Strength reliability and in vitro degradation of three-dimensional powder printed strontium-substituted magnesium phosphate scaffolds

Strontium ions (Sr2+) are known to prevent osteoporosis and also encourage bone formation. Such twin requirements have motivated researchers to develop Sr-substituted biomaterials for orthopaedic applications. The present study demonstrates a new concept of developing Sr-substituted Mg-3(PO4)(2) - based biodegradable scaffolds. In particular, this work reports the fabrication, mechanical properties with an emphasis on strength reliability as well as in vitro degradation of highly biodegradable strontium-incorporated magnesium phosphate cements. These implantable scaffolds were fabricated using three-dimensional powder printing, followed by high temperature sintering and/or chemical conversion, a technique adaptable to develop patient-specific implants. A moderate combination of strength properties of 36.7 MPa (compression), 242 MPa (bending) and 10.7 MPa (tension) were measured. A reasonably modest Weibull modulus of up to 8.8 was recorded after uniaxial compression or diametral tensile tests on 3D printed scaffolds. A comparison among scaffolds with varying compositions or among sintered or chemically hardened scaffolds reveals that the strength reliability is not compromised in Sr-substituted scaffolds compared to baseline Mg-3(PO4)(2). The micro-computed tomography analysis reveals the presence of highly interconnected porous architecture in three-dimension with lognormal pore size distribution having median in the range of 17.74-26.29 mu m for the investigated scaffolds. The results of extensive in vitro ion release study revealed passive degradation with a reduced Mg2+ release and slow but sustained release of Sr2+ from strontium-substituted magnesium phosphate scaffolds. Taken together, the present study unequivocally illustrates that the newly designed Sr-substituted magnesium phosphate scaffolds with good strength reliability could be used for biomedical applications requiring consistent Sr2+-release, while the scaffold degrades in physiological medium. Statement of significance The study investigates the additive manufacturing of scaffolds based on different strontium-substituted magnesium phosphate bone cements by means of three-dimensional powder printing technique (3DPP). Magnesium phosphates were chosen due to their higher biodegradability compared to calcium phosphates, which is due to both a higher solubility as well as the absence of phase changes (to low soluble hydroxyapatite) in vivo. Since strontium ions are known to promote bone formation by stimulating osteoblast growth, we aimed to establish such a highly degradable magnesium phosphate ceramic with an enhanced bioactivity for new bone ingrowth. After post-processing, mechanical strengths of up to 36.7 MPa (compression), 24.2 MPa (bending) and 10.7 MPa (tension) could be achieved. Simultaneously, the failure reliability of those bioceramic implant materials, measured by Weibull modulus calculations, were in the range of 4.3-8.8. Passive dissolution studies in vitro proved an ion release of Mg2+ and PO43- as well as Sr2+, which is fundamental for in vivo degradation and a bone growth promoting effect. In our opinion, this work broadens the range of bioceramic bone replacement materials suitable for additive manufacturing processing. The high biodegradability of MPC ceramics together with the anticipated promoting effect on osseointegration opens up the way for a patient-specific treatment with the prospect of a fast and complete healing of bone fractures. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Generation of large-scale vortex dislocations in a three-dimensional wake-type flow

Numerical study of three-dimensional evolution of wake-type flow and vortex dislocations is performed by using a compact finite diffenence-Fourier spectral method to solve 3-D incompressible Navier-Stokes equations. A local spanwise nonuniformity in momentum defect is imposed on the incoming wake-type flow. The present numerical results have shown that the flow instability leads to three-dimensional vortex streets, whose frequency, phase as well as the strength vary with the span caused by the local nonuniformity. The vortex dislocations are generated in the nonuniform region and the large-scale chain-like vortex linkage structures in the dislocations are shown. The generation and the characteristics of the vortex dislocations are described in detail.

Three-Dimensional Network Model And Its Parameter Calibration

A material model, whose framework is parallel spring-bundles oriented in 3-D space, is proposed. Based on a discussion of the discrete schemes and optimum discretization of the solid angles, a 3-D network cell consisted of one-dimensional components is developed with its geometrical and physical parameters calibrated. It is proved that the 3-D network model is able to exactly simulate materials with arbitrary Poisson ratio from 0 to 1/2, breaking through the limit that the previous models in the literature are only suitable for materials with Poisson ratio from 0 to 1/3. A simplified model is also proposed to realize high computation accuracy within low computation cost. Examples demonstrate that the 3-D network model has particular superiority in the simulation of short-fiber reinforced composites.

Three-dimensional instability of an oscillating viscous flow past a circular cylinder

A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three-dimensional incompressible Navier-Stokes equations. The transition from two- to three-dimensional flow structures along the axial direction due to the vortical instability appears, and the three-dimensional structures lie alternatively on the two sides of the cylinder. Numerical study has been taken for the Keulegan-Carpenter( KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600. The force behaviors are also studied by solving the Morison equation. Calculated results agree well with experimental data and theoretical prediction.

Seismic Responses of a Hemispherical Alluvial Valley to SV Waves: A Three-Dimensional Analytical Approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Two-Dimensional Kinetics Of Beta(2)-Integrin And Icam-1 Bindings Between Neutrophils And Melanoma Cells In A Shear Flow

Cell adhesion, mediated by specific receptor-ligand interactions, plays an important role in biological processes such as tumor metastasis and inflammatory cascade. For example, interactions between beta(2)-integrin ( lymphocyte function-associated antigen-1 and/or Mac-1) on polymorphonuclear neutrophils (PMNs) and ICAM-1 on melanoma cells initiate the bindings of melanoma cells to PMNs within the tumor microenvironment in blood flow, which in turn activate PMN-melanoma cell aggregation in a near-wall region of the vascular endothelium, therefore enhancing subsequent extravasation of melanoma cells in the microcirculations. Kinetics of integrin-ligand bindings in a shear flow is the determinant of such a process, which has not been well understood. In the present study, interactions of PMNs with WM9 melanoma cells were investigated to quantify the kinetics of beta(2)-integrin and ICAM-1 bindings using a cone-plate viscometer that generates a linear shear flow combined with a two-color flow cytometry technique. Aggregation fractions exhibited a transition phase where it first increased before 60 s and then decreased with shear durations. Melanoma-PMN aggregation was also found to be inversely correlated with the shear rate. A previously developed probabilistic model was modified to predict the time dependence of aggregation fractions at different shear rates and medium viscosities. Kinetic parameters of beta(2)-integrin and ICAM-1 bindings were obtained by individual or global fittings, which were comparable to respectively published values. These findings provide new quantitative understanding of the biophysical basis of leukocyte-tumor cell interactions mediated by specific receptor-ligand interactions under shear flow conditions.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Nonequilibrium statistical mechanics of one-dimensional turbulence

The method of statistical mechanics is applied to the study of the one-dimensional model of turbulence proposed in an earlier paper. The closure problem is solved by the variational approach which has been developed for the three-dimensional case, yielding two integral equations for two unknown functions. By solving the two integral equations, the Kolmogorov k−5/3 law is derived and the (one-dimensional) Kolmogorov constant Ko is evaluated, obtaining Ko=0.55, which is in good agreement with the result of numerical experiments on one-dimensional turbulence.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.