Title:
[Mathematical simulation of biomechanical background of osteophyte formation in cervical vertebra].

Abstract:
The aim of this study was to simulate different types of cervical vertebra loading and to find out whether mechanical stress would concentrate in regions known in clinical practice as predilection sites for osteophyte formation. The objective was to develop a theoretical model that would elucidate clinical observations concerning the predilection site of bone remodelling in view of the physiological changes inside the cervical vertebral body.
A real 3D-geometry of the fourth cervical vertebra had been made by the commercially available system ATOS II. This is a high-resolution measuring system using principles of optical triangulation. This flexible optical measuring machine projects fringe patterns on the surface of a selected object and the pattern is observed with two cameras. 3D coordinates for each camera pixel were calculated with high precision and a polygon mesh of the object's surface was further generated. In the next step an ANSYS programme was used to calculate strains and stresses in each finite element of the virtual vertebra. The applied forces used in the experiment corresponded in both magnitude and direction to physiological stress. Mechanical loading in neutral position was characterized by a distribution of 80% mechanical stress to the vertebral body and 10% to each of the zygoapophyseal joints. Hyperlordotic loading was simulated by 60% force transfer to the vertebral body end-plate and 20% to each of the small joint while kyphotic loading involved a 90% load on the vertebral body endplate and 5% on each facet.
Mechanical stress distribution calculated in a neutral position of the model correlated well with bone mineral distribution of a healthy vertebra, and verified the model itself. The virtual mechanical loading of a vertebra in kyphotic position concentrated deformation stress into the uncinate processes and the dorsal apophyseal rim of the vertebral body. The simulation of mechanical loading in hyperlordosis, on the other hand, shifted the region of maximum deformation into the articulation process of the Z-joint. All locations are known as areas of osteophyte formation in degenerated cervical vertebrae.
The theoretical model developed during this study corresponded well with human spine behaviour in terms of predilection sites for osteodegenerative changes, as observed in clinical practice. A mathematical simulation of mechanical stress distribution in pre-operative planning may lead to the optimisation of post-operative anatomical relationship between adjacent vertebrae. Such improvement in our surgical practice may further reduce the incidence of degenerative changes in adjacent motion segments of the cervical spine and possibly also lead to better subjective and clinical results after cervical spine reconstruction.