Biomechanical modelling of segmental instrumentation for surgical correction of 3D spinal deformities using Euler-Bernoulli thin-beam elastic deformation equations

A simplified computer-modelling technique intended to analyse 3D spinal deformity correction with segmental instrumentation is presented. The spine was modelled as a thin beam-composed structure linked by implants to two deformable rods. The Landau vector representation of Euler-Bernoulli beam elastic deformation equations was used to formulate the simulation approach. All types of essential deformation (bending, torsion, tension, compression) were considered. An iterative numerical method was proposed to obtain an appropriate load, able to deform the spine axial curve to the desired post-operative shape. A simulation based on the spine of a real scoliotic patient (thoracic and lumbar Cobb angles: 39degrees and 8degrees), corrected using surgical instrumentation intervention, is presented. Force loads within the range of 20-350 N were able to deform the pre-operational spine axial curve to the post-operational one with a root mean square approximation error of 3.7 mm. Similarly good corrections were obtained using different force patterns. This highlights the uncertainty of which corresponding surgical instrumentation to use. Such uncertainty is related to the 'ill-posed problems' property of mechanical systems.