Parametric modeling of the intervertebral disc space in 3D: application to CT images of the lumbar spine

Abstract

Gradual degeneration of intervertebral discs of the lumbar spine is one of the most common causes of low back pain. Although conservative treatment for low back pain may provide relief to most individuals, surgical intervention may be required for individuals with significant continuing symptoms, which is usually performed by replacing the degenerated intervertebral disc with an artificial implant. For designing implants with good bone contact and continuous force distribution, the morphology of the intervertebral disc space and vertebral body endplates is of considerable importance. In this study, we propose a method for parametric modeling of the intervertebral disc space in three dimensions (3D) and show its application to computed tomography (CT) images of the lumbar spine. The initial 3D model of the intervertebral disc space is generated according to the superquadric approach and therefore represented by a truncated elliptical cone, which is initialized by parameters obtained from 3D models of adjacent vertebral bodies. In an optimization procedure, the 3D model of the intervertebral disc space is incrementally deformed by adding parameters that provide a more detailed morphometric description of the observed shape, and aligned to the observed intervertebral disc space in the 3D image. By applying the proposed method to CT images of 20 lumbar spines, the shape and pose of each of the 100 intervertebral disc spaces were represented by a 3D parametric model. The resulting mean (±standard deviation) accuracy of modeling was 1.06±0.98mm in terms of radial Euclidean distance against manually defined ground truth points, with the corresponding success rate of 93% (i.e. 93 out of 100 intervertebral disc spaces were modeled successfully). As the resulting 3D models provide a description of the shape of intervertebral disc spaces in a complete parametric form, morphometric analysis was straightforwardly enabled and allowed the computation of the corresponding heights, widths and volumes, as well as of other geometric features that in detail describe the shape of intervertebral disc spaces.

Keywords: Computed tomography (CT); Intervertebral disc space; Lumbar spine; Parametric modeling; Superquadrics; Three-dimensional (3D) images; Total disc replacement.