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.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

Northern hemispheric winter warming pattern after tropical volcanic eruptions: Sensitivity to the ozone climatology

An important key for the understanding of the dynamic response to large tropical volcanic eruptions is the warming of the tropical lower stratosphere and the concomitant intensification of the polar vortices. Although this mechanism is reproduced by most general circulation models today, most models still fail in producing an appropriate winter warming pattern in the Northern Hemisphere. In this study ensemble sensitivity experiments were carried out with a coupled atmosphere-ocean model to assess the influence of different ozone climatologies on the atmospheric dynamics and in particular on the northern hemispheric winter warming. The ensemble experiments were perturbed by a single Tambora-like eruption. Larger meridional gradients in the lower stratospheric ozone favor the coupling of zonal wind anomalies between the stratosphere and the troposphere after the eruption. The associated sea level pressure, temperature, and precipitation patterns are more pronounced and the northern hemispheric winter warming is highly significant. Conversely, weaker meridional ozone gradients lead to a weaker response of the winter warming and the associated patterns. The differences in the number of stratosphere-troposphere coupling events between the ensembles experiments indicate a nonlinear response behavior of the dynamics with respect to the ozone and the volcanic forcing.

Synthesis and Structural Elucidation of Triazolylmolybdenum(VI) Oxide Hybrids and Their Behavior as Oxidation Catalysts

A large family of bifunctional 1,2,4-triazole molecular tectons (tr) has been explored for engineering molybdenum(VI) oxide hybrid solids. Specifically, tr ligands bearing auxiliary basic or acidic groups were of the type amine, pyrazole, 1H-tetrazole, and 1,2,4-triazole. The organically templated molybdenum(VI) oxide solids with the general compositions [MoO3(tr)], [Mo2O6(tr)], and [Mo2O6(tr)(H2O)2] were prepared under mild hydrothermal conditions or by refluxing in water. Their crystal structures consist of zigzag chains, ribbons, or helixes of alternating cis-{MoO4N2} or {MoO5N} polyhedra stapled by short [N–N]-tr bridges that for bitriazole ligands convert the motifs into 2D or 3D frameworks. The high thermal (235–350 °C) and chemical stability observed for the materials makes them promising for catalytic applications. The molybdenum(VI) oxide hybrids were successfully explored as versatile oxidation catalysts with tert-butyl hydroperoxide (TBHP) or aqueous H2O2 as an oxygen source, at 70 °C. Catalytic performances were influenced by the different acidic–basic properties and steric hindrances of coordinating organic ligands as well as the structural dimensionality of the hybrid.

Strain-induced structural instability in FeRh

We perform density functional calculations to investigate the structure of the intermetallic alloy FeRh under epitaxial strain. Bulk FeRh exhibits a metamagnetic transition from a low-temperature antiferromagnetic (AFM) phase to a ferromagnetic phase at 350 K, and its strain dependence is of interest for tuning the transition temperature to the room-temperature operating conditions of typical memory devices. We find an unusually strong dependence of the structural energetics on the choice of exchange-correlation functional, with the usual local density approximation yielding the wrong ground-state structure, and generalized gradient (GGA) extensions being in better agreement with the bulk experimental structure. Using the GGA we show the existence of a metastable face-centered-cubic-like AFM structure that is reached from the ground-state body-centered-cubic-like AFM structure by following the epitaxial Bain path. We show that the behavior is well described using nonlinear elasticity theory, which captures the softening and eventual sign change of the orthorhombic shear modulus under compressive strain, consistent with this structural instability. Finally, we predict the existence of an additional unit-cell-doubling lattice instability, which should be observable at low temperature.

Adsorption behavior of redox-active suppressor additives: Combined electrochemical and STM studies

The redox chemistry and the related surface phase behavior of Safranine (SAF) and Janus Green B (JGB) have been studied by means of cyclic voltammetry in combination with in situ Scanning Tunneling Microscopy using HOPG (Highly Oriented Pyrolytic Graphite) and single crystalline Cu(1 0 0) as model substrates, both revealing different widths of the accessible potential windows. JGB and SAF serve as prototypical heterocyclic suppressor/leveler additives that are used for the metallization of 3D-TSVs (3D Through Silicon Vias) following a classical "leveling" concept. SAF can be considered as the reductive decomposition product of JGB that is formed at the copper/electrolyte interface upon electroplating. Both additives reveal a pronounced pH-dependent redox-chemistry with redox-transitions lying close to or even beyond the anodic limit of the copper potential window. Affected by these redox-processes are in particular the aromatic cores of those heterocycles that can be (quasi)reversibly reduced by a two electron transfer process within the potential window of copper. Therefore we identify the reduced form of those dyes as the active components for the suppressing/leveling effect in copper plating. STM data clearly shows a dye surface phase behavior that is crucially determined by its potential-dependent redox-chemistry. This will be exemplarily discussed for the SAF dye. On chloride-modified Cu(1 0 0) mono-reduced SAF forms a structurally well-defined monolayer of cationic stacking polymers. However, this coupled anion/cation layer reveals only minor suppressing capabilities with respect to the copper dissolution and deposition processes. Complete reduction of the aromatic heterocycle finally leads to the 3D precipitation of hydrophobic reaction products. 3D clusters of this SAF precipitate are discussed as the active structural motif for the suppressing effect of these dyes. (C) 2011 Elsevier Ltd. All rights reserved.

Regional structural characteristics of bovine periodontal ligament samples and their suitability for biomechanical tests

Mechanical testing of the periodontal ligament requires a practical experimental model. Bovine teeth are advantageous in terms of size and availability, but information is lacking as to the anatomy and histology of their periodontium. The aim of this study, therefore, was to characterize the anatomy and histology of the attachment apparatus in fully erupted bovine mandibular first molars. A total of 13 teeth were processed for the production of undecalcified ground sections and decalcified semi-thin sections, for NaOH maceration, and for polarized light microscopy. Histomorphometric measurements relevant to the mechanical behavior of the periodontal ligament included width, number, size and area fraction of blood vessels and fractal analysis of the two hard-soft tissue interfaces. The histological and histomorphometric analyses were performed at four different root depths and at six circumferential locations around the distal and mesial roots. The variety of techniques applied provided a comprehensive view of the tissue architecture of the bovine periodontal ligament. Marked regional variations were observed in width, surface geometry of the two bordering hard tissues (cementum and alveolar bone), structural organization of the principal periodontal ligament connective tissue fibers, size, number and numerical density of blood vessels in the periodontal ligament. No predictable pattern was observed, except for a statistically significant increase in the area fraction of blood vessels from apical to coronal. The periodontal ligament width was up to three times wider in bovine teeth than in human teeth. The fractal analyses were in agreement with the histological observations showing frequent signs of remodeling activity in the alveolar bone - a finding which may be related to the magnitude and direction of occlusal forces in ruminants. Although samples from the apical root portion are not suitable for biomechanical testing, all other levels in the buccal and lingual aspects of the mesial and distal roots may be considered. The bucco-mesial aspect of the distal root appears to be the most suitable location.

The Relationship Between Sociosexuality and Aspects of Body Image in Men and Women: A Structural Equation Modeling Approach

The present study investigated the association between individual differences in sociosexual orientation and four aspects of body image in 156 male and 136 female students. While men were characterized by a less restricted sociosexual orientation, higher self-perceived physical attractiveness, and more pronounced self-rated physical assertiveness, women placed more emphasis on accentuation of body presentation. Structural equation modeling revealed significant positive relationships between sociosexual attitudes and physical attractiveness and accentuation of body presentation as well as between sociosexual behavior and physical attractiveness for the total sample. When introducing sex as a grouping variable, the attitudinal and behavioral components of sociosexuality were reliably related to both physical attractiveness and accentuation of body presentation as two aspects of body image in men, but not in women. Furthermore, our findings suggest that accentuation of body presentation represents a goal-directed behavior in men to increase the likelihood of having uncommitted sex but serves additional functions widely unrelated to unrestrictive sociosexual behavior in women.

A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro

Purpose Femoral fracture is a common medical problem in osteoporotic individuals. Bone mineral density (BMD) is the gold standard measure to evaluate fracture risk in vivo. Quantitative computed tomography (QCT)-based homogenized voxel finite element (hvFE) models have been proved to be more accurate predictors of femoral strength than BMD by adding geometrical and material properties. The aim of this study was to evaluate the ability of hvFE models in predicting femoral stiffness, strength and failure location for a large number of pairs of human femora tested in two different loading scenarios. Methods Thirty-six pairs of femora were scanned with QCT and total proximal BMD and BMC were evaluated. For each pair, one femur was positioned in one-legged stance configuration (STANCE) and the other in a sideways configuration (SIDE). Nonlinear hvFE models were generated from QCT images by reproducing the same loading configurations imposed in the experiments. For experiments and models, the structural properties (stiffness and ultimate load), the failure location and the motion of the femoral head were computed and compared. Results In both configurations, hvFE models predicted both stiffness (R2=0.82 for STANCE and R2=0.74 for SIDE) and femoral ultimate load (R2=0.80 for STANCE and R2=0.85 for SIDE) better than BMD and BMC. Moreover, the models predicted qualitatively well the failure location (66% of cases) and the motion of the femoral head. Conclusions The subject specific QCT-based nonlinear hvFE model cannot only predict femoral apparent mechanical properties better than densitometric measures, but can additionally provide useful qualitative information about failure location.

In situ dehydration behavior of zeolite-like pentagonite: A single-crystal X-ray study

The structural modifications upon heating of pentagonite, Ca(VO)(Si4O10)·4H2O (space group Ccm21, a=10.3708(2), b=14.0643(2), c=8.97810(10) Å, V=1309.53(3) Å3) were investigated by in situ temperature dependent single-crystal X-ray structure refinements. Diffraction data of a sample from Poona district (India) have been measured in steps of 25 up to 250 °C and in steps of 50 °C between 250 and 400 °C. Pentagonite has a porous framework structure made up by layers of silicate tetrahedra connected by V4+O5 square pyramids. Ca and H2O molecules are extraframework occupants. Room temperature diffraction data allowed refinement of H positions. The hydrogen-bond system links the extraframework occupants to the silicate layers and also interconnects the H2O molecules located inside the channels. Ca is seven-fold coordinated forming four bonds to O of the tetrahedral framework and three bonds to extraframework H2O. The H2O molecule at O9 showing a high displacement parameter is not bonded to Ca. The dehydration in pentagonite proceeds in three steps. At 100 °C the H2O molecule at O8 was released while O9 moved towards Ca. As a consequence the displacement parameter of H2O at O9 halved compared to that at room temperature. The unit-cell volume decreased to 1287.33(3) Å3 leading to a formula with 3H2O per formula unit (pfu). Ca remained seven-fold coordinated. At 175 °C Ca(VO)(Si4O10)·3H2O transformed into a new phase with 1H2O molecule pfu characterized by doubling of the c axis and the monoclinic space group Pn. Severe bending of specific TOT angles led to contraction of the porous three-dimensional framework. In addition, H2O at O9 was expelled while H2O at O7 approached a position in the center of the channel. The normalized volume decreased to 1069.44(9) Å3. The Ca coordination reduced from seven- to six-fold. At 225 °C a new anhydrous phase with space group Pna21 but without doubling of c had formed. Release of H2O at O7 caused additional contraction of TOT angles and volume reduction (V=1036.31(9) Å3). Ca adopted five-fold coordination. During heating excursion up to 400 °C this anhydrous phase remained preserved. Between room temperature and 225 °C the unit-cell volume decreased by 21% due to dehydration. The dehydration steps compare well with the thermo-gravimetric data reported in the literature.

In situ dehydration behavior of zeolite-like cavansite: A single-crystal X-ray study

To track dehydration behavior of cavansite, Ca(VO)(Si4O10)·4H2O space group Pnma, a = 9.6329(2), b = 13.6606(2), c = 9.7949(2) Å, V = 1288.92(4) Å3 single-crystal X-ray diffraction data on a crystal from Wagholi quarry, Poona district (India) were collected up to 400 °C in steps of 25 °C up to 250 °C and in steps of 50 °C between 250 and 400 °C. The structure of cavansite is characterized by layers of silicate tetrahedra connected by V4+O5 square pyramids. This way a porous framework structure is formed with Ca and H2O as extraframework occupants. At room temperature, the hydrogen bond system was analyzed. Ca is eightfold coordinated by four bonds to O of the framework structure and four bonds to H2O molecules. H2O linked to Ca is hydrogen bonded to the framework and also to adjacent H2O molecules. The dehydration in cavansite proceeds in four steps.At 75 °C, H2O at O9 was completely expelled leading to 3 H2O pfu with only minor impact on framework distortion and contraction V = 1282.73(3) Å3. The Ca coordination declined from originally eightfold to sevenfold and H2O at O7 displayed positional disorder.At 175 °C, the split O7 sites approached the former O9 position. In addition, the sum of the three split positions O7, O7a, and O7b decreased to 50% occupancy yielding 2 H2O pfu accompanied by a strong decrease in volume V = 1206.89(8) Å3. The Ca coordination was further reduced from sevenfold to sixfold.At 350 °C, H2O at O8 was released leading to a formula with 1 H2O pfu causing additional structural contraction (V = 1156(11) Å3). At this temperature, Ca adopted fivefold coordination and O7 rearranged to disordered positions closer to the original O9 H2O site.At 400 °C, cavansite lost crystallinity but the VO2+ characteristic blue color was preserved. Stepwise removal of water is discussed on the basis of literature data reporting differential thermal analyses, differential thermo-gravimetry experiments and temperature dependent IR spectra in the range of OH stretching vibrations.

High-Pressure Behavior and Phase Stability of Al5BO9, a Mullite-Type Ceramic Material

Phase stability, elastic behavior, and pressure-induced structural evolution of synthetic boron-mullite Al5BO9 (a = 5.6780(7), b = 15.035(6), and c =7.698(3) Å, space group Cmc21, Z = 4) were investigated up to 25.6(1) GPa by in situ single-crystal synchrotron X-ray diffraction with a diamond anvil cell (DAC) under hydrostatic conditions. No evidence of phase transition was observed up to 21.7(1) GPa. At 25.6(1) GPa, the refined unit-cell parameters deviated significantly from the compressional trend, and the diffraction peaks appeared broader than at lower pressure. At 26.7(1) GPa, the diffraction pattern was not indexable, suggesting amorphization of the material or a phase transition to a high-pressure polymorph. Fitting the P–V data up to 21.7(1) GPa with a second-order Birch–Murnaghan Equation-of-State, we obtained a bulk modulus KT0 = 164(1) GPa. The axial compressibilities, here described as linearized bulk moduli, are as follows: KT0(a) = 244(9), KT0(b) = 120(4), and KT0(c) = 166(11) GPa (KT0(a):KT0(b):KT0(c) = 2.03:1:1.38). The structure refinements allowed a description of the main deformation mechanisms in response to the applied pressure. The stiffer crystallographic direction appears to be controlled by the infinite chains of edge-sharing octahedra running along [100], making the structure less compressible along the a-axis than along the b- and c-axis.

Distortion-sensitive insight into the pretransitional behavior of 4- n -octyloxy-4′-cyanobiphenyl (8OCB)

Results of studies of the static and dynamic dielectric properties in rod-like 4-n-octyloxy-4'-cyanobiphenyl (8OCB) with isotropic (I)–nematic (N)–smectic A (SmA)–crystal (Cr) mesomorphism, combined with measurements of the low-frequency nonlinear dielectric effect and heat capacity are presented. The analysis is supported by the derivative-based and distortion-sensitive transformation of experimental data. Evidence for the I–N and N–SmA pretransitional anomalies, indicating the influence of tricritical behavior, is shown. It has also been found that neither the N phase nor the SmA phase are uniform and hallmarks of fluid–fluid crossovers can be detected. The dynamics, tested via the evolution of the primary relaxation time, is clearly non-Arrhenius and described via τ(T) = τc(T−TC)−phgr. In the immediate vicinity of the I–N transition a novel anomaly has been found: Δτ ∝ 1/(T − T*), where T* is the temperature of the virtual continuous transition and Δτ is the excess over the 'background behavior'. Experimental results are confronted with the comprehensive Landau–de Gennes theory based modeling.

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.