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Scaphoid fractures are difficult to diagnose with current imaging modalities. It is unknown whether the shape of the scaphoid bone, assessed by statistical shape modeling, can be used to differentiate between fractured and non-fractured bones. Therefore, the aim of this study was to investigate whether the presence of a scaphoid fracture is associated with shape modes of a statistical shape model (SSM). Forty-one high-resolution peripheral quantitative computed tomography (HR-pQCT) scans were available from patients with a clinically suspected scaphoid fracture of whom 15 patients had a scaphoid fracture. The scans showed no motion artefacts affecting bone shape. The scaphoid bones were semi-automatically contoured, and the contours were converted to triangular meshes. The meshes were registered, followed by principal component analysis to determine mean shape and shape modes describing shape variance. The first five out of the forty shape modes cumulatively explained 87.8% of the shape variance. Logistic regression analysis was used to study the association between shape modes and fracture presence. The regression models were used to classify the 41 scaphoid bones as fractured or non-fractured using a cut-off value that maximized the sum of sensitivity and specificity. The classification of the models was compared with fracture diagnosis on HR-pQCT. A regression model with four shape modes had an area under the ROC-curve of 72.3% and correctly classified 75.6% of the scaphoid bones (fractured: 60.0%, non-fractured: 84.6%). To conclude, fracture presence in patients with a clinically suspected scaphoid fracture appears to be associated with the shape of the scaphoid bone., (Copyright © 2021 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Mechanical analysis of animal long bones often makes use of beam theory to estimate tissue properties from bending tests. An earlier study (van Lenthe et al., 2008) found that beam theory leads to a considerable underestimation of the Young's modulus of mice femora. However, we hypothesized that beam theory might still be an accurate tool for the determination of bone strength from experimental data. The first goal was to test this hypothesis, along with checking if the underestimation of the tissue modulus is also valid for rat femurs. The second goal was to investigate if micro-FE and beam theory would yield similar increases in Young's moduli and yield stress during aging. Twelve rat femurs (12 and 16 weeks old) were scanned using micro-CT and subjected to a three-point bending test from which the bending stiffness and the yield force were obtained. The Young's modulus and yield stress then were calculated by regressing the experimental results with results obtained from beam theory and micro-FE analysis based on the micro-CT scans. It was found that bone strength calculated using beam theory overestimated that calculated from micro-FE by 8.0%. The Young's modulus did not significantly differ. When comparing age groups, similar increases in tissue modulus and yield strength were found for beam theory and micro-FE, with significant differences only for the micro-FE yield stress. We concluded that the use of beam theory to calculate bone yield strength from 3-point bending test results of rat femurs leads to its overprediction., Competing Interests: Declaration of Competing Interest Bert van Rietbergen is a consultant for Scanco Medical AG. Andrés Julián Arias-Moreno and Keita Ito do not have any conflict of interest., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5-5 mL/min (or in terms of fluid velocity: 0.166-1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments., (Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Recently, micro-Finite Element (micro-FE) analysis based on High Resolution peripheral Quantitative CT (HRpQCT) images was introduced to quantify the state of fracture healing (de Jong et al., 2014). That study suggested that the direct post-fracture stiffness may be overestimated by micro-FE. The aim of this study was to investigate this further by measuring the loss in stiffness of cancellous bone samples under compressive loading and to compare this with predictions based on micro-FE analyses and bone microstructural and fracture morphology. Sixty porcine trabecular cores were micro-CT scanned and tested in compression before and after inducing a fracture in 4 different manners. The loss in stiffness as measured in the experiment was compared to that calculated from micro-FE analysis. Additionally, bone morphology parameters and fracture thickness were calculated. The experimentally measured loss in stiffness ranged from 37% to 80%. The losses calculated from the micro-FE analyses were lower and ranged from 36% to 61%, while in one case an increase in stiffness was calculated. For 2 of the 4 experiments, the results of the experiment and micro-FE analyses were significantly different. Only for very smooth fractures good agreement was obtained between FE and experimental results. The loss in stiffness did not correlate with any investigated bone morphology parameter or the thickness of the fracture region. It was concluded that micro-FE analysis can severely overestimate the stiffness of fractured bone depending on the type of fracture, but in the case of smooth fractures good estimates are possible., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The personalization of trabecular micro-architecture has been recently shown to be important in patient-specific biomechanical models of the femur. However, high-resolution in vivo imaging of bone micro-architecture using existing modalities is still infeasible in practice due to the associated acquisition times, costs, and X-ray radiation exposure. In this study, we describe a statistical approach for the prediction of the femur micro-architecture based on the more easily extracted subject-specific bone shape and mineral density information. To this end, a training sample of ex vivo micro-CT images is used to learn the existing statistical relationships within the low and high resolution image data. More specifically, optimal bone shape and mineral density features are selected based on their predictive power and used within a partial least square regression model to estimate the unknown trabecular micro-architecture within the anatomical models of new subjects. The experimental results demonstrate the accuracy of the proposed approach, with average errors of 0.07 for both the degree of anisotropy and tensor norms., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models. A DB of 33 human proximal femurs was generated from micro-CT scans with a nominal isotropic resolution of 82 µm. Continuum FE models were generated from the images using a pre-defined mesh template in combination with an iso-anatomic mesh morphing tool. Each element within the mesh template is at a specific anatomical location. For each element within the cancellous bone, a spherical region around the element centroid with a radius of 2mm was defined. Bone volume fraction and the mean-intercept-length fabric tensor were analyzed for that region. Ten femurs were used as test cases. For each test femur, four different models were generated: (1) an orthotropic model based on micro-CT fabric measurements (gold standard), (2) an orthotropic model based on the fabric derived from the best-matched database model, (3) an isotropic-I model in which the fabric tensor was set to the identity tensor, and (4) a second isotropic-II model with its total bone stiffness fitted to the gold standard. An elastic-plastic damage model was used to simulate failure and post failure behavior during a fall to the side. The results show that all models produce a similar stress distribution. However, compared to the gold standard, both isotropic-I and II models underestimated the stress/damage distributions significantly. We found no significant difference between DB-derived and gold standard models. Compared to the gold standard, the isotropic-I models further underestimated whole bone stiffness by 26.3% and ultimate load by 14.5%, while these differences for the DB-derived orthotropic models were only 4.9% and 3.1% respectively. The results indicate that the concept of using a DB to estimate patient-specific anisotropic material properties can considerably improve the results. We expect that this approach can lead to more accurate results in particular for cases where bone anisotropy plays an important role, such as in osteoporotic patients and around implants., (© 2013 Elsevier Ltd. All rights reserved.)

High-resolution in vivo bone micro-architecture assessment, as possible now for the distal forearm, in combination with bone remodelling simulation algorithms could, eventually, predict patient-specific bone morphology changes. To simulate load-adaptive bone remodelling, however, physiological loading conditions must be defined. In this paper we test a previously developed algorithm to estimate such physiological loading conditions from the bone micro-architecture. The aims of this study were to investigate if realistic boundary forces and moments are predicted for the scanned distal radius section and how these predicted forces and moments should be distributed to the scanned section in order to obtain a load transfer similar to that in situ. Images at in vivo resolution were generated for the clinically measured section of nine distal radius cadaver bones, converted to micro-finite element models and used for load estimation. Models of the full distal radius were created to analyse tissue loading distributions of the sections in situ. It was found that predicted forces and moments at the boundaries of the scanned region varied considerably but, when translated to equivalent radiocarpal joint forces, agreed well with values reported in the literature. Bone tissue loading distribution was in best agreement with in situ distributions when loading was applied to an extra layer of material at both ends of the clinical scan region. The agreement of the predicted loading to previous studies and the wide range of predicted loading values indicate that subject-specific bone loading estimation is possible and necessary., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Continuum finite element (FE) models of bones are commonly generated based on CT scans. Element material properties in such models are usually derived from bone density values using some empirical relationships. However, many different empirical relationships have been proposed. Most of these will provide isotropic material properties but relationships that can provide a full orthotropic elastic stiffness tensor have been proposed as well. Presently it is not clear which of these relationships best describes the material behavior of bone in continuum models, nor is it clear to what extent anisotropic models can improve upon isotropic models. The best way to determine the accuracy of such relationships for continuum analyses would be by quantifying the accuracy of the calculated stress/strain distribution, but this requires an accurate reference distribution that does not depend on such empirical relationships. In the present study, we propose a novel approach to generate such a reference stress distribution. With this approach, stress results obtained from a micro-FE model of a whole bone, that can represent the bone trabecular architecture in detail, are homogenized and the homogenized stresses are then used as a reference for stress results obtained from continuum models. The goal of the present study was to demonstrate this new approach and to provide examples of comparing continuum models with anisotropic versus isotropic material properties. Continuum models that implemented isotropic and orthotropic material definitions were generated for two proximal femurs for which micro-FE results were available as well, one representing a healthy and the other an osteoporotic femur. It was found that the continuum FE stress distributions calculated for the healthy femur compared well to the homogenized results of the micro-FE although slightly better for the orthotropic model (r=0.83) than for the isotropic model (r=0.79). For the osteoporotic bone also, the orthotropic model did better (r=0.83) than the isotropic model (r=0.77). We propose that this approach will enable a more relevant and accurate validation of different material models than experimental methods used so far., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

We previously developed a load-adaptive bone modelling and remodelling simulation model that can predict changes in the bone micro-architecture as a result of changes in mechanical loading or cell activity. In combination with a novel algorithm to estimate loading conditions, this offers the possibility for patient-specific predictions of bone modelling and remodelling. Based on such models, the underlying mechanisms of bone diseases and/or the effects of certain drugs and their influence on the bone micro-architecture can be investigated. In the present study we test the ability of this approach to predict changes in bone micro-architecture during hypoparathyroidism (HypoPT), as an illustrative example. We hypothesize that, apart from reducing bone turnover, HypoPT must also lead to increased osteocyte mechanosensitivity in order to explain the changes in bone mass seen in patients. Healthy human iliac crest biopsies were used as the starting point for the simulations that mimic HypoPT conditions and the resultant micro-architectures were compared to age-matched clinical HypoPT biopsies. Simulation results were in good agreement with the clinical data when osteocyte mechanosensitivity was increased by 40%. In conclusion, the results confirm our hypothesis, and also demonstrate that patient-specific bone modelling and remodelling simulations are feasible., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

A three-dimensional digital image correlation technique is presented for strain measurements in open-cell structures such as trabecular bone. The technique uses high-resolution computed tomography images for displacement measurements in the solid structure. In order to determine the local strain-state within single trabeculae, a tetrahedronization method is used to fill the solid structure with tetrahedrae. Displacements are calculated at the nodes of the tetrahedrae. The displacement data is subsequently converted to a deformation tensor in each of the tetrahedral element centers with a least-squares estimation method. Because the trabeculae are represented by a mesh, it is possible to deform this mesh according to the deformation tensor and, at the same time, visualize the calculated local strain in the deformed mesh with a finite element post-processing tool. In this way, the deformation of a single trabecula from an aluminum foam sample was determined and validated with rendered images of the three-dimensional sample. A precision analysis showed that a rigid translation or rotation does not affect the accuracy. Typical values for the standard deviation in the displacement and strain components are 2.0 microm and 0.01, respectively. Presently, the precision limits the technique to strain measurements beyond the yield strain.

Trabecular bone structure may complement bone volume/total volume fraction (BV/TV) in the prediction of the mechanical properties. Nonetheless, the direct in vivo use of information pertaining to trabecular bone structure necessitates some predictive analytical model linking structure measures to mechanical properties. In this context, the purpose of this study was to combine BV/TV and topological parameters so as to better estimate the mechanical properties of trabecular bone. Thirteen trabecular bone mid-sagittal sections were imaged by magnetic resonance (MR) imaging at the resolution of 117 x 117x 300 microm(3). Topological parameters were evaluated in applying the 3D-line skeleton graph analysis (LSGA) technique to the binary MR images. The same images were used to estimate the elastic moduli by finite element analysis (FEA). In addition to the mid-sagittal section, two cylindrical samples were cored from each vertebra along vertical and horizontal directions. Monotonic compression tests were applied to these samples to measure both vertical and horizontal ultimate stresses. BV/TV was found as a strong predictor of the mechanical properties, accounting for 89-94% of the variability of the elastic moduli and for 69-86% of the variability of the ultimate stresses. Topological parameters and BV/TV were combined following two analytical formulations, based on: (1) the normalization of the topological parameters; and on (2) an exponential fit-model. The normalized parameters accounted for 96-98% of the variability of the elastic moduli, and the exponential model accounted for 80-95% of the variability of the ultimate stresses. Such formulations could potentially be used to increase the prediction of the mechanical properties of trabecular bone.

In micro finite element analyses (microFEA) of cancellous bone, the 3D-imaging data that the FEA-models are based on, contain a range of gray-values. In the construction of the eventual FEA-model, these gray-values are commonly thresholded. Although thresholding is successful at small voxel sizes, at larger voxel sizes there is substantial loss of trabecular connectivity. We propose a new method: the gray-value method, where the microFEA-models use the information within the 3D-imaging data directly, without prior thresholding. Our question was twofold. First, how does the gray-value method compare to both plain and mass-compensated thresholding? Second, what is the effect of element size on the results obtained with the gray-value method? We used nine microCT-scans of human vertebral cancellous bone. These were degraded to represent different resolutions, and converted into microFEA-models using plain thresholding, mass-compensated thresholding, and the gray-value method. The apparent elastic moduli of the specimens were determined using microFEA. The different methods were compared on the basis of the apparent elastic moduli, compared to those calculated for a 28 microm reference model. The results showed that the gray-value method greatly improves the results relative to other methods. The gray-value method gives accurate predictions of the apparent elastic moduli, for voxel sizes up to one trabecular thickness (Tb.Th.). For voxel sizes greater than one Tb.Th. the accuracy, although still better than for both thresholding methods, becomes increasingly worse.

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.

Cancellous bone architecture and mechanics are intimately related. The trabecular architecture of cancellous bone is considered determined by its mechanical environment (Wolff's law), and the mechanical properties of cancellous bone are inversely determined by the trabecular architecture and material properties. Much effort has been spent in expressing these relations, but the techniques and variables necessary for this have not been fully identified. It is obvious, however, that some measure of architectural anisotropy (fabric) is needed. Within the last few years, volume-based measures of fabric have been introduced as alternatives to the mean intercept length method, which has some theoretical problems. This paper seeks to answer which of four different fabric measures best predicts finite element calculated mechanical anisotropy directions. Twenty-nine cancellous bone specimens were three-dimensionally reconstructed using the automated serial sectioning technique. A series of large-scale finite-element analyses were performed on each of the three-dimensional reconstructions to calculate the compliance matrix for each specimen, from which the mechanical principal directions were derived. The architectural anisotropy was determined in three-dimensional space for each specimen using mean intercept length (MIL), volume orientation (VO), star volume distribution (SVD) and star length distribution (SLD). Each of the architectural anisotropy results were expressed by a fabric tensor. Architectural main directions were determined from the fabric tensors and compared with the FE-calculated mechanical anisotropy directions. All architectural measures predicted the mechanical main directions rather well, which supports the assumption that mechanical anisotropy directions are aligned with fabric directions. MIL showed a significant, though very small (1.4 degrees), deviation from the primary mechanical direction. VO had difficulty in determining secondary and tertiary mechanical directions; its mean deviation was 8.9 degrees. SVD and SLD provided marginally better predictors of mechanical anisotropy directions than MIL and VO.

A major problem threatening the long-term integrity of total hip replacement is the loss of proximal bone often found around noncemented stems in the long term. It is generally accepted that 'stress shielding' is the cause for this problem: after implantation of the prosthesis the surrounding bone is partially 'shielding' from load carrying and starts to resorb. One of the proposed answers to this problem is the application of press-fitted stems. These smooth-surfaced implants are thought to provoke higher proximal bone loading, and, hence, less stress shielding than bonded implants, because they are wedged into the femur every time when loaded. However, in a two-year experiment in dogs, similar amounts of resorption of the proximal cortex were found around press-fitted and bonded implants. The question arises how similar resorption patterns can develop under completely different stress conditions, and whether this phenomenon can be explained by adaptive bone remodeling theories based on Wolff's law. In the present study an answer was sought for this question. An advanced iterative computer simulation model was used to analyze the remodeling process in the animal experiment. Three-dimensional finite element models were constructed from the animal experimental configuration, in which smooth, press-fitted stems were applied unilaterally in the canine. The FE model was integrated with iterative remodeling procedures, validated in earlier studies. In the model an appropriate non-linear representation of the loose bone-implant interface was realized, also capable of simulating the proximal interface gap that was found around the uncoated implants. The simulation models predicted similar amounts of proximal bone loss and distal bone densification as found in the animal model. Hence, the cortical bone loss could indeed be predicted by the strain-adaptive bone remodeling theory. By unraveling the simulation process, the question stated above could be answered. Densification of the distal bone bed during the initial remodeling process was found to cause reduced axial stem displacement (elastic subsidence), decreasing the wedging effect of the stem and, hence, decreasing the loading of the proximal bone, resulting in proximal bone loss. Hence, whereas in the case of bonded stems the proximal resorption process develops monotonously to a new equilibrium, the process around smooth, press-fitted stems develops nonmonotonously. This is due primarily to the unbonded interface conditions and the development of a proximal fibrous membrane. The remodeling process then gradually causes the stem to be jammed in the distal diaphyses (proximal 'stress bypass').