A reduced-order model of the spine to study pediatric scoliosis

The S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work, we proposed a reduced-order model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one Lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern, showing that for rods deforming in a Loop1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the Loop2 shape, the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves-Lenke 1 and Lenke 5. Our S-shaped elastic rod model generates deformations that are similar to those of a pediatric spine with the same sagittal curvature characteristics and it can differentiate between the clinically observed deformation patterns.