Shear-induced force transmission in a multicomponent,multicell model of the endothelium

Haemodynamic forces applied at the apical surface of vascular endothelial cells (ECs) provide the mechanical signals at intracellular organelles and through the inter-connected cellular network. The objective of this study is to quantify the intracellular and intercellular stresses in a confluent vascular EC monolayer. A novel three-dimensional, multiscale and multicomponent model of focally adhered ECs is developed to account for the role of potential mechanosensors (glycocalyx layer, actin cortical layer, nucleus, cytoskeleton, focal adhesions (FAs) and adherens junctions (ADJs)) in mechanotransmission and EC deformation. The overriding issue addressed is the stress amplification in these regions, which may play a role in subcellular localization of mechanotransmission. The model predicts that the stresses are amplified 250–600-fold over apical values at ADJs and 175–200-fold at FAs for ECs exposed to a mean shear stress of 10 dyne cm⁻². Estimates of forces per molecule in the cell attachment points to the external cellular matrix and cell–cell adhesion points are of the order of 8 pN at FAs and as high as 3 pN at ADJs, suggesting that direct force-induced mechanotransmission by single molecules is possible in both. The maximum deformation of an EC in the monolayer is calculated as 400 nm in response to a mean shear stress of 1 Pa applied over the EC surface which is in accord with measurements. The model also predicts that the magnitude of the cell–cell junction inclination angle is independent of the cytoskeleton and glycocalyx. The inclination angle of the cell–cell junction is calculated to be 6.6° in an EC monolayer, which is somewhat below the measured value (9.9°) reported previously for ECs subjected to 1.6 Pa shear stress for 30 min. The present model is able, for the first time, to cross the boundaries between different length scales in order to provide a global view of potential locations of mechanotransmission.     

Growth of fibroblast and vascular smooth muscle cells in fibroin/collagen scaffold

In our recent study, a novel fibroin/collagen scaffold with improved mechanical properties and controllable porous structure was prepared through freeze–drying method. In this research, the cyto-compatibility was further studied, using fibroblast and vascular smooth muscle cells (VSMC) as the model cells. MTT results indicated that the growth of fibroblast and VSMC both further improved in the fibroin/collagen scaffold than in pure fibroin scaffolds. The confocal and SEM results showed that fibroblast cells and VSMCs had better adhesion and spreading properties in the fibroin/collagen scaffolds. Although further studies, such as the extracellular matrix production and the functional gene expression, are necessary to clarify the biocompatibility of the fibroin/collagen scaffolds, the present results indicate that the fibroin/collagen scaffold is a new scaffold material suitable for tissue engineering. On the other hand, the mild and all-aqueous preparation processes also make it possible to embed different growth factors inside the scaffolds to maximize cell functions and the formation of specific tissues.     

A novel strategy to graft RGD peptide on biomaterials surfaces for endothelization of small-diamater vascular grafts and tissue engineering blood vessel

To improve the performance of small-diamater vascular grafts, endothelization of biomaterials surfaces and tissue engineering are more promising strategies to fabricate small-diamater vascular grafts. In this study, a Gly-Arg-Gly-Asp-Ser-Pro (GRGDSP) peptide was grafted on the surfaces of poly(carbonate urethane)s (PCUs), with photoactive 4-benzoylbenzoic acid (BBA) by UV irradiation. The photoactive peptides (BBM-GRGDSP) were synthesized with classical active ester of peptide synthesis. The modified surfaces of PCU with the photoactive RGD peptides were characterized by water contact angle measurement and X-ray Photoelectron Spectroscopy (XPS), which results suggested that the peptides were successfully grafted on the PCU surfaces. The effect of these modified surfaces on endothelial cells (ECs) adhesion and proliferation was examined over 72 h. PCU surfaces coupled with the synthetic photoactive RGD peptides, as characterized with phase contrast microscope and the metabolic activity (MTT) assay enhanced ECs proliferation and spreading with increasing concentration of RGD peptides grafted on their surfaces. Increased retention of ECs was also observed on the polymers surfaces under flow shear stress conditions. The results demonstrated that GRGDSP peptides grafted on the surfaces of polymers with photoactive 4-benzoylbenzoic acids could be an efficient method of fabrication for artificial small-diamater blood vessels. The modified polymer is expected to be used for small-diamater vascular grafts and functional tissue engineered blood vessels to improve ECs adhesion and retention on the polymer surfaces under flow shear stress conditions.     

On semi-infinite crack problems in elastic-plastic bodies; uniqueness and examples

First, the conditions for uniqueness of the stress boundary value problem for infinite cracks in elastic-plastic bodies are discussed on the basis of the Laurent series representation of the plastic boundary in an elastic perfectly plastic body in anti-plane strain (mode III).Next, for two cases, exact closed-form solutions of the shape of the elastic-plastic boundary are found in terms of elementary functions. A crack under shear stress acting on its surfaces, and a crack under constant remote shear stress σ^∞₁₃=−p, are considered. In the first case, also the complete stress distribution is obtained, for the second the physical coordinates as functions of stresses are found.The new elastic-plastic solutions are compared with ones predicted by linear elastic fracture mechanics.     

Endothelial cell culture model for replication of physiological profiles of pressure, flow, stretch, and shear stress in vitro

The phenotype and function of vascular cells in vivo are influenced by complex mechanical signals generated by pulsatile hemodynamic loading. Physiologically relevant in vitro studies of vascular cells therefore require realistic environments where in vivo mechanical loading conditions can be accurately reproduced. To accomplish a realistic in vivo-like loading environment, we designed and fabricated an Endothelial Cell Culture Model (ECCM) to generate physiological pressure, stretch, and shear stress profiles associated with normal and pathological cardiac flow states. Cells within this system were cultured on a stretchable, thin (～500 μm) planar membrane within a rectangular flow channel and subject to constant fluid flow. Under pressure, the thin planar membrane assumed a concave shape, representing a segment of the blood vessel wall. Pulsatility was introduced using a programmable pneumatically controlled collapsible chamber. Human aortic endothelial cells (HAECs) were cultured within this system under normal conditions and compared to HAECs cultured under static and "flow only" (13 dyn/cm(2)) control conditions using microscopy. Cells cultured within the ECCM were larger than both controls and assumed an ellipsoidal shape. In contrast to static control control cells, ECCM-cultured cells exhibited alignment of cytoskeletal actin filaments and high and continuous expression levels of β-catenin indicating an in vivo-like phenotype. In conclusion, design, fabrication, testing, and validation of the ECCM for culture of ECs under realistic pressure, flow, strain, and shear loading seen in normal and pathological conditions was accomplished. The ECCM therefore is an enabling technology that allows for study of ECs under physiologically relevant biomechanical loading conditions in vitro.     

Influence of initial stress on fracture of a halfspace containing a penny-shaped crack under radial shear

In this study, an axisymmetrical problem for a penny-shaped crack under radial shear is considered. The crack is located parallel to the surface of a halfspace, which is subjected to initial stress parallel to the crack plane. An approach proposed by Guz (1983) in the framework of the three-dimensional linearised solid mechanics is used. Analysis involves reducing the problem to a system of Fredholm integral equations of the second kind, where the solutions are identified with harmonic potential functions. The representations of the stress intensity factors K _I and K _II near the crack edges are obtained. These stress intensity factors are both influenced by the initial stress.     

Association between erythrocyte dynamics and vessel remodelling in developmental vascular networks

Sprouting angiogenesis is an essential vascularization mechanism consisting of sprouting and remodelling. The remodelling phase is driven by rearrangements of endothelial cells (ECs) within the post-sprouting vascular plexus. Prior work has uncovered how ECs polarize and migrate in response to flow-induced wall shear stress (WSS). However, the question of how the presence of erythrocytes (widely known as red blood cells (RBCs)) and their impact on haemodynamics affect vascular remodelling remains unanswered. Here, we devise a computational framework to model cellular blood flow in developmental mouse retina. We demonstrate a previously unreported highly heterogeneous distribution of RBCs in primitive vasculature. Furthermore, we report a strong association between vessel regression and RBC hypoperfusion, and identify plasma skimming as the driving mechanism. Live imaging in a developmental zebrafish model confirms this association. Taken together, our results indicate that RBC dynamics are fundamental to establishing the regional WSS differences driving vascular remodelling via their ability to modulate effective viscosity.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

C beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

The paper deals with the development and computational assessment of three- and two-node beam finite elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered composite and sandwich beams. RZT is a recently proposed structural theory that accounts for the stretching, bending, and transverse shear deformations, and which provides substantial improvements over previously developed zigzag and higher-order theories. This new theory is analytically rigorous, variationally consistent, and computationally attractive. The theory is not affected by anomalies of most previous zigzag and higher-order theories, such as the vanishing of transverse shear stress and force at clamped boundaries. In contrast to Timoshenko theory, RZT does not employ shear correction factors to yield accurate results. From the computational mechanics perspective RZT requires C⁰-continuous shape functions and thus enables the development of efficient displacement-type finite elements. The focus of this paper is to explore several low-order beam finite elements that offer the best compromise between computational efficiency and accuracy. The initial attention is on the choice of shape functions that do not admit shear locking effects in slender beams. For this purpose, anisoparametric (aka interdependent) interpolations are adapted to approximate the four independent kinematic variables that are necessary to model the planar beam deformations. To achieve simple two-node elements, several types of constraint conditions are examined and corresponding deflection shape-functions are derived. It is recognized that the constraint condition requiring a constant variation of the transverse shear force gives rise to a remarkably accurate two-node beam element. The proposed elements and their predictive capabilities are assessed using several elastostatic example problems, where simply supported and cantilevered beams are analyzed over a range of lamination sequences, heterogeneous material properties, and slenderness ratios.     

Methods for calculating stress intensity factors in anisotropic materials: Part II—Arbitrary geometry

The problem of a crack in a general anisotropic material under conditions of linear elastic fracture mechanics (LEFM) is examined. In Part I, three methods were presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a symmetry plane and the crack front is along the z-axis. These included displacement extrapolation, the M-integral and the separated J-integrals.In this study, general material anisotropy is considered in which the material and crack coordinates may be at arbitrary angles. A three-dimensional treatment is required for this situation in which there may be two or three modes present. A three-dimensional M-integral is extended to obtain stress intensity factors. It is applied to several test problems, in which excellent results are obtained. Results are obtained for a Brazilian disk specimen made of isotropic and cubic material. Two examples for the latter are examined with material coordinates rotated with respect to the crack axes.     

Selective endothelial cells adhesion to Arg-Glu-Asp-Val peptide functionalized polysaccharide multilayer

Thrombosis and in-stent restenosis are the main obstacles in the healing process after cardiovascular surgery. A promising way to achieve the healing process after percutaneous transluminal coronary angioplasty followed by stenting may rely on the rapid in situ endothelialization on the materials of implants. Several requirements are raised to achieve in situ endothelialization, of which the specifically endothelial cells (ECs) homing and the non-specific cells repulsion come first. In this work, heparin/chitosan multilayer was constructed with thromboresistant and non-specifically cell-resistant properties. The specific ECs adhesive peptide sequence Arg-Glu-Asp-Val (REDV) was then immobilized onto the pristine multilayer and the cell responses of ECs and smooth muscle cells (SMCs) were verified. It is interesting that ECs selective attachment was obtained on the REDV functionalized multilayer, whereas the multilayer maintains resisting to the SMCs. These results show that the REDV functionalized cell-resistant heparin/chitosan multilayer is a ECs selective surface, which may have great potential in cardiovascular biomaterials for in situ endothelialization.     

Generalized stress intensity factors of V-shaped notch in a round bar under torsion, tension, and bending

In this study, generalized stress intensity factors K_I,λ1, K_II,λ2, and K_III,λ4 are calculated for a V-shaped notched round bar under tension, bending, and torsion using the singular integral equation of the body force method. The body force method is used to formulate the problem as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in an infinite body. In order to analyze the problem accurately, the unknown functions are expressed as piecewise smooth functions using three types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity and the skew-symmetric stress singularity. Generalized stress intensity factors at the notch tip are systematically calculated for various shapes of V-shaped notches. Normalized stress intensity factors are given by using limiting solutions; they are almost determined by notch depth alone, and almost independent of other geometrical parameters. The accuracy of Benthem-Koiter’s formula proposed for a circumferential crack is also examined through the comparison with the present analysis.     

Interlaminar shear fracture of chopped strand mat glass fibre-reinforced polyester laminates

The interlaminar shear fracture of chopped strand mat glass fibre-reinforced polyester laminates has been studied both experimentally and analytically. Lap shear (double-grooved) specimens were used to measure the interlaminar shear strength and the cracking mechanism was studied using photomicrography. The finite element method was used to calculate the stress distribution along the shear surface and the mixed-mode stress intensity factors K_I and K_II. The length of the shear surface was found to have a significant effect on the results. Based on the experimental and analytical results, the validity of the British Standard for GRP pressure vessels (BS4994, 1973) was evaluated and the critical stress intensity factors K_Ic and K_IIc for this material were estimated.     

Effect of Hypergravity on Endothelial Cell Function and Gene Expression

It is well known that endothelial cells (ECs), which play a major role in cardiovascular system functioning, are very sensitive to mechanical stimuli. It has been demonstrated that changes in inertial conditions (i.e. microgravity and hypergravity) can affect both phenotypic and genotypic expression in ECs. In this report we describe the effects of hypergravity on ECs isolated from bovine aorta (BAECs). ECs were repeatedly exposed to discontinuous hypergravity conditions (5 × 10 min at 10×g with 10 min at 1×g between sets), simulated in a hyperfuge. Then, cell morphology and metabolism were analyzed by autofluorescence techniques. The phenotypic expression of cytoskeleton constituents (β-actin, vimentin, tubulin), adhesion and survival signals (integrins), mediators of inflammation and angiogenesis was evaluated by immunocytofluorescence. Quantitative PCR (Q-PCR) with Low Density Arrays (LDAs) was used to evaluate modifications in gene expression. After hypergravity exposure, no significant changes were observed in cell morphology and energy metabolism. Cells remained adherent to the substratum, but integrin distribution was modified. Accordingly, the cytoskeletal network reorganized, documenting cell activation. There was a reduction in expression of genes controlling vasoconstriction and inflammation. Proapoptotic signals were downregulated. On the whole, the results documented that hypergravity exposure maintained EC survival and function by activation of adaptive mechanisms.     

Rear actomyosin contractility-driven directional cell migration in three-dimensional matrices: a mechano-chemical coupling mechanism

Cell migration is of vital importance in many biological processes, including organismal development, immune response and development of vascular diseases. For instance, migration of vascular smooth muscle cells from the media to intima is an essential part of the development of atherosclerosis and restenosis after stent deployment. While it is well characterized that cells use actin polymerization at the leading edge to propel themselves to move on two-dimensional substrates, the migration modes of cells in three-dimensional matrices relevant to in vivo environments remain unclear. Intracellular tension, which is created by myosin II activity, fulfils a vital role in regulating cell migration. We note that there is compelling evidence from theoretical and experimental work that myosin II accumulates at the cell rear, either isoform-dependent or -independent, leading to three-dimensional migration modes driven by posterior myosin II tension. The scenario is not limited to amoeboid migration, and it is also seen in mesenchymal migration in which a two-dimensional-like migration mode based on front protrusions is often expected, suggesting that there may exist universal underlying mechanisms. In this review, we aim to shed some light on how anisotropic myosin II localization induces cell motility in three-dimensional environments from a biomechanical view. We demonstrate an interesting mechanism where an interplay between mechanical myosin II recruitment and biochemical myosin II activation triggers directional migration in three-dimensional matrices. In the case of amoeboid three-dimensional migration, myosin II first accumulates at the cell rear to induce a slight polarization displayed as a uropod-like structure under the action of a tension-dependent mechanism. Subsequent biochemical signalling pathways initiate actomyosin contractility, producing traction forces on the adhesion system or creating prominent motile forces through blebbing activity, to drive cells to move. In mesenchymal three-dimensional migration, cells can also take advantage of the elastic properties of three-dimensional matrices to move. A minor myosin isoform, myosin IIB, is retained by relatively stiff three-dimensional matrices at the posterior side, then activated by signalling cascades, facilitating prominent cell polarization by establishing front–back polarity and creating cell rear. Myosin IIB initiates cell polarization and coordinates with the major isoform myosin IIA-assembled stress fibres, to power the directional migration of cells in the three-dimensional matrix.     

Stress intensity factor analysis of a three-dimensional interface crack between dissimilar anisotropic materials

A new numerical method to calculate the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials was developed. In this study, the M-integral method was employed for mode separation of the SIFs. The moving least-square method was utilized to calculate the M-integral. Using the M-integral with the moving least-square method, SIFs can be automatically calculated with only the nodal displacements from the finite element method (FEM). Here, SIFs analyses of some typical three-dimensional problems are demonstrated. Excellent agreement was achieved between the numerical results obtained by the present method and the corresponding results proposed by other researchers. In addition, the SIFs of a single-edge crack, a through crack, and a semi-circular crack between two anisotropic solids in three-dimensional structures were analyzed.     

Analytical stress intensity factor solutions for resistance and friction stir spot welds in lap-shear specimens of different materials and thicknesses

In this paper, analytical stress intensity factor and J integral solutions for resistance and friction stir spot welds without and with gap and bend in lap-shear specimens of different materials and thicknesses are developed. The J integral and stress intensity factor solutions for spot welds are first presented in terms of the structural stresses for a strip model. Analytical structural stress solutions for spot welds without and with gap and bend in lap-shear specimens are then developed based on the closed-form structural stress solutions for a rigid inclusion in a finite thin plate subjected to various loading conditions. With the available structural stress solutions, the analytical J integral and stress intensity factor solutions can be obtained as functions of the applied load, the elastic material property parameters, and the geometric parameters of the weld and specimen. The analytical stress intensity factor solutions are selectively validated by the results of three-dimensional finite element analyses for a spot weld with ideal geometry and for a friction stir spot weld with complex geometry, gap and bend. The stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of dissimilar magnesium, aluminum and steel sheets with equal and different thicknesses are then presented in the normalized forms as functions of the ratio of the specimen width to the weld diameter. Finally, general trends and simple estimation methods of the stress intensity factor and J integral solutions at the critical locations of spot welds in lap-shear specimens of different materials and thicknesses are given for convenient engineering applications.     

Dynamic stress intensity factors due to scattering of harmonic waves by a crack in an infinite medium

An analytical method for calculating dynamic stress intensity factors in the mixed mode (combination of opening and sliding modes) using complex functions theory is presented. The crack is in infinite medium and subjected to the plane harmonic waves. The basis of the method is grounded on solving the two‐dimensional wave equations in the frequency domain and complex plane using mapping technique. In this domain, solution of the resulting partial differential equations is found in the series of the Hankel functions with unknown coefficients. Applying the boundary conditions of the crack, these coefficients are calculated. After solving the wave equations, the stress and displacement fields, also the J‐integrals are obtained. Finally using the J‐integrals, dynamic stress intensity factors are calculated. Numerical results including the values of dynamic stress intensity factors for a crack in an infinite medium subjected to the dilatation and shear harmonic waves are presented.     

On the effect of shear stresses on the fibre failure behaviour in CFRP

Parts made of carbon fibre reinforced plastics (CFRP) are being increasingly used in high performance parts subjected to very high loads. Nevertheless, the failure behaviour of these materials is still not understood completely. One important open question is whether superimposed shear stresses influence the fibre failure due to high fibre parallel tension or compression. Under these loading conditions the predictions of common failure criteria, e.g. Tsai/Wu, Hashin and Puck, are inconsistent with one another. At the Institute of Plastics Processing (IKV) in Aachen, Germany, extensive mechanical tests are conducted to clarify this situation by experimental results. The outcome so far shows that there is no significant effect of a shear stress on the fibre parallel tensile strength. The effect on the fibre parallel compression strength is not clear without ambiguity. A low shear stress does not cause a reduction of the strength, whereas shear of moderate magnitude seems to promote the development of a compression failure of the fibres. Nevertheless, this statement needs to be verified, because the loading case of fibre parallel compression combined with high superimposed shear stress could not be examined so far.