Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

A hardware-based multi-disciplinary design optimization method for aeronautical applications

There are many applications in aeronautics where there exist strong couplings between disciplines. One practical example is within the context of Unmanned Aerial Vehicle(UAV) automation where there exists strong coupling between operation constraints, aerodynamics, vehicle dynamics, mission and path planning. UAV path planning can be done either online or offline. The current state of path planning optimisation online UAVs with high performance computation is not at the same level as its ground-based offline optimizer's counterpart, this is mainly due to the volume, power and weight limitations on the UAV; some small UAVs do not have the computational power needed for some optimisation and path planning task. In this paper, we describe an optimisation method which can be applied to Multi-disciplinary Design Optimisation problems and UAV path planning problems. Hardware-based design optimisation techniques are used. The power and physical limitations of UAV, which may not be a problem in PC-based solutions, can be approached by utilizing a Field Programmable Gate Array (FPGA) as an algorithm accelerator. The inevitable latency produced by the iterative process of an Evolutionary Algorithm (EA) is concealed by exploiting the parallelism component within the dataflow paradigm of the EA on an FPGA architecture. Results compare software PC-based solutions and the hardware-based solutions for benchmark mathematical problems as well as a simple real world engineering problem. Results also indicate the practicality of the method which can be used for more complex single and multi objective coupled problems in aeronautical applications.

A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Simulations of the effect of waveguide cross-section on quantum dot – plasmon coupling

Quantum dot - plasmon waveguide systems are of interest for the active control of plasmon propagation, and consequently, the development of active nanophotonic devices such as nano-sized optical transistors. This paper is concerned with how varying aspect ratio of the waveguide crosssection affects the quantum dot - plasmon coupling. We compare a stripe waveguide with an equivalent nanowire, illustrating that both waveguides have a similar coupling strength to a nearby quantum dot for small waveguide cross-section, thereby indicating that stripe lithographic waveguides have strong potential use in quantum dot –plasmon waveguide systems. We also demonstrate that changing the aspect ratio of both stripe and wire waveguides can increase the spontaneous emission rate of the quantum dot into the plasmon mode, by up to a factor of five. The results of this paper will contribute to the optimisation of quantum dot - plasmon waveguide systems and help pave the way for the development of active nanophotonics devices.

Development of the sustainable building and construction products industry in Australia

This paper draws on a major study the authors conducted for the Australian Government in 2009. It focuses on the diffusion issues surrounding the uptake of sustainable building and construction products in Australia. Innovative sustainable products can minimise the environmental impact during construction, while maximising asset performance, durability and re-use. However, there are significant challenges faced by designers and clients in the selection of appropriate sustainable products in consideration of the integrated design solution, including overall energy efficiency, water conservation, maintenance and durability, low-impact use and consumption. The paper is a review of the current state of sustainable energy and material product innovations in Australia. It examines the system dynamics surrounding these innovations as well as the drivers and obstacles to their diffusion throughout the Australian construction industry. The case product types reviewed comprise: solar energy technology, small wind turbines, advanced concrete technology, and warm-mixed asphalt. The conclusions highlight the important role played by Australian governments in facilitating improved adoption rates. This applies to governments in their various roles, but particularly as clients/owners, regulators, and investors in education, training, research and development. In their role as clients/owners, the paper suggests that government can better facilitate innovation within the construction industry by adjusting specification policies to encourage the uptake of sustainable products. In the role as regulators, findings suggest governments should be encouraging the application of innovative finance options and positive end-user incentives to promote sustainable product uptake. Also, further education for project-based firms and the client/end users about the long-term financial and environmental benefits of innovative sustainable products is required. As more of the economy’s resources are diverted away from business-as-usual and into the use of sustainable products, some project-based firms may face short-term financial pain in re-shaping their businesses. Government policy initiatives can encourage firms make the necessary adjustments to improve innovative sustainable product diffusion throughout the industry.