Spine slenderness and wedging in adolescent idiopathic scoliosis and in asymptomatic population: an observational retrospective study

Abstract

Purpose

The origin of the deformity due to adolescent idiopathic scoliosis (AIS) is not known, but mechanical instability of the spine could be involved in its progression. Spine slenderness (the ratio of vertebral height to transversal size) could facilitate this instability, thus playing a role in scoliosis progression. The purpose of this work was to investigate slenderness and wedging of vertebrae and intervertebral discs in AIS patients, relative to their curve topology and to the morphology of control subjects.

Methods

A total of 321 AIS patients (272 girls, 14 ± 2 years old, median Risser sign 3, Cobb angle 35° ± 18°) and 83 controls were retrospectively included (56 girls, median Risser 2, 14 ± 3 years). Standing biplanar radiography and 3D reconstruction of the spine were performed. Geometrical features were computed: spinal length, vertebral and disc sizes, slenderness ratio, frontal and sagittal wedging angles. Measurement reproducibility was evaluated.

Results

AIS girls before 11 years of age had slightly longer spines than controls (p = 0.04, Mann–Whitney test). AIS vertebrae were significantly more slender than controls at almost all levels, almost independently of topology. Frontal wedging of apical vertebrae was higher in AIS, as expected, but also lower junctional discs showed higher wedging than controls.

Conclusion

AIS patients showed more slender spines than the asymptomatic population. Analysis of wedging suggests that lower junctional discs and apex vertebra could be locations of mechanical instability. Numerical simulation and longitudinal clinical follow-up of patients could clarify the impact of wedging, slenderness and growth on the biomechanics of scoliosis progression.

Graphic abstract

These slides can be retrieved under Electronic Supplementary Material.

Appendix

The slenderness ratio of a rod was defined by Timoshenko and Gere as $r = H \cdot \sqrt {A/I}$, where H is the rod length (or height), A is the cross-sectional area and I is the smallest second moment of area [27]. It is thus defined to take into account not only the cross-sectional area, but also its shape. An example can illustrate the physical meaning of slenderness ratio; imagining a rod with a perfectly elliptical cross-sectional area, of radiuses a and b, the two second moments of inertia would be $I_{1} = \pi /4 \cdot ab^{3}$ and $I_{2} = \pi /4 \cdot a^{3} b$. Assuming a > b, then I₁< I₂, so the smallest second moment of area is I₁. Remembering that the area of an ellipse is A = πab, the slenderness ratio reduces to:

$$ r = H \cdot \sqrt {\frac{\pi ab}{{\pi /4 \cdot ab^{3} }}} = H\sqrt {\frac{4}{{b^{2} }}} = \frac{2H}{b}. $$

Therefore, the slenderness ratio of a rod with an elliptical cross section is directly proportional to its length and inversely proportional to its smallest dimensions. In order words, the rod’s instability increases with an increase in length and with a decrease in its smallest side. Indeed, the rod’s feature leading to instability will be its smallest side, not its largest.

Of course, the vertebral cross-sectional area is not elliptical; however, the second moments of inertia of each endplate can be calculated through integral calculus, and they will retain their sensitivity to the shape of the area. Moreover, since the two endplates do not have the same shape and size, the average of their respective minimum second moments of inertia can be calculated. Finally, the vertebral body height can be used to replace the rod’s length.