Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towardsthe prediction of extended vertebral collapse may help in assessing fracture stability in future work.

Experimental validation of a mean field model of mineralized collagen fiber arrays at two levels of hierarchy

In the course of this study, stiffness of a fibril array of mineralized collagen fibrils modeled with a mean field method was validated experimentally at site-matched two levels of tissue hierarchy using mineralized turkey leg tendons (MTLT). The applied modeling approaches allowed to model the properties of this unidirectional tissue from nanoscale (mineralized collagen fibrils) to macroscale (mineralized tendon). At the microlevel, the indentation moduli obtained with a mean field homogenization scheme were compared to the experimental ones obtained with microindentation. At the macrolevel, the macroscopic stiffness predicted with micro finite element (μFE) models was compared to the experimental stiffness measured with uniaxial tensile tests. Elastic properties of the elements in μFE models were injected from the mean field model or two-directional microindentations. Quantitatively, the indentation moduli can be properly predicted with the mean-field models. Local stiffness trends within specific tissue morphologies are very weak, suggesting additional factors responsible for the stiffness variations. At macrolevel, the μFE models underestimate the macroscopic stiffness, as compared to tensile tests, but the correlations are strong.

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.

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.

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.

Study of Heavy-ion Induced Fission for Heavy Element Synthesis

Fission fragment mass distributions were measured in heavy-ion induced fission of 238U. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model for the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that sub-barrier energies can be used for heavy element synthesis.

Microbe sampling by mucosal dendritic cells is a discrete, MyD88-independent step in DeltainvG S. Typhimurium colitis.

Intestinal dendritic cells (DCs) are believed to sample and present commensal bacteria to the gut-associated immune system to maintain immune homeostasis. How antigen sampling pathways handle intestinal pathogens remains elusive. We present a murine colitogenic Salmonella infection model that is highly dependent on DCs. Conditional DC depletion experiments revealed that intestinal virulence of S. Typhimurium SL1344 DeltainvG mutant lacking a functional type 3 secretion system-1 (DeltainvG)critically required DCs for invasion across the epithelium. The DC-dependency was limited to the early phase of infection when bacteria colocalized with CD11c(+)CX3CR1(+) mucosal DCs. At later stages, the bacteria became associated with other (CD11c(-)CX3CR1(-)) lamina propria cells, DC depletion no longer attenuated the pathology, and a MyD88-dependent mucosal inflammation was initiated. Using bone marrow chimeric mice, we showed that the MyD88 signaling within hematopoietic cells, which are distinct from DCs, was required and sufficient for induction of the colitis. Moreover, MyD88-deficient DCs supported transepithelial uptake of the bacteria and the induction of MyD88-dependent colitis. These results establish that pathogen sampling by DCs is a discrete, and MyD88-independent, step during the initiation of a mucosal innate immune response to bacterial infection in vivo.

Preliminary Study on Finite Element Simulation for Optimizing Acetabulum Reorientation after Periacetabular Osteotomy

Periacetabular osteotomy (PAO) is an effective approach for surgical treatment of hip dysplasia. The aim of PAO is to increase acetabular coverage of the femoral head and to reduce contact pressures by reorienting the acetabulum fragment after PAO. The success of PAO significantly depends on the surgeon’s experience. Previously, we have developed a computer-assisted planning and navigation system for PAO, which allows for not only quantifying the 3D hip morphology for a computer-assisted diagnosis of hip dysplasia but also a virtual PAO surgical planning and simulation. In this paper, based on this previously developed PAO planning and navigation system, we developed a 3D finite element (FE) model to investigate the optimal acetabulum reorientation after PAO. Our experimental results showed that an optimal position of the acetabulum can be achieved that maximizes contact area and at the same time minimizes peak contact pressure in pelvic and femoral cartilages. In conclusion, our computer-assisted planning and navigation system with FE modeling can be a promising tool to determine the optimal PAO planning strategy.

Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fracture is a common medical problem in osteoporotic individuals. The quantitative computed tomography (QCT)-based finite element (FE) method may be used to predict vertebral strength in vivo, but needs to be validated with experimental tests. The aim of this study was to validate a nonlinear anatomy specific QCT-based FE model by using a novel testing setup. Thirty-seven human thoracolumbar vertebral bone slices were prepared by removing cortical endplates and posterior elements. The slices were scanned with QCT and the volumetric bone mineral density (vBMD) was computed with the standard clinical approach. A novel experimental setup was designed to induce a realistic failure in the vertebral slices in vitro. Rotation of the loading plate was allowed by means of a ball joint. To minimize device compliance, the specimen deformation was measured directly on the loading plate with three sensors. A nonlinear FE model was generated from the calibrated QCT images and computed vertebral stiffness and strength were compared to those measured during the experiments. In agreement with clinical observations, most of the vertebrae underwent an anterior wedge-shape fracture. As expected, the FE method predicted both stiffness and strength better than vBMD (R2 improved from 0.27 to 0.49 and from 0.34 to 0.79, respectively). Despite the lack of fitting parameters, the linear regression of the FE prediction for strength was close to the 1:1 relation (slope and intercept close to one (0.86 kN) and to zero (0.72 kN), respectively). In conclusion, a nonlinear FE model was successfully validated through a novel experimental technique for generating wedge-shape fractures in human thoracolumbar vertebrae.

Evaluating atmospheric methane inversion model results for Pallas, northern Finland

A state-of-the-art inverse model, CarbonTracker Data Assimilation Shell (CTDAS), was used to optimize estimates of methane (CH4) surface fluxes using atmospheric observations of CH4 as a constraint. The model consists of the latest version of the TM5 atmospheric chemistry-transport model and an ensemble Kalman filter based data assimilation system. The model was constrained by atmospheric methane surface concentrations, obtained from the World Data Centre for Greenhouse Gases (WDCGG). Prior methane emissions were specified for five sources: biosphere, anthropogenic, fire, termites and ocean, of which bio-sphere and anthropogenic emissions were optimized. Atmospheric CH 4 mole fractions for 2007 from northern Finland calculated from prior and optimized emissions were compared with observations. It was found that the root mean squared errors of the posterior esti - mates were more than halved. Furthermore, inclusion of NOAA observations of CH 4 from weekly discrete air samples collected at Pallas improved agreement between posterior CH 4 mole fraction estimates and continuous observations, and resulted in reducing optimized biosphere emissions and their uncertainties in northern Finland.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Comparison of Mixed and Kinematic Uniform Boundary Conditions in Homogenized Elasticity of Femoral Trabecular Bone Using Microfinite Element Analyses

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Micro-finite element (microFE) analysis allows computing the apparent elastic properties of trabecular bone biopsies, but the results depend on the type of applied boundary conditions (BCs). In this study, 167 femoral trabecular cubic biopsies with a side length of 5.3 mm were analyzed using microFE analysis to compare their stiffness systematically with kinematic uniform boundary conditions (KUBCs) and periodicity-compatible mixed uniform boundary conditions (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset-Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length. Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset-Curnier model predicted apparent elastic constants successfully in both cases with adjusted coefficients of determination of 0.986 for KUBCs and 0.975 for PMUBCs. The role of these boundary conditions in finite element analyses of whole bones and bone-implant systems will need to be investigated in future work.

The Interplay between Melting, Refertilization and Carbonatite Metasomatism in Off-Cratonic Lithospheric Mantle under Zealandia: an Integrated Major, Trace and Platinum Group Element Study

It is widely accepted that stabilization of the continental crust requires the presence of sub-continental lithospheric mantle. However, the degree of melt depletion required to stabilize the lithosphere and whether widespread refertilization is a significant process remain unresolved. Here, major and trace element, including platinum group elements (PGE), characterization of 40 mantle xenoliths from 13 localities is used to constrain the melt depletion, refertilization and metasomatic history of lithospheric mantle underneath the micro-continent Zealandia. Our previously published Re–Os isotopic data for a subset of these xenoliths indicate Phanerozoic to Paleoproterozoic ages and, reinterpreted with the new major and trace element data presented here, demonstrate that a large volume (>2 million km3) of lithospheric mantle with an age of 1·99 ± 0·21 Ga is present below the much younger crust of Zealandia. A peritectic melting model using moderately incompatible trace elements (e.g. Yb) in bulk-rocks demonstrates that these peridotites experienced a significant range of degrees of partial melting, between 3 and 28%. During subsolidus equilibration clinopyroxene gains significant rare earth elements (REE), which then leads to the underestimation of the degree of partial melting by ≤12% in fertile xenoliths. A new approach taking into account the effects of subsolidus re-equilibration on clinopyroxene composition effectively removes discrepancies in the calculated degree of melting and provides consistent estimates of between 4 and 29%. The estimated amount of melting is independent of the Re–Os model ages of the samples. The PGE patterns record simple melt depletion histories and the retention of primary base metal sulfides in the majority of the xenoliths. A rapid decrease in Pt/IrN observed at c. 1·0 wt % Al2O3 is a direct result of the exhaustion of sulfide in the mantle residue at c. 20–25% partial melting and the inability of Pt to form a stable alloy phase. Major elements preserve evidence for refertilization by a basaltic component that resulted in the formation of secondary clinopyroxene and low-forsterite olivine. The majority of xenoliths show the effects of cryptic metasomatic overprinting, ranging from minor to strong light REE enrichments in bulk-rocks (La/YbN = 0·16–15·9). Metasomatism is heterogeneous, with samples varying from those with weak REE enrichment and notable positive Sr and U–Th anomalies and negative Nb–Ta anomalies in clinopyroxene to those that have extremely high concentrations of REE, Th–U and Nb. Chemical compositions are consistent with a carbonatitic component contributing to the metasomatism of the lithosphere under Zealandia. Notably, the intense metasomatism of the samples did not affect the PGE budget of the peridotites as this was controlled by residual sulfides.

DISCHARGE PLANNING: A PROCESS MODEL

As the requirements for health care hospitalization have become more demanding, so has the discharge planning process become a more important part of the health services system. A thorough understanding of hospital discharge planning can, then, contribute to our understanding of the health services system. This study involved the development of a process model of discharge planning from hospitals. Model building involved the identification of factors used by discharge planners to develop aftercare plans, and the specification of the roles of these factors in the development of the discharge plan. The factors in the model were concatenated in 16 discrete decision sequences, each of which produced an aftercare plan.^ The sample for this study comprised 407 inpatients admitted to the M. D. Anderson Hospital and Tumor Institution at Houston, Texas, who were discharged to any site within Texas during a 15 day period. Allogeneic bone marrow donors were excluded from the sample. The factors considered in the development of discharge plans were recorded by discharge planners and were used to develop the model. Data analysis consisted of sorting the discharge plans using the plan development factors until for some combination and sequence of factors all patients were discharged to a single site. The arrangement of factors that led to that aftercare plan became a decision sequence in the model.^ The model constructs the same discharge plans as those developed by hospital staff for every patient in the study. Tests of the validity of the model should be extended to other patients at the MDAH, to other cancer hospitals, and to other inpatient services. Revisions of the model based on these tests should be of value in the management of discharge planning services and in the design and development of comprehensive community health services.^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^