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Quadrupedal Mechanics - Anatomy & Physiology (view source)
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The stage of contraction at which the force produced by a muscle is optimal is therefore quite limited. The implications of this in the design of the musculoskeletal system will be discussed later in section 7.
The stage of contraction at which the force produced by a muscle is optimal is therefore quite limited. The implications of this in the design of the musculoskeletal system will be discussed later in section 7.
=='''Muscle mechanics'''==
==='''Contractile units in series and in parallel'''===
The effect of arranging sarcomeres in series can be visualised by considering two muscles doing work by lifting a weight. In Fig. 5.1 a, a single muscle contracts maximally to lift a weight W through a distance d. If two similar muscles are arranged in series (Fig. 5.1 b), both muscles act equally on the weight. Each contracts the distance d, so the total distance contracted is 2d. The total contractile force is equal to the contractile force of one of them, but by an in-series arrangement, the range of contraction has been doubled.
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.
:::::'''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, and not on the geometrical arrangement.
==='''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.
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.
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.
:::::'''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).
:::::'''5.3 Sarcomeres in series'''
:::::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'''===
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).
:::::'''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.
==='''Torque and equilibria'''===
Torque is the product of the force and the perpendicular distance from the force to the pivot (Figs. 5.4 and 5.5). The concept of torque is much more useful in estimating the effects of muscles on joints than a concept of levers, since forces often act in an arc about a joint pivot, for a reason already discussed (Fig. 3.3).
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.
:::::'''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.
:::::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.
:::::'''5.6 Strap muscles'''
:::::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.
==='''Fibrous architecture of muscles'''===
An equally important aspect of design affecting strength and range of movement of muscles is their fibrous architecture. Here, "fibrous" refers not only to muscle fibres, but to collagen fibres also. In the simplest case, fibres within the muscle are aligned parallel to the force vector of the whole muscle. Such muscles are called strap muscles (Fig. 5.6). Their range of contraction and their strength depends on their shape, because this determines the number of sarcomeres in series or in parallel. Only one combination of range and strength will fit into a particular space in the body. The use of strap muscles in musculoskeletal design is therefore limited.
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.
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.
:::::'''Fig 5.7 Pennate muscles'''
:::::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.
:::::'''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.
==='''Some muscles look like feathers'''===
Muscles with the fibres at an angle to the force vector are termed pennate (L. penna, feather). Not all the work done in this type of muscle is useful in the direction of action of the muscle. Tendons of pennate muscles may be central (Fig. 5.7 c) or they may form a tendinous sheet on the surface of the muscle (Figs. 5.7 b, c), called an aponeurosis (Gr. apo, from; neuros, nerve) because the ancient Greeks did not distinguish properly between nerves, ligaments and tendons. The appearance of the fibrous connective tissue of an aponeurosis may at first give a misleading impression of the arrangement of the muscle fibres within.
Pennate muscles need this collagenous framework to link the increased number of sarcomeres in parallel. Also, because of the increased force of pennate muscles, there must be a proportionate increase in the strength, and hence the transverse sectional area, of tendons of origin and insertion (Fig. 5.7).
==='''When muscles become ligaments'''===
With increasing pennation, the range of contraction decreases and the strength increases (Fig. 5.8). The limit is reached when the muscle fibres become too short to function and the muscle becomes entirely ligamentous. This occurs in certain muscles as an effect of body size (Chapter 7).
How do contracting muscles fit into a limited space?
Pennate muscles change shape during contraction in a manner different from strap muscles. A contraction of a strap muscle by 30% results in an increase in transverse sectional area of 30% since the volume of the muscle is constant. On the other hand, it is possible for a pennate muscle to contract without an increase in the transverse sectional area of the muscle (Fig. 5.9). This is important where muscles must lie in a constricted region, such as within the antebrachial or crural fascial sheaths.
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.
:::::'''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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[[Category:Musculoskeletal System - Anatomy & Physiology]]
[[Category:Musculoskeletal System - Anatomy & Physiology]]