La torsion géométrique dans la scoliose idiopathique

The intention of this thesis is to study the geometrical torsion phenomenon in scoliosis with the hypothesis that three-dimensional (3-D) scoliotic deformities can be represented by a spatial curve characterized and described from curvature and geometric torsion properties, defined mathematically by Frenet's formulas. To test this hypothesis, three novel approaches of 3-D curvilinear modeling of the spine were investigated. From these, a geometric model that accurately represents the 3-D geometry of common scoliotic deformities was proposed for the evaluation and interpretation of geometric torsion. A clinical study was conducted to evaluate the reliability of geometric torsion as a 3-D index of idiopathic scoliosis deformities.

A radiographical 3-D reconstruction technique developed at Ecole Polytechnique of Montreal and establish in a clinical environment (Montreal Sainte-Justine Hospital) was used to reconstruct left and right pedicles bases and estimate the vertebral centroid location, approximately, the center of the vertebral foramen. The first approach of scoliotic spinal modeling fitted segments of elliptical helices to the 3-D reconstructed thoracic and lumbar vertebral centroids.

An alternative method was to represent the spine with parametric functions of Fourier series fitted by least square techniques. This second approach was more effective than the elliptical helices approach for representing lumbar and thoracic scoliotic geometries and allowed evaluation of torsion at every point along the modeled spine avoiding any loss of information.

The third approach was based on the statistical interpolation method of kriging. The torsion of the simulated spines was estimated from models using the best kriging functions and was found to be more accurate (1.46 × 10⁻⁵ ± 1.18 × 10⁻⁴ mm⁻¹ to 1.2 × 10⁻⁵ ± 7.11 × 10⁻⁵mm⁻¹) than the torsion obtained from simple least square Fourier series method (5.25 × 10⁻³ ± 3.71 × 10⁻³ mm⁻¹) when compared with the analytical torsion.

The application of the “corrected” Fourier series approach to real data of healthy and scoliotic subjects verified the bi-directional torsion phenomenon behavior of right thoracic-left lumbar curves and confirmed that the geometric torsion have extreme values at the curve limits (end vertebrae), whereas the torsion is nearly zero at the apexes.

The novel approach of Fourier series, including a corrective technique for torsion spikes, allowed characterization of the 3-D morphology of scoliotic deformities. This provided a better understanding of the geometric torsion phenomenon in idiopathic scoliosis. The observation of geometric torsion patterns led to a novel classification system that includes both three-dimensional and torsional descriptions of scoliotic deformities. (Abstract shortened by UMI.)