Continuous model of the human scoliotic spine

Abstract

The human scoliotic spine is mathematically modelled by employing the classical non-linear theory of curved beam-columns. A realistically representative muscle force system is included in the model. Scoliosis due to asymmetrical bi-lateral musucular contractions has been studied and arbitrary large displacements and curvatures are allowed. The two-dimensional model allowing curvature in the frontal plane can show the progression of a scoliotic curve from an initially straight configuration. For various parameter values, particularly muscle asymmetry, the model attempts to simulate the progression of actual scoliotic curves. Onc these curves have been simulated, forces corresponding to corrective surgical systems are applied to the scoliotic spine. The corresponding corrected curves are then compared with those produced by a finite element model and also to the actual clinical curve. The comparisons were very favourable, considering the simplicity of the continuous model. The commonly observed phenomenon of the scoliotic curve lying to the weaker side of the back in terms of muscle strength is reproduced and explained by the model. The possible usefulness of continuous spinal models to analyse the overall deformation of the spine under various loading conditions can then be deduced.