10 Biomechanics and Reduction of Scoliosis
The spinal-deformity surgeon applies forces to favorably affect the spine’s geometry and morphology. To accomplish this, patients are placed in a thoraco-lumbo-sacral orthosis (TLSO) or force anchors are inserted into the vertebrae. Forces are also applied to the spine when physical therapy is prescribed. The force may be applied by the adjacent muscles of the spine, passively through the surrounding soft tissues, or directly to the vertebrae by instrumentation. In each instance, the forces applied are directed to counteract an abnormal group of forces that are producing spinal imbalance. The spine surgeon must be able to identify, locate, and correct those abnormal forces so as to achieve correction of a deformity and subsequent spinal balance. The forces should be applied harmoniously, to prevent stress risers; safely, to preserve the integrity of the surrounding anatomy; and efficiently, to achieve the desired spinal profile.
This chapter describes the mechanisms of failure of a long slender column such as the spinal column and describes the forces that cause that failure. These forces and others that contribute to the progression of a spinal deformity will be defined as critical forces (Fcr) or abnormal forces (Fab). Corrective forces (F+) are applied by the surgeon. The mode of application of these forces is important to understand, and the effect of these forces will be described and identified. F+ are applied to the spine via longitudinal members through force anchors, which are any devices used to transmit applied forces to the spine. They include hooks, screws, and wires. Techniques for enhancing the efficiency of force transmission by instrumentation, as well as failure of the implants used to transmit forces, will be presented together with pertinent metallurgical and biomechanical concepts.
It is the authors’ belief that a firm knowledge of the mechanical behavior of soft tissue, the effect of deforming and F+ applied to the spine, and techniques for applying corrective forces will improve the surgeon’s ability to correct spinal deformities.
The Biomechanics of the Spine: A Biological Column
Leonhard Euler in the 1700s discovered a relationship between the dimensions of a long slender column and the force needed to cause the failure of that column by buckling. The beam theory was developed from this and from the work of Bernoulli. The beam theory allows the prediction of load-carrying characteristics and deflection of a simple beam. The relationship is valid for an ideal column that is perfectly straight, homogenous in composition, and free of all and any initial stresses. The relationship of forces and failure of a beam derived by Euler and Bernoulli is:
Critical force = KπEI/L 2
where E = the modulus of elasticity of the beam (slope of the stress-strain curve)
I = moment of inertia (resistance of the beam to bending)
L = length of the beam
K = a constant depending on the conditions of end support of the beam
The failure of columns may vary according to their geometry. Short, wide columns may fail by yielding ( Figs. 10.1 , 10.2 ). Long, slender columns fail by buckling ( Figs. 10.3, 10.4 ).
The Fcr needed for buckling is proportional to the moment of inertia, I, and the modulus of elasticity, E, and not to the strength of the column, as one might expect.
Boundary conditions have an effect on the critical load capacity of a slender column. The critical boundary conditions for column stability are the type of mechanical supports provided at the ends of the column. The greater the resistance to bending at the ends, the more stable the column will be. However, boundary conditions also reflect other physical conditions or properties of the surrounding environment. Boundary conditions usually model supports, but may also model load points and moments. In the case of a spinal column, the surrounding bone and soft tissue would affect its mechanical behavior. Boundaries may determine the mode of bending and the number of inflection points of a column. An inflection point occurs when the curvature of a column changes from concave to convex. The closer the inflection points are to one another, the greater the load capacity of the column.
In Euler’s formula, the modulus of elasticity, E, the moment of inertia, I, for the structure, and π are constants. The modulus of elasticity is defined as the slope of the stress-strain curve for the beam material in the elastic region ( Fig. 10.5 ). Additionally, the beam in Euler’s formula must be made of a single material that is homogeneous and isotropic. The spine is neither. Therefore, Euler’s formula cannot be applied directly to the spine. However, the “effective” stiffness of the materials of which it is composed, and their interactions with surrounding structures, are directly proportional to the Fcr for the spinal column. The moment of inertia, I, is the resistance to bending of the cross-section of a structure, and is a function of the structure’s geometry. In Euler’s formula, I must be uniform along the length of the beam to which the formula applies. This is not true for the spine, and the formula therefore cannot be applied directly to the spine. The diameter or breadth of the cross-section of the beam is the critical dimension for I. The resistance to bending of the beam is roughly proportional to the fourth power of its diameter. Therefore, if one spine is 20% smaller in diameter than another, its I would be only 41% that of the wider spine, and its Fcr would be ~41% less.
The Fcr needed for buckling of the beam in Euler’s formula is inversely proportional to the length of the beam squared. Increasing the length of the beam significantly reduces the force needed to produce buckling of the beam. This relationship is appealing in that adolescent idiopathic scoliosis (AIS) occurs during a rapid growth spurt when the length of the spine is rapidly changing. It may also reflect variations in the mechanical properties of the spine that predispose to its buckling. More specifically, changes in E for that individual spine may reduce the Fcr needed for its buckling. The changes may affect ligaments, discs, and bone itself during the period of rapid growth, thereby predisposing the spine to buckling. Also of interest is Dickson’s concept of thoracic lordosis (bending) as the driving force in the development of thoracic scoliosis.
Euler’s equation does not specifically reflect the mechanical behavior for a spine, for the following reasons:
The structure must consist of an isotropic material, and must have equal physical properties along all of its axes. It must therefore be made of a homogenous material. The axial skeleton does not meet these criteria. It is composed of bone (compact and cancellous), ligaments, and discs. All of which have nonhomogeneous and anisotropic properties.
The spine in its normal state is prebuckled. The spine has normal sagittal contours, cervical lordosis, thoracic kyphosis, and lumbar lordosis. This condition is not included in Euler’s equation.
Scoliosis develops slowly over time; it is not a sudden, catastrophic event as is the buckling of a beam.
To satisfy Euler’s equation, a column must be a one-dimensional object, be straight, have a distributed load that is contained in one plane, and must be without torsion. Once again the geometry and mechanics of the axial skeleton do not meet these criteria.
The conditions in Euler’s formula do predict the failure of a long slender column resembling what is seen in scoliosis. Variations in the E of the spine will predispose to buckling and allow buckling to occur.
Euler, however, gives further insight into the etiology of scoliosis. The terms in his equation are constants except for the length of a given column. Yet spines of a given length do not often progress to develop a given curvature or geometry (moment of inertia, I). The remaining variable is E, the modulus of elasticity. This modulus is a function of the mechanical behavior of the material of which Euler’s beam is made. The value of E may vary among spines of a given length if the biological substrate should change. Variations in supporting spinal muscle composition, strength, or both may also result in a global change in the E of the spine. The Fcr needed to produce buckling should not be the focus of attention, but rather factors that alter the composition of the biological substrate. These changes may affect the overall strength of the spine more substantially and allow buckling. Decreasing the value of E would result in reducing Fcr, perhaps resulting in a deformity. A genetic predisposition that resulted in a change in the mechanical properties of the soft tissue of the back, uncoupled neuro-osseous growth, or an anterior-posterior growth mismatch could all affect the value of E of the spinal column. The Fcr needed to precipitate changes in the value of E for the spine could be such that a smaller Fcr would produce a deformity, thereby increasing the risk for curve development in an individual.
Vertebral Rotation and Coupled Motion
The preceding formulae describing beam deflection and buckling assume that the bending or buckling of the beam or both will occur about the neutral axis. The neutral axis is in the cross-section of a beam or shaft along which there are no longitudinal stresses or strains. If the section is symmetric (in both geometry and materials), the neutral axis is at the geometric centroid. Bending of the beam or shaft about the geometric centroid will not produce rotation. If, however, the axis of rotation is not the neutral axis then rotation will occur with bending. This relationship is called coupled motion. Rotation will result in lateral bending and lateral bending will result in rotation. Coupled motion is the basis for correction of a spinal curve using the derota-tion maneuver. Derotation of the spine will result in decreasing the lateral bend of a spinal curve. The correction can be achieved without elongation, and a distraction force is therefore not required.
Anterior Overgrowth Theory
Uncoupling of Anterior and Posterior Spinal Growth
The spine grows or elongates by anterior and posterior column growth. A balance between these two directions of growth will result in the normal coronal and sagittal planes of the spine. Uncoupled growth, as seen with anterior overgrowth, will result in a deformity. Anterior overgrowth with posterior tethering causes rotation and bending of the spine.1 This has been called rotational lordosis, and results in lordosis, rotation, and lateral deviation.2
Scoliosis is an axial rotational deformity. Although it has been postulated as a cause of scoliosis, no empirical evidence exists for rotation as a causative factor in initiating the deformity in scoliosis. Anterior vertebral overgrowth has also been postulated as a causative factor, yet this is difficult to prove in a human or animal model. By using a finite-element model of the human spine including the rib cage, Azegami has attempted to create a deformity by rapid apical vertebral growth.3 Azegami was able to achieve a 23-degree curve with 7 degrees of rotation by producing rapid growth of the vertebral bodies from T4 to T10. This model provided the proof that uncoupled vertebral growth can precipitate a three dimensional (3D) vertebral deformity similar to scoliosis ( Fig. 10.6 ).
Force Application in the Creation of a Deformity
A 3D spinal deformity may be simulated by the application of force.4 A model of the thoracolumbar spine was made with vertebrae composed of a synthetic resin and silicon discs. The model was fixed to a metal frame, and the spinal deformation caused by loading was determined relative to 3D coordinates set in the frame. The application of forces to the spine may result in scoliosis. However, these forces must be applied in a distinct order. The most severe scoliosis occurs when the order of loading is rotation, followed by lordosis, followed by lateral flexion ( Fig. 10.7 ).
Therefore, factors that promote buckling of the spinal column and the development of scoliosis include:
Uncoupled anterior-posterior vertebral growth (vertebral growth modulation)
Application of an Fcr to the column (Euler’s equation)
Application of force to the spine to produce rotation of the vertebral column followed by lordosis and lateral bending (asymmetrical loading)
Biomechanics of Surgical Correction of Scoliosis
F+ required to overcome or reverse the Fcr causing an abnormal spinal curvature must reverse the lateral bending and the rotation of the spine. Because lateral bending and rotation are coupled, a reversal of one will affect the other. How should the F+ be applied in such a situation? The location of the axis of rotation of the spine will explain the forces required to achieve correction of a deformity.
The Instantaneous Axis of Rotation
The instantaneous axis of rotation (IAR) is a point about which all other parts of a structure will rotate. It constitutes the center about which the muscles and instrumentation applied to a spinal curve exert their moment during flexion, extension, and torsion. The axis of rotation always migrates to the stiffest part of the structure. This is the mechanical premise for all osteotomies including pedicle subtraction osteotomy (PSO), the Smith-Peterson osteotomy (SPO), and Ponte’s innovative osteotomy for kyphosis. As the posterior column of the spine is compromised and shortened, the IAR migrates to the anterior column. The spine rotates about the anterior column. This allows the restoration of sagittal alignment without destroying the anterior column.
Positive Mechanical Advantage
Increasing the moment arm (the distance over which a force is applied from the IAR) has a positive mechanical advantage. Less force is required to achieve the same moment.
Moment = Force × Distance
F+ applied at a distance from the IAR will have a mechanical advantage in controlling and correcting a deformity. Where is the IAR of the spine? Where is the IAR of a scoliotic spine ( Fig. 10.8 )?
The IAR of the spine in rotation is located in the region of the spinal canal. Structures located at a distance from the axis of rotation will have an advantage in controlling motion. This is called a positive mechanical advantage and is the result of a force applied at a distance from the IAR.
The greater the distance from the IAR for a given force the larger the moment observed. If the IAR is located in the anterior column of the spine, the facet joints will have a positive mechanical advantage in resisting rotation, owing to their distance from the IAR and the consequently larger moment arm ( Fig. 10.9 ). If the IAR is located in the middle or posterior column, the disc has a mechanical advantage owing to the resultingly larger moment arm ( Fig. 10.10 ). The IAR for the human spine in rotation is located in the vicinity of the middle column. Structures at a distance from the IAR have a mechanical advantage in resisting rotation, and forces applied further from the IAR have a mechanical advantage in promoting rotation. The clinical application for this is multifold. First, the use of pedicle screws in a construct for correcting a thoracic deformity, and the three-column purchase achieved, significantly improves the ability to predictably treat the entire deformity. Traditionally, the problem of inadequate fixation of the spine and the inability of the construct being used to achieve fixation to withstand the magnitude and vector of the corrective forces applied has often led to minimal correction of an axial deformity. Put simply, posterior instrumentation with a hook (a form of single-column fixation)-and-rod system could not generate sufficient torque for the needed vertebral rotation because the axis of hook fixation was posterior to that of vertebral rotation. This has been validated by studies showing the limited rotational correction achieved with a hook-and-rod construct.5 The use of pedicle-screw instrumentation and the ability to provide a biomechanically superior construct has advanced the approach to treating spinal deformities posteriorly. With the resulting improved purchase and the freedom to develop corrective tools that increase the distance from the IAR, a rapid evolution of surgical techniques has dramatically improved the coronal and rotational correction of spinal deformities. The most poignant example of this is the technique for direct vertebral body derotation (DVR). Lee and colleagues showed significant coronal-, axial-, and sagittal-plane correction with this technique.6 The authors’ (JA and PC) evaluated CT scans confirmed and quantitated the significantly better axial-plane correction achieved with an all-pedicle-screw (60%) construct than with a hook-and-rod construct (22%).
Furthermore, Suk et al concluded that the pedicle-screw fixation technique effectively spares fusion levels at the distal end of a construct by improving the 3D correction of a deformity and proposed a strategy for determining distal fusion levels based on the neutral vertebrae and potentially shortening curves in single-curve constructs.
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