Calibration of the mechanical properties in a finite element model of a lumbar vertebra under dynamic compression up to failure

Abstract

Finite element models (FEM) dedicated to vertebral fracture simulations rarely take into account the rate dependency of the bone material properties due to limited available data. This study aims to calibrate the mechanical properties of a vertebral body FEM using an inverse method based on experiments performed at slow and fast dynamic loading conditions. A detailed FEM of a human lumbar vertebral body (23,394 elements) was developed and tested under compression at 2,500 and 10 mm s⁻¹. A central composite design was used to adjust the mechanical properties (Young modulus, yield stress, and yield strain) while optimizing four criteria (ultimate strain and stress of cortical and trabecular bone) until the failure load and energy at failure reached experimental results from the literature. At 2,500 mm s⁻¹, results from the calibrated simulation were in good agreement with the average experimental data (1.5% difference for the failure load and 0.1% for the energy). At 10 mm s⁻¹, they were in good agreement with the average experimental failure load (0.6% difference), and within one standard deviation of the reported range of energy to failure. The proposed method provides a relevant mean to identify the mechanical properties of the vertebral body in dynamic loadings.