Muscle Mechanics Bill Sellers Email: wis@mac.com This lecture can be found at: http://mac-huwis.lut.ac.uk/~wis/lectures/ Muscles are not straightforward linear tension generators but behave in quite unexpected ways. This lecture looks at how muscles perform: their mechanical properties and how they behave when they are generating tension. Figure 1 Testing muscle [Keynes & Aidley 2001] You can investigate muscle mechanics by evaluating the performance of a human subject but because you are working with a complex machine it can be difficult to interpret your findings. It is much simpler to work with isolated muscles that can be tested analytically in the laboratory. The traditional preparations shown in figure 1 usually use frog gastrocnemius muscles so they do not need to be kept warm and the muscle is tested in two modes: isometric where the length of the muscle is not allowed to alter, and isotonic where the load is kept constant. Isometric loading can be achieved in human subjects using a dynamometer grip strength dynamometers being the commonest device. Isotonic loading is achieved by lifting weights slowly. Figure 2 Muscle twitch & tetanus [Keynes & Aidley 2001]
In an isolated muscle experiment you have precise control over the stimulation of the nerve. If the nerve is given a single, short pulse as a stimulus then the muscle produces a characteristic response known as a twitch. This is a short spasm of contraction that rapidly generates a small amount of force and then declines to zero over a longer period. If a second stimulus is applied before the twitch has decayed to zero then you get a summation effect with a peak force that is higher than that of a single twitch: this is known as mechanical summation. If a third stimulus has a similar additive effect. If a slow train of stimuli are given then the force trace is like the one shown in figure 2 with the force reaching a bumpy plateau. With a faster train of stimuli a higher plateau is reached and the force curve is now smooth. This is known as tetanus. The frequency of stimulus required for a smooth response is the fusion frequency. Figure 3 Muscle fibre recruitment [Winter 1990] The stimulus frequency is not the only control over the tension generated. The size of the stimulus in an in vitro experiment controls the number of nerve fibres that get activated and hence the number of motor units that contract. This effect can be seen in vivo (figure 3). Electromyography (EMG) records the electrical activity of a muscle. If a muscle is contracting very weakly only a single motor unit may be activated. As tension is increased additional motor units get recruited. Figure 4 Size principle [Winter 1990]
The order in which motor units get recruited is not random. Smaller motor units get recruited first followed by larger ones (see figure 4). This makes sense because small motor units are used for fine control which is required at low forces. At higher forces small changes in force are not necessary. If big motor units fired off force you would not be able to apply very small forces at all. Figure 5 Contraction timing [Winter 1990] When a muscle is stimulated it does not instantly produce force. As can be seen from figure 5 there is a delay in tension production after electrical activity is detected. The force builds up to its maximum fairly slowly. Similarly there is a lag in tension reduction after electrical activity ceases. Figure 6 Length/Tension curve [Winter 1990] As we have seen previously the force that can be produced by a given muscle depends on the length of the muscle. This can be seen in figure 6 along with a diagram of the overlapping actin and myosin filaments that explain why this occurs. This diagram is actually a little misleading since it reports the force generated by active contraction of the muscle. This is not the only way that force is generated in the body.
Figure 7 Active and passive force [McGinnis 1999] A muscle consists of an active force generating component and a parallel connective tissue component. This connective tissue does not actively generate force but if it is stretched beyond its resting length it acts just like a rubber band and produces a passive, elastic force. Figure 7 shows the effect of both of these force generating elements on the actual force output of a muscle. As you can see forcibly stretching a muscle well beyond its resting length will generate a force higher than that produced by active contraction. Figure 8 Example of muscle stretch [McGinnis 1999] Figure 8 shows how the effect of muscle length can be demonstrated on the hamstrings. The hamstrings (except for the short head of biceps femoris) act over both the hip joint and the knee joint: they extend the hip and flex the knee. Thus when the hip is extended the muscle is already shorter than its resting length and unable to produce its maximum amount of force. If the hip is flexed then the longer hamstring are able to apply a higher force to flex the knee.
Figure 9 Force/Velocity curve [McGinnis 1999] As well as the length of a muscle having an effect on the maximum force it can generate, so does the contraction velocity. That means that if a muscle is contracting rapidly it cannot generate as much force as when it is stationary, and an even greater force is required to stretch a maximally active muscle (see figure 9). Figure 10 The effect of contraction velocity [McGinnis 1999] Figure 10 tries to make this clear. Imagine that you are bench pressing a heavy weight. The maximum weight you can lift off your chest rapidly is quite low. The maximum weight you can lift slowly is somewhat higher, and the maximum weight you can maintain the height of is higher still. An even higher weight will force you to lower it slowly. This relates exactly to graph in figure 9. A muscle applying force without shortening is known as an isometric contraction. A muscle applying force and shortening is a concentric contraction. A muscle applying force but being extended anyway is performing an eccentric contraction. Figure 11 Examples of concentric and eccentric muscle activity [McGinnis 1999] Concentric muscle activity is what we normally think about muscles doing. We do not think much about isometric activity but we use it all the time to maintain posture. Eccentric muscle activity is also common and is often used at the ends of activities to slow down movements and is obviously used in situations when energy is being lost such as walking down stairs or landing from a jump. Figure 11 shows some examples.
Figure 12 Fast and slow twitch muscles [Keynes & Aidley 2001] Just to make life more complicated it turns out that the contraction speed of muscle fibres is also not constant. Experiments on isolated muscles have revealed two distinct populations of muscle fibres that have different time courses for the basic twitch response: so called fast twitch and slow twitch fibres. Figure 13 Histology of muscle fibre types [Wheater et al. 1979] These different fibre types can also be identified by using stains that are specific for ATPase activity. It turns out that the fibres differ in their metabolism as well as their twitch response. Some muscle fibres are primarily used for rapid bursts of activity. These are (unsurprisingly) the fast twitch fibres and they obtain their energy using the anaerobic, glycolytic pathway. However this type of muscle fibre fatigues very quickly. It relies on locally stored glycogen for its energy source and this is rapidly depleted. It also produces lactic acid which is toxic and needs to be oxidised after the activity has finished this is the oxygen debt that sprinters build up. For slower, sustained activity slow twitch fibres operate aerobically. They can continue to produce force for long periods without significant fatigue. There is also a third type of fibre that has intermediate properties and can metabolise either aerobically or anaerobically. As you can see from figure 13 these fibre types have a variety of names. And as you should suspect from the fact that they are numbered there are some other fibre type subgroupings.
Figure 14 Fish musculature [Alexander 1992] Fibre types seem to depend on the muscle usage. Sprinters develop more fast twitch fibres and fewer slow twitch ones. The converse is true for long distance runners. Muscle biopsy is sometimes used to assess the fibre type composition of an athlete s muscles to check on the progress of training or rehabilitation. However human muscles are always fairly mixed in terms of fibre type: they always appear the same approximate colour overall. However some birds and fish have extreme fibre type compositions. Thus the dark meat of chicken legs is almost entirely slow twitch and the white meat in the breast is fast twitch. This corresponds to the fact that chickens are mostly terrestrial and they use their legs for sustained locomotion whereas their wings are for escape flights and need to contract rapidly but only for short periods of time. Birds such as pigeons that fly over longer distances have dark breast meat. In figure 14 you can see the two types of muscle in the body of a fish. The central dark area is slow, aerobic muscle that powers sustained swimming and the paler areas are fast, anaerobic muscle used for short bursts of speed (prey capture and escape). Figure 15 Muscle fibre arrangement [Netter 1997] The arrangement of the muscle fibres also has an important role to play. As you can see from figure 15 the muscle fibre direction is not always in the same direction as the line of pull of
the muscle. You can also see just how many individual muscles we have be glad this is not an anatomy course! Figure 16 Types of pennation [McGowan 1999] When the line of action of the muscle does not match the line of action of the fibres then the muscle is known as pennate. There are a number of sub-classifications illustrated in figure 16 but the important property of these pennate muscles is the angle of pennation: the angle between the two lines of action. Figure 17 Physiological cross-section area [McGinnis 1999] The maximum force a muscle can generate depends on its physiological cross-section area. In fact the maximum force can be calculated by multiplying the PCA by constant (approximately 20 to 100 N.cm -2 ). In a non-pennate muscle this is simply the area of a slice taken in the middle of a muscle perpendicular to the line of pull. However as can be seen from figure 17 this would miss some of the muscle fibres. In this case the cross-sectional area would need to be taken perpendicular (at right angles) to the average fibre direction so as to include all the fibres in the muscle.
Figure 18 Effect of pennation angle on cross-section area [McGinnis 1999] Figure 18 shows how the cross-sectional area is effected by the pennation angle but there is another factor that needs to be taken into account. The angle of pennation has increased the cross-sectional area but the line of pull is no longer the same as the line of pull of the muscle. To compensate for this we need to multiply by the cosine of the pennation angle (this will be 1.0 when the angle is 0 and 0.0 when the angle is 90 ). We can express these relationships as a series of equations: Equation 1. F max = PCA K Where F max is the maximum force the muscle can generate, PCA is the physiological cross sectional area and K is a constant (20 to 100 N.cm -2 ). For non-pennate muscles Equation 2. PCA = m / (ρ L) Where m is the mass of the muscle, ρ is its density (1.056 g.cm -2 ) and L is the length of the muscle fibres. For pennate muscles Equation 3. Where θ is the angle of pennation. PCA = m cos θ / (ρ L)
The length of the muscle fibres depends on the exact geometry of the muscle but tends to be much smaller in pinnate muscles so although cos θ is 1.0, the PCA of a pinnate muscle of given mass will be larger than the same sized non-pennate muscle. Figure 19 Some example PCA values [Winter 1990] Figure 19 shows how the pennation angle varies among some of the muscles in the hind limb. The high pennation angle of the calf muscles (Soleus and Gastrocnemius) allows them to produce more force for their size. Figure 20 Effect of pennation angle on length change [McGinnis 1999] In case you think that pennation gives you something for nothing it is worth remembering that the amount a muscle can contract depends on its fibre length. Muscles fibres can contract to about 60% of their resting length. Since the muscle fibres in pennate muscles are shorter than the non-pennate equivalent the amount of contraction is similarly reduced. In addition since the line of contraction is not the same as the line of action you need to put in the cos θ factor too. All in all pennation is a non-ideal mechanism. The most efficient option is to have the line of action parallel to the muscle fibres any angular difference means that energy (as we shall see later) is wasted producing tension in directions where it cannot be used. However the physical layout of the skeleton is such that we often need high absolute forces rather than contraction distance and pennation is a mechanism that allows this. Bibliography Alexander RMcN. Exploring Biomechanics. 1992 New York: Scientific American Library.
Keynes RD, Aidley DJ. Nerve and Muscle. 2001 Cambridge: Cambridge University Press. McGinnis PM. Biomechanics of Sport and Exercise. 1999 Chamapaign, IL: Human Kinetics. McGowan C. A practical guide to vertebrate mechanics. 1999 Cambridge: Cambridge University Press. Netter FH. Atlas of human anatomy. 1997 East Hanover, New Jersey: Novartis. Wheater PR, Burkitt HG, Daniels VG. Functional Histology. 1979 Edinburgh: Churchill Livingstone Winter DA. Biomechanics and motor control of human movement. 1990 (2nd ed.) New York: John Wiley & Sons.