Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R2 = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.

In situ micropillar compression reveals superior strength and ductility but an absence of damage in lamellar bone

Ageing societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the hierarchical organization of bone. Here, we investigate the mechanical response under monotonic and cyclic compression of both single osteonal lamellae and macroscopic samples containing numerous osteons. Micropillar compression tests in a scanning electron microscope, microindentation and macroscopic compression tests were performed on dry ovine bone to identify the elastic modulus, yield stress, plastic deformation, damage accumulation and failure mechanisms. We found that isolated lamellae exhibit a plastic behaviour, with higher yield stress and ductility but no damage. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behaviour of bone at the microscale to a quasi-brittle response driven by the growth of cracks along interfaces or in the vicinity of pores at the macroscale.

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.

Judaeus christicida gravissime peccans et vapulans : sive perspicua & solida demonstratio, caedem & rejectionem Jesu Nazareni veram esse causam praesentis diuturni Judaeorum exilii, omnisque illorum miseriae originem ; cum app. dissertationis philologicae ejusdem argumenti

von Joh. Jac. Schudt

Judaeus christicida gravissime peccans et vapulans : sive perspicua et solida demonstratio, caedem & rejectionem Jesu Nazareni veram esse causam praesentis tam diuturni Judaeorim exilii, onmisque illiorum miseriae originem ; cum app. dissertationis philologicae ejusdem argumenti ; cui accedunt addiamenti loco, 2 orationes ...

von Joh. Jac. Schudt

Compendium historiae Judaicae, de origine, incrementis & rebus gestis Judaeorum, ad ductum Justini Histor. libr. XXXVI potissimum ex gentilium scriptoribus collectum ... : acc. app.

Joh. Jacobi Schudt

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Brevis institutio linguae Syriacae ... Hebraicae antque Chaldaicae, nuper emissis, harmonica, ad collegiorum usum conscripta a Georgio Christiano Bürklino

Johann Heinrich Mai

Brevis institutio linguae Hebraicae, ad Schickardi atque Wasmuthi grammaticas praecipue accommodata, tertia vice auctius et emendatius emissa, opera ac studio Georgii Christiani Bürklini

Johann Heinrich Mai

Deliciae hebraeo-philologicae sive Tractatus de studio linguae et philologiae hebraicae : cum appendice de adventu Messiae ex Vaticinio Malach. III, I

Joh. Jacobi Schudt

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.

Genius et indoles linguae sanctae sive commentarius grammaticus & criticus ...

auctore Joh. Jacobo Schudt

Joh. Jacobi Schudt Specimen compendii philologici in usum studiosae juventutis quae in academiis, gymnasiis et scholis inferioribus Philologiae et antiquitatibus ... methodo per quaestiones et responsiones adornandi

Text lat. u. hebr.

Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

Rede über den falschen Religionseifer : gehalten im Münster zu Straßburg, am ersten Tage des Jänners 1792

von Johann Jakob Kämmerer