Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.

Spin injection in two-dimensional layered materials and local magnetoresistance side-effects

180 p.

Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.

Blind column selection protocol for two-dimensional high performance liquid chromatography

The selection of two orthogonal columns for two-dimensional high performance liquid chromatography (LC×LC) separation of natural product extracts can be a labour intensive and time consuming process and in many cases is an entirely trial-and-error approach. This paper introduces a blind optimisation method for column selection of a black box of constituent components. A data processing pipeline, created in the open source application OpenMS®, was developed to map the components within the mixture of equal mass across a library of HPLC columns; LC×LC separation space utilisation was compared by measuring the fractional surface coverage, fcoverage. It was found that for a test mixture from an opium poppy (Papaver somniferum) extract, the combination of diphenyl and C18 stationary phases provided a predicted fcoverage of 0.48 and was matched with an actual usage of 0.43. OpenMS®, in conjunction with algorithms designed in house, have allowed for a significantly quicker selection of two orthogonal columns, which have been optimised for a LC×LC separation of crude extractions of plant material.

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional (2-D) Markovian jump systems (MJSs) described by the Roesser model with interval time-varying delays. The transition probabilities of the jumping process/Markov chain are assumed to be uncertain, that is, they are not exactly known but can be estimated. A Lyapunov-like scheme is first extended to 2-D MJSs with delays. Based on some novel 2-D summation inequalities proposed in this paper, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs) which can be computationally solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Stationary phase characterisation and method development for fast two-dimensional HPLC

Fundamental improvements to the experimental protocol of two-dimensional high performance liquid chromatography were developed to accomplish truly quantitative analyses of complex natural products. This included developing novel measurement techniques to elucidate the retention behaviour of monolithic columns. Approaches to streamline chromatographic method development were also explored.

Three-dimensional slope stability charts for frictional fill materials placed on purely cohesive clay

This paper investigates slope stability and produces a set of stability charts for three-dimensional (3D) slopes for a specific case in which frictional fill materials are placed on purely cohesive clay. As slopes are not usually plane strain in nature and are influenced by physical boundaries, this study uses a 3D analysis using the finite-element LB limit analysis method. Stability charts are convenient tools for geotechnical engineers during design in practice. For comparison purposes, the results from two-dimensional (2D) analyses are also discussed. The results from this study quantify the increase in the factors of safety obtained when 3D conditions are analyzed as opposed to the more traditional 2D.

Topological insulating phases from two-dimensional nodal loop semimetals

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator’s Chern number is the phase-winding number of the mass gap terms on the loop.We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field’s vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

Amniotic fluid stem cells produce robust mineral deposits on biodegradable scaffolds

Insufficient availability of osteogenic cells limits bone regeneration through cell-based therapies. This study investigated the potential of amniotic fluid–derived stem (AFS) cells to synthesize mineralized extracellular matrix within porous medical-grade poly-e-caprolactone (mPCL) scaffolds. The AFS cells were initially differentiated in two-dimensional (2D) culture to determine appropriate osteogenic culture conditions and verify physiologic mineral production by the AFS cells. The AFS cells were then cultured on 3D mPCL scaffolds (6-mm diameter9-mm height) and analyzed for their ability to differentiate to osteoblastic cells in this environment. The amount and distribution of mineralized matrix production was quantified throughout the mPCL scaffold using nondestructive micro computed tomography (microCT) analysis and confirmed through biochemical assays. Sterile microCT scanning provided longitudinal analysis of long-term cultured mPCL constructs to determine the rate and distribution of mineral matrix within the scaffolds. The AFS cells deposited mineralized matrix throughout the mPCL scaffolds and remained viable after 15 weeks of 3D culture. The effect of predifferentiation of the AFS cells on the subsequent bone formation in vivo was determined in a rat subcutaneous model. Cells that were pre-differentiated for 28 days in vitro produced seven times more mineralized matrix when implanted subcutaneously in vivo. This study demonstrated the potential of AFS cells to produce 3D mineralized bioengineered constructs in vitro and in vivo and suggests that AFS cells may be an effective cell source for functional repair of large bone defects

Interactions between human osteoblasts and prostate cancer cells in a novel 3D in vitro model

Cell-cell and cell-matrix interactions play a major role in tumor morphogenesis and cancer metastasis. Therefore, it is crucial to create a model with a biomimetic microenvironment that allows such interactions to fully represent the pathophysiology of a disease for an in vitro study. This is achievable by using three-dimensional (3D) models instead of conventional two-dimensional (2D) cultures with the aid of tissue engineering technology. We are now able to better address the complex intercellular interactions underlying prostate cancer (CaP) bone metastasis through such models. In this study, we assessed the interaction of CaP cells and human osteoblasts (hOBs) within a tissue engineered bone (TEB) construct. Consistent with other in vivo studies, our findings show that intercellular and CaP cell-bone matrix interactions lead to elevated levels of matrix metalloproteinases, steroidogenic enzymes and the CaP biomarker, prostate specific antigen (PSA); all associated with CaP metastasis. Hence, it highlights the physiological relevance of this model. We believe that this model will provide new insights for understanding of the previously poorly understood molecular mechanisms of bone metastasis, which will foster further translational studies, and ultimately offer a potential tool for drug screening. © 2010 Landes Bioscience.

Bioengineered 3D platform to explore cell-ECM interactions and drug resistance of epithelial ovarian cancer cells

The behaviour of cells cultured within three-dimensional (3D) structures rather than onto two-dimensional (2D) culture plastic more closely reflects their in vivo responses. Consequently, 3D culture systems are becoming crucial scientific tools in cancer cell research. We used a novel 3D culture concept to assess cell-matrix interactions implicated in carcinogenesis: a synthetic hydrogel matrix equipped with key biomimetic features, namely incorporated cell integrin-binding motifs (e.g. RGD peptides) and the ability of being degraded by cell-secreted proteases (e.g. matrix metalloproteases). As a cell model, we chose epithelial ovarian cancer, an aggressive disease typically diagnosed at an advanced stage when chemoresistance occurs. Both cell lines used (OV-MZ-6, SKOV-3) proliferated similarly in 2D, but not in 3D. Spheroid formation was observed exclusively in 3D when cells were embedded within hydrogels. By exploiting the design flexibility of the hydrogel characteristics, we showed that proliferation in 3D was dependent on cell-integrin engagement and the ability of cells to proteolytically remodel their extracellular microenvironment. Higher survival rates after exposure to the anti-cancer drug paclitaxel were observed in cell spheroids grown in hydrogels (40-60%) compared to cell monolayers in 2D (20%). Thus, 2D evaluation of chemosensitivity may not reflect pathophysiological events seen in patients. Because of the design flexibility of their characteristics and their stability in long-term cultures (28 days), these biomimetic hydrogels represent alternative culture systems for the increasing demand in cancer research for more versatile, physiologically relevant and reproducible 3D matrices.

Dynamics of attacker–defender dyads in Association Football : parameters influencing decision-making

Previous work on pattern-forming dynamics of team sports has investigated sub-phases of basketball and rugby union by focussing on one-versus-one (1v1) attacker-defender dyads. This body of work has identified the role of candidate control parameters, interpersonal distance and relative velocity, in predicting the outcomes of team player interactions. These two control parameters have been described as functioning in a nested relationship where relative velocity between players comes to the fore within a critical range of interpersonal distance. The critical influence of constraints on the intentionality of player behaviour has also been identified through the study of 1v1 attacker-defender dyads. This thesis draws from previous work adopting an ecological dynamics approach, which encompasses both Dynamical Systems Theory and Ecological Psychology concepts, to describe attacker-defender interactions in 1v1 dyads in association football. Twelve male youth association football players (average age 15.3 ± 0.5 yrs) performed as both attackers and defenders in 1v1 dyads in three field positions in an experimental manipulation of the proximity to goal and the role of players. Player and ball motion was tracked using TACTO 8.0 software (Fernandes & Caixinha, 2003) to produce two-dimensional (2D) trajectories of players and the ball on the ground. Significant differences were found for player-to-ball interactions depending on proximity to goal manipulations, indicating how key reference points in the environment such as the location of the goal may act as a constraint that shapes decision-making behaviour. Results also revealed that interpersonal distance and relative velocity alone were insufficient for accurately predicting the outcome of a dyad in association football. Instead, combined values of interpersonal distance, ball-to-defender distance, attacker-to-ball distance, attacker-to-ball relative velocity and relative angles were found to indicate the state of dyad outcomes.

Hyaluronic acid : evaluation as a potential delivery vehicle for vitronectin:growth factor complexes in wound healing applications

We have previously reported that novel vitronectin:growth factor (VN:GF) complexes significantly increase re-epithelialization in a porcine deep dermal partial-thickness burn model. However, the potential exists to further enhance the healing response through combination with an appropriate delivery vehicle which facilitates sustained local release and reduced doses of VN:GF complexes. Hyaluronic acid (HA), an abundant constituent of the interstitium, is known to function as a reservoir for growth factors and other bioactive species. The physicochemical properties of HA confer it with an ability to sustain elevated pericellular concentrations of these species. This has been proposed to arise via HA prolonging interactions of the bioactive species with cell surface receptors and/or protecting them from degradation. In view of this, the potential of HA to facilitate the topical delivery of VN:GF complexes was evaluated. Two-dimensional (2D) monolayer cell cultures and 3D de-epidermised dermis (DED) human skin equivalent (HSE) models were used to test skin cell responses to HA and VN:GF complexes. Our 2D studies revealed that VN:GF complexes and HA stimulate the proliferation of human fibroblasts but not keratinocytes. Experiments in our 3D DED-HSE models showed that VN:GF complexes, both alone and in conjunction with HA, led to enhanced development of both the proliferative and differentiating layers in the DED-HSE models. However, there was no significant difference between the thicknesses of the epidermis treated with VN:GF complexes alone and VN:GF complexes together with HA. While the addition of HA did not enhance all the cellular responses to VN:GF complexes examined, it was not inhibitory, and may confer other advantages related to enhanced absorption and transport that could be beneficial in delivery of the VN:GF complexes to wounds.

Development of a 3D culture system to study the skeletal metastasis of prostate cancer

In the cancer research field, most in vitro studies still rely on two-dimensional (2D) cultures. However, the trend is rapidly shifting towards using a three-dimensional (3D) culture system. This is because 3D models better recapitulate the microenvironment of cells, and therefore, yield cellular and molecular responses that more accurately describe the pathophysiology of cancer. By adopting technology platforms established by the tissue engineering discipline, it is now possible to grow cancer cells in extracellular matrix (ECM)-like environments and dictate the biophysical and biochemical properties of the matrix. In addition, 3D models can be modified to recapitulate different stages of cancer progression for instance from the initial development of tumor to metastasis. Inevitably, to recapitulate a heterotypic condition, comprising more than one cell type, it requires a more complex 3D model. To date, 3D models that are available for studying the prostate cancer (CaP)-bone interactions are still lacking. Therefore, the aim of this study is to establish a co-culture model that allows investigation of direct and indirect CaP-bone interactions. Prior to that, 3D polyethylene glycol (PEG)-based hydrogel cultures for CaP cells were first developed and growth conditions were optimised. Characterization of the 3D hydrogel cultures show that LNCaP cells form a multicellular mass that resembles avascular tumor. In comparison to 2D cultures, besides the difference in cell morphology, the response of LNCaP cells to the androgen analogue (R1881) stimulation is different compared to the cells in 2D cultures. This discrepancy between 2D and 3D cultures is likely associated with the cell-cell contact, density and ligand-receptor interactions. Following the 3D monoculture study, a 3D direct co-culture model of CaP cells and the human tissue engineered bone (hTEBC) construct was developed. Interactions between the CaP cells and human osteoblasts (hOBs) resulted in elevation of Matrix Metalloproteinase 9 (MMP9) for PC-3 cells and Prostate Specific Antigen (PSA) for LNCaP cells. To further investigate the paracrine interaction of CaP cells and (hOBs), a 3D indirect co-culture model was developed, where LNCaP cells embedded within PEG hydrogels were co-cultured with hTEBC. It was found that the cellular changes observed reflect the early event of CaP colonizing the bone site. In the absence of androgens, interestingly, up-regulation of PSA and other kallikreins is also detected in the co-culture compared to the LNCaP monoculture. This non androgenic stimulation could be triggered by the soluble factors secreted by the hOB such as Interleukin-6. There are also decrease in alkaline phosphatase (ALP) activity and down-regulation of genes of the hOB when co-cultured with LNCaP cells that have not been previously described. These genes include transforming growth factor β1 (TGFβ1), osteocalcin and Vimentin. However, no changes to epithelial markers (e.g E-cadherin, Cytokeratin 8) were observed in both cell types from the co-culture. Some of these intriguing changes observed in the co-cultures that had not been previously described have enriched the basic knowledge of the CaP cell-bone interaction. From this study, we have shown evidence of the feasibility and versatility of our established 3D models. These models can be adapted to test various hypotheses for studies pertaining to underlying mechanisms of bone metastasis and could provide a vehicle for anticancer drug screening purposes in the future.

3D mesenchymal stem/stromal cell osteogenesis and autocrine signalling

Mesenchymal stem/stromal cells (MSC) are rapidly becoming a leading candidate for use in tissue regeneration, with first generation of therapies being approved for use in orthopaedic repair applications. Capturing the full potential of MSC will likely require the development of novel in vitro culture techniques and devices. Herein we describe the development of a straightforward surface modification of an existing commercial product to enable the efficient study of three dimensional (3D) human bone marrow-derived MSC osteogenic differentiation. Hundreds of 3D microaggregates, of either 42 or 168 cells each, were cultured in osteogenic induction medium and their differentiation was compared with that occurring in traditional two dimensional (2D) monolayer cultures. Osteogenic gene expression and matrix composition was significantly enhanced in the 3D microaggregate cultures. Additionally, BMP-2 gene expression was significantly up-regulated in 3D cultures at day 3 and 7 by approximately 25- and 30-fold, respectively. The difference in BMP-2 gene expression between 2D and 3D cultures was negligible in the more mature day 14 osteogenic cultures. These data support the notion that BMP-2 autocrine signalling is up-regulated in 3D MSC cultures, enhancing osteogenic differentiation. This study provides both mechanistic insight into MSC differentiation, as well as a platform for the efficient generation of microtissue units for further investigation or use in tissue engineering applications.