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.

青少年特发性脊柱侧凸 (AIS) 脊柱弯曲的几种分类系统已被开发出来以指导手术决策。当前的分类系统基于一或两个解剖平面的脊柱畸形模式或畸形程度。考虑到 AIS 中脊柱畸形的 3D 性质，这些分类无法完整捕获脊柱的曲线。我们提出了一种基于轴向平面的分类，并表明使用微分几何对 3D 脊柱曲线进行数学分析，支持该分类系统中亚型之间的差异。我们在 30 名右胸 AIS 患者的队列中计算了整个脊柱中心线的扭动和扭曲，这是 Călugăreanu-White-Fuller 定理的要素。我们还根据胸椎曲线尾部的椎骨旋转方向发生变化的椎骨水平对该队列进行手动分类：第一组为腰椎（V 形轴向投影），第二组为胸腰椎（S 形轴向投影）。这些手动分类亚组之间脊柱曲线的扭动和扭曲显着不同。我们的手动分类区分了右胸 AIS 的轴向亚组，并得到了整个曲线在三个维度的数学规范的支持。