Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness than Other Morphological Variables

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

Reconstructing Arguments: Formalization and Reflective Equilibrium

Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate formalization. This paper explores how the method of reflective equilibrium can be used for modelling the complexity of such reconstructions and for justifying the various steps involved. The proposed approach is illustrated and tested in a detailed reconstruction of the beginning of Anselm’s De casu diaboli.

Synthesis, structure and magnetic properties of cobalt(II) and copper(II) coordination polymers assembled by phthalate and 4-methylimidazole

New coordination polymers [M(Pht)(4-MeIm)2(H2O)]n (M=Co (1), Cu (2); Pht2−=dianion of o-phthalic acid; 4-MeIm=4-methylimidazole) have been synthesized and characterized by IR spectroscopy, X-ray crystallography, thermogravimetric analysis and magnetic measurements. The crystal structures of 1 and 2 are isostructural and consist of [M(4-MeIm)2(H2O)] building units linked in infinite 1D helical chains by 1,6-bridging phthalate ions which also act as chelating ligands through two O atoms from one carboxylate group in the case of 1. In complex 1, each Co(II) atom adopts a distorted octahedral N2O4 geometry being coordinated by two N atoms from two 4-MeIm, three O atoms of two phthalate residues and one O atom of a water molecule, whereas the square-pyramidal N2O3 coordination of the Cu(II) atom in 2 includes two N atoms of N-containing ligands, two O atoms of two carboxylate groups from different Pht, and a water molecule. An additional strong O–H⋯O hydrogen bond between a carboxylate group of the phthalate ligand and a coordinated water molecule join the 1D helical chains to form a 2D network in both compounds. The thermal dependences of the magnetic susceptibilities of the polymeric helical Co(II) chain compound 1 were simulated within the temperature range 20–300 K as a single ion case, whereas for the Cu(II) compound 2, the simulations between 25 and 300 K, were made for a linear chain using the Bonner–Fisher approximation. Modelling the experimental data of compound 1 with MAGPACK resulted in: g=2.6, |D|=62 cm−1. Calculations using the Bonner–Fisher approximation gave the following result for compound 2: g=2.18, J=–0.4 cm−1.

Temporal variability of damage potential on roads as a conceptual contribution towards a short-term avalanche risk simulation

The fatality risk caused by avalanches on road networks can be analysed using a long-term approach, resulting in a mean value of risk, and with emphasis on short-term fluctuations due to the temporal variability of both, the hazard potential and the damage potential. In this study, the approach for analysing the long-term fatality risk has been adapted by modelling the highly variable short-term risk. The emphasis was on the temporal variability of the damage potential and the related risk peaks. For defined hazard scenarios resulting from classified amounts of snow accumulation, the fatality risk was calculated by modelling the hazard potential and observing the traffic volume. The avalanche occurrence probability was calculated using a statistical relationship between new snow height and observed avalanche releases. The number of persons at risk was determined from the recorded traffic density. The method resulted in a value for the fatality risk within the observed time frame for the studied road segment. The long-term fatality risk due to snow avalanches as well as the short-term fatality risk was compared to the average fatality risk due to traffic accidents. The application of the method had shown that the long-term avalanche risk is lower than the fatality risk due to traffic accidents. The analyses of short-term avalanche-induced fatality risk provided risk peaks that were 50 times higher than the statistical accident risk. Apart from situations with high hazard level and high traffic density, risk peaks result from both, a high hazard level combined with a low traffic density and a high traffic density combined with a low hazard level. This provided evidence for the importance of the temporal variability of the damage potential for risk simulations on road networks. The assumed dependence of the risk calculation on the sum of precipitation within three days is a simplified model. Thus, further research is needed for an improved determination of the diurnal avalanche probability. Nevertheless, the presented approach may contribute as a conceptual step towards a risk-based decision-making in risk management.