external forces by the difference in energy consumption between unloaded running or cycling (no external loads) and running or cycling against wind, gravity (moving on a slope) or other impeding forces (Asmussen and Bonde Petersen 1974a; Zacks 1973; Lloyd and Zacks 1972). This apparent efficiency is seen as a more reliable measure for muscle efficiency since energy consumption which is used in the gross efficiency also reflects energy which is used for internal work (acceleration and deceleration of the limbs, muscle contractions in the cardio-respiratory system, isometric contractions to maintain equilibrium, etc.). The studies on apparent efficiencies show values of 36-69% (Asmussen and Bonde Petersen 1974a; Zacks 1973; Lloyd and Zacks 1972; Pugh 1971). The validity of base-line subtractions as performed in the calculation of apparent efficiency is discussed by Stainsby et al. (1980). These authors argue that such base-line subtractions are not allowed since they produce efficiencies for muscular work which are much larger than the basic efficiency which is reported for individual muscles. These authors of course are quite correct in their statement that the efficiency of a movement involving

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several muscles can by no means be larger than the efficiency of the individual muscles. So either the base-line subtractions are not allowed or the maximal muscular efficiency is larger than the 30% (product of eP and e,, see section 2.4.) mentioned in their study. The question arises if it is reasonable to speculate about a mechanical efficiency higher than 25-30%. With respect to the phosphorylative coupling efficiency eP the literature shows values between 40% and 66% (Stainsby et al. 1980; Whipp and Wasserman 1969; Astrand and Rodahl 1977). This eP is estimated on the basis of the second law of thermodynamics which states that only a part of the entire enthalpy change in a chemical reaction can be used for work. This amount of energy is called the free energy (or: Gibbs free energy) AG. The rest is necessary to increase the entropy (Whipp and Wasserman 1969; Astrand and Rodahl 1977; Woledge 1971). It is a problem that AC cannot be measured during in vivo conditions while the change in entropy cannot be measured at all. The estimation of AC is based on measurements of AG, under standard conditions. It is known that in vivo conditions AG will be strongly influenced by temperature, pH and by the concentrations of the reaction products involved. For these reasons Astrand and Rodahl (1977) state that the calculation of ep is hampered by severe uncertainty. According to the definition of e, (see 2.4) there are no thermodynamic constraints to a total mechanical efficiency e, close to that of ep. The entropy change in ATP-hydrolysis is already incorporated in ep (Astrand and Rodahl 1977). The contraction coupling efficiency thus shows how much of the free energy conserved as ATP (which in principle could be available for mechanical work) is actually used for external work. Therefore this term is also called: the efficiency of the contractile process per se (Alexander and Goldspink 1977). One of the reasons that e, will be lower than 1.0 is that some ATP will be necessary for ion jumping. The values mentioned in the literature vary from e, = 49% in cycling (Whipp and Wasserman 1969) to e, = 75% for slow animal muscles reported by Alexander and Goldspink (1977). The latter authors indicate that the transduction of energy at the cross bridge level is probably extremely efficient given the right conditions. So it seems that literature provides no decisive arguments against a mechanical efficiency higher than 25-30s.

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4. An alternative view In this chapter an alternative view will be presented which might explain both the effects of a pre-stretch movement on force and work output as well as the effect of a pre-stretch on mechanical efficiency during movements with a cyclic pattern. This alternative view is based on considerations derived from literature concerning enthalpy production and chemical changes of ATP and PC (phosphoryl creatine). These considerations will be discussed first. 4.1. Enthaipy production

and chemical costs

During a contraction a muscle produces heat which is far in excess of the rate of heat production of a resting muscle. This heat production is often seen as an index of the cross bridge turnover rate (Homsher et al. 1981) although part of the heat production is believed to be independent of the acto-myosin system (Woledge 1971). During an isometric contraction, the heat production can be subdivided into three parts: the activation heat, the labile heat and the stable heat (Woledge 1971; Alexander and Goldspink 1977; Curtin and Woledge 1977). Woledge (1971) presented mathematical relations for the heat production rate for frog muscles at 0°C during isometric contraction:

where i?, = 1.5 P, gcm/sec, A, = 0.32 POgcm/sec, A, = 0.26 PO gcm/sec, a=30 set-’ and b = 1.0 set-’ and P, is the maximal force of the muscle. The first term represents the activation heat, the second term the labile heat and the third term the stable heat. During isotonic contractions the rate of heat production is significantly higher than during isometric contraction. (Fenn effect; Woledge 1971; Alexander and Goldspink 1977; Irving and Woledge 1981a; Hill 1970). A qualitative impression of the heat rate as a function of time in both situations is presented in fig. 2. These curves concerning the heat rate were derived from curves of total heat production presented by Woledge (1971). Based on measurements of the amount of ATP and PC splitting it is known that these chemical changes can mainly account for the stable part of the heat production (A, in eq. (7)). The rest is called “the

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319

unexplained heat” (Alexander and Goldspink 1977; Curtin and Woledge 1977; Woledge 1971). This obviously is heat which is liberated without the hydrolyses at ATP (Woledge 1971). The unexplained heat is much larger in isotonic contractions than in isometric contractions, if heat and work are compared with the splitting of ATP and PC (Curtin et al. 1974; Irving and Woledge 1981b; Curtin and Woledge 1979a, b). During and after relaxation the opposite seems true: a post-contractile phosphate splitting occurs which is not accompanied by significant heat production, the heat production being less than what one would expect on the basis of PC splitting (Woledge 1971). In particular the shortening heat seems to be reversed completely in a few seconds after its occurrence by means of ATP splitting (Homsher et al. 1981). With respect to these phenomena Woledge (1971) concludes that the nature of the primary reaction which drives contraction is still unknown. If one assumes that the hydrolysis of ATP takes place during the attached state of a cross bridge or at the time that the cross bridge detaches, the problem of the unexplained heat remains unsolved. In recent publications however a new hypothesis is presented which might solve the problem of unexplained heat and ATP-splitting during and after relaxation. Woledge (1971) already indicated that the stable heat is closely related to ATP-splitting during contraction since this stable heat is strongly decreased in poisoned muscles where the creatine

0

d.5 time

1,

1’. 0 S

)

Fig. 2. Heat rate during isometric and isotonic twitch contractions (deduced from Woledge (1971)). At t,, the isotonic contraction is blocked. Heat rate in arbitrary units (au.).

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phosphotransferase (Lohmanns reaction) is blocked. The labile heat is not influenced by this poisoning. The labile heat appears to be strongly reduced in the second contraction of two successive isometric and isotonic contractions (Curtin and Woledge 1977; Irving and Woledge 1981b) particularly if the time interval between the contractions is very short (< 0.25 set). However, not only is the amount of unexplained heat much smaller in the second isotonic contraction but also the amount of external work (Irving and Woledge 1981b). Homsher et al. (1981) compared the heat production and chemical change during quick shortening following 2 second isometric contraction with the same variables during the third second of an isometric contraction. In a third experiment these variables were measured after the quick shortening was ended. The results show that after the initial phase of the contractions (the first second was not analysed) there was no unexplained enthalpy (heat) during isometric contraction while the amount of unexplained enthalpy (heat + work) during quick shortening (6.5 mJ/g) was almost completely counterbalanced after shortening since in that phase 6.2 mJ/g less enthalpy was liberated than what could be expected on the basis of PC-splitting. The amount of PC-splitting during isometric contraction and during rapid shortening was equal. The authors of these studies conclude that obviously ATP hydrolysis can take place after contraction (Irving and Woledge 1981a; Homsher et al. 1981). The original cross bridge states seem to be repopulated (in part) after shortening. So, cross bridge detachment seems to take place without the hydrolysis of ATP. (Homsher et al. 1981). The total cross bridge cycle thus can be subdivided into two parts. From its original state (A) the cross bridge can attach, pull (do work) and release heat (while doing work), after detachment (state B) the cross bridge is restored to state A by a pathway involving ATP-hydrolysis (Irving and Woledge 1981a). Since the rate constant of particularly the transition from state B to A seems to be limited, many cross bridges are repopulated after the contraction. This explains why the second of two successive contractions shows less unexplained heat and less mechanical work (Irving and Woledge 1981b). Based on this theory a model of muscular contraction was hypothesized which might explain many of the experiments concerning the effects of a pre-stretch.

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4.2. The model The model presented by Irving and Woledge (1981a) suggests that the original state of a cross bridge can be described as a state (A) where the cross bridge is charged with energy which can be used partly for mechanical work, the other part being released as heat. After doing work the cross bridge has lost this type of potential energy (state B) and must be reloaded at the expense of the hydrolysis of ATP. (Irving and Woledge 1981a). The experiments of Homsher et al. (1981) suggest that the total heat liberation during and after contraction (which in this model means: during the transition in the attached state from A to B and during the transition in the detached state from B to A) agrees with the corresponding phosphagen split. Though the nature of the actual reactions is not known yet, this way of acting can completely explain why a delay in time exists between heat production and ATP and PC splitting. Fig. 3 shows an extension of the model of Irving and Woledge (1981a). Before the contraction starts, the cross bridge is in the de-

LOADED

I I

UNLOADED

work +’ AH I

ATTACHED

DETACHED

-I\-

ATP

ADp+P+ AH=

I Fig. 3. A hypothetical model of a cross bridge cycle. The loaded state means that the cross bridge can do mechanical work. The total enthalpy production (AH, + AF,) equals the enthalpy production associated with the hydrolysis of ATP. According to Irving and Woledge (1981a), the rate constant k, of the transition A, + B, is substantially larger than the rate constant k, of the transition B, + A, which involves the hydrolysis of ATP.

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Schenau / Elastic

enerp

tached loaded state A,. At contraction the cross bridge attaches (AZ) produces work and heat (AH,) and thus loses its potential energy. The unloaded cross bridge (B,) detaches to B, and is reloaded from B, to A, during the detached state releasing heat AH,.. Irving and Woledge (1981a) indicated that the rate constant k, depends on the velocity of shortening and can be high at quick shortening (30 set-’ in their experiments) while the rate constant k, is limited to about 5 sect’. So at the end of quick shortening B, and B, will be the predominant states (Irving and Woledge 1981a). The main assumption made in the present study is that this model, which was developed by Irving and Woledge (1981a) to explain shortening heat, is valid for all types of contraction. It is assumed that the majority of the unexplained heat is caused by this delay in time betwen the different states of a complete cross bridge cycle, the stable heat being a measure for complete cross bridge cycles during a contraction and the unstable heat being a measure for incomplete cycles. Such a relation between unstable heat and unexplained heat was already suggested by Curtin and Woledge (1979b). This assumption concerning the generalization of the model presented in fig. 3 can completely explain why for example the second of two successive isometric contractions shows less unexplained heat than the first one (Curtin and Woledge 1977): At the onset of the second contraction not all cross bridges which were unloaded during the first contraction will be reloaded. So during the second contraction less cross bridges will be available to attach (produce force or do work). A few more considerations and assumptions are necessary to explain the experiments described in section 2 of this paper. 4.2. I. The slack of a muscle The considerable shortening of the sarcomeres at the onset of an isometric contraction to take up the slack of the muscle (see section 3.4) does need a number of cross bridges. Particularly at the first one or two tenths of a second some cross bridges will have to do work (transition A, to B, or B,) which does not contribute to external work. During short lasting contractions (e.g. less than one second) many of these cross bridges will not be reloaded until the contraction is ended and cannot be applied again during this contraction. Henceforth the occurrence of this “waste” of potential energy of cross bridges at the onset of a contraction will be called INWASTE (Initial Wastage of cross bridges).

G.J. van Ingen Schenau / Elastic energy

INWASTE contraction

of course will also occur starting from rest.

at the onset

323

of a concentric

4.2.2. Time constants According to Huxley and Simmons (1971) the rate of force development at the onset of a contraction is coupled to an increasing number of attached cross bridges. This means that not all available cross bridges attach at the same time after the onset of the activation, which could be explained by differences in rate constants between different fibre types. In the light of the proposed model (fig. 3) this can only be the case if the rate constant k, is influenced by fibre type. This seems in accordance with the shorter rise time seen in faster muscles (the velocity of shortening during the taking up of the slack is higher). According to the measurements of phosphagen splitting during contraction (reflected by the release of stable heat) a number of the unloaded cross bridges will be reloaded already shortly after unloading. The post-contractile phosphagen splitting which shows an increased rate up to 30 set or more after contraction shows that other cross bridges seem to be reloaded after longer time intervals. This could mean that the rate constant k, (fig. 3) is actually a mean value (which also will be determined by fibre type) of a process of reloading which might be described by the theories of probability. The instantaneous force velocity curve can thus be explained as a decreasing chance for the cross bridges to be attached at increasing contraction velocities. A comparable explanation was already presented by Alexander and Goldspink (1977), and Irving and Woledge (1981a). 4.2.3. Isometric and eccentric contraction During an eccentric contraction the metabolic energy requirement is much lower than during isometric or concentric contraction. This is measured both with respect to phosphagen splitting (Curtin and Davies 1974), as well as with respect to oxygen consumption (Abbott et al. 1952; Bigland-Ritchie and Woods 1976). Particularly at relatively slow eccentric contraction velocities, the splitting of ATP during contraction can be extremely low (25% of the requirements during an isometric contraction; Curtin and Davies 1974). Stainsby (1976) argues that during eccentric contractions the muscle acts as though it were a mechanical brake, the mechanical efficiency of negative work being a

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Table 1 Relative contributions to eq. (7). Contraction 0.1 0.2 0.3 0.4 0.5 1.0

time (set)

of different

types of heat production

Activation 46 31 24 20 17 10

heat (W)

in an isometric

contraction

according

Labile heat (%)

Stable heat (%)

29 36 38 40 40 39

25 33 38 40 43 51

meaningless expression. Curtin and Davies (1974) suggest that during eccentric contractions the cross bridges can attach and develop tension without breaking down ATP. So the ATP breakdown is mainly due to tension-independent processes (Curtin and Davies 1974). Though no studies are known where the post-contractile phosphate splitting after eccentric contractions were measured, the agreement with oxygen measurements during cyclic movements shows that this conclusion concerning the low costs might also be true in the light of the model of fig. 3. So it seems likely that during eccentric contraction most cross bridges can transit from state A, to A, and vice versa without passing state B, and B,. During isometric contraction first some INWASTE occurs but after taking up the slack no further waste of cross bridges might be expected. The total costs of an isometric contraction thus is strongly influenced by the INWASTE particularly at short lasting contractions. If a muscle is stretched under the influence of an external force the slack is taken up by this force and no INWASTE is necessary to build up force. An eccentric contraction can be seen as an isometric contraction without INWASTE. 4.2.4. The effect of pre-stretch If a muscle is stretched by an external force prior to concentric contraction it can be expected that, particularly in short lasting contractions, more cross bridges are available during concentric contraction than in a concentric contraction without pre-stretch. As far as the muscle is concerned, the pre-stretch movement simply seems to prevent INWASTE. This means that the extra work done by a previously stretched muscle as well as the high mechanical efficiency seen in running can both be explained by the same phenomenon: the

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325

prevention of INWASTE. Eq. (7) might provide some information about the relative contribution of INWASTE in isometric or concentric contractions as a function of contraction time. Table 1 shows the percentages of the contributions of the different types of heat production. If it is assumed that activation heat is mainly the heat liberated as a result of INWASTE the influence of INWASTE on the total energetical costs can be calculated.

5. Applications 5.1. Applications

to isolated muscles

5. I. 1. Mechanical efficiency An estimation of the influence of INWASTE on the mechanical efficiency can be deduced from the chemical changes in eccentric, isometric and concentric contractions as reported by Curtin and Davies (1974). This study shows that an eccentric contraction (of frog sartorius muscle) costs about 0.20 ~mol.g-lsec-’ ATP breakdown and an isometric contraction about 0.70 pmol.g-‘see-‘. If it is assumed that the corresponds with the mean costs during an isomet0.20 pmol.g-‘see-’ ric contraction after force development (tension independent processes and a limited number of complete cross bridge cycles per second) then of the total isometric costs could be seen as about 50 pmol.g-‘set-’ INWASTE. At a concentric contraction velocity of one muscle length per second ATP breakdown was about 1.2 pmol.g-‘see-‘. By giving the muscle a pre-stretch during the onset of its contraction, INWASTE can be prevented. So given a mechanical efficiency of 30%, these data might show that the chemical costs in a concentric can be reduced to 70 pmol.g-‘see-’ by a preliminary counter movement. This might result in an increase of the mechanical efficiency from 30% to 51%. It must be noted however that the calculations used can only provide a rough impression of the influence of a pre-stretch since it is hampered by several uncertainties. Human muscles might perform quite differently under other conditions. On the other hand one can argue that many experiments showing a mechanical efficiency of about 30% were measured using frog muscles at 0°C. 5.1.2. Potentiation of the muscle The alternative view not only provides an explanation

for events

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which were thus far explained by muscle elasticity but can also explain of a muscle (see 2.1): If a muscle is the concept of “potentiation” stretched during the onset of its activation more cross bridges will be available during the subsequent concentric contraction than when a muscle contracts without pre-stretch. On the other hand quick release will transit a number of cross bridges from A, to B, or B, and since it takes considerable time before these bridges will be reloaded, the lower force after a quick release (Hill 1970; Abbott and Aubert 1952; Curtin and Woledge 1979a, b) seems to be simply related to the decreased number of attached bridges. Hill’s argument in favour of the storage and utilisation of elastic energy based on the fact that a muscle can always do work (starting from an isometric contraction) even at its maximal contraction velocity can also be explained with help of the model of the present study. At the onset of the contraction many cross bridges will be in state A, so they all are able to transit to B, and B, independently of the contraction speed. After the onset of the contraction the probability of a cross bridge to attach (and do work again one or more times) will strongly decrease at higher contraction speeds (shorter contraction times). 5.1.3. Enthalpy production The differences in enthalpy liberation between isometric and isotonic contractions as presented in fig. 2 can also be explained. During concentric contraction (betwen t = 0 and tl) many cross bridges transit from state A, via B, to B, releasing much heat (AH,). After the activation heat liberation the heat liberation during isometric contraction reflects complete cross bridge cycles (releasing AH, and AH,) at a small cycle time (0.2-0.34 set; Curtin et al. 1974; Irving and Woledge 1981a). At t, the isotonic contraction is blocked. The majority of the cross bridges is in state B, and will (at slow rate) be repopulated to state A, releasing only small amounts of A Hr. Finally it must be emphasized that the model presented in this study is just a preliminary alternative for the present models of the acto-myosin system. It cannot account for all events which occur in isolated muscles (as is the case with other models). Further experimental justification and completion will be necessary to test the assumptions made. Nevertheless the model can account for many events in human movements which, as was shown in section 2.2, cannot be explained by elastic capacities of the muscle.

G.J. uan Ingen Schennu / Elastic energy

5.2. Applications

321

to complex movements

In section 3 it was shown that many assumptions concerning the role of muscle elasticity and total storage of elastic energy in complex human movements cannot hold. In this section the model is applied to complex movements as far as not discussed in the preceding section. 5.2. I, Jumping Apart from assumptions concerning storage of elastic energy or alternatives, it can be argued that the effect of a pre-stretch movement can be explained with help of some simple mechanical considerations. In fig. 4 the foot reaction force patterns of one subject during a squat jump and during a counter movement jump are presented. This fig. shows that in the counter movement jump the negative velocity of the body center of gravity (cg) has to be decelerated by a force larger than the gravity force (mg). In a continuing movement this means that the foot reaction force in the counter movement (CMJ) has reached almost its maximum at the onset of concentric contraction (tr) of the muscles involved. In the squat jump (SJ) the foot reaction force at the onset of concentric contraction equals gravity (mg). The main difference between both jumps apparently seems to be a difference in force level at the onset of concentric contraction. Due to the fact that it takes time to develop force (the rise time) the effect of the squat jump is hampered by the fact that part of the total possible shortening distance of the muscles is covered with muscle forces which are not the maximal forces given the muscle length and contraction velocity in that phase of the contraction. So the effect of a pre-stretch can simply be explained by the prevention of the rise time during concentric contraction. Asmussen and Sorensen (1971) showed comparable differences in arm movements with and without pre-stretch. The differences in force level at the onset of concentric contraction, of course, will also exist if the work output of isolated muscles with and without pre-stretch are compared. Apart from the problem why force development takes time, the problem seems not to be why pre-stretched muscles can do more work but rather why they can do more work at lower cost as seen in jumping (Asmussen and Bonde Petersen 1974a; Thys et al. 1972) and in running (Taylor and Heglund 1982; Pierrynowski et al. 1981; Cavagna and Kaneko 1977). If it is assumed that the extra work done in the CMJ is entirely the

G.J. uan Ingen Schenau / Elasfic energy

328

\

\ \

:

\

\ :

_.....*... -.. *. .*: .:* *.

\

\

CMJ \ \ \ \

w

\ \ \ \

\ jooms

0

, ] z

5

I

0.4

m/s

0.1

m SJ

,: I

time

1 FZ

\

w

. . . . . ..I .,.*.,..,......,...

t1 . . ..*......-.*

\

1’

\ \ \

::

mg

\

8’

\

:’ ;*’ ***

\ \ \ \ b

FZ t

\

0

Fig. 4. The ground reaction force F,, the position z, velocity u, and acceleration a, of the body center of gravity (cg) during the counter movement jump (CMJ) and the squat jump (SJ). z = 0 is the position of the cg while standing (knee angle: 180”). Preceding the jump F, equals gravity (mg) and a, = 0. Even if the position z0 of cg at the point of deepest knee flexion is equal in both jumps, the CMJ has the advantage of a large force at the onset (I~) of leg extension since in this jump the force has already been built up during the deceleration of the downward velocity of the cg during the counter movement.

G.J. uun Ingen Schenau / Elastic energy

329

result of an extra amount of elastic energy stored in the SEC during the counter movement (see section 2), it is logical to attribute differences in extra work to differences in elastic capacity. Viitasalo and Bosco (1982) showed that subjects with a high percentage of fast twitch fibres in their vastus lateralis muscle do not jump higher in the CMJ than subjects with a low percentage of fast twitch fibres. In the SJ however the difference between the groups was about 30%, the slow twitch group jumping much lower than during the CMJ while the fast twitch group reached almost the same jumping height as in the CMJ. The authors argue that utilisation of elastic energy was possibly better in subjects having a low percentage of fast twitch muscle fibres (high percentage slow twitch fibres). In the light of the points made above (the influence of rise time) and in the light of the negligible capacity for muscles to store elastic energy this explanation seems rather far-fetched. The rise time of a muscle is strongly determined by fibre type. During the CMJ the differences in rise time do not influence the force development during leg extension since this force development was already performed during the counter movement. During the SJ however this difference will strongly influence the force development during push off. Differences in elastic capacity as a function of sex (Komi and Bosco 1978) will at least on part be explained by differences in rise time since for example Komi and Karlsson (1978) showed that young females have considerable longer rise times during leg extension than young males. Part of the differences however might originate from differences in tendon elasticity. Bosco et al. (1982a, 1982b) showed that the elastic behaviour decreases in the CMJ when compared with the SJ if the knee flexion angles are small. Such results are difficult to explain in the light of the formulae for storage of elastic energy (eqs. (5) and (6)) since one needs both torque and angular displacement. In the light of the results discussed in sections 3.2 and 3.3 showing that SEC is mainly located in the tendons the explanation of Bosco et al. (1982a, 1982b) is unconvincing since given a fixed characteristic between moment and stretch a smaller stretch will always yield a smaller amount of elastic energy. In the light of the present view the results of Bosco et al. are easily interpreted: in short concentric contractions the relative influence of INWASTE on the total work done will be much larger than during longer contractions. A comparable effect of INWASTE will have played a role in the experiments reported by Stainsby (1970,1976) and Stainsby and Barclay

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G.J. uan Ingen Schenau / Elastic energy

(1971, 1972). In these in situ experiments on dog skeletal muscles oxygen consumption was measured as a function of different types of load. The dynamic experiments were performed with very small concentric contraction distances (about 5-6% of resting length; Stainsby 1970). The results show little or no relation between external work in concentric contractions and oxygen consumption. Moreover there is almost no difference in oxygen consumption between isometric and concentric contractions. Given the small shortening distance it can be expected that INWASTE plays a dominant role in the total energy consumption in both types of contraction leading to non-significant differences. This influence of INWASTE lays burden on the arguments used by Stainsby et al. (1980) with respect to the validity of baseline subtractions. Apart from the disputable upper limit of the mechanical efficiency (see section 3.6) it seems that the examples used by these authors which were based on their dog muscle experiments were severe overestimations of the effect of a baseline subtraction in calculating apparent efficiency. It seems that the experiments of Stainsby and Barclay actually provide evidence for the existence of INWASTE since the relation between external work and oxygen consumption in movements with considerable shortening lengths of the involved muscles is beyond dispute. 5.2.2. Running and cycling In the preceding section (4) it was already discussed that it is not likely that the amount of external power in running is strongly overestimated. The only conclusion therefore has to be that either significant utilisation of elastic energy has to occur or the mechanical efficiency e, has to be higher than 35% (or both). It was shown that INWASTE can strongly reduce e, particularly in short lasting contractions. During running the extensors of the knee as well as the plantar flexors are stretched preceding concentric contraction. In this type of locomotion thus INWASTE can be prevented. According to emg activity patterns (Houtz and Fischer 1959; Faria and Cavanagh 1978) such a pre-stretch does not occur during cycling. Many experiments to determine e, for complex movements however were performed with the help of bicycle ergometer tests. The value of eP = 49% reported by Whipp and Wasserman (1969) showing a total e, of about 30% was also derived by bicycle ergometry and will thus be influenced by

G.J. uan Ingen Schenau / Elastic energy

331

INWASTE. So it is likely that running is performed closely to the optimal e, and that in cycling energy is wasted due to the repeated necessity to take up the slack of the muscles every time before they can do external work. The effectiveness of this type of locomotion is mainly due to the transmission of the external muscle work to the propulsion on the wheel. In running most of the external work is used to accelerate and decelerate the lower extremities while much negative work will be done during knee flexion and dorsiflexion. In running and cycling against horizontal or vertical impeding forces (Asmussen and Bonde Petersen 1974a; Zacks 1973; Lloyd and Zacks 1972; Pugh 1971) of course the same difference is apparent and can completely explain why external work during running is much more efficient than during cycling. The higher the external loads the higher the activation level of the involved muscles will be and the higher INWASTE will be in cycling (more motor units will be involved in taking up the slack). With the concept of storage of elastic energy it is difficult to explain the high efficiencies in running. Storage and reutilisation of elastic energy can only take place if there is energy available which can be stored. In these experiments, however, work is done against external forces. This work is lost and cannot be conserved as might be possible in unloaded running or during knee bending experiments with rebound. Finally it will be discussed that the model presented in this study might explain why large animals can run more efficiently than small animals (Heglund et al. 1982; Taylor and Heglund 1982). The authors assume that the large animals will utilise relatively more elastic energy although Heglund et al. suggest that a difference in step frequency might also play a (minor) role. In the light of INWASTE this last suggestion can probably completely explain the differences mentioned: the higher the step frequency at a given speed the higher the contribution of INWASTE will be, particularly in all those muscles which contract isometrically, for example to maintain equilibrium.

6. Conclusion In conclusion it can be stated that given the limited elastic capacity of muscles and tendons the concept of storage and re-utilisation of elastic energy cannot explain many of the results reported with respect to the

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