Quadrupedal Mechanics - Anatomy & Physiology

1 Introduction

Anatomy should be studied using mechanical principles

It is debatable whether the mysteries of life can be interpreted entirely by physical laws, but it is unquestionably true that life cannot be understood without reference to these laws. Thus we cannot interpret, for instance, the nature of an injury to the suspensory ligament of a horse, or the symptoms of a congenital abnormality of the hip of a dog, unless we understand the reason for the particular design of these structures in the normal living animal. The description of structure alone, as encountered in most textbooks of veterinary anatomy, is less interesting and more difficult to learn. Crushed under a load of facts, the student quickly discovers there is no incentive to reason for her or himself.

By applying mechanical principles to the musculoskeletal system of quadrupeds, this book attempts to explain the complexities of body structure. Hopefully, the reader will also gain a greater appreciation of the beauty of animal form and function. Of course, the ideas expressed here are not the last word on the subject. If argument is provoked, this book will be serving its purpose all the more.

The animal machine

A machine is a device for applying forces; an animal is therefore a machine. Force is developed in an animal's muscles, and is transmitted to its site of application by the supporting tissues composed of bone, cartilage, tendon and ligament. These tissues together form the musculoskeletal system.

The animal machine has some remarkable properties not found in man-made machines. Try to envision something man-made that grows without interruption to function, that if damaged or fatigued it can repair itself by replacement of component parts, frequently with little impairment to function, that can adjust in response to demand, such as adaptation to exercise, and that is constructed to last literally a life time. As well, the animal machine can also be a source of pleasure to those who participate in or view athletic performances. And last, we usually take it for granted that the animal machine should contribute in no small way to world agriculture, trade and nutrition: some parts of this machine are good to eat.

No matter how you view it, this book deals with an extraordinary machine.

2 Elasticity: external forces and stored energy

What this machine is made of: passive and active tissues

Fig. 2.1 Tissues of the musculoskeletal system.

The tissues of the musculoskeletal system are bone, cartilage, ligament, tendon, fascia and muscle (Fig. 2.1). The non-muscular parts support the body passively by resisting forces that are applied to the body from outside (extrinsic) or those that are created intrinsically within the body. The most significant extrinsic forces are the earth's gravitational force on the mass of the animal, and the reaction of the ground. An animal, once it is born, must spend most of its life battling with gravity and the problems of contact with ground surfaces.

Animals also derive support from the activity of their muscles, as evidenced from the inability of an anesthetised animal to stand. This active type of support will be discussed in Sections 4 and 5.

Fig. 2.1 Tissues of the musculoskeletal system.

This is a stylised view of the lateral aspect of the proximal left forelimb of the sheep. The skeleton is made of bones and cartilages. A combination of ligaments, muscles & tendons, and sheets of fascia, examples of which are shown, hold these together. Without these soft tissues around them, the jointed bones will not support the weight of the sheep.

The elasticity of tissues

An appreciation of the concept of elasticity is essential to understanding the mechanics of animals.

All materials are elastic to a lesser or a greater extent, even tissues like bone that seem to be stiff rather than elastic. The stiffness is only relative. After being deformed by an external force, all tissues must return to their original shape. If they did not, the body would be permanently deformed. Elasticity is a special function of the passive musculoskeletal tissues.

Elasticity is measured by determining the effect of stress, defined as force per unit area, on the shape of the material. When this stress acts in only one direction, this shape change is measured as strain, the distortion per original unit distance, expressed as a percentage.

Fig. 2.2 Stress, strain and elastic energy

At a particular percentage of strain, ρ, a stiffer material will store more elastic energy than a more elastic tissue. Suppose that at this strain percentage, the material can no longer be deformed without damage. Fracture will occur, and because the stiffer material releases more energy it will shatter rather that suffering a simple break. Bone fractures are discussed later in Chapter 3.

Fig. 2.2 Stress, strain & elastic energy

Two linearly elastic tissues A and B have stress - strain curves as shown. At any given value of stress, ρ, the energy absorbed by A, represented here by the area beneath the curve, is less than that absorbed by B. A is stiffer than B. If A and B were bones, A would be the more mineralised.

Fig. 2.3 Elasticity

When an elastic material is strained, work is done on it and energy is stored in it. Elastic energy is a form of potential energy. A rubber ball falling on to a hard surface converts what was previously kinetic energy into elastic energy on impact. This elastic energy is released again as kinetic energy when the ball bounces. The ball does not, however, attain the same height as previously. The elastic framework of an animal’s body behaves similarly, as it bounces up and down during running (Fig. 2.4). Some of the kinetic energy is lost as heat. The less energy lost in this way, the greater the elastic resilience of the material. Resilience is the work recovered from a material in elastic recoil, expressed as a percentage of the work previously done in straining it (Fig. 2.5). Passive musculoskeletal tissues should be as resilient as possible, to conserve energy.

Fig. 2.3 Elasticity

The force F tenses a block of material of transverse sectional area A and length l, producing a deformation e. In Figure 2.3A, stress is proportional to strain. The slope of this line is the elastic modulus.

Upon removal of the stress, the block returns to its original shape. The block is perfectly elastic. In Figure 2.3B, the elastic modulus is not constant; with more stress, a disproportionate deformation is produced.

For this reason, and also because when the stress is removed some of the deformation remains, the block in this instance is imperfectly elastic. Such a residual deformation is not useful in animal mechanics.

Fig. 2.4 Elastic resilience

Elastic resilience

When an elastic material is strained, work is done on it and energy is stored in it. Elastic energy is a form of potential energy. A rubber ball falling on to a hard surface converts what was previously kinetic energy into elastic energy on impact. This elastic energy is released again as kinetic energy when the ball bounces. The ball does not, however, attain the same height as previously. The elastic framework of an animal’s body behaves similarly, as it bounces up and down during running (Fig. 2.4). Some of the kinetic energy is lost as heat. The less energy lost in this way, the greater the elastic resilience of the material. Resilience is the work recovered from a material in elastic recoil, expressed as a percentage of the work previously done in straining it (Fig. 2.5). Passive musculoskeletal tissues should be as resilient as possible, to conserve energy.

Fig. 2.4 Elastic resilience

The work done in deforming the material is Fd, the product of force and distance. This is the area under the curve made during the application of the force (blue). The work done by the elastic restoring force is the area under the curve made during the removal of the deforming force (red hatching). In this example, these two areas are not the same. The difference in area is the energy lost as heat. The resilience is the red hatched area as a percentage of the blue area.

Fig. 2.5 A hopping kangaroo

Fig. 2.5 A hopping kangaroo

Compare the angle of the hock joint when the limb bears weight, and when not weight-bearing. The passive tissues supporting this joint store energy in A and release it in B. At hopping speeds of between 10 and 35 km/h, kangaroo locomotion is remarkably efficient. This is due to the almost 100% resilience of the elastic support of the hock joint.

Fig. 2.6 Elastin in the nuchal ligament of a sheep

Fig. 2.6 Elastin in the nuchal ligament of a sheep

a. Loose connective tissues surrounding the ligament.

b. Elastin fibres, stained with Verhoeff’s hematoxylin, in the ligament.

What makes materials elastic? The elasticity of materials comes about in several different ways:

Molecular elasticity: Stress may produce a molecular change. The keratinous structures of mammals (hair, wool, hooves and horns) are elastic because the keratin molecule changes from a tight helix to an extended form when it is stretched.

Crystalline elasticity: Stress on a material such as steel results in changes in distances between atoms. A large stress produces only a small distortion. The elasticity is therefore low.

Rubbery elasticity: The elasticity of the most elastic materials results from the cross-linking of long, flexible, convoluted polymers. In rubber, these cross-links are formed by sulphur during the process of vulcanisation. Distortion of a block of rubber results in a distortion of each molecule, which is restored when the stress is removed. Cross-linking is necessary to prevent the molecules from slipping past each other. Elasticity of rubber is lost when there are too many cross-links or when the temperature is too low. Several biological materials show rubbery elasticity. In vertebrates, elastin is present in thin strands in loose connective tissue, providing the extreme elasticity of such tissues as the dermis. It predominates in the middle coat of the wall of large arteries and in the nuchal ligament of herbivores (Figs. 2.6, 2.7). It is not fibrous, but consists of thin homogeneous strands. Its elasticity is similar to that of lightly vulcanised rubber.

Fig 2.7 A grazing cow

Fig.2.7 A grazing cow.

Herbivores have heavy heads held at the end of a long neck. As they flex their neck to graze, the nuchal ligament is strained by 50%. The elastic energy stored is released as the head is raised, so that little muscular effort is needed. A spring loaded garage door borrows this principle from the cow.

Fibrous elasticity: Polymeric molecules derive their elasticity by being arranged partly in ordered patterns to form crystalline regions, and partly with a random arrangement in amorphous regions. Examples of elastic materials of this kind include synthetic textiles like nylon and polyester, and natural ones like silk. Collagen, the main component of the passive musculoskeletal system, also has polymeric molecules, with the crystalline part composed of aligned and cross-linked molecules, appearing as fibrils (Figs. 2.8, 2.9). The molecules are aligned in a specific direction to form fibrils.

Fig. 2.8 Molecular structure of collagen in a tendon, diagrammatic

The significance of collagen

The fibrous elastomer collagen is by far the most predominant passive supporting substance in vertebrates. 20% of the protein of a mouse is collagen. Tendon, ligament and dermis are almost pure collagen, and it is a major constituent of bone and fibrocartilage. Few tissues lack it entirely. Collagen quality is of commercial interest because it determines the tenderness and appropriate cooking methods of different muscles, at different stages of growth.

Fig. 2.8 Molecular structure of collagen in a tendon, diagrammatic

Tendon structure as envisaged by:

a., protein chemistry;

b., c., and d., X-ray diffraction;

d., electron microscopy;

e., light microscopy and

f., as seen grossly in a large animal.

Fig. 2.9 Collagen structure, viewed electron-microscopically

Collagen molecules, fibrils and fibres

Collagen fibrils are formed when three tropocollagen molecules, each consisting of three helically arranged polypeptide chains 280 nm long, coil helically together, and align with other such "super helices". These polymeric molecules each overlap about one quarter of their length, so that an axial periodicity of 60-70 nm is visible with the electron microscope (Fig. 2.9). A collagen fibre is formed from bundles of fibrils (Fig. 2.8). Single collagen fibres are visible with the light microscope in connective tissues. They accumulate in bundles or sheets to form the gross structures ligaments, tendons and fasciae.

Fig. 2.9 Collagen structure, viewed electron-microscopically

Magnification x25,000.

Lateral accessoriometacarpal ligament of a horse.

• collagen fibrils, sectioned longitudinally

• collagen fibrils sectioned transversely

(from Deane, Massey thesis, 1991).