A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Composite electrospun scaffolds for engineering tubular bone grafts

In this study, poly (e-caprolactone) [PCL] and its collagen composite blend (PCL=Col) were fabricated to scaffolds using electrospinning method. Incorporated collagen was present on the surface of the fibers, and it modulated the attachment and proliferation of pig bone marrow mesenchymal cells (pBMMCs). Osteogenic differentiation markers were more pronounced when these cells were cultured on PCL=Col fibrous meshes, as determined by immunohistochemistry for collagen type I, osteopontin, and osteocalcin. Matrix mineralization was observed only on osteogenically induced PCL=Col constructs. Long bone analogs were created by wrapping osteogenic cell sheets around the PCL=Col meshes to form hollow cylindrical cell-scaffold constructs. Culturing these constructs under dynamic conditions enhanced bone-like tissue formation and mechanical strength.We conclude that electrospun PCL=Col mesh is a promising material for bone engineering applications. Its combination with osteogenic cell sheets offers a novel and promising strategy for engineering of tubular bone analogs.

The effect of unlocking RGD-motifs in collagen I on pre-osteoblast adhesion and differentiation

Denaturation of extracellular matrix proteins exposes cryptic binding sites. It is hypothesized that binding of cell adhesion receptors to these cryptic binding sites regulates cellular behaviour during tissue repair and regeneration. To test this hypothesis, we quantify the adhesion of pre-osteoblastic cells to native (Col) and partially-denatured (pdCol) collagen I using single-cell force spectroscopy. During early stages of cell attachment (≤180 s) pre-osteoblasts (MC3T3-E1) adhered significantly stronger to pdCol compared to Col. RGD (Arg-Gly-Asp)-containing peptides suppressed this elevated cell adhesion. We show that the RGD-binding α5β1- and αv-integrins mediated pre-osteoblast adhesion to pdCol, but not to Col. On pdCol pre-osteoblasts had a higher focal adhesion kinase tyrosine-phosphorylation level that correlated with enhanced spreading and motility. Moreover, pre-osteoblasts cultured on pdCol showed a pronounced matrix mineralization activity. Our data suggest that partially-denatured collagen exposes RGD-motifs that trigger binding of α5β1- and αv-integrins. These integrins initiate cellular processes that stimulate osteoblast adhesion, spreading, motility and differentiation. Taken together, these quantitative insights reveal an approach for the development of alternative collagen I- based surfaces for tissue engineering applications.

In vitro and in vivo analysis of co-electrospun scaffolds made of medical grade poly(epsilon-caprolactone) and porcine collagen

In this study, a nanofiber mesh made by co-electrospinning medical grade poly(epsilon-caprolactone) and collagen (mPCL/Col) was fabricated and studied. Its mechanical properties and characteristics were analyzed and compared to mPCL meshes. mPCL/Col meshes showed a reduction in strength but an increase in ductility when compared to PCL meshes. In vitro assays revealed that mPCL/Col supported the attachment and proliferation of smooth muscle cells on both sides of the mesh. In vivo studies in the corpus cavernosa of rabbits revealed that the mPCL/Col scaffold used in conjunction with autologous smooth muscle cells resulted in better integration with host tissue when compared to cell free scaffolds. On a cellular level preseeded scaffolds showed a minimized foreign body reaction.

Combining electrospun scaffolds with electrosprayed hydrogels leads to three-dimensional cellularization of hybrid constructs

A common problem in the design of tissue engineered scaffolds using electrospun scaffolds is the poor cellular infiltration into the structure. To tackle this issue, three approaches to scaffold design using electrospinning were investigated: selective leaching of a water-soluble fiber phase (poly ethylene oxide (PEO) or gelatin), the use of micron-sized fibers as the scaffold, and a combination of micron-sized fibers with codeposition of a hyaluronic acid-derivative hydrogel, Heprasil. These designs were achieved by modifying a conventional electrospinning system with two charged capillaries and a rotating mandrel collector. Three types of scaffolds were fabricated: medical grade poly(epsilon-caprolactone)/collagen (mPCL/Col) cospun with PEO or gelatin, mPCL/Col meshes with micron-sized fibers, and mPCL/Col microfibers cosprayed with Heprasil. All three scaffold types supported attachment and proliferation of human fetal osteoblasts. However, selective leaching only marginally improved cellular infiltration when compared to meshes obtained by conventional electrospinning. Better cell penetration was seen in mPCL/Col microfibers, and this effect was more pronounced when Heprasil regions were present in the structure. Thus, such techniques could be further exploited for the design of cell permeable fibrous meshes for tissue engineering applications.

Frequency Domain Characterization Of Sliding Mode Control Of An Inverter Used In DSTATCOM Application

In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode

This article deals with the non-linear oscillations assessment of a distribution static comensator ooperating in voltage control mode using the bifurcation theory. A mathematical model of the distribution static compensator in the voltage control mode to carry out the bifurcation analysis is derived. The stabiity regions in the Thevein equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers are computed. The AC and DC capacitor impacts on the stability are analyzed through the bifurcation theory. The observations are verified through simulaation studies. The computation of the stability region allows the assessment of the stable operating zones for a power system that includes a distribution static compensator operating in the voltage mode.

Of ivory towers and boundary spanners

We all live in a yellow submarine… When I go to work in the morning, in the office building that hosts our BPM research group, on the way up to our level I come by this big breakout room that hosts a number of computer scientists, working away at the next generation software algorithms and iPad applications (I assume). I have never actually been in that room, but every now and then the door is left ajar for a while and I can spot couches, lots (I mean, lots!) of monitors, the odd scientist, a number of Lara Croft posters, and the usual room equipment you’d probably expect from computer scientists (and, no, it’s not like that evil Dennis guy from the Jurassic Park movie, buried in chips, coke, and flickering code screens… It’s also not like the command room from the Nebuchadnezzar, Neo’s hovercraft in the Matrix movies, although I still strongly believe these green lines of code make a good screensaver).

Subchondral bone osteoblasts can induce chondrocyte mineralization during osteoarthritis and this process is relevant to cartilage degradation

Pathological mineralization of articular cartilage is a characteristic feature of osteoarthritis (OA); however, the underlying mechanisms, and their relevance to cartilage degeneration, are not clear. The involvement of subchondral bone changes in OA have been reported previously with the characterization of abnormal subchondral bone mineral density (BMD), osteiod volume, altered bone mechanical parameters and an increase in bone turnover markers. A number of osteoarthritic animal models have demonstrated that subchondral bone changes often precede cartilage degeneration. In this study site specific localization of mineralization markers were detected in the OA cartilage. Chondrocytes and osteoblasts derived from OA cartilage and subchondral bone showed a significant increase in the mRNA expressions of mineralization markers. Interestingly, osteoblasts from OA subchondral bone could significantly decrease cartilage matrix expression; whereas, increase mineralization of chondrocytes (Figure 1). Osteogenic factors, such as CBFA1, ALP, and type X collagen (Col-X), were detected in chondrocytes under mineralization conditions (Figure 2). Furthermore, chondrocyte mineralization was followed by increased mRNA and protein levels of MMP-2, MMP-9 and MMP-13, all of which are detrimental to cartilage integrity in vivo. The data reported here suggests that the upregulation of subchondral bone-mineralization, typical of OA progression, causes cartilage mineralization, and that the mineralization of chondrocytes induce increased MMP levels with a subsequent degradation of the articular cartilage.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.