Anisotropic Matrix Research Articles

The influence of matrix integrity on stress-fiber remodeling in 3D

Matrix anisotropy is important for long term in vivo functionality. However, it is not fully understood how to guide matrix anisotropy in vitro. Experiments suggest actin-mediated cell traction contributes. Although F-actin in 2D displays a stretch-avoidance response, 3D data are lacking. We questioned how cyclic stretch influences F-actin and collagen orientation in 3D. Small-scale cell-populated fibrous tissues were statically constrained and/or cyclically stretched with or without biochemical agents. A rectangular array of silicone posts attached to flexible membranes constrained a mixture of cells, collagen I and matrigel. F-actin orientation was quantified using fiber-tracking software, fitted using a bi-model distribution function. F-actin was biaxially distributed with static constraint. Surprisingly, uniaxial cyclic stretch, only induced a strong stretch-avoidance response (alignment perpendicular to stretching) at tissue surfaces and not in the core. Surface alignment was absent when a ROCK-inhibitor was added, but also when tissues were only statically constrained. Stretch-avoidance was also observed in the tissue core upon MMP1-induced matrix perturbation. Further, a strong stretch-avoidance response was obtained for F-actin and collagen, for immediate cyclic stretching, i.e. stretching before polymerization of the collagen. Results suggest that F-actin stress-fibers avoid cyclic stretch in 3D, unless collagen contact guidance dictates otherwise.

Multiple anisotropic collisions for advection–diffusion Lattice Boltzmann schemes

This paper develops a symmetrized framework for the analysis of the anisotropic advection–diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.

STRESS-FIBER REMODELING IN 3D: ‘CONTACT GUIDANCE VS STRETCH AVOIDANCE’

Abstract When engineering heart valves in vitro, matrix anisotropy is considered important for long-term in vivo functionality. However, it is not fully understood how to guide, maintain and control matrix anisotropy. Experiments suggest that collagen anisotropy is affected by actin-mediated cell traction and associated cellular orientation. Although cellular orientation in 2D can be manipulated via imposed uniaxial cyclic stretch, 3D data are lacking. We questioned how cyclic stretch influences actin and collagen orientation in 3D constructs. A novel micro-tissue platform system was designed, able to dynamically and biochemically load small-scale cell-populated fibrous tissues. Flexible membranes of Bioflex culture plates were provided with a rectangular array silicone posts. These silicone posts constrained a contracting gel mixture of human vena saphena cells (HVSC), collagen type I and matrigel. The constrained tissues were subjected to pure uniaxial cyclic stretch (10%, 0.5Hz, in the presence or absence of agents) on the Flexcell system. F-actin was taken as a measure for the cell traction direction, and the F-actin orientation was quantified throughout the complete tissue thickness (~ 300m) using fiber-tracking software, and was fitted using a bi-model distribution function. Uniaxial cyclic stretching for 3 days (preceded by 3 days of static constraint) resulted in stress-fibers that were oriented perpendicular to the stretching direction only at tissue surfaces, as generally observed in 2D. Strikingly, however, in the tissue core F-actin (and cell) and collagen orientation was biaxial. Immediate cyclic stretching, starting before polymerization of the collagen matrix, resulted in a strong stretch avoidance throughout the tissue, of both F-actin and collagen. We systematically investigated the effect of biochemical treatment, including MMP1 to perturb matrix integrity, MMP-1 + ROCK-inhibitor to counteract the possible MMP1-induced response, as well the effect of a lower and a higher initial collagen density. Experimental data suggests that F-actin stress-fibers avoid cyclic stretch in 3D, unless collagen contact guidance dictates otherwise.

A strain space soil model with evolving stiffness anisotropy

A complete formulation of the BRICK soil model in general strain space is presented herein for the first time. Like all elasto-plastic constitutive models, BRICK exhibits some anisotropic behaviour, owing to the development of plastic strains once its yield surfaces are engaged. However, an abundance of laboratory and field evidence demonstrates that stiffness anisotropy is also significant within the elastic domain. Because of the inseparable nature of strength and stiffness in BRICK, the simple use of an anisotropic elastic stiffness matrix would result in an unrealistically high degree of strength anisotropy. Therefore, in addition to the established BRICK formulation, this paper also presents a novel framework to introduce stiffness anisotropy by transforming the coordinate system in which the model is based. The transformed coordinate system evolves to enable a constant-volume condition during shearing at critical state, reflecting the reorganisation of the soil fabric. The superior performance of the enhanced BRICK model over the classic model is demonstrated by a variety of conventional and non-conventional laboratory tests on London Clay.

Transfer Printing of Cell Layers with an Anisotropic Extracellular Matrix Assembly using Cell‐Interactive and Thermosensitive Hydrogels

AbstractThe structure of tissue plays a critical role in its function and therefore a great deal of attention has been focused on engineering native tissue‐like constructs for tissue engineering applications. Transfer printing of cell layers is a new technology that allows controlled transfer of cell layers cultured on smart substrates with defined shape and size onto tissue‐specific defect sites. Here, the temperature‐responsive swelling‐deswelling of the hydrogels with groove patterns and their versatile and simple use as a template to harvest cell layers with anisotropic extracellular matrix assembly is reported. The hydrogels with a cell‐interactive peptide and anisotropic groove patterns are obtained via enzymatic polymerization. The results show that the cell layer with patterns can be easily transferred to new substrates by lowering the temperature. In addition, multiple cell layers are stacked on the new substrate in a hierarchical manner and the cell layer is easily transplanted onto a subcutaneous region. These results indicate that the evaluated hydrogel can be used as a novel substrate for transfer printing of artificial tissue constructs with controlled structural integrity, which may hold potential to engineer tissue that can closely mimic native tissue architecture.

A computational model of in vitro angiogenesis based on extracellular matrix fibre orientation

Recent interest in the process of vascularisation within the biomedical community has motivated numerous new research efforts focusing on the process of angiogenesis. Although the role of chemical factors during angiogenesis has been well documented, the role of mechanical factors, such as the interaction between angiogenic vessels and the extracellular matrix, remains poorly understood. In vitro methods for studying angiogenesis exist; however, measurements available using such techniques often suffer from limited spatial and temporal resolutions. For this reason, computational models have been extensively employed to investigate various aspects of angiogenesis. This paper outlines the formulation and validation of a simple and robust computational model developed to accurately simulate angiogenesis based on length, branching and orientation morphometrics collected from vascularised tissue constructs. Microvessels were represented as a series of connected line segments. The morphology of the vessels was determined by a linear combination of the collagen fibre orientation, the vessel density gradient and a random walk component. Excellent agreement was observed between computational and experimental morphometric data over time. Computational predictions of microvessel orientation within an anisotropic matrix correlated well with experimental data. The accuracy of this modelling approach makes it a valuable platform for investigating the role of mechanical interactions during angiogenesis.

Numerical models of shear-induced melt band formation with anisotropic matrix viscosity

When a system of partial melt is subjected to an externally driven strain-rate, an instability can occur whereby bands of low and high porosity form. Theory and numerical simulations have shown that if the matrix viscosity is isotropic and strain-rate independent, the bands grow fastest when parallel to the direction of maximum compression of the externally imposed flow. However, experiments indicate that bands form at angles that differ by roughly 25° from the direction of maximum compression even when the matrix viscosity is strain-rate independent. Recently, Takei and Holtzman (2009c) have argued that the matrix viscosity is likely to be anisotropic when partial melt is present because of the anisotropic arrangement of melt at the grain scale. These authors also presented a theoretical expression for the stress tensor in the presence of this anisotropy and a linear theory of band formation that indicated that bands would form at angles that are in accord with the results of experiments. In this contribution, I present the results of linear theory and full nonlinear simulations of band formation under simple shear with anisotropic viscosity. I show that, even when the viscosity is strain-rate independent, the resulting bands form at low angles in accord with experiments if the anisotropy reflects a distribution of melt in pockets aligned parallel to the direction of maximum compression. If instead the anisotropy represents melt that is aligned at low angles to the shear plane, as seen in highly deformed experiments, the melt bands rapidly rotate to high angles. In that case, another mechanism is required to maintain the bands at low angles. The effects of buoyant melt are also investigated and bands are shown to grow at the same rate as when buoyancy is absent, but with an additional secondary preferred orientation.

NMR and NBO calculation of benzimidazoles and pyrimidines: Nano physical parameters investigation

Six theoretical methods were used for the calculation of physical parameters for derivatives of pyrimidines and benzimidazols. We used Gaussian 98 at NMR and NBO calculations by using HF method with 6-31G, 6-31G* and 6-31+G basis set and B3LYP, BLYP and B3PW91 methods with 6-31G basis set. Chemical shift was drawn curve for all of the atoms in each molecule. The thermo chemical parameters including thermal energy(ΔE), atomic charges, chemical shift anisotropy(δ), asymmetry parameter(η), chemical shift anisotropy(∆σ), dipole orientation, isotropic, anisotropic, NMR determinant and distance matrix compounds. Also the natural bond orbital (NBO) analysis has been performed which seem informative to show some important atomic and structural features. Key words: Benzimidazoles, pyrimidines, NBO analysis, Nano physical parameters.

Experimental and theoretical study on time dependence of the quasi-piezoelectric d33 coefficients of cellular piezoelectret film

The voided charged polymer film, also called piezoelectret, has a very large quasi-piezoelectric coefficient in the thickness direction, and has emerged as a new kind of electromechanical transducer materials. Piezoelectret film is usually prepared from polymer by means of biaxial stretching and electric charging process. Due to the inherent viscosity of polymer, the quasi-piezoelectric d33 coefficient of cellular piezoelectret film usually depends on the pressure and time of the measurement. In this article, experiments were carried out on the time spectra of quasi-piezoelectric d33 coefficient in the thickness direction for cellular linear Polypropylene piezoelectret film. To study the effect of void microstructures on the time-dependence of quasi-piezoelectric d33 coefficient, samples of three different thicknesses were tested under two different pressures. The micromechanical theory for viscoelastic composite was extended to predict the electromechanical properties of voided charged polymer film. The voids with surplus charges, which can be piezoelectriclike under deformation, are considered as ellipsoidal heterogeneous piezoelectric inclusions, while the viscous polymer is taken as the matrix. In Laplace transformed space, the generalized Eshelby tensor is formulated for the isotropic nonpolar matrix as well as for the anisotropic matrix. The Mori–Tanaka average scheme is used to find the overall electromechanical properties. Time dependence of the effective properties in real space can be studied by Laplacian inversion. Sensitivity analysis to various parameters is investigated for time dependence of the effective properties, including effective elastic moduli and the quasi-piezoelectric coefficients. Theoretical simulation was presented and comparison with experimental results was conducted. Both qualitative analysis and quantitative comparison with experiments show that this theoretical formulation can predict the time dependence of the effective properties of voided charged piezoelectret film.

Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method

The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo in Transp Porous Media 84:511–532, 2010) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady-state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given.

On the existence of Eshelby’s equivalent ellipsoidal inclusion solution

The existence of Eshelby’s equivalent inclusion solution is proved for a non-degenerate ‘transformed’ ellipsoidal inhomogeneity in an infinite anisotropic linear elastic matrix. We prove the invertibility of the fourth rank tensor expression, , where C is the stiffness tensor of the matrix, C′ is the stiffness tensor of the inhomogeneity, I is the Eshelby tensor, and is the symmetric identity tensor. Taking advantage of the positive definiteness of certain tensor expressions, a proof-by-contradiction using energy arguments is posited that eliminates the possibility that the above expression is singular. Because the tensor expression is non-singular, it can always be inverted and Eshelby’s equivalent ellipsoidal inclusion method can be used to find the stress and strain fields in both the matrix and inhomogeneity.

A technique for physical realization of anisotropic density matrices with application to acoustic beam shifters

Physical realization of acoustic metamaterials is so far at its initial stages, with attempts to use periodic patterns of engineered material structures to achieve various material properties that would yield the required wave propagation patterns. Phononic crystals are by far the most advanced technique for such realization. In the current work, a new technique for developing a realizable engineered periodic material structure is developed, where the anisotropic material density matrix arising from the linear coordinate transformation of the acoustic domain is rotated to align with its principal axis, resulting in a decoupled diagonal density matrix with entries representing the eigenvalues of the original anisotropic matrix. This allows for selecting feasible material properties that would achieve the targeted wave propagation patterns. The proposed approach is then utilized in modeling an acoustic wave shifting device with controllable directivity and dispersion characteristics. The linear coordinate transformation of the proposed wave shifter is augmented with an additional degree of freedom to simultaneously control the directivity and dispersion characteristics. The resulting anisotropic density matrix is manipulated using the developed technique and corresponding isotropic phononic cell structure is developed. Implementing the new isotropic phononic cell structure resulted in achieving the targeted wave control patterns. The theory governing the design of this class of acoustic metamaterials is introduced, and the parameters that control the tuning of the directivity and dispersion characteristics are presented in detail. With such capabilities, the proposed feasibly realizable acoustic metamaterials will be capable of controlling the wave propagation both in the spatial and spectral domains.

Cyclic strain anisotropy regulates valvular interstitial cell phenotype and tissue remodeling in three-dimensional culture

Many planar connective tissues exhibit complex anisotropic matrix fiber arrangements that are critical to their biomechanical function. This organized structure is created and modified by resident fibroblasts in response to mechanical forces in their environment. The directionality of applied strain fields changes dramatically during development, aging, and disease, but the specific effect of strain direction on matrix remodeling is less clear. Current mechanobiological inquiry of planar tissues is limited to equibiaxial or uniaxial stretch, which inadequately simulates many in vivo environments. In this study, we implement a novel bioreactor system to demonstrate the unique effect of controlled anisotropic strain on fibroblast behavior in three-dimensional (3-D) engineered tissue environments, using aortic valve interstitial fibroblast cells as a model system. Cell seeded 3-D collagen hydrogels were subjected to cyclic anisotropic strain profiles maintained at constant areal strain magnitude for up to 96h at 1Hz. Increasing anisotropy of biaxial strain resulted in increased cellular orientation and collagen fiber alignment along the principal directions of strain and cell orientation was found to precede fiber reorganization. Cellular proliferation and apoptosis were both significantly enhanced under increasing biaxial strain anisotropy (P<0.05). While cyclic strain reduced both vimentin and alpha-smooth muscle actin compared to unstrained controls, vimentin and alpha-smooth muscle actin expression increased with strain anisotropy and correlated with direction (P<0.05). Collectively, these results suggest that strain field anisotropy is an independent regulator of fibroblast cell phenotype, turnover, and matrix reorganization, which may inform normal and pathological remodeling in soft tissues.

Modeling microstructural effects in dilatational plasticity of polycrystalline materials

In a recent paper [1] we presented a new constitutive model for the viscoplastic response of polycrystalline aggregates accounting for local anisotropy induced by crystal plasticity and dilatational effects associated with the presence of intergranular cavities. In this contribution we provide a summary of our findings, as well as previously unpublished details of the numerical algorithm underlying this novel formulation. The formulation is based on homogenization and captures microstructural effects on the dilatational plastic behavior of polycrystalline materials. These effects are relevant to many engineering problems in which the presence of cavities embedded in a heterogeneous and anisotropic polycrystalline matrix must be accounted for, and for which standard polycrystalline models of incompressible plasticity, or dilatational plasticity formulations for voided materials with uniform properties of the matrix, have been proven to be insufficient. The present approach makes use of variational linear-comparison homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, single-crystal anisotropy, etc.) and triaxiality on the dilatational viscoplastic behavior of voided fcc polycrystals.

NMR and natural bond orbital (NBO) calculation of glyoxals: Nano physical parameter investigation

In this article, six theoretical methods have been used for calculation of physical parameters in five derivatives of glyoxals. We calculated physical parameters like atomic charges, energy (ΔE), chemical shift anisotropy (δ), asymmetry parameter (η), chemical shift anisotropy (∆σ), dipole moment, isotropic, anisotropic, NMR determinant and distance matrix determinant. In this work, we used Gaussian 98 at NMR and natural bond orbital (NBO) calculation by using HF method with 6-31G, 6-31G*, 6-31+G basis set and B3LYP, BLYP and B3PW91 methods with 6-31G basis set. GIAO magnetic shielding for studied molecules was obtained using Gauss view program. Chemical shift curve was drawn for all of the atoms in each molecule.

Long term performance cobalt oxide silica membrane module for high temperature H2 separation

Here we show the long term performance at high temperatures of a multi-tube module containing 8 membranes in 4 parallel lines with a total of 545 cm2 area. The membranes were prepared via thin film dip coating of cobalt oxide silica (CoOxSi) sol–gel on tubular alumina supports. A preliminary study found that the sol–gel containing 20 mol% cobalt oxide formed the best microporous structure with the highest surface area and pore volume. All resulting membranes delivered permeances of ∼1 × 10−7 mol m−2 s−1Pa−1 at 500 °C, indicating a high repeatability for the membrane fabrication process. The permselectivities of helium (He) and hydrogen (H2) over carbon dioxide (CO2) and nitrogen (N2) increased from 10–20 at 100 °C to values close to 1000 at 500 °C. Additionally, the apparent energies of activation (Eact) for the smaller kinetic diameter gases He and H2 at 12.2 and 19.5 kJ mol−1 were high and contrary to the negative values for larger gases N2 and CO2 at −1.8 and −7.4 kJ mol−1. These remarkable results were attributed to the molecular sieving mechanism of the microporous silica which was enhanced by the embedding of cobalt oxide into the matrix, delivering structural control with an average pore size of 3 Å. The Eact for H2 permeance was higher than that of He, indicating that the cobalt oxide played an important role in H2transport. Two membrane lines performed exceptionally well for binary gas mixture processing with H2 purity reaching values close to 100% in the permeate stream for argon (Ar) concentrations of up to 80% in the retentate stream. A major finding here is that the binary gas selectivity was independent of temperature, contrary to the permselectivity observed for single gas permeance. Further, the H2 flow rate was greatly affected by the concentration of Ar in the mixture, while the temperature dependency played only a marginal role. In particular, competitive adsorption in the percolative pathways containing pore constrictions or bottlenecks of the anisotropic CoOxSi matrix allowed Ar to impede H2 diffusion. Finally, the CoOxSi membranes proved thermally stable and robust for 2000 h of testing for various thermal cycles up to 500 °C.

Abnormal Growth Mechanisms of Goss Grains in Grain-Oriented Electrical Steels

The possible mechanisms concerning abnormal growth of Goss grains in grain oriented electrical steels were investigated. The density of inhibitor particles near sheet surface, where the Goss grains located, was lower than that in center layer before secondary recrystallization, and the grains near surface could grow more easily because of reduced pinning effect. Few Goss grains could survive the growth competition and reach the sheet surface, after which the inhibitor particles inside the Goss grains coarsened slower. The phenomenon resulted in easy growth of the Goss grains at the expense of smaller neighboring grains while they could hardly be consumed by larger neighboring grains during the high temperature secondary recrystallization. Very large final size of the Goss grains was then obtained. The mechanisms were discussed based on the hot rolling characteristics and the elastic anisotropy of the ferrite matrix.

Extensions of the Shape Functions with Penalization Parameterization for Composite-Ply Optimization

Nomenclature C = linear anisotropic material stiffness matrix of the ply l Ci = linear anisotropic material stiffness matrix of the candidate orientation i in the physical ply l n = number of candidate orientations in the ply l wi = weighting factor for the candidate orientation i in the ply l SFP = Shape Functions with Penalization R, S, T = design variables in the SFP material parameterization p = exponent used in the SFP parameterization

Subcellular Positioning: Unstable Filaments On the Move

A key question in cell biology is how proteins and entire protein complexes localize to defined subcellular positions in non-compartmentalized cells or within cell compartments. A recent report involving computational modeling and live-cell imaging suggests that dynamically unstable protein filaments provide an adaptable and versatile positioning system.

Derivation of Pekar's Polarons from a Microscopic Model of Quantum Crystal

A polaron is an electron interacting with a polar crystal, which is able to form a bound state by using the distortions of the crystal induced by its own density of charge. In this paper we derive Pekar's famous continuous model for polarons (in which the crystal is replaced by a simple effective Coulomb self-attraction) by studying the macroscopic limit of the reduced Hartree-Fock theory of the crystal. The macroscopic density of the polaron converges to that of Pekar's nonlinear model, with a possibly anisotropic dielectric matrix. The polaron also exhibits fast microscopic oscillations which contribute to the energy at the same order, but whose characteristic length is small compared to the scale of the polaron. These oscillations are described by a simple periodic eigenvalue equation. Our approach also covers multi-polarons composed of several electrons, repelling each other by Coulomb forces.