Experimental and computational approach investigating burst fracture augmentation using PMMA and calcium phosphate cements

Experimental and Computational Comparison of Intervertebral Disc Bulge for Specimen-Specific Model Evaluation Based on Imaging

Finite element modelling of the spinal unit is a promising preclinical tool to assess the biomechanical outcome of emerging interventions. Currently, most models are calibrated and validated against range of motion and rarely directly against soft-tissue deformation. The aim of this contribution was to develop an in vitro methodology to measure disc bulge and assess the ability of different specimen-specific modelling approaches to predict disc bulge. Bovine bone-disc-bone sections (N = 6) were prepared with 40 glass markers on the intervertebral disc surface. These were initially magnetic resonance (MR)-imaged and then sequentially imaged using peripheral-qCT under axial compression of 1 mm increments. Specimen-specific finite-element models were developed from the CT data, using three different methods to represent the nucleus pulposus geometry with and without complementary use of the MR images. Both calibrated specimen-specific and averaged compressive material properties for the disc tissues were investigated. A successful methodology was developed to quantify the disc bulge in vitro, enabling observation of surface displacement on qCT. From the finite element model results, no clear advantage was found in using geometrical information from the MR images in terms of the models' ability to predict stiffness or disc bulge for bovine intervertebral disc.

Effect of pedicle screw angles on the fracture risk of the human vertebra: A patient-specific computational model

The assessment of a human vertebra's stability after a screws fixation procedure and its fracture risk is still an open clinical problem. The accurate evaluation of fracture risk requires that all fracture mechanical determinants such as geometry, constitutive behavior, loading modes, and screws angulation are accounted for, which requires biomechanics-based analyses. As such, in the present work we investigate the effect of pedicle screws angulation on a patient-specific model of non osteoporotic lumbar vertebra, derived from clinical CT images. We propose a novel computational approach of fracture analysis and compare the effects of fixation stability in the lumbar spine. We considered a CT-based three-dimensional FE model of bilaterally instrumented L4 vertebra virtually implanting pedicle screws according to clinical guidelines. Nine screws trajectories were selected combining three craniocaudal and mediolateral angles, thus investigated through a parametric computational analysis. Bone was modeled as an elastic material with element-wise inhomogeneous properties fine-tuned on CT data. We implemented a custom algorithm to identify the thin cortical layer correctly from CT images ensuring reliable material properties in the computational model. Physiological motion (i.e., flexion, extension, axial rotation, lateral bending) was further accomplished by simultaneously loading the vertebra and the implant. We simulated local progressive damage of the bone by using a quasi-static force-driven incremental approach and considering a stress-based fracture criterion. Ductile-like and brittle-like fractures were found. Statistical analyses show significant differences comparing screws trajectories and averaging the results among six loading modes. In particular, we identified the caudomedial trajectory as the least critical case, thus safer from a clinical perspective. Instead, medial and craniolaterally oriented screws entailed higher peak and average stresses, though no statistical evidence classified such loads as the most critical scenarios. A quantitative validation procedure will be required in the future to translate our findings into clinical practice. Besides, to apply the results to the target osteoporotic population, new studies will be needed, including a specimen from an osteoporotic patient and the effect of osteoporosis on the constitutive model of bone.

Material property calibration is more important than element size and number of different materials on the finite element modelling of vertebral bodies: A Taguchi study

Finite element (FE) modelling of a vertebral body (VB) is considered challenging due to the many parameters involved such as element size and type, and material properties. Previous studies have reported how these parameters affect the mechanical behaviour of a VB model; however, most studies just compared results without any specific statistical tool to quantify their influence. The Taguchi Method (TM) has been successfully used in manufacturing and biomechanics to evaluate process parameters and to determine optimum set-up conditions. This study aimed to evaluate the influence of the main finite element modelling parameters on the mechanical behaviour of a VB model using the Taguchi Method. A FE model was developed based on a C2 juvenile porcine vertebral body and three of the most commonly used modelling parameters were evaluated using TM in terms of the change in the predicted stiffness in comparison to experimental values: element size, number of different material properties for VB (based on grey-scale bins) and calibration factor for grey-scale to density to Young's Modulus equation. The influence of the combined factors was also assessed. The Taguchi analysis showed that the three factors are independent. The calibration factor is the main contributor, accounting for 97% of the predicted stiffness, with the value of 0.03 most closely aligning the numerical and experimental results. Element size accounted for 2% of the predicted stiffness, with 0.75 mm being the optimal, while the number of grey-scale bins influenced the results by less than 1%. Our findings indicate that the calibration factor is the main modelling parameter, with the element size and number of bins accounting for less than 3% of the predicted stiffness. Therefore, calibration of material properties should be done based on a large number of samples to ensure reliable results.

A Novel Modelling Methodology Which Predicts the Structural Behaviour of Vertebral Bodies under Axial Impact Loading: A Finite Element and DIC Study

Cervical spine injuries (CSIs) arising from collisions are uncommon in contact sports, such as rugby union, but their consequences can be devastating. Several FE modelling approaches are available in the literature, but a fully calibrated and validated FE modelling framework for cervical spines under compressive dynamic-impact loading is still lacking and material properties are not adequately calibrated for such events. This study aimed to develop and validate a methodology for specimen-specific FE modelling of vertebral bodies under impact loading. Thirty-five (n = 35) individual vertebral bodies (VBs) were dissected from porcine spine segments, potted in bone cement and μCT scanned. A speckle pattern was applied to the anterior faces of the bones to allow digital image correlation (DIC), which monitored the surface displacements. Twenty-seven (n = 27) VBs were quasi-statically compressively tested to a load up to 10 kN from the cranial side. Specimen-specific FE models were developed for fourteen (n = 14) of the samples in this group. The material properties were optimised based on the experimental load-displacement data using a specimen-specific factor (kGSstatic) to calibrate a density to Young’s modulus relationship. The average calibration factor arising from this group was calculated (K¯GSstatic) and applied to a control group of thirteen (n = 13) samples. The resulting VB stiffnesses was compared to experimental findings. The final eight (n = 8) VBs were subjected to an impact load applied via a falling mass of 7.4kg at a velocity of 3.1ms⁻¹. Surface displacements and strains were acquired from the anterior VB surface via DIC, and the impact load was monitored with two load cells. Specimen-specific FE models were created for this dynamic group and material properties were assigned again based on the density–Young’s modulus relationship previously validated for static experiments, supplemented with an additional factor (KGSdynamic). The optimised conversion factor for quasi-static loading, K¯GSstatic, had an average of 0.033. Using this factor, the validation models presented an average numerical stiffness value 3.72% greater than the experimental one. From the dynamic loading experiments, the value for KGSdynamic was found to be 0.14, 4.2 times greater than K¯GSstatic. The average numerical stiffness was 2.3% greater than in the experiments. Almost all models presented similar stiffness variations and regions of maximum displacement to those observed via DIC. The developed FE modelling methodology allowed the creation of models which predicted both static and dynamic behaviour of VBs. Deformation patterns on the VB surfaces were acquired from the FE models and compared to DIC data, achieving high agreement. This methodology is now validated to be fully applied to create whole cervical spine models to simulate axial impact scenarios replicating rugby collision events.

Implicit and explicit finite element models predict the mechanical response of calcium phosphate-titanium cranial implants

The structural integrity of cranial implants is of great clinical importance, as they aim to provide cerebral protection after neurosurgery or trauma. With the increased use of patient-specific implants, the mechanical response of each implant cannot be characterized experimentally in a practical way. However, computational models provide an excellent possibility for efficiently predicting the mechanical response of patient-specific implants. This study developed finite element models (FEMs) of titanium-reinforced calcium phosphate (CaP-Ti) implants. The models were validated with previously obtained experimental data for two different CaP-Ti implant designs (D1 and D2), in which generically shaped implant specimens were loaded in compression at either quasi-static (1 mm/min) or impact (5 kg, 1.52 m/s) loading rates. The FEMs showed agreement with experimental data in the force-displacement response for both implant designs. The implicit FEMs predicted the peak load with an underestimation for D1 (9%) and an overestimation for D2 (11%). Furthermore, the shape of the force-displacement curves were well predicted. In the explicit FEMs, the first part of the force-displacement response showed 5% difference for D1 and 2% difference for D2, with respect to the experimentally derived peak loads. The explicit FEMs efficiently predicted the maximum displacements with 1% and 4% difference for D1 and D2, respectively. Compared to the CaP-Ti implant, an average parietal cranial bone FEM showed a stiffer response, greater energy absorption and less deformation under the same impact conditions. The framework developed for modelling the CaP-Ti implants has a potential for modelling CaP materials in other composite implants in future studies since it only used literature based input and matched boundary conditions. Furthermore, the developed FEMs make an important contribution to future evaluations of patient-specific CaP-Ti cranial implant designs in various loading scenarios.

Optimizing computational methods of modeling vertebroplasty in experimentally augmented human lumbar vertebrae

Vertebroplasty has been widely used for the treatment of osteoporotic compression fractures but the efficacy of the technique has been questioned by the outcomes of randomized clinical trials. Finite-element (FE) models allow an investigation into the structural and geometric variation that affect the response to augmentation. However, current specimen-specific FE models are limited due to their poor reproduction of cement augmentation behavior. The aims of this study were to develop new methods of modeling the vertebral body in both a nonaugmented and augmented state. Experimental tests were conducted using human lumbar spine vertebral specimens. These tests included micro-computed tomography imaging, mechanical testing, augmentation with cement, reimaging, and retesting. Specimen-specific FE models of the vertebrae were made comparing different approaches to capturing the bone material properties and to modeling the cement augmentation region. These methods significantly improved the modeling accuracy of nonaugmented vertebrae. Methods that used the registration of multiple images (pre- and post-augmentation) of a vertebra achieved good agreement between augmented models and their experimental counterparts in terms of predictions of stiffness. Such models allow for further investigation into how vertebral variation influences the mechanical outcomes of vertebroplasty.

Examination of an in vitro methodology to evaluate the biomechanical performance of nucleus augmentation in axial compression

Intervertebral disc degeneration is one of the leading causes of back pain, but treatment options remain limited. Recently, there have been advances in the development of biomaterials for nucleus augmentation; however, the testing of such materials preclinically has proved challenging. The aim of this study was to develop methods for fabricating and testing bone-disc-bone specimens in vitro for examining the performance of nucleus augmentation procedures. Control, nucleotomy and treated intervertebral disc specimens were fabricated and tested under static load. The nucleus was removed from nucleotomy specimens using a trans-endplate approach with a bone plug used to restore bony integrity. Specimen-specific finite element models were developed to elucidate the reasons for the variations observed between control specimens. Although the computational models predicted a statistically significant difference between the healthy and nucleotomy groups, the differences found experimentally were not significantly different. This is likely due to variations in the material properties, hydration and level of annular collapse. The deformation of the bone was also found to be non-negligible. The study provides a framework for the development of testing protocols for nucleus augmentation materials and highlights the need to control disc hydration and the length of bone retained to reduce inter-specimen variability.

Methodology to Produce Specimen-Specific Models of Vertebrae: Application to Different Species

Image-based continuum-level finite element models have been used for bones to evaluate fracture risk and the biomechanical effects of diseases and therapies, capturing both the geometry and tissue mechanical properties. Although models of vertebrae of various species have been developed, an inter-species comparison has not yet been investigated. The purpose of this study was to derive species-specific modelling methods and compare the accuracy of image-based finite element models of vertebrae across species. Vertebral specimens were harvested from porcine (N = 12), ovine (N = 13) and bovine (N = 14) spines. The specimens were experimentally loaded to failure and apparent stiffness values were derived. Image-based finite element models were generated reproducing the experimental protocol. A linear relationship between the element grayscale and elastic modulus was calibrated for each species matching in vitro and in silico stiffness values, and validated on independent sets of models. The accuracy of these relationships were compared across species. Experimental stiffness values were significantly different across species and specimen-specific models required species-specific linear relationship between image grayscale and elastic modulus. A good agreement between in vitro and in silico values was achieved for all species, reinforcing the generality of the developed methodology.

In silico investigation of vertebroplasty as a stand-alone treatment for vertebral burst fractures

BACKGROUND

The use of percutaneous vertebroplasty as a stand-alone treatment for stable vertebral burst fractures has been investigated in vitro and in clinical studies. These studies present inconsistent results on the mechanical response of vertebroplasty-treated burst fractures. In addition, observations of the loss of sagittal alignment after vertebroplasty raise questions on the applicability of vertebroplasty for burst fractures. Therefore, the aim of this study was to investigate the mechanical stability of burst fractures after stand-alone treatment by vertebroplasty.

METHODS

Finite element simulations were performed with models generated from two laboratory-induced burst fractures in human thoracolumbar specimens. The burst fracture models were virtually injected with various cement volumes using a unipedicular or bipedicular approach. The models were subjected to four individual loads (compression, lateral bending, extension and torsion) and a multi-axial load case in the physiological range.

FINDINGS

All treated burst fractures showed improvements in stiffness and a reduction in inter-fragmentary displacements, thus potentially providing a suitable mechanical environment for fracture healing. However, large volumes of the trabecular bone (<43%), cement (<53%) and bone-cement composite (<58%) were predicted to experience strain levels exceeding the yield point. While damage was not specifically modeled, this implies a potential collapse of the treated vertebra due to local failure.

INTERPRETATION

To improve the primary stability and to prevent the collapse of treated burst fractures, the use of posterior instrumentation is suggested as an adjunct to vertebroplasty.

Computational modelling of bone augmentation in the spine

Computational models are gaining importance not only for basic science, but also for the analysis of clinical interventions and to support clinicians prior to intervention. Vertebroplasty has been used to stabilise compression fractures in the spine for years, yet there are still diverging ideas on the ideal deposition location, volume, and augmentation material. In particular, little is known about the long-term effects of the intervention on the surrounding biological tissue. This review aims to investigate computational efforts made in the field of vertebroplasty, from the augmentation procedure to strength prediction and long-term in silico bone biology in augmented human vertebrae. While there is ample work on simulating the augmentation procedure and strength prediction, simulations predicting long-term effects are lacking. Recent developments in bone remodelling simulations have the potential to show adaptation to cement augmentation and, thus, close this gap.