Search

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times., (© 2019 John Wiley & Sons, Ltd.)

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Boundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from [Formula: see text] scans of femoral heads and vertebral bodies. They were converted into [Formula: see text] models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs- and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors, and model parameters [Formula: see text] (Poisson's ratio) [Formula: see text] and [Formula: see text] (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on [Formula: see text]. However, KUBCs- and PMUBCs-based [Formula: see text] and [Formula: see text], respectively, decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

Background: Osteochondroplasty of the head-neck region is performed on patients with cam femoroacetabular impingement (FAI) without fully understanding its repercussion on the integrity of the femur. Cam-type FAI can be surgically and reproducibly induced in the ovine femur, which makes it suitable for studying corrective surgery in a consistent way. Finite element models built on quantitative CT (QCT) are computer tools that can be used to predict femoral strength and evaluate the mechanical effect of surgical correction., Questions/purposes: We asked: (1) What is the effect of a resection of the superolateral aspect of the ovine femoral head-neck junction on failure load? (2) How does the failure load after osteochondroplasty compare with reported forces from activities of daily living in sheep? (3) How do failure loads and failure locations from the computer simulations compare with the experiments?, Methods: Osteochondroplasties (3, 6, 9 mm) were performed on one side of 18 ovine femoral pairs with the contralateral intact side as a control. The 36 femurs were scanned via QCT from which specimen-specific computer models were built. Destructive compression tests then were conducted experimentally using a servohydraulic testing system and numerically via the computer models. Safety factors were calculated as the ratio of the maximal force measured in vivo by telemeterized hip implants during the sheep's walking and running activities to the failure load. The simulated failure loads and failure locations from the computer models were compared with the experimental results., Results: Failure loads were reduced by 5% (95% CI, 2%-8%) for the 3-mm group (p = 0.0089), 10% (95% CI, 6%-14%) for the 6-mm group (p = 0.0015), and 19% (95% CI, 13%-26%) for the 9-mm group (p = 0.0097) compared with the controls. Yet, the weakest specimen still supported more than 2.4 times the peak load during running. Strong correspondence was found between the simulated and experimental failure loads (R 2 = 0.83; p < 0.001) and failure locations., Conclusions: The resistance of ovine femurs to fracture decreased with deeper resections. However, under in vitro testing conditions, the effect on femoral strength remains small even after 9 mm correction, suggesting that femoral head-neck osteochondroplasty could be done safely on the ovine femur. QCT-based finite element models were able to predict weakening of the femur resulting from the osteochondroplasty., Clinical Relevance: The ovine femur provides a seemingly safe platform for scientific evaluation of FAI. It also appears that computer models based on preoperative CT scans may have the potential to provide patient-specific guidelines for preventing overcorrection of cam FAI.

Trabecular bone score (TBS) rests on the textural analysis of dual-energy X-ray absorptiometry (DXA) to reflect the decay in trabecular structure characterizing osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible because prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly owing to an unrealistic setup and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings were used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation ("full vertebra"); 2) via the classical endplate embedding ("vertebral body"); or 3) via a ball joint to induce anterior wedge failure ("vertebral section"). High-resolution peripheral quantitative computed tomography (HR-pQCT) scans acquired from prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (F(exp)) and apparent failure stress (σexp) was assessed, and their relative contribution to a multilinear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with F(exp) and σexp , except for the "vertebral body" case (r(2) = 0.396, p = 0.028). Aside from the "vertebra section" setup where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing setup, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk., (© 2015 American Society for Bone and Mineral Research.)

Purpose: Investigation of trabecular bone strength and compaction is important for fracture risk prediction. At 1-2% compressive strain, trabecular bone undergoes strain softening, which may lead to numerical instabilities and mesh dependency in classical local damage-plastic models. The aim of this work is to improve our continuum damage-plastic model of bone by reducing the influence of finite element mesh size under large compression., Methodology: This spurious numerical phenomenon may be circumvented by incorporating the nonlocal effect of cumulated plastic strain into the constitutive law. To this end, an over-nonlocal implicit gradient model of bone is developed and implemented into the finite element software ABAQUS using a user element subroutine. The ability of the model to detect the regions of bone failure is tested against experimental stepwise loading data of 16 human trabecular bone biopsies., Findings: The numerical outcomes of the nonlocal model revealed reduction of finite element mesh dependency compared with the local damage-plastic model. Furthermore, it helped reduce the computational costs of large-strain compression simulations., Originality: To the best of our knowledge, the proposed model is the first to predict the failure and densification of trabecular bone up to large compression independently of finite element mesh size. The current development enables the analysis of trabecular bone compaction as in osteoporotic fractures and implant migration, where large deformation of bone plays a key role., (Copyright © 2015 John Wiley & Sons, Ltd.)

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphology-elasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography (μCT) reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae, and iliac crest were analyzed. Their morphology was assessed via 25 variables and their stiffness tensor (CFE) was computed from six independent load cases using micro finite element (μFE) analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multiple linear regression model of the dependent variable CFE. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of CFE(r(2) adj  = 0.889), especially in combination with fabric anisotropy (r(2) adj  = 0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (r(2) adj  = 0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric anisotropy further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric anisotropy are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and postelastic properties., (© 2015 American Society for Bone and Mineral Research.)

Vertebral compression fractures are becoming increasingly common. Patient-specific nonlinear finite element (FE) models have shown promise in predicting yield strength and damage pattern but have not been experimentally validated for clinically relevant vertebral fractures, which involve loading through intervertebral discs with varying degrees of degeneration up to large compressive strains. Therefore, stepwise axial compression was applied in vitro on segments and performed in silico on their FE equivalents using a nonlocal damage-plastic model including densification at large compression for bone and a time-independent hyperelastic model for the disc. The ability of the nonlinear FE models to predict the failure pattern in large compression was evaluated for three boundary conditions: healthy and degenerated intervertebral discs and embedded endplates. Bone compaction and fracture patterns were predicted using the local volume change as an indicator and the best correspondence was obtained for the healthy intervertebral discs. These preliminary results show that nonlinear finite element models enable prediction of bone localisation and compaction. To the best of our knowledge, this is the first study to predict the collapse of osteoporotic vertebral bodies up to large compression using realistic loading via the intervertebral discs., (Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.)

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units., (Copyright © 2013 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The scaphoid is the most frequently fractured carpal bone. When investigating fixation stability, which may influence healing, knowledge of forces and moments acting on the scaphoid is essential. The aim of this study was to evaluate cartilage contact forces acting on the intact scaphoid in various functional wrist positions using finite element modeling. A novel methodology was utilized as an attempt to overcome some limitations of earlier studies, namely, relatively coarse imaging resolution to assess geometry, assumption of idealized cartilage thicknesses and neglected cartilage pre-stresses in the unloaded joint. Carpal bone positions and articular cartilage geometry were obtained independently by means of high resolution CT imaging and incorporated into finite element (FE) models of the human wrist in eight functional positions. Displacement driven FE analyses were used to resolve inter-penetration of cartilage layers, and provided contact areas, forces and pressure distribution for the scaphoid bone. The results were in the range reported by previous studies. Novel findings of this study were: (i) cartilage thickness was found to be heterogeneous for each bone and vary considerably between carpal bones; (ii) this heterogeneity largely influenced the FE results and (iii) the forces acting on the scaphoid in the unloaded wrist were found to be significant. As major limitations, accuracy of the method was found to be relatively low, and the results could not be compared to independent experiments. The obtained results will be used in a following study to evaluate existing and recently developed screws used to fix scaphoid fractures., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

Every year, 500,000 osteoporotic vertebral compression fractures occur in Europe. Quantitative computed tomography (QCT)-based finite element (FE) voxel models predict ultimate force whether they simulate vertebral bodies embedded in polymethylmethacrylate (PMMA) or vertebral sections with both endplates removed. To assess the effect of endplate removal in those predictions, non-linear FE analyses of QCT-based voxel models of human vertebral bodies were performed. High resolution pQCT images of 11 human lumbar vertebrae without posterior elements were coarsened to clinical resolution and bone volume fraction was used to determine the elastic, plastic and damage behavior of bone tissue. Three model boundary conditions (BCs) were chosen: the endplates were cropped (BC1, BC2) or voxel layers were added on the intact vertebrae to mimic embedding (BC3). For BC1 and BC3, the bottom nodes were fully constrained and the top nodes were constrained transversely while both node sets were freed transversely for BC2. Axial displacement was prescribed to the top nodes. In each model, we compared ultimate force and damage distribution during post-yield loading. The results showed that ultimate forces obtained with BC3 correlated perfectly with those computed with BC1 (R(2)=0.9988) and BC2 (R(2)=0.9987), but were in average 3.4% lower and 6% higher respectively. Moreover, good correlation of damage distribution calculated for BC3 was found with those of BC1 (R(2)=0.92) and BC2 (R(2)=0.73). This study demonstrated that voxel models of vertebral sections provide the same ultimate forces and damage distributions as embedded vertebral bodies, but with less preprocessing and computing time required., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

This study validated two different high-resolution peripheral quantitative computer tomography (HR-pQCT)-based finite element (FE) approaches, enhanced homogenised continuum-level (hFE) and micro-finite element (μFE) models, by comparing them with compression test results of vertebral body sections. Thirty-five vertebral body sections were prepared by removing endplates and posterior elements, scanned with HR-pQCT and tested in compression up to failure. Linear hFE and μFE models were created from segmented and grey-level CT images, and apparent model stiffness values were compared with experimental stiffness as well as strength results. Experimental and numerical apparent elastic properties based on grey-level/segmented CT images (N=35) correlated well for μFE (r2=0.748/0.842) and hFE models (r2=0.741/0.864). Vertebral section stiffness values from the linear μFE/hFE models estimated experimental ultimate apparent strength very well (r2=0.920/0.927). Calibrated hFE models were able to predict quantitatively apparent stiffness with the same accuracy as μFE models. However, hFE models needed no back-calculation of a tissue modulus or any kind of fitting and were computationally much cheaper.

Osteoporotic vertebral fractures constitute a major clinical problem in ageing societies. A third of all vertebral fractures is caused by falls, 15% by lifting heavy loads or traffic accidents and over 50% are not relatable to a traumatic event. In the latter case vertebrae show sinter processes which indicate the accumulation of damage and permanent deformation. Accumulated damage may not be visible on radiographs but increases the risk of fracture and could lead to vertebral collapse. Clear understanding of the accumulation of damage and residual strains and their dependence on loading mode and direction is important for understanding vertebral fractures. Altogether, 251 cylindrical samples (8×18-25mm) were obtained from 50 male and 54 female fresh frozen human vertebrae (T1-L3) of 65 (21-94) years. Vertebrae were randomly assigned to three groups cranial-caudal, anterior-posterior and latero-lateral. Specimens were mechanically loaded in compression, tension or torsion in five load steps at a strain rate of 0.2%/s. Three conditioning cycles were driven per load step. Stress-strain curves were reconstructed from the force-displacement or from the moment-twist angle curves. Damage accumulated from 0 to 86% in compression, from 0 to 76% in tension and from 0 to 86% in torsion through the five load steps. Residual strains accumulated from 0 to -0.008mm/mm in compression, 0 to 0.006mm/mm in tension and 0 to 0.026rad/rad in torsion. Significantly less damage (p<0.05) but not residual strains accumulated in transverse directions. This study provides detailed experimental insights into the damage behaviour of vertebral trabecular bone under various loads occurring in vivo. Damage but not residual strain evolution seems to be anisotropic. Both seem to evolve differently under different loading modes. The results could be of importance in understanding vertebral fractures., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Using the three-dimensional morphological data provided by computed tomography, finite element (FE) models can be generated and used to compute the stiffness and strength of whole bones. Three-dimensional constitutive laws capturing the main features of bone mechanical behavior can be developed and implemented into FE software to enable simulations on complex bone structures. For this purpose, a constitutive law is proposed, which captures the compressive behavior of trabecular bone as a porous material with accumulation of irreversible strain and loss of stiffness beyond its yield point and softening beyond its ultimate point. To account for these features, a constitutive law based on damage coupled with hardening anisotropic elastoplasticity is formulated using density and fabric-based tensors. To prevent mesh dependence of the solution, a nonlocal averaging technique is adopted. The law has been implemented into a FE software and some simple simulations are first presented to illustrate its behavior. Finally, examples dealing with compression of vertebral bodies clearly show the impact of softening on the localization of the inelastic process.

Osteoporosis-related vertebral fractures represent a major public health problem. Anatomy-specific CT-based finite element (FE) simulations could help in identifying which vertebrae have the highest risk of fracture and thus help to decide upon the need for vertebroplasty or other surgical intervention. Continuum level FE simulations require effective macroscopic material properties of the vertebra. Micro finite element (microFE) models can be used to circumvent the difficult experiments that are necessary to determine these effective properties. From a quantitative point of view, these microFE models depend critically on the chosen trabecular tissue properties. The question remains whether linear elastic microFE models of vertebral trabecular bone with and without specimen-specific tissue properties yield similar results as non-destructive macroscopic experiments under moist conditions. microFE models were set up from microCT scans with specimen-specific or average tissue moduli measured by nanoindentation under dry and wet testing conditions. Non-destructive macroscopic mechanical compression, tension and torsion tests were performed. Experimentally obtained and simulated apparent stiffnesses were compared. No significant difference was found when comparing microFE simulations with wet tissue properties and experiments for tension, compression and torsion (p>0.05). Concordance correlation coefficients were high for tension and compression (r(c)(wet)>or=0.96,p<0.05) but moderate for torsion (r(c)(wet)=0.81,p<0.05). The agreement between simulation and experiment was confirmed by Bland-Altman plots which showed mean differences

Continuum finite element (FE) models are standard tools for determination of biomechanical properties of bones and bone-implant systems. This study investigates the accuracy of an enhanced continuum FE model by taking muFE as the gold standard. The enhanced continuum models account for trabecular bone morphology (density and fabric) as well as for an anatomically correct cortical shell. Vertebral body slice models are extracted from high-resolution CT images using an algorithm proposed in [Pahr and Zysset, 2008b. From high-resolution CT data to FE models: development of an integrated modular framework. Computer Methods in Biomechanics and Biomedical Engineering, in press.]. Three different models are generated: the proposed enhanced density-fabric-based model with a subject-specific cortex and two classical isotropic density-only models, with and without explicit modeling of the cortical shell. The material property errors of the used morphology-elasticity relationship are minimized by using elasticity tensors from 60 cubical muFE models which are cropped from the trabecular centrums of the investigated vertebral bodies. Two different boundary conditions-kinematic [Van Rietbergen et al., 1995. A new method to determine trabecular bone elastic properties and loading using micromechanical FE models. Journal of Biomechanics 28 (1), 69-81] and mixed [Pahr, D.H., Zysset, P.K., 2008a. Influence of boundary conditions on computed apparent elastic properties of cancellous bone. Biomechanics and Modeling in Mechanobiology 7, 463-476.]-are used in these FE models. After removal of the endplates, compressive and antero-posterior shear loading is applied on the investigated vertebral bodies. Individual error sources are studied in more detail by loading also the trabecular centrum (removed shell) and the cortical shell alone. It is found that the cortex-only models need a correction of the shell thickness when transforming from a voxel to a smooth description. The trabecular centrum alone gives too stiff and too soft a response using material calibration with kinematic and mixed boundary conditions, respectively. A comparison of the whole vertebral body stiffnesses shows that an orthotropic cancellous bone material calibrated with kinematic boundary conditions corresponds best with muFE. Taken together, the proposed enhanced homogenized surface-based FE model is structurally more accurate than density-only models.

This work introduces a novel method of automating the process of patient-specific finite element (FE) model development using a mapped mesh technique. The objective is to map a predefined mesh (template) of high quality directly onto a new bony surface (target) definition, thereby yielding a similar mesh with minimal user interaction. To bring the template mesh into correspondence with the target surface, a deformable registration technique based on the FE method has been adopted. The procedure has been made hierarchical allowing several levels of mesh refinement to be used, thus reducing the time required to achieve a solution. Our initial efforts have focused on the phalanx bones of the human hand. Mesh quality metrics, such as element volume and distortion were evaluated. Furthermore, the distance between the target surface and the final mapped mesh were measured. The results have satisfactorily proven the applicability of the proposed method.