© 2000 by The Society for Integrative and Comparative Biology
Relationship Between Structure and Mechanical Function of the Tissues of the Intervertebral Joint1
1 Department of Bio-Medical Physics & Bioengineering, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK
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This paper reviews our current understanding of the relationship between the structures and properties of the tissues of the spine and their mechanical functions. Emphasis is on the human lumbar spine. Vertebrae consist of a core of cancellous bone (low density) surrounded by a shell of cortical bone (high stiffness); as a result they have high stiffness but low mass. The intervertebral disc is able to withstand compression because of the swelling pressure exerted by the nucleus pulposus which is constrained, radially, by the annulus fibrosus. Thus the disc acts as a thick-walled pressure vessel. Collagen fibers within the annulus provide reinforcement during compression, bending and torsion of the disc. Collagen fibers also provide tensile reinforcement and prevent tears spreading across ligaments. The ligamenta flava contain elastic fibers (low stiffness and low strength) with collagen fibers (high stiffness and high strength). In the unstretched ligamenta flava, the collagen fibers have almost random orientations but they become aligned as the ligament is stretched. This structure enables the high extensibility of elastic fibers to be exploited but protects them from damage at high strains. The structure of the interspinous ligament suggests that its main function is to attach the thoracolumbar fascia to the posterior spine. Thus the fascia is maintained in tension when stretched by the abdominal muscles. This and other observations indicate the importance of muscles for maintaining the stability of the spinal column.
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INTRODUCTION |
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SYNOPSISINTRODUCTIONVERTEBRAEINTERVERTEBRAL DISCSLIGAMENTSZYGAPOPHYSEAL JOINTSCONCLUSIONSReferences |
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This paper is concerned with the relationship between the structures and properties of the tissues of the spine and their mechanical functions. The emphasis is on the lumbar region of the human spine but results from other mammals will be used when they are considered to be suitable models for human tissue. There are two extreme approaches to understanding the mechanical behaviour of the spine. One is to formulate a model for the spine as a whole (Meakin et al., 1998
). An example of this approach is a model in which flexion of the spine is considered as an oscillation of an Euler pendulum; in this model the curved structure of the vertical human spine is considered to be a buckled column (Meakin et al., 1996). "Top down" models of this kind need not incorporate the detailed properties of all the components; however, the properties of the components are expected to have the required mechanical stiffness and strength to function as a part the system. The alternative, "bottom up," approach aims to synthesise an understanding of the system from a knowledge of the properties of its components. In practice, the two approaches are complementary in that models of one kind can influence the development of the other. However, the approach adopted in this paper is to consider the spine in terms of its component parts.
The smallest unit of the spine which we need to consider, if we are to understand the mechanical functions of its tissues, consists of two vertebrae and the flexible tissues which join them together. This unit is sometimes called a "motion segment" and is illustrated in Figure 1; further information on the anatomy of the human spine and detailed anatomical drawings are given in Bogduk (1997). Clearly Figure 1 represents an idealised structure since there is specialisation of structure and function along the spinal column, even in the lumbar region. For example, the most caudal joint in the lumbar spine is the lumbo-sacral in which the upper sacral vertebra (S1) is very different from the lower vertebra in Figure 1. Nevertheless, an understanding of how the tissues function in a "typical" motion segment is expected to provide insights on their behaviour in the intact spine. The effects of aging, degeneration and pathology on these tissues have important implications for the human spine but are beyond the scope of this paper which is concerned primarily with normal tissues.
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In this paper, tissues are considered to be part of: a vertebra (including its posterior elements); an intervertebral disc (nucleus pulposus and annulus fibrosus); the ligamentous system (anterior and posterior longitudinal ligaments, ligamenta flava, interspinous and supraspinous ligaments but excluding the capsular ligaments of the zygapophyseal joints); the zygapophyseal joints (see Fig. 1). The intervertebral joint is considered to consist of the flexible disc, with the longitudinal ligaments, attached to rigid vertebral bodies. However, the behaviour of this joint is affected by the other ligaments and by the tissues of the zygapophyseal joint. Some authors use the term "intervertebral joint" differently and may even include the zygapophyseal joints as part of it. The parts of the motion segment will be considered in turn; the paper concludes with some general comments on how they function together in the intact spine.
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VERTEBRAE |
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Functions
Each vertebra consists of a roughly cylindrical vertebral body and the posterior elements. The pedicles, which emerge posteriorly on the right and left sides, form the base of the neural arch which is completed by the laminae; the function of the arch is to protect the spinal cord or cauda equina. The processes which are attached to the neural arch provide attachment sites for ligaments and tendons.
Both the vertebral body and the posterior elements consist mainly of cancellous bone which is coated with a thin layer of cortical bone. They resemble "sandwich structures" in which a core of material of low density is stiffened by a skin of material which has a much higher stiffness and strength but which has a higher density. Synthetic sandwich structures were originally developed for making aircraft structures because they combine reasonable stiffness with low mass (Gordon, 1978).
There are several reasons why vertebrae should be stiff and they need to have a low mass to minimise the expenditure of energy in locomotion. Clearly, the vertebral arch needs to be stiff in order to protect the spinal cord (or caudal equina). A compliant arch would deform appreciably under the action of muscle forces and might then impinge upon the nervous tissue. The vertebral bodies need to have sufficient stiffness to maintain height when subjected to compressive forces. These forces are exerted by the axial components of muscle forces, as evidenced by the high pressure within an intervertebral disc while sitting (Nachemson, 1987), as well as by body weight and external loads. Finally, stiff bones are essential for effective control of movement. Forces exerted by the muscles should lead to bending or torsion at the required joints but not elsewhere in the body, at least not to any appreciable extent.
Compressive, torsional and flexural stiffness
The vertebral body will be used to illustrate how a core of cancellous bone, surrounded by a thin shell of cortical bone, can give rise to a structure which is a compromise between high stiffness and low mass. It is modelled as a cylinder of radius r and height h with a coaxial cylindrical cancellous core of radius ro; hence, the thickness of the cortical shell is r – ro. The mass of the cortical shell is given by
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where 
is the density of cortical bone.
The compressive stiffness for the cortical shell is given by
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where E is the Young's modulus of cortical bone. (Equations 2, 3 and 5 can be derived easily from standard results which are tabulated and simply explained by Gordon, 1978). The compressive stiffness is defined so that dividing the value of an applied compressive force by Sc yields the resulting decrease in height. Thus, from equation 2, (r2 – ro2) should be sufficiently large to achieve the required stiffness but h should be as low as possible both to increase the stiffness (eq. 2) and to reduce the mass (eq. 1) which explains the squat shape of human lumbar vertebrae. In practice, an intact vertebral body has a much higher stiffness than that of the cortical shell alone because the shell stiffens the cancellous bone by restricting its radial expansion during axial compression (Bryce et al., 1995). When the cancellous bone loses trabecullae, during osteoporosis, the vertebral bodies are liable to damage from crush fractures (Eastell et al., 1991). This model assumes that cancellous bone makes a negilgible direct contribution to the resistance of a vertebra to compression. It is likely to be somewhat simplified for two reasons. Firstly, there is some regional variation in the compressive stiffness of the cancellous bone (Keller et al., 1989), suggesting that there is likely to be some regional variation in function. Secondly, there are changes in the anisotropy of cancellous bone, associated with bone loss (Nicholson et al., 1997), suggesting that it does not act simply as an anisotropic filler.
The flexural stiffness of the cortical shell of a cylindrical vertebral body is given by
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This equation was derived by considering the shell to be a cylindrical cantilever whose stiffness is the force applied to one end divided by the deflection of that end. A compromise between high flexural stiffness and low mass is achieved by a high value of
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Hence, ro as well as r needs to be high and h needs to be low to achieve high flexural stiffness with low mass. This result is consistent with the structure of a human lumbar vertebra which can be considered as a squat cylinder of cancellous bone surrounded by a thin shell of cortical bone, ensuring that both ro and r have high values.
Finally, the torsional stiffness (usually called the "torsional rigidity") of the cortical shell is given by
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which is calculated from the applied torque divided by the resulting torsion angle. Here G is the rigidity or shear modulus which is related to E by
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where the Poisson's ratio, 
, is a constant for a given direction in a given type of bone (Cowin, 1989). In order to achieve a compromise between high torsional stiffness and low mass, the shell requires a high value of
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Hence the requirement to achieve torsional stiffness with low mass is exactly the same as for flexural stiffness (high r, high ro and low h), leading to a squat cylinder of cancellous bone surrounded by a thin shell of cortical bone.
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INTERVERTEBRAL DISCS |
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Nucleus pulposus
The nucleus pulposus (abbreviated to "nucleus") forms the soft centre of the intervertebral disc and exerts a turgor or swelling pressure which enables the disc to withstand axial load (Maroudas and Urban, 1980
). This swelling pressure arises because the nucleus has a high concentration of proteoglycans which attract water. The nucleus is contained radially by the annulus fibrosus (abbreviated to "annulus" and axially by the cartilage end-plates of the disc. The annulus is a hollow cylinder which surrounds the nucleus. It consists of a series of cylindrical layers called "lamellae." Thus the outermost lamella forms the outer margin of the annulus all around the disc, i.e. anteriorly, laterally and posteriorly. Similarly, the innermost lamella defines an inner margin all around the disc. The inner lamellae of the annulus merge into the end-plates to contain the nucleus (Aspden et al., 1981).
When the disc is subjected to axial compression, both the inner and outer margins of the annulus bulge outwards as a result of the increased pressure in the nucleus. This result was demonstrated by placing metal markers in the annulus of an excised disc and obtaining radiographs at various stages of compression (Krag et al., 1987); similar experiments were also performed using magnetic resonance imaging and nylon monofilament markers (Chiu et al., 1995). More recently, sheep discs were sectioned in the sagittal plane, while frozen, to lock in the internal pressure; the cut surface was then sealed with a transparent window and video images recorded during compression of the thawed specimen (Meakin, 1998). The inner and outer margins of the annulus were observed to bulge outwards but when the nucleus was removed the inner margins bulged inwards (Fig. 2). This result agrees, apart from some details, with the observations of Seroussi et al. (1989) who used the technique of Krag et al. (1987), described above. These observations are consistent with the predictions of finite element models (Goel et al., 1995; Meakin, 1998) and with some magnetic resonance images of intact human discs during in vitro compression before and after partial removal of the nucleus (Meakin, 1998).
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The observations described in this section indicate that, during compression of the disc, the nucleus behaves like a fluid in a thick-walled pressure vessel. In practice, the disc also has to withstand bending and torsion. Magnetic resonance images of human volunteers show that, during flexion, compression of the anterior annulus displaces the nucleus posteriorly and, during extension, compression of the posterior annulus displaces the nucleus anteriorly (Fennell et al., 1996
); similar results were obtained previously on cadaveric specimens (Krag et al., 1987; Seroussi et al., 1989). Although the behaviour of the nucleus in the disc resembles a fluid and it can be modelled as a fluid with a bulk modulus of 1720 MPa (Meakin, 1998), this is a simplification of its mechanical properties since it can withstand compression (Leahy and Hukins, 1997) and shear (Iatridis et al., 1996). Furthermore, the human nucleus loses water and becomes more solid-like during aging and degeneration of the disc (Coventry et al., 1945); these changes can be readily detected by magnetic resonance imaging (Hickey et al., 1986). Thus the loss of water from the nucleus, which accompanies aging, is expected to influence the mechanical response of the disc to compression but this influence has yet to be investigated systematically.
Annulus fibrosus
The annulus can be considered as a thick-walled pressure vessel containing the nucleus (Hukins, 1992). Then the walls have to withstand a radial stress and a tangential stress whose directions are shown in Figure 3. The radial stress is compressive, i.e., it tends to compress the annulus in the radial direction, and the tangential stress is tensile, i.e., it tends to stretch the annulus in the tangential direction. The magnitudes of both stresses decrease from the inner to the outer lamellae.
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Although the annulus contains the high-pressure nucleus, it is able to withstand some axial compression directly itself. The reason is that, like the nucleus, it exerts a swelling pressure as a result of water being attracted by its proteoglycans. However, the proteoglycan content is much higher in the inner lamellae than in the outer; consequently the water content is greater in the inner lamellae (Lyons et al., 1981
). The decrease in water content matches the decrease in radial stress predicted from the behaviour of a thick-walled pressure vessel (Hukins, 1992). Experimental measurements of pressure in a compressed cadaveric disc (McNally and Adams, 1992) also decrease from the inner to the outer annulus, as predicted (Hukins, 1992). The annulus is able to withstand tension because it is reinforced by collagen fibers. In a single lamella, the collagen fibres are parallel and tilted, with respect to the axis of the disc, by about 65°; this tilt angle is the same in the fetus as in the adult and does not change appreciably with aging (Hickey and Hukins, 1980a, 1982; Hukins et al., 1987). Collagen fibers provide tensile reinforcement provided they are stretched by the stress applied to a tissue (Hukins, 1982). In a simple model, in which compression leads to uniform radial expansion of a cylindrical disc, the fibers will be strained by compression provided their tilt angle exceeds 54.7° (Broberg and von Essen, 1980; Hickey and Hukins, 1980b; Klein et al., 1982; Hukins, 1988). When bulging is taken into account, the tilt angle must be slightly greater (around 65°) as observed experimentally (Klein et al., 1983; Hukins, 1988; McNally and Arridge, 1995).
The high concentration of collagen fibers in the outer lamellae provides tensile reinforcement during bending and torsion of the disc. This explains why the collagen content is greatest in the outer lamellae; if the annulus had to function solely as a pressure vessel, the collagen content would be expected to be higher in the inner lamellae where the (tangential) tensile stress would be greatest. Reinforcement during bending can be illustrated by flexion which will stretch the posterior annulus. The collagen fibers in the posterior annulus are then stretched and those in the outer posterior annulus are stretched most of all. Similarly, the fibers in the outer anterior annulus will be stretched most in extension. In lateral bending, fibers in the outer annulus will also be stretched most—on the left side when bending right and vice versa. Figure 4 shows a fiber in a single lamella being stretched by torsion. Torsion of a cylindrical disc about its axis moves the end A of the fibre to A', so that it is stretched and provides reinforcement. For a given value of the torsion angle, 
, the increase in fiber length increases with radius, r, so that the fibers of the outer annulus provide the most tensile reinforcement. Note also, that fibers in adjacent lamellae, which are tilted in the opposite direction cannot provide reinforcement when the disc is subjected to torsion in the direction shown. However, they do provide reinforcement for torsion in the opposite direction. Thus only half the fibers are able to provide tensile reinforcement during torsion in a given direction. More quantitative details on how the fibers are stretched by torsion are given elsewhere (Hukins, 1988). The quantitative theory also predicts that fibers reorient during compression, bending and torsion of the disc; this reorientation has been measured experimentally and shown to be in reasonable agreement with theoretical predictions (Klein and Hukins, 1982a, b).
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LIGAMENTS |
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Longitudinal ligaments
The longitudinal ligaments are flat bands of roughly parallel collagen fibers which merge into the outer lamellae of the annulus fibrosus. It is clear, from their position, that the anterior ligament will be stretched by extension and that the posterior ligament will be stretched by flexion of the spine. This expectation has been confirmed by measurements on cadaveric specimens (Panjabi et al., 1982
). However, the restoring force exerted by the stretched posterior ligament will be less than that exerted by the much broader anterior ligament. Therefore, the posterior ligament is expected to be less important for resisting flexion than the anterior ligament is for resisting extension.
The wavy structure of the collagen fibers in these ligaments makes them extensible at low strains but stiffer at higher strains (Hukins et al., 1990a). Thus the restoring force which the stretched ligaments exert to oppose extension (anterior ligament) or flexion (posterior ligament) will increase at higher bending angles. This property may enable them to protect the fibers of the annulus by restricting the range of flexion-extension. Both reflected light and scanning electron microscopy show the wavy structure of these ligaments. Scanning electron micrographs of ligaments, fixed when unstretched and at a strain of 0.03, show initial stretching consists of straightening the wavy fibers (Kirby et al., 1989); the collagen stiffness is not fully exploited until the fibers are completely straightened. Similar results were obtained on unfixed material using reflected light microscopy and x-ray diffraction, which allows the spread of fiber orientations to be measured directly (Kirby et al., 1989; Hukins et al., 1990a).
The longitudinal ligaments have been used to demonstrate the ability of collagen fibers to deflect fractures and so toughen connective tissues, i.e., these ligaments withstand an appreciable load even after they are damaged (Sikoryn and Hukins, 1988). Video recordings were made of the ligaments while they were stretched to failure. Figure 5 shows a ligament which has been stretched to 2.5 times its original length. Tears have formed in the weak proteoglycan gel but have not propagated right across the tissue because they have been deflected by the stronger fibers. Thus the ligament is still able to withstand the applied load even though it is damaged. This ligament did not fail completely until stretched to four times its original length.
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Ligamenta flava
The ligamenta flava are stretched during flexion of the spine. Since the spine flexes about an axis in the disc nucleus or inner annulus (Klein and Hukins, 1983
), the ligamenta flava are stretched further than is the posterior longitudinal ligament during flexion (Panjabi et al., 1982). Hence they must be capable of stretching further without being damaged. It is possible that the ligamenta flava provide some resistance to flexion and so, like the posterior longitudinal ligament, protect the posterior annulus.
Ligamenta flava contain about twice as many elastic fibers as collagen fibers. Elastic fibres consist mainly of the rubber-like protein elastin and are highly extensible. Histological sections show that the ligaments consist of densely packed elastic fibers which appear to have narrow collagen fibers dispersed between them. X-ray diffraction enables the orientation of the collagen fibers to be measured (Kirby et al., 1989; Hukins et al., 1990). Figure 6 shows that the fibers are almost randomly oriented in the ligament before it is stretched. As the ligament is stretched, along its axis, the fibers become more highly aligned (Fig. 6). However, they are not as highly aligned as in unstretched longitudinal ligaments until the ligament has stretched to 1.5 times its original length. Since the collagen fibers are stiffer than the elastic fibers, the stiffness of the ligament increases as it is stretched.
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The structure of the ligamenta flava enables them to be stretched to high strains without damage. At low strains the collagen fibers have almost random orientations. The ligament is then highly extensible because of the low stiffness of its elastic fibers and because few of the stiffer collagen fibers are oriented so that they will be stretched. As the strain increases, the stiffer and stronger collagen fibers become more highly aligned, thus stiffening the ligament and protecting the weaker elastic fibers from damage. As a result, a ligamentum flavum can be stretched to four times its original length without any sign of damage. Thus the initially almost random orientation of collagen fibers enables the high extensibility of elastin to be exploited but alignment protects the elastin at higher strains.
Interspinous and supraspinous ligaments
The collagen fibers in the interspinous ligament spread out, in a fan-like arrangement, about a direction parallel to the spinous processes of the vertebrae which they link (Aspden et al., 1987; Hukins et al., 1990a). However, there have been several conflicting reports in the literature on their orientations. The observed pattern of orientations means that the collagen fibers are not stretched by flexion, or any other movement of the spine. Indeed, flexion simply causes the fibers to fan out more (Aspden et al., 1987). Thus the main function of this ligament does not appear to be to resist flexion. A more plausible funtion for the interspinous ligament is to transfer stress from the thoraco-lumbar fascia to the posterior spinal column (Tesh et al., 1987; Hukins et al., 1990a); maintenance of stress in the fascia may increase the efficiency of the erector spinae muscles during lifting (Hukins et al., 1990b).
In most human spines, the supraspinous ligament terminates between the third and fifth lumbar vertebra (Rissanen, 1960; Myklebust et al., 1988; Hukins et al., 1990a). It appears to be a loose, fatty structure with little tensile strength. Its function is not clear but it may act as a subcutaneous cushion to protect the posterior spine.
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ZYGAPOPHYSEAL JOINTS |
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The zygapophyseal joints are synovial joints between the articular processes. They are formed between the facets of the medial surfaces of the superior articular processes, on one vertebra, and the facets on the lateral surfaces of the inferior articular processes, on another vertebra (Fig. 7). In the human lumbar spine their angulation limits torsion, at a single intervertebral joint, to about 3° (Adams and Hutton, 1981
). This is simply because torsion to the left closes the right-hand joint until the facets impinge. In addition, torsion to the left is resisted by tension in the capsular ligaments of the left-hand joint (Panjabi et al., 1982). Thus, the zygapophyseal joints protect the intervertebral disc from excessive torsion in the human lumbar spine.
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CONCLUSIONS |
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The intervertebral disc confers torsional and flexural flexibility on the spine. It is protected, in extension, by the anterior longitudinal ligament and, in flexion, by the posterior ligaments of the spine—the posterior longitudinal ligament and the ligamenta flava. Collagen fibers are capable of deflecting tears in ligaments so that they do not spread across the tissue and cause sudden failure. As a result, ligaments are able to withstand tension even after they are damaged. Collagen fibers can also reinforce the annulus of the disc and ligaments, provided they are stretched when the tissue is stretched. They are, therefore, able to reinforce the disc in bending and torsion, and the longitudinal ligaments when they are stretched. The structure of the ligmenta flava, which contain both collagen and elastic fibers enables them to withstand higher strains than the posterior longitudinal ligament. Higher strains are imposed on the ligamanta flava than on the posterior longitudinal ligament when both are stretched during flexion of the spine. In the human lumbar spine, torsion is limited to about 3° by the zygapophyseal joints which, therefore, protect the intervertebral disc. Synthetic ligaments, made from polyester braid, attached to the vertebrae in surgery, can be used to extend the spine so that the zygapophyseal joints lock; the tension in these "ligaments" then prevents excessive flexion, extension and torsion of a damaged intervertebral joint (Leahy et al., 2000
). The muscles which initiate joint movement are attached to the vertebral processes by tendons. The vertebrae must be sufficiently strong to withstand these forces and sufficiently stiff to ensure that flexion and torsion are restricted to the joints. At the same time, they should have as low a mass to avoid using excess energy in locomotion. The requirement for high stiffness with low mass is achieved by combining an inner region of cancellous bone (low mass) with an outer shell of cortical bone (high stiffness).
The vertebral bodies and intervertebral discs also have to withstand high compressive loads. These loads arise from the axial component of the forces exerted by the muscles which initiate bending and torsion, as well as from body weight and external loads. The nucleus pulposus of the disc exerts a turgor which acts an a hydrostatic pressure to support an applied load, in much the same way as pneumatic pressure in a tyre supports the weight of a vehicle. The annulus fibrosus then acts as a thick-walled pressure vessel to contain this internal pressure.
However, it is not always valid to consider the spine simply as a column of bones and joints. It appears that the function of the interspinous ligament may be to maintain the tension in the thoraco-lumbar fascia. The fascia is placed in tension by the abdominal muscles (Tesh et al., 1987) leading to an increase in abdominal pressure. An increase in abdominal pressure has been observed, in humans, during lifting and is often supposed to provide additional support to the spinal column (Aspden, 1987). Antagonist muscles also provide an active component for stiffening the spine, especially in the control of motion (Hukins, 1995).
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ACKNOWLEDGMENTS |
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Our recent research on the spine has been performed in collaboration with Richard Aspden, Steven Harvey, Johanna Leahy, Katharine Mathias, Duncan Shepherd and Douglas Wardlaw. Financial support has been provided by the Biotechnology and Biological Sciences Research Council, the Scottish Higher Education Funding Council (as part of the Joint Equipment Initiative), Smith and Nephew Group Research and Surgicraft Ltd.
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1 From the Symposium The Function and Evolution of the Vertebrate Axis presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 6–10 January 1999, at Denver, Colorado.
2 E-mail: d.hukins{at}biomed.abdn.ac.uk
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References |
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