Why Change Gaits? Recruitment of Muscles and Muscle Fibers as a Function of Speed and Gait

Transcription

1 AMER. ZOOL., 18: (1978). Why Change Gaits? Recruitment of Muscles and Muscle Fibers as a Function of Speed and Gait C. RICHARD TAYLOR Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts SYNOPSIS Muscles shorten, stay the same length and are stretched while they are active during normal modes of terrestrial locomotion. The relative importance of these different types of muscular activity changes as animals change gait. Energy is conserved during a walk by an alternate storage and recovery of gravitational potential energy within each stride, as in an inverted pendulum. In order for this transfer of energy to take place, muscular activity is required to hold the limb rigid while the animal rotates over it. Energy is conserved by a spring mechanism during running, trotting, galloping, and hopping. Energy is stored when active muscles and their tendons are stretched and recovered as they subsequently shorten. The recruitment patterns of motor units as a function of speed therefore, depends on the type of muscular activity as well as the force exerted. Discontinuities in the cross sectional area of active fibers with increasing speed have been observed at the trot-gallop transition. It is suggested that at this point the trunk is recruited as an additional spring enabling more energy to be stored elastically. It is concluded that we must consider what muscles are doing during normal modes of locomotion before we become too involved in designing schemes of motor unit recruitment. INTRODUCTION Most of us think of muscles as biological machines which generate force, shorten, and perform mechanical work. We like to evaluate their performance in terms of how efficiently they can convert metabolic energy into mechanical work. Furthermore, those of us who are zoologists believe that natural selection has produced muscles which operate at near "maximal" efficiency during normal locomotion. We believe that patterns of recruitment of muscles and of motor units within muscles have evolved which enable muscles to operate near their maximal efficiency as the forces exerted by the muscles increase with increasing speed. There is no question that this view of muscular function has served us well and led us to uncover important generalities. In classic studies, Henneman and his colleagues (Henneman and Olson, 1965; Henneman,?( al., 1965) demonstrated an orderly recruitment pattern of motor units within a muscle that was dependent on the force exerted by the This work was supported by NIH Grant #AM to C. Richard Taylor and NIH Grant #AM to Robert Armstrong. muscle. Small units, innervated by small motor neurons, were recruited at low tensions. Larger units were progressively recruited with increasing force. A similar sequential recruitment of fibers with increasing force and velocity has been observed in bicyclists by Gollnick, et al. (1974). Using glycogen depletion as evidence of fiber activity, these authors found that slow oxidative fibers were utilized at low forces and velocities, and larger fast gylcolytic fibers were added with increasing force and velocity. All of these experiments, however, have involved relatively simple muscular events. The active muscles either generated isometric tension or shortened. During normal modes of terrestrial locomotion active muscles are stretched and may store energy which is subsequently recovered. Under these circumstances the concepts of muscular efficiency and orderly recruitment of motor units may cloud, rather than clarify, our understanding of how muscles are operating. In this paper, I should like to consider the different mechanical mechanisms associated with the various gaits that terrestrial animals use as they move along the 153

2 154 C. RICHARD TAYLOR ground and to show that these mechanisms involve different types of muscular activity. Then I should like to hypothesize that the changes in muscular activity which occur as animals change from a trot to a gallop involve switching from a smaller to a larger spring. Finally, I should like to discuss some experiments that this hypothesis has suggested and to review the results of these experiments in light of our "two-spring" model. PENDULUMS AND SPRINGS In recent studies, Cavagna, et al. (1977) have found that terrestrial vertebrates change mechanical mechanisms for minimizing the energy expenditure of their muscles as they change gait. Walking in bipedal birds and mammals and in quadrupedal mammals involves an alternate exchange between kinetic energy and gravitational potential energy of the center of mass within each stride, in a manner analagous to an inverted pendulum. As much as 60-70% of the absolute energy changes involved in raising and reaccelerating the center of mass of an animal within each stride may be accounted for by this exchange, and only the remaining 30-40% need be supplied by the muscles. Running, trotting and hopping involve a spring-type mechanism for minimizing energy expenditure by the muscles. This type of mechanism involves stretching of active muscles and tendons during part of the stride when an animal decelerates and brakes its fall, allowing for a storage of energy in these elastic elements. This stored energy is then recovered during the subsequent part of the stride when the animal reaccelerates upwards and forwards. Galloping involves a combination of these two mechanisms at lower speeds, with the spring becoming progressively more important, until at the highest galloping speeds, the animal "bounces" first on its front and then on its rear legs. The evidence for the spring mechanism came from a comparison of mechanical power output with metabolic power input. Storage and recovery of energy in elastic elements had to be evoked when the mechanical power output of the animal exceeded the metabolic power input to the muscle (assuming 75% of the energy was lost before it could be used by the muscle).' Not surprisingly, the hopping kangaroo provided the best evidence for the spring mechanism. The kangaroo was the obvious choice for a comparative physiologist wanting to study elastic storage and recovery of energy. T. J. Dawson, of the University of New South Wales in Australia, spent part of a sabbatical year in my laboratory and brought with him some big red kangaroos. We trained these animals to hop on treadmills while we measured the rate at which they consumed oxygen (Dawson and Taylor, 1973). Using the energetic equivalent of 4.8 cal/ml O 2, we were easily able to convert the rate at which the kangaroo consumed oxygen into metabolic power input. We were quite surprised to find that once the kangaroo began to hop (at a speed of approximately 7-8 km/hr), metabolic power input remained about the same or even decreased slightly as the animals increased speed (up to km/hr, which was as fast as our treadmills would go) (Fig. 1). When we had a measure of metabolic power input of hopping kangaroos, what we needed was a measure of mechanical power output. Giovanni Cavagna of the University of Milan in Italy, had designed and constructed a series of force plates which could be used as an ergometer to measure the work involved in height and speed changes in the center of mass of an animal as it ran along the ground (Cavagna, 1975). Cavagna, who has pioneered in studies of elastic storage of muscles, was enthusiastic about hopping kangaroos across his force plate, so a graduate student, Norman Heglund, and I packed up our kangaroos, as well as a variety of other mammals and bipedal birds and headed for Milan. We were not disappointed with the results of this trip. 1 Approximately 2/3 3/4 of the energy contained in carbon-carbon bonds is lost in the production of ATP. It seems most reasonable to calculate muscular efficiency in terms of energy contained in the ATP that is used to produce mechanical work, as is usually done in in vitro muscle studies.

3 SPEED, GAIT, AND ACTIVITY OF MUSCLES A. OXYGEN CONSUMPTION CM o ii.o 'i CO 1 ' o ^ i 1 I I 1 I h. B. STRIDE FREQUENCY H h H I I 1 I h C STRIDE LENGTH entapedol FIG. 1 Once a big red kangaroo (MegaUia rufa) started to hop, steady state oxygen consumption (top) and stride frequency (middle) changed only slightly as speed increased from 7 to 25 km/hr. An increased 10 SPEED hopping- 15 km-hr stride length (bottom) accounted for most of the increase in speed (reproduced from Dawson and Taylor, 1973 with permission of the authors and the editors of Nature). We found that the kangaroo is indeed an elastic animal and that at a speed of 30 km/hr the muscles are supplying only 1/3 of the power required to lift and reaccelerate the center of mass within each stride. The remaining 2/3 of the power plus all of the power required to move the limbs relative to the center of mass had to be stored elastically in one part of the stride and recovered during another. From these studies (Cavagna, et al., 1977) and other studies by Cavagna and his colleagues on

4 156 C. RICHARD TAYLOR humans (Cavagna and Kaneko, 1977; Cavagna, et al., 1964) it seems possible to conclude with certainty that humans, dogs, monkeys, and springhares, as well as kangaroos, rely on power recovered from elastic elements as they run, trot, gallop, or hop. CHANGING FROM TROT TO GALLOP: ADDING SPRINGS? Both trotting and galloping involve a spring mechanism, but are the same muscle groups involved in the elastic storage? We have come to believe that animals switch from smaller, stiffer springs to a longer, more compliant one as they change from a trot to a gallop. What led us to this belief? Again it was the kangaroo that started us thinking about a two spring system. The kangaroo hopped at almost the same frequency over the entire range of speeds that we studied (Fig. 1). Its hopping frequency increased by less than 5% as the animal doubled speed. This constant frequency was very suggestive of a resonant spring system, but where was the spring? Since the large Achilles tendon loaded and unloaded quickly when the foot was in contact with the ground, it was hard to see how it could function as a resonant spring system which determined stride frequency. We interested T. A. McMahon from the Division of Engineering and Applied Physics at Harvard in this problem and looked around for a mechanical analog. A man on a pogo stick seemed a good first approximation of a kangaroo, the spring of the pogo stick taking the place of the Achilles tendon. This pogo system had the advantage of enabling us to replace the spring with a stiffer or a more compliant one. We found that changing the spring stiffness had little effect on hopping frequency. In fact, the hopping frequency remained about the same even when we took away the pogo stick. Then it dawned on us that it was probably the bending of the back that was setting frequency. Now hopping in bipeds seemed remarkably like galloping in quadrupeds widi the bending trunk serving as a large compliant spring in both cases. We decided to measure galloping frequency in all the animals around the lab which would gallop on a treadmill. We found that once an animal started to gallop, its frequency remained nearly constant as speed increased (Fig. 2), just as we had found with hopping frequency in the kangaroo (Heglund, et al., 1974). Galloping frequency varied widi the size of the animal and was proportional to (body weight)" 014 (Fig. 3). Much to our delight, the bipedal kangaroo hopped at about the same frequency at which a quadruped of the same weight galloped (Fig. 3). T. A. McMahon developed a dimensional argument to show how resonant frequency would vary with body size if the trunk and limbs were a large multi-jointed spring (McMahon, 1975). His analysis predicted that frequency for a resonant spring system would vary as (body weight)" 0125, very close to our results. Why do animals switch from a trot to a gallop? We formed a rather simplistic model of a two spring system to explain the change in gait. During running or trotting we hypothesized that the springs are the muscles and tendons of the limbs. As animals increase speed, the time of contact with the ground decreases and the force exerted increases. An animal would need a stiffer spring in order to store additional energy as it ran at higher speeds. As an animal increased its speed within a trot it could increase the stiffness of the spring system by recruiting more fibers in its limb muscles. However, some point would be reached where a bigger spring should be recruited to store more energy. We postulated that this point occurred when animals changed from a trot to a gallop (Heglund' et al., 1974). The bending trunk seemed an attractive candidate for our bigger spring. The limbs could be considered as springs in series with the trunk during a gallop. More energy could be stored in a larger displacement of this longer, more compliant spring. As the animal increased its speed within a gallop the stiffness of this larger spring could increase in the same manner as the stiffness of the smaller limb springs had within a trot.

5 SPEED, GAIT, AND ACTIVITY OF MUSCLES 157 WALK g MOUSE 360g RAT SPEED FIG. 2 Stride frequency of mouse, rat, dog and horse as a function of speed. The relationship between speed and stride frequency changes from gait to gait. Once an animal begins to gallop, stride frequency changes very little with increasing speed. The TESTING OUR MODEL This simplistic two spring model of trotting and galloping is useful only in as far as it suggests experiments to test it. We have investigated three of the models' predictions. First, muscles should become active while they are being stretched if they are to store energy elastically. This activity should occur in the limb muscles, both as the animal decelerates and brakes its fall during the stance phase and just before reversal of limb direction during the swing phase. This type of muscular activity should become more important as force, power and elastic storage increase with speed. Secondly, some trunk muscles should be recruited when an animal starts to gallop. Thirdly, there should be a redistribution of elastic storage from the limbs to the trunk resulting in a decreased cross sectional area of active muscles in the limbs as the animal changes from a trot to a gallop. Howard Seeherman, Xorman Heglund, Cynthia Allen, Peggy McCutchin and I 9200 g DOG km- hr" TROT GALLOP O TROT-GALLOP TRANSITION ,000 g HORSE trot-gallop transition is marked with a large open circle (reproduced from Heglund, el al., 1974 with permission from the authors and the editors of Science). have measured the electrical activity of major limb and trunk muscles of dogs as a function of speed and gait while they ran at a constant average speed on a treadmill. We have found two pieces of evidence which support our spring hypothesis (unpublished observations). In a number of the muscles where elastic storage is possible, we have found that as an animal increased speed the muscle was active for a proportionally greater fraction of time while it was being stretched. The firing of the biceps femoris provides a good example of an increase in this type of activity during reversal of direction of the limb (Fig. 4). We also found the predicted recruitment of trunk muscles: the iliocoslalis lumborum was inactive at a walk and a trot, and became active at a gallop. Both of these observations are in accord with the predictions of our two spring model. One of the most interesting predictions of our hypothesis is the decrease in cross sectional area of active muscles as animals change from a trot to a gallop. But how does one measure the cross sectional area

6 158 C. RICHARD TAYLOR GALLOPING SLOPE -.14 o 3 io z MICE ^ _ RAJS " DOG 10 IO J BODY WEIGHT FIG. 3 Stride frequency at the transition point from trot to gallop (see Fig. 2) plotted against body mass on logarithmic coordinates. The relationship is: f = 269 W~ 14 where f is strides per minute and W is body mass in kg. The correlation coefficient for this line ~- i J>OGS KANGAROOS 3 10" (grams) - ORSES of active fibers in an animal as it trots and gallops? Robert Armstrong of Boston University suggested that we might biopsy muscles as an animal trotted or galloped and use glycogen depletion within a fiber as evidence of fiber activity. We selected the dog as our first choice for an experimental animal because it ran so well on a treadmill and was extremely tractable. We ran the dogs and took muscle biopsy samples at rest and after running. After about six months of hard work, we found that this technique could not be applied to dogs. Their muscles simply didn't deplete enough glycogen to see any recruitment pattern. At this point we decided to look for an animal in which all of the muscle fibers relied extensively on glycogen as a substrate during locomotion. Pamela Chassin, an undergraduate student working in my laboratory, had just found that lions exceeded their maximum aerobic capacity as they switched from a walk to a trot (Chassin et al., 1976). Here were anicalculated by the method of least squares is Data for kangaroo hopping frequency from Davvson and Taylor, 1973 superimposed on the graph as open circles, but was not used in the linear regression (redrawn from Heglund, et al., 1974). mals whose muscles must rely extensively on glycogen as a substrate during all of their trotting and galloping speeds. For this reason we switched from dogs to lions as experimental animals, and we focused on changes in glycogen depletion patterns at the trot-gallop transition. Working with lions turned out to be no picnic, particularly while we were taking samples of their muscles (a procedure which seemed to engender a hearty dislike of the experimenters by the lions). We were limited to young animals where we were still able to keep the upper hand. For these reasons, we sampled only two muscles, the biceps femoris and the long head of the triceps brachii. We found marked discontinuities both in types of fibers and in the cross sectional area of muscle showing depletion as animals changed from a trot to a gallop (Armstrongs al., 1977). In the triceps we found significant rates of glycogen depletion in the fast glycolytic fibers at a fast trot, but not at a slow gallop

7 m. biceps femoris WALK km-hr" 1 j S O TROT-8.3 km hr"' m foot dam I 0» GALLOP-24.8 km hr H footdowi I I (ran foot IB I franw*il2 fool down tranm I (ram* "Mi mw FIG. 4 Electrical activity and changes in length of the biceps femoris at a walk, trot, and gallop. The relative importance of muscular activity while the muscle was being stretched increased with increasing speed, and the activity while the muscle shortened became relatively less important (unpublished data from our laboratory),

8 160 C. RICHARD TAYLOR Triceps Brachii M WALK Biceps Femoris M 10 TROT 10 SPEED (km % hr- 1 ) GALLOP FIG. 5 Rate of glycogen depletion from each of the three types of muscle fibers (triangles represent fast glycolytic, squares fast oxidative, and circles slow oxidative fibers) of triceps brachii and biceps femoris muscle of a lion as a function of speed and gait. The fast glycolytic fibers of the triceps became active as trotting speed increased, were inactive at a slow gallop, and became active again at a fast gallop. This is in accord with the two spring model discussed in the text. The depletion patterns observed in the biceps femoris muscle are puzzling, however, it would not form part of the two spring system (reproduced from Armstrong, et al. (1977) with permission of the authors and the editors of J. Appl. Physiol.). (Fig. 5). All of the glycogen loss during the slow gallop occurred in the oxidative fibers. The cross sectional muscle area of the triceps showing depletion decreased from 60% of the muscle to 28% as the lion switched from a fast trot to a slow gallop (even though it was moving at a higher speed relative to the tread) (Fig. 6). It then increased to about 45% as the animal increased its galloping speed. The depletion pattern in the biceps femoris was quite different than the pattern we observed for the triceps. Rates of depletion in the two fast twitch fiber tvpes were relatively high a: the slower speed in each gait, but then declined as the lions increased their speed within the gait (Fig. 5). The cross sectional area of the biceps showing glycogen depletion was fairly constant throughout the entire range of trotting speeds at about 19% of the muscle (Fig. 6). It was elevated during a slow gallop to about 29% and then declined at an increasing galloping speed to about 12%. The results from the triceps are in accord with the predictions of our two spring model. This is one of the muscles which the trotting or galloping animal would "bounce" on as it lands and then take off again. The results from the biceps femoris are puzzling. This muscle would not make up part of the 2-spring system, but should be involved in storing and then recovering energy as the rear limb reversed its direction. While the results from our glycogen depletion studies on lions are tantalizing, they are far from conclusive. We need to show that: similar recruitment patterns occur in other animals as they change from a trot to a gallop; that all of the active fibers show some depletion; and that if we in- % OF MUSCLE CROSS-SECTION SHOWING GLYCOGEN DEPLETION Triceps Brachii M I Biceps Femoris M 10 SPEED (km x hr 1 ) FIG. 6 Percent of the cross sectional area of triceps brachii and biceps femoris of a lion showing glycogen depletion at a walk, trot and gallop. The cross sectional area of the triceps showing depletion increased during a trot and dropped suddenly as the lion switched gait to a slow gallop. It then increased as the lion increased speed of galloping. This is in accord with the two spring model discussed in the text. The biceps femoris is included to show a more puzzling depletion pattern (reproduced from Armstrong et al. (1977) with the permission of the authors and the editors oij. Appl. Phyuol.). 20

9 crease the force exerted by a muscle, we can observe a corresponding increase in cross sectional area of active fibers. These are some of the problems that Ted Goslow, Bob Armstrong and I are currently working on. CONCLUSIONS It is clear that we have just begun to scratch the surface in our understanding of how muscles are functioning during normal locomotion. I hope that this paper has brought to your attention that all three types of muscular activity must be taken into account, i.e., when the active muscle shortens, stays the same length or is stretched. The relative importance of these different types of muscular activity changes as animals change gaits and perform different tasks. When a walking animal is "pole valuting" over its rigid limb, some muscles must keep the limb rigid. If muscles are to serve as springs, they must be active when external forces are acting on them in order to store energy. Muscles are going to have to shorten and provide the forces necessary for animals to accelerate and reach some constant speed. We must be careful neither to make locomotion so complex that it defies analysis, nor so simple that it defies reality. We must look to see what the animals are doing and then make reasonable simplifications as we design our experiments. SPEED, GAIT, AND ACTIVITY OF MUSCLES 161 REFERENCES Armstrong, R. B., P. Marum, C. W. Saubert IV, H. J. Seeherman, and C. R. Taylor Muscle fiber activity as a function of speed and gait. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 43: Cavagna, G. A Force plates as ergometers. J. Appl. Physiol. 39: Cavagna, G. A., N. C. Heglund, and C. R. Taylor Mechanical work in terrestrial locomotion: Two basic mechanisms for minimizing energy expenditure. Am. J. Physiol. 233:R243-R261. Cavagna, G. A., and M. Kaneko Mechanical work and efficiency in level walking and running. J. Physiol. (London) 268: Cavagna, G. A., F. P. Saibene, and R. Margaria Mechanical work in running. J. Appl. Physiol. 19: Chassin, P. S., C. R. Taylor, N. C. Heglund, and H. J. Seeherman Locomotion in lions: Energetic cost and maximum aerobic capacity. Physiol. Zool. 49:1-10. Dawson, T. J., and C. R. Taylor Energetic cost of locomotion in kangaroos. Nature. 246: Gollnick, P. D., K. Piehl, and B. Saltin Selective glycogen depletion pattern in human muscle fibers after exercise of varying intensity and at varying pedal rates. J. Physiol. (London) 241: Heglund, N. C, C. R. Taylor, and T. A. McMahon Scaling stride frequency and gait to animal size: Mice to horses. Science. 186: Henneman, E. and C. B. Olson Relations between structure and function in the design of skeletal muscles. J. Neurophysiol. 28: Henneman, E., G. Somjen, and D. O. Carpenter Excitability and inhibitability of motoneurons of different sizes. J. Neurophysiol. 28: McMahon, T. A Using body size to understand the structural design of animals: Quadrupedal locomotion. J. Appl. Physiol. 39: