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In torsion fractures, (Fig. 3.4 D) shear stress occurs over the entire shaft of a long bone, and is greatest at the periosteal surface. The result is a spiralling fracture.

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[[File:QMFig 3.4.png|thumb|'''Fig.3.4 Ways in which a long bone may fracture''']]

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:::::'''3.4 Ways in which a long bone may fracture'''

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:::::'''Fig.3.4 Ways in which a long bone may fracture'''

:::::The type of external load applied to a bone will determine the pattern of the fracture:

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::::::B Compression

::::::C Bending (tension and compression)

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::::::D Torsion (shear).

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::::::D Torsion (shear).

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==='''The role of tendons'''===

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'''Antifriction devices associated with tendons'''

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==='''Antifriction devices associated with tendons'''===

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[[File:QMFig 3.5.png|thumb|'''Fig.3.5 Structures reducing friction between tendon and bone''']]

Limbs are, of course, not straight, and the angles of joints can change markedly. Tendons allow the transmission of a force round these angles. The simplest way to smooth their passage is to provide a cushion. This is a bursa (Latin, wine sac made of goatskin), a pouch lined by synovial membrane and filled with synovial fluid. This lies between the tendon and the bone (Fig. 3.5 a), or it may wrap around the tendon to form a synovial sheath (Fig. 3.5 b). Sheaths are often held in place by transversely arranged collagenous structures, retinacula. A further adaptation occurs when the surface of the bone becomes changed to articular cartilage and forms one boundary of the bursal cavity. A pulley-like arrangement is formed (Fig 3.5 c).

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:::::'''3.5 Structures reducing friction between tendon and bone'''

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:::::'''Fig.3.5 Structures reducing friction between tendon and bone'''

:::::(a) to (d) represent increasing complexity

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::::::c. articular cartilage, bursa and retinaculum

::::::d. sesamoid bone, articular cartilage, synovial joint and collateral sesamoid ligaments

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==='''Shearing within tendons'''===

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==='''The lubrication of joints: multigrade specification'''===

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[[File:QMFig 3.6.png|thumb|'''Fig.3.6 The largest sesamoid bone''']]

The lubrication fluid of bursae, synovial sheaths and joints is secreted from protrusions of synovial membrane, synovial villi, located in loose parts of the joint capsule away from any compressed surfaces. This is synovial fluid. In a normal synovial sac, only a small amount of fluid is present. The viscosity of this clear or pale yellow liquid is more during slow movement, which is when the rate of shear is low. But when the shear rates are highest, the viscosity becomes much lower. The fluid drag and hence the supporting ability of the joint is therefore greatest when the limb is quietly bearing weight; the impedance is conveniently reduced for fast movements.

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:::::'''3.6 The largest sesamoid bone'''

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:::::'''Fig.3.6 The largest sesamoid bone'''

:::::The patella (b) is interposed in the tendon of insertion of the quadriceps muscles (a), that insert on the tibial tuberosity through the patellar ligament (c). The patella is held in place by collateral femoropatellar ligaments (d), and the hinge movement of the joint is maintained by the collateral femorocrural ligaments (e).

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==='''The resistance of joint surfaces to wear'''===

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==='''A muscle either makes movement, or prevents it: Action or heat?'''===

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[[File:QMFig 4.1.png|thumb|'''Fig.4.1 Muscle structure 1''']]

Forces produced within muscles achieve animal posture and motion. A muscle (Fig 4.1 a, b) consists of a large number of fibres (Fig 4.1 c) arranged in such a way that a force is developed between the two ends of the muscle when the fibres are stimulated by electrical impulses coming from nerves. This force may cause movement, but if the force is no greater than opposing forces either within the animal's body (i.e. from antagonist muscles) or acting externally on the animal's body (such as the force of gravity), no movement will result.

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:::::'''Fig. 4.1 Muscle structure 1'''

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:::::'''Fig. 4.1 Muscle structure 1'''

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:::::The semitendinosus muscle of a dog, as seen by the unaided eye (a & b), and in transverse section with the light microscope (c).

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:::::The semitendinosus muscle of a dog, as seen by the unaided eye (a & b), and in transverse section with the light microscope (c).

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==='''The contractile proteins of muscle''' ===

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~~===~~'''~~The contractile proteins of muscle~~''' ~~===~~

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[[File:QMFig 4.2.jpg|thumb|'''Fig.4.2 Muscle structure 2''']]

To understand the nature of a muscular force, we must appreciate the molecular and filamentous structure of muscle. Muscle is a machine largely constructed from two proteins, actin and myosin. Actin can exist in a globular form of molecular weight 45,000 and a diameter of 5.5 nm, which readily aggregates to form a long filament (Fig. 4.2 d), each filament contains two strands of spherical actin molecules, twisted on each other.

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:::::'''Fig.4.2 Muscle structure 2'''

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:::::'''Fig.4.2 Muscle structure 2'''

::::::Skeletal muscle fibre in longitudinal section;

::::::a, as visualised by the light microscope;

::::::b & c, by the electron microscope; and

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::::::d, as reconstructed from crystallographic X-ray

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::::::d, as reconstructed from crystallographic X-ray

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==='''The appearance of muscle using electron microscopy'''===

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==='''Sliding filaments and the site of the contractile force'''===

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[[File:QMFig 4.3.png|thumb|'''Fig.4.3 Sliding filaments in muscle''' ]]

Muscle contraction is caused by a sliding of the two sets of filaments past each other. The action sites are the crossbridges between the heads of the myosin molecules and the thin filaments. Crossbridges on opposite ends of the thick filaments are directed in opposite directions. Stimulation of activity at the crossbridges therefore creates a mechanical force tending to bring the thick and thin filaments into greater overlap, decreasing the distance between the Z discs, or sarcomere length, and shortening the muscle. The sarcomere is therefore the fundamental contractile unit of muscle.

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:::::'''Fig. 4.3 Sliding filaments in muscle'''

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:::::The sarcomere can normally contract to 44% of its fully stretched length. At its optimal length of 2.2 µm, the thin filaments are maximally in apposition with the crossbridges of the thick filaments.

==='''Linear motors'''===

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A muscle is a linear motor. Most man-made motors are not linear, since they take advantage of the wheel, a device not possible in animals. A man-made machine using a linear motor is the magnetic railway, where a magnetic field both lifts the train off the track, and provides a linear thrust. If we accept the fossil record, the muscle machine preceded electric motors and internal combustion engines, and indeed the also very modern invention of the wheel, by 70 million years.

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A muscle is a linear motor. Most man-made motors are not linear, since they take advantage of the wheel, a device not possible in animals. A man-made machine using a linear motor is the magnetic railway, where a magnetic field both lifts the train off the track, and provides a linear thrust. If we accept the fossil record, the muscle machine preceded electric motors and internal combustion engines, and indeed the also very modern invention of the wheel, by 70 million years.

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==='''The force of a muscle depends on sarcomere length'''===

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:~~::::'''Fig~~. 4.~~3 Sliding filaments in muscle~~'''

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[[File:QMFig 4.4.png|thumb|'''Fig. 4.4 Tension in muscle''']]

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~~:::::The sarcomere can normally contract to 44% of its fully stretched length~~. ~~At its optimal length of 2~~.~~2 µm, the thin filaments are maximally~~ in ~~apposition with the crossbridges of the thick filaments.~~

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~~==='''The force of a~~ muscle ~~depends on sarcomere length~~'''~~===~~

The dimensions of the sarcomere determine the extent to which muscle cells can be stretched or contracted. When fully stretched the sarcomere length cannot exceed 3.6 µm without the fibre losing the ability to contract again (Fig. 4.3). As the muscle contracts, more and more crossbridges are brought into use. The force produced increases (Fig. 4.4) until all the crossbridges between thick and thin filaments can be used. At this point, simply because of the dimensions of the filaments, the sarcomere length is 2.2 µm, i.e. 59% of the fully stretched length. This is the optimal length. With further contraction, no more crossbridges can be used, in fact there is interference by overlapping of thin filaments and the force produced declines. When the sarcomere length is 1.6 µm, the muscle can contract no further without penetration of the Z discs by thick filaments, and resulting damage. The sarcomere, and hence the entire muscle cell in which the sarcomeres are in series, is now 44% of the fully stretched length. These measurements made by electron microscopists can be verified by using a device as simple as a ruler, since they agree with measurements of the range of contraction of muscle fibres (and the macroscopically visible fibre bundles) in the limb muscles of animals.

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:::::'''Fig. 4.4 Tension in muscle'''

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:::::'''Fig. 4.4 Tension in muscle'''

:::::Tension is maximal at a sarcomere length of 2.2 µm. A muscle, therefore, will have only one optimal length for developing tension.

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==='''Getting the most out of restricted muscle performance'''===

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Similarly, we can consider two muscles in parallel (Fig 5.1 c). When they lift a weight W, each muscle shares the load. Hence each has half the load (W/2) and therefore contracts half the distance (d/2). It would take a load of 2W to make the muscles contract a distance d. So, if sarcomeres in muscle are arranged in parallel this would result in a doubling of the force produced, but the range of contraction in this case would be no greater than that of a single muscle.

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[[File:QMFig 5.1muscle.png|thumb|'''Fig 5.1 The effect of the strength of muscles in series and in parallel''']]

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:::::'''Fig 5.1 The effect of the strength of muscles in series and in parallel'''

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:::::'''Fig 5.1 The effect of the strength of muscles in series and in parallel'''

:::::A muscle contracts a distance d and lifts a weight W against gravity (a). When two such muscles are in series, the distance lifted is 2d (b). Each muscle is effectively loaded as in (a). When the muscles are in parallel, as in (c), the load is shared and the muscles can lift twice the weight 2W through their contraction distance d. Note that the work done (2d x W, or d x 2W) in lifting the weight by pairs of muscles is the same regardless of their configuration. Similarly the work done by a muscle depends on the number of contractile units (sarcomeres) within it (hence its weight), and not on the geometrical arrangement of the contractile units (or, in the arrangement shown in the diagrams, its shape).

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==='''Movement strength and work'''===

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==='''Movement, strength and work'''===

Range of contraction is therefore proportional to the number of sarcomeres in series, or the length of the muscle fibre. The force produced (strength) is proportional to the number of sarcomeres in parallel, or, since the contents of a fibre are predominantly myofibrils, to the transverse sectional area of the muscle fibre. The strength of muscle is approximately 0.3 MN.m–2 of transverse sectional area. Note that the work done by a muscle (force x distance) is the same in both cases (Fig 5.1). The possible work that a muscle can do, or mechanical energy that it can generate, is proportional to the total number of sarcomeres or, in other words, to the mass of the whole muscle.

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[[File:QMFig 5.2.png|thumb|'''Fig 5.2 Sarcomeres in parallel''']]

Consider two activities of a cat. A large force is required to accelerate the mass of the body from the position of crouching, ready to spring. The more sarcomeres that are in parallel, i.e. the greater the transverse area of the muscles brought into use, the greater the acceleration. A cat in this stance arranges its hind limbs and back to recruit as many as possible sarcomeres in parallel (Fig 5.2 a). It also positions each sarcomere at the optimum length for the development of a contractile force (Fig 4.3). You can easily observe this by watching a kitten at play, pretending to stalk and spring.

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A galloping cat protracts the forelimbs to lengthen the stride as much as possible (Fig 5.3). This movement demands of the muscles protracting the forelimbs a large range of contraction. The muscle involved must have as many as possible sarcomeres in series.

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:::::'''Fig 5.2 Sarcomeres in parallel'''

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:::::'''Fig 5.2 Sarcomeres in parallel'''

:::::In (a), a cat is crouching ready to spring. The propulsive force will be provided by the extensors of the vertebral column x, and the extensors of the hip y. These are the most massive muscles in the body, and a high number of their sarcomeres are therefore in parallel. The result of the contraction is seen in (b).

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[[File:QMFig 5.3.png|thumb|'''5.3 Sarcomeres in series''']]

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~~:::::'''5.3 Sarcomeres in series'''~~

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:::::In the stage of the gallop of the cat in which the forelimb is retracted, the brachiocephalic muscle (dotted line) is fully stretched (a). When the forelimb is protracted, (b) this muscle is fully contracted. During contraction of the muscle, the forelimb is not in contact with the ground; the muscle accelerates only the limb and not the whole cat. The emphasis is therefore on range of movement rather than strength; the sarcomeres in this muscle are therefore predominantly in series.

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:::::'''5.3 Sarcomeres in series'''

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:::::In the stage of the gallop of the cat in which the forelimb is retracted, the brachiocephalic muscle (dotted line) is fully stretched (a). When the forelimb is protracted, (b) this muscle is fully contracted. During contraction of the muscle, the forelimb is not in contact with the ground; the muscle accelerates only the limb and not the whole cat. The emphasis is therefore on range of movement rather than strength; the sarcomeres in this muscle are therefore predominantly in series.

==='''Each muscle is a unique organ delivering unique torques'''===

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[[File:QMFig 5.4.png|thumb|'''Fig 5.4 Torque in the elbow joint''']]

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Muscle fibres are incorporated into organs, which are recognised anatomically as muscles. These organs are separated by connective tissue sheets or fasciae that permit individual movement. Although several muscles might act over the same joint (for instance there are at least 17 named muscles acting over the hip joint of the dog), each muscle can be defined by its origin and insertion. This endows some joints with a variety of movements (Chapter 8), usually about a point at the centre of an arc about which the joint hinges or rotates. This point is therefore a joint pivot, and the muscles acting over the joint provide turning movements or torques in directions dependent on their skeletal attachments (Fig. 5.4).

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:::::'''Fig 5.4 Torque in the elbow joint'''

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:::::'''Fig 5.4 Torque in the elbow joint'''

:::::Torque is the product of the force and the perpendicular distance from the pivot it acts over. In this hinge joint, the pivot is in the centre of an arc formed by the condyles of the humerus. The protruding length of the olecranon process of the ulna (d) increases the torque (F x d) that the force (F) produced by the triceps brachii muscle is able to apply to the elbow in attempting to prevent the forced flexion of the elbow joint, as demonstrated here.

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==='''Torque and equilibria'''===

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In a state of equilibrium, the torques about a pivot balance each other in all directions. These torques usually include that produced by the force of gravity. The torque of postural muscles opposes the gravitational torque.

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[[File:QMFig 5.5.png|thumb|'''Fig 5.5 The effect of the site of muscle attachments''']]

:::::'''Fig 5.5 The effect of the site of muscle attachments on the torque produced by muscles over the hip joint'''

:::::The turning effect of a force about a pivot P, the torque, depends on the magnitude of the force and its perpendicular distance from the pivot d1, d2, d3 or l. In the diagram, the middle gluteal and the semimembranosus muscles turn the femur about the hip bone. Assuming the forces to be equal, the magnitude of the torque is greatest for the superficial part of the semimembranosus muscle and least for the middle gluteal muscle since d2 > d3 > d1. The torques of each of these muscles summate, and produce a propulsive force on the ground. The perpendicular distance of the propulsive force on the ground from the pivot, l, is much greater than the perpendicular distance of any muscle from the hip.

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[[File:QMFig 5.6.png|thumb|'''5.6 Strap muscles''']]

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~~:::::~~In propulsion, the torque of certain muscles at a pivot results in a force where the foot contacts the ground (Fig. 5.5). The propulsive force at the foot is less than the force of muscle contraction. The advantage is, however, that the range of movement at the foot will be greater than the range of contraction of any of the muscles. The power for propulsion comes from a concentration of forces about the hip (Fig. 5.2). Use the concept of torques to consider how limb design must optimise the muscular forces that accelerate hip extension, while optimising stride length. The properties of limbs are discussed further in Chapter 8.

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In propulsion, the torque of certain muscles at a pivot results in a force where the foot contacts the ground (Fig. 5.5). The propulsive force at the foot is less than the force of muscle contraction. The advantage is, however, that the range of movement at the foot will be greater than the range of contraction of any of the muscles. The power for propulsion comes from a concentration of forces about the hip (Fig. 5.2). Use the concept of torques to consider how limb design must optimise the muscular forces that accelerate hip extension, while optimising stride length. The properties of limbs are discussed further in Chapter 8.

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:::::Diagrammatic representations of two muscles of similar mass but different shape. Mechanical values are given for the muscles relative to 100 for the muscle a. The “functional transverse area” is indicated by the dotted lines. Tendons of origin and insertion must be related in thickness to the strength of the muscle in series with them.

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==='''Fibrous architecture of muscles'''===

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Muscles of the same shape can behave very differently

Figure 5.7 compares three muscles of the same mass, and the same general shape. Each of these muscles could fit into the same space in the body. If the fibres are parallel to the force vector of the whole muscle (Fig. 5.7 a), the number of sarcomeres in series is maximal, and the number of sarcomeres in parallel is minimal, for a muscle of this shape. The fibrous architecture of such a strap muscle gives maximal range of movement, and minimal strength.

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[[File:QMFig 5.7.png|thumb|'''Fig 5.7 Pennate muscles''']]

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[[File:QMFig 5.8.png|thumb|'''Fig 5.8 Extremes of pennation'']]

If the fibres are aligned at an angle to the force vector of the whole muscle (Fig. 5.7 b, c), the effective force and range of movement of each fibre is reduced since it is proportional to the cosine of this angle. Compared with Fig. 5.7 a, the number of sarcomeres in series has been reduced, and the number of sarcomeres in parallel has been increased. Thus the force has been increased in spite of the angulation of the fibres, but the range of contraction has been decreased. In the direction of the fibres, the work done during contraction is similar for the three muscles, since their mass is the same.

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:::::Diagrammatic representations of three muscles of similar mass but different shape but of widely varying fibrous architecture. Approximate values for range of contraction, force and work are given for the pennate muscles b and c, relative to those of the strap muscle a = 100, when the angle of pennation  = 25°. The "functional transverse area" is indicated by the dotted lines. Note that the effect of pennation has been to reduce the range of contraction and the work effective in the direction of contraction, but to increase the force. Note also that the more sarcomeres that are in parallel within the muscle, the more tendinous apparatus must be in series with it.

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:::::'''Fig 5.8 Extremes of pennation'''

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:::::'''Fig 5.8 Extremes of pennation'''

:::::The properties of a muscle vary with the proportion of collagen built into its architecture, even though its external appearance, as judged by its shape and size, remain much the same.

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Note that the decreased range of movement of a pennate muscle can be compensated for by an appropriate change in its skeletal attachments. (Fig. 5.5); a strong pennate muscle, such as the deep gluteal muscle, can still deliver an effective propulsive force at the foot even though its force is directed close to the pivot at the hip.

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[[File:QMFig 5.9.png|thumb|'''Fig 5.9 Contraction of a pennate muscle'']]

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:::::'''Fig 5.9 Contraction of a pennate muscle'''

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:::::'''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.

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<br />

=='''Muscle metabolism'''==

==='''Fast and slow twitch muscles'''===

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[[File:QMFig 6.1.png|thumb|'''Fig 6.1 Intrinsic speed of contraction of muscle fibres''']]

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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.

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:::::'''Fig 6.1 Intrinsic speed of contraction of muscle fibres'''

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[[File:QMFig 6.2.png|thumb|'''Fig 6.2 Muscular deceleration''']]

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~~::::~~:'''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.

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:::::'''Fig 6.2 Muscular deceleration'''

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:::::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.

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:::::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.

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==='''Resistance involves work although no external work is done'''===

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[[File:QMFig 6.3.png|thumb|'''Fig 6.3 Limb posture''']]

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).

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[[File:QMFig 6.4.png|thumb|'''Fig 6.4 Intrinsic speed and endurance in muscle fibres''']]

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).

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[[File:QMFig 6.5new.png|thumb|'''Fig 6.5 Heterogeneous distribution of fibre types within a muscle''']]

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.

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[[File:QMFig 6.6.png|thumb|'''Fig 6.6 Recruitment of fibres during various activities of a muscle''']]

:::::'''Fig 6.3 Limb posture'''

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:::::'''Fig 6.6 Recruitment of fibres during various activities of a muscle'''

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:::::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.

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:::::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.

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==='''Adaptations for speed'''===

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==='''Fibres specialised for endurance'''===

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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.

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[[File:QMFig 6.7.png|thumb|'''Fig 6.7 Aerobic and anaerobic metabolism in a muscle''']]

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:::::'''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.

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==='''The relationship of endurance to function'''===

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==='''Endurance depends on muscle use'''===

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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.

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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.

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=='''Scaling effects on quadrupedal design'''==

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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.

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[[File:QMFig 7.1.png|thumb|'''Fig 7.1 Isometric cubes''']]

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:::::An edge of cube (b) has twice the length of an edge of cube (a). The scale factor f = 2.

+

[[File:QMFig 7.2.png|thumb|'''Fig 7.2 Three approximately isometric breeds of dog''']]

:::::'''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.

+

:::::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'''===

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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!

+

[[File:QMFig 7.3.png|thumb|'''Fig 7.3 Top speed of mammals''']]

−

:::::'''Fig 7.3 Top speed of mammals'''

+

:::::'''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'''===

−

~~===~~'''~~Proportional and disproportional development~~'''~~===~~

+

[[File:QMFig 7.4.png|thumb|'''Fig 7.4 Relative growth of tissues in a beef carcass''']]

+

[[File:QMFig 7.5.png|thumb|''Fig 7.5 Allometry of bones according to Galileo''']]

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'''

+

:::::'''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'''

+

:::::'''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".

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==='''Allometry and scaling'''===

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[[File:QMFig 7.6A.png|thumb|'''Fig 7.6 Bone proportions in terrestrial quadrupeds''']]

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).

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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'''

+

[[File:QMFig 7.7.png|thumb|''Fig 7.7 Postnatal change in shape of the radius and ulna of the pig''']]

+

[[File:QMFig 7.8.png|thumb|'''Fig 7.8 Postnatal growth of muscle and bone in the pig''']]

+

[[File:QMFig 7.9.png|thumb|'''Fig 7.9 Muscle and bone proportions in mature animals of different size''' ]]

+

[[File:QMFig 7.10.png|thumb|'''Fig 7.10 The effect of body size on histochemical fibre type populations''']]

+

:::::'''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'''

+

:::::'''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'''

+

:::::'''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'''

+

:::::'''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'''

+

:::::'''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.

+

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==='''Patterns of limb joint movement'''===

−

The possible movements in the corresponding joints between the forelimb and hindlimb have some similarities between the different limb segments:

+

The possible movements in the corresponding joints between the forelimb and hindlimb have some similarities between the different limb segments:

+

{| class="wikitable collapsible"

+

|'''Forelimb'''

+

! '''Hindlimb'''

+

! '''Axes of movement'''

+

|-

+

| Shoulder

+

| Hip

+

| Flexion-extension; Adduction-abduction; Rotation

+

|-

+

| Elbow

+

| Stifle

+

| Flexion-extension; Rotation

+

|-

+

| Carpus

+

| Tarsus

+

| Flexion-extension

+

|-

+

| Metacarpophalangeal

+

| Metatarsophalangeal

+

| Flexion-extension

+

|-

+

| Interphalangeal

+

| Interphalangeal

+

| Flexion-extension

+

|}

The axes of movement thus become more restricted distally. A limb can be regarded as an extensible rod, rather freely moveable about the shoulder and hip joints, and extensible because flexion and extension are possible in all joints, in an alternating pattern distally as far as the metacarpophalangeal joints (Fig. 8.1). Proximally, the more complex movements are matched by the complexity of the muscles surrounding these joints.

+

[[File:QMFig 8.1.png|thumb|'''Fig 8.1 Flexion and extension of the limbs of the horse during the gallop''']]

+

:::::'''Fig 8.1 Flexion and extension of the limbs of the horse during the gallop'''

−

~~:::::'''Fig 8.1 Flexion and extension of the limbs of the horse during the gallop'''~~

+

:::::Note the extreme flexion of joints distal to the stifle and elbow during protraction, the interdependence of stifle and hock movement, and that the flexion position differs markedly between forelimb and hindlimb.

−

:::::Note the extreme flexion of joints distal to the stifle and elbow during protraction, the interdependence of stifle and hock movement, and that the flexion position differs markedly between forelimb and hindlimb.

−

==='''Limbs as struts'''===

The trunk of the quadruped is supported on four struts. If static support of the trunk were their only function, these struts would be straight. Flexion of the joints of the limb results in a torque exerted by gravity on each joint (Fig 6.3). Larger mammals, for example the giraffe and the elephant (Fig. 8.2) stand with straight limbs to minimise this torque; smaller animals are able to oppose the torque more easily with muscular force. Recall that the smaller animal is relatively stronger (Chapter 7).

+

[[File:QMFig 8.2.png|thumb|'''Fig 8.2 Size effects on mammalian skeletons''']]

Each joint of the strut needs a mechanism to prevent flexion, especially in large animals like a horse in which a “stay apparatus” is defined; each joint is supported against gravity by a ligamentous or an extremely pennate arrangement of muscles (Fig. 5.8). Denervation of any of the muscles shown in Fig. 6.3 would reduce the animal's ability to bear weight on the limb. Each of these muscles has been chosen deliberately because it acts over only one joint. This single-joint muscle system is assisted and sometimes superseded by a two-joint muscle system to be described later in this chapter.

−

+

:::::'''Fig 8.2 Size effects on mammalian skeletons'''

−

:::::'''Fig 8.2 Size effects on mammalian skeletons'''

:::::The torque exerted by gravity about the limb joints is reduced in the larger species by increasing the angles of flexion.

−

:::::These animals also show a feature of the vertebral column discussed in Chapter 9. The cat (c) and the rat (d) have cranially directed vertebral spines in the caudal series, with the tenth and twelfth thoracic vertebrae, respectively, anticlinal. The bending imposed on the vertebral column of the elephant (a) and the giraffe (b) necessitates caudally directed lumbar vertebral spines.

+

:::::These animals also show a feature of the vertebral column discussed in Chapter 9. The cat (c) and the rat (d) have cranially directed vertebral spines in the caudal series, with the tenth and twelfth thoracic vertebrae, respectively, anticlinal. The bending imposed on the vertebral column of the elephant (a) and the giraffe (b) necessitates caudally directed lumbar vertebral spines.

−

==='''How each limb is attached to the trunk'''===

The most stable quadrupedal posture results from splaying the limbs. However, even in giraffes the attachments of the limbs to the trunk are so designed that they can maintain the basically unstable equilibrium of a heavy load supported on nearly vertical piles. In the hindlimb, the proximal segment of the limb, the hip bone, is fused to the vertebral column and to the contralateral segment (Fig. 8.3 a). The effective postural attachment for the hindlimb is therefore the hip joint. This spherical joint allows flexion–extension, adduction–abduction and rotation freely. Postural control is therefore dependent on muscles fixing the joint, particularly to prevent abduction and flexion. That muscles are necessary for the stabilisation of the hip is evident when you see a weakened cow trying to stand on smooth concrete.

−

+

[[File:QMFig 8.3.png|thumb|'''Fig 8.3 Pivots for the limbs of the dog''']]

The proximal segment of the forelimb, the scapula, has no direct bony attachment to the vertebral column. Posture is maintained by the transmission of the gravitational force not through bone, but through the muscle fibres of m. serratus ventralis, which carries the trunk between the two forelimb struts as a sling (Fig. 8.3 b). Since there is no bony joint, all axes of movement are possible, and all extrinsic muscles of the forelimb are needed to stabilise the attachment of the prop. In the transverse plane, in particular mm rhomboideus and trapezius act as abductors and m. pectoralis superficialis acts as an adductor of the limb.

−

:::::'''Fig 8.3 Pivots for the limbs of the dog'''

+

:::::'''Fig 8.3 Pivots for the limbs of the dog'''

−

:::::Cranial view of the articulations between the pelvic girdle (a) and the pectoral girdle (b). The level of each pivot is shown with arrows. Detachment of the scapula from a bony connection with the trunk raises the pivot to the level of entry of nerves and blood vessels to the limb.

+

:::::Cranial view of the articulations between the pelvic girdle (a) and the pectoral girdle (b). The level of each pivot is shown with arrows. Detachment of the scapula from a bony connection with the trunk raises the pivot to the level of entry of nerves and blood vessels to the limb.

==='''Limbs as pendulums'''===

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The main movement for propulsion is protraction—retraction. It is useful to regard each limb as a pendulum, swinging in a sagittal plane. During slow locomotion, the pivot for the hindlimb is the hip joint (Fig 8.4 a). For the forelimb, the pivot is not the shoulder, but is more proximal (Figs 5.3, 8.3 b, 8.4 b).

−

+

[[File:QMFig 8.4.png|thumb|'''Fig 8.4 Limb movements of a walking cat''']]

−

:::::'''Fig 8.4 Limb movements of a walking cat'''

+

:::::'''Fig 8.4 Limb movements of a walking cat'''

::::::1 Foot leaves ground.

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::::::2. Foot contacts ground. Stifle, hock and elbow are extending.

::::::2-1 Retraction, or stance phase. Stifle, hock and elbow continue extending. Hip and shoulder are lowered slightly.

−

:::::The movements of the joints of each limb are small compared with the movements of the limb as a whole. The movement during walking is therefore best described as that of a pendulum with a pivot at the hip for the hindlimb. The pivot for the forelimb, however, lies proximally to the shoulder joint.

+

The movements of the joints of each limb are small compared with the movements of the limb as a whole. The movement during walking is therefore best described as that of a pendulum with a pivot at the hip for the hindlimb. The pivot for the forelimb, however, lies proximally to the shoulder joint.

==='''The effect of size on pendulums'''===

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The centre of gravity of the limb is made as proximal as possible (Fig. 8.5 b). First, the bellies of muscles operating distal joints should lie close to the pivot, transmitting their force by means of long tendons. This is made easier if propulsive muscles operate mainly about the pivot, rather than by bending the limb distally. Fig. 8.4 shows that in walking, the limb is indeed an almost rigid pendulum. If distal joints have fewer axes of movement than proximal joints, the tendinous control apparatus is much simplified. We saw earlier in this chapter that this is the case. Also, the muscles responsible for fixing each joint lie proximally to the joint (Fig. 6.3). An additional advantage of having muscles located proximally is that they are then closer to the heart, thus reducing the length of the vascular channels and thereby improving the efficiency of the blood supply.

Secondly, the structures forming a friction contact with the ground must be light, whether they be naturally grown keratin, or metal shoes. The ungulate (hooved animal) evolved for this reason.

+

[[File:QMFig 8.5.png|thumb|'''Fig 8.5 Improvements to pendulum design''']]

+

[[File:QMFig 8.6.png|thumb|'''Fig 8.6 Phylogenetic elongation of the distal end of the mammalian limb''' ]]

Thirdly, the number of digits can be reduced, effectively to two in many artiodactyls (even toed ungulates) and to one in some perissodactyls (odd toed ungulates). A single structure is stronger than a paired structure of the same weight and length. Thus even in artiodactyls, fusion of the metapodial segment often occurs. Such a reduction in digits enhances cursorial (Latin: cursor, runner) ability and sacrifices the ability to use hands for specialised procedures.

−

:::::'''Fig 8.5 Improvements to pendulum design'''

+

:::::'''Fig 8.5 Improvements to pendulum design'''

:::::Modifications to a basic pendulum (a) that increase the natural frequency of oscillation (b, e) or the distance moved by the tip in each swing (c, d).

−

:::::'''Fig 8.6 Phylogenetic elongation of the distal end of the mammalian limb'''

+

:::::'''Fig 8.6 Phylogenetic elongation of the distal end of the mammalian limb'''

−

:::::Comparison of the hind limb of the bear (a), dog (b) and deer (c) shows both a progressive elongation of the distal segments of the limb and a progressive incorporation of the distal segments into the limb pendulum from the plantigrade (a) to the digitigrade (b) and unguligrade (c) stance, as the limb becomes cursorily adapted.

+

:::::Comparison of the hind limb of the bear (a), dog (b) and deer (c) shows both a progressive elongation of the distal segments of the limb and a progressive incorporation of the distal segments into the limb pendulum from the plantigrade (a) to the digitigrade (b) and unguligrade (c) stance, as the limb becomes cursorily adapted.

==='''Balancing the pendulum'''===

The distal limb segments should be as long as possible (Fig. 8.5 c). This is achieved either by actual elongation of the distal segments relative to the proximal segments (Figs. 8.2 and 8.6), or by incorporation of the distal segments into the pendulum by running on the tip of the toes (Fig. 8.6).

−

+

[[File:QMFig 8.7.png|thumb|'''Fig 8.7 Adaptation of the pectoral girdle in a cursorial mammal''']]

The pivot of the pendulum should be as proximal as possible (Fig. 8.5 d). Some mammals have a complete bony pectoral girdle, which compels the forelimb to pivot from the shoulder joint (Fig. 8.7 a). A cursorial adaptation has been the reduction of bony elements of the pectoral girdle, freeing the scapula and allowing the limb to pivot from a point proximal to the shoulder (Figs. 5.3, 8.3 b, 8.4 b, 8.7 b). The dorsal border of the scapula moves cranially in limb retraction (Fig. 5.3). This enables muscles connecting the scapula to the head and neck (Mm rhomboideus, trapezius and serratus ventralis), and movements of the neck, to assist retraction. In galloping, in which the footfalls of the forelimb closely follow one another, the head is lowered during retraction and raised during protraction.

The pivot is moved into the vertebral column in animals that gallop with a flexible column. This applies to forelimbs and hindlimbs, and not only elongates the pendulum but enables axial muscles to participate in propulsion (Fig. 5.3).

−

:::::'''Fig 8.7 Adaptation of the pectoral girdle in a cursorial mammal'''

+

:::::'''Fig 8.7 Adaptation of the pectoral girdle in a cursorial mammal'''

:::::In the echidna (a), the clavicle and the coracoid form two complete bony bridges between the scapula and the sternum. In the dog (b), only remnants of these bridges remain, represented by the coracoid process of the scapula and a fibrous or occasionally ossified tendinous intersection within the brachiocephalicus muscle. The pivot for the forelimb can be located proximally to the shoulder.

−

==='''Reciprocating the pendulum'''===

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==='''Short and longheaded muscles'''===

Over most joints, there are muscles with actions limited to a particular single joint, as in Fig. 6.3, and other muscles that, in addition, act over adjacent joints (Fig. 8.8). It is convenient to call muscles acting over a single joint "shortheaded", and muscles acting over more than one joint, "longheaded". This nomenclature concurs with, for instance, that used for the long head of M. triceps brachii, as well as the short and long digital extensor muscles of the hindlimb.

+

[[File:QMFig 8.8.png|thumb|'''Fig 8.8 Short and longheaded muscles''']]

−

+

:::::'''Fig 8.8 Short and longheaded muscles'''

−

:::::'''Fig 8.8 Short and longheaded muscles'''

:::::The pairs of counteractive muscles shown in the hindlimb of the dog (a) are m. rectus femoris and m. semitendinosus, as longheaded muscles, and m. vastus lateralis and m. adductor as shortheaded muscles. Muscle lengths are compared between the flexed hip and stifle position (b) and the extended position (c). The longheaded muscles tend to maintain a constant length over a natural range of limb function.

−

==='''A severe restriction on muscle function: active insufficiency'''===

+

[[File:QMFig 8.9.png|thumb|'''Fig 8.9 The contribution of a longheaded muscle to the standing jump of the cat''']]

There is a problem associated with shortheaded muscles that is fundamental to the design of limbs. For any muscle, there is only one stage at which the force is maximal over the whole range over which the muscle contracts (Fig. 4.4). A shortheaded muscle is therefore properly effective at only one angle of the joint over which it acts. A muscle is therefore insufficient because of the way its contractile mechanism works. A muscle with its sarcomeres at any length other than near 2.2 µm is said to be actively insufficient.

−

+

:::::'''Fig 8.9 The contribution of a longheaded muscle to the standing jump of the cat'''

−

:::::'''Fig 8.9 The contribution of a longheaded muscle to the standing jump of the cat'''

:::::The semitendinosus muscle (dashed outline) has the same length when the hindlimb is in the fully flexed position as it does with the limb in the fully extended position. This muscle therefore assists hip extension without changing from its optimal length. It is able to do this only by the counteractive action of stifle extensors.

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==='''A severe restriction on limb function: passive insufficiency'''===

+

[[File:QMFig 8.10.png|thumb|'''Fig 8.10 Ligamentous adaptations of longhead muscles''']]

Even when a longheaded muscle is a strap muscle and has the longest range of contraction possible (44% of fully stretched length: see Fig. 4.3), it is not possible to allow for full independent movement of both the joints it acts over. Thus when the hip of any quadruped, and also any but the most limber human, is fully flexed, the stifle cannot be fully extended. In this case, the semitendinosus muscle is insufficient but for a different reason to that for the actively insufficient shortheaded muscle described above. Longheaded muscles are intrinsically passively insufficient, especially so when they are highly pennate.

+

:::::'''Fig 8.10 Ligamentous adaptations of longhead muscles'''

−

~~:::::'''Fig 8.10 Ligamentous adaptations of longhead muscles'''~~

+

:::::M. fibularis of the horse is entirely ligamentous. Stifle flexion (b) therefore produces hock flexion automatically, and M. gastrocnemius is kept at optimal length. The action of M. flexor digitorum superficialis also ensures that stifle extension (a) is also accompanied by hock extension. The position of the limb in (a) and (b) represent the retraction and protraction phases of a fast gallop as in Fig. 8.1.

−

:::::M. fibularis of the horse is entirely ligamentous. Stifle flexion (b) therefore produces hock flexion automatically, and M. gastrocnemius is kept at optimal length. The action of M. flexor digitorum superficialis also ensures that stifle extension (a) is also accompanied by hock extension. The position of the limb in (a) and (b) represent the retraction and protraction phases of a fast gallop as in Fig. 8.1.

−

==='''Limbs are controlled proximally by key joints and nerves'''===

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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.

+

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.

−

=='''The design of the vertebral trunk'''==

−

==='''The trunk is a horizontal beam

+

==='''The trunk is a horizontal beam'''===

The body of the dog shown in Fig. 9.1 a is represented mechanically by a beam, the vertebral column A–D, 45 cm long with a uniformly distributed load of 0.2 kg.cm–2 (the neck and trunk), and a concentrated load cranially of 2 kg (the head). The total weight is therefore 11 kg. With the fore and hindlimbs each represented each by one simple strut and placed as shown at B and C, the opposing reaction forces can be calculated as 7.9 kg for the forelimbs and 3.1 kg for the hindlimbs. This turns out to be approximately the situation in a real dog in which the weight borne by the forelimb is about twice that borne by the hindlimb. Since the weight of the hindlimb of the dog is about the same as that of the forelimb, one must conclude that the weight of hindlimb in excess of what is needed for postural support is available for propulsion; in other words the forelimb and the hindlimb of the dog differ in their postural and propulsive roles. The forelimb supports and balances, the hindlimb pushes.

−

+

[[File:QMFig 9.1.png|thumb|'''Fig 9.1 Bending in the vertebral column''']]

In Fig. 9.1c, muscles preventing bending include (a) the epaxial muscles of the neck and thorax, (b) the hypaxial muscles of the thorax, and (c), the hypaxial muscles of the lumbar region. Props assisting the action of these muscles and the ligaments shown are (p) the spinous process of the axis, (q) the spinous process of the first thoracic vertebra (together with adjacent spinous processes), (r) the spinous process of the anticlinal vertebra (eleventh thoracic), (s) the sacrum and (t) the costal arch.

(u) and (v) are the forelimb and hindlimb respectively. Note that the shape of the vertebral column is opposite to that of the bending moments shown in Fig. 9.1b for the horizontal beam A — D.

−

:::::'''Fig 9.1 Bending in the vertebral column'''

+

:::::'''Fig 9.1 Bending in the vertebral column'''

:::::The trunk of a dog is represented in Fig. 9.1a by a horizontal beam A — D, 45 cm long with a uniformly distributed load of 0.2 kg.cm-1, together with a concentrated load cranially of 2 kg (the head). The total weight is 11 kg. With the limbs placed as shown, the opposing reaction forces are 7.9 kg in the forelimb and 3.1 kg in the hindlimb. Bending moments along the vertebral column are shown graphically in Fig. 9.1b.

−

==='''Forces along the beam'''===

+

[[File:QMFig 9.2.png|thumb|'''Fig 9.2 Transverse section of a pig at the thoracolumbar junction''']]

The skeleton of the trunk is a row of separate bones, the vertebral column, on its own hardly a stable bridge. Its rigidity is maintained to a large extent by a compressive force produced in the massive muscle surrounding the column (Fig. 9.2). As a bridge, therefore, this structure is comparable to prestressed concrete. We have already seen that the trabecular network is oriented axially within the vertebral bodies, to resist the tensile stress (Fig. 3.2). When the axial muscles are relaxed as during anesthesia, the vertebral column is no longer rigid.

Rigidity of the vertebral column is attained also by the supraspinous and dorsal and ventral longitudinal ligaments (Figs. 9.2 and 9.3) and by the shape of the synovial intervertebral (zygapophyseal) joints.

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:::::'''Fig 9.2 Transverse section of a pig at the thoracolumbar junction'''

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:::::'''Fig 9.2 Transverse section of a pig at the thoracolumbar junction'''

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~~:::::Caudal aspect, showing the intervertebral joint and the structures supporting the vertebral column.~~

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:::::Caudal aspect, showing the intervertebral joint and the structures supporting the vertebral column.

==='''The effect of gravity on the beam'''===

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==='''Inclined spinous processes'''===

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[[File:QMFig 9.3.png|thumb|'''Fig 9.3 Median section of an intervertebral joint in the thoracic region''']]

We can tell the direction of the forces on the spinous processes of the vertebrae by the way they lean, as you can easily tell in which direction the contestants in a tug-of-war are pulling, and resisting being pulled. Mechanical struts are more effective when a force is applied to them at an acute angle rather than a right angle. Therefore, the tall spines of the cranial thoracic vertebrae slope caudally. In the cat, this occurs as far caudally as the tenth thoracic vertebrae (Fig. 8.2), and the eleventh in the dog (Fig. 9.1 c).

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:::::'''Fig 9.3 Median section of an intervertebral joint in the thoracic region'''

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:::::'''Fig 9.3 Median section of an intervertebral joint in the thoracic region'''

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~~:::::Structures are shown which resist bending or hydrostatically distribute a uniform compression stress on the vertebral bodies.~~

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:::::Structures are shown which resist bending or hydrostatically distribute a uniform compression stress on the vertebral bodies.

==='''Flexibility of the vertebral column'''===

Apart from the joint between the first two cervical vertebrae, the intervertebral joints are not synovial joints. It is important that joints in a column under compression should be able to distribute pressure evenly over the opposing surfaces of the vertebral bodies, regardless of the angle of the joint. Intervertebral movement and even pressure distribution are achieved hydrostatically by the nucleus pulposus between each body (Figs. 9.2, 9.3). The change in shape of this mucoprotein gel with movement of the joint is accommodated by the annulus fibrosis, a lamellar arrangement of collagen fibres. The lamellae pass from vertebra to vertebra with their fibres crossing each other obliquely. They are therefore constructed to withstand the tensile stress imposed by the bending of the vertebral column, and also to prevent rupture of the nucleus pulposus. The mechanical and morphological concept suggested by the term intervertebral disc is misleading.

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==='''This rigid beam can be flexible'''

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==='''This rigid beam can be flexible'''===

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[[File:QMFig 9.4.png|thumb|'''Fig 9.4 Flexibility of the vertebral column in galloping animals''']]

In the dog, the maximum movement occurs between the segments around the tenth and the eleventh thoracic vertebrae. These segments are the most vulnerable to the injury of intervertebral structures. This is especially so in dogs with short legs which must use their vertebral column to a greater extent for propulsion than long legged dogs.

The flexibility of the vertebral column varies between species. A galloping horse maintains an almost rigid back (Fig. 9.4 a). This is also true for some of the fastest terrestrial animals, the gazelles and antelopes, some of which are small (Fig. 9.4 b). This is in contrast with the cheetah (Fig. 9.4 c). The big cats, which have flexible vertebral columns, spend little of their time standing, as compared with herbivores of equivalent size, which have more rigid columns. The axial muscles of herbivores are presumably more postural in function than those of carnivores and the smaller animals.

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:::::'''Fig 9.4 Flexibility of the vertebral column in galloping animals'''

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:::::'''Fig 9.4 Flexibility of the vertebral column in galloping animals'''

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:::::The diagrams on the left represent full extension and the right side, full flexion of the vertebral column. The horse (a) and the gazelle (b) do not flex their backs appreciably, in contrast with the cheetah, (c).

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:::::The diagrams on the left represent full extension and the right side, full flexion of the vertebral column. The horse (a) and the gazelle (b) do not flex their backs appreciably, in contrast with the cheetah, (c).

==='''The vertebral column in locomotion'''===

The locomotory apparatus of the trunk is driven by the caudal epaxial muscles, notably the longissimus muscle (Fig. 9.2) and its attachments. In the species in which the apparatus is well developed, such as rodents, felids and canids, the attachments of the longissimus muscle to the spinous and transverse processes of the caudal thoracic and lumbar vertebrae are functionally strengthened by an angling of these processes away from the direction of tension. Thus, the transverse processes of the lumbar vertebrae slope cranially and ventrally. For the spinous processes, the effect is opposite to that seen in the cranial segments of the vertebral column where they slope caudally against the tension in the dorsal stays of the cervicothoracic region (Fig. 9.1 c). There is therefore an anticlinal vertebra, which represents the changing point (Fig. 8.2). In species that presumably do not use their vertebral column effectively to lengthen the hindlimb pendulum in locomotion, an anticlinal vertebra is absent.

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We can now proceed to consider the action of the trunk and limbs as used by quadrupeds in performing ~~unusual~~ tasks.

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We can now proceed to consider the action of the trunk and limbs as used by quadrupeds in performing usual tasks.

=='''Locomotion'''==

==='''The standing quadruped'''===

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[[File:QMFig 10.1.png|thumb|'''Fig 10.1 Location of the centre of gravity of a horse''' ]]

The location of the centre of gravity of a horse is shown in Fig. 10.1. In the horse, 55% of the weight of the body is supported by the forelimbs and 45% by the hindlimbs. A horse usually rests one hindlimb while standing, but can do so for a forelimb only with difficulty. Relatively more weight is presumably supported by the forelimb of the bison and by the hindlimb of the rabbit (Fig. 10.2). The dog carries two thirds of its weight on its forelimbs and one third on its hindlimbs (Fig. 9.1).

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[[File:QMFig 10.2.png|thumb|'''Fig 10.2 Species differences in the location of the centre of gravity''']]

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:::::'''Fig 10.1 Location of the centre of gravity of a horse'''

:::::This is found in a transverse plane immediately caudal to the xiphoid process, and in a dorsal plane between the ventral and middle thirds of the trunk.

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:::::'''Fig 10.2 Species differences in the location of the centre of gravity'''

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:::::Compare these probable locations in the bison (a) and rabbit (b) with that determined for the horse in Fig. 10.1.

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:::::Compare these probable locations in the bison (a) and rabbit (b) with that determined for the horse in Fig. 10.1.

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==='''Using the head to change the centre of gravity'''===

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[[File:QMFig 10.3.png|thumb|'''Fig 10.3 Use of the head and neck to alter the centre of gravity''']]

The function of the limbs as struts in supporting the trunk, and the function of the trunk as a supporting beam, have already been discussed. The remaining major bulk of the body, the head and neck, is also important in the standing quadruped because of its influence on the centre of gravity. Raising the head will bring it nearer to the trunk in the dorsal plane, and lowering it to bring the neck parallel to the trunk axis will increase this distance. Thus raising the head moves the centre of gravity caudally, removing weight from the forelimbs, and lowering it moves the centre of gravity cranially, increasing weight on the forelimbs (Fig. 10.3). Thus when a lame forelimb takes weight, the head is raised to relieve it. When one wishes to lift a forefoot of a horse or ox, its head should be raised and move laterally away from the foot to be lifted. On the other hand, it should be lowered with a hindfoot is to be lifted. An animal can be prevented from kicking with its hindlimb by holding its head high.

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[[File:QMFig 10.4.png|thumb|'''Fig 10.4 Curvature of the vertebral column in the sitting cat''']]

:::::'''Fig 10.3 Use of the head and neck to alter the centre of gravity'''

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:::::'''Fig 10.4 Curvature of the vertebral column in the sitting cat'''

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:::::The shape of the thoracic cage (doted outline) is maintained by bending the vertebral column predominantly near the thoracolumbar junction.

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:::::The shape of the thoracic cage (doted outline) is maintained by bending the vertebral column predominantly near the thoracolumbar junction.

==='''Motion without change of location'''===

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'''Standing up:''' The smaller the animal, the more easily it can spring to its feet with a sudden back movement, but even horses can manage to do this. A slower, more deliberate movement is, for the dog, cat and pig, essentially the reverse process of lying down. Cattle and sheep raise themselves up on to their hindlimbs first, then on to their flexed carpuses. The horse rolls its trunk to sternal recumbency, collects its four legs underneath, and then protracts and extends its forelimbs, raising its cranial trunk before its caudal trunk, by pushing its weight over its forelimbs with a thrust from the hindlimbs.

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[[File:QMFig 10.5.png|thumb|'''Fig 10.5 Stable positions for the horse on its hindlimbs''']]

'''Standing on hindlimbs:''' In order to achieve this, the centre of gravity must lie vertically above the hindfeet (Fig. 10.5 a, b). This is easier for horses than cattle. Horses can prance and kick with their forelimbs, but cattle cannot. A copulating bull can maintain the position only briefly, and uses the cow for support. Standing on hindlimbs is especially easy for animals with a more caudally located centre of gravity (Fig. 10.2 b).

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[[File:QMFig 10.6.png|thumb|'''Fig 10.6 Propulsion and friction forces''']]

:::::'''Fig 10.5 Stable positions for the horse on its hindlimbs'''

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:::::'''Fig 10.6 Propulsion and friction forces'''

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:::::The insertion of a plate between the hose and the ground enables the forces acting on the body during a propulsive movement of the hindlimbs during the gallop to be visualised.

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:::::The insertion of a plate between the hose and the ground enables the forces acting on the body during a propulsive movement of the hindlimbs during the gallop to be visualised.

==='''Propulsive force'''===

A propulsive force, applied to the limb to retract it, propels the animal over the ground. Opposing the propulsive force is friction force, acting between the animal body and the ground. It is the friction force that acts in the direction of movement. This is best visualised by interposing a plate between the animal and the ground (Fig. 10.6). When there is no friction between the plate and the ground, the propulsive force accelerates the plate and not the animal body. If the friction force equals the propulsion force, the plate remains at rest, and the animal is accelerated. Friction, which is usually thought to oppose motion, is essential for locomotion. The construction of the surface contact with the ground is vitally important and is often a source of breakdown in running animals, just as it is for motor vehicles.

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[[File:QMFig 10.7.png|thumb|'''Fig 10.7 The propulsive apparatus of the greyhound''']]

In animals that use their vertebral column in running, the fore and hindlimb pendulums swing about a pivot near the thoracolumbar junction (Fig. 10.7). Axial muscles and extrinsic limb muscles acting over this pivot produce the propulsive thrust.

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:::::(a) Hindlimb. Retraction is brought about by the extensors of the vertebral column (x, m. longissimus and its dorsal aponeurosis) and the extensors of the hip (y, the middle gluteal muscle and z, the caudal thigh muscles).

:::::(b) Forelimb. Retraction is brought about by the flexors of the vertebral column (w, the external abdominal oblique muscle and x, rectus abdominis), and suitably placed muscles of the forelimb (y, latissimus dorsi and z, the deep pectoral muscle).

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==='''Gaits'''===

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All animals use the slow walk at times when stability is important, for example when walking over rough terrain and by animals bearing awkward loads. It is visualised by a gait diagram in Fig. 10.10 a.

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[[File:QMFig 10.8.png|thumb|'''Fig 10.8 Support triangles''']]

:::::'''Fig 10.8 Support triangles'''

:::::When a horse stands on all four feet, its centre of gravity lies as shown diagrammatically in dorsal view (a), cranial to the diagonals between the feet. Either hindfoot can now be lifted without change in weight distribution, because the centre of gravity lies within the triangle of support formed by the other three feet (b, c). Raising the head as in Fig.10.3 a directs the centre of gravity caudally. In (d), either forefoot can now be lifted. The centre of gravity need not be directed so far caudally if the head deviates to the side; if it deviates to the left, the right forefoot can be lifted (e).

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[[File:QMFig 10.9.png|thumb|'''Fig 10.9 Head, neck, trunk and tail movements during the slow walk''']]

:::::'''Fig 10.9 Head, neck, trunk and tail movements during the slow walk'''

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:::::If protraction of the left hind limb in (a) produces the axial displacement shown in (b), the left forefoot can be lifted and the limb protracted. Forelimb protraction straightens the body axis and prepares it for the same movement on the opposite side of the body (c, d). Using this slow gait, even a highly adapted cursorial animal uses to some extent the same axial movements for locomotion as an animal with only rudimentary limbs.

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:::::If protraction of the left hind limb in (a) produces the axial displacement shown in (b), the left forefoot can be lifted and the limb protracted. Forelimb protraction straightens the body axis and prepares it for the same movement on the opposite side of the body (c, d). Using this slow gait, even a highly adapted cursorial animal uses to some extent the same axial movements for locomotion as an animal with only rudimentary limbs.

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==='''The fast walk'''===

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[[File:QMFig 10.10.png|thumb|'''Fig 10.10 Extreme forms of symmetrical gaits of the horse'''']]

If the sequence in the slow walk is speeded up to any extent, the next foot in the sequence will be off the ground before the previous limb moved has contacted the ground. Thus, for a time, there are only two feet left on the ground (Fig. 10.10 b). The animal would fall over if stopped at certain stages of the cycle. Stability is achieved by a dynamic rather than a static equilibrium. For the heaviest quadrupeds, such as elephants, the fast walk represents the greatest degree of static instability allowable, and it is their fastest gait. Horses, and in particular some breeds such as the Tennessee Walking Horse, can be trained to perform a variety of styles of fast walk with names such as "paso", "slow gait", "running walk", "rack" and "plantation gait", useful because of the smoothness for the rider.

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:::::'''Fig 10.10 Extreme forms of symmetrical gaits of the horse'''

:::::From a, b to c or a, b to d there are progressively shorter periods of contact of each foot with the ground.

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:::::All these gaits are symmetrical because the time interval between footfalls of pairs of forefeet or hindfeet is always one half of a stride interval. Thus there is symmetry between right and left sides of the body. Pale blue horseshoe = left footfall; Dark blue horseshoe = right footfall.

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:::::All these gaits are symmetrical because the time interval between footfalls of pairs of forefeet or hindfeet is always one half of a stride interval. Thus there is symmetry between right and left sides of the body. Pale blue horseshoe = left footfall; Dark blue horseshoe = right footfall.

==='''Two–beat symmetrical gaits'''===

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==='''Asymmetrical gaits'''===

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When the footfalls of a pair of forefeet or hindfeet are unevenly spaced in time, the gait is asymmetrical. Symmetrical gaits are all some variant of the gallop, which is a general term. The beat is therefore composed of couplets, separated by pauses, and one foot is a leading foot. For the horse at least, the leading foot for the forelimbs is conventionally the second foot of the couplet to strike the ground (Fig. 10.11 c: 6th stage). The leading forelimb is always on the inside of a turn (Fig. 10.12). A galloping horse changes its lead during the stage when both forelimbs are off the ground (Fig. 10.11: 2nd stage). It may be necessary for a horse to change lead during a jump in order to prepare for a turn immediately on landing.

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[[File:QMFig 10.11.png|thumb|'''Fig 10.11 Forms of asymmetrical gaits''']]

:::::'''Fig 10.11 Forms of asymmetrical gaits'''

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:::::Dark blue footprint = right footfall.

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[[File:QMFig 10.12.png|thumb|'''Fig 10.12 Limb sequencing at a galloping turn''']]

:::::'''Fig 10.12 Limb sequencing at a galloping turn'''

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:::::The zebra is turning to its left. The right forefoot contacts the ground first and the leading (left) limb is on the inside of the turn.

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:::::The zebra is turning to its left. The right forefoot contacts the ground first and the leading (left) limb is on the inside of the turn.

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==='''Transverse and rotary sequence'''===

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4.Finally, both extended and gathered suspension occurs in the fast springing gallop of the rabbit, carnivores (Fig. 10.11 d) and some artiodactyls.

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[[File:QMFig 10.13.png|thumb|'''Fig 10.13 Basic patterns of footfalls in asymmetric gaits''' ]]

:::::'''Fig 10.13 Basic patterns of footfalls in asymmetric gaits'''

:::::The canter is a transverse gallop, modified to a three beat gait.

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The half bound occurs when a spring is made using both hindlimbs together, but the animal lands on one forefoot before the other, as seen in rabbits and hares.

The running jump occurs in with a springing gallop during the stage of extended suspension (Fig. 10.11 d: 4th stage). In the horse, the jump is not part of a normal gallop.

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[[File:QMFig 10.14.png|thumb|'''Fig 10.14 The running jump of a horse''']]

:::::'''Fig 10.14 The running jump of a horse'''

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The kinetic energy of the horse has been partly stored as elastic energy in the hindlimbs; this energy can subsequently be released to oppose gravity. The necessity for a concept of elasticity in quadrupedal mechanics cannot be overstated.

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~~{{unfinished}}~~

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[[Category:Musculoskeletal System - Anatomy & Physiology]]

Alexander Davies

249

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Quadrupedal Mechanics - Anatomy & Physiology (view source)

Revision as of 09:23, 29 November 2013