Bone Abstracts

The present study introduces in silico analysis of osteoporotic lumbar vertebrae L₁ due to dynamic compressive load.

Objective: To define the reduction of load carrying capacity caused by various grades of osteoporosis.

Materials and methods: The three-dimensional inhomogeneous continuum problem was formulated for simulation purposes. The L₁ vertebra model consists of cortical shell, trabecular network and posterior elements. Bone tissues are modelled as elastoplastic and transversally isotropic solid. External loads are transmitted via weaker elastic intervertebral disks. The influence of osteoporotic aging was modelled by reducing the thickness of cortical shell and the elasticity modulus of trabecular network. Power law describes osteoporotic degradation of elasticity properties against density. The three-dimensional FE model was developed and the parametric study of various grades of low bone density and the reduced thickness of the cortical shell was performed. The failure load is evaluated by applying the von Mises-Hencky strength criterion.

Results: The numerical results of parametric study showed a significant dependence between the values of failure load and state of bone tissue. The failure load appears while dynamic load pressure reaches 0.3 MPa for model with 0.2 mm cortical shell width, on condition where apparent density of trabecular bone is <0.25 g/cm³. At the same time, the model with 0.5 mm cortical shell could carry the twice higher load pressure or 0.6 MPa, while apparent density of trabecular bone was 0.10 g/cm³. The model of healthy bone was resistant to 0.75 MPa load with the load-carrying capacity of bone about 20%, while the decrease of the thickness of cortical shell by 0.1 mm reduces the load-carrying capacity by 25%.

Conclusion: Parametric study demonstrates the decisive role of the cortical shell, the thickness of which was figured as the primary parameter of strength of the whole lumbar vertebrae body.