Efficiency of vertebrate locomotory muscles

In this paper we will examine the efficiency of vertebrate striated muscle during terrestrial locomotion. First we will examine whole animal locomotion, then we will review some recent experiments on isolated frog and rat muscle, and finally we will conclude by looking at isolated muscles in the context of the whole animal in order to speculate on how the muscles are used during a ‘natural’ activity such as locomotion.

In order to calculate the efficiency of locomotion in whole animals it is only necessary to measure the metabolic power input and the mechanical power output. We will use body size and speed of locomotion as independent variables in order to manipulate both the power input and the power output over a wide range of values.

It may at first be difficult to understand what work is done by the muscles during steady speed locomotion on level ground. No work is being done to increase the average kinetic energy of the body since the average speed is constant ; and no work is done to increase the average potential energy of the body since the average height of the centre of mass is also constant. Work is done to overcome the resistance of friction ; there is wind friction, friction against the ground, and friction within the body itself. The work required to overcome wind resistance has been calculated for humans, who present a relatively large frontal area to the air during running. Wind resistance accounts for less than 2% of the total mechanical power output at 2·8ms ⁻¹, and less than 8 % at 8·3 m s⁻¹ (Heglund, 1979). No work is done against the ground unless the subject deflects the ground (such as running in sand) or slips. Frictional losses within the body mainly occur within the muscles. Antagonist muscles can do work on each other, but this appears to be relatively minor. (Alexander & Vernon, 1975, have calculated that this accounts for only about 15 % of the total positive work performed by a kangaroo hopping at 5·5 ms⁻¹.)

Most of the positive work of terrestrial locomotion involves: (i) maintaining the oscillations of the kinetic and potential energy of the centre of mass of the body as it goes up and down and accelerates and decelerates within each step; and (ii) maintaining the oscillations in kinetic energy of the limbs and other parts of the body relative to the centre of mass as they alternately move back and forth each step. Within each step the work done by the muscles to increase the instantaneous kinetic or potential energy of the body during a positive work phase is subsequently reabsorbed by the muscles during a negative work phase and either dissipated as frictional heat within the muscle or stored elastically for use during the positive work phase of the next cycle. We cannot determine what fraction of the energy absorbed-during the negative work phase is dissipated as heat or is stored elastically.

The weight-specific metabolic power input to an animal increases linearly with speed and is much higher in smaller animals. In contrast, the positive mechanical power required during locomotion increases curvilinearly with speed and is independent of size of the animal. For example, if we compare a 30 g quail to a 100 kg ostrich moving at 3ms⁻¹, we find that the quail is consuming oxygen per gram of tissue at a rate 15 times higher than the ostrich, but the two animals are doing work at about the same rate per gram of tissue. The ratio of the power output to the metabolism may be considered the positive work efficiency as defined by equation 1 ; we find that this efficiency increases with speed in all of the animals, and increases with increasing body size. The peak value measured in quail was 7 %, while that measured in humans and kangaroos was over 70 %.

This result is intriguing because it is not what any of the current models of animal locomotion would predict. Several questions need to be answered, (i) Why is the efficiency of the large animals so high? 70 % is unreasonably high in the light of the muscle experiments previously done by A. V. Hill and others, as discussed in the next section of this paper, (ii) Why is the efficiency of the small animals so low? Again, classical thought on this would predict a peak efficiency approaching 25% for all animals, (iii) Why does the efficiency increase continuously with increasing running speed? Simply on the basis of the force-velocity curve the efficiency should be zero at zero shortening velocity (the work done is zero because the displacement is zero), attain a maximum at an intermediate shortening velocity, and then go back down to zero at the maximum shortening velocity (the work done is zero because the force is zero). The isolated muscle experiments will answer some of these questions, and raise new ones as well.

While it is conceptually easy to measure the metabolic power input and mechanical power output of animals over a relatively wide size range, we have little control over, and sometimes are not even able to measure, many other important variables concerning muscular efficiency. Isolated muscle experiments, on the other hand, allow us directly to control many of the parameters of interest (e.g. stimulation patterns, shortening velocity, etc.), often at the expense of other parameters (e.g. recruitment patterns of different fibres within a muscle, maintenance of the blood supply, etc.).

Relatively few measurements of efficiency have been made in isolated muscles ; the energy input has always been calculated as the heat evolved by the muscle : efficiency = work/(work + heat) (Hill, 1939; Woledge, 1968; Gibbs & Gibson, 1972; Wendt & Gibbs, 1973). The peak efficiency determined in every case, excluding tortoise muscle, was less than 25 %.

In recent experiments we measured the mechanical efficiency in isolated frog sartorii, rat extensor digitorum longus (EDL, a primarily fast fibre muscle) and rat soleus (a primarily slow fibre muscle) by measuring the mechanical work done and the subsequent recovery oxygen consumption. The muscles, about the size of a paper match (so that oxygen diffusion is not a problem) were placed in a sealed glass chamber full of oxygenated saline. The muscles were connected to a force transducer at one end, and to an electronically controlled lever system at the other end. An oxygen electrode measured the decrease in the chamber ⁠, from which the oxygen consumption could be calculated. A computer controlled the stimulation and length changes of the muscle ; the work done could be calculated from the developed force and length changes of the muscle. In an effort to simulate the way muscles are used during locomotion, shortening was immediately preceded by stretching of the contracting muscle. In this situation part of the positive work done during shortening can be derived from mechanical energy stored in the muscle during the negative work phase (i.e. during stretching). For comparison, the efficiency was also measured during shortening under identical conditions, except that shortening occurred from a state of isometric contraction. This is a situation where only chemical energy can be the origin of the work done.

The net weight-specific oxygen consumed per stimulus, the weight-specific work done per stimulus during shortening from an isometric contraction, and the efficiency of work production are shown as a function of contraction velocity in Fig. 1. In the sartorius both the oxygen consumption and the positive work appear to increase linearly with contraction velocity up to a speed of about 1·0 muscle lengths⁻¹. The EDL oxygen consumption and work initially increase, then decrease with increasing speed. In the soleus the data are too few to describe a function, however oxygen consumption appears to be nearly independent of speed and the work appears to reach a maximum at intermediate speeds.

The oxygen consumption and work per stimulus decrease markedly from the sartorius to the EDL and from the EDL to the soleus, yet the efficiency differs much less. The efficiency increases to 25 % in the sartorius; it was not possible to obtain reliable data at speeds of contraction greater than 1·5 lengths s⁻¹ because there was a redevelopment of tension at the end of the shortening. The peak efficiency in the EDL is about 19%, occurring at a speed of shortening of 1·0 lengths⁻¹. In the soleus the peak efficiency is about 15 % at 0·5 lengthss⁻¹.

The oxygen consumption of a muscle does not seem to be drastically affected by a pre-stretch, as shown in Fig. 2 (the dotted lines in Fig. 2 are redrawn from Fig. 1 for comparison). On the contrary, the pre-stretch had a marked effect on the work performed during the subsequent shortening in all three muscles. The average ratio of work performed after a pre-stretch to the work performed at the same contraction velocity but without a pre-stretch was 1·3 in the sartorius, 3·4 in the EDL and 3·2 in the soleus.

The positive work efficiency after a pre-stretch is much greater than that measured without a pre-stretch, attaining peak values of about 38 % in the sartorius, 50 % in the EDL and 40 % in the soleus. The peak efficiencies measured with and without a prestretch seem to occur at similar speeds of contraction. In the mammalian muscles, the positive work efficiency after a pre-stretch tends to remain relatively high at the high speeds of contraction; at the highest speeds measured, the ratio of the efficiency after pre-stretch to the efficiency without pre-stretch was about 6 in the EDL and 2 in the soleus.

The ‘economy’ of the EDL and soleus was measured in the experiments without a pre-stretch as the tension-time integral divided by the energetic equivalent of the net oxygen consumed. The soleus is about twice as economical as the EDL over the entire range of shortening speeds. These data allow us to make a distinction between muscles that are able to maintain tension economically (e.g. soleus), and muscles that are able to produce positive work (e.g. EDL). Slow muscle will be particularly suitable for postural needs, whereas fast muscle will be more efficient in maintaining tension over a greater displacement during shortening at a given speed.

The intercept of energy expenditure vs speed relationship in sartorius represents the energy expenditure during an isometric contraction; this value (573 mJ g⁻¹ stimulus⁻¹) is in good agreement with previous findings on the same muscle (Kushmerick & Paul, 1976; Chapman, Gibbs & Loiselle, 1982; Hill, 1972; Baskin, 1965).

The additional energy, above the isometric value, spent during shortening (Fenn effect) should be about twice the work done plus twice the shortening heat in the sartorius (assuming the recovery heat equals the initial energy output). The work done has been measured for each sartorius, and the shortening heat was calculated from the normalized a coefficient of 455 g cm⁻² given by Abbott (1951) and the shortening distance for each muscle. The calculated values of additional energy are, on average, 20 % greater than the values actually measured.

Wendt & Gibbs (1973) and Gibbs & Gibson (1972) measured the efficiency of rat EDL and soleus at 27 °C with a myothermic technique. They found peak efficiency values of 9·5 % with 1-s tetani and 16% with 0·5-s tetani in the EDL, and 18·5 % in the soleus. They conclude that the fast-twitch EDL muscle sacrifices energetic economy in return for speed of response. This conclusion is not supported by the present efficiency measurements, but is in agreement with our measurements of economy.

The increase in the efficiency due to a pre-stretch is greater in the mammalian muscles than in the sartorii. This may be due to : (a) a relatively greater compliance of the tendons of mammalian muscles (particularly of EDL), since a greater compliance will allow more mechanical energy to be stored during the stretch for a given increase of the force ; and (b) the greater speeds of shortening attained in the experiments on mammalian muscle. In fact, contrary to the work done by the contractile component, the release of the mechanical energy stored during stretching is unaffected by the high speeds of shortening.

The first of the three questions about whole animal locomotion that we wanted to answer in the isolated muscle experiments concerned the high peak efficiency in large animals. Positive work efficiencies of > 0·7 were observed in man and kangaroo at high speeds of running and hopping, exercises in which the muscles shorten immediately after being forcibly stretched. The efficiencies measured in the isolated mammalian muscles approach these high values due to an increase in the positive work done after a pre-stretch. Clearly the mechanical energy stored within the muscle (tendons and cross-bridges) during the negative work phase can be recovered and used in the positive work phase.

We do not have a clear answer to the second question, concerning the low efficiency in small animals. However, our data on the economy of muscles comprised of slow contracting fibres (soleus) relative to muscles comprised of fast contracting fibres (EDL) may be at least part of the answer, since small animals have muscles of higher contraction velocity than the homonymous muscles of large animals. It could be that the cost of maintaining tension dominates the cost of locomotion in small animals. Efficiency, which is concerned with work production rather than force generation, may therefore not be a productive way of analysing the cost of locomotion. In this regard it is interesting to note that, over a wide range of speed, the metabolic energy consumption of mammalian muscle, as shown in Figs 1 and 2, is nearly independent of the speed of contraction, the presence or absence of a pre-stretch, or even the amount of work done ; although it is very dependent upon the intrinsic velocity of the muscle (i.e. ‘fast’ vs ‘slow’ as discussed in many other papers in this volume). The paper by Taylor in this volume gives several predictions based on this ‘cost of maintaining tension’ to the cost of terrestrial locomotion.

The final question asked on the basis of the whole animal experiments concerned the means by which the efficiency was maintained at high levels even at the highest speeds of locomotion; in fact in all animals studied, the peak efficiency occurred at the highest running speeds. The present experiments show that previous stretching of the contracting muscle is the only way to maintain a high efficiency during high speeds of shortening. In the EDL, for example, at shortening speeds sufficient for the efficiency measured without a pre-stretch to drop nearly to zero (5 lengths s⁻¹), the efficiency measured after a pre-stretch remains higher than even the peak efficiency measured with no pre-stretch (Fig. 2).

This work was supported by NIH AM06022, NSF PCM7823319 and PCM8317800 and CNR 79.02366.65.