Finite element analysis for prediction of bone strength

Article preview View full access options BoneKEy Reports | Review Print Email Share/bookmark Finite element analysis for prediction of bone strength Philippe K Zysset, Enrico Dall'Ara, Peter Varga & Dieter H Pahr Affiliations Corresponding author BoneKEy Reports (2013) 2, Article number: 386 (2013) doi:10.1038/bonekey.2013.120 Received 03 January 2013 Accepted 25 June 2013 Published online 07 August 2013 Article tools Citation Reprints Rights & permissions Abstract Abstract• References• Author information Finite element (FE) analysis has been applied for the past 40 years to simulate the mechanical behavior of bone. Although several validation studies have been performed on specific anatomical sites and load cases, this study aims to review the predictability of human bone strength at the three major osteoporotic fracture sites quantified in recently completed in vitro studies at our former institute. Specifically, the performance of FE analysis based on clinical computer tomography (QCT) is compared with the ones of the current densitometric standards, bone mineral content, bone mineral density (BMD) and areal BMD (aBMD). Clinical fractures were produced in monotonic axial compression of the distal radii, vertebral sections and in side loading of the proximal femora. QCT-based FE models of the three bones were developed to simulate as closely as possible the boundary conditions of each experiment. For all sites, the FE methodology exhibited the lowest errors and the highest correlations in predicting the experimental bone strength. Likely due to the improved CT image resolution, the quality of the FE prediction in the peripheral skeleton using high-resolution peripheral CT was superior to that in the axial skeleton with whole-body QCT. Because of its projective and scalar nature, the performance of aBMD in predicting bone strength depended on loading mode and was significantly inferior to FE in axial compression of radial or vertebral sections but not significantly inferior to FE in side loading of the femur. Considering the cumulated evidence from the published validation studies, it is concluded that FE models provide the most reliable surrogates of bone strength at any of the three fracture sites.

Comparison of theoretical fixation stability of three devices employed in medial opening wedge high tibial osteotomy: a finite element analysis.

BACKGROUND Medial open wedge high tibial osteotomy is a well-established procedure for the treatment of unicompartmental osteoarthritis and symptomatic varus malalignment. We hypothesized that different fixation devices generate different fixation stability profiles for the various wedge sizes in a finite element (FE) analysis. METHODS Four types of fixation were compared: 1) first and 2) second generation Puddu plates, and 3) TomoFix plate with and 4) without bone graft. Cortical and cancellous bone was modelled and five different opening wedge sizes were studied for each model. Outcome measures included: 1) stresses in bone, 2) relative displacement of the proximal and distal tibial fragments, 3) stresses in the plates, 4) stresses on the upper and lower screw surfaces in the screw channels. RESULTS The highest load for all fixation types occurred in the plate axis. For the vast majority of the wedge sizes and fixation types the shear stress (von Mises stress) was dominating in the bone independent of fixation type. The relative displacements of the tibial fragments were low (in μm range). With an increasing wedge size this displacement tended to increase for both Puddu plates and the TomoFix plate with bone graft. For the TomoFix plate without bone graft a rather opposite trend was observed.For all fixation types the occurring stresses at the screw-bone contact areas pulled at the screws and exceeded the allowable threshold of 1.2 MPa for at least one screw surface. Of the six screw surfaces that were studied, the TomoFix plate with bone graft showed a stress excess of one out of twelve and without bone graft, five out of twelve. With the Puddu plates, an excess stress occurred in the majority of screw surfaces. CONCLUSIONS The different fixation devices generate different fixation stability profiles for different opening wedge sizes. Based on the computational simulations, none of the studied osteosynthesis fixation types warranted an intransigent full weight bearing per se. The highest fixation stability was observed for the TomoFix plates and the lowest for the first generation Puddu plate. These findings were revealed in theoretical models and need to be validated in controlled clinical settings.

Cement distribution, volume, and compliance in vertebroplasty: some answers from an anatomy-based nonlinear finite element study

STUDY DESIGN: The biomechanics of vertebral bodies augmented with real distributions of cement were investigated using nonlinear finite element (FE) analysis. OBJECTIVES: To compare stiffness, strength, and stress transfer of augmented versus nonaugmented osteoporotic vertebral bodies under compressive loading. Specifically, to examine how cement distribution, volume, and compliance affect these biomechanical variables. SUMMARY OF BACKGROUND DATA: Previous FE studies suggested that vertebroplasty might alter vertebral stress transfer, leading to adjacent vertebral failure. However, no FE study so far accounted for real cement distributions and bone damage accumulation. METHODS: Twelve vertebral bodies scanned with high-resolution pQCT and tested in compression were augmented with various volumes of cements and scanned again. Nonaugmented and augmented pQCT datasets were converted to FE models, with bone properties modeled with an elastic, plastic and damage constitutive law that was previously calibrated for the nonaugmented models. The cement-bone composite was modeled with a rule of mixture. The nonaugmented and augmented FE models were subjected to compression and their stiffness, strength, and stress map calculated for different cement compliances. RESULTS: Cement distribution dominated the stiffening and strengthening effects of augmentation. Models with cement connecting either the superior or inferior endplate (S/I fillings) were only up to 2 times stiffer than the nonaugmented models with minimal strengthening, whereas those with cement connecting both endplates (S + I fillings) were 1 to 8 times stiffer and 1 to 12 times stronger. Stress increases above and below the cement, which was higher for the S + I cases and was significantly reduced by increasing cement compliance. CONCLUSION: The developed FE approach, which accounts for real cement distributions and bone damage accumulation, provides a refined insight into the mechanics of augmented vertebral bodies. In particular, augmentation with compliant cement bridging both endplates would reduce stress transfer while providing sufficient strengthening.

Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography

The alveolated structure of the pulmonary acinus plays a vital role in gas exchange function. Three-dimensional (3D) analysis of the parenchymal region is fundamental to understanding this structure-function relationship, but only a limited number of attempts have been conducted in the past because of technical limitations. In this study, we developed a new image processing methodology based on finite element (FE) analysis for accurate 3D structural reconstruction of the gas exchange regions of the lung. Stereologically well characterized rat lung samples (Pediatr Res 53: 72-80, 2003) were imaged using high-resolution synchrotron radiation-based X-ray tomographic microscopy. A stack of 1,024 images (each slice: 1024 x 1024 pixels) with resolution of 1.4 mum(3) per voxel were generated. For the development of FE algorithm, regions of interest (ROI), containing approximately 7.5 million voxels, were further extracted as a working subunit. 3D FEs were created overlaying the voxel map using a grid-based hexahedral algorithm. A proper threshold value for appropriate segmentation was iteratively determined to match the calculated volume density of tissue to the stereologically determined value (Pediatr Res 53: 72-80, 2003). The resulting 3D FEs are ready to be used for 3D structural analysis as well as for subsequent FE computational analyses like fluid dynamics and skeletonization.

Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation

Purpose The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. Results The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). Conclusions The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

Comparative effects of Teriparatide and Risedronate in glucocorticoid‐induced osteoporosis in men: 18‐month results of the EuroGIOPs trial

Data on treatment of glucocorticoid-induced osteoporosis (GIO) in men are scarce. We performed a randomized, open-label trial in men who have taken glucocorticoids (GC) for ≥3 months, and had an areal bone mineral density (aBMD) T-score ≤ –1.5 standard deviations. Subjects received 20 μg/d teriparatide (n = 45) or 35 mg/week risedronate (n = 47) for 18 months. Primary objective was to compare lumbar spine (L1–L3) BMD measured by quantitative computed tomography (QCT). Secondary outcomes included BMD and microstructure measured by high-resolution QCT (HRQCT) at the 12th thoracic vertebra, biomechanical effects for axial compression, anterior bending, and axial torsion evaluated by finite element (FE) analysis from HRQCT data, aBMD by dual X-ray absorptiometry, biochemical markers, and safety. Computed tomography scans were performed at 0, 6, and 18 months. A mixed model repeated measures analysis was performed to compare changes from baseline between groups. Mean age was 56.3 years. Median GC dose and duration were 8.8 mg/d and 6.4 years, respectively; 39.1% of subjects had a prevalent fracture, and 32.6% received prior bisphosphonate treatment. At 18 months, trabecular BMD had significantly increased for both treatments, with significantly greater increases with teriparatide (16.3% versus 3.8%; p = 0.004). HRQCT trabecular and cortical variables significantly increased for both treatments with significantly larger improvements for teriparatide for integral and trabecular BMD and bone surface to volume ratio (BS/BV) as a microstructural measure. Vertebral strength increases at 18 months were significant in both groups (teriparatide: 26.0% to 34.0%; risedronate: 4.2% to 6.7%), with significantly higher increases in the teriparatide group for all loading modes (0.005 < p < 0.015). Adverse events were similar between groups. None of the patients on teriparatide but five (10.6%) on risedronate developed new clinical fractures (p = 0.056). In conclusion, in this 18-month trial in men with GIO, teriparatide showed larger improvements in spinal BMD, microstructure, and FE-derived strength than risedronate.

Compressive strength of elderly vertebrae is reduced by disc degeneration and additional flexion

Computer tomography (CT)-based finite element (FE) models assess vertebral strength better than dual energy X-ray absorptiometry. Osteoporotic vertebrae are usually loaded via degenerated intervertebral discs (IVD) and potentially at higher risk under forward bending, but the influences of the IVD and loading conditions are generally overlooked. Accordingly, magnetic resonance imaging was performed on 14 lumbar discs to generate FE models for the healthiest and most degenerated specimens. Compression, torsion, bending, flexion and extension conducted experimentally were used to calibrate both models. They were combined with CT-based FE models of 12 lumbar vertebral bodies to evaluate the effect of disc degeneration compared to a loading via endplates embedded in a stiff resin, the usual experimental paradigm. Compression and lifting were simulated, load and damage pattern were evaluated at failure. Adding flexion to the compression (lifting) and higher disc degeneration reduces the failure load (8–14%, 5–7%) and increases damage in the vertebrae. Under both loading scenarios, decreasing the disc height slightly increases the failure load; embedding and degenerated IVD provides respectively the highest and lowest failure load. Embedded vertebrae are more brittle, but failure loads induced via IVDs correlate highly with vertebral strength. In conclusion, osteoporotic vertebrae with degenerated IVDs are consistently weaker—especially under lifting, but clinical assessment of their strength is possible via FE analysis without extensive disc modelling, by extrapolating measures from the embedded situation.

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient R2≥0.93. As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.

Fast Prediction of Femoral Biomechanics Using Supervised Machine Learning and Statistical Shape Modeling

Finite element (FE) analysis is an important computational tool in biomechanics. However, its adoption into clinical practice has been hampered by its computational complexity and required high technical competences for clinicians. In this paper we propose a supervised learning approach to predict the outcome of the FE analysis. We demonstrate our approach on clinical CT and X-ray femur images for FE predictions ( FEP), with features extracted, respectively, from a statistical shape model and from 2D-based morphometric and density information. Using leave-one-out experiments and sensitivity analysis, comprising a database of 89 clinical cases, our method is capable of predicting the distribution of stress values for a walking loading condition with an average correlation coefficient of 0.984 and 0.976, for CT and X-ray images, respectively. These findings suggest that supervised learning approaches have the potential to leverage the clinical integration of mechanical simulations for the treatment of musculoskeletal conditions.

Iron(III)-Pivalate-Based Complexes with Tetranuclear {Fe-4(mu(3)-O)(2)}(8+) Cores and N-Donor Ligands: Formation of Cluster and Polymeric Architectures

Different synthetic routes have been used for the preparation of a new tetranuclear [Fe4O2(O2CCMe3)(8)(bpm)] cluster (1) and a one-dimensional coordination polymer [Fe4O2-(O2CCMe3)(8)(hmta)](n) (2) (bpm = 2,2'-bipyrimidine and hmta = hexamethylenetetramine). For cluster 1, two structural isomers, 1a and 1b center dot 3MeCN, have been found. X-ray crystallographic analysis showed that all complexes consist of a central {Fe-4(mu(3)-O)(2)}(8+) core. In 1a, metal ions in the core are additionally linked by six bridging pivalates as two other pivalates and a bpm ligand are chelated to Fe-III ions, whereas in cluster 1b, metal ions in the {Fe-4(mu(3)-O)(2)}(8+) core are linked by seven bridging pivalates and only one carboxylate as well as bpm are chelated to the iron centers. In coordination polymer 2, [Fe4O2(O2CCMe3)(8)] clusters are bridged by hmta ligands to form zigzag chains. Magnetic measurements have been carried out to characterize these complexes and revealed antiferromagnetic interactions between Fe-III ions with best-fit parameters of J(wb) = -72.2 (1a) and -88.7 cm(-1) (1b) for wing...body interactions.

Determination of histopathological tumor grade in neuroepithelial brain tumors by using spectral pattern analysis of in vivo spectroscopic data

OBJECT: In this study, 1H magnetic resonance (MR) spectroscopy was prospectively tested as a reliable method for presurgical grading of neuroepithelial brain tumors. METHODS: Using a database of tumor spectra obtained in patients with histologically confirmed diagnoses, 94 consecutive untreated patients were studied using single-voxel 1H spectroscopy (point-resolved spectroscopy; TE 135 msec, TE 135 msec, TR 1500 msec). A total of 90 tumor spectra obtained in patients with diagnostic 1H MR spectroscopy examinations were analyzed using commercially available software (MRUI/VARPRO) and classified using linear discriminant analysis as World Health Organization (WHO) Grade I/II, WHO Grade III, or WHO Grade IV lesions. In all cases, the classification results were matched with histopathological diagnoses that were made according to the WHO classification criteria after serial stereotactic biopsy procedures or open surgery. Histopathological studies revealed 30 Grade I/II tumors, 29 Grade III tumors, and 31 Grade IV tumors. The reliability of the histological diagnoses was validated considering a minimum postsurgical follow-up period of 12 months (range 12-37 months). Classifications based on spectroscopic data yielded 31 tumors in Grade I/II, 32 in Grade III, and 27 in Grade IV. Incorrect classifications included two Grade II tumors, one of which was identified as Grade III and one as Grade IV; two Grade III tumors identified as Grade II; two Grade III lesions identified as Grade IV; and six Grade IV tumors identified as Grade III. Furthermore, one glioblastoma (WHO Grade IV) was classified as WHO Grade I/II. This represents an overall success rate of 86%, and a 95% success rate in differentiating low-grade from high-grade tumors. CONCLUSIONS: The authors conclude that in vivo 1H MR spectroscopy is a reliable technique for grading neuroepithelial brain tumors.

Safety of Active Implantable Devices during MRI Examinations: A Finite Element Analysis of an Implantable Pump

The goal of this study was to propose a general numerical analysis methodology to evaluate the magnetic resonance imaging (MRI)-safety of active implants. Numerical models based on the finite element (FE) technique were used to estimate if the normal operation of an active device was altered during MRI imaging. An active implanted pump was chosen to illustrate the method. A set of controlled experiments were proposed and performed to validate the numerical model. The calculated induced voltages in the important electronic components of the device showed dependence with the MRI field strength. For the MRI radiofrequency fields, significant induced voltages of up to 20 V were calculated for a 0.3T field-strength MRI. For the 1.5 and 3.0T MRIs, the calculated voltages were insignificant. On the other hand, induced voltages up to 11 V were calculated in the critical electronic components for the 3.0T MRI due to the gradient fields. Values obtained in this work reflect to the worst case situation which is virtually impossible to achieve in normal scanning situations. Since the calculated voltages may be removed by appropriate protection circuits, no critical problems affecting the normal operation of the pump were identified. This study showed that the proposed methodology helps the identification of the possible incompatibilities between active implants and MR imaging, and can be used to aid the design of critical electronic systems to ensure MRI-safety

Continuous Flow Analysis of labile iron in ice-cores

The important active and passive role of mineral dust aerosol in the climate and the global carbon cycle over the last glacial/interglacial cycles has been recognized. However, little data on the most important aeolian dust-derived biological micronutrient, iron (Fe), has so far been available from ice-cores from Greenland or Antarctica. Furthermore, Fe deposition reconstructions derived from the palaeoproxies particulate dust and calcium differ significantly from the Fe flux data available. The ability to measure high temporal resolution Fe data in polar ice-cores is crucial for the study of the timing and magnitude of relationships between geochemical events and biological responses in the open ocean. This work adapts an existing flow injection analysis (FIA) methodology for low-level trace Fe determinations with an existing glaciochemical analysis system, continuous flow analysis (CFA) of ice-cores. Fe-induced oxidation of N,N′-dimethyl-p-pheylenediamine (DPD) is used to quantify the biologically more important and easily leachable Fe fraction released in a controlled digestion step at pH ∼1.0. The developed method was successfully applied to the determination of labile Fe in ice-core samples collected from the Antarctic Byrd ice-core and the Greenland Ice-Core Project (GRIP) ice-core.

Clinical versus pre-clinical FE models for vertebral body strength predictions

The finite element analysis is an accepted method to predict vertebral body compressive strength. This study compares measurements obtained from in vitro tests with the ones from two different simulation models: clinical quantitative computer tomography (QCT) based homogenized finite element (hFE) models and pre-clinical high-resolution peripheral QCT-based (HR-pQCT) hFE models. About 37 vertebral body sections were prepared by removing end-plates and posterior elements, scanned with QCT (390/450μm voxel size) as well as HR-pQCT (82μm voxel size), and tested in compression up to failure. Non-linear viscous damage hFE models were created from QCT/HT-pQCT images and compared to experimental results based on stiffness and ultimate load. As expected, the predictability of QCT/HR-pQCT-based hFE models for both apparent stiffness (r2=0.685/0.801r2=0.685/0.801) and strength (r2=0.774/0.924r2=0.774/0.924) increased if a better image resolution was used. An analysis of the damage distribution showed similar damage locations for all cases. In conclusion, HR-pQCT-based hFE models increased the predictability considerably and do not need any tuning of input parameters. In contrast, QCT-based hFE models usually need some tuning but are clinically the only possible choice at the moment.