Part I Muscle: The Motor

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Brian Bennett Willis
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1 Part I Muscle: The Motor Introduction The locomotor system of vertebrates may be considered as an ensemble of motors (the striated muscles) capable to transform chemical energy into mechanical energy by doing work on a machine (the skeletal levers of the limbs) that utilizes this work to promote the motion of the body relative to the surrounding. Of these two components of the locomotor system, the machine is certainly the simplest: a passive system having the function to equilibrate the external load with the force exerted by muscles. An important result of the machine to the goal of locomotion is to amplify the displacement, i.e. to make the displacement of the point where the external load is applied (for example at the extremity of the limbs) much larger than the displacement of the point where the muscular force is applied (the insertion of muscle on the bone). Obviously, the amplification of the displacement implies a reduction of the force since, neglecting friction, the mechanical work (force times displacement) must be equal at the input and the output of the lever system. The success of the machine in transforming the work done by muscles into a forward displacement of the body with a minimum of energy expenditure will be discussed in the second part of this book. Some aspects of the muscular function will be discussed in the first part. Before doing this however it is necessary to consider the general role that muscular function plays during locomotion. The Motor Function of Muscle If a muscle shortens the distance ΔL and lifts the weight P its force performs the mechanical positive work W + = PΔL. This function of muscle is that of a motor. A motor transforms a kind of energy into another. For example, the motor of a car transforms the chemical energy of fuel into mechanical energy by an explosion within the cylinder causing the displacement of the piston. Also the muscle transforms chemical energy into mechanical energy and heat (Fig. I.1). This transformation however takes place in a more silent and ordered way than in the

2 2 Part I Muscle: The Motor combustion engine. The chemical energy transformed is that of the energetic reserves (glycogen, lipids) maintained thanks to the introduction of food. For a better understanding of the meaning of this transformation, suppose that in the example of Fig. I.1 the weight lifted by muscle laid initially on a table. In this case, at the end of positive work, the gravitational potential energy of the weight is increased. This increase in mechanical energy outside the muscle could take place thanks to a decrease of the chemical energy at disposal within the muscle. The same reasoning holds when, rather than lifting a weight, the positive work done by muscle is utilized to accelerate a mass (increment of the kinetic energy of the mass) or to withstand friction (increment of the heat outside the muscle, i.e. increment of kinetic energy of the molecules of the surrounding). Fig. I.1 Motor function of muscle: force and displacement vectors overlap. The load is sufficiently small to allow muscle shortening while doing positive work. The mechanical energy created by muscle is found at the end of shortening as gravitational potential energy

3 Part I Muscle: The Motor 3 The Braking Function of Muscle The other muscular function, less studied and known, even if, as we will see, equally important, is that to work as a brake. This function takes place when an active muscle (i.e. stimulated, not relaxed) instead of shortening is forcibly stretched by an external force. In this case one says that the muscle performs negative mechanical work (more exactly one ought to say that the muscular force performs negative mechanical work). If the force stretching the muscle is F and the lengthening of the muscle is ΔL, the negative work is W = F ( ΔL). In this case, mechanical work is done on the muscle, not by the muscle, i.e. mechanical energy enters the muscle instead of leaving the muscle. In the preceding example, we can imagine that the weight, too heavy to be lifted, is laid from the table to the ground stretching the active muscle (Fig. I.2). The mechanical energy existing outside the muscle after the negative muscular work is less than that existing before, the difference being absorbed by the muscle working as a brake. However the muscle had to be active (not relaxed) to sustain the weight while laying it down on the floor. This activity requires the utilization of chemical potential energy. Therefore, also during negative work muscles consume chemical energy. The braking function of muscle takes place with a mechanism, not yet completely known, which is exceptional compared with that of other motors constructed by man. In fact during negative work the force developed by muscle is directed, as during positive work, towards the center of muscle. Nevertheless, during negative work the extremities of muscle are forcibly averted away from the center of muscle against their tendency to approach each other (for this reason negative work is also called eccentric and the positive work is also called concentric ). As if in a car the wheels were forced to turn backward forcing the pistons to move against the gas exploding in the cylinder, or a functioning electrical motor were not only stopped, but also forced to turn backwards as in a dynamo! Contrary to these paradoxical cases, forcing the muscle to lengthen against the force it exerts is a normal physiological requirement, taking place without muscle damage, a requirement, which, as we will see below, is essential to accomplish most common activities. When Muscles Work as a Motor and When as a Brake? A General View We can classify all muscular exercises on the basis of the ratio between negative and positive work done by the muscular force as qualitatively shown in Fig. I.3. It can be seen that only in some exercises the muscular force performs almost solely positive work, namely the ratio between negative and positive work approaches zero, W /W + 0. In some of these exercises most of the positive work done by the muscles is dissipated by external friction, as in pumping blood by the heart, during respiration, in swimming or in some kind of flying, such as soaring. In other exercises positive work is done to increase the average gravitational potential energy of the body or of other objects (for example in uphill locomotion), or to increase the average

4 4 Part I Muscle: The Motor Fig. I.2 Braking function of muscle: force and displacement vectors have opposite direction. The load is too large to be lifted or even sustained by the active muscle, with the consequence that the weight lengthens the muscle: the muscular force performs negative work. During lengthening the gravitational potential energy is absorbed by the contracting muscle and transformed in part into heat. The transformation into heat is complete at the end of the lowering of the load and after muscle relaxation

5 Part I Muscle: The Motor 5 kinetic energy of the body or of other objects, (for example at the start of a race), or to increase the elastic potential energy of some structures (for example to expand the lungs during inspiration). However, locomotion uphill, start of the race and breathing are indicated in Fig. I.3 at a value of W /W + > 0 because also in these exercises the braking function of muscles may be appreciable. For example, during quiet breathing the muscles perform positive work (during inspiration) but also negative work (at the beginning of the expiration, see Fig. I.4) with the result that W /W + = 0.25 (Agostoni et al. 1970). Negative work becomes obviously preponderant, W /W + > 1, when the average mechanical energy of the body decreases, as in downhill locomotion or at the end of a race (right-hand of Fig. I.3). In the center of Fig. I.3 is indicated an important class of exercises where the negative work done by the muscles almost equals the positive work, i.e. W /W + 1. This class of exercises includes all kinds of legged terrestrial locomotion (walk, run, trot, gallop, hopping, etc.) provided that locomotion takes place on the level and at a constant speed (as we will see the instantaneous forward velocity of the body is not constant during the step: with constant speed we indicate that the average velocity during the step is unchanged in successive steps). During running on the level at a constant step-average speed we feel our muscles contracting actively and our energy expenditure is evidently increased relative to the resting condition indicating that muscular force performs positive work. What is used for the positive work done by the muscles? Air resistance is negligible except at high running speeds (Hill 1928) and no work is done against the frictional force on the ground if no skidding takes place. In fact work is force times displacement and if the foot does not move relatively to the ground the work done against the frictional force offered by the ground is nil. It is not nil when we run on sand and, in fact, we feel the difference (Lejeune et al. 1998). Therefore, a negligible amount of the positive work done by the muscles is dissipated against external friction. Since gravitational potential energy and kinetic energy of the body are unchanged at the end of the run on the level at a constant step-average speed, the positive work done by the muscles is found neither as an average increase in gravitational potential energy, as when climbing a hill, nor as an average increase in kinetic energy, as at the start of a race. Where does it go? The answer is that positive work done by the muscles is used to increase temporarily the kinetic and/or the gravitational potential energy of the body and of the limbs (in one phase of the step), but subsequently these energies return into the muscles themselves when these decelerate and/or lower the body with a braking action on the body and the limbs (negative work) in another phase of the step. In other words, in terrestrial locomotion on the level at a constant step-average speed, the muscles create mechanical energy to destroy it immediately after: this, as we will see, decreases the efficiency of legged terrestrial locomotion relative to other kind of locomotion as some type of flying and swimming. In conclusion, the schema of Fig. I.3 shows that the combination of the motor and braking functions of muscle is a general condition, taking place in a variety of exercises. This fact implies two questions, which open two important lines of

6 6 Part I Muscle: The Motor research: why the braking function of muscle takes place and what consequences it implies in the muscular function. An answer to the first question is searched with the study of the mechanics of locomotion; the second with the study of muscle physiology. Interaction Between Motor and Braking Functions of Muscle As mentioned above, the physiology of muscular contraction has been mainly studied in experimental conditions similar to those found in exercises classified in the left extremity of Fig. I.3 (execution of positive work only, Fig. I.3). In all the other cases not only chemical energy, but also mechanical energy enters the muscle while active, and the question arises if and to what extent, this mechanical energy input, taking place during negative work, modifies muscular function during the subsequent positive work. In other words, does the muscular contraction when only positive work is done follow the same laws as when negative work is done before positive work? As we will see, these laws differ appreciably. However, the Fig. I.3 Only in few exercises muscular force performs almost solely positive work (motor function, left) or almost solely negative work (brake function, right). In most cases, both positive and negative work are done, indicating that negative work is not only a laboratory maneuver, but also a common physiological function of muscle, particularly exploited in terrestrial locomotion

Part I Muscle: The Motor 7 Fig. I.4 The left panel shows the tidal volume (upper tracing) and the electrical activity of the diaphragm (lower tracing) during quiet breathing of man (courtesy of Citterio and Agostoni).

7 Part I Muscle: The Motor 7 Fig. I.4 The left panel shows the tidal volume (upper tracing) and the electrical activity of the diaphragm (lower tracing) during quiet breathing of man (courtesy of Citterio and Agostoni). The diaphragm performs positive work during inspiration, negative work during the first part of the expiration and relaxes before the following phase of positive work. This succession does not allow recovery of energy eventually stored within the muscle during the negative work phase since any possible potential energy is converted into heat during relaxation. On the contrary this recovery is possible in a jump (right panel) when the activity of the extensors of the leg (lower tracing) takes place during the lowering (negative work) and the lift (positive work) of the center of mass of the body (upper tracing) without relaxation between the two phases (From Cavagna et al. 1971) modification of muscular contraction induced by negative work takes place only in those exercises where positive work follows negative work without relaxation of the muscle. Consider the two examples of Fig. I.4. During quiet breathing the diaphragm contracts actively doing positive work during the inspiration (as indicated by the electromyographic record below the spirometric record), does negative work at the beginning of the expiration and subsequently relaxes before the successive phase of positive work. In this case the mechanical energy absorbed and possibly stored by the muscle during negative work will not modify its contraction during positive work. In fact, the muscle returns to its initial condition during relaxation and forgets any possible effect of the mechanical energy input. In case of a jump, on the contrary, the mechanical energy which enters the muscles during the lowering of the center of mass of the body (negative work phase) has the possibility to modify muscular contraction taking place immediately after during the lift of the center of mass (positive work phase), without relaxation of muscles between negative and positive work. The effect of negative work relies on several other factors that will be discussed later on, such as the velocity and the amplitude of the length change of muscle during stretching and subsequent shortening, the time interval between negative and positive work, the average muscle length, the amount of muscle activation and the

8 8 Part I Muscle: The Motor temperature. All these conditions are established by the mechanics of the exercise. The schema of Fig. I.3 shows that, ceteris paribus, the effect will be larger the greater the ratio W /W + (therefore the effect will be greater in running than in cycling). On the other hand, in exercises were this ratio is the same (e.g. walking and running on the level at a constant step-average speed), the conditions to attain the maximum effect of the mechanical energy absorbed by the muscles may differ considerably (as we will see these conditions are different in running and in walking). In the first section of this book (Muscle), the muscular function will be analyzed in two parts. The first part will explain the mechanics of muscular contraction without a previous input of mechanical energy (extreme left of the schema in Fig. I.3). The second part will describe the mechanics of muscular contraction taking place after an input of mechanical energy (a condition that will increasingly apply moving from left to right in the schema of Fig. I.3). Methods classically used to study the mechanics of muscular contraction (isometric, isotonic, isovelocity contraction and quick-release), and essential of the functional anatomy of muscle are first briefly described. I leave to the Methods section of papers quoted in this book the description of more sophisticated procedures aimed to study muscular function at a molecular level (laser trap, x-ray). A second section of this book (Locomotion), will describe different types of legged terrestrial locomotion, in humans and animals grouped in the two basic mechanisms of walking and running. An attempt is made, where possible, to explain, at least qualitatively, some characteristics of locomotion on the basis of the properties of muscular contraction analyzed in the first section. References Agostoni E, Campbell EJM, Freedman S (1970) The mechanical work of breathing. In: Campbell EJM, Agostoni E, Newsom Davis J (eds) The respiratory muscles, 2nd edn. Lloyd-Luke, London, pp Cavagna GA, Komarek L, Citterio G, Margaria R (1971) Power output of the previously stretched muscle. Med Sport 6: Hill AV (1928) The air-resistance to a runner. P Roy Soc Lond B Bio 102: Lejeune TM, Willems PA, Heglund NC (1998) Mechanics and energetics of human locomotion on sand. J Exp Biol 201:

Brawn behind performance. John Milton BIO-39

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