Mathematical modelling of cervical spine dynamics under impulse impacts

The paper is devoted to the mathematical modelling of the heard–neck system dynamics during impulse acceleration, which arises in the case of the ground and air vehicle crushes. Analysis of previous papers showed that the main limiting factors are, on the one hand, very complicated inner structure of the neck, and on the other hand, incomplete knowledge of the mechanical properties of the muscles and intervertebral discs. For this reason, complex mechanical models do not have sufficient experimental validation. In this regard, the authors proposed a simple mechanical model of the “head–neck” system with eight degrees of freedom. They are the rotation angles of the head and seven cervical vertebrae. These angles are considered as generalized coordinates. The intervertebral discs are modeled as hinge joints provided with helical springs and dampers. When modelling a large number of neck muscles, they were integrated into two groups of muscles-antagonists, each of which is represented in the model as generalized muscle. The model motion is described by a system of ordinary differential equations obtained by Lagrange's method. The coordination between a model head motion and a volunteer head motion served as the model adequacy criterion. The assessment of discordance was performed by the method of least squares. For the search of the unknown model parameters the minimization of this discordance was executed. In doing so the Nelder–Mead method was applied. The Akima splines were used for a experimental data approximation and for search of unknown model parameters. Refs 23. Figs 12.