Éric Wagnac

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2-L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate? Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5 degrees /ms.

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.

A New Method to Generate a Patient-Specific Finite Element Model of the Human Buttocks

Finite element (FE) models are very efficient tools to study internal stresses in human structures that induce severe pressure sores. Unfortunately, methods currently used to generate FE models are not suitable for clinical application involving wheelchair users. A clinical-oriented method, based on calibrated-biplanar radiographs, was therefore developed to generate a subject-specific FE model of the buttocks in a non-weighted sitting position. The model was then used to analyze the stress distribution within the buttocks and compare two wheelchair seat cushions designs. Additional radiographs and pressure measurements in a weighted sitting position were acquired to validate the FE model experimentally. Results from the FE model were in good agreement with experimental data and related literature. An internal peak pressure of 45.3 kPa was observed while seated on a flat foam cushion, corresponding to an interface pressure of 23.6 kPa. Both pressures occurred underneath the ischial tuberosities. When compared to the flat foam cushion, the contoured foam cushion reduced internal and interface peak pressures by 18% and 33%, respectively. The method developed in this study has a great potential for clinical use. The FE model, by predicting realistic stress distributions, allows for the selection of a convenient wheelchair seat cushion.

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.

Minimizing Pedicle Screw Pullout Risks: A Detailed Biomechanical Analysis of Screw Design and Placement

Study Design: Detailed biomechanical analysis of the anchorage performance provided by different pedicle screw designs and placement strategies under pullout loading. Objective: To biomechanically characterize the specific effects of surgeon-specific pedicle screw design parameters on anchorage performance using a finite element model. Summary of Background Data: Pedicle screw fixation is commonly used in the treatment of spinal pathologies. However, there is little consensus on the selection of an optimal screw type, size, and insertion trajectory depending on vertebra dimension and shape. Methods: Different screw diameters and lengths, threads, and insertion trajectories were computationally tested using a design of experiment approach. A detailed finite element model of an L3 vertebra was created including elastoplastic bone properties and contact interactions with the screws. Loads and boundary conditions were applied to the screws to simulate axial pullout tests. Force-displacement responses and internal stresses were analyzed to determine the specific effects of each parameter. Results: The design of experiment analysis revealed significant effects (P<0.01) for all tested principal parameters along with the interactions between diameter and trajectory. Screw diameter had the greatest impact on anchorage performance. The best insertion trajectory to resist pullout involved placing the screw threads closer to the pedicle walls using the straightforward insertion technique, which showed the importance of the cortical layer grip. The simulated cylindrical single-lead thread screws presented better biomechanical anchorage than the conical dual-lead thread screws in axial loading conditions. Conclusions: The model made it possible to quantitatively measure the effects of both screw design characteristics and surgical choices, enabling to recommend strategies to improve single pedicle screw performance under axial loading.

Method to Geometrically Personalize a Detailed Finite-Element Model of the Spine

To date, developing geometrically personalized and detailed solid finite-element models (FEMs) of the spine remains a challenge, notably due to multiple articulations and complex geometries. To answer this problem, a methodology based on a free-form deformation technique (kriging) was developed to deform a detailed reference finite-element mesh of the spine (including discs and ligaments) to the patient-specific geometry of 10- and 82-year-old asymptomatic spines. Different kriging configurations were tested: with or without smoothing, and control points on or surrounding the entire mesh. Based on the results, it is recommended to use surrounding control points and smoothing. The mean node to surface distance between the deformed and target geometries was 0.3 ± 1.1 mm. Most elements met the mesh quality criteria (95%) after deformation, without interference at the articular facets. The methods novelty lies in the deformation of the entire spine at once, as opposed to deforming each vertebra separately, with surrounding control points and smoothing. This enables the transformation of reference vertebrae and soft tissues to obtain complete and personalized FEMs of the spine with minimal postprocessing to optimize the mesh.

Biomechanical analysis of pedicle screw pullout strength

Pedicle screws are widely used to treat severe cases of spinal pathologies and traumas. It is performed by inserting pedicle screws and connecting instrumentation rods in order to realign the vertebrae. In vitro experiments such as axial pullout tests provide insight into the biomechanics of screw–bone interactions, but show inherent limitations in terms of inter-individual variability (bone density, pedicle morphology, etc.) and reproducibility. The objective of this study was to develop a finite element model to simulate and biomechanically evaluate the pullout forces and stiffness of different pedicle screw designs and insertion techniques.

Biomechanics of thoracolumbar junction vertebral fractures from various kinematic conditions

Thoracolumbar spine fracture classifications are mainly based on a post-traumatic observation of fracture patterns, which is not sufficient to provide a full understanding of spinal fracture mechanisms. This study aimed to biomechanically analyze known fracture patterns and to study how they relate to fracture mechanisms. The instigation of each fracture type was computationally simulated to assess the fracture process. A refined finite element model of three vertebrae and intervertebral connective tissues was subjected to 51 different dynamic loading conditions divided into four categories: compression, shear, distraction and torsion. Fracture initiation and propagation were analyzed, and time and energy at fracture initiation were computed. To each fracture pattern described in the clinical literature were associated one or several of the simulated fracture patterns and corresponding loading conditions. When compared to each other, torsion resulted in low-energy fractures, compression and shear resulted in medium energy fractures, and distraction resulted in high-energy fractures. Increased velocity resulted in higher-energy fracture for similar loadings. The use of a finite element model provided quantitative characterization of fracture patterns occurrence complementary to clinical and experimental studies, allowing to fully understand spinal fracture biomechanics.

Detailed modelling of the lumbar spine for trauma applications: preliminary results

Spinal trauma resulting from motor vehicle accidents, sports and military injuries and falls are a major cause of long-term disability inducing major socio-economic consequences. In the last decade, many mathematical models of the lumbar spine were used as surrogate experiments to provide significant knowledge on biomechanics of spinal trauma (Gilbertson et al. 1995, Yang et al. 2006). Unfortunately, very few of these models present the ability to thoroughly investigate the complex injury mechanisms and kinematics involved in spinal trauma, mostly due to geometrical, material and loading oversimplifications. This study aims to create an advanced finite element model (FEM) of the lumbar spine for trauma applications.

Pedicle Screw Fixation Under Nonaxial Loads: A Cadaveric Study

Study Design. An experimental study of pedicle screw fixation in human cadaveric vertebrae. Objective. The aim of this study was to experimentally characterize pedicle screw fixation under nonaxial loading and to analyze the effect of the surgeons’ screw and placement choices on the fixation risk of failure. Summary of Background Data. Pedicle screw fixation performance is traditionally characterized with axial pullout tests, which do not fully represent the various tridimensional loads sustained by the screws during correction maneuvers of severe spinal deformities. Previous studies have analyzed the biomechanics of nonaxial loads on pedicle screws, but their effects on the screw loosening mechanisms are still not well understood. Methods. A design of experiment (DOE) approach was used to evaluate 2 screw thread designs (single-lead and dual-lead threads), 2 insertion trajectories in the transverse and sagittal planes, and 2 loading directions (lateral and cranial). Pedicle screws were inserted in both pedicles of 12 cadaveric lumbar vertebrae for a total of 24 tests. Four sinewave loading cycles (0–400 N) were applied, orthogonally to the screw axis, at the screw head. The resulting forces, displacements, and rotations of the screws were recorded. Results. In comparison to the other cycles, the first loading cycle revealed important permanent deformation of the bone (mean permanent displacement of the screw head of 0.79 mm), which gradually accumulated over the following cycles to 1.75 mm on average (plowing effect). The cranial loading direction caused significantly lower (P < 0.05) bone deformation than lateral loading. The dual-lead screw had a significantly higher (P < 0.05) initial stiffness than the single-lead thread screw. Conclusions. Nonaxial loads induce screw plowing that lead to bone compacting and subsequent screw loosening or even bone failure, thus reducing the pedicle screw fixation strength. Lateral loads induce greater bone deformation and risks of failure than cranial loads. Level of Evidence: N/A