Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads.

Under fast dynamic loading conditions (e.g. high-energy impact), the load rate dependency of the intervertebral disc (IVD) material properties may play a crucial role in the biomechanics of spinal trauma. However, most finite element models (FEM) of dynamic spinal trauma uses material properties derived from quasi-static experiments, thus neglecting this load rate dependency. The aim of this study was to identify hyperelastic material properties that ensure a more biofidelic simulation of the IVD under a fast dynamic compressive load. A hyperelastic material law based on a first-order Mooney-Rivlin formulation was implemented in a detailed FEM of a L2-L3 functional spinal unit (FSU) to represent the mechanical behavior of the IVD. Bony structures were modeled using an elasto-plastic Johnson-Cook material law that simulates bone fracture while ligaments were governed by a viscoelastic material law. To mimic experimental studies performed in fast dynamic compression, a compressive loading velocity of 1 m/s was applied to the superior half of L2, while the inferior half of L3 was fixed. An exploratory technique was used to simulate dynamic compression of the FSU using 34 sets of hyperelastic material constants randomly selected using an optimal Latin hypercube algorithm and a set of material constants derived from quasi-static experiments. Selection or rejection of the sets of material constants was based on compressive stiffness and failure parameters criteria measured experimentally. The two simulations performed with calibrated hyperelastic constants resulted in nonlinear load-displacement curves with compressive stiffness (7335 and 7079 N/mm), load (12,488 and 12,473 N), displacement (1.95 and 2.09 mm) and energy at failure (13.5 and 14.7 J) in agreement with experimental results (6551 ± 2017 N/mm, 12,411 ± 829 N, 2.1 ± 0.2 mm and 13.0 ± 1.5 J respectively). The fracture pattern and location also agreed with experimental results. The simulation performed with constants derived from quasi-static experiments showed a failure energy (13.2 J) and a fracture pattern and location in agreement with experimental results, but a compressive stiffness (1580 N/mm), a failure load (5976 N) and a displacement to failure (4.8 mm) outside the experimental corridors. The proposed method offers an innovative way to calibrate the hyperelastic material properties of the IVD and to offer a more realistic simulation of the FSU in fast dynamic compression.

Biomechanical analysis of pedicle screw placement: a feasibility study.

In spinal instrumentation surgery, the optimal placement of pedicle screws that takes into account the cortical/cancellous bone quality, geometry and property distribution, and screw design is still undetermined despite several in vitro experiments. The objective of this study was to evaluate the feasibility of using a detailed finite element model (FEM) of an instrumented vertebra to simulate screw axial pull-out and to analyze the bone-screw mechanical interaction. The FEM was built using CT-scan images of the L3 vertebra (0.6mm thick contiguous slices) of a 50th percentile human male volunteer, in order to virtually implant a fully customizable pedicle screw in a straight-forward position. The 753,000 elements model takes into account local cortical bone thickness and integrates advanced material behavior (elasto-plastic) laws that simulate bone failure. Screw axial pull-out was simulated and compared to in vitro experimental data, and the stress distribution at the screw thread-bone interface was analyzed. The simulated screw pull-out force (non-linear response with a failure at 640N) was within the range of experimental data (500-660N). Von Mises stresses in the bony structures were concentrated around the root of each internal thread, with the maximum stress located near the first proximal thread, in the cortical bone of the posterior wall of the pars. This study shows the feasibility and relevance of using a detailed FEM to simulate screw pull-out and to analyze the bone-screw mechanical interaction.

Substantial vertebral body osteophytes protect against severe vertebral fractures in compression.

Recent findings suggest that vertebral osteophytes increase the resistance of the spine to compression. However, the role of vertebral osteophytes on the biomechanical response of the spine under fast dynamic compression, up to failure, is unclear. Seventeen human spine specimens composed of three vertebrae (from T5-T7 to T11-L1) and their surrounding soft tissues were harvested from nine cadavers, aged 77 to 92 years. Specimens were imaged using quantitative computer tomography (QCT) for medical observation, classification of the intervertebral disc degeneration (Thomson grade) and measurement of the vertebral trabecular density (VTD), height and cross-sectional area. Specimens were divided into two groups (with (n = 9) or without (n = 8) substantial vertebral body osteophytes) and compressed axially at a dynamic displacement rate of 1 m/s, up to failure. Normalized force-displacement curves, videos and QCT images allowed characterizing failure parameters (force, displacement and energy at failure) and fracture patterns. Results were analyzed using chi-squared tests for sampling distributions and linear regression for correlations between VTD and failure parameters. Specimens with substantial vertebral body osteophytes present higher stiffness (2.7 times on average) and force at failure (1.8 times on average) than other segments. The presence of osteophytes significantly influences the location, pattern and type of fracture. VTD was a good predictor of the dynamic force and energy at failure for specimens without substantial osteophytes. This study also showed that vertebral body osteophytes provide a protective mechanism to the underlying vertebra against severe compression fractures.

Finite element analysis of the influence of loading rate on a model of the full lumbar spine under dynamic loading conditions.

Despite an increase in the number of experimental and numerical studies dedicated to spinal trauma, the influence of the rate of loading or displacement on lumbar spine injuries remains unclear. In the present work, we developed a bio-realistic finite element model (FEM) of the lumbar spine using a comprehensive geometrical representation of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The FEM was validated against published experimental data and used to compare the initiation sites of spinal injuries under low (LD) and high (HD) dynamic compression, flexion, extension, anterior shear, and posterior shear. Simulations resulted in force-displacement and moment-angular rotation curves well within experimental corridors, with the exception of LD flexion where angular stiffness was higher than experimental values. Such a discrepancy is attributed to the initial toe-region of the ligaments not being included in the material law used in the study. Spinal injuries were observed at different initiation sites under LD and HD loading conditions, except under shear loads. These findings suggest that the strain rate dependent behavior of spinal components plays a significant role in load-sharing and failure mechanisms of the spine under different loading conditions.

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

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.