Calcium ions promote osteogenic differentiation and mineralization of human dental pulp cells : implication for pulp capping materials

Calcium (Ca) is the main element of most pulp capping materials and plays an essential role in mineralization. Different pulp capping materials can release various concentrations of Ca ions leading to different clinical outcomes. The purpose of this study was to investigate the effects of various concentrations of Ca ions on the growth and osteogenic differentiation of human dental pulp cells (hDPCs). Different concentrations of Ca ions were added to growth culture medium and osteogenic inductive culture medium. A Cell Counting Kit-8 (CCK-8) was used to determine the proliferation of hDPCs in growth culture medium. Osteogenic differentiation and mineralization were measured by alkaline phosphatase (ALP) assay, Alizarin red S/von kossa staining, calcium content quantitative assay. The selected osteogenic differentiation markers were investigated by quantitative real-time polymerase chain reaction (qRT-PCR). Within the range of 1.8–16.2 mM, increased concentrations of Ca ions had no effect on cell proliferation, but led to changes in osteogenic differentiation. It was noted that enhanced mineralized matrix nodule formation was found in higher Ca ions concentrations; however, ALP activity and gene expression were reduced. qRT-PCR results showed a trend towards down-regulated mRNA expression of type I collagen (COL1A2) and Runx2 at elevated concentrations of Ca ions, whereas osteopontin (OPN) and osteocalcin (OCN) mRNA expression was significantly up-regulated. Ca ions content in the culture media can significantly influence the osteogenic properties of hDPCs, indicating the importance of optimizing Ca ions release from dental pulp capping materials in order to achieve desirable clinical outcomes.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum.

Diffusion determinants for passive building technologies

This summary is based on an international review of leading peer reviewed journals, in both technical and management fields. It draws on highly cited articles published between 2000 and 2009 to investigate the research question, "What are the diffusion determinants for passive building technologies in Australia?". Using a conceptual framework drawn from the innovation systems literature, this paper synthesises and interprets the literature to map the current state of passive building technologies in Australia and to analyse the drivers for, and obstacles to, their optimal diffusion. The paper concludes that the government has a key role to play through its influence over the specification of building codes.

Corona ions from high-voltage power lines : nature of emission and dispersion

Positive and negative small ions, aerosol ion and number concentration and dc electric fields were monitored at an overhead high-voltage power line site. We show that the emission of corona ions was not spatially uniform along the lines and occurred from discrete components such as a particular set of spacers. Maximum ion concentrations and atmospheric dc electric fields were observed at a point 20 m downwind of the lines. It was estimated that less than 7% of the total number of aerosol particles was charged. The electrical parameters decreased steadily with further downwind distance but remained significantly higher than background.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

The cementogenic differentiation of periodontal ligament cells via the activation of Wnt/β-catenin signalling pathway by Li+ ions released from bioactive scaffolds

Lithium (Li) has been widely used as a long-term mood stabilizer in the treatment of bipolar and depressive disorders. Li+ ions are thought to enhance the remyelination of peripheral nerves and also stimulate the proliferation of neural progenitor cells and retinoblastoma cells via activation of the Wnt/β-catenin signalling pathway. Until now there have been no studies reporting the biological effects of released Li+ in bioactive scaffolds on cemetogenesis in periodontal tissue engineering applications. In this study, we incorporated parts of Li+ ions into the mesoporous bioactive glass (MBG) scaffolds and showed that this approach yielded scaffolds with a favourable composition, microstructure and mesopore properties for cell attachment, proliferation, and cementogenic differentiation of human periodontal ligament-derived cells (hPDLCs). We went on to investigate the biological effects of Li+ ions themselves on cell proliferation and cementogenic differentiation. The results showed that 5% Li+ ions incorporated into MBG scaffolds enhanced the proliferation and cementogenic differentiation of hPDLCs on scaffolds, most likely via activation of Wnt/β-catenin signalling pathway. Further study demonstrated that Li+ ions by themselves significantly enhanced the proliferation, differentiation and cementogenic gene expression of PDLCs. Our results indicate that incorporation of Li+ ions into bioactive scaffolds is a viable means of enhancing the Wnt canonical signalling pathway to stimulate cementogenic differentiation of PDLCs.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Preparation, characterisation and in vivo osteogenesis of mesoporous bioactive glasses

Bone defects, especially large bone defects, remain a major challenge in orthopaedic surgery. Autologous bone transplantation is considered the most effective treatment, but insufficient donor tissue, coupled with concerns about donor site morbidity, has hindered this approach in large-scale applications. Alternative approaches include implanting biomaterials such as bioactive glass (BG), which has been widely used for bone defect healing, due to having generally good biocompatibility, and can be gradually biodegraded during the process of new bone formation. Mesoporous bioactive glass (MBG) is a newly developed bioactive glass which has been proven to have enhanced in-vitro bioactivity; however the in-vivo osteogenesis has not been studied. A critical problem in using the bone tissue engineering approach to restore large bone defects is that the nutrient supply and cell viability at the centre of the scaffold is severely hampered since the diffusion distance of nutrients and oxygen for cell survival is limited to 150-200µm. Cobalt ions has been shown to mimic hypoxia, which plays a pivotal role in coupling angiogenesis with osteogenesis in-vivo by activating hypoxia inducing factor-1α (HIF-1α) transcription factor, subsequently initiating the expression of genes associated with tissue regeneration. Therefore, one aim of this study is to investigate the in-vivo osteogenesis of MBG by comparison with BG and β-TCP, which are widely used clinically. The other aim is to explore hypoxia-mimicking biomaterials by incorporating Cobalt into MBG and β-TCP. MBG and β-TCP incorporated with 5% cobalt (5Co-MBG and 5CCP) have also been studied in-vivo to determine whether the hypoxic effect has a beneficial effect on the bone formation. The composition and microstructure of synthesised materials (BG, MBG, 5Co-MBG, 5CCP) were characterised, along with the mesopore properties of the MBG materials. Dissolution and cytotoxicity of the Co-containing materials were also investigated. Femoral samples with defects harvested at 4 and 8 weeks were scanned using micro-CT followed by processing for histology (H&E staining) to determine bone formation. Histology of MBG showed a slower rate of bone formation at 4 weeks than BG, however at 8 weeks it could be clearly seen that MBG had more bone formation. The in-vivo results show that the osteogenesis of MBG reciprocates the enhanced performance shown in-vitro compared to BG. Dissolution study showed that Co ions can be efficiently released from MBG and β-TCP in a controllable way. Low amounts of Co incorporated into the MBG and β-TCP showed no significant cytotoxicity and the Co-MBG powders maintained a mesopore structure although not as highly ordered as pure MBG. Preliminary study has shown that Co incorporated samples showed little to no bone formation, instead incurring high lymphocyte activity. Further studies need to be done on Co incorporated materials to determine the cause for high lymphocyte activity in-vivo, which appear to hinder bone formation. In conclusion, this study demonstrated the osteogenic activity of MBG and provided some valuable information of tissue reaction to Co-incorporated MBG and TCP materials.