Chapter 30 Practical Anatomy and Fundamental Biomechanics

Narayan Yoganandan, Curtis A. Dickman, Edward C. Benzel

Vertebral Column

The human spinal column consists of 33 vertebrae interconnected by intervertebral discs, facet capsules, and ligaments. Normally, there are 7 cervical (C1-7), 12 thoracic (T1-12), 5 lumbar (L1-5), 5 fused sacral (S1-5), and 4 separate coccygeal bones. The first three regions are flexible. The most common variations include sacralization of the fifth lumbar vertebra or lumbarization of the first sacral vertebra. Ventral and dorsal views of the spinal column with the skull are shown in Figure 30-1. The normal adult vertebral column has four curvatures. The cervical and lumbar regions are lordotic and the thoracic and lumbosacral regions are kyphotic. The lordotic curvature is convex ventrally, and the kyphotic curvature is concave ventrally. The thoracic and lumbosacral kyphotic curvatures exist in utero and are called the primary curvatures. The cervical and lumbar lordotic curvatures develop with the raising of the head postnatally and the assumption of the erect posture. The cervical curvature is shallow; it begins at the dens of the axis and terminates at T2. The lumbar lordosis develops due to the upright position of the trunk. The sacral curvature is relatively smooth and concave. Variations in the disc and vertebral body dimensions form and maintain these curvatures; they are often modified by age-related changes of the vertebrae, osteophyte development, trauma, congenital malformations, neurologic disorders, and imbalances of the paraspinal muscles. The center of gravity of the spinal column generally passes from the dens of the axis through the vertebra to the promontory of the sacrum.¹ The center of gravity of the body is located just ventral to the sacral promontory (Fig. 30-2). The vertebral column has different types of articulations: cartilaginous joints between the vertebral bodies, apophyseal joints between vertebral arches, unique articulations between the axis (C2) and atlas (C1), and skull-C1 articulation.

FIGURE 30-1 Human spinal column and skull: dorsal view (left); right lateral view (center); anterior view (right), all illustrating the cervical, thoracic, and lumbar vertebrae, sacrum, and coccyx.

(From Sances A Jr, Weber RC, Larson SJ, et al: Bioengineering analysis of head and spine injuries. Crit Rev Bioeng 5:79–122, 1981.)

FIGURE 30-2 Human vertebral column showing the line of gravity.

(From Woodburne RT: Essentials of human anatomy, 7th ed, Oxford, England, 1982, Oxford University Press.)

Vertebrae

Each vertebra consists of a cylindrically shaped body ventrally and an arch dorsally, and all encase the spinal cord and nerve roots. The outer shell of the vertebral body consists of a thin layer of relatively rigid compact cortical bone. This outer shell houses an inner core of soft and porous cancellous bone containing bone marrow. The structure of the cortical bone is aligned in vertical lamellae to resist compressive forces. The trabeculae of the cancellous bone are ordered like columns, and they resist a variety of loads. The rostral and caudal surfaces of the vertebral body are generally concave and are separated and bound together by the fibrocartilaginous discs. The dorsal arch is composed of the laminae, pedicles, spinous processes, and facet joints. Pedicles are stout bars of bone extending dorsolaterally from the rostral aspect of the vertebral body. The laminae extend dorsally, immediately from the pars interarticularis. They fuse in the midline to form the dorsal wall of the spinal canal. The laminae are oblong plates with a sloping surface. The spinous process arises from the junction of the laminae. The orientation of the spinous process depends on the region of the spine (cervical, thoracic, and lumbar). The cervical transverse processes arise from each side of the vertebral body near the junction of the pedicle and body. The thoracic and lumbar transverse processes arise from the junction of the pars interarticularis and pedicle. The transverse and spinous processes serve as attachments for muscles and ligaments. The articular processes arise from the pars interarticularis, interposed between the pedicles, laminae, and facet joints. Generally, superior articular processes project cranially with the articulating surface of facet on the dorsal surface. Typically, the inferior articular processes project caudally with the articular surface facing ventrally. A thin layer of hyaline cartilage lines the surface of each facet, which is a synovial joint, lined with synovium, and surrounded by a capsule. Characteristic features of cervical, thoracic, and lumbar vertebrae are described in what follows.

Cervical Vertebrae

These vertebrae are smaller in size compared with those in the thoracic and lumbar regions. They are cylindrically shaped and are wider in the transverse than anteroposterior (AP) diameters. The size gradually increases from C3 to C7. The pedicles are short and project dorsolaterally. They arise from the vertebral body midway between the rostral and caudal surfaces. The arch is composed of paired pedicles and articular facets, as well as the lamina and spinous processes. The laminae are narrow and overlap. The spinous processes are short and are usually bifid from C3 to C6. The transverse processes are unique. They contain the transverse foramen from C1 to C6, which transmits the vertebral artery. The anatomy of a typical cervical vertebra (C3-7) is shown in Figure 30-3. The pars interarticularis in the cervical spine is termed the lateral masses. The superior and inferior facets extend from the lateral masses. The facets from C2-3 to C6-7 are oriented approximately 45 degrees with respect to the horizontal and are aligned with a coronal orientation to their surfaces. The first cervical vertebra (C1), or atlas, is ring shaped and supports the cranium. The atlas consists of a bony ring with stout lateral masses and anterior and posterior arches. It has large lateral masses containing the horizontally oriented facet surfaces. Rostral facets articulate with the occipital condyles of the skull, and the inferior facets articulate with the rostral facets of C2. The axis (C2) has a unique shape with a transitional morphology; it has a well-developed vertebral body with the odontoid process projecting rostrally. Its broad sloping superior facets extend laterally from the body.

FIGURE 30-3 A and B, Anatomy of a typical cervical vertebra.

Thoracic Vertebrae

These vertebrae are somewhat heart shaped and are intermediate in size between the lumbar and cervical vertebrae. The anatomy of a typical thoracic vertebra is shown in Figure 30-4A. It exhibits costal facets on each side at the junction of the body and pedicle and on transverse processes. These facets are unique (Fig. 30-4B). The costal facets are also seen on the transverse processes (except for T10-12). Vertebrae at the rostral and caudal regions have some transitional morphologic features; that is, T1 to T4 vertebrae have some cervical features, and T9 to T12 have some lumbar features. The surface area gradually increases from T1 to T12. The middle four vertebrae have almost equal lateral and AP dimensions. Lateral dimensions increase toward the cervical and lumbar extremes of the thoracic region. The spinous processes of the first, second, eleventh, and twelfth vertebrae are horizontal; the third, fourth, ninth, and tenth are oblique; and the fifth to eighth spinous processes overlap and are long and vertical. The size of transverse processes increases progressively from T1 to T12. The cervical features of T1 include the superior vertebral notch, and the lumbar features of T12 include the lateral direction of the inferior articular processes. The laminae are broad and sloping, and they overlap one another like shingles on a roof. The thoracic facets are oriented along the coronal plane. At the thoracolumbar junction, they assume a more oblique sagittal orientation.

FIGURE 30-4 Typical thoracic vertebra. A, In addition to the rib articulations, note the orientation of the articulating facets. B, Drawing of thoracic spine showing nature of rib articulation to two vertebrae each.

Lumbar Vertebrae

Vertebral bodies in this region are the largest and typically increase in the diameter caudally. They are larger in the transverse width than their AP diameter; a concavity of the vertebral body gives rise to an hourglass profile and a kidney-shaped cross section. The bodies of L1-2 vertebrae are deeper dorsally. The L4-5 vertebrae are deeper ventrally, whereas the L3 vertebra is transitional. The laminae are relatively broad, wide, and minimally overlap. The interlaminar spaces are covered by the ligaments and by large oblong and horizontal spinous processes. Long, thin, slender horizontal transverse processes incline slightly rostrally in the lower two lumbar segments. The transverse process of L3 projects the farthest and that of L5 spreads ventrally. The fifth lumbar vertebra represents the transition from the lumbar to the sacral spine. It is substantially taller ventrally. This contributes to the lumbosacral angle. The thick and conical transverse process arises from the junction of the pars and the pedicle of L5. The anatomy of a typical lumbar vertebra is shown in Figure 30-5.

FIGURE 30-5 Anatomy of a lumbar vertebra.

Sacrum and Coccyx

The sacrum is formed by the fusion of the costal ligaments and the transverse processes. It is triangular in form, concave, and relatively smooth on its pelvic surface. It is convex and highly irregular dorsally. Five sacral bodies are demarcated by four transverse lines that end laterally in four pairs of ventral sacral foramina. The bilateral foramina are rounded laterally to indicate the courses of the emerging nerves. The coccyx may be a single bone fused from coccygeal elements, or the first segment may be separate from the other. These vertebrae are reduced in size, and they have no laminae, pedicles, or spinous processes.

Vertebral End Plates

These are formed by the rostral and caudal surfaces of the vertebral body. They are composed of concave surfaces of approximately 1.3-mm-thick cortical bone. The cartilaginous end plates are the superior and inferior thin planar surfaces of the intervertebral disc. They are the transition components between the fibrocartilaginous disc and the vertebral end plates. Each cartilaginous end plate is fused to the vertebral end plate by a calcium layer termed the lamina cribrosa, a sievelike surface that permits osmotic diffusion. Nutrients for the disc penetrate through the small pores at the lamina cribs.

Intervertebral Discs

The most rostral intervertebral disc space is located between the second and third cervical vertebrae and the most caudal disc is between the L5 and S1 vertebrae. Twenty-three discs span the vertebral column between C2 and S1. Discs demonstrate regional geometric variations that parallel morphologic differences in the vertebral bodies. The discs account for approximately one third to one fifth of the total height of the vertebral column. Four concentrically arranged components are often identified in the intervertebral discs: an outer alternating layer of collagen fibers that form the peripheral rim of the anulus fibrosus, a fibrocartilage component that forms a major portion of the anulus fibrosus, a transitional region between the central nucleus pulposus where the anulus and nucleus merge, and the nucleus pulposus. The core of the disc, termed the nucleus pulposus, is made of a soft, pulpy, highly elastic mucoprotein gel. The nucleus contains various mucopolysaccharides with relatively few collagen fibers and a high water content. The anulus fibers pass obliquely from the vertebral body above and below and are arranged in a helicoid manner. The anulus is composed of concentric layers of fibrous tissue. The orientation of the fibers within each layer is the same. The orientation of the fibers in adjacent layers differs by 30 degrees (Fig. 30-6). The disc undergoes age-related changes. At birth, the disc has four distinct anatomic regions. However, the distinguishing features disappear as age transforms the disc into fibrocartilage and the number and size of the collagen fibers increases. With age, the macromolecular framework consists of collagen, proteoglycans, a noncollagenous matrix of proteins, glycol proteins, and small amounts of elastin. The elastic fibers are made of a central amorphous zone and a peripheral rim of dense microfibers. The arrangement of the fibers in the nucleus is irregular. The disc is approximately cylindrical with different ventral and dorsal heights. Typical cross sections of the disc resemble an ellipse in the cervical region, a rounded triangle in the thoracic region, and an ellipse in the lumbar region. Generally, midthoracic discs are mostly circular in cross section. In contrast, midcervical intervertebral discs are less circular. Like the vertebral body, cross-sectional areas of the disc increase from C2 to T1.

FIGURE 30-6 Intervertebral disc. A, The nucleus and anulus fibrosus. The anulus is made of laminated bands of fibers arranged concentrically. B, The anulus fibers and their orientation.

(From White AA, Panjabi MM: Clinical biomechanics of the spine, ed 2, Philadelphia, 1990, JB Lippincott.)

Ligaments

Ligaments are multilayered and are composed primarily of elastin and collagen. Ligaments connect adjacent vertebrae and may extend over several segments along the spinal column. Ligaments and joint capsules, while permitting normal spinal motion, restrict excessive motion.

Anterior Longitudinal Ligament

This ligament is continuous and spans the entire length of the vertebral column. It begins at the occiput as the anterior occipitoatlantal membrane and continues down to the sacrum covering one fourth to one third of the ventral circumference of the vertebral bodies and discs. It consists primarily of long-ranged collagen fibers aligned in interdigitizing layers. The deepest layer extends between the adjacent vertebrae, binding to the edges of the intervertebral discs. The middle layer binds the vertebral bodies and the discs over three levels, and the superficial fibers extend approximately four to five levels. The ligament is thickest over the concavity of the vertebral body blending into the periosteum.

Posterior Longitudinal Ligament

This ligament also traverses the entire length of the spinal column. It begins at C2 as the tectorial membrane and continues to the sacrum with fibers spreading out at the disc level and narrowing at the middle of the vertebral body. This ligament consists of several layers with the deep fibers extending only to adjacent vertebrae and the stronger superficial fibers spanning several levels. Whereas the ligament closely adheres to the disc anulus, it attaches only marginally to the vertebral body. This ligament is much thinner over the vertebral body and over the disc (by a factor of approximately one half) and is thickest in the thoracic region. Both the posterior and anterior longitudinal ligaments have a longitudinal (rostral to caudal) fiber orientation.

Ligamenta Flava

These are broad paired ligaments that connect spinal laminae. They arise from the ventral surface of the caudal lamina and attach to the dorsal border of the adjacent rostral lamina. They are discontinuous at midvertebral levels and in the midline. They extend laterally to the joint capsules and become confluent. These ligaments extend from C1-2 to L5-S1 levels. They have a high elastin content and are yellow. The ligamenta flava are the most elastic tissues in the human body. The capsular ligaments attach the adjacent vertebra to articular joints. The fibers are longer and slacker in the cervical region than in the thoracic and lumbar regions. The fibers are perpendicular to the plane of the articular surfaces.

Interspinous and Supraspinous Ligaments

These ligaments connect the adjacent spinous processes. They are composed predominantly of elastin. The interspinous ligaments attach from the base to the tip of each spinous process. They start at C2-3 and terminate at L5-S1. Both spinous ligaments are most prominent in the lumbar region. In contrast, the supraspinous ligament begins at the most dorsal aspect of the spinous process of C7 and continues into the lumbosacral region. The supraspinous ligament is primarily associated with the ligamentum nuchae of the neck contacting the spinous processes at their tips. It is the continuation of the ligamentum nuchae in the cervical spine. The ligament fibers end between the L3 and L5 levels. Figure 30-7A illustrates the ligamentous structures in the sagittal and axial planes.

FIGURE 30-7 A, Sagittal and axial section through the lumbar spine demonstrating the associated ligaments. B, Schematic diagram of the upper cervical (occiput-C1-2) spinal region emphasizing the ligaments. Cut-away posterolateral view showing the relative location of the major ligaments.

(A, From Sances A Jr, Myklebust JB, Maiman DJ, et al: The biomechanics of spinal injuries. Crit Rev Biomed Eng 11:1–76, 1984, with permission.)

Upper Cervical Spine Ligaments

Upper cervical ligaments span from the occiput to C2 (see Fig. 30-7B). Beginning ventrally, the anterior longitudinal ligament is renamed as the anterior atlanto-occipital membrane from C1 to the occiput. The apical ligament attaches from the tip of the odontoid process of C2 to the basion of the occiput. The alar ligaments connect the rostrolateral aspect of the odontoid process and run obliquely to the occipital condyles. The cruciate ligament has ascending and descending bands and a strong transverse portion that courses dorsal to the odontoid process and attaches to tubercles on the medial aspects of the lateral masses of the atlas. The vertical cruciate ligament attaches from the occiput, just dorsal to the apical ligament, and intertwines with its transverse portion. The descending band attaches to the dorsocaudal aspect of the body of C2. The tectorial membrane attaches to the ventral one third of the basiocciput just dorsal to the vertical cruciate ligament. This ligament tapers caudally to become continuous with the posterior longitudinal ligament. Finally, the posterior atlanto-occipital membrane connects the rostral aspect of the dorsal arch of C1 to the occiput.

Muscles

The superficial muscles of the rostral thoracic region and dorsal neck originate from thoracic spinous processes and insert laterally on the scapula. The muscles are attached medially to the ligamentum nuchae, which is a fibrous intermuscular septum. The sternocleidomastoid muscles arise from the sternum and the clavicle, and they insert into the mastoid process of the occipital bone. In the lower thoracic and lumbar regions, several muscles make up the superficial layer. The most prominent muscle is the latissimus dorsi, which arises from the spinous processes of the lower thoracic vertebrae and extends as a sheet across to the ventral axilla. Both the intercostal muscles and serratus posterior muscles arise from the ribs in different directions. Muscles encircling the abdominal region include the external and internal obliques and the transversus abdominis. The rectus abdominis muscle is located in the ventral abdominal wall. Deeper muscles ventral to the vertebral column are less prominent than the dorsal muscles. In the cervical region, the longus coli muscle passes from the atlas to the transverse processes of C3 to C6. Deep lateral muscles include the anterior scalenus, the longus capitis, and the intertransverse muscles. They also attach to the transverse processes.

In the thoracic region, the longus coli muscle extends only a few segments. In the lower thoracic and upper lumbar region, however, the lateral muscle groups are prominent, especially the psoas, intertransverse, and quadratus lumborum muscles. The iliopsoas muscles originate from the lateral aspects of the vertebral bodies and extend to the femur. As in the rest of the spine, the intertransverse muscles extend between the transverse processes. The quadratus lumborum also originates from the transverse processes and runs obliquely to the lateral ileum. Beneath the trapezius muscle, the splenius capitis muscle arises from the lower ligamentum nuchae and the cervical and upper six thoracic transverse processes, to attach to the occiput. The narrowest muscle, the splenius cervicis, originates only from the upper six thoracic spinous processes to insert on the posterior tubercles of C1 to C3. The adjacent deeper layer includes the semispinalis capitis and semispinalis cervicis muscles. The more medial semispinalis cervicis arises from the transverse and articular processes of the upper thoracic vertebrae inserting into the spinous process of the cervical spine. The lateral muscle originates from the transverse processes of C3 to C6 and inserts on the occipital bone. The deepest muscles of this group include the iliocostalis and longissimus cervicis, which arise from the upper thoracic ribs and transverse processes, respectively, to end on the transverse processes and facets of C4 to C7. Other deep muscles include the rectus capitis and capitis obliques, which serve as head extensors.

In the thoracic and lumbar regions, the erector spinae muscle group lies in the vertebrocostal groove directly under the thoracolumbar fascia. This muscle group begins as a tendon attached broadly to the dorsocaudal sacrum and iliac crest and extends the entire length of the spine. Its columns are composed of shorter fascicles. The lateral column represents the iliocostalis muscles, the intermediate column represents the longissimus muscles, and the middle column represents the semispinalis muscles.

The iliocostalis muscles arise from the iliac crest and insert on the angles of each of the ribs (iliocostalis lumborum and thoracis) as well as the cervical transverse processes. The longissimus represents the largest column. It arises from the transverse process at the lowest spinal levels and inserts into the transverse processes rostrally with the most rostral fibers inserting onto the mastoid process of the skull. The narrow spinalis muscle arises from the spinous processes of the sacrum and inserts into the higher spinous processes.

Deep to the erector spinae muscle lie the paravertebral or transverse spinal muscles. These muscles, including the semispinalis discussed previously, have their origins primarily from the vertebral transverse process and insert into the spinous process. The semispinalis group is continuous in the cervical and thoracic regions. The multifidus muscle is different in the cervical and lumbar areas, where the attachments are to the articular joint, but in the thoracic region the attachments are to the transverse processes. This muscle is thickest in the lumbar region.

Spinal Cord

The spinal cord and nerve roots traverse the spinal canal. The spinal cord is approximately 40 to 45 cm long in the adult and usually terminates at L1-2. The rostral cord at the level of the foramen magnum is continuous with the medulla oblongata. The dura mater, the pia mater, and the arachnoid are the three membranes that cover the spinal cord. The spinal cord is suspended in the spinal canal by dentate ligaments. These arise from the pia and are attached to the dura. Usually, the spinal cord terminates approximately at the caudal aspect of the L1 vertebral body. The cauda equina consists of the nerve roots, which have not exited through their neural foramina. Spinal nerves are composed of a dorsal sensory root and a ventral motor root. With the exception of the C1 and C2 contributions to the spinal accessory nerve, nerve roots leave the spinal canal via the neural foramina. Anatomically, the spinal cord is divided into five sections: 8 cervical, 12 thoracic, 5 lumbar and 5 sacral, and 1 coccygeal. Figure 30-8A shows a schematic of the spinal cord, indicating the relationship among spinal segments, nerves, and vertebral bodies.

FIGURE 30-8 Diagrams of the human spinal cord. A, Sagittal view showing relationships among spinal segments, spinal nerves, and vertebral bodies (left); dorsal view illustrating various spinal land masses (right). B, Diagrammatic axial section of the spinal cord demonstrating the somatotopic orientation of spinal tracts (left); diagrammatic axial section of the spinal canal at the level of the midlumbar spine (right). Note the orientation of the neural elements (clusters); the lower elements are situated most medially and those preparing to exit the spinal canal most laterally. C, Spinal canal diameter versus spinal level. The width (solid line) and depth (dashed line) of the canal are depicted separately. D, A diagrammatic representation of the respective shapes and sizes of a typical spinal canal in the cervical (left), thoracic (middle), and lumbar (right) regions.

(A, Modified from Carpenter MB: Human neuroanatomy, 7th ed, Baltimore, 1976, Williams & Wilkins. B, From Benzel EC: Stability and instability of the spine. In Benzel EC, editor: Biomechanics of spine stabilization, principles and clinical practice, New York, 1995, McGraw-Hill, pp 25–40. C, Data from references 67–70. D, From Sances A Jr, Weber RC, Larson SJ, et al: Bioengineering analysis of head and spine injuries. Crit Rev Bioeng 5:79–122, 1981.)

The tracts within the spinal cord in the cervical and thoracic regions and nerve roots in the lumbar region are somatotopically oriented. The cortical spinal tracts are somatotopically arranged so that hand function is located more medially, whereas the foot function is located laterally. The spinothalamic tract is arranged so that hand sensation is located most medially and ventrally, and the sacral sensation is located most dorsally and laterally. The posterior columns are similarly arranged in a somatotopic manner. In the lumbar region, the nerve roots are arranged so that the lower sacral segments are located most medially and the exiting upper lumbar regions most laterally (Fig. 30-8B).

In a normal spine, spinal canal dimensions and hence the subarachnoid space are generous except in the midthoracic region (Fig. 30-8C). In the case of preexisting spinal stenosis, the factor of safety is reduced. This is important during a spinal instrumentation procedure that might impinge on the neural elements (e.g., sublaminar wire or hook placement). The lumbar spinal canal depth does not change significantly as one descends from the upper to the lower lumbar regions; however, its width increases (see Fig. 30-8C). The lumbar and sacral spinal canal cross-sectional areas are also more generous than in other areas of the spine. It contains the cauda equina, which consists of peripheral nerves and is relatively resistant to traumatic insults. For both reasons, posttraumatic neural element injury in the lumbar region is less severe than that associated with comparable deformation in the other regions of the spinal column, particularly the midthoracic area. The respective shapes of the typical spinal canal in the cervical, thoracic, and lumbar regions are depicted in Figure 30-8D.

Fundamental Biomechanics

Biomechanics is defined as the application of the principles of engineering and computers to solve biologic problems. Clinical biomechanics of the spine refers to the understanding of the normal and the pathologic functions of the human vertebral column due to the application of mechanical insult. The insult could be in the form of traumatic dynamic forces, deformations, and/or slowly applied loads to the spine.² Several terms are explained to facilitate a better understanding of clinical spinal biomechanics.

Scalar and Vector

A scalar is a quantity defined by its magnitude. It is directionally independent. Energy absorbed by the cervical spine due to the application of a load is an example of a scalar. In contrast, a vector possesses both magnitude and direction. Forces applied to the spine can be broken down into the components of vectors. To accomplish this, a reference system must be chosen. Force can be defined as an action that tends to change the state of the rest of the body to which it is applied. Force is a scalar. Force applied in a particular direction is often termed as the force vector or load vector. In biomechanics, force and load are used synonymously. Because the spine is not rigid, the application of force results in deformations.

Cartesian Coordinate System

The right-handed Cartesian system of reference is commonly adopted in spine biomechanics. The system consists of three axes: x, y, and z. Rotational and translational movements can occur along and about these axes. Translational movements are considered positive if the movements occur along the positive direction of the axis; it is considered negative if the moments are in the negative direction. Similarly, a clockwise rotation around an axis looking from the origin of the coordinate system toward the positive direction of the axis is termed positive rotation, whereas the counterclockwise rotation is termed negative. Figure 30-9 illustrates the right-handed Cartesian coordinate system of reference with the z-axis oriented along the caudal to rostral direction, the x-axis along the dorsal to ventral direction, and the y-axis along the right-to-left direction. For the right-handed system, this results in a positive flexion moment (extension being negative), positive moment left-to-right lateral bending (right-to-left lateral bending is a negative moment), and positive twisting right axial rotation moment (left axial rotation is a negative moment). This reference system has been adopted by the American Standard for Testing Materials. Once the coordinate system of reference is chosen, the force vector can be divided into its components.

FIGURE 30-9 Schematic representation of the spine and three-dimensional coordinate axes. Linear forces are designated Fx, Fy, and Fz, and moments are designated Mx, My, and Mz. A positive x-force is dorsal to ventral, a positive y-force is from right to left, and a positive z-force is from caudal to rostral. A positive x-moment is right-lateral bending, a positive y-moment is flexion, and a positive z-moment is left axial rotation.

Deformation

Deformation can be translational and/or rotational. Translational deformation results in a change in the length of the body. Rotational deformation results in a change in the angle of the body to which the force is applied. Deformations result in strains.

Strain is defined as the change in unit length (linear) or change in unit angle (shear) in the body subjected to a force (vector). There are two types of strain: normal and shear. Normal strain is defined as the change in the length divided by the original length. Shear strain is defined as the change in the right angle (90 degrees). When a deformable body is subjected to a load vector, deformations occur, resulting in strains. The deformation along the direction of the force application is termed axial strain, whereas the deformation transverse to the direction of application of the force is often termed the transverse strain. The ratio of the lateral (transverse) to the longitudinal (axial) strain is termed Poisson’s ratio.

Kinetics and Kinematics

The study of the mechanics of the body in relation to the forces and the deformations is kinetics. In contrast, kinematics deals with the motion of the body (deformations) independent of the forces responsible for the deformations. Both the terms are applicable to the biomechanics of the spine.

Force Deformation Response

Because of the deformability characteristics of the spine, the application of an external force or a load vector results in deformations. Energy is frequently used to relate the force and the deformation; it represents the amount of work done by a force on a body. It is defined as the area under the force deformation curve. In contrast, stiffness is defined as the ratio of force to deformation. Because the force deformation characteristics of a spinal structure are not always linear (Fig. 30-10), the most linear portion of the curve is often selected for obtaining the maximum stiffness of the structure. Analysis of the typical force deflection characteristics of the spinal structure (example of a functional unit) is given subsequently. Response is nonlinear; that is, force does not increase linearly with the deformation or vice versa. Within the principles of structural mechanics, this biomechanical load deflection response has been classified into the physiologic loading phase; the traumatic loading phase; and the failure, or the posttraumatic, loading phase. The stiffness response of the structure has been used to derive these biomechanical classifications. This system has been used to design a schema to evaluate the onset of spinal injury due to external load. This may help define the mechanism of spinal disorders.

FIGURE 30-10 Typical nonlinear response of the lumbar spine, indicating the different stages in the biomechanical characteristics of the structure.

(From Yoganandan N, Larson SJ, Gallagher M, et al: Correlation of microtrauma in the lumbar spine with intraosseous pressures. Spine 19:435–440, 1994.)

In the physiologic loading phase, the spinal structure acts as an integral unit, and the stiffness increases gradually to a maximum value. During this phase, the structure obtains its highest stiffness; consequently, its resistance increases with the externally applied loads. This region represents the highest mechanical efficiency domain in the structural response. Trauma does not occur during this region of loading. With the increase in the application of load, yielding of the structures occurs. This is identified biomechanically by the onset of decreased stiffness for the first time during the loading process. Previous studies have demonstrated microfailures during this phase of loading.³ The end of this traumatic range is characterized by changes in the stiffness that correspond to the ultimate load-carrying capacity of the structure. After reaching its peak during the physiologic loading phase, the stiffness gradually decreases to zero at the end of the traumatic loading phase, indicating that the structure has reached its ultimate load-carrying capacity. In the subsequent phase (i.e., the posttraumatic loading phase), the structure responds with negative resistance; that is, an increase in the deformation results in a decrease of the load. Trauma has been identified on radiographs when the structure has been loaded to this level. Based on the simple fundamental force deformation response and using the stiffness as a mechanics-based criterion, studies have indicated that microtrauma may initiate the loss of a local component before the structure has reached its ultimate load-carrying capacity.^4,⁵ In other words, even under subfailure loading, the structure may exhibit signs of weakness or microfailure.

Flexibility, Stiffness, and Range of Motion

Flexibility is defined as the inverse of stiffness (i.e., ratio of the deformation to an applied load). Flexibility and stiffness are inversely interchangeable in spinal biomechanics. Another quantity, the range of motion, is frequently used in spinal biomechanics. This refers to the deformation from one extreme to the other extreme under the physiologic range of translation or rotation of an intervertebral joint.

Coupling

Because of the three-dimensional nature of the spinal structure, motions are coupled. Coupling is defined as the capacity of the spine to move in translations and/or rotations independent of the principal motion. In other words, it represents obligatory movements of the spine (translations or rotations) that always accompany a primary motion. Both principal and coupled motions exist in the spine.⁶ Principal motion can be defined as the motion associated with the direction or the plane of application of the external force. Any out-of-phase motion is the coupled motion. For example, axial rotation of the upper cervical spine is usually coupled with lateral bending.⁷ Similarly, in the lower cervical spine, axial rotation and lateral bending of the vertebra in the opposite direction are usually coupled (Fig. 30-11).

FIGURE 30-11 The coupling phenomenon is the relationship between lateral bending and rotation in the cervical and lumbar regions. This is depicted (A) diagrammatically and (B) anatomically. The coupling phenomenon results in rotation in opposite directions of these two regions. The thoracic spine does not exhibit significant coupling.

(From Benzel EC: Stability and instability of the spine. In Benzel EC, editor: Biomechanics of spine stabilization, principles and clinical practice, New York, 1995, McGraw-Hill, pp 25–40.)

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