Alison C. Jones

Finite element analysis of the spine: Towards a framework of verification, validation and sensitivity analysis

A number of papers have recently emphasised the importance of verification, validation and sensitivity testing in computational studies within the field of biomechanical engineering. This review examines the methods used in the development of spinal finite element models with a view to a standardised framework of verification, validation and sensitivity analysis. The scope of this paper is restricted to models of the vertebra, the intervertebral disc and short spinal segments. In the case of single vertebral models, specimen-specific methods have been developed, which allow direct validation against experimental tests. The focus of intervertebral disc modelling has been on representing the complex material properties and further sensitivity testing is required to fully understand the relative roles of these input parameters. In order to construct complex multi-component short segment models, many geometric and material parameters are required, some of which are yet to be fully characterised. There are also major challenges in terms of short segment model validation. Throughout the review, areas of good practise are highlighted and recommendations for future development are proposed, taking a step towards more robust spinal modelling procedures, promoting acceptance from the wider biomechanics community.

Periprosthetic fracture fixation of the femur following total hip arthroplasty: a review of biomechanical testing.

BACKGROUND periprosthetic femoral fracture can occur following total hip arthroplasty. Fixation of these fractures are challenging due to the combination of fractured bone with an existing prosthesis. There are several clinical studies reporting the failure of fixation methods used for these fractures, highlighting the importance of further biomechanical studies in this area. METHODS the current literature on biomechanical models of periprosthetic femoral fracture fixation is reviewed. The methodologies involved in the experimental and computational studies of this fixation are described and compared. FINDINGS areas which require further investigation are highlighted and the potential use of finite element analysis as a computational tool to test the current fixation methods is addressed. INTERPRETATION biomechanical models have huge potential to assess the effectiveness of different fixation methods. Experimental in vitro models have been used to mimic periprosthetic femoral fracture fixation however, the numbers of measurements that are possible in these studies are relatively limited due to the cost and data acquisition constraints. Computer modelling and in particular finite element analysis is a complimentary method that could be used to examine existing protocols for the treatment of periprosthetic femoral fracture and, potentially, find optimum fixation methods for specific fracture types.

Development of specimen-specific finite element models of human vertebrae for the analysis of vertebroplasty:

Abstract The aim of this study was to determine the accuracy of specimen-specific finite element models of untreated and cement-augmented vertebrae by direct comparison with experimental results. Eleven single cadaveric vertebrae were imaged using micro computed tomography (mCT) and tested to failure in axial compression in the laboratory. Four of the specimens were first augmented with PMMA cement to simulate a prophylactic vertebroplasty. Specimen-specific finite element models were then generated using semi-automated methods. An initial set of three untreated models was used to determine the optimum conversion factors from the image data to the bone material properties. Using these factors, the predicted stiffness and strength were determined for the remaining specimens (four untreated, four augmented). The model predictions were compared with the corresponding experimental data. Good agreement was found with the non-augmented specimens in terms of stiffness (root-mean-square (r.m.s.) error 12.9 per cent) and strength (r.m.s. error 14.4 per cent). With the augmented specimens, the models consistently overestimated both stiffness and strength (r.m.s. errors 65 and 68 per cent). The results indicate that this method has the potential to provide accurate predictions of vertebral behaviour prior to augmentation. However, modelling the augmented bone with bulk material properties is inadequate, and more detailed modelling of the cement region is required to capture the bone—cement interactions if the models are to be used to predict the behaviour following vertebroplasty.

Assessment of factors influencing finite element vertebral model predictions.

This study aimed to establish model construction and configuration procedures for future vertebral finite element analysis by studying convergence, sensitivity, and accuracy behaviors of semiautomatically generated models and comparing the results with manually generated models. During a previous study, six porcine vertebral bodies were imaged using a microcomputed tomography scanner and tested in axial compression to establish their stiffness and failure strength. Finite element models were built using a manual meshing method. In this study, the experimental agreement of those models was compared with that of semiautomatically generated models of the same six vertebrae. Both manually and semiautomatically generated models were assigned gray-scale-based, element-specific material properties. The convergence of the semiautomatically generated models was analyzed for the complete models along with material property and architecture control cases. A sensitivity study was also undertaken to test the reaction of the models to changes in material property values, architecture, and boundary conditions. In control cases, the element-specific material properties reduce the convergence of the models in comparison to homogeneous models. However, the full vertebral models showed strong convergence characteristics. The sensitivity study revealed a significant reaction to changes in architecture, boundary conditions, and load position, while the sensitivity to changes in material property values was proportional. The semiautomatically generated models produced stiffness and strength predictions of similar accuracy to the manually generated models with much shorter image segmentation and meshing times. Semiautomatic methods can provide a more rapid alternative to manual mesh generation techniques and produce vertebral models of similar accuracy. The representation of the boundary conditions, load position, and surrounding environment is crucial to the accurate prediction of the vertebral response. At present, an element size of 2x2x2 mm(3) appears sufficient since the error at this size is dominated by factors, such as the load position, which will not be improved by increasing the mesh resolution. Higher resolution meshes may be appropriate in the future as models are made more sophisticated and computational processing time is reduced.

Periprosthetic Femoral Fracture — A Biomechanical Comparison Between Vancouver Type B1 and B2 Fixation Methods

Current clinical data suggest a higher failure rate for internal fixation in Vancouver type B1 periprosthetic femoral fracture (PFF) fixations compared to long stem revision in B2 fractures. The aim of this study was to compare the biomechanical performance of several fixations in the aforementioned fractures. Finite element models of B1 and B2 fixations, previously corroborated against in vitro experimental models, were compared. The results indicated that in treatment of B1 fractures, a single locking plate can be without complications provided partial weight bearing is followed. In case of B2 fractures, long stem revision and bypassing the fracture gap by two femoral diameters are recommended. Considering the risk of single plate failure, long stem revision could be considered in all comminuted B1 and B2 fractures.

Derivation of inter-lamellar behaviour of the intervertebral disc annulus

The inter-lamellar connectivity of the annulus fibrosus in the intervertebral disc has been shown to affect the prediction of the overall disc behaviour in computational models. Using a combined experimental and computational approach, the inter-lamellar mechanical behaviour of the disc annulus was investigated under conditions of radial loading. Twenty-seven specimens of anterior annulus fibrosus were dissected from 12 discs taken from four frozen ovine thoracolumbar spines. Specimens were grouped depending on their radial provenance within the annulus fibrosus. Standard tensile tests were performed. In addition, micro-tensile tests under microscopy were used to observe the displacement of the lamellae and inter-lamellar connections. Finite elements models matching the experimental protocols were developed with specimen-specific geometries and boundary conditions assuming a known lamellar behaviour. An optimisation process was used to derive the interface stiffness values for each group. The assumption of a linear cohesive interface was used to model the behaviour of the inter-lamellar connectivity. The interface stiffness values derived from the optimisation process were consistently higher than the corresponding lamellar values. The interface stiffness values of the outer annulus were from 43% to 75% higher than those of the inner annulus. Tangential stiffness values for the interface were from 6% to 39% higher than normal stiffness values within each group and similar to values reported by other investigators. These results reflect the intricate fibrous nature of the inter-lamellar connectivity and provide values for the representation of the inter-lamellar behaviour at a continuum level.

The Effect of Fracture Stability on the Performance of Locking Plate Fixation in Periprosthetic Femoral Fractures

Periprosthetic femoral fracture (PFF) fixation failures are still occurring. The effect of fracture stability and loading on PFF fixation has not been investigated and this is crucial for optimum management of PFF. Models of stable and unstable PPFs were developed and used to quantify the effect of fracture stability and loading in a single locking plate fixation. Stress on the plate was higher in the unstable compared to the stable fixation. In the case of unstable fractures, it is possible for a single locking plate fixation to provide the required mechanical environment for callus formation without significant risk of plate fracture, provided partial weight bearing is followed. In cases where partial weight bearing is unlikely, additional biological fixation could be considered.

Evaluation of a new approach for modelling the screw-bone interface in a locking plate fixation: A corroboration study

Computational modelling of the screw–bone interface in fracture fixation constructs is challenging. While incorporating screw threads would be a more realistic representation of the physics, this approach can be computationally expensive. Several studies have instead suppressed the threads and modelled the screw shaft with fixed conditions assumed at the screw–bone interface. This study assessed the sensitivity of the computational results to modelling approaches at the screw–bone interface. A new approach for modelling this interface was proposed, and it was tested on two locking screw designs in a diaphyseal bridge plating configuration. Computational models of locked plating and far cortical locking constructs were generated and compared to in vitro models described in prior literature to corroborate the outcomes. The new approach led to closer agreement between the computational and the experimental stiffness data, while the fixed approach led to overestimation of the stiffness predictions. Using the new approach, the pattern of load distribution and the magnitude of the axial forces, experienced by each screw, were compared between the locked plating and far cortical locking constructs. The computational models suggested that under more severe loading conditions, far cortical locking screws might be under higher risk of screw pull-out than the locking screws. The proposed approach for modelling the screw–bone interface can be applied to any fixation involved application of screws.

Rigid versus flexible plate fixation for periprosthetic femoral fracture—Computer modelling of a clinical case

A variety of plate designs have been implemented for treatment of periprosthetic femoral fracture (PFF) fixation. Controversy, however, exists with regard to optimum fixation methods using these plates. A clinical case of a PFF fixation (Vancouver type C) was studied where a rigid locking plate fixation was compared with a more flexible non-locking approach. A parametric computational model was developed in order to understand the underlying biomechanics between these two fixations. The model was used to estimate the overall stiffness and fracture movement of the two implemented methods. Further, the differing aspects of plate design and application were incrementally changed in four different models. The clinical case showed that a rigid fixation using a 4.5 mm titanium locking plate with a short bridging length did not promote healing and ultimately failed. In contrast, a flexible fixation using 5.6 mm stainless steel non-locking plate with a larger bridging length promoted healing. The computational results highlighted that changing the bridging length made a more substantial difference to the stiffness and fracture movement than varying other parameters. Further the computational model predicted the failure zone on the locking plate. In summary, rigid fracture fixation in the case of PFF can suppress the fracture movement to a degree that prevents healing and may ultimately fail. The computational approach demonstrated the potential of this technique to compare the stiffness and fracture movement of different fixation constructs in order to determine the optimum fixation method for PFF.

The effect of collagen fibril orientation on the biphasic mechanics of articular cartilage

The highly inhomogeneous distribution of collagen fibrils may have important effects on the biphasic mechanics of articular cartilage. However, the effect of the inhomogeneity of collagen fibrils has mainly been investigated using simplified three-layered models, which may have underestimated the effect of collagen fibrils by neglecting their realistic orientation. The aim of this study was to investigate the effect of the realistic orientation of collagen fibrils on the biphasic mechanics of articular cartilage. Five biphasic material models, each of which included a different level of complexity of fibril reinforcement, were solved using two different finite element software packages (Abaqus and FEBio). Model 1 considered the realistic orientation of fibrils, which was derived from diffusion tensor magnetic resonance images. The simplified three-layered orientation was used for Model 2. Models 3-5 were three control models. The realistic collagen orientations obtained in this study were consistent with the literature. Results from the two finite element implementations were in agreement for each of the conditions modelled. The comparison between the control models confirmed some functions of collagen fibrils. The comparison between Models 1 and 2 showed that the widely-used three-layered inhomogeneous model can produce similar fluid load support to the model including the realistic fibril orientation; however, an accurate prediction of the other mechanical parameters requires the inclusion of the realistic orientation of collagen fibrils.