This research sought a mathematical model to relate the postero-anterior (PA) and lateral (LAT) views of the spinal curve in scoliosis in an attempt to justify the acquisition of only One X-ray, thereby reducing patient exposure to harmful X-radiation while preserving complete 3D characterization of the spine. Using powerful developments in functional statistics and machine learning, no such relation could be found. Thus, this research sustained the clinical decision to acquire two biplanar X-rays and supported current research in 3D spinal curvature analysis.

Scoliosis is monitored through full spinal X-rays, and this serial protocol causes an increased incidence of cancer development. This research sustains the clinical decision at Hôpital Sainte-Justine in Montréal and elsewhere to acquire postero-anterior (PA) and lateral (LAT) X-rays, despite the increased exposure to X-radiation. Indeed, geometrically, these two views are required to reconstruct the spine in 3D. However, under the assumption of strong physiological patterns between the PA and LAT views of the spinal curve, one of these X-rays may be redundant for some or all patients. The purpose of this study was to seek this a priori assumption.

To this end, a database consisting of three hundred and sixty-nine spinal reconstructions from distinct patients was used. Two powerful geometric modeling approaches were exploited: functional data analysis and minimum noise fractions. These resulted in five comprehensive, uncorrelated and noise-insensitive features in each plane. Simple linear regression yielded no relation that was statistically significant (p< 0.05) and genereralizable to a set of previously unseen samples. Therefore, nonlinear relational modeling was attempted using support vector regression, a recent advance in machine learning theory. This tool was incapable of identifying a robust regression, suggesting that the PA and LAT views are mathematically independent. Thus, this study highlights the necessity of two biplanar X-rays to evaluate scoliotic deformities and fully characterize spinal shape. Further, this study supports the practical insufficiency observed by clinical staff with respect to current 2D scoliosis classifications that has resulted in current efforts to propose 3D classification schemes.