Mathematical relationships between bone density and mechanical properties: a literature review

ASSESSMENT OF OSTEOPOROTIC FEMORAL FRACTURE RISK: FINITE ELEMENT METHOD AS A POTENTIAL REPLACEMENT FOR CURRENT CLINICAL TECHNIQUES

Femoral fracture risk prediction is a necessary step preceding effective pharmacological intervention or pre-operative planning. Current clinical methods for fracture risk prediction rely on 2D imaging methods and have limited predictive value. Researchers are therefore trying to find improved methods for fracture prediction. During last few decades, many studies have focused on integration of 3D imaging techniques and the finite element (FE) method to improve the accuracy of fracture assessment techniques. In this paper, we review the recent advances in FE and other techniques for predicting the risk of femoral fractures. Based on a number of selected studies, the different steps that are involved in generation of patient-specific FE models are reviewed with particular emphasis on the fracture criteria. The inaccuracies that might arise due to the imperfections of the involved steps are also discussed. It is concluded that compared to image- and geometry-based techniques, FE is a more promising approach for prediction of fracture loads. However, certain technological advancements in FE modeling protocols are required before FE modeling can be recruited in clinical settings.

An optimization algorithm for individualized biomechanical analysis and simulation of tibia fractures

An algorithmic strategy to determine the minimal fusion area of a tibia pseudarthrosis to achieve mechanical stability is presented. For this purpose, a workflow capable for implementation into clinical routine workup of tibia pseudarthrosis was developed using visual computing algorithms for image segmentation, that is a coarsening protocol to reduce computational effort resulting in an individualized volume-mesh based on computed tomography data. An algorithm detecting the minimal amount of fracture union necessary to allow physiological loading without subjecting the implant to stresses and strains that might result in implant failure is developed. The feasibility of the algorithm in terms of computational effort is demonstrated. Numerical finite element simulations show that the minimal fusion area of a tibia pseudarthrosis can be less than 90% of the full circumferential area given a defined maximal von Mises stress in the implant of 80% of the total stress arising in a complete pseudarthrosis of the tibia.

TO WHAT EXTENT THE COMBINATION OF STEM LENGTH AND STEM INCLINATION DO AFFECT THE PERFORMANCE OF THE TIBIAL COMPONENT IN KNEE IMPLANTS?

Mechanical loosening, instability, mechanical fractures and poor quality of bone are some factors that strongly influence the deterioration of knee implants. After a total knee replacement (TKR), proximal tibial bone suffers a resorption due to stress-shielding caused by the implant. The formation of weakening bone zones and loss of bone is one of the most clinical concerns. The aim of this work is to evaluate the geometry of the implant stem to improve the implant lifespan. A three-dimensional model of the tibial component has been generated using computerized tomographies (CT) reconstruction and CAD software. Stresses distribution at the interface bone-implant considering several combinations of stem lengths and stem inclinations have been analyzed using finite element analysis (FEA). High levels of resorption risk have been observed, when using different stem-lengths and varus inclination.

Design, materials, and mechanobiology of biodegradable scaffolds for bone tissue engineering

A review about design, manufacture, and mechanobiology of biodegradable scaffolds for bone tissue engineering is given. First, fundamental aspects about bone tissue engineering and considerations related to scaffold design are established. Second, issues related to scaffold biomaterials and manufacturing processes are discussed. Finally, mechanobiology of bone tissue and computational models developed for simulating how bone healing occurs inside a scaffold are described.

Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest fractal analysis as a promising approach to quantify morpho-functional changes in both aging and pathology. In this particular context, fractal lacunarity seems to be the proper tool to characterize TBA texture as it is able to describe both discontinuity of bone network and sizes of bone marrow spaces, whose changes are an index of bone fracture risk. In this paper, an original method of MRI texture analysis, based on TBA fractal lacunarity is described and discussed in the light of new perspectives for early diagnosis of osteoporotic fractures.

Singularity-free finite element model of bone through automated voxel-based reconstruction

Computed tomography (CT) provides both anatomical and density information about tissues. Bone is segmented by raw images and Finite Element Method (FEM) voxel-based meshing technique is achieved by matching each CT voxel to a single finite element (FE). As a consequence of the automated model reconstruction, unstable elements - i.e. elements insufficiently anchored to the whole model and thus potentially involved in partial rigid body motion - can be generated, a crucial problem in obtaining consistent FE models, hindering mechanical analyses. Through the classification of instabilities on topological connections between elements, a numerical procedure is proposed in order to avoid unconstrained models.

The degenerative state of the intervertebral disk independently predicts the failure of human lumbar spine to high rate loading: an experimental study

BACKGROUND

In the elderly, 30%-50% of patients report a fall event to precede the onset of vertebral fractures. The dynamic characteristics of the spine determine the peak forces on the vertebrae in a fall. However, we know little about the effect of intervertebral disk degeneration on the failure of human spines under the high loading rates associated with such falls. We hypothesized that MR estimates of disk hydration and viscoelastic properties will provide better estimates of failure strength than bone density alone.

METHODS

Seventeen L1-L3 human spine segments were imaged (magnetic resonance imaging, dual-energy X-ray absorptiometry), their dynamic responses quantified using pendulum based impact, and the spines tested to failure under high rate loading simulating a fall event. The spines' stiffness and damping constants were computed (Kelvin-Voigt model) with disk hydration and geometry assessed from T2 and proton density images.

FINDINGS

Under impact, the spines exhibited a second-order underdamped response with stiffness and damping ranging (17.9-754.5) kN/m and (133.6-905.3) Ns/m respectively. Damping, but not stiffness, was negatively correlated with higher ultimate strength (P<0.05). Higher bone mineral density and MR-estimated disk hydration correlated with higher ultimate strength (P<0.01 for both). No such correlations were observed for the T2 values. Adding disk hydration yielded a 20% increase in the model's association with failure load compared to bone density alone (MANOVA, P<0.001).

INTERPRETATION

The strong correlation between disk viscoelastic properties and MR-estimated hydration with the spine segments' ultimate strength clearly demonstrates the need to include disk degeneration as part of fracture risk assessment in the elderly spine.

A QCT-Based Nonsegmentation Finite Element Head Model for Studying Traumatic Brain Injury

In the existing finite element head models (FEHMs) that are constructed from medical images, head tissues are usually segmented into a number of components according to the interior anatomical structure of the head. Each component is represented by a homogenous material model. There are a number of disadvantages in the segmentation-based finite element head models. Therefore, we developed a nonsegmentation finite element head model with pointwise-heterogeneous material properties and corroborated it by available experiment data. From the obtained results, it was found that although intracranial pressures predicted by the existing (piecewise-homogeneous) and the proposed (pointwise-heterogeneous) FEHM are very similar to each other, strain/stress levels in the head tissues are very different. The maximum peak strains/stresses predicted by the proposed FEHM are much higher than those by the existing FEHM, indicating that piecewise-homogeneous FEHM may have underestimated the stress/strain level induced by impact and thus may be inaccurate in predicting traumatic brain injuries.

Biomechanics and mechanobiology of trabecular bone: a review

Trabecular bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. Studying the mechanical properties of trabecular bone is important, since trabecular bone is the main load bearing bone in vertebral bodies and also transfers the load from joints to the compact bone of the cortex of long bones. This review article highlights the high dependency of the mechanical properties of trabecular bone on species, age, anatomic site, loading direction, and size of the sample under consideration. In recent years, high resolution micro finite element methods have been extensively used to specifically address the mechanical properties of the trabecular bone and provide unique tools to interpret and model the mechanical testing experiments. The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabecular bone microstructure and macrostructure and corresponding mechanical properties such as elastic properties and strength.

Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption

Patient-specific analysis of bones is considered an important tool for diagnosis and treatment of skeletal diseases and for clinical research aimed at understanding the etiology of skeletal diseases and the effects of different types of treatment on their progress. In this article, we discuss how integration of several important components enables accurate and cost-effective patient-specific bone analysis, focusing primarily on patient-specific finite element (FE) modeling of bones. First, the different components are briefly reviewed. Then, two important aspects of patient-specific FE modeling, namely integration of modeling components and automation of modeling approaches, are discussed. We conclude with a section on validation of patient-specific modeling results, possible applications of patient-specific modeling procedures, current limitations of the modeling approaches, and possible areas for future research.

Four decades of finite element analysis of orthopaedic devices: where are we now and what are the opportunities?

Finite element has been used for more than four decades to study and evaluate the mechanical behaviour total joint replacements. In Huiskes seminal paper "Failed innovation in total hip replacement: diagnosis and proposals for a cure", finite element modelling was one of the potential cures to avoid poorly performing designs reaching the market place. The size and sophistication of models has increased significantly since that paper and a range of techniques are available from predicting the initial mechanical environment through to advanced adaptive simulations including bone adaptation, tissue differentiation, damage accumulation and wear. However, are we any closer to FE becoming an effective screening tool for new devices? This review contains a critical analysis of currently available finite element modelling techniques including (i) development of the basic model, the application of appropriate material properties, loading and boundary conditions, (ii) describing the initial mechanical environment of the bone-implant system, (iii) capturing the time dependent behaviour in adaptive simulations, (iv) the design and implementation of computer based experiments and (v) determining suitable performance metrics. The development of the underlying tools and techniques appears to have plateaued and further advances appear to be limited either by a lack of data to populate the models or the need to better understand the fundamentals of the mechanical and biological processes. There has been progress in the design of computer based experiments. Historically, FE has been used in a similar way to in vitro tests, by running only a limited set of analyses, typically of a single bone segment or joint under idealised conditions. The power of finite element is the ability to run multiple simulations and explore the performance of a device under a variety of conditions. There has been increasing usage of design of experiments, probabilistic techniques and more recently population based modelling to account for patient and surgical variability. In order to have effective screening methods, we need to continue to develop these approaches to examine the behaviour and performance of total joint replacements and benchmark them for devices with known clinical performance. Finite element will increasingly be used in the design, development and pre-clinical testing of total joint replacements. However, simulations must include holistic, closely corroborated, multi-domain analyses which account for real world variability.

Less than full circumferential fusion of a tibial nonunion is sufficient to achieve mechanically valid fusion--proof of concept using a finite element modeling approach

BACKGROUND

Although minimally invasive approaches are widely used in many areas of orthopedic surgery nonunion therapy remains a domain of open surgery. Some attempts have been made to introduce minimally invasive procedures into nonunion therapy. However, these proof of concept studies showed fusion rates comparable to open approaches never gaining wider acceptance in the clinical community. We hypothesize that knowledge of mechanically relevant regions of a nonunion might reduce the complexity of percutaneous procedures, especially in complex fracture patterns, and further reduce the amount of cancellous bone that needs to be transplanted. The aim of this investigation is to provide a proof of concept concerning the hypothesis that mechanically stable fusion of a nonunion can be achieved with less than full circumferential fusion.

METHODS

CT data of an artificial tibia with a complex fracture pattern and anatomical LCP are converted into a finite element mesh. The nonunion area is segmented. The finite element mesh is assigned mechanical properties according to data from the literature. An optimization algorithm is developed that reduces the number of voxels in the non union area until the scaled von Mises stress in the implant reaches 20% of the maximum stress in the implant/bone system that occurs with no fusion in the nonunion area at all.

RESULTS

After six iterations of the optimization algorithm the number of voxels in the nonunion area is reduced by 96.4%, i.e. only 3.6% of voxels in the non union area are relevant for load transfer such that the von Mises stress in the implant/bone system does not exceed 20% of the maximal scaled von Mises stress occurring in the system with no fusion in the non union area at all.

CONCLUSIONS

The hypothesis that less than full circumferential fusion is necessary for mechanical stability of a nonunion is confirmed. As the model provides only qualitative information the observed reduction of fusion area may not be taken literally but needs to be calibrated in future experiments. However this proof of concept provides the mechanical foundation for further development of minimally invasive approaches to delayed union and nonunion therapy.

A novel method to assess primary stability of press-fit acetabular cups

Initial stability is an essential prerequisite to achieve osseointegration of press-fit acetabular cups in total hip replacements. Most in vitro methods that assess cup stability do not reproduce physiological loading conditions and use simplified acetabular models with a spherical cavity. The aim of this study was to investigate the effect of bone density and acetabular geometry on cup stability using a novel method for measuring acetabular cup micromotion. A press-fit cup was inserted into Sawbones® foam blocks having different densities to simulate normal and osteoporotic bone variations and different acetabular geometries. The stability of the cup was assessed in two ways: (a) measurement of micromotion of the cup in 6 degrees of freedom under physiological loading and (b) uniaxial push-out tests. The results indicate that changes in bone substrate density and acetabular geometry affect the stability of press-fit acetabular cups. They also suggest that cups implanted into weaker, for example, osteoporotic, bone are subjected to higher levels of micromotion and are therefore more prone to loosening. The decrease in stability of the cup in the physiological model suggests that using simplified spherical cavities to model the acetabulum over-estimates the initial stability of press-fit cups. This novel testing method should provide the basis for a more representative protocol for future pre-clinical evaluation of new acetabular cup designs.

Human proximal femur bone adaptation to variations in hip geometry

The study of bone mass distribution at proximal femur may contribute to understand the role of hip geometry on hip fracture risk. We examined how bone mineral density (BMD) of proximal femur adapts to inter individual variations in the femoral neck length (FNL), femoral neck width (FNW) and neck shaft angle (NSA). A parameterized and dimensionally scalable 3-D finite element model of a reference proximal femur geometry was incrementally adjusted to adopt physiological ranges at FNL (3.90-6.90cm), FNW (2.90-3.46cm), and NSA (109-141º), yielding a set of femora with different geometries. The bone mass distribution for each femur was obtained with a suitable bone remodelling model. The BMDs at the integral femoral neck (FN) and at the intertrochanteric (ITR) region, as well as the BMD ratio of inferomedial to superolateral (IM:SL) regions of FN and BMD ratio of FN:ITR were used to represent bone mass distribution. Results revealed that longer FNLs present greater BMD (g/cm(3)) at the FN, mainly at the SL region, and at the ITR region. Wider FNs were associated with reduced BMD at the FN, particularly at the SL region, and at the ITR region. Larger NSAs up to 129° were associated with BMD diminutions at the FN and ITR regions and with increases of the IM:SL BMD ratio while NSAs larger than 129° resulted in decrease of the IM:SL BMD ratio. These findings suggest hip geometry as moderator of the mechanical loading influence on bone mass distribution at proximal femur with higher FNL favoring the BMD of FN and ITR regions and greater FNW and NSA having the opposite effect. Augmented values of FNL and FNW seem also to favor more the BMD at the superolateral than at the inferomedial FN region.

Metals for bone implants. Part 1. Powder metallurgy and implant rendering

New metal alloys and metal fabrication strategies are likely to benefit future skeletal implant strategies. These metals and fabrication strategies were looked at from the point of view of standard-of-care implants for the mandible. These implants are used as part of the treatment for segmental resection due to oropharyngeal cancer, injury or correction of deformity due to pathology or congenital defect. The focus of this two-part review is the issues associated with the failure of existing mandibular implants that are due to mismatched material properties. Potential directions for future research are also studied. To mitigate these issues, the use of low-stiffness metallic alloys has been highlighted. To this end, the development, processing and biocompatibility of superelastic NiTi as well as resorbable magnesium-based alloys are discussed. Additionally, engineered porosity is reviewed as it can be an effective way of matching the stiffness of an implant with the surrounding tissue. These porosities and the overall geometry of the implant can be optimized for strain transduction and with a tailored stiffness profile. Rendering patient-specific, site-specific, morphology-specific and function-specific implants can now be achieved using these and other metals with bone-like material properties by additive manufacturing. The biocompatibility of implants prepared from superelastic and resorbable alloys is also reviewed.

Pullout strength of cancellous screws in human femoral heads depends on applied insertion torque, trabecular bone microarchitecture and areal bone mineral density

For cancellous bone screws, the respective roles of the applied insertion torque (TInsert) and of the quality of the host bone (microarchitecture, areal bone mineral density (aBMD)), in contributing to the mechanical holding strength of the bone-screw construct (FPullout), are still unclear. During orthopaedic surgery screws are tightened, typically manually, until adequate compression is attained, depending on surgeons' manual feel. This corresponds to a subjective insertion torque control, and can lead to variable levels of tightening, including screw stripping. The aim of this study, performed on cancellous screws inserted in human femoral heads, was to investigate which, among the measurements of aBMD, bone microarchitecture, and the applied TInsert, has the strongest correlation with FPullout. Forty six femoral heads were obtained, over which microarchitecture and aBMD were evaluated using micro-computed tomography and dual X-ray absorptiometry. Using an automated micro-mechanical test device, a cancellous screw was inserted in the femoral heads at TInsert set to 55% to 99% of the predicted stripping torque beyond screw head contact, after which FPullout was measured. FPullout exhibited strongest correlations with TInsert (R=0.88, p<0.001), followed by structure model index (SMI, R=-0.81, p<0.001), bone volume fraction (BV/TV, R=0.73, p<0.001) and aBMD (R=0.66, p<0.01). Combinations of TInsert with microarchitectural parameters and/or aBMD did not improve the prediction of FPullout. These results indicate that, for cancellous screws, FPullout depends most strongly on the applied TInsert, followed by microarchitecture and aBMD of the host bone. In trabecular bone, screw tightening increases the holding strength of the screw-bone construct.

A comparative study of orthotropic and isotropic bone adaptation in the femur

Functional adaptation of the femur has been studied extensively by embedding remodelling algorithms in finite element models, with bone commonly assumed to have isotropic material properties for computational efficiency. However, isotropy is insufficient in predicting the directionality of bone's observed microstructure. A novel iterative orthotropic 3D adaptation algorithm is proposed and applied to a finite element model of the whole femur. Bone was modelled as an optimised strain-driven adaptive continuum with local orthotropic symmetry. Each element's material orientations were aligned with the local principal stress directions and their corresponding directional Young's moduli updated proportionally to the associated strain stimuli. The converged predicted density distributions for a coronal section of the whole femur were qualitatively and quantitatively compared with the results obtained by the commonly used isotropic approach to bone adaptation and with ex vivo imaging data. The orthotropic assumption was shown to improve the prediction of bone density distribution when compared with the more commonly used isotropic approach, whilst producing lower comparative mass, structurally optimised models. It was also shown that the orthotropic approach can provide additional directional information on the material properties distributions for the whole femur, an advantage over isotropic bone adaptation. Orthotropic bone models can help in improving research areas in biomechanics where local structure and mechanical properties are of key importance, such as fracture prediction and implant assessment.

Estimating the density of femoral head trabecular bone from hip fracture patients using computed tomography scan data

The purpose of this study was to compare computed tomography density ( ρCT) obtained using typical clinical computed tomography scan parameters to ash density ( ρash), for the prediction of densities of femoral head trabecular bone from hip fracture patients. An experimental study was conducted to investigate the relationships between ρash and ρCT and between each of these densities and ρbulk and ρdry. Seven human femoral heads from hip fracture patients were computed tomography–scanned ex vivo, and 76 cylindrical trabecular bone specimens were collected. Computed tomography density was computed from computed tomography images by using a calibration Hounsfield units–based equation, whereas ρbulk, ρdry and ρash were determined experimentally. A large variation was found in the mean Hounsfield units of the bone cores (HUcore) with a constant bias from ρCT to ρash of 42.5 mg/cm3. Computed tomography and ash densities were linearly correlated ( R2 = 0.55, p < 0.001). It was demonstrated that ρash provided a good estimate of ρbulk ( R2 = 0.78, p < 0.001) and is a strong predictor of ρdry ( R2 = 0.99, p < 0.001). In addition, the ρCT was linearly related to ρbulk ( R2 = 0.43, p < 0.001) and ρdry ( R2 = 0.56, p < 0.001). In conclusion, mineral density was an appropriate predictor of ρbulk and ρdry, and ρCT was not a surrogate for ρash. There were linear relationships between ρCT and physical densities; however, following the experimental protocols of this study to determine ρCT, considerable scatter was present in the ρCT relationships.

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Predicting Bone Remodeling in Response to Total Hip Arthroplasty: Computational Study Using Mechanobiochemical Model

Periprosthetic bone loss following total hip arthroplasty (THA) is a serious concern leading to the premature failure of prosthetic implant. Therefore, investigating bone remodeling in response to hip arthroplasty is of paramount for the purpose of designing long lasting prostheses. In this study, a thermodynamic-based theory, which considers the coupling between the mechanical loading and biochemical affinity as stimulus for bone formation and resorption, was used to simulate the femoral density change in response to THA. The results of the numerical simulations using 3D finite element analysis revealed that in Gruen zone 7, after remarkable postoperative bone loss, the bone density started recovering and got stabilized after 9% increase. The most significant periprosthetic bone loss was found in Gruen zone 7 (−17.93%) followed by zone 1 (−13.77%). Conversely, in zone 4, bone densification was observed (+4.63%). The results have also shown that the bone density loss in the posterior region of the proximal metaphysis was greater than that in the anterior side. This study provided a quantitative figure for monitoring the distribution variation of density throughout the femoral bone. The predicted bone density distribution before and after THA agree well with the bone morphology and previous results from the literature.

How accurately can we predict the fracture load of the proximal femur using finite element models?

BACKGROUND

Current clinical methods for fracture prediction rely on two-dimensional imaging methods such as dual-energy X-ray absorptiometry and have limited predictive value. Several researchers have tried to integrate three-dimensional imaging techniques with the finite element (FE) method to improve the accuracy of fracture predictions. Before FE models could be used in clinical settings, a thorough validation of their accuracy is required. In this paper, we try to evaluate the current state of accuracy of subject-specific FE models that are used for prediction of the fracture load of proximal femora.

METHODS

All the studies that have used FE for prediction of fracture load and have compared the predicted fracture load with experimentally measured fracture loads in vitro are identified through a systematic search of the literature. A quantitative analysis of the results of those studies has been carried out to determine the absolute prediction error, percentage error, and linear correlations between predicted and measured fracture loads.

FINDINGS

The reported coefficients of determination (R(2)) vary between 0.773 and 0.96 while the percentage error in prediction of fracture load varies between 5 and 46% with most studies reporting percentage errors between 10 and 20%.

INTERPRETATION

We conclude that FE models, which are currently used only experimentally, are in general more accurate than clinically used fracture risk assessment techniques. However, the accuracy of FE models depends on the details of their modeling methodologies. Therefore, modeling procedures need to be optimized and standardized before FE could be used in clinical settings.

Novel injectable biomaterials for bone augmentation based on isosorbide dimethacrylic monomers

Drawbacks with the commonly used PMMA-based bone cements, such as an excessive elastic modulus and potentially toxic residual monomer content, motivate the development of alternative cements. In this work an attempt to prepare an injectable biomaterial based on isosorbide-alicyclic diol derived from renewable resources was presented. Two novel dimethacrylic monomers ISDGMA - 2,5-bis(2-hydroxy-3-methacryloyloxypropoxy)-1,4:3,6-dianhydro-sorbitol and ISETDMA - dimethacrylate of ethoxylated isosorbide were synthesized and used to prepare a series of low-viscosity compositions comprising bioactive nano-sized hydroxyapatite in the form of a two-paste system. Formulations exhibited a non-Newtonian shear-thinning behavior, setting times between 2.6 min and 5.3 min at 37°C and maximum curing temperatures of 65°C. Due to the hydrophilic nature of ISDGMA, cured compositions could absorb up to 13.6% water and as a result the Young's modulus decreased from 1,429 MPa down to 470 MPa. Both, poly(ISDGMA) and poly(ISETDMA) were subjected to a MTT study on mice fibroblasts (BALB/3T3) and gave relative cell viabilities above 70% of control. A selected model bone cement was additionally investigated using human osteosarcoma cells (SaOS-2) in an MTS test, which exhibited concentration-dependent cell viability. The preliminary results, presented in this work reveal the potential of two novel dimethacrylic monomers in the preparation of an injectable biomaterial for bone augmentation, which could overcome some of the drawbacks typical for conventional acrylic bone cement.

DIFFERENCES BETWEEN CONTRALATERAL BONES OF THE HUMAN LOWER LIMBS: A MULTISCALE INVESTIGATION

This study addressed side asymmetry between human lower limb long bones.

A multiscale approach was taken to investigate differences between contralateral femurs, tibias and fibulas, at body-level (total-body CT-scans, anatomical dissection), organ-level (volume and moments of areas; structural stiffness and strain distribution in bending and torsions) and tissue-level (mineral density, elastic modulus, hardness).

Because of the large amount of measurements taken, the study was limited to two donors. However, high statistical power within the same donor was achieved thanks to a large number of highly-repeatable measurements. Muscle cross-sections suggested that both donors were right-legged. The right bones had higher structural stiffness (up to +115%, statistically significant, except for the tibia). The right bones also experienced generally lower strain than the contralateral ones (up to -25%, statistically significant). The right bones had larger volume (up to +16%) and moments of area (up to +116%, statistically significant in most cases) than the left ones. Difference in tissue density between contralateral bones (< 7%) was not statistically significant in most cases. Also the differences found in elastic modulus of the femur cortical tissue (2–5%) were not statistically significant. Similarly, tissue hardness in the right bones was only marginally higher than in the contralateral ones (+1% to +4%, not statistically significant). Therefore, it seems that structural differences between contralateral bones associated with laterality are mainly explained by differences in bone quantity (volume) and organization (area moments). Bone tissue quality (density, hardness) seems to give a marginal contribution to structural side asymmetry.

The micro-structure of bone trabecular fracture: an inter-site study

Trabecular bone fracture represents a major health problem, therefore the improvement of its assessment is mandatory for the reduction of the economic and social burden. The micro-structure of the trabecular bone was found to have an important effect on trabecular mechanical behavior. Nonetheless, the high variability of the trabecular micro-structure suggests a search for the local characteristics leading to the fracture. This work concerns the study of the local trabecular fracture zone and its morphometrical characterization, aiming to prediction of the probable fracture zone. Ninety micro-CT datasets acquired before and after the mechanical compression of 45 trabecular specimens were analyzed. Specimens were extracted from the lower limbs of two donors: 4 femora and 4 tibiae. A previously validated tool for the identification of the 3D fracture zone was applied and the local fracture zone was identified and analyzed in all the specimens. Fifteen morphometrical parameters were extracted for each local fracture zone. Standard statistical non-parametric analysis was performed to compare fractured and un-fractured zones together with a classification analysis for the prediction of the fracture zone. The statistical analysis showed strong statistical difference in the micro-structure of the trabecular fractured zone compared to the un-fractured one. Ten out of 15 measured parameters, like SMI, Tb.Th, BV/TV, off-axis angle, BS/BV and others, showed a statistical difference between full 3D fractured and un-fractured zones. Nonetheless, a satisfactory classification of the fractured zone was possible with none of the identified parameters. On the other hand, a total classification accuracy of 95.5% was presented by the application of a linear classifier based on a combination of the most representative parameters, like BS/BV and the off-axis angle. The study points out the local essence and peculiar characteristics of the fracture zone, it highlights the weakness of some parameters in discriminate between fractured and un-fractured zones and encourage focussing the future studies over the local fracture zone itself with the aim to identify objective differences that could one day lead to the improvement of clinical assessment of fracture risk.

Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula

Patient-specific biomechanical models including patient-specific finite-element (FE) models are considered potentially important tools for providing personalized healthcare to patients with musculoskeletal diseases. A multi-step procedure is often needed to generate a patient-specific FE model. As all involved steps are associated with certain levels of uncertainty, it is important to study how the uncertainties of individual components propagate to final simulation results. In this study, we considered a specific case of this problem where the uncertainties of the involved steps were known and the aim was to determine the uncertainty of the predicted strain distribution. The effects of uncertainties of three important components of patient-specific models, including bone density, musculoskeletal loads and the parameters of the material mapping relationship on the predicted strain distributions, were studied. It was found that the number of uncertain components and the level of their uncertainty determine the uncertainty of simulation results. The 'average' uncertainty values were found to be relatively small even for high levels of uncertainty in the components of the model. The 'maximum' uncertainty values were, however, quite high and occurred in the areas of the scapula that are of the greatest clinical relevance. In addition, the uncertainty of the simulation result was found to be dependent on the type of movement analysed, with abduction movements presenting consistently lower uncertainty values than flexion movements.

Improved fracture risk assessment based on nonlinear micro-finite element simulations from HRpQCT images at the distal radius

More accurate techniques to estimate fracture risk could help reduce the burden of fractures in postmenopausal women. Although micro-finite element (µFE) simulations allow a direct assessment of bone mechanical performance, in this first clinical study we investigated whether the additional information obtained using geometrically and materially nonlinear µFE simulations allows a better discrimination between fracture cases and controls. We used patient data and high-resolution peripheral quantitative computed tomography (HRpQCT) measurements from our previous clinical study on fracture risk, which compared 100 postmenopausal women with a distal forearm fracture to 105 controls. Analyzing these data with the nonlinear µFE simulations, the odds ratio (OR) for the factor-of-risk (yield load divided by the expected fall load) was marginally higher (1.99; 95% confidence interval [CI], 1.41-2.77) than for the factor-of-risk computed from linear µFE (1.89; 95% CI, 1.37-2.69). The yield load and the energy absorbed up to the yield point as computed from nonlinear µFE were highly correlated with the initial stiffness (R(2)  = 0.97 and 0.94, respectively) and could therefore be derived from linear simulations with little loss in precision. However, yield deformation was not related to any other measurement performed and was itself a good predictor of fracture risk (OR, 1.89; 95% CI, 1.39-2.63). Moreover, a combined risk score integrating information on relative bone strength (yield load-based factor-of-risk), bone ductility (yield deformation), and the structural integrity of the bone under critical loads (cortical plastic volume) improved the separation of cases and controls by one-third (OR, 2.66; 95% CI, 1.84-4.02). We therefore conclude that nonlinear µFE simulations provide important additional information on the risk of distal forearm fractures not accessible from linear µFE nor from other techniques assessing bone microstructure, density, or mass.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography–based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

Compressive fatigue life of subchondral bone of the metacarpal condyle in thoroughbred racehorses

In racehorses, fatigue related subchondral bone injury leads to overt fracture or articular surface collapse and subsequent articular cartilage degeneration. We hypothesised that the fatigue behaviour of equine subchondral bone in compression follows a power law function similar to that observed in cortical and trabecular bone. We determined the fatigue life of equine metacarpal subchondral bone in-vitro and investigated the factors influencing initial bone stiffness. Subchondral bone specimens were loaded cyclically in compression [54MPa (n=6), 66MPa (n=6), 78MPa (n=5), and 90MPa (n=6)] until failure. The fatigue life curve was determined by linear regression from log transformed number of cycles to failure and load. A general linear model was used to investigate the influence of the following variables on initial Young's Modulus: age (4-8years), specimen storage time (31-864days), time in training since most recent rest period (6-32weeks), limb, actual density (1.6873-1.8684g/cm(3)), subchondral bone injury grade (0-3), and cause of death (fatigue injury vs. other). Number of cycles to failure was (median, range) 223,603, 78,316-806,792 at 54MPa; 69,908, 146-149,855 at 66MPa; 13204, 614-16,425 at 78MPa (n=3); and 4001, 152-11,568 at 90MPa. The fatigue life curve was σ=112.2-9.6 log10Nf, (R(2)=0.52, P<0.001), where Nf is number of cycles to failure and σ is load. Removal of the three horses with the highest SCBI grade resulted in: σ=134.2-14.1 log10Nf, (R(2)=0.72, P<0.001). Initial Young's Modulus (mean±SD) was 2500±494MPa (n=22). Actual density (ρ) was the only variable retained in the model to describe initial Young's Modulus (E): E=-8196.7+5880.6ρ, (R(2)=0.34, P=0.0044). The fatigue behaviour of equine subchondral bone in compression is similar to that of cortical and trabecular bone. These data can be used to model the development of SCBI to optimize training regimes.

Does cancellous screw insertion torque depend on bone mineral density and/or microarchitecture?

During insertion of a cancellous bone screw, the torque level reaches a plateau, at the engagement of all the screw threads prior to the screw head contact. This plateau torque (T(Plateau)) was found to be a good predictor of the insertion failure torque (stripping) and also exhibited strong positive correlations with areal bone mineral density (aBMD) in ovine bone. However, correlations between T(Plateau) and aBMD, as well as correlations between T(Plateau) and bone microarchitecture, have never been explored in human bone. The aim of this study was to determine whether T(Plateau), a predictor of insertion failure torque, depends on aBMD and/or bone microarchitecture in human femoral heads. Fifty-two excised human femoral heads were obtained. The aBMD and microarchitecture of each specimen were evaluated using dual X-ray Absorptiometry and micro-computed tomography. A cancellous screw was inserted into specimens using an automated micro-mechanical test device, and T(Plateau) was calculated from the insertion profile. T(Plateau) exhibited the strongest correlation with the structure model index (SMI, R=-0.82, p<0.001), followed by bone volume fraction (BV/TV, R=0.80, p<0.01) and aBMD (R=0.76, p<0.01). Stepwise forward regression analysis showed an increase for the prediction of T(Plateau) when aBMD was combined with microarchitectural parameters, i.e., aBMD combined with SMI (R(2) increased from 0.58 to 0.72) and aBMD combined with BV/TV and BS/TV (R(2) increased from 0.58 to 0.74). In conclusion, T(Plateau), a strong predictor for insertion failure torque, is significantly dependent on bone microarchitecture (particularly SMI and BV/TV) and aBMD.

Comparison of patella bone strain between females with and without patellofemoral pain: a finite element analysis study

Elevated bone principal strain (an indicator of potential bone injury) resulting from reduced cartilage thickness has been suggested to contribute to patellofemoral symptoms. However, research linking patella bone strain, articular cartilage thickness, and patellofemoral pain (PFP) remains limited. The primary purpose was to determine whether females with PFP exhibit elevated patella bone strain when compared to pain-free controls. A secondary objective was to determine the influence of patella cartilage thickness on patella bone strain. Ten females with PFP and 10 gender, age, and activity-matched pain-free controls participated. Patella bone strain fields were quantified utilizing subject-specific finite element (FE) models of the patellofemoral joint (PFJ). Input parameters for the FE model included (1) PFJ geometry, (2) elastic moduli of the patella bone, (3) weight-bearing PFJ kinematics, and (4) quadriceps muscle forces. Using quasi-static simulations, peak and average minimum principal strains as well as peak and average maximum principal strains were quantified. Cartilage thickness was quantified by computing the perpendicular distance between opposing voxels defining the cartilage edges on axial plane magnetic resonance images. Compared to the pain-free controls, individuals with PFP exhibited increased peak and average minimum and maximum principal strain magnitudes in the patella. Additionally, patella cartilage thickness was negatively associated with peak minimum principal patella strain and peak maximum principal patella strain. The elevated bone strain magnitudes resulting from reduced cartilage thickness may contribute to patellofemoral symptoms and bone injury in persons with PFP.

Advanced CT based in vivo methods for the assessment of bone density, structure, and strength

Based on spiral 3D tomography a large variety of applications have been developed during the last decade to asses bone mineral density, bone macro and micro structure, and bone strength. Quantitative computed tomography (QCT) using clinical whole body scanners provides separate assessment of trabecular, cortical, and subcortical bone mineral density (BMD) and content (BMC) principally in the spine and hip, although the distal forearm can also be assessed. Further bone macrostructure, for example bone geometry or cortical thickness can be quantified. Special high resolution peripheral CT (hr-pQCT) devices have been introduced to measure bone microstructure for example the trabecular architecture or cortical porosity at the distal forearm or tibia. 3D CT is also the basis for finite element analysis (FEA) to determine bone strength. QCT, hr-pQCT, and FEM are increasingly used in research as well as in clinical trials to complement areal BMD measurements obtained by the standard densitometric technique of dual x-ray absorptiometry (DXA). This review explains technical developments and demonstrates how QCT based techniques advanced our understanding of bone biology.

Validation of density-elasticity relationships for finite element modeling of human pelvic bone by modal analysis

In total hip arthroplasty and particularly in revision surgery, computer assisted pre-operative prediction of the best possible anchorage strategy for implant fixation would be a great help to the surgeon. Computer simulation relies on validated numerical models. In the current study, three density-elasticity relationships (No. 1-3) from the literature for inhomogeneous material parameter assignment from CT data in automated finite element (FE) modeling of long bones were evaluated for their suitability for FE modeling of human pelvic bone. Numerical modal analysis was conducted on 10 FE models of hemipelvic bone specimens and compared to the gold standard provided by experimental modal analysis results from a previous in-vitro study on the same specimens. Overall, calculated resonance frequencies came out lower than measured values. Magnitude of mean relative deviation of numerical resonance frequencies with regard to measured values is lowest for the density-elasticity relationship No. 3 (-15.9%) and considerably higher for both density-elasticity relationships No. 1 (-41.1%) and No. 2 (-45.0%). Mean MAC values over all specimens amount to 77.8% (No. 1), 78.5% (No. 2), and 83.0% (No. 3). MAC results show, that mode shapes are only slightly influenced by material distribution. Calculated resonance frequencies are generally lower than measured values, which indicates, that numerical models lack stiffness. Even when using the best suited (No. 3) out of three investigated density-elasticity relationships, in FE modeling of pelvic bone a considerable underestimation of model stiffness has to be taken into account.