Using Statistical Shape and Appearance Modelling to characterise the 3D shape and material properties of human lumbar vertebrae: A proof of concept study.

Patient variation affects the outcomes of a range of spinal interventions, from disc replacement to vertebral fixation and vertebroplasty. Statistical Shape and Appearance Modelling (SSAM) can be used to describe anatomical variation and pathological differences within the population. To better understand how bone density and shape variation affect load transfer with respect to surgical treatments, Finite Element (FE) models can be generated from a SSAM. The aim for this study is to understand whether geometric and density variation as well as multiple vertebral levels can be incorporated into a single SSAM and whether this can be used to investigate the relationships between, and effects of, the various modes of variation. FE models of 14 human lumbar vertebrae that had been µCT imaged and validated through experimental testing were used as input specimens for a SSAM. The validity of the SSAM was evaluated by using principal component analysis to identify the primary modes of geometric and bone density variation and comparing to those in the input set. FE models were generated from the SSAM to examine the response to loading. The mean error between the input set and generated models for volume, mean density and FE compressive stiffness were 10%, 3% and 10% respectively. Principal Component (PC) 1 captured the majority of the bone density variation. The remaining PCs described specific geometric variation. The FE models generated from the SSAM showed the variations in vertebral stiffness as a result of complex relationships between bone density and shape. The SSAM created has limited data for its input set, however, it acts as a proof of concept for the novel combination of material and shape variation into a single shape model. This approach and the tools developed can be applied to wider patient groups and treatment scenarios to improve patient stratification and to optimise treatments.

Review of in vitro mechanical testing for intervertebral disc injectable biomaterials.

Many early stage interventions for intervertebral disc degeneration are under development involving injection of a biomaterial into the affected tissue. Due to the complex mechanical behaviour of the intervertebral disc, there are challenges in comprehensively evaluating the performance of these injectable biomaterials in vitro. The aim of this review was to examine the different methods that have been developed to mechanically test injectable intervertebral disc biomaterials in an in vitro disc model. Testing methods were examined with emphasis on overall protocol, artificial degeneration method, mechanical testing regimes and injection delivery. Specifically, the effects of these factors on the evaluation of different aspects of device performance was assessed. Broad testing protocols varied between studies and enabled evaluation of different aspects of an injectable treatment. Studies employed artificial degeneration methodologies which were either on a macro scale through mechanical means or on a microscale with biochemical means. Mechanical loading regimes differed greatly across studies, with load being either held constant, ramped to failure, or applied cyclically, with large variability on all loading parameters. Evaluation of the risk of herniation was possible by utilising ramped loading, whereas cyclic loading enabled the examination of the restoration of mechanical behaviour for initial screening of biomaterials and surgical technique optimisation studies. However, there are large variations in the duration or tests, and further work is needed to define an appropriate number of cycles to standardise this type of testing. Biomaterial delivery was controlled by set volume or haptic feedback, and future investigations should generate evidence applying physiological loading during injection and normalisation of injection parameters based on disc size. Based on the reviewed articles and considering clinical risks, a series of recommendations have been made for future intervertebral disc mechanical testing.

Peptide:glycosaminoglycan hybrid hydrogels as an injectable intervention for spinal disc degeneration.

Degeneration of the spinal discs is a major cause of back pain. During the degeneration process, there is a loss of glycosaminoglycans (GAGs) from the proteoglycan-rich gel in the disc's nucleus, which adversely alters biomechanical performance. Current surgical treatments for back pain are highly invasive and have low success rates; there is an urgent need for minimally-invasive approaches that restore the physiological mechanics of the spine. Here we present an injectable peptide:GAG hydrogel that rapidly self-assembles in situ and restores the mechanics of denucleated intervertebral discs. It forms a gel with comparable mechanical properties to the native tissue within seconds to minutes depending on the peptide chosen. Unlike other biomaterials that have been proposed for this purpose, these hybrid hydrogels can be injected through a very narrow 25 G gauge needle, minimising damage to the surrounding soft tissue, and they mimic the ability of the natural tissue to draw in water by incorporating GAGs. Furthermore, the GAGs enhance the gelation kinetics and thermodynamic stability of peptide hydrogels, significantly reducing effusion of injected material from the intervertebral disc (GAG leakage of 8 ± 3% after 24 h when peptide present, compared to 39 ± 3% when no peptide present). In an ex vivo model, we demonstrate that the hydrogels can restore the compressive stiffness of denucleated bovine intervertebral discs. Compellingly, this novel biomaterial has the potential to transform the clinical treatment of back pain by resolving current surgical challenges, thus improving patient quality of life.

Comparative finite-element analysis: a single computational modelling method can estimate the mechanical properties of porcine and human vertebrae.

Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.

An analytical calculation of the fluid load support fraction in a biphasic material: an alternative technique.

BACKGROUND: The fluid load support fraction (W(F)/W(T)) can be used to define the mechanical contribution of the interstitial fluid (W(F)) to the total force (W(T)) in the deformation of cartilage. Traditionally, W(F)/W(T) is calculated using complex experimental setups or time-consuming micromechanical poroelastic Finite Element (FE) simulations. AIM: To define and validate a fast and efficient technique to predict W(F)/W(T) using an analytical approach that can be applied without micromechanical detail or experimental measurement. METHODOLOGY: Poroelastic FE simulations defined accurate values of W(F)/W(T) for a range of loading configurations and were used to validate subsequent predictions. The analytical prediction of W(F)/W(T) used elastic contact mechanics to calculate W(F), and viscoelastic FE representation to calculate W(T). Subsequently, these independent calculations of W(F) and W(T) provided values of W(F)/W(T) that were compared with the poroelastic FE calculations. RESULTS AND DISCUSSION: The analytical prediction of W(F)/W(T) proved effective and suitably accurate (mean difference S<0.05). This technique demonstrated how W(F) and W(T) can be determined independently, without a biphasic constitutive model. Here we used viscoelasticity to calculate W(T) as an example, however, W(T) could be measured experimentally or predicted computationally.

Trabecular level analysis of bone cement augmentation: a comparative experimental and finite element study.

The representation of cement-augmented bone in finite element (FE) models of vertebrae following vertebroplasty remains a challenge, and the methods of the model validation are limited. The aim of this study was to create specimen-specific FE models of cement-augmented synthetic bone at the microscopic level, and to develop a new methodology to validate these models. An open cell polyurethane foam was used reduce drying effects and because of its similar structure to osteoporotic trabecular bone. Cylindrical specimens of the foam were augmented with PMMA cement. Each specimen was loaded to three levels of compression inside a micro-computed tomography (µCT) scanner and imaged both before compression and in each of the loaded states. Micro-FE models were generated from the unloaded µCT images and displacements applied to match measurements taken from the images. A morphological comparison between the FE-predicted trabecular deformations and the corresponding experimental measurements was developed to validate the accuracy of the FE model. The predicted deformation was found to be accurate (less than 12% error) in the elastic region. This method can now be used to evaluate real bone and different types of bone cements for different clinical situations.

Modelling cement augmentation: a comparative experimental and finite element study at the continuum level.

Subject-specific computational models of anatomical components can now be generated from image data and used in the assessment of orthopaedic interventions. However, little work has been undertaken to model cement-augmented bone using these methods. The purpose of this study was to investigate different methods of representing a trabecular-like material (open-cell polyurethane foam, Sawbone, Sweden) augmented with poly(methyl methacrylate) (PMMA) bone cement in a finite element (FE) model. Three sets of specimens (untreated, fully augmented with cement, partially augmented with cement) were imaged using micro computed tomography (microCT) and tested under axial compression. Subject-specific continuum level FE models were built based on the microCT images. Using the first two sets of models, the material conversion factors between image greyscale and mechanical properties for the pure synthetic bone and cement-augmented composite were determined iteratively by matching the FE predictions to the experimental measurements. By applying these greyscale related mechanical properties to the FE models of the partially augmented specimens, the predicted stiffness was found to be more accurate (approximately 5 per cent error) than using homogeneous properties for the augmented and synthetic bone regions (approximately 18 per cent error). It was also found that the predicted stiffness using the modulus of pure cement to define the augmented region was overestimated, and generally the apparent elastic modulus was dominated by the properties of the synthetic bone.

Optimisation of the mechanical and handling properties of an injectable calcium phosphate cement.

Calcium phosphate cements have the potential to be successful in minimally invasive surgical techniques, like that of vertebroplasty, due to their ability to be injected into a specific bone cavity. These bone cements set to produce a material similar to that of the natural mineral component in bone. Due to the ceramic nature of these materials they are highly brittle and it has been found that they are difficult to inject. This study was carried out to determine the factors that have the greatest effect on the mechanical and handling properties of an apatitic calcium phosphate cement with the use of a Design of Experiments (DoE) approach. The properties of the cement were predominantly influenced by the liquid:powder ratio and weight percent of di-sodium hydrogen phosphate within the liquid phase. An optimum cement composition was hypothesised and tested. The mechanical properties of the optimised cement were within the clinical range for vertebroplasty, however, the handling properties still require improvement.

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

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 (microCT) 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.

The biomechanical response of spinal cord tissue to uniaxial loading.

The spinal cord is an integral component of the spinal column and is prone to physical injury during trauma or more long-term pathological insults. The development of computational models to simulate the cord-column interaction during trauma is important in developing a proper understanding of the injury mechanism. Such models would be invaluable in seeking both preventive strategies that reduce the propensity for injury and identifying specific treatment regimes. However, these developments are hampered by the limited information available on the structural and mechanical properties of this soft tissue owing to the difficulty in handling this material in a cadaveric situation. The purpose of the present paper is to report the rapid deterioration in the quality of the tissues once excised, which provides a further challenge to the successful elucidation of the structural properties of the tissue. In particular, the tangent modulus of the tissue is seen to increase sharply over a period of 72 h.

The biomechanical effect of vertebroplasty on the adjacent vertebral body: a finite element study.

The increased use of vertebroplasty for the treatment of osteoporotic vertebral compression fractures has led to concerns that the technique may increase the risk of fracture in the adjacent vertebrae. The aim of this study was to simulate the biomechanical effects of vertebroplasty using an osteoporotic two-vertebrae finite element model. Following a simulated compression fracture, the model was augmented with one of three volumes of PMMA-based cement or left untreated. Upon reloading, an increase in segment stiffness was found with increasing volumes of cement. However, in all the treated models there was an increase in endplate deflection into the adjacent vertebra causing plastic failure of the surrounding trabecular bone. More damage was caused in the adjacent vertebra of the treated models than in the untreated model. The model results suggest that clinicians should be wary of using standard vertebroplasty cements to treat compression fractures in patients with highly osteoporotic bone.

The biomechanics of vertebroplasty: a review.

Percutaneous vertebroplasty and kyphoplasty are being used extensively in the United States for the treatment of osteoporotic vertebral compression fractures. Although short-term clinical outcomes appear favourable, long-term data are not yet available and it is becoming increasingly important to understand how the underlying biomechanics of the spine are altered by the procedure. In vitro experimental studies have investigated the effect of cement augmentation on individual vertebra and short spinal segments. For individual vertebra, vertebroplasty appears to increase or return strength to the prefracture level, whereas the stiffness is not always restored. However for multiple-vertebra segments, the strength of the unit as a whole appears to decrease, with failure occurring in the non-augmented vertebrae. Both finite element (FE) and experimental studies have shown that the volume of cement injected affects the restoration of strength and stiffness. The type of cement appears to have less of an effect. Although biomechanical studies of the vertebroplasty process have indicated that the procedure has the potential to restore vertebral strength and stiffness, further work is necessary to understand fully the effects of the augmentation process on the surrounding structures if the treatment is to be fully optimized. This paper is a review of the biomechanical data available on vertebroplasty.

A dynamic investigation of the burst fracture process using a combined experimental and finite element approach.

Spinal burst fractures account for about 15% of spinal injuries and, because of their predominance in the younger population, there are large associated social and healthcare costs. Although several experimental studies have investigated the burst fracture process, little work has been undertaken using computational methods. The aim of this study was to develop a finite element model of the fracture process and, in combination with experimental data, gain a better understanding of the fracture event and mechanism of injury. Experimental tests were undertaken to simulate the burst fracture process in a bovine spine model. After impact, each specimen was dissected and the severity of fracture assessed. Two of the specimens tested at the highest impact rate were also dynamically filmed during the impact. A finite element model, based on CT data of an experimental specimen, was constructed and appropriate high strain rate material properties assigned to each component. Dynamic validation was undertaken by comparison with high-speed video data of an experimental impact. The model was used to determine the mechanism of fracture and the postfracture impact of the bony fragment onto the spinal cord. The dissection of the experimental specimens showed burst fractures of increasing severity with increasing impact energy. The finite element model demonstrated that a high tensile strain region was generated in the posterior of the vertebral body due to the interaction of the articular processes. The region of highest strain corresponded well with the experimental specimens. A second simulation was used to analyse the fragment projection into the spinal canal following fracture. The results showed that the posterior longitudinal ligament became stretched and at higher energies the spinal cord and the dura mater were compressed by the fragment. These structures deformed to a maximum level before forcing the fragment back towards the vertebral body. The final position of the fragment did not therefore represent the maximum dynamic canal occlusion.

Measurement of canal occlusion during the thoracolumbar burst fracture process.

Post-injury CT scans are often used following burst fracture trauma as an indication for decompressive surgery. Literature suggests, however, that there is little correlation between the observed fragment position and the level of neurological injury or recovery. Several studies have aimed to establish the processes that occur during the fracture using indirect methods such as pressure measurements and pre/post impact CT scans. The purpose of this study was to develop a direct method of measuring spinal canal occlusion during a simulated burst fracture by using a high-speed video technique. The fractures were produced by dropping a mass from a measured height onto three-vertebra bovine specimens in a custom-built rig. The specimens were constrained to deform only in the impact direction such that pure compression fractures were generated. The spinal cord was removed prior to testing and the video system set up to film the inside of the spinal canal during the impact. A second camera was used to film the outside of the specimen to observe possible buckling during impact. The video images were analysed to determine how the cross-sectional area of the spinal canal changed during the event. The images clearly showed a fragment of bone being projected from the vertebral body into the spinal canal and recoiling to the final resting position. To validate the results, CT scans were taken pre- and post-impact and the percentage canal occlusion was calculated. There was good agreement between the final canal occlusion measured from the video images and the CT scans.