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

Finite element analysis of vertebroplasty in the osteoporotic T11-L1 vertebral body: Effects of bone cement formulation

Vertebral compression fractures are one of the most severe clinical consequences of osteoporosis and the most common fragility fracture afflicting 570 and 1070 out of 100,000 men and women worldwide, respectively. Vertebroplasty (VP), a minimally invasive surgical procedure that involves the percutaneous injection of bone cement, is one of the most efficacious methods to stabilise osteoporotic vertebral compression fractures. However, postoperative fracture has been observed in up to 30% of patients following VP. Therefore, this study aims to investigate the effect of different injectable bone cement formulations on the stress distribution within the vertebrae and intervertebral discs due to VP and consequently recommend the optimal cement formulation. To achieve this, a 3D finite element (FE) model of the T11-L1 vertebral body was developed from computed tomography scan data of the spine. Osteoporotic bone was modeled by reducing the Young's modulus by 20% in the cortical bone and 74% in cancellous bone. The FE model was subjected to different physiological movements, such as extension, flexion, bending, and compression. The osteoporotic model caused a reduction in the average von Mises stress compared with the normal model in the T12 cancellous bone and an increment in the average von Mises stress value at the T12 cortical bone. The effects of VP using different formulations of a novel injectable bone cement were modeled by replacing a region of T12 cancellous bone with the materials. Due to the injection of the bone cement at the T12 vertebra, the average von Mises stresses on cancellous bone increased and slightly decreased on the cortical bone under all loading conditions. The novel class of bone cements investigated herein demonstrated an effective restoration of stress distribution to physiological levels within treated vertebrae, which could offer a potential superior alternative for VP surgery as their anti-osteoclastogenic properties could further enhance the appeal of their fracture treatment and may contribute to improved patient recovery and long-term well-being.

A 20-Year Review of Biomechanical Experimental Studies on Spine Implants Used for Percutaneous Surgical Repair of Vertebral Compression Fractures

A vertebral compression fracture (VCF) is an injury to a vertebra of the spine affecting the cortical walls and/or middle cancellous section. The most common risk factor for a VCF is osteoporosis, thus predisposing the elderly and postmenopausal women to this injury. Clinical consequences include loss of vertebral height, kyphotic deformity, altered stance, back pain, reduced mobility, reduced abdominal space, and reduced thoracic space, as well as early mortality. To restore vertebral mechanical stability, overall spine function, and patient quality of life, the original percutaneous surgical intervention has been vertebroplasty, whereby bone cement is injected into the affected vertebra. Because vertebroplasty cannot fully restore vertebral height, newer surgical techniques have been developed, such as kyphoplasty, stents, jacks, coils, and cubes. But, relatively few studies have experimentally assessed the biomechanical performance of these newer procedures. This article reviews over 20 years of scientific literature that has experimentally evaluated the biomechanics of percutaneous VCF repair methods. Specifically, this article describes the basic operating principles of the repair methods, the study protocols used to experimentally assess their biomechanical performance, and the actual biomechanical data measured, as well as giving a number of recommendations for future research directions.

Using inverse finite element analysis to identify spinal tissue behaviour in situ

In computational modelling of musculoskeletal applications, one of the critical aspects is ensuring that a model can capture intrinsic population variability and not only representative of a "mean" individual. Developing and calibrating models with this aspect in mind is key for the credibility of a modelling methodology. This often requires calibration of complex models with respect to 3D experiments and measurements on a range of specimens or patients. Most Finite Element (FE) software's do not have such a capacity embedded in their core tools. This paper presents a versatile interface between Finite Element (FE) software and optimisation tools, enabling calibration of a group of FE models on a range of experimental data. It is provided as a Python toolbox which has been fully tested and verified on Windows platforms. The toolbox is tested in three case studies involving in vitro testing of spinal tissues.

Properties of PMMA end cap holders affect FE stiffness predictions of vertebral specimens

Bone cement is often used, in experimental biomechanics, as a potting agent for vertebral bodies (VB). As a consequence, it is usually included in finite element (FE) models to improve accuracy in boundary condition settings. However, bone cement material properties are typically assigned to these models based on literature data obtained from specimens created under conditions which often differ from those employed for cement end caps. These discrepancies can result in solids with different material properties from those reported. Therefore, this study aimed to analyse the effect of assigning different mechanical properties to bone cement in FE vertebral models. A porcine C2 vertebral body was potted in bone cement end caps, μCT scanned, and tested in compression. DIC was performed on the anterior surface of the specimen to monitor the displacement. Specimen stiffness was calculated from the load-displacement output of the materials testing machine and from the machine load output and average displacement measured by DIC. Fifteen bone cement cylinders with dimensions similar to the cement end caps were produced and subjected to the same compression protocol as the vertebral specimen and average stiffness and Young moduli were estimated. Two geometrically identical vertebral body FE models were created from the μCT images, the only difference residing in the values assigned to bone cement material properties: in one model these were obtained from the literature and in the other from the cylindrical cement samples previously tested. The average Youngs modulus of the bone cement cylindrical specimens was 1177 ± 3 MPa, considerably lower than the values reported in the literature. With this value, the FE model predicted a vertebral specimen stiffness 3% lower than that measured experimentally, while when using the value most commonly reported in similar studies, specimen stiffness was overestimated by 150%.

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.

Estimating tissue-level properties of porcine talar subchondral bone

Tissue-level properties of bone play an important role when characterising apparent-level bone biomechanical behaviour and yet little is known about its effect at this hierarchical level. In combination with trabecular morphological data these properties can be used to predict bone strength, which becomes an invaluable tool for clinicians in patient treatment planning. This study developed specimen-specific micro-finite element (μFE) models using validated continuum-level models, containing grayscale-derived material properties, to indirectly establish tissue-level properties of porcine talar subchondral bone. Specimen-specific continuum finite element (hFE) models of subchondral trabecular bone were setup using μCT data of ten cylindrical specimens extracted from juvenile porcine tali. The models were validated using quasi-static uniaxial compression testing. Validated hFE models were used to calibrate the tissue modulus of corresponding μFE models by minimising the difference between the μFE and hFE stiffness values. Key trabecular morphological indices (BV/TV, DA, Conn.D, Tb.Th, EF) were evaluated. Good agreement was observed between hFE models and experiment (CCC = 0.66). Calibrated E_tiss was 504 ± 37.65 MPa. Average BV/TV and DA for μFE specimens were 0.37 ± 0.05 and 0.68 ± 0.11, respectively. BV/TV (r² = 0.667) correlated highly with μFE stiffness. The small intra-specimen variation to tissue-level properties suggests that variations to apparent-level stiffness originate from variations to microarchitecture rather than tissue mechanical properties.

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.

Hip stem fatigue: : The implications of increasing patient mass

General trends of increasing body mass index have been observed in many western countries along with an increasing demand for joint replacement. Standards have been developed for testing the fatigue properties of femoral stems; however, the loads that these apply are based on a historic patient weight and may not be valid in the current patient population. Several fatigue tests were conducted using distally fixed titanium alloy stems positioned according to the ISO standard but with a cyclic load based on a current 75th percentile patient sample. Smaller sized stems (currently not weight restricted) fractured in; 30,000 cycles, while larger sized stems were found to have excellent durability under loads simulating walking and stumbling. The results suggest that while the fatigue properties of medical grade titanium are very good, the ISO pre-clinical durability testing standard does not represent the influence of femoral offset or stem size sufficiently to reflect safe design practice.

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.

Annulus fibrosus functional extrafibrillar and fibrous mechanical behaviour: experimental and computational characterisation

The development of current surgical treatments for intervertebral disc damage could benefit from virtual environment accounting for population variations. For such models to be reliable, a relevant description of the mechanical properties of the different tissues and their role in the functional mechanics of the disc is of major importance. The aims of this work were first to assess the physiological hoop strain in the annulus fibrosus in fresh conditions (n = 5) in order to extract a functional behaviour of the extrafibrillar matrix; then to reverse-engineer the annulus fibrosus fibrillar behaviour (n = 6). This was achieved by performing both direct and global controlled calibration of material parameters, accounting for the whole process of experimental design and in silico model methodology. Direct-controlled models are specimen-specific models representing controlled experimental conditions that can be replicated and directly comparing measurements. Validation was performed on another six specimens and a sensitivity study was performed. Hoop strains were measured as 17 ± 3% after 10 min relaxation and 21 ± 4% after 20-25 min relaxation, with no significant difference between the two measurements. The extrafibrillar matrix functional moduli were measured as 1.5 ± 0.7 MPa. Fibre-related material parameters showed large variability, with a variance above 0.28. Direct-controlled calibration and validation provides confidence that the model development methodology can capture the measurable variation within the population of tested specimens.

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.

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.

Histopathology in 3D: From three-dimensional reconstruction to multi-stain and multi-modal analysis

Light microscopy applied to the domain of histopathology has traditionally been a two-dimensional imaging modality. Several authors, including the authors of this work, have extended the use of digital microscopy to three dimensions by stacking digital images of serial sections using image-based registration. In this paper, we give an overview of our approach, and of extensions to the approach to register multi-modal data sets such as sets of interleaved histopathology sections with different stains, and sets of histopathology images to radiology volumes with very different appearance. Our approach involves transforming dissimilar images into a multi-channel representation derived from co-occurrence statistics between roughly aligned images.

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.

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

The aim of the study was to use a computational and experimental approach to evaluate, compare and predict the ability of calcium phosphate (CaP) and poly (methyl methacrylate) (PMMA) augmentation cements to restore mechanical stability to traumatically fractured vertebrae, following a vertebroplasty procedure. Traumatic fractures (n = 17) were generated in a series of porcine vertebrae using a drop-weight method. The fractured vertebrae were imaged using μCT and tested under axial compression. Twelve of the fractured vertebrae were randomly selected to undergo a vertebroplasty procedure using either a PMMA (n = 6) or a CaP cement variation (n = 6). The specimens were imaged using μCT and re-tested. Finite element models of the fractured and augmented vertebrae were generated from the μCT data and used to compare the effect of fracture void fill with augmented specimen stiffness. Significant increases (p < 0.05) in failure load were found for both of the augmented specimen groups compared to the fractured group. The experimental and computational results indicated that neither the CaP cement nor PMMA cement could completely restore the vertebral mechanical behavior to the intact level. The effectiveness of the procedure appeared to be more influenced by the volume of fracture filled rather than by the mechanical properties of the cement itself.

A parametric finite element analysis of the compacted bone–cement interface following balloon kyphoplasty

Treating fractures of the spine is a major challenge for the medical community with an estimated 1.4 million fractures per annum worldwide. While a considerable volume of study exists on the biomechanical implications of balloon kyphoplasty, which is used to treat these fractures, the influence of the compacted bone–cement region properties on stress distribution within the vertebral body remains unknown. The following article describes a novel method for modelling this compacted bone–cement region using a geometry-based approach in conjunction with the knowledge of the bone volume fractions for the native and compacted bone regions. Three variables for the compacted region were examined, as follows: (1) compacted thickness, (2) compacted region Young’s modulus and (3) friction coefficient. Results from the model indicate that the properties of the compacted bone–cement region can affect stresses in the cortical bone and cement by up to +28% and −40%, respectively. These findings demonstrate the need for further investigation into the effects of the compacted bone–cement interface using computational and experimental methods on multi-segment models.

Vertebroplasty: Patient and treatment variations studied through parametric computational models

BACKGROUND

Vertebroplasty is increasingly used in the treatment of vertebral compression fractures. However there are concerns that this intervention may lead to further fractures in the adjacent vertebral segments. This study was designed to parametrically assess the influence of both treatment factors (cement volume and number of augmentations), and patient factors (bone and disc quality) on the biomechanical effects of vertebroplasty.

METHODS

Specimen-specific finite element models of two experimentally-tested human three-vertebral-segments were developed from CT-scan data. Cement augmentation at one and two levels was represented in the respective models and good agreement in the predicted stiffness was found compared to the corresponding experimental specimens. Parametric variations of key variables associated with the procedure were then studied.

FINDINGS

The segmental stiffness increased with disc degeneration, with increasing bone quality and to a lesser extent with increasing cement volume. Cement modulus did not have a great influence on the overall segmental stiffness and on the change in the elemental stress in the adjoining vertebrae. However, following augmentation, the stress distribution in the adjacent vertebra changed, indicating possible load redistribution effects of vertebroplasty.

INTERPRETATION

This study demonstrates the importance of patient factors in the outcomes of vertebroplasty and suggests that these may be one reason for the variation in clinical results.

Unsupervised content classification based nonrigid registration of differently stained histology images

Registration of histopathology images of consecutive tissue sections stained with different histochemical or immunohistochemical stains is an important step in a number of application areas, such as the investigation of the pathology of a disease, validation of MRI sequences against tissue images, multiscale physical modeling, etc. In each case, information from each stain needs to be spatially aligned and combined to ascertain physical or functional properties of the tissue. However, in addition to the gigabyte-size images and nonrigid distortions present in the tissue, a major challenge for registering differently stained histology image pairs is the dissimilar structural appearance due to different stains highlighting different substances in tissues. In this paper, we address this challenge by developing an unsupervised content classification method that generates multichannel probability images from a roughly aligned image pair. Each channel corresponds to one automatically identified content class. The probability images enhance the structural similarity between image pairs. By integrating the classification method into a multiresolution-block-matching-based nonrigid registration scheme (N. Roberts, D. Magee, Y. Song, K. Brabazon, M. Shires, D. Crellin, N. Orsi, P. Quirke, and D. Treanor, "Toward routine use of 3D histopathology as a research tool," Amer. J. Pathology, vol. 180, no. 5, 2012.), we improve the performance of registering multistained histology images. Evaluation was conducted on 77 histological image pairs taken from three liver specimens and one intervertebral disc specimen. In total, six types of histochemical stains were tested. We evaluated our method against the same registration method implemented without applying the classification algorithm (intensity-based registration) and the state-of-the-art mutual information based registration. Superior results are obtained with the proposed method.

Percutaneous spinal fixation simulation with virtual reality and haptics

BACKGROUND

In this study, we evaluated the use of a part-task simulator with 3-dimensional and haptic feedback as a training tool for percutaneous spinal needle placement.

OBJECTIVE

To evaluate the learning effectiveness in terms of entry point/target point accuracy of percutaneous spinal needle placement on a high-performance augmented-reality and haptic technology workstation with the ability to control the duration of computer-simulated fluoroscopic exposure, thereby simulating an actual situation.

METHODS

Sixty-three fellows and residents performed needle placement on the simulator. A virtual needle was percutaneously inserted into a virtual patient's thoracic spine derived from an actual patient computed tomography data set.

RESULTS

Ten of 126 needle placement attempts by 63 participants ended in failure for a failure rate of 7.93%. From all 126 needle insertions, the average error (15.69 vs 13.91), average fluoroscopy exposure (4.6 vs 3.92), and average individual performance score (32.39 vs 30.71) improved from the first to the second attempt. Performance accuracy yielded P = .04 from a 2-sample t test in which the rejected null hypothesis assumes no improvement in performance accuracy from the first to second attempt in the test session.

CONCLUSION

The experiments showed evidence (P = .04) of performance accuracy improvement from the first to the second percutaneous needle placement attempt. This result, combined with previous learning retention and/or face validity results of using the simulator for open thoracic pedicle screw placement and ventriculostomy catheter placement, supports the efficacy of augmented reality and haptics simulation as a learning tool.

An experimentally validated finite element method for augmented vertebral bodies

BACKGROUND

Finite element models of augmented vertebral bodies require a realistic modelling of the cement infiltrated region. Most methods published so far used idealized cement shapes or oversimplified material models for the augmented region. In this study, an improved, anatomy-specific, homogenized finite element method was developed and validated to predict the apparent as well as the local mechanical behavior of augmented vertebral bodies.

METHODS

Forty-nine human vertebral body sections were prepared by removing the cortical endplates and scanned with high-resolution peripheral quantitative CT before and after injection of a standard and a low-modulus bone cement. Forty-one specimens were tested in compression to measure stiffness, strength and contact pressure distributions between specimens and loading-plates. From the remaining eight, fourteen cylindrical specimens were extracted from the augmented region and tested in compression to obtain material properties. Anatomy-specific finite element models were generated from the CT data. The models featured element-specific, density-fabric-based material properties, damage accumulation, real cement distributions and experimentally determined material properties for the augmented region. Apparent stiffness and strength as well as contact pressure distributions at the loading plates were compared between simulations and experiments.

FINDINGS

The finite element models were able to predict apparent stiffness (R(2)>0.86) and apparent strength (R(2)>0.92) very well. Also, the numerically obtained pressure distributions were in reasonable quantitative (R(2)>0.48) and qualitative agreement with the experiments.

INTERPRETATION

The proposed finite element models have proven to be an accurate tool for studying the apparent as well as the local mechanical behavior of augmented vertebral bodies.

Development of calcium phosphate cement for the augmentation of traumatically fractured porcine specimens using vertebroplasty

The study aim was to develop and apply an experimental technique to determine the biomechanical effect of polymethylmethacrylate (PMMA) and calcium phosphate (CaP) cement on the stiffness and strength of augmented vertebrae following traumatic fracture. Twelve burst type fractures were generated in porcine three-vertebra segments. The specimens were randomly split into two groups (n=6), imaged using microCT and tested under axial loading. The two groups of fractured specimens underwent a vertebroplasty procedure, one group was augmented with CaP cement designed and developed at Queen's University Belfast. The other group was augmented with PMMA cement (WHW Plastics, Hull, UK). The specimens were imaged and re-tested . An intact single vertebra specimen group (n=12) was also imaged and tested under axial loading. A significant decrease (p<0.01) was found between the stiffness of the fractured and intact groups, demonstrating that the fractures generated were sufficiently severe, to adversely affect mechanical behaviour. Significant increase (p<0.01) in failure load was found for the specimen group augmented with the PMMA cement compared to the pre-augmentation group, conversely, no significant increase (p<0.01) was found in the failure load of the specimens augmented with CaP cement, this is attributed to the significantly (p<0.05) lower volume of CaP cement that was successfully injected into the fracture, compared to the PMMA cement. The effect of the percentage of cement fracture fill, cement modulus on the specimen stiffness and ultimate failure load could be investigated further by using the methods developed within this study to test a more injectable CaP cement.

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.

FINITE ELEMENT ANALYSIS OF A MODEL OF SIMULATED VERTEBRAL CEMENT AUGMENTATION: INFLUENCE OF THE REPRESENTATION OF THE SHAPE OF THE CEMENT DOMAIN ON BIOMECHANICAL PARAMETERS

Vertebral cement augmentation is rapidly becoming the modality of choice for treating patients who are experiencing severe and persistent pain because of osteoporosis-induced vertebral compression fracture(s). The resulting cement domain (the part of the vertebral body (VB) filled with the cement) has an irregular or complicated shape. In literature reports of finite element analysis (FEA) of models of simulated vertebral cement augmentation, a variety of representations of the shape of the cement domain have been used. In the literature, only very limited attention has been given to the issue of the influence of cement domain shape representation on biomechanical parameters for a given combination of model and loading. This issue is the subject of the present work, with the model being of the L1-L3 motion segments. Augmentation of an unfractured L2 (prophylactic augmentation) was simulated, three cement domain shapes were considered — namely, solid cylinder, with rounded edges; two prolate spheroids; and oblate spheroid — and the applied loading comprised a simultaneous application of a uniform compressive pressure of 0.53 MPa (equivalent to an 800-N compression load) and a counter-clockwise-acting axial rotation moment of 1 Nm to the superior surface of L1. It was found that (1) while the cement domain shape representation has a marked influence on the mean von Mises stress (σAVM), the maximum von Mises stress (σMVM), and the strain energy density (MSED) distribution in the cement domain, its influence on each of these parameters in each of the biological tissues in the model as well as on the total segmental range of motion is minimal and (2) for σAVM and σMVM, the lowest value of each of these parameters was obtained when the oblate spheroid model was used. From both clinical and computational perspectives, these findings are significant. For example, the latter finding suggests that there is scope for researching the combination of key process variables used, such as the cement chemistry, the cement delivery system, and the augmentation technique/approach, that would ensure that the final cement domain shape in cement-augmented VBs of patients be oblate spheroid on a consistent and predictable basis.

The use of preserved tissue in finite element modelling of fresh ovine vertebral behaviour

The aim of this study was to investigate whether the predicted finite element (FE) stiffness of vertebral bone is altered when using images of preserved rather than fresh tissue to generate specimen-specific FE models. Fresh ovine vertebrae were used to represent embalmed (n = 3) and macerated dry-bone (n = 3) specimens and treated accordingly. Specimens were scanned pre- and post-treatment using micro-computed tomography. A constant threshold level derived from these images was used to calculate the respective bone volume fraction (BV/TV) from which the conversion factor validated for fresh tissue was used to determine material properties that were assigned to corresponding FE models. Results showed a definite change in the BV/TV between the fresh and the preserved bone. However, the changes in the predicted FE stiffness were not generally greater than the variations expected from assignment of loading and boundary conditions. In conclusion, images of preserved tissue can be used to generate FE models that are representative of fresh tissue with a tolerable level of error.

A new material mapping procedure for quantitative computed tomography-based, continuum finite element analyses of the vertebra

Inaccuracies in the estimation of material properties and errors in the assignment of these properties into finite element models limit the reliability, accuracy, and precision of quantitative computed tomography (QCT)-based finite element analyses of the vertebra. In this work, a new mesh-independent, material mapping procedure was developed to improve the quality of predictions of vertebral mechanical behavior from QCT-based finite element models. In this procedure, an intermediate step, called the material block model, was introduced to determine the distribution of material properties based on bone mineral density, and these properties were then mapped onto the finite element mesh. A sensitivity study was first conducted on a calibration phantom to understand the influence of the size of the material blocks on the computed bone mineral density. It was observed that varying the material block size produced only marginal changes in the predictions of mineral density. Finite element (FE) analyses were then conducted on a square column-shaped region of the vertebra and also on the entire vertebra in order to study the effect of material block size on the FE-derived outcomes. The predicted values of stiffness for the column and the vertebra decreased with decreasing block size. When these results were compared to those of a mesh convergence analysis, it was found that the influence of element size on vertebral stiffness was less than that of the material block size. This mapping procedure allows the material properties in a finite element study to be determined based on the block size required for an accurate representation of the material field, while the size of the finite elements can be selected independently and based on the required numerical accuracy of the finite element solution. The mesh-independent, material mapping procedure developed in this study could be particularly helpful in improving the accuracy of finite element analyses of vertebroplasty and spine metastases, as these analyses typically require mesh refinement at the interfaces between distinct materials. Moreover, the mapping procedure is not specific to the vertebra and could thus be applied to many other anatomic sites.

Replicating interbody device subsidence with lumbar vertebrae surrogates

Bone surrogates are proposed alternatives to human cadaveric vertebrae for assessing interbody device subsidence. A synthetic vertebra with representations of cortices, endplates and cancellous bone was recently developed as an alternative surrogate to polyurethane foam blocks. The ability of the two surrogates to replicate subsidence has not been fully assessed, and was evaluated by indenting them with ring-shaped indenters and comparing their performance with human cadaveric vertebrae using qualitative characteristics and indentation metrics. The sensitivity of each surrogate to a centrally or peripherally placed indenter was of particular interest. Many indentation characteristics of the foam blocks were similar to those of human cadaveric vertebrae, except their insensitivity to centrally and peripherally placed indenters, owing to their homogeneous mechanical properties. This is distinctly different from the cadaveric vertebrae, where a peripherally placed indenter indented significantly less than a centrally placed indenter, because of endplates. By contrast, the synthetic vertebra was sensitive to peripherally placed indenters owing to its bi-material composition, including a thickened peripheral endplate. However, an overly strong synthetic endplate resulted in unrepresentative indentation shape and depth. Both surrogates produced similar results to human cadaveric vertebrae in certain respects, but neither is accurate enough in terms of material property distribution to model subsidence completely in human cadaveric vertebrae.

A Mixed Boundary Representation to Simulate the Displacement of a Biofluid by a Biomaterial in Porous Media

Characterization of the biomaterial flow through porous bone is crucial for the success of the bone augmentation process in vertebroplasty. The biofluid, biomaterial, and local morphological bone characteristics determine the final shape of the filling, which is important both for the post-treatment mechanical loading and the risk of intraoperative extraosseous leakage. We have developed a computational model that describes the flow of biomaterials in porous bone structures by considering the material porosity, the region-dependent intrinsic permeability of the porous structure, the rheological properties of the biomaterial, and the boundary conditions of the filling process. To simulate the process of the substitution of a biofluid (bone marrow) by a biomaterial (bone cement), we developed a hybrid formulation to describe the evolution of the fluid boundary and properties and coupled it to a modified version of Darcy’s law. The apparent rheological properties are derived from a fluid-fluid interface tracking algorithm and a mixed boundary representation. The region- specific intrinsic permeability of the bone is governed by an empirical relationship resulting from a fitting process of experimental data. In a first step, we verified the model by studying the displacement process in spherical domains, where the spreading pattern is known in advance. The mixed boundary model demonstrated, as expected, that the determinants of the spreading pattern are the local intrinsic permeability of the porous matrix and the ratio of the viscosity of the fluids that are contributing to the displacement process. The simulations also illustrate the sensitivity of the mixed boundary representation to anisotropic permeability, which is related to the directional dependent microstructural properties of the porous medium. Furthermore, we compared the nonlinear finite element model to different published experimental studies and found a moderate to good agreement (R2=0.9895 for a one-dimensional bone core infiltration test and a 10.94–16.92% relative error for a three-dimensional spreading pattern study, respectively) between computational and experimental results.

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.

The role of cortical shell and trabecular fabric in finite element analysis of the human vertebral body

Classical finite element (FE) models can estimate vertebral stiffness and strength with much lower computational costs than muFE analyses, but the accuracy of these models rely on calibrated material properties that are not necessarily consistent with experimental results. In general, trabecular bone material properties are scaled with computer tomography (CT) density alone, without accounting for local variations in anisotropy or micro-architecture. Moreover, the cortex is often omitted or assigned with a constant thickness. In this work, voxel FE models, as well as surface-based homogenized FE models with topologically-conformed geometry and assigned with experimentally validated properties for bone, were developed from a series of 12 specimens tested up to failure. The effects of changing from a digital mesh to a smooth mesh, including a cortex of variable thickness and/or including heterogeneous trabecular fabric, were investigated. In each case, FE predictions of vertebral stiffness and strength were compared with the experimental gold-standard, and changes in elastic strain energy density and damage distributions were reported. The results showed that a smooth mesh effectively removed zones of artificial damage locations occurring in the ragged edges of the digital mesh. Adding an explicit cortex stiffened and strengthened the models, unloading the trabecular centrum while increasing the correlations to experimental stiffness and strength. Further addition of heterogeneous fabric improved the correlations to stiffness (R(2)=0.72) and strength (R(2)=0.89) and moved the damage locations closer to the vertebral endplates, following the local trabecular orientations. It was furthermore demonstrated that predictions of vertebral stiffness and strength of homogenized FE models with topologically-conformed cortical shell and heterogeneous trabecular fabric correlated well with experimental measurements, after assigning purely experimental data for bone without further calibration of material laws at the macroscale of bone. This study successfully demonstrated the limitations of current classical FE methods and provided valuable insights into the damage mechanisms of vertebral bodies.

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.