The role of the Womersley number in pulsatile blood flow : a theoretical study of the Casson model

Injury mechanisms and stress distribution patterns are important in the clinical evaluation of spinal injuries. Recognition and interpretation of the failure patterns help to determine spinal instability and consequently the choice of treatment. Although, the biomechanics responses of the atlas have received much attention, it has not been investigated using theoretical modeling. Mathematical techniques such as finite element model will provide further understanding to the injury mechanisms of the atlas, which is important for the prevention, diagnosis, and treatment of spinal injuries. In the present study, a detailed three-dimensional finite element model of the human atlas (C1) was constructed, with the geometrical data obtained using a three-dimensional digitizer. Anterior arch, superior/inferior articular processes, transverse processes, posterior arch and posterior tubercule were modeled using eight-noded brick elements. Using the material properties from literature, the 7808-finite element model was exercised under three simulated axial compressive mode of pressure loading and boundary conditions to investigate the sites of failure reported in vivo and in vitro. This report demonstrates high concentration of localized stress at the anterior and posterior archs of the atlas, which agrees well with those reported in the literature. Furthermore, under simulated hyperextension, our results agreed well with the experimental findings, which show that the groove of the posterior arch is subjected to enormous bending moment. The close agreement of the failure location provided confidence to perform further analysis and in vitro experiments. These results may be potentially used to supplement experimental research in understanding the clinical biomechanics of the atlas.