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Quadrupedal Mechanics - Anatomy & Physiology (view source)
Revision as of 06:08, 1 May 2013
, 06:08, 1 May 2013→Allometry and scaling
:::::'''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.
:::::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.
=='''The design of limbs'''==
==='''Axes of joint movement'''===
The skeleton of each limb is divided into movable segments. Movement is possible because of the presence of synovial joints between each segment. Restrictions are placed on the actions of different joints so that they act in different ways. These restrictions are:
::1. The shape of the joint surfaces.
::2. The ligaments surrounding the joint (for example a hinge joint will have ligaments that restrict the movement to only one plane).
::3. The ranges of contraction of muscles, (for example, dorsal flexion of the metacarpo-phalangeal joint is restricted by the interosseous muscle or interosseous ligament as in Fig. 2.16).
::4. The shape of the limb (for example, flexion of the stifle is restricted by contact of the crus with the thigh).
For each joint, there are four possible axes of movement, each affected to varying extents by the above restrictions. These are:
::1. Flexion – extension; a change of angle in a sagittal plane (hinge joint)
::2. Adduction – abduction; a change of angle in a transverse plane
::3. Rotation; movement around the axis of the limb; and
::4. Gliding; movement without change of angle, in a plane transverse to the axis of the limb.
Combinations of these movements are usual, but it is convenient to consider each one separately.
==='''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 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.
:::::'''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.
==='''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).
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'''
:::::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.
==='''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.
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'''
:::::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'''===
The important movements of each limb as a whole are:
::a.Flexion and extension, to alter the length of the limb (Fig. 8.1).
::b.Protraction and retraction, in which the limb swings cranially and caudally, respectively, in a sagittal plane (Fig. 8.4).
::c.Adduction and abduction, in a transverse plane, which Fig 8.3 suggests must occur in the hindlimb at the hip and in the forelimb at the shoulder or between the forelimb and the trunk.
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).
:::::'''Fig 8.4 Limb movements of a walking cat'''
::::::1 Foot leaves ground.
::::::1-2 Protraction, or swing phase. Slight initial flexion of stifle, hock and elbow. Hip and shoulder elevate slightly.
::::::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 effect of size on pendulums'''===
If a pendulum swings at its natural frequency of oscillation, this frequency is inversely proportional to the square root of its length. We presume that at the natural frequency of oscillation, propulsion will involve the least effort. Natural frequency therefore scales as f–1/2. The distance moved by the tip of the pendulum at each swing, the stride length, scales as f; this distance multiplied by frequency is the speed of the animal and therefore scales as
f–1/2.f = f1/2. We conclude that if a dog and a horse, with a scale factor of 4, are walking at an easy speed, the horse walks only twice as fast as the dog. This does not, of course, contradict the idea that dogs and horses have a rather similar maximum speed of running (Fig. 7.3).
==='''Improvements to pendulum design'''===
If the natural frequency of oscillation of the pendulum involves least effort, it is advantageous to make this frequency as high as possible while maintaining limb length as long as possible so as not to reduce stride length. This is achieved in four ways.
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.
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'''
:::::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'''
:::::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).
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'''
:::::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'''===
The pendulum should be long in retraction, but short in protraction (Fig. 8.5 e). At slow speeds, it is no advantage to shorten the protracting limb since the limb swings at a natural, low frequency (Fig. 8.4). At fast speeds, the protracting limb is flexed as much as possible (Fig. 8.1).
==='''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.
:::::'''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'''===
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'''
:::::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.
==='''“Antagonism” and “Counter activity”'''===
This naturally creates a problem in the design of limbs. The propulsive thrust, as well as the resistance to gravitational force, should be optimal over a whole range of joint angles, if the system is to be useful under a variety of positions and circumstances. The solution to the problem is found in the presence of longheaded muscles, of which there are many in both fore and hindlimbs. The so–called “antagonistic” muscles, M. rectus femoris and M. semitendinosus give an example. They are usually called "antagonistic" because they have opposite effects on the hip and stifle joints (Fig. 8.8). However, because the hip and stifle often flex and extend together (Fig. 8.9), such longheaded muscles appear to act together to a common purpose, rather than antagonistically. The term "counteractive", implying neutralisation of effect rather than opposition, is therefore more appropriate.
==='''So muscles work without changing length!'''===
The angles of the hip and stifle in Fig. 8.8 represent the fully flexed (b) and extended (c) position of the dog's hindlimb. The lengths of the two longheaded muscles have changed less than the shortheaded muscles. It seems possible, then, that limbs move while many of their muscles remain at optimal length for force production. This is borne out in Fig. 8.9, in which it appears that the caudal thigh muscles of the cat can propel the whole body into the air without change of length. In order to resolve this apparent contradiction, perhaps one should consider that counteractive longheaded muscles make small contractions alternately, like sliding ratchets. Limbs, with their array of linear motors, work as hard as a kind of machine that humans have not yet got round to inventing!
==='''Reciprocating joints'''===
Such a mechanism should also be able to solve a similar problem as the limbs support the weight of the standing animal, providing again that the angles of the hip and stifle are fixed in relation to one another. The shorter the range of contraction of the muscles in a longheaded muscle system, as would occur by an increasing degree of pennation, the more interdependent would be the movement of the two joints. In an extreme case, the muscles are ligamentous, and the movement of one joint cannot occur without movement of the other. A clinically relevant example is the M. fibularis tertius of the horse (Fig. 8.10). Being entirely tendinous, hock flexion must follow stifle flexion obligatorily, unless M. fibularis tertius has been ruptured by injury. Because the ranges of contraction of the counteractive M. gastrocnemius and M. flexor digitorum superficialis are small, stifle fixation in the horse results in almost complete fixation of the hock, and stifle and hock movements are almost totally interdependent (Fig. 8.1). Such an arrangement has been called a “reciprocal apparatus”, and is an important part of the stay apparatus in large animals.
==='''A severe restriction on limb function: passive insufficiency'''===
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'''
:::::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'''===
At the expense of joint independence, muscles in the brachial and femoral regions control much of the action of limbs. This is true even for the interdigital joints, since the digital flexors and extensors are longheaded muscles that arise, by no accident, proximally to the elbow and stifle. The control of elbow and stifle fixation and movement is critical for all the more distal joints. The elbow and stifle joints have therefore been appropriately called key joints of the limbs. The nerves innervating muscles fixing these two joints are therefore key nerves.
==='''Using short- and long-headed muscles together'''===
Animals in which stifle and hock action are less interdependent need a shortheaded muscle to fix the hock. This is the m. soleus (Fig. 6.2 b), often used as a model of a muscle with a high proportion of slow twitch, decelerating fibres. Well developed in the cat but absent in the dog, one can deduce that m. soleus frees the cat's hind limb from a merely postural and cursorial function for such activities as tree climbing. M. soleus becomes less significant, or absent, in the larger animals with limbs functioning only for weight bearing and running.
Having considered several aspects of how the limbs are attached to the trunk and how each limb, on its own, contributes to postural and locomotion, we now begin to investigate the mechanics of the whole animal.
==='''A safely factor limits how fast limbs can move'''===
==='''A safely factor limits how fast limbs can move'''===