Chapter 7 Basic biomechanics
Movements
There are two types of motion that a bone may undergo: translation and rotation. The essence of translation is that every point on the bone moves in the same direction and to the same extent (Fig. 7.1). Translation occurs whenever a single force or a net single force acts on a bone, and any force that tends to cause translation is called a shear force.
Rotation is characterised by all the points on a bone moving in parallel around a curved path centred on some fixed point. The points move in a similar direction but to different extents depending on their radial distance from the fixed point which is known as the centre of rotation (Fig. 7.2). Rotation occurs when two unaligned forces act in opposing directions on different parts of the bone, forming what is known as a force couple (see Fig. 7.2), and the net force tending to cause rotation is referred to as the torque. Depending on circumstances, torque may be the result of two opposed forces which may both be muscular actions, or they may be a muscular action and a ligamentous resistance, or they may be gravity opposed by either muscular action or ligamentous resistance.
When a rotating bone is considered in three dimensions it can be seen that all the points throughout the bone can be grouped into individual planes that lie parallel to the direction of motion (Fig. 7.3). In each plane, the points move about a centre located in that plane, and when all the centres of all the planes are lined up they depict a straight line that forms what is known as the axis of rotation of the bone.
Planes of movement
Both translation and rotation can occur in either of two opposite senses which can be variously defined according to circumstances or convention. For example, the motion can be upwards or downwards, forwards or backwards, clockwise or anticlockwise, and in some conventions positive (+) or negative (−). Furthermore, in three-dimensional space, translation or rotation can occur in any of three fundamental planes. In anatomical terms, these planes are the sagittal, coronal and horizontal planes (Fig. 7.4). Backward or forward rotations are movements in the sagittal plane, as are translations in the backward or forward direction. Side-bending is rotation in the coronal plane, and twisting is rotation in the horizontal plane. A sideways gliding movement across the horizontal plane would be horizontal translation, while movements up or down are described as coronal translations.
Biomechanists prefer to define movements in relation to three imaginary axes drawn through the body, which are labelled X, Y and Z.1,2 The X axis passes sideways through the body; the Y axis passes through it vertically; and the Z axis passes through it from back to front (Fig. 7.5). Movements can then be described as along or around any particular axis. Thus, sagittal translation is translation along the Z axis; sideways gliding movements are translations along the X axis; and up and down movements are along the Y axis. Forward bending is rotation around the X axis; side-bending is rotation about the Z axis; and twisting movements are rotations around the Y axis. The key to this nomenclature lies in the prepositions used. Translations are movements along one of the axes while rotations are movements around one of the axes.
The advantage of the biomechanists’ convention is that the dimensions of movements are accurately and unambiguously defined. However, the terms ‘X’, ‘Y’ and ‘Z’ are unfamiliar and anonymous to all except to those who use them regularly. The terms ‘sagittal’, ‘coronal’ and ‘horizontal’ are somewhat more meaningful because of their use in other areas of anatomy, and these are the terms used in this text. In the anatomical system the movements are perceived to occur in or along the plane in question, irrespective of whether the movement is a translation or a rotation. For reference, the equivalence of various terms derived from the anatomical system, the biomechanists’ convention and colloquial vocabulary is shown in Table 7.1.
Table 7.1 Descriptive terms of motion. By convention, the direction of any rotation is defined according to the direction of movement of the most anterior point on the bone
| Anatomical system | Biomechanical system | Colloquial description |
|---|---|---|
| Anterior sagittal translation | +Z translation | Forward slide or glide |
| Posterior sagittal translation | −Z translation | Backward slide |
| Cephalad coronal translation | +Y translation | Longitudinal or axial distraction |
| Caudal coronal translation | −Y translation | Longitudinal or axial compression |
| Left horizontal translation | +X translation | Left lateral slide |
| Right horizontal translation | −X translation | Right lateral slide |
| Anterior sagittal rotation | +X rotation | Forward bend, ‘flexion’ |
| Posterior sagittal rotation | −X rotation | Backward bend, ‘extension’ |
| Left coronal rotation | −Z rotation | Left lateral bend |
| Right coronal rotation | +Z rotation | Right lateral bend |
| Left horizontal rotation | +Y rotation | Left axial rotation |
| Right horizontal rotation | −Y rotation | Right axial rotation |
Because of difficulties in appreciating the distinctions between translations and rotations in the horizontal and coronal planes, the term ‘axial’ has been introduced in Table 7.1. Thus, the term ‘axial rotation’ replaces ‘horizontal rotation’ to refer to rotation in the horizontal plane, i.e. around the long axis of the body. The term ‘axial translation’ replaces ‘coronal translation’ to refer to movement up or down, or along the long axis of the body, and to distinguish this movement from sideways translations in the horizontal plane, which are described as horizontal or lateral translations.
To specify the direction of axial translations, the terms ‘cephalad’, meaning towards the head, and ‘caudad’, meaning towards the tail, are used in Table 7.1. Although perhaps cumbersome and unfamiliar, these terms are accurate and applicable in all situations. The more familiar terms ‘upward’ and ‘downward’ are applicable for axial translations in the upright position but they are not strictly applicable in describing motions of vertebrae in patients who might be lying down. To overcome this difficulty, the more colloquial terms of ‘distraction’ and ‘compression’ are more usually used instead of ‘cephalad’ and ‘caudad axial translation’. Similarly, the term ‘lateral bending’ is more convenient and is preferred to ‘coronal rotation’.
In this text, the term ‘sagittal’ rotation is strictly used to refer to forward and backward rotatory movements. Although the terms ‘flexion’ and ‘extension’ are commonly used to describe this motion, these terms are insufficiently accurate when applied to movements of individual lumbar vertebrae. Flexion and extension are not pure movements of the lumbar vertebrae because, as will be shown in Chapter 8, these movements involve a combination of both sagittal translation and sagittal rotation. The terms ‘flexion’ and ‘extension’ may be used to describe forward bending and backward bending of the lumbar spine in a general sense, but in relation to movements of individual vertebrae it should be understood that the terms refer to a combination of both sagittal rotation and sagittal translation.
The relevance of these explicit definitions of motion is extensive. In the first instance, the motion of individual vertebrae is often complex, and no single term can describe the motion. Nevertheless, it can always be described as some combination of the fundamental movements listed in Table 7.1. Furthermore, each component of motion of the lumbar spine is exerted and resisted by different mechanisms, and to appreciate how these mechanisms act, each needs to be analysed in relation to the particular component of motion that it controls. This type of analysis is undertaken in Chapter 8.
Stress–strain
To stretch a collagen fibre, a force must be applied to it. Once it starts to stretch, the fibre resists elongation by generating a resisting force due to the chemical bonds between collagen fibrils, between tropocollagen molecules, between collagen fibres, and between collagen fibres and proteoglycans (see Ch. 2). By convention, the applied or elongating force is known as the applied stress and the extent to which a fibre is elongated is known as the strain. Stress is measured in units of force (newtons) and strain is measured as the fractional or percentage increase in length relative to initial length. Thus a fibre of length L0 when stretched to a new length L1 undergoes a strain of L1/L0 or L1/L0 × 100%.
