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

Biomechanics of immature human cortical bone: A systematic review

The whole bone geometry, microstructure, and mechanical properties of mature human bone are widely reported; however, immature bone (0-18 years) has not been similarly robustly characterized. There is an interest in analyzing and predicting the mechanical loading conditions associated with long bone diaphyseal fractures attributed to trauma in children. Thus, understanding the mechanical properties of immature bone in a temporal reference frame is an essential first step to understand diaphyseal fractures of pediatric long bones. The purpose of this systematic review was to ask, what is the state of knowledge regarding the 1) evolution of whole bone geometry and microstructure of immature pediatric bone as a function of maturation and 2) cortical bone density and experimental quasi-static mechanical properties at the tissue level in the diaphyseal region of immature pediatric long bones? The systematic search yielded 36 studies of the whole bone geometry, microstructure, and mechanical properties of immature pediatric long bones. The elastic modulus, yield stress, and ultimate stress were shown to generally increase with maturation, whereas the yield strain was approximately invariant; however, the specific year-to-year progression of these properties could not be characterized from the limited studies available. The results of this systematic search indicate there is a dearth of knowledge associated with the biomechanics of cortical bone from immature pediatric long bones; it also provides a basis for computational studies of immature human long bones. Additional biomechanical studies of immature human bone are necessary to develop a robust catalogue, which can be used in broad applications to understand fracture mechanics, bone pathologies, and athletic injury in the pediatric setting.

An Adaptable Computed Tomography-Derived Three-Dimensional-Printed Alignment Fixture Minimizes Errors in Radius Biomechanical Testing

Biomechanical testing of long bones can be susceptible to errors and uncertainty due to malalignment of specimens with respect to the mechanical axis of the test frame. To solve this problem, we designed a novel, customizable alignment and potting fixture for long bone testing. The fixture consists of three-dimensional-printed components modeled from specimen-specific computed tomography (CT) scans to achieve a predetermined specimen alignment. We demonstrated the functionality of this fixture by comparing benchtop torsional test results to specimen-matched finite element models and found a strong correlation (R2 = 0.95, p < 0.001). Additional computational models were used to estimate the impact of malalignment on mechanical behavior in both torsion and axial compression. Results confirmed that torsion testing is relatively robust to alignment artifacts, with absolute percent errors less than 8% in all malalignment scenarios. In contrast, axial testing was highly sensitive to setup errors, experiencing absolute percent errors up to 50% with off-center malalignment and up to 170% with angular malalignment. This suggests that whenever appropriate, torsion tests should be used preferentially as a summary mechanical measure. When more challenging modes of loading are required, pretest clinical-resolution CT scanning can be effectively used to create potting fixtures that allow for precise preplanned specimen alignment. This may be particularly important for more sensitive biomechanical tests (e.g., axial compressive tests) that may be needed for industrial applications, such as orthopedic implant design.

Limit analysis of human proximal femur

A limit analysis numerical approach oriented to predict the peak/collapse load of human proximal femur, under two different loading conditions, is presented. A yield criterion of Tsai-Hu-type, expressed in principal stress space, is used to model the orthotropic bone tissues. A simplified human femur 3D model is envisaged to carry on numerical simulation of in-vitro tests borrowed from the relevant literature and to reproduce their findings. A critical discussion, together with possible future developments, is presented.

Single-level subject-specific finite element model can predict fracture outcomes in three-level spine segments under different loading rates

Osteoporosis-related vertebral compression fracture can occur under normal physiological activities. Bone metastasis is another source of vertebral fracture. Different loading rates, either high-energy traumas such as falls or low-energy traumas under normal physiological activities, can result in different fracture outcomes. The aim of the current study was to develop a quantitative computed tomography-based finite element analysis (QCT/FEA) technique for single vertebral bodies to predict fracture strength of three-level spine segments. Developed QCT/FEA technique was also used to characterize vertebral elastic moduli at two loading rates of 5 mm/min, representing a physiologic loading condition, and 12000 mm/min, representing a high-energy trauma. To this end, a cohort of human spine segments divided into three groups of intact, defect, and augmented were mechanically tested to fracture; then, experimental stiffness and fracture strength values were measured. Outcomes of this study showed no significant difference between the elastic modulus equations at the two testing speeds. Areal bone mineral density measured by dual x-ray absorptiometry (DXA/BMD) explained only 53% variability (R² = 0.53) in fracture strength outcomes. However, QCT/FEA could explain 70% of the variability (R² = 0.70) in experimentally measured fracture strength values. Adding disk degeneration grading, testing speed, and sex to QCT/FEA-estimated fracture strength values further increased the performance of our statistical model by 14% (adjusted R² of 0.84 between the prediction and experimental fracture forces). In summary, our results indicated that a single-vertebra model, which is computationally less expensive and more time efficient, is capable of estimating fracture outcomes with acceptable performance (range: 70-84%).

Material properties of human vertebral trabecular bone under compression can be predicted based on quantitative computed tomography

Background

The prediction of the stability of bones is becoming increasingly important. Especially osteoporotic vertebral body fractures are a growing problem and an increasing burden on the health system. Therefore, the aim of this study was to provide the best possible description of the relationship between the material properties of human vertebral trabecular bone measured under the most physiological conditions possible and the bone mineral density (BMD) determined by clinical quantitative computed tomography (QCT).

Methods

Forty eight cylindric cancellous bone samples with a diameter of 7.2 mm obtained from 13 human fresh-frozen lumbar vertebrae from 5 donors (3 men, 2 women) have been used for this study. After the specimens were temporarily reinserted into the vertebral body, the QCT was performed. For mechanical testing, the samples were embedded in a load-free manner using polymethylmetacrylate (PMMA). The surrounding test chamber was filled with phosphate buffered saline (PBS) and heated to 37 °C during the test. After 10 preconditioning load cycles, destructive testing was performed under axial compression. After determining the fracture site, BMD has been evaluated in this region only. Regression analyses have been performed.

Results

Fracture site had an average length of 2.4 (±1.4) mm and a position of 43.9 (±10.9) percent of the measurement length from the cranial end. No fracture reached the embedding. The average BMD at the fracture site was 80.2 (±28.7 | min. 14.5 | max. 137.8) mgCaHA/ml.

In summary the results of the regression analyses showed for all three parameters a very good quality of fit by a power regression.

Conclusion

The results of this study show that QCT-based bone density measurements have a good predictive power for the material properties of the vertebral cancellous bone measured under near to physiological conditions. The mechanical bone properties of vertebral cancellous bone could be modelled with high accuracy in the investigated bone density range.

A computational framework for crack propagation in spatially heterogeneous materials

This paper presents a mathematical formulation and numerical modelling framework for brittle crack propagation in heterogeneous elastic solids. Such materials are present in both natural and engineered scenarios. The formulation is developed in the framework of configurational mechanics and solved numerically using the finite-element method. We show the methodology previously established for homogeneous materials without the need for any further assumptions. The proposed model is based on the assumption of maximal dissipation of energy and uses the Griffith criterion; we show that this is sufficient to predict crack propagation in brittle heterogeneous materials, with spatially varying Young's modulus and fracture energy. Furthermore, we show that the crack path trajectory orientates itself such that it is always subject to Mode-I. The configurational forces and fracture energy release rate are both expressed exclusively in terms of nodal quantities, avoiding the need for post-processing and enabling a fully implicit formulation for modelling the evolving crack front and creation of new crack surfaces. The proposed formulation is verified and validated by comparing numerical results with both analytical solutions and experimental results. Both the predicted crack path and load-displacement response show very good agreement with experiments where the crack path was independent of material heterogeneity for those cases. Finally, the model is successfully used to consider the real and challenging scenario of fracture of an equine bone, with spatially varying material properties obtained from CT scanning. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Finite Element Analysis of Fracture Fixation

PURPOSE OF REVIEW

Fracture fixation aims to provide stability and promote healing, but remains challenging in unstable and osteoporotic fractures with increased risk of construct failure and nonunion. The first part of this article reviews the clinical motivation behind finite element analysis of fracture fixation, its strengths and weaknesses, how models are developed and validated, and how outputs are typically interpreted. The second part reviews recent modeling studies of the femur and proximal humerus, areas with particular relevance to fragility fractures.

RECENT FINDINGS

There is some consensus in the literature around how certain modeling aspects are pragmatically formulated, including bone and implant geometries, meshing, material properties, interactions, and loads and boundary conditions. Studies most often focus on predicted implant stress, bone strain surrounding screws, or interfragmentary displacements. However, most models are not rigorously validated. With refined modeling methods, improved validation efforts, and large-scale systematic analyses, finite element analysis is poised to advance the understanding of fracture fixation failure, enable optimization of implant designs, and improve surgical guidance.

On challenges in clinical assessment of hip fracture risk using image-based biomechanical modelling: a critical review

INTRODUCTION

Hip fracture is a common health risk among elderly people, due to the prevalence of osteoporosis and accidental fall in the population. Accurate assessment of fracture risk is a crucial step for clinicians to consider patient-by-patient optimal treatments for effective prevention of fractures. Image-based biomechanical modeling has shown promising progress in assessment of fracture risk, and there is still a great possibility for improvement. The purpose of this paper is to identify key issues that need be addressed to improve image-based biomechanical modeling.

MATERIALS AND METHODS

We critically examined issues in consideration and determination of the four biomechanical variables, i.e., risk of fall, fall-induced impact force, bone geometry and bone material quality, which are essential for prediction of hip fracture risk. We closely inspected: limitations introduced by assumptions that are adopted in existing models; deficiencies in methods for construction of biomechanical models, especially for determination of bone material properties from bone images; problems caused by separate use of the variables in clinical study of hip fracture risk; availability of clinical information that are required for validation of biomechanical models.

RESULTS AND CONCLUSIONS

A number of critical issues and gaps were identified. Strategies for effectively addressing the issues were discussed.

Proximal Tibia Bone Stiffness and Strength in HR-pQCT- and QCT-Based Finite Element Models

Injury to the ACL significantly increases the risk of developing post-traumatic osteoarthritis. Following injury, considerable focus is placed on visualizing soft tissue changes using MRI, but there is less emphasis on the alterations to the underlying bone. It has recently been shown using high-resolution peripheral quantitative computed tomography (HR-pQCT) that significant reductions in bone quality occur in the knee post ACL-injury. Despite the ability of HR-pQCT to show these changes, the availability of scanners and computational time requirements required to assess bone stiffness and strength with HR-pQCT limit its widespread clinical use. As such, the objective of this study was to determine if clinical quantitative CT (QCT) finite element models (QCT-FEMs) can accurately replicate HR-pQCT FEM proximal tibial stiffness and strength. From FEMs of 30 participants who underwent both QCT and HR-pQCT bilateral imaging, QCT-FEMs were strongly correlated with HR-pQCT FEM stiffness (R² = 0.79). When QCT-FEM bone strength was estimated using the reaction force at 1% apparent strain, strong correlations were observed (R² = 0.81), with no bias between HR-pQCT FEMs and non-linear QCT-FEMs. These results indicate that QCT-FEMs can accurately replicate HR-pQCT FEM stiffness and strength in the proximal tibia. Although these models are not able to replicate the trabecular structure or tissue-level strains, they require significantly reduced computational time and use widely available clinical-CT images as input, which make them an attractive choice to monitor bone density, stiffness and strength alterations, such as those that occur post ACL-injury.

Atlas of Human Skeleton Hardness Obtained Using the Micro-indentation Technique

Objectives

Measure and systematically evaluate the distribution of microhardness in the human skeleton.

Methods

Three fresh corpses were obtained, aged 62 (male), 45 (female), and 58 years (male). Soft tissues were removed, and all axial and unilateral appendicular bones were freshly harvested. All three skeletons were examined by X‐ray and computed tomography (CT) to exclude skeletal pathology. Only bones from donors with no known skeletal pathology were included in the study. Axial and unilateral appendicular skeleton bones from each of the three donors were obtained, except for ear ossicles, hyoid bone, tailbone, and 14 phalanges of the foot, for which samples were difficult to obtain. Precision bone specimens with a thickness of 3 mm, which were cut with a Buehler IsoMet 11‐1280‐250 low‐speed diamond saw (Buehler, USA), were obtained from all important anatomic sites in a direction perpendicular to the mechanical axis of each bone. Micro‐indentation (the Vickers hardness test) was performed on the surface of each specimen using a microhardness tester with a diamond indenter. Hardness value (HV) was computed for each indentation. Each bone specimen was divided into several regions of interest. Indentations were carefully made and computed. Then we analyzed the data to identify hardness distribution rules at different anatomic sites.

Results

In total, 5360 indentations were made in 1072 regions of interest in each donor. Hardness of the axial and appendicular bones were all inhomogeneous depending on the anatomic sites, but the distribution of microhardness followed certain rules. The mean hardness value ranged from 24.46 HV (HV = hardness value, kgf/mm²) for the sacrum to 53.20 HV for the shaft of the tibia. The diaphysis was harder than the metaphysis, and the proximal and distal epiphysis had lower values (8.85%– 40.39%) than the diaphysis. Among the long bone diaphyses, the tibia cortical bone (51.20 HV) was the hardest, harder than the humerus (47.25 HV), the ulna (43.26 HV), the radius (42.54 HV), and the femur (47.53 HV). However, in some anatomic sites such as the lumbar vertebra (cortical bone 32.86 HV, cancellous bone 31.25 HV), the cortical shells were sometimes not harder than the internal cancellous bones. The lumbar vertebra (32.86 HV) was harder than the cervical vertebra (28.51 HV) and the thoracic vertebra (29.01 HV).

Conclusions

The distribution of microhardness in the human skeleton follows certain rules. These distribution rules could be used to predict the mechanical properties of bone and progress in this field could provide data for the basis of a new three‐dimensional printing technique, which may lead to new perspectives for custom‐made implants.

In Silico Clinical Trials in the Orthopedic Device Industry: From Fantasy to Reality?

The orthopedic device industry relies heavily on clinical evaluation to confirm the safety, performance, and clinical benefits of its implants. Limited sample size often prevents these studies from capturing the full spectrum of patient variability and real-life implant use. The device industry is accustomed to simulating benchtop tests with numerical methods and recent developments now enable virtual "in silico clinical trials" (ISCT). In this article, we describe how the advancement of computer modeling has naturally led to ISCT; outline the potential benefits of ISCT to patients, healthcare systems, manufacturers, and regulators; and identify how hurdles associated with ISCT may be overcome. In particular, we highlight a process for defining the relevant patient risks to address with ISCT, the utility of a versatile software pipeline, the necessity to ensure model credibility, and the goal of limiting regulatory uncertainty. By complementing-not replacing-traditional clinical trials with computational evidence, ISCT provides a viable technical and regulatory strategy for characterizing the full spectrum of patients, clinical conditions, and configurations that are embodied in contemporary orthopedic implant systems.

Evaluation of fixation after plating of distal radius fractures - a validation study

We used five fresh-frozen cadavers with 10 upper limbs to evaluate by finite element analysis (FEA) the plate fixation of distal radius fractures. The distal radius of the cadavers was fractured using a comminution fracture model. Plate fixation was performed using Synthes VATCP. Compression tests were performed on these specimens and force displacement curves were obtained. FEA was performed using Mechanical Finder. The Keyak, Keller vertebra, Carter, and Matsuyama conversion equations without contact analysis, and the Matsuyama equations with contact analysis, were used for the boundary conditions. We found strong positive correlations with the Matsuyama conversion equations either with or without contact analysis. The validated FEA model will be used for preoperative simulation of actual fractures.

The presence of Wormian bones increases the fracture resistance of equine cranial bone

Wormian (intrasutural) bones are small, irregular bones, that are found in the cranial sutures of the skull. The occurrence of Wormian bones in human skulls has been well documented but few studies have detected the presence of such bones in domestic animals. Although some research has linked the presence of Wormian bones to bone pathology, its anatomical significance in healthy individuals is not known. To the best of our knowledge, no previous study has examined the biomechanical features of Wormian bone. This study uses microCT imaging of the parietal bone region to determine the frequency of occurrence of Wormian bones in horse skulls and, through 3-point bending tests, to calculate the mechanical differences that result from the presence of such bones. In addition, bone properties such as bone mineral density (BMD) and stiffness were measured and analysed to determine the influence of Wormian bone. Our findings on 54 specimens taken from 10 horses (ages ranging from 4 to 29 years) showed that Wormian bone was present in 70% of subjects and that its occurrence was unrelated to age or sex. 3-point bend tests revealed that the stiffness normalised by cross section area (P = 0.038) was lower in samples where Wormian bone was present. An idealised Finite Element simulation confirmed that the presence of Wormian bone reduced the maximum stress and strain, as well as their distribution throughout the sample. We consequently conclude that the presence of Wormian bones, which are confined to the calvaria, increase the compliance of the bone and reduce the likelihood of skull fracture. As all skull samples were collected from a local abattoir, ethical approval was not required for this work.

Virtual mechanical tests out-perform morphometric measures for assessment of mechanical stability of fracture healing in vivo

Finite element analysis with models derived from computed tomography (CT) scans is potentially powerful as a translational research tool because it can achieve what animal studies and cadaver biomechanics cannot-low-risk, noninvasive, objective assessment of outcomes in living humans who have actually experienced the injury, or treatment being studied. The purpose of this study was to assess the validity of CT-based virtual mechanical testing with respect to physical biomechanical tests in a large animal model. Three different tibial osteotomy models were performed on 44 sheep. Data from 33 operated limbs and 20 intact limbs was retrospectively analyzed. Radiographic union scoring was performed on the operated limbs and physical torsional tests were performed on all limbs. Morphometric measures and finite element models were developed from CT scans and virtual torsional tests were performed to assess healing with four material assignment techniques. In correlation analysis, morphometric measures and radiographic scores were unreliable predictors of biomechanical rigidity, while the virtual torsion test results were strongly and significantly correlated with measured biomechanical test data, with high absolute agreement. Overall, the results validated the use of virtual mechanical testing as a reliable in vivo assessment of structural bone healing. This method is readily translatable to clinical evaluation for noninvasive assessment of the healing progress of fractures with minimal risk. Clinical significance: virtual mechanical testing can be used to reliably and noninvasively assess the rigidity of a healing fracture using clinical-resolution CT scans and that this measure is superior to morphometric and radiographic measures.

Damage tolerance and toughness of elderly human femora

Observations of elastic instability of trabecular bone cores supported the analysis of cortical thickness for predicting bone fragility of the hip in people over 60 years of age. Here, we falsified the hypothesis that elastic instability causes minimal energy fracture by analyzing, with a micrometric resolution, the deformation and fracture behavior of entire femora. Femur specimens were obtained from elderly women aged between 66 - 80 years. Microstructural images of the proximal femur were obtained under 3 - 5 progressively increased loading steps and after fracture. Bone displacements, strain, load bearing and energy absorption capacity were analyzed. Elastic instability of the cortex appeared at early loading stages in regions of peak compression. No elastic instability of trabecular bone was observed. The subchondral bone displayed local crushing in compression at early loading steps and progressed to 8 - 16% compression before fracture. The energy absorption capacity was proportional to the displacement. Stiffness decreased to near-zero values before fracture. Three-fourth of the fracture energy (10.2 - 20.2 J) was dissipated in the final 25% force increment. Fracture occurred in regions of peak tension and shear, adjacent to the location of peak compression, appearing immediately before fracture. Minimal permanent deformation was visible along the fracture surface. Elastic instability modulates the interaction between cortical and trabecular bone promoting an elastically stable fracture behavior of the femur organ, load bearing capacity, toughness, and damage tolerance. These findings will advance current methods for predicting hip fragility.

Long-term mechanical properties of a novel low-modulus bone cement for the treatment of osteoporotic vertebral compression fractures

In spite of the success of vertebroplasty (VP) and balloon kyphoplasty (BKP), which are widely used for stabilizing painful vertebral compression fractures, concerns have been raised about use of poly(methyl methacrylate) (PMMA) bone cements for these procedures since the high compressive modulus of elasticity (E) of the cement is thought to be one of the causes of the higher number of adjacent-level vertebral fractures. Therefore, bone cements with E comparable to that of cancellous bone have been proposed. While the quasi-static compressive properties of these so-called "low-modulus" cements have been widely studied, their fatigue performance remains underassessed. The purpose of the present study was to critically compare a commercial bone cement (control cement) and its low-modulus counterpart on the basis of quasi-static compressive strength (CS), E, fatigue limit under compression-compression loading, and release of methyl methacrylate (MMA). At 24 h, mean CS and E of the low-modulus material were 72% and 77% lower than those of the control cement, whereas, at 4 weeks, mean CS and E were 60% and 54% lower, respectively. The fatigue limit of the control cement was estimated to be 43-45 MPa compared to 3-5 MPa for the low-modulus cement. The low-modulus cement showed an initial burst release of MMA after 24 h followed by a plateau, similar to many other commercially available cements, whereas the control cement showed a much lower, stable release from day 1 and up to 1 week. The low-modulus cement may be a promising alternative to currently available PMMA bone cements, with the potential for reducing the incidence of adjacent fractures following VP/BKP.

Evaluation of patient tissue selection methods for deriving equivalent density calibration for femoral bone quantitative CT analyses

Osteoporosis affects an increasing number of people every year and patient specific finite element analysis of the femur has been proposed to identify patients that could benefit from preventative treatment. The aim of this study was to demonstrate, verify, and validate an objective process for selecting tissues for use as the basis of phantomless calibration to enable patient specific finite element analysis derived hip fracture risk prediction. Retrospective reanalysis of patient computed tomography (CT) scans has the potential to yield insights into more accurate prediction of osteoporotic fracture. Bone mineral density (BMD) specific calibration scans are not typically captured during routine clinical practice. Tissue-based BMD calibration can therefore empower the retrospective study of patient CT scans captured during routine clinical practice. Together the method for selecting tissues as the basis for phantomless calibration coupled with the post-processing steps for deriving a calibration equation using the selected tissues provide an estimation of quantitative equivalent density results derived using calibration phantoms. Patient tissues from a retrospective cohort of 211 patients were evaluated. The best phantomless calibration resulted in a femoral strength (FS) [N] bias of 0.069 ± 0.07% over FS derived from inline calibration and a BMD [kg/cm³] bias of 0.038 ± 0.037% over BMD derived from inline calibration. The phantomless calibration slope for the best method presented was within the range of patient specific calibration curves available for comparison and demonstrated a small bias of 0.028 ± 0.054 HU/(mg/cm³), assuming the Mindways Model 3 BMD inline calibration phantom as the gold standard. The presented method of estimating a calibration equation from tissues showed promise for CT-based femoral fracture analyses of retrospective cohorts without readily available calibration data.

QCT-FE modeling of the proximal tibia: Effect of mapping strategy on convergence time and model accuracy

Quantitative computed tomography (QCT) based finite element (FE) modeling, referred to as QCT-FE, has seen rapid growth and application for modeling bone mechanics. With this approach, varying bone material properties are set via experimentally-derived density-modulus equations. One challenge though associated with QCT-FE is to identify the appropriate mapping strategy for assigning elastic moduli to elements. The goal of this study was to evaluate different QCT-FE mapping strategies to identify the optimum approach with fastest convergence rate and highest accuracy. Four proximal tibial medial compartments were imaged using QCT and experimentally tested to characterize proximal tibial subchondral bone stiffness at four surface points, resulting in a total of 16 indentation measures. Three material mapping methods were analyzed: (1) constant-E where an average elastic modulus was assigned to each element; (2) node-based where the material properties were first mapped on nodes then interpolated to Gaussian integration points; and (3) element-based in which the material properties were directly assigned to Gaussian integration points. Different element sizes were assessed with edge-lengths ranging from 0.9 to 3 mm. Results indicated that all converged models showed similar coefficient-of-determination (R²) and normalized root-mean-square errors (RMSE%). Though, the constant-E and node-based methods converged with the element edge-length of 1.5 mm (prediction error of 4.8% and 2.5%, respectively) whereas the element-based method converged with a larger element having an edge-length 2.5 mm (error = 4.9%). In conclusion, the element-based method, with a larger element size, resulted in similar predictive accuracy, faster convergence and shorter run-times relative to the constant-E and node-based approaches. As such, we recommend the element-based method for future subject-specific QCT-FE modeling.

Fractal lacunarity of trabecular bone in vertebral MRI to predict osteoporotic fracture risk in over-fifties women. The LOTO study

BACKGROUND

Osteoporotic fractures are a major cause of morbidity in the elderly. Menopausal women represent the population with the highest risk of early osteoporosis onset, often accompanied by vertebral fractures (VF). Bone mineral density (BMD) is commonly assessed by dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnosis; however, BMD alone does not represent a significant predictor of fracture risk. Bone microarchitecture, instead, arises as a determinant of bone fragility independent of BMD. High-resolution magnetic resonance imaging (MRI) is an effective noninvasive/nonionizing tool for in vivo characterisation of trabecular bone microarchitecture (TBA). We have previously set up an MRI method able to characterise TBA changes in aging and osteoporosis by one parameter, trabecular bone lacunarity parameter β (TBLβ). Fractal lacunarity was used for TBA texture analysis as it describes discontinuity of bone network and size of bone marrow spaces, changes of which increase the risk of bone fracture. This study aims to assess the potential of TBLβ method as a tool for osteoporotic fracture risk.

METHODS

An observational, cross-sectional, and prospective study on over-50s women at risk for VF was designed. TBLβ, our index of osteoporotic fracture risk, is the main outcome measure. It was calculated on lumbar vertebra axial images, acquired by 1.5 T MRI spin-echo technique, from 279 osteopenic/osteoporotic women with/without prior VF. Diagnostic power of TBLβ method, by Receiver Operating Characteristics (ROC) curve and other diagnostic accuracy measurements were compared with lumbar spine DXA-BMD.

RESULTS

Baseline results show that TBLβ is able to discriminate patients with/without prevalent VF (p = 0.003). AUC (area under the curve from ROC) is 0.63 for TBLβ, statistically higher (p = 0.012) than BMD one (0.53). Contribution of TBLβ to prevalent VF is statistically higher (p < 0.001) than BMD (sensitivity: 66% vs. 52% respectively; OR: 3.20, p < 0.0001 for TBLβ vs. 1.31, p = 0.297 for BMD). Preliminary 1-year prospective results suggest that TBA contribution to incident VF is even higher (sensitivity: 73% for TBLβ vs. 55% for BMD; RR: 3.00, p = 0.002 for TBLβ vs. 1.31, p = 0.380 for BMD).

CONCLUSION

Results from this study further highlight the usefulness of TBLβ as a biomarker of TBA degeneration and an index of osteoporotic fracture risk.

Implementation and validation of finite element model of skull deformation and failure response during uniaxial compression

Numerical studies aimed at evaluating head injury due to externally applied loading can be made more biofidelic by incorporating nonlinear mechanism-based and microstructurally-inspired material models representing the mechanical response and fracture (failure or injury) of the human skull bone. Thus, incorporation of these mechanism-based models would increase the ability of simulations of mechanical impact to identify more realistic fracture-based injuries at clinical relevancy, such as linear (tensile), depressed (compressive), or penetration (shear). One of the challenges for accurate modeling of the mechanical response of the human skull is the intricate location dependent heterogeneous mesostructural arrangement of bone within the structure of the skull. Recently, a power-law relationship between the localized bone volume fraction (BVF) and modulus (E) within the human skull was developed based on quasi-static compression experiments. However, the parameters of the power-law were optimized and obtained using approximations which were not experimentally or computationally validated for the actual heterogeneous 3D bone structure. Here, a hybrid experimental-modeling-computational (HEMC) based concept was used to develop a microstructurally compatible detailed meso-scale finite element (FE) model of the heterogeneous microstructure of one of the human skull bone coupons previously used to derive the E-BVF relationship. Finite elements were mapped to the corresponding regions from microcomputed tomography images, and the BVF of each element was identified. Then, element-specific moduli were calculated from the E-BVF power relationship. The goal of the simulations was twofold: to assess the assumptions used to derive the E-BVF relationship from the linear regime of the experimental response, and also to model the subsequent deviation from linearity. Using the E-BVF relationship, the 3D simulation was able to match the experimentally measured global modulus to within 3%. After validating the E-BVF power law using the initial linear response, to develop and validate failure models, the following steps were completed. The subsequent deviation of the mechanical response from its initial linearity was assumed to be due to failure of elements either by compression or tension. Elemental microstructure-specific compressive and tensile failure thresholds (σ_f) for each element were modeled by BVF (f_BV) power functional relationships of the form: [Formula: see text] MPa. The initial leading coefficients (σ_f,0) for compression and tension were derived from prior reported experimental work. Through incorporating element-level failure and then iterating the leading coefficients, the simulation was able to represent the nonlinearity of the stress-strain curve and its catastrophic failure in the experiment. Evolution of the measured non-uniform full-strain-fields on two surfaces of the coupon, showing the localized regions of failure, was compared between experiment and simulation, and was approximately similar, thus validating the developed HEMC procedure and failure models. The simulation methodology developed here allowed for identification of failure location within the skull coupon specimen, thereby providing a tool to predict the localized failure (fracture or injury) initiation within the human skull in FE simulations at larger length scales.

Mechanical and morphological characterization of PMMA/bone composites in human femoral heads

PMMA bone cement has gained an important place in a variety of orthopaedic applications in the femur. However, appropriate data on the mechanical properties of bone-cement composites from the human femur are lacking. Therefore, the goal of this study was to determine the morphological and quasi-static compressive properties of proximal femoral bone-cement composites. Thirty trabecular bone specimens were extracted from fifteen pairs of human femoral heads using specimen-specific cutting guides to ensure an accurate alignment with the main trabecular direction (MTD). One specimen from each pair was augmented with PMMA bone cement, while the other one was left untreated. Specimens were scanned with μCT to determine morphological parameters and tested in quasi-static compression until failure. We found that the long axis of the specimens was highly aligned with the MTD (mean error < 5°). A higher compressive modulus and ultimate strength were observed for the bone-cement composite specimens (E = 5.7 ± 0.4 GPa; σ_u = 77.9 ± 5.1 MPa) compared to the bone only specimens (E = 2.9 ± 0.7 GPa; σ_u = 19.0 ± 5.8 MPa). Furthermore, the composites had a higher modulus, but lower strength than cement itself (E = 5.0 ± 0.3 GPa; σ_u = 85.9 ± 2.7 MPa) and the composite modulus was significantly correlated with the bone volume fraction (BV/TV). These results are in contrast to previous findings on human vertebral bone, where the composite was more compliant than cement and no correlation was found between BV/TV and the composite modulus. Thus, properties of bone-cement composites cannot simply be applied across different anatomical sites; the site-specific differences in bone density and trabecular alignment should be taken into account. Collectively, the present results suggest that at low BV/TV, cement dominates the composite properties, while at high BV/TV, the contribution of bone becomes apparent, revealing a positive relationship between BV/TV and the on-axis modulus.

A Review on Recent Advances in the Constitutive Modeling of Bone Tissue

PURPOSE OF REVIEW

Image-based finite element analysis (FEA) to predict and understand the biomechanical response has become an essential methodology in musculoskeletal research. An important part of such simulation models is the constitutive material model of which recent advances are summarized in this review.

RECENT FINDINGS

The review shows that existing models from other fields were introduced, such as cohesion zone (cortical bone) or phase-field models (trabecular bone). Some progress has been made in describing cortical bone involving physical mechanisms such as microcracks. Problems with validations at different length scales remain a problem. The improvement of recent constitutive models is partially obscured by uncertainties that affect overall predictions, such as image quality and calibration or boundary conditions. Nevertheless, in vivo CT-based FEA simulations based on a sophisticated constitutive behavior are a very valuable tool for clinical-related osteoporosis research.

Influence of material properties and boundary conditions on patient-specific models

Patient-specific finite element models (PSFEM) are becoming more and more used. Different methods for assigning their material properties were studied on PSFEMs of 9 tibias along with the minimal required length of the CT acquisition window. Material properties are generally attributed to the PSFEM using relationships linking the grayscale of CT scans to the elasticity moduli. Using cortical-specific and trabecular-specific relationships or a generic one, did not result in significant differences. However, the use of homogeneous elastic moduli in the cortical and trabecular regions led to considerable differences. The result highlight that the PSFEM must comprise at least 40% of the tibia to ensure consistent results in the proximal 20%.

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.

Understanding the Patterns of Deformity of Wrist Fractures Using Computer Analysis

Computer modeling of the wrist has followed other fields in the search for descriptive methods to understand the biomechanics of injury. Using patient-specific 3D computer models, we may better understand the biomechanics of wrist fractures in order to plan better care. We may better estimate fracture morphology and stability and evaluate surgical indications, design more adequate or effective surgical approaches and develop novel methods of therapy. The purpose of this review is to question the actual advances made in the understanding of wrist fractures using computer models.

Estimation of mass apparent density and Young's modulus of femoral neck-head region

The purpose of this study is to estimate mass apparent density and Young's modulus to investigate biomechanical properties of the proximal femur bone. In this study eleven specimens of sheep femur bone having age between 1-1.25 years and human femur bone having age between 14 and 81years are used. In the present study, the first technique attempts to estimate the density from the image-based Hounsfield unit which is obtained directly from a computed tomography image. The modulus of elasticity is estimated from density-elasticity relation which is available in the literature. Another technique is used to develop a correlation between computed apparent density and greyscale based coefficient obtained by material mapping method using commercial Simpleware ScanIP software. Estimated mean deviation in apparent mass density and Young's modulus is 4.34% and 4.69% in sheep bone and 4.35% and 4.94% in human bone respectively. It is found that apparent density and Young's modulus obtained shows close agreement with values reported in the literature. Moreover, the study attempts to build up a new material model between human and sheep for orthopaedics clinical trials and research in Indian context. In addition, it is also observed that bone mass density of sheep is 1.60 times human. This method can also be useful to study and analyse biomechanical properties of the human femur bone.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Femoral bone mineral density distribution is dominantly regulated by strain energy density in remodeling

BACKGROUND

It is well known that there is a relationship between bone strength and the forces that are daily applied to the bone. However, bone is a highly heterogeneous material and it is still not clear how mechanical variables regulate the distribution of bone mass in a femur.

METHODS

We studied the role of four mechanical variables, i.e. principal tensile/compressive stress, von Mises stress, and strain energy density (SED), in the regulation of bone mineral density (BMD) distribution in the human femur. The actual BMD in a femur was extracted from quantitative computed tomography (QCT) and used as a reference for comparison. A finite element model of the femur was constructed from the same set of QCT scans and then used in iterative simulations of femur remodeling under stance and walking loading. The finite element model was initially assigned a homogeneous BMD distribution. During the remodeling, femur BMD was locally modified according to one of the four mechanical variables. The simulations were stopped when BMD change in two consecutive iterations was adequately small. The four simulated BMD patterns were then compared with the actual BMD.

RESULTS

It was found that the BMD pattern regulated by SED had the best similarity with the actual BMD. The medullary canal was successfully reproduced by simulated remodeling, indicating that in addition to its biological functions, the medullary canal has important biomechanical functions.

CONCLUSIONS

Both the actual and simulated BMD distributions showed that the proximal femur has much lower BMD than the femur shaft, which may explain why hip fractures most often occur at the proximal femur.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

Despite evidence of the biomechanical role of cortical bone, current state of the art finite element models of the proximal femur built from clinical CT data lack a subject-specific representation of the bone cortex. Our main research hypothesis is that the subject-specific modelling of cortical bone layer from CT images, through a deconvolution procedure known as Cortical Bone Mapping (CBM, validated for cortical thickness and density estimates) can improve the accuracy of CT-based FE models of the proximal femur, currently limited by partial volume artefacts. Our secondary hypothesis is that a careful choice of cortical-specific density-elasticity relationship may improve model accuracy. We therefore: (i) implemented a procedure to include subject-specific CBM estimates of both cortical thickness and density in CT-based FE models. (ii) defined alternative models that included CBM estimates and featured a cortical-specific or an independently optimised density-elasticity relationship. (iii) tested our hypotheses in terms of elastic strain estimates and failure load and location prediction, by comparing with a published cohort of 14 femurs, where strain and strength in stance and fall loading configuration were experimentally measured, and estimated through reference FE models that did not explicitly model the cortical compartment. Our findings support the main hypothesis: an explicit modelling of the proximal femur cortical bone layer including CBM estimates of cortical bone thickness and density increased the FE strains prediction, mostly by reducing peak errors (average error reduced by 30%, maximum error and 95th percentile of error distribution halved) and especially when focusing on the femoral neck locations (all error metrics at least halved). We instead rejected the secondary hypothesis: changes in cortical density-elasticity relationship could not improve validation performances. From these improved baseline strain estimates, further work is needed to achieve accurate strength predictions, as models incorporating cortical thickness and density produced worse estimates of failure load and equivalent estimates of failure location when compared to reference models. In summary, we recommend including local estimates of cortical thickness and density in FE models to estimate bone strains in physiological conditions, and especially when designing exercise studies to promote bone strength.

Biomechanical comparison of anterior cruciate ligament repair with internal brace augmentation versus anterior cruciate ligament repair without augmentation

BACKGROUND

Newer repair techniques of anterior cruciate ligament tears, including augmentation with internal brace, have shown promising clinical results. Few biomechanical studies exist comparing anterior cruciate ligament repair only versus repair with internal brace. The purpose of this study was to compare the load to failure and stiffness of anterior cruciate ligament repair with internal brace augmentation versus repair-only.

METHODS

Proximal femoral avulsion type anterior cruciate ligament injuries were created in 20 cadaver knees. Anterior cruciate ligament repair-only or repair with internal brace was performed using arthroscopic tools. Load to failure and failure modes were collected, with calculations of stiffness and energy to failure performed.

FINDINGS

The average load to failure for the internal brace group was higher than the repair-only group: 693 N (SD 248) versus 279 N (SD 91), P = .002. The stiffness and energy to failure values were higher for the internal brace group than the repair-only group: 83 N/mm versus 58 N/mm, P = .02 and 16.88 J (SD 12.44) versus 6.91 J (SD 2.49), P = .04, respectively. Failure modes differed between groups (P = .00097) with 80% failure in the repair-only due to suture pull through the anterior cruciate ligament and 90% failure in the internal brace group due to suture button pull through the femur.

INTERPRETATION

There was higher load to failure, stiffness, and energy to failure for the internal brace group compared to the repair-only group, and a high positive correlation between bone density and load to failure for the internal brace group.

CLINICAL SIGNIFICANCE

Anterior cruciate ligament repair with internal brace augmentation demonstrates significantly higher load to failure. It may be a useful adjunct to protect the anterior cruciate ligament repair from failure during the early stages of healing.

How screw connections influence the primary stability of acetabular cups under consideration of different bone models

Introduction

Good osteointegration of implants requires sufficient primary stability. Aim of this study was to examine the influence of screw fixation on the primary stability of press-fit cups.

Methods

Two press-fit acetabular cups were tested with regard to the influence and number of screws and their primary stability.

Results

For the relatively thin-walled Allofit®-S cup, an influence of the number of screws on the different forms of movement could be demonstrated.

Conclusions

We see a clear influence of the cup wall thickness on the elastic deformability and accordingly on the primary stability of the examined cups.

Empirical relationships between bone density and ultimate strength: A literature review

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Multiscale design of artificial bones with biomimetic elastic microstructures

Cancellous bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. The hierarchical architecture makes cancellous bone a prime example of a lightweight natural material that combines strength with toughness. Better understanding the mechanics of cancellous bone is of interest for the diagnosis of bone diseases, the evaluation of the risk of fracture, and for the design of artificial bones and bone scaffolds for tissue engineering. A multiscale optimization method to maximize the stiffness of artificial bones using biomimetic cellular microstructures described by a finite set of geometrical micro-parameters is presented here. The most outstanding characteristics of its implementation are the use of: an interior point optimization algorithm, a precalculated response surface methodology for the evaluation of the elastic tensor of the microstructure as an analytical function of the micro-parameters, and the adjoint method for the computation of the sensitivity of the macroscopic mechanical response to the variation of the micro-parameters. The performance and effectiveness of the tool are evaluated by solving a problem that consists in finding the optimal distribution of the microstructures for a proximal end of a femur subjected to physiological loads. Two strategies for the specification of the solid volume fraction constraints are assessed. The results are compared with data of a computed tomography study of an actual human bone. The model successfully predicts the main features of the spatial arrangement of the trabecular and cortical microstructures of the natural bone.

Influence of conservative endodontic access and the osteoporotic bone on the restoration material adhesive behavior through finite element analysis

Assess, using finite element analysis, the adhesive behavior of Class I restorations under physiological occlusal loads on an endodontically treated first upper premolar with conventional and conservative crown opening surrounded by alveolar bone in normal and osteoporotic conditions. For this, four virtual models were used: M1-conservative access/normal bone; M2-conventional access/normal bone; M3-conservative access/osteoporotic bone; M4-conventional access/osteoporotic bone. On enamel, under axial load, the highest peaks occurred on conventional models and, under oblique load, the highest peaks occurred on conservative opening models. The bone condition showed no influence on the adhesive behavior. On dentin, under axial load, the models showed similar behaviors, regardless of the bone condition; under oblique load, the highest incidence of forces occurred on the distal region of the palatal root canal entrance and the highest peak was observed in the conventional opening model with normal bone. Also, under oblique load, conventional opening models showed larger values on dentin for the normal bone and similar for the osteoporotic. The conclusions shows higher displacement tensile strength peaks were observed in the conventional models, which can lead to a greater risk of adhesive failure on class I restorations with this opening. Therefore, a conservative opening would be recommended to avoid opening clinical complications. The bone condition showed no significant influence on adhesive behavior, except for dentin under oblique load, where conventional models showed larger values relative to normal bone and similar to the osteoporotic bone.

Characterization of Newly Developed Zinc Composite with the Content of 8 wt.% of Hydroxyapatite Particles Processed by Extrusion

Zinc and its alloys belong to a group of biodegradable materials, which can be potentially used for the preparation of temporary orthopedic implants. The research of biodegradable zinc materials revealed a lot of limitations; however, the new processing approaches of those materials can enhance their properties, which are insufficient for now. In this study, the zinc composite with 8 wt.% of hydroxyapatite (Zn/HA8) prepared for the first time by extrusion process was characterized from the point of view of the structural, mechanical and corrosion properties. The extrusion process led to good integrity of the interfaces between the zinc and hydroxyapatite particles. Mechanical behavior confirmed the role of hydroxyapatite as a defect in the material structure, which led to a decrease of the Zn/HA8 mechanical properties by approximately 30% (compressive yield strength (CYS) = 154 MPa Zn, 113 MPa Zn/HA8). Despite that, the Zn/HA8 composite showed sufficient mechanical properties for cancellous bone replacement and reached the lower limit for cortical bone. Additionally, the presence of hydroxyapatite caused the preferential precipitation of hydroxyapatite (HA) from the solution and can lead to a significant enhancement of the tissue/implant interface interactions.

System reliability analysis of the scoliosis disorder

BACKGROUND

Scoliosis is a spine abnormal deviation, which is an idiopathic disorder among children and adolescents. As a matter of the fact, distribution of loads on the patient's spine and load-carrying capacity of the vertebral column are both random variables. Therefore, the probabilistic approach may consider as a sophisticated method to deal with this problem.

METHOD

Reliability analysis is a probabilistic-based approach to consider the uncertainties of load and resistance of the vertebral column. The main contribution of this paper is to compare the reliability level of a normal and scoliosis spinal. To do so, the numerical analyses associated with the inherent random parameters of bones and applied load are performed. Then, the reliability indices for all vertebrae and discs are determined. Accordingly, as the main innovation of this paper, the system reliability indices of the spinal column for both normal and damaged backbone systems are represented.

RESULTS

Based on the required reliability index for normal spinal curvature the target system reliability level for scoliosis disorder is proposed.

CONCLUSION

Since the proposed target reliability index is based on the strength limit state of the vertebral column, it can be considered as a reliability level for any proposed treatment approaches.

Influence of the Acetabular Cup Material on the Shell Deformation and Strain Distribution in the Adjacent Bone-A Finite Element Analysis

In total hip arthroplasty, excessive acetabular cup deformations and altered strain distribution in the adjacent bone are potential risk factors for implant loosening. Materials with reduced stiffness might alter the strain distribution less, whereas shell and liner deformations might increase. The purpose of our current computational study was to evaluate whether carbon fiber-reinforced poly-ether-ether-ketones with a Young´s modulus of 15 GPa (CFR-PEEK-15) and 23 GPa (CFR-PEEK-23) might be an alternative shell material compared to titanium in terms of shell and liner deformation, as well as strain distribution in the adjacent bone. Using a finite element analysis, the press-fit implantation of modular acetabular cups with shells made of titanium, CFR-PEEK-15 and CFR-PEEK-23 in a human hemi-pelvis model was simulated. Liners made of ceramic and polyethylene were simulated. Radial shell and liner deformations as well as strain distributions were analyzed. The shells made of CFR-PEEK-15 were deformed most (266.7 µm), followed by CFR-PEEK-23 (136.5 µm) and titanium (54.0 µm). Subsequently, the ceramic liners were radially deformed by up to 4.4 µm and the polyethylene liners up to 184.7 µm. The shell materials slightly influenced the strain distribution in the adjacent bone with CFR-PEEK, resulting in less strain in critical regions (<400 µm/m or >3000 µm/m) and more strain in bone building or sustaining regions (400 to 3000 µm/m), while the liner material only had a minor impact. The superior biomechanical properties of the acetabular shells made of CFR-PEEK could not be determined in our present study.

Morphological and Apparent-Level Stiffness Variations Between Normal and Osteoarthritic Bone in the Humeral Head

Osteoarthritis (OA) is characterized by morphological changes that alter bone structure and mechanical properties. This study compared bone morphometric parameters and apparent modulus between humeral heads excised from end-stage OA patients undergoing total shoulder arthroplasty (n = 28) and non-pathologic normal cadavers (n = 28). Morphometric parameters were determined in central cores, with regional variations compared in four medial to lateral regions. Linear regression compared apparent modulus, morphometric parameters, and age. Micro finite element models estimated trabecular apparent modulus and derived density-modulus relationships. Significant differences were found for bone volume fraction (p < 0.001) and trabecular thickness (p < 0.001) in the most medial regions. No significant differences occurred between morphometric parameters and apparent modulus or age, except in slope between groups for apparent modulus versus trabecular number (p = 0.021), and in intercept for trabecular thickness versus age (p = 0.040). Significant differences occurred in both slope and intercept between density-modulus regression fits for each group (p ≤ 0.001). The normal group showed high correlations in the power-fit (r²  = 0.87), with a lower correlation (r²  = 0.61) and a more linear relationship, in the OA group. This study suggests that alterations in structure and apparent modulus persist mainly in subchondral regions of end-stage OA bone. As such, if pathologic regions are removed during joint replacement, computational models that utilize modeling parameters from non-pathologic normal bone may be applied to end-stage OA bone. An improved understanding of humeral trabecular bone variations has potential to improve the surgical management of end-stage OA patients. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:503-509, 2020.

Elementwise material assignment in reconstructed or transformed patient-specific FEA models developed from CT scans

In patient-specific finite element modeling, elementwise material assignment calculates local mechanical properties from the underlying CT data. If meshes must be transformed, for example to reconstruct broken bones, this elementwise material mapping is not possible using commercial software. Accordingly, we developed an algorithm to transform and reconstruct CT scans and fill gaps at discontinuities. Virtual mechanical testing showed that iterative reconstruction retains material heterogeneity with minimal strain artifacts and achieves whole-bone mechanics clinically equivalent (within 5%) to homogeneous models. This approach may expand the range of clinical CT scans that are viable for virtual biomechanics by allowing defect repair.

Age-related periosteal expansion at femoral neck among elderly women may maintain bending stiffness, but not femoral strength

Periosteal expansion and bone loss have opposite effects on femur strength. Their combined effect has not been fully understood. Our investigation using a recently developed beam model suggested that periosteal expansion may maintain femur bending stiffness among elderly women, but not help preserve femoral strength and reduce hip fracture risk.

INTRODUCTION

Periosteal expansion and bone loss are two accompanying biological phenomena in old population. Their combined effect on bone stiffness, strength, and fracture risk is still not clear, because previous studies have reported contradictory results.

METHODS

A recently developed DXA (dual-energy X-ray absorptiometry)-based beam model was applied to study the effect at the femoral neck. We first made a theoretical analysis. Then, a clinical cohort consisting of 961 women (316 hip fractures and 645 controls, age of 75.9 ± 7.1) was used to investigate the associations quantitatively. We investigated (1) correlations of femoral-neck width and bone mineral density with femoral stiffness and strength; (2) correlations of femoral stiffness, strength, and hip fracture risk index with age; (3) associations of femoral stiffness, strength and fracture risk index with actual fracture status, measured by the area under the curve (AUC) and odds ratio (OR).

RESULTS

The investigation results showed that (i) femoral-neck width had stronger correlation with femoral bending stiffness (r = 0.61-0.82, p < 0.001) than with the other stiffness components, while bone mineral density had stronger correlation with axial/shearing stiffness (r = 0.84-0.97, p < 0.001), strength (r = 0.85-0.92, p < 0.001), and fracture risk index (r = -0.61-0.62, p < 0.001) than with bending stiffness. (ii) The association between femoral bending stiffness and age was insignificant (r = - 0.06-0.05, r > 0.05); The associations of axial/shearing stiffness (r = - 0.27--0.20, p < 0.001), strength (r = - 0.28, p < 0.001), and fracture risk index (r = 0.38, p < 0.001) with age were significant. (iii) Fracture risk index had the strongest association with actual fracture status (AUC = 0.75, OR = 3.19), followed by strength (AUC = 0.74, OR = 2.84) and axial/shearing stiffness (AUC = 0.56-0.65, OR = 2.39-2.49). Femoral bending stiffness had the weakest association (AUC = 0.48-0.69, OR = 1.42-2.09).

CONCLUSION

We concluded that periosteal expansion may be adequate to maintain femoral bending stiffness among elderly women, but it may not help preserve strength and reduce hip fracture risk.

Experimental Validation of an ITAP Numerical Model and the Effect of Implant Stem Stiffness on Bone Strain Energy

The Intraosseous Transcutaneous Amputation Prosthesis (ITAP) offers transfemoral amputees an ambulatory method potentially reducing soft tissue complications seen with socket and stump devices. This study validated a finite element (in silico) model based on an ITAP design and investigated implant stem stiffness influence on periprosthetic femoral bone strain. Results showed good agreement in the validation of the in silico model against the in vitro results using uniaxial strain gauges and Digital Image Correlation (DIC). Using Strain Energy Density (SED) thresholds as the stimulus for adaptive bone remodelling, the validated model illustrated that: (a) bone apposition increased and resorption decreased with increasing implant stem flexibility in early stance; (b) bone apposition decreased (mean change = − 9.8%) and resorption increased (mean change = 20.3%) from distal to proximal in most stem stiffness models in early stance. By engineering the flow of force through the implant/bone (e.g. by changing material properties) these results demonstrate how periprosthetic bone remodelling, thus aseptic loosening, can be managed. This paper finds that future implant designs should be optimised for bone strain under a variety of relevant loading conditions using finite element models to maximise the chances of clinical success.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

The status and challenges of replicating the mechanical properties of connective tissues using additive manufacturing

The ability to fabricate complex structures via precise and heterogeneous deposition of biomaterials makes additive manufacturing (AM) a leading technology in the creation of implants and tissue engineered scaffolds. Connective tissues (CTs) remain attractive targets for manufacturing due to their "simple" tissue compositions that, in theory, are replicable through choice of biomaterial(s) and implant microarchitecture. Nevertheless, characterisation of the mechanical and biological functions of 3D printed constructs with respect to their host tissues is often limited and remains a restriction towards their translation into clinical practice. This review aims to provide an update on the current status of AM to mimic the mechanical properties of CTs, with focus on arterial tissue, articular cartilage and bone, from the perspective of printing platforms, biomaterial properties, and topological design. Furthermore, the grand challenges associated with the AM of CT replacements and their subsequent regulatory requirements are discussed to aid further development of reliable and effective implants.

Predicting bone strength from CT data: Clinical applications

In this review we summarise over 15 years of research and development around the prediction of whole bones strength from Computed Tomography data, with particular reference to the prediction of the risk of hip fracture in osteoporotic patients. We briefly discuss the theoretical background, and then provide a summary of the laboratory and clinical validation of these modelling technologies. We then discuss the three current clinical applications: in clinical research, in clinical trials, and in clinical practice. On average the strength predicted with finite element models (QCT-FE) based on computed tomography is 7% more accurate that that predicted with areal bone mineral density from Dual X-ray Absorptiometry (DXA-aBMD), the current standard of care, both in term of laboratory validation on cadaver bones and in terms of stratification accuracy on clinical cohorts of fractured and non-fractured women. This improved accuracy makes QCT-FE superior to DXA-aBMD in clinical research and in clinical trials, where the its use can cut in half the number of patients to be enrolled to get the same statistical power. For routine clinical use to decide who to treat with antiresorptive drugs, QCT-FE is more accurate but less cost-effective than DXA-aBMD, at least when the decision is on first line treatment like bisphosphonates. But the ability to predict skeletal strength from medical imaging is now opening a number of other applications, for example in paediatrics and oncology.