Density functional theory study of the {\alpha} --> {\omega} martensitic transformation in titanium induced by hydrostatic pressure

The martensitic {\alpha} --> {\omega} transition was investigated in Ti under hydrostatic pressure. The calculations were carried out using the density functional theory (DFT) framework in combination with the Birch-Murnaghan equation of state. The calculated ground-state properties of {\alpha} and {\omega} phases of Ti, their bulk moduli and pressure derivatives are in agreement with the previous experimental data. The lattice constants of {\alpha} and {\omega}-phase at 0 K were modeled as a function of pressure from 0 to 74 GPa and 0 to 119 GPa, respectively. It is shown that the lattice constants vary in a nonlinear manner upon compression. The calculated lattice parameters were used to describe the {\alpha} --> {\omega} transition and show that the phase transition can be obtained at 0 GPa and 0 K.Comment: 6 pages, 5 figure

An Integrated Qualitative and Quantitative Biochemical Model Learning Framework Using Evolutionary Strategy and Simulated Annealing

The authors would like to thank the support on this research by the CRISP Project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative.Peer reviewedPublisher PD

Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

[EN] In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The parameters defined in this step are related to the volumetric BMD considering that bone mineralization process occurs at the smallest scale length of the bone tissue. Then, a thorough description provides the details of the numerical models and the assumptions adopted to estimate the elastic behaviour of the forward scale lengths. The results highlight the noticeable influence of the BMD on the elastic modulus of lamellar bone. Power law regressions fit the Young's moduli, shear stiffness moduli and Poisson ratios. In addition, the explicit expressions obtained are applied to the estimation of the elastic constants of cortical bone. At this scale length, a representative unit cell of cortical bone is analysed including the fibril orientation pattern given by Wagermaier et al. (Biointerphases 1:1-5, 2006) and the BMD distributions observed by Granke et al. (PLoS One 8:e58043, 2012) for the osteon. Results confirm that fibril orientation arrangement governs the anisotropic behaviour of cortical bone instead of the BMD distribution. The novel explicit expressions obtained in this work can be used for improving the accuracy of bone fracture risk assessment.The authors acknowledge the Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46641-R and to the Generalitat Valenciana for Programme PROMETEO 2016/007. The authors declare that they have no conflict of interestVercher Martínez, A.; Giner Maravilla, E.; Belda, R.; Aigoun, A.; Fuenmayor Fernández, F. (2018). Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach. Biomechanics and Modeling in Mechanobiology. 17(2):449-464. https://doi.org/10.1007/s10237-017-0971-xS449464172Akiva U, Wagner HD, Weiner S (1998) Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci 33:1497–1509Ascenzi A, Bonucci E (1967) The tensile properties of single osteons. Ana Rec 158:375–386Barbour KE, Zmuda JM, Strotmeyer ES, Horwitz MJ, Boudreau R, Evans RW, Ensrud K, Petit MA, Gordon CL, Cauley JA (2013) Correlates of trabecular and cortical volumetric bone mineral density of the radius and tibia older men: the osteoporotic fractures in men study. 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The influence of anisotropy in numerical modelling of orthogonal cutting of cortical bone

Cutting operations in bone are involved in surgical treatments in orthopaedics and traumatology. The importance of guaranteeing the absence of damage in the living workpiece is equivalent in this case to ensuring surface quality. The knowledge in this field is really far from the expertise in industrial cutting of mechanical components. Modeling of bone cutting is a challenge strongly dependent on the accurate modeling of mechanical behaviour of the bone. This paper focuses on modeling of orthogonal cutting of cortical bone. The intrinsic anisotropic nature of the cortical bone that makes it comparable to a composite material is taken into account. The influence of anisotropy is analysed comparing this behaviour with an isotropic approach. It is shown that both chip morphology and temperature are affected by the anisotropy of the cortical bone that acts as a workpiece.The authors acknowledge the financial support for the work to the Ministry of Economy and Competitiveness of Spain under the Project DPI2011-25999 and DPI2013-46643-R.Santiuste, C.; Rodríguez Millán, M.; Giner Maravilla, E.; Miguélez, H. (2014). The influence of anisotropy in numerical modelling of orthogonal cutting of cortical bone. Composite Structures. 116:423-431. doi:10.1016/j.compstruct.2014.05.031S42343111

Reliable computation of PID gain space for general second-order time-delay systems

<p>This paper addresses the problem of determining the stability gain space of a PID controller for general second-order time-delay systems. First, a review of existing results and the associated drawbacks is presented. Subsequently, a new algorithm to compute the entire PID stability gain space is developed. The new algorithm is based upon existing results on the relationship between the stability of a quasi-polynomial and its derivatives, an extended version of the Hermit–Biehler theorem, and also the Nyquist criterion. The algorithm entails extraction of an admissible range for the PID parameter <i>K</i>_<i>p</i>, and then based on this range, a stability region in the (<i>K</i>_<i>i</i> − <i>K</i>_<i>d</i>) plane is computed. Well-known examples are studied to demonstrate the reliability and accuracy of the results.</p

Characterization of the MPS I-H knock-in mouse reveals increased femoral biomechanical integrity with compromised material strength and altered bone geometry

Mucopolysaccharidosis type I (MPS I), is an autosomal recessive lysosomal storage disorder caused by a deficiency in the α-L-iduronidase enzyme, resulting in decreased enzymatic activity and accumulation of glycosaminoglycans. The disorder phenotypically manifests with increased urine glycosaminoglycan excretion, facial dysmorphology, neuropathology, cardiac manifestations, and bone deformities. While the development of new treatment strategies have shown promise in attenuating many symptoms associated with the disorder, the bone phenotype remains unresponsive. The aim of this study was to investigate and further characterize the skeletal manifestations of the Idua-W392X knock-in mouse model, which carries a nonsense mutation corresponding to the IDUA-W402X mutation found in Hurler syndrome (MPS I-H) patients. μCT analysis of the microarchitecture demonstrated increased cortical thickness, trabecular number, and trabecular connectivity along with decreased trabecular separation in the tibiae of female homozygous Idua-W392X knock-in (IDUA−/−) mice, and increased cortical thickness in male IDUA−/− tibiae. Cortical density, as determined by μCT, and bone mineral density distribution, as determined by quantitative backscattered microscopy, were equivalent in IDUA−/− and wildtype (Wt) bone. However, tibial porosity was increased in IDUA−/− cortical bone. Raman spectroscopy results indicated that tibiae from female IDUA−/− had decreased phosphate to matrix ratios and increased carbonate to phosphate ratios compared to Wt female tibiae, whereas these ratios remained equivalent in male IDUA−/− and Wt tibiae. Femora demonstrated altered geometry and upon torsional loading to failure analysis, female IDUA−/− mouse femora exhibited increased torsional ultimate strength, with a decrease in material strength relative to Wt littermates. Taken together, these findings suggest that the IDUA−/− mutation results in increased bone torsional strength by altering the overall bone geometry and the microarchitecture which may be a compensatory response to increased porosity, reduced bone tensile strength and altered physiochemical composition

Characterization of the MPS I-H knock-in mouse reveals increased femoral biomechanical integrity with compromised material strength and altered bone geometry

Mucopolysaccharidosis type I (MPS I), is an autosomal recessive lysosomal storage disorder caused by a deficiency in the α-L-iduronidase enzyme, resulting in decreased enzymatic activity and accumulation of glycosaminoglycans. The disorder phenotypically manifests with increased urine glycosaminoglycan excretion, facial dysmorphology, neuropathology, cardiac manifestations, and bone deformities. While the development of new treatment strategies have shown promise in attenuating many symptoms associated with the disorder, the bone phenotype remains unresponsive. The aim of this study was to investigate and further characterize the skeletal manifestations of the Idua-W392X knock-in mouse model, which carries a nonsense mutation corresponding to the IDUA-W402X mutation found in Hurler syndrome (MPS I-H) patients. μCT analysis of the microarchitecture demonstrated increased cortical thickness, trabecular number, and trabecular connectivity along with decreased trabecular separation in the tibiae of female homozygous Idua-W392X knock-in (IDUA-/-) mice, and increased cortical thickness in male IDUA-/- tibiae. Cortical density, as determined by μCT, and bone mineral density distribution, as determined by quantitative backscattered microscopy, were equivalent in IDUA-/- and wildtype (Wt) bone. However, tibial porosity was increased in IDUA-/- cortical bone. Raman spectroscopy results indicated that tibiae from female IDUA-/- had decreased phosphate to matrix ratios and increased carbonate to phosphate ratios compared to Wt female tibiae, whereas these ratios remained equivalent in male IDUA-/- and Wt tibiae. Femora demonstrated altered geometry and upon torsional loading to failure analysis, female IDUA-/- mouse femora exhibited increased torsional ultimate strength, with a decrease in material strength relative to Wt littermates. Taken together, these findings suggest that the IDUA-/- mutation results in increased bone torsional strength by altering the overall bone geometry and the microarchitecture which may be a compensatory response to increased porosity, reduced bone tensile strength and altered physiochemical composition