Global 3D parameter of the spine: application of Călugăreanu-White-Fuller theorem in classification of pediatric spinal deformity

Several classification systems of the spinal curves in adolescent idiopathic scoliosis (AIS) have been developed to guide surgical decision-making. The current classification systems are based on the spinal deformity patterns or deformity magnitudes in one or two anatomical planes. Considering the 3D nature of the spinal deformity in AIS, these classifications fail to capture the spine's curve in its entirety. We proposed a classification based on the axial plane and showed that mathematical analysis of the 3D spinal curve, using differential geometry, supports the differences between the subtypes in this classification system. We calculated the writhe and twist of the entire spinal centerline, elements of the Călugăreanu-White-Fuller theorem, in a cohort of 30 right thoracic AIS patients. We also classified this cohort manually based on the vertebral level at which the direction of vertebral rotation caudal to the thoracic curve changes: Lumbar in Group I (V-shaped axial projection) or thoracolumbar in Group II (S-shaped axial projection). The writhe and twist of the spinal curve were significantly different between these manual classification subgroups. Our manual classification distinguished the axial subgroups of right thoracic AIS supported by mathematical specifications of the entire curve in three dimensions. Graphical abstract.