Introduction: Elucidation of the exact cause of adolescent idiopathic scoliosis (AIS) remains an elusive goal. The intervertebral disc is one of the many areas that have been investigated in an effort to find a cause for this condition. We hypothesize that a qualitative change in the orientation of collagen fibers in the annular layers of the disc could cause the deformity seen in AIS. This paper presents a mathematical model of such a change and how it could produce appropriate deforming forces. Hypothesis: In the normal disc the collagen fibers are obliquely orientated. Fibers in adjacent lamellae are orientated in opposing directions. This means that as forces are transmitted from a compressed nucleus to the annular fibers there is no net force tending to rotate one vertebra with respect to its neighbour. If there is a preponderance of fibers running in one direction as the nucleus is compressed there will be a net resultant force perpendicular to the long axis of the spine tending to produce an intervertebral rotation. This intervertebral rotation, applied to successive spinal segments will cause a scoliotic deformity.

Model: The highly oriented structure of the AF suggests the utility of an explicit representation of the collagen fibres and their mechanical contribution to disc function. In our study we have considered two groups of fibres, representing the clockwise and counter clockwise fibres in the disc. The AF is considered as a continuum containing two populations of fibres assumes to be of equal density and uniform distribution within an isotropic material as originally described by Spencer. Nuclear compression as a result of growth was modelled as a tendency to produce increased intervertebral separation of spinal segments and examined whether the resultant transformation that leads to a scoliotic pattern of deformity. Based on anatomical data from literature the positions of the 12 nodes that represent the thoracic vertebrae are applied to the model. The three-dimensional location of each vertebral body is defined. We store the coordinates of thoracic vertebrae in a three-dimensional matrix. In the present study in order to involve the translation operation in our transformation, we have used the homogeneous transformation matrix or Denavit & Hartenberg matrix.

In the present model for the initial set of transformations the reference axis is chosen to be the lowest vertebral axis (T-12) and remains unchanged throughout the transformation. All elements of the spine above the reference axis are transformed (translated and rotated). After completion of this iteration and storing the values for the origin coordinate and vector values in the next level of the matrix, the next reference axis is chosen. For the second axis everything above the axis will be transformed in the same way with the current axis and the one preceding it remaining unchanged. Therefore for each transformation a new reference axis is taken and the transformations are applied to all vectors and origins above it leaving all elements preceding it unchanged by the transformation.

Results: The first part of the model shows that rotational displacement increases linearly with changes in the fibre ratio. Rotational displacement on the other hand occurs independently of distraction of the vertebral bodies. When the rotational displacement is applied to a series of segments it produces alterations of curvature in the three planes. Specifically it produces a lateral curvature in the coronal plane and a hypokyphotic curvature in the saggital plane. The magnitude of these displacements varies with the imbalance in fibre ratio. Discussion: The proposed changes in annular fiber orientation have been modeled using accepted mathematical methods. These changes will produce an intervertebral rotation whose magnitude depends on the degree of fiber imbalance akin to that seen in AIS. When the displacements produced by this rotation being applied to a series of segments is modeled, it will produce a three dimensional deformity similar to that seen in AIS. Ongoing histological studies are being performed to see if the proposed imbalance can be identified in patients with AIS. Such a fiber orientation anomaly may be genetically determined by some fashion of directional sense gene and may be the aetiological basis for AIS.