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Quadrupedal Mechanics - Anatomy & Physiology (view source)
Revision as of 05:32, 1 May 2013
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:::::'''Fig 5.9 Contraction of a pennate muscle'''
:::::'''Fig 5.9 Contraction of a pennate muscle'''
:::::A fibre maintains a constant volume during contraction. Its areas of attachment to the tendons of origin and insertion are also constant. This figure shows a single muscle fibre with solid outlines in only two dimensions, stretched in (a) and contracted in (b). The following argument is, however, correct for a three dimensional structure. Because the area of the parallelogram shaped fibre is constant, its length of attachment x is constant, and its area is x. y, y = y'. Therefore although the individual fibres of the muscle increase in thickness during contraction, the pennate muscle as a whole does not.
:::::A fibre maintains a constant volume during contraction. Its areas of attachment to the tendons of origin and insertion are also constant. This figure shows a single muscle fibre with solid outlines in only two dimensions, stretched in (a) and contracted in (b). The following argument is, however, correct for a three dimensional structure. Because the area of the parallelogram shaped fibre is constant, its length of attachment x is constant, and its area is x. y, y = y'. Therefore although the individual fibres of the muscle increase in thickness during contraction, the pennate muscle as a whole does not.
=='''Muscle metabolism'''==
==='''Fast and slow twitch muscles'''===
Skeletal muscle fibres of mammals, with few exceptions, respond to stimulation by an electrical impulse arriving at their surface with a twitch. The impulse becomes propagated throughout the fibre, the fibre contracts as a unit, and then relaxes as a unit. This is in distinction to a non-propagated impulse found in the slow fibres of lower vertebrates, and in smooth muscle. The tension curves produced during a twitch are shown in Fig. 6.1, for single muscle fibres.
Mammalian muscles have a fibre population more or less clearly divided into two types, either fast twitch or slow twitch. Fast twitch fibres use energy for contraction at a higher rate than slow twitch fibres. They are useful where rapid movement is the main consideration. We should expect the muscles about to be used by the cat in Fig. 5.2 a to have a high proportion of fast twitch fibres, since rapid acceleration of the body mass, i.e. propulsion, is their prime function.
:::::'''Fig 6.1 Intrinsic speed of contraction of muscle fibres'''
:::::Twitch response in two types of muscle fibre of the gastrocnemius muscle of the cat, following an intracellular stimulation of motor neurons with a depolarizing pulse lasting 0.5 ms.
:::::'''Fig 6.2 Muscular deceleration'''
:::::As a horse lands from a high jump, the elbow is flexing slightly. The fibres of the triceps brachii muscle elongate while the crossbridges of its sliding filaments absorb the kinetic energy of the horse and convert it into heat. In preventing collapse of the elbow joint, the muscle does no mechanical work.
==='''Resistance involves work although no external work is done'''===
Some muscles have a high proportion of slow twitch fibres, using energy at a low rate. They are especially useful where a force slows down or movement prevention is required. This decelerating action requires relatively little energy, which is released as heat. The term "isometric", usually used to describe these fibres, is misleading, since this type of muscle action can take place while a muscle is being stretched, if the muscle is resisting stretch. This "braking" action of muscles occurs, for instance, in certain forelimb muscles when a horse lands from a jump (Fig. 6.2). Slow twitch muscle fibres usually predominate at sites where they are able to oppose the force of gravity, both in standing and moving animals, as in the example just given. In limbs, such postural muscles act over joints that would otherwise flex and cause the limb to collapse (Fig. 6.3).
Fast twitch fibres differ from slow twitch fibres in several ways. Fast contraction demands fast control of the stimulating mechanisms with in the fast twitch fibre: thus there is more sarcoplasmic reticulum in these fibres. There is also an enzymatic difference in the rate at which myosin adenosine triphosphate (ATP) is split. Fast twitch fibres have a high activity, and slow twitch fibres have a low activity of the enzyme myosin adenosine triphosphatase (myosin ATPase). Fortunately for the easy study of the contraction speeds of different muscles, a histochemical method exists that differentiates between the two fibre types. This is because each fibre type has a different myosin isoenzyme, the difference in the enzyme activity of which is exaggerated at a high pH. By this means, fast and slow twitch fibres can be visualised in histological sections (Fig. 6.4).
Muscles may have both propulsive and postural roles. Several muscles with broad attachments possess a high population density of slow twitch fibres nearest the pivot over which the muscle acts, and a high density of fast twitch fibres towards the periphery (Fig. 6.5). During standing or quiet walking, only the area of the semitendinosus muscle in which slow twitch fibres are dense is active (Fig. 6.6). The area dense in fast twitch fibres is recruited only during more violent activity. We have already discussed the mechanics of different areas of such a muscle (Fig. 5.4). The heterogeneity of fibre type distribution within a muscle may arise because of the necessity for fast twitch fibres to have a greater torque. Another advantage of this arrangement will be explained shortly.
:::::'''Fig 6.3 Limb posture'''
:::::Single joint muscles of the forelimb (a) and hindlimb (b) of a cat. The labels indicate the muscle, the osseous and tendinous structures assisting the postural function of the muscle, and the joint over which each muscle acts.
:::::'''Fig 6.4 Intrinsic speed and endurance of muscle fibres'''
:::::Transverse serial sections of the pig diaphragm, stained for myosin ATPase activity
:::::(a), a strong reaction indicating a high intrinsic speed of contraction, and succinate dehydrogenase activity.
:::::(b), a dense reaction indicating a high mitochondrial density and therefore high endurance. All slow twitch fibres have high endurance. Some fast twitch fibres have high endurance; others have low endurance. Single joint muscles form only a small part of limb muscle mass: most large muscles act over two joints
:::::'''Fig 6.5 Heterogeneous distribution of fibre types within a muscle'''
:::::Transverse section of the distal part of the thigh of a sheep, showing the variation in myosin ATPase low fibre population density within the semitendinosus muscle. The white region represents a density of 3 - 6%, mid pink area a density of 7 - 9%, while the dark pink area has 20 - 30% of all fibres within the region. Myosin ATPase low fibres, which depend entirely on an oxygen-supply for their metabolism, tend to lie closest to their blood-supply.
:::::'''Fig 6.6 Recruitment of fibres during various activities of a muscle'''
:::::Simultaneous electromyographic recordings from an area of the semitendinosus muscle of the sheep (Fig. 6.5) with a dense myosin ATPase low (AL) fibre population, and an area with a sparse AL fibre population density. In (a), the sheep is supporting weight on the limb, in (b) it is walking quietly and in (c) it is kicking violently.
==='''Adaptations for speed'''===
The speed with which a muscle can move a part of the body can be due to one or several of the following independent factors:
1.The rate of energy conversion within the fibres of the muscle, which affects the intrinsic speed of contraction of each sarcomere (Fig. 6.1).
2.The number of sarcomeres in series. When each sarcomere contracts simultaneously, the resultant effect is summation of the distance moved in unit time. A thin strap muscle therefore contracts, between origin and insertion, faster than a thick strap muscle or a pennate muscle of the same mass.
3.The angle of pennation, during a contraction (Fig. 5.7).
4.The skeletal attachments, which affects the torque of the muscle relative to the point of application of the force (Fig. 5.5).
==='''Fibres specialised for endurance'''===
There are only two characteristics of a single sarcomere of mechanical significance. The first is the intrinsic speed of contraction, already described. The second is the ability of the sarcomere to sustain a contraction during repetitive rapid stimulation, or tetanus. This ability has been called nonfatiguability, but might be better termed endurance. Endurance is directly dependent on the capacity of a sarcomere to derive energy by aerobic metabolism, whether from nutrients stored within the muscle fibre (intrinsic nutrients) or carried to the fibre in the blood (extrinsic nutrients).
Thus a typical high endurance fibre is relatively small to allow for diffusion of oxygen and nutrients, has a rich blood supply, an intrinsic nutrient supply that must be burnt aerobically (triglyceride), a high density of mitochondria, a high activity of enzymes of the tricarboxylic acid cycle (Fig. 6.7) and a high density of oxygen carrying pigment (cytochromes and myoglobin). Because of this last property, high endurance fibres provide the colouring of red muscles, and are sometimes called red fibres.
:::::'''Fig 6.7 Aerobic and anaerobic metabolism in muscle'''
:::::The dotted line excludes the metabolic processes in muscle that use an extrinsic source of energy and oxygen, and that require the removal of metabolites from the muscle fibre. Under these circumstances, 3 moles of ATP are regenerated per mole of glucose consumed. In contrast, 36 moles are regenerated per mole of glucose metabolised through the citric acid cycle. The latter process is, however, effective only if an adequate blood supply is available. This cannot occur for all muscles during all periods of activity.
==='''The relationship of endurance to function'''===
Endurance is a property especially desirable in slow twitch, decelerating fibres. Muscles or parts of muscles predominantly postural in function are therefore aerobic and red. The part of the muscle closest to the blood supply often contains a predominance of slow twitch fibres (Fig. 6.5); the fibres using oxygen and blood born nutrients aggregate near their source of sustenance.
But not only slow twitch fibres are frequently used muscles and therefore need endurance. Well used muscles such as the diaphragm and the extrinsic ocular muscles contain large numbers of fast twitch, aerobic fibres. Also most muscles contain a significant proportion of these fibres, particularly in animals with the opportunity or necessity for plenty of exercise.
Intrinsic speed of contraction and endurance are separate properties and can vary independently within particular muscle fibres (Fig. 6.4). A fast twitch fibre that is used frequently will be aerobic; otherwise it does not need a rich blood supply. An anaerobic fibre can satisfy an occasional demand for sudden powerful movements by deriving energy from an intrinsic glycogen store. Anaerobic energy production is only about one-tenth as efficient as aerobic energy production (Fig. 6.7). It is useful only when a good blood supply is not possible; there is far more muacle in a body to be continually supplied aerobically. The subsequent build-up of lactic acid constitutes an "oxygen debt" that can only be "paid" during a rest period.
==='''Endurance depends on muscle use'''===
A characteristic of animals reared without normal muscle usage, for example pigs and broiler chickens, is an abundance of muscle fibres with low aerobic capacity and associated pigment. In domestic pigs the deep red part of M. semimembranosus, for example, contains a high proportion of aerobic fibres that are used for posture and quiet propulsion even in a closely confined animal. In contrast with the superficial fibres that are all too seldom used for propulsion, and are very pale. A similar comparison can be made with the red leg muscles and pale wing muscles of broiler chickens. Yet another example is the endurance of a hare that with its red musculature can lead a pack of hounds for an hour, and a rabbit that, with a sudden burst of energy, finds a burrow and time to repay the oxygen debt of its pale musculature. Athletic ability and its improvement by training are also related to an improved aerobic capacity of muscles along with an accompanying cardiovascular fitness.
=='''Scaling effects on quadrupedal design'''==
==='''The problem of size'''===
The size of structures is limited by their function. All mitochondria, and all muscle fibres, generally the same size, regardless of the mature body size of the animal in which they are found. But the femur of a mouse and a horse are greatly different in size. What functional limits are there to the sizes of various structures? Why is the femur of a small animal readily repairable, whereas a fracture in the femur of a horse cannot usually be treated? For an explanation, it is necessary to understand how the basic dimensions of length, area and volume vary with the size of an object, and what the significance of each to function is.
==='''Isometry'''===
In Fig. 7.1 the length lb of an edge of cube b is twice the length la of an edge of cube a. The scale factor, f, relating a and b is 2. If instead of length, we compare areas, a face of cube b has 4 times the area of a face of cube a; the ratio of these areas is f2 = 4. And the volume of cube b is f3 = 8 times the volume of cube a. This result is true for any two similar shaped figures, regardless of their shape. Such figures are called isometric (Gr. isos, equal; metron, measure). Although even identical twins can virtually never be precisely isometric, in the natural world isometry is often a useful first approximation in the comparison of two organisms and their components. This can be true in a familiar example of different breeds of dogs.
Fig. 7.2 shows a Great Dane and a Fox Terrier, drawn to scale. The shape of their bodies is quite similar; their size difference differs by a scale factor f = 2. The ratio of two corresponding areas, such as the transverse sectional area of the semitendinosus muscle or the total surface area of the body, is f2 = 4. The ratio of two corresponding volumes, such as the volume of the thoracic cavity, the stomach or the left ventricle of the heart, is f3 = 8. The scale factor for the Great Dane and the Chihuahua is f = 4; in this case, corresponding areas have a ratio of f2 = 16 and volumes, a ratio of f3 = 64 between the two breeds.
:::::'''Fig 7.1 Isometric cubes'''
:::::An edge of cube (b) has twice the length of an edge of cube (a). The scale factor f = 2.
:::::'''Fig 7.2 Three approximately isometric breeds of dog'''
:::::Outline of a Great Dane (a), a Fox Terrier (b), and a Chihuahua (c). The height at the withers for each dog is = 80 cm, = 40 cm, = 20 cm. Therefore the scale factor for (a) and (b), and for (b) and (c) is f = 2; for (a) and (c) the scale factor f = 4.
==='''The strength of the small'''===
These geometrical relationships are important because some mechanical properties of the body depend on area, and some on volume. For example, since the overall density of animal tissues is similar, the weight of an animal depends on volume. The Fox Terrier weighs 6 kg. The Great Dane would therefore weigh 7 x f3 = 56 kg. We have argued that the strength of a muscle is proportional to the transverse sectional area of its fibres acting in parallel. Using the muscles of its forelimbs, neck and jaws, the Great Dane would therefore carry f2 = 4 times more weight in his mouth than the Fox Terrier. Relative to body weight, however, the Great Dane is weaker; his relative strength is f2/f3 = 1/f = 0.5 times that of the smaller dog.
Assuming isometry, the smaller an animal, the greater its relative strength. An ant can lift many times its own weight, not because it is differently constructed from a horse, but because it is smaller. In fact, a horse–sized animal constructed like an ant would be too weak even to left its legs.
==='''Energy, speed and endurance of isometric animals'''===
The assumption of isometry between animals enables us to make predictions. We have already stated that body weight should scale as f3, and that the strength of muscles, either singly or in total, will scale as f 102. But the work muscles can do (force x distance) is related to muscle mass (Chapter 5) and therefore scales as f3. Total body energy is therefore proportional to body mass M. During locomotion, this becomes converted to kinetic energy E:
E = Mv2, where v is velocity.
Both E and M scale as f3, v must therefore be a constant. Regardless of body size, isometric animals can propel their bodies at the same speed. Fig. 7.3 shows that this is to some extent true, for real animals.
During the hunt, what is the outcome of a tiny hare chased by larger hounds, chased in turn by even larger mounted huntsmen? The nutrient store of the body is also proportional to body mass. While maintaining maximum energy output, the time taken for nutritional exhaustion scales as f3, and since velocity is the same, the distance travelled before nutritional exhaustion scales as f3. The advantage of size is the ability to travel fast for longer. Small animals maintain prolonged activity only by continual nutritional replenishment. The size progression of hare, hound and horse must be reversed in terms of either athletic ability or cunning, if the hunt is to last long enough to be "sporting". Perhaps the only cunning the huntsman employs is to use the large nutritional stores of his horse!
:::::'''Fig 7.3 Top speed of mammals'''
:::::The cheetah, gazelles and antelopes are the fastest of all terrestrial animals. Another group of fast mammals include the horse, hound and hare. The slowest mammals include the mouse and elephant. In none of these groups does body size appear an advantage or a constraint to running speed.
==='''Proportional and disproportional development'''===
Isometry is a particular case of allometry (Gr. allos, other; metron, measure). Both terms relate to the measurement of the proportions of two components, or a component and the whole, during the development of an organism. Isometry refers to proportionate development, and allometry to disproportionate development. Development may be within a species, describing growth patterns (ontogenic allometry), or between species, describing evolutionary patterns (phylogenic allometry). Partly because body dimensions bear power functional relationships and partly because growth is a multiplicative process, it is convenient to study developmental patterns on logarithmic scales. When a double logarithmic linear relationship has a slope b=1, two weight components develop isometrically: when b < 1 or b > 1, they develop allometrically (Fig. 7.4).
:::::'''Fig 7.4 Relative growth of tissues in a beef carcass'''
:::::Total carcass muscle weight grows isometrically with body weight, since the slope of the regression on logarithmic scales, b, equals 1. For bone and fat, however, the slopes of the regressions lines are not equal to 1; bone grows slower and fat faster than the body as a whole.
:::::The values are for female Jersey cattle.
:::::'''Fig 7.5 Allometry of bones according to Galileo'''
:::::"To give a short example of what I mean, I once drew the shape of a bone, lengthened only three times, and then thickened in such proportion that it could function in its large animal relatively as the smaller bone serves the smaller animal; here are the pictures. You see how disproportionate the shape becomes in the enlarged bone. From this it is manifest that if one wished to maintain in an enormous giant those proportions of members that exist in an ordinary man, it would be necessary to find either much harder and more resistant material to form his bones, or else to allow his robustness to be proportionately weaker than in men of average stature; otherwise, growing to unreasonable height, he would be seen crushed by his own weight and fallen".
:::::Galileo Galilei: Discourses & Mathematical Demonstrations concerning Two New Sciences pertaining to Mechanics and Local Motions. 1638.
==='''Allometry and scaling'''===
Allometry is important mechanically if we recognise that developmental patterns in the musculoskeletal system arise because of scaling. Does a newborn animal differ in musculoskeletal proportions from an adult because of its size? Is a species of small size inevitably different in musculoskeletal proportions from a large maturing species?
The scaling problem that has interested investigators since Galileo (Fig. 7.5) is that while body weight scales as f3, the structures supporting it scale as f2. Many have followed Galileo to the conclusion that larger animals compensate by developing disproportionately more massive limbs. However, Fig. 7.6 shows that a million-fold increase in body weight is insufficient to reveal a consistent change in the proportions of forelimb bones of quadrupeds. Neither is the change in shape of the bones of the pig during a nearly one hundredfold increase in body weight from birth to maturity consistent with the idea of more massive skeletons in heavier animals (Fig. 7.7).
Postnatally, the proportion of bone in the body declines (Figs. 7.4 and 7.8). Apparently, an immature animal needs a greater proportion of its body as bone because growing bone is less mineralised. Bone mineral, however, maintains a constant proportion of carcass weight (Fig. 7.8). Muscle tissue, forming approximately 40% of the body mass, is too large a proportion of body mass to adapt by increasing this proportion. To scale with the same static muscle strength as a mouse, an elephant would need to be almost 100% muscle! In fact real mammals of different size, within and between species, have approximately the same muscularity (Figs. 7.4, 7.8 and 7.9).
:::::'''Fig 7.6 Bone proportions in terrestrial quadrupeds'''
:::::Animals can vary in size with no apparent necessity for changes in skeletal proportions.
:::::'''Fig 7.7 Postnatal change in shape of the radius and ulna of the pig'''
:::::The bones are drawn to the same length. Unossifiied regions of the immature bones are shown blue-grey. There is no apparent requirement for the bone in the adult to be more massive than that in the neonate.
:::::'''Fig 7.8 Postnatal growth of muscle and bone in the pig'''
:::::During a hundred-fold increase in carcass weight, from which the variable effect of adipose tissue has been removed, total muscle and the mineral content of the limb bones grow proportionately. "Bone", which here includes periosteal, cartilage and medullary tissues, comprises a greater proportion of the carcass in the immature animal than in the adult.
:::::'''Fig 7.9 Muscle and bone proportions in mature animals of different size'''
:::::There is no apparent need for animals differing in size as much as do dogs and horses, to support and propel themselves using a different proportion of muscle and bone in their bodies.
:::::'''Fig 7.10 The effect of body size on histochemical fibre type populations'''
:::::A schematic representation of the relative density of the myosin in ATPase low fibre type of fibre, as observed in transverse sections of the semitendinosus muscle of seven species of mammals. The density in the deep part of the muscle, as well as the extent throughout the muscle, of myosin ATPase low fibres increases with increasing size of the animal.
==='''A safely factor limits how fast limbs can move'''===
The problem is resolved if we accept that the total quantity of bone and muscle in an animal is related to dynamic rather than static function. For bone, the ability to absorb energy of impact during locomotion is much more critical than the ability to support a static load. This energy absorption ability is proportional to mass and scales as f3. If bones bore only static loads, it is the mouse, as it exists, that has the massive skeleton relative to the horse! For muscle, the rate of energy production is more critical than static strength. We have seen that maximum velocity is constant, regardless of body size (Fig 7.3). The limb movements of large animals must therefore be relatively slow. Supposing that a dog and a horse scale linearly at f=4, and run at the same speed, stride frequency, and hence the intrinsic speed of contraction of the muscles accelerating the limbs, is slower in the horse, scaling as 1/f = 1/4. The muscles of the large animal contract at a slower rate. It would be very dangerous for the horse if the limbs had the same stride frequency as the dog. Indeed large animals have a higher proportion of slow twitch fibres than smaller species (Fig. 7.10).
There is a safety factor that limits the rate of limb movement in larger animals. In order to support static loads, both the tissues supporting the animal, and the tissues propelling it, have no need for disproportionate development.
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[[Category:Musculoskeletal System - Anatomy & Physiology]]
[[Category:Musculoskeletal System - Anatomy & Physiology]]