Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems

Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion. In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research. The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting. The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

The interplay between chondrocyte redifferentiation pellet size and oxygen concentration

Chondrocytes dedifferentiate during ex vivo expansion on 2-dimensional surfaces. Aggregation of the expanded cells into 3-dimensional pellets, in the presence of induction factors, facilitates their redifferentiation and restoration of the chondrogenic phenotype. Typically 1×105–5×105 chondrocytes are aggregated, resulting in “macro” pellets having diameters ranging from 1–2 mm. These macropellets are commonly used to study redifferentiation, and recently macropellets of autologous chondrocytes have been implanted directly into articular cartilage defects to facilitate their repair. However, diffusion of metabolites over the 1–2 mm pellet length-scales is inefficient, resulting in radial tissue heterogeneity. Herein we demonstrate that the aggregation of 2×105 human chondrocytes into micropellets of 166 cells each, rather than into larger single macropellets, enhances chondrogenic redifferentiation. In this study, we describe the development of a cost effective fabrication strategy to manufacture a microwell surface for the large-scale production of micropellets. The thousands of micropellets were manufactured using the microwell platform, which is an array of 360×360 µm microwells cast into polydimethylsiloxane (PDMS), that has been surface modified with an electrostatic multilayer of hyaluronic acid and chitosan to enhance micropellet formation. Such surface modification was essential to prevent chondrocyte spreading on the PDMS. Sulfated glycosaminoglycan (sGAG) production and collagen II gene expression in chondrocyte micropellets increased significantly relative to macropellet controls, and redifferentiation was enhanced in both macro and micropellets with the provision of a hypoxic atmosphere (2% O2). Once micropellet formation had been optimized, we demonstrated that micropellets could be assembled into larger cartilage tissues. Our results indicate that micropellet amalgamation efficiency is inversely related to the time cultured as discreet microtissues. In summary, we describe a micropellet production platform that represents an efficient tool for studying chondrocyte redifferentiation and demonstrate that the micropellets could be assembled into larger tissues, potentially useful in cartilage defect repair.

Influence of drying conditions on the moisture diffusion during single stage and two stage fluidized bed drying of bovine intestine for pet food

Bovine intestine samples were heat pump fluidized bed dried at atmospheric pressure and at temperatures below and above the material freezing points equipped with a continuous monitoring system. The investigation of the drying characteristics has been conducted in the temperature range -10~25oC and the airflow in the range 1.5~2.5 m/s. Some experiments were conducted as a single temperature drying experiments and others as two stage drying experiments employing two temperatures. An Arrhenius-type equation was used to interpret the influence of the drying air parameters on the effective diffusivity, calculated with the method of slopes in terms of energy activation, and this was found to be sensitivity of the temperature. The effective diffusion coefficient of moisture transfer was determined by Fickian method using uni-dimensional moisture movement in both moisture, removal by evaporation and combined sublimation and evaporation. Correlations expressing the effective moisture diffusivity and drying temperature are reported.

Automatic query expansion : a structural linguistic perspective

A user’s query is considered to be an imprecise description of their information need. Automatic query expansion is the process of reformulating the original query with the goal of improving retrieval effectiveness. Many successful query expansion techniques ignore information about the dependencies that exist between words in natural language. However, more recent approaches have demonstrated that by explicitly modeling associations between terms significant improvements in retrieval effectiveness can be achieved over those that ignore these dependencies. State-of-the-art dependency-based approaches have been shown to primarily model syntagmatic associations. Syntagmatic associations infer a likelihood that two terms co-occur more often than by chance. However, structural linguistics relies on both syntagmatic and paradigmatic associations to deduce the meaning of a word. Given the success of dependency-based approaches and the reliance on word meanings in the query formulation process, we argue that modeling both syntagmatic and paradigmatic information in the query expansion process will improve retrieval effectiveness. This article develops and evaluates a new query expansion technique that is based on a formal, corpus-based model of word meaning that models syntagmatic and paradigmatic associations. We demonstrate that when sufficient statistical information exists, as in the case of longer queries, including paradigmatic information alone provides significant improvements in retrieval effectiveness across a wide variety of data sets. More generally, when our new query expansion approach is applied to large-scale web retrieval it demonstrates significant improvements in retrieval effectiveness over a strong baseline system, based on a commercial search engine.

First-principle studies of the formation and diffusion of hydrogen vacancies in magnesium hydride

Ab initio density functional theory (DFT) calculations are performed to study the formation and diffusion of hydrogen vacancies on MgH2(110) surface and in bulk. We find that the formation energies for a single H-vacancy increase slightly from the surface to deep layers. The energies for creating adjacent surface divancacies at two inplane sites and at an inplane and a bridge site are even smaller than that for the formation of a single H-vacancy, a fact that is attributed to the strong vacancy−vacancy interactions. The diffusion of an H-vacancy from an in-plane site to a bridge site on the surface has the smallest activation barrier calculated at 0.15 eV and should be fast at room temperature. The activation barriers computed for H-vacancy diffusion from the surface into sublayers are all less than 0.70 eV, which is much smaller than the activation energy for desorption of hydrogen on the MgH2(110) surface (1.78−2.80 eV/H2). This suggests that surface desorption is more likely than vacancy diffusion to be rate determining, such that finding effective catalyst on the MgH2 surface to facilitate desorption will be very important for improving overall dehydrogenation performance.

Atomic hydrogen diffusion in novel magnesium nanostructures : the impact of incorporated subsurface carbon atoms

Ab initio Density Functional Theory (DFT) calculations are performed to study the diffusion of atomic hydrogen on a Mg(0001) surface and their migration into the subsurface layers. A carbon atom located initially on a Mg(0001) surface can migrate into the sub-surface layer and occupy a fcc site, with charge transfer to the C atom from neighboring Mg atoms. The cluster of postively charged Mg atoms surrounding a sub-surface C is then shown to facilitate the dissociative chemisorption of molecular hydrogen on the Mg(0001) surface, and the surface migration and subsequent diffusion into the subsurface of atomic hydrogen. This helps rationalize the experimentally-observed improvement in absorption kinetics of H2 when graphite or single walled carbon nanotubes (SWCNT) are introduced into the Mg powder during ball milling.

Computer modeling of diffusion in biological tissues

Molecular-level computer simulations of restricted water diffusion can be used to develop models for relating diffusion tensor imaging measurements of anisotropic tissue to microstructural tissue characteristics. The diffusion tensors resulting from these simulations can then be analyzed in terms of their relationship to the structural anisotropy of the model used. As the translational motion of water molecules is essentially random, their dynamics can be effectively simulated using computers. In addition to modeling water dynamics and water-tissue interactions, the simulation software of the present study was developed to automatically generate collagen fiber networks from user-defined parameters. This flexibility provides the opportunity for further investigations of the relationship between the diffusion tensor of water and morphologically different models representing different anisotropic tissues.

A study of the diffusion characteristics of normal, delipidized and relipidized articular cartilage using magnetic resonance imaging

This paper assesses the capacity to provide semipermeability of the synthetic layer of surface-active phospholipids created to replace the depleted surface amorphous layer of articular cartilage. The surfaces of articular cartilage specimens in normal, delipidized, and relipidized conditions following incubation in dipalmitoyl-phosphatidylcholine and palmitoyl-oleoyl-phosphatidylcholine components of the joint lipid mixture were characterized nanoscopically with the atomic force microscope and also imaged as deuterium oxide (D2O) diffused transiently through these surfaces in a magnetic resonance imaging enclosure. The MR images were then used to determine the apparent diffusion coefficients in a purpose-built MATLAB®-based algorithm. Our results revealed that all surfaces were permeable to D2O, but that there was a significant difference in the semipermeability of the surfaces under the different conditions, relative to the apparent diffusion coefficients. Based on the results and observations, it can be concluded that the synthetic lipid that is deposited to replace the depleted SAL of articular cartilage is capable of inducing some level of semipermeability.

Term associations in query expansion : a structural linguistic perspective

Many successful query expansion techniques ignore information about the term dependencies that exist within natural language. However, researchers have recently demonstrated that consistent and significant improvements in retrieval effectiveness can be achieved by explicitly modelling term dependencies within the query expansion process. This has created an increased interest in dependency-based models. State-of-the-art dependency-based approaches primarily model term associations known within structural linguistics as syntagmatic associations, which are formed when terms co-occur together more often than by chance. However, structural linguistics proposes that the meaning of a word is also dependent on its paradigmatic associations, which are formed between words that can substitute for each other without effecting the acceptability of a sentence. Given the reliance on word meanings when a user formulates their query, our approach takes the novel step of modelling both syntagmatic and paradigmatic associations within the query expansion process based on the (pseudo) relevant documents returned in web search. The results demonstrate that this approach can provide significant improvements in web re- trieval effectiveness when compared to a strong benchmark retrieval system.

International tax and the Australian wine industry: Is your client’s product destined to sail the seven seas?

The export market for Australian wine continues to grow at a rapid rate, with imported wines also playing a role in market share in sales in Australia. It is estimated that over 60 per cent of all Australian wine is exported, while 12 per cent of wine consumed in Australia has overseas origins. In addition to understanding the size and direction (import or export) of wines, the foreign locales also play an important role in any tax considerations. While the export market for Australian produced alcohol continues to grow, it is into the Asian market that the most significant inroads are occurring. Sales into China of bottled wine over $7.50 per litre recently overtook the volume sold our traditional partners of the United States and Canada. It is becoming easier for even small to medium sized businesses to export their services or products overseas. However, it is vital for those businesses to understand the tax rules applying to any international transactions. Specifically, one of the first tax regimes that importers and exporters need to understand once they decide to establish a presence overseas is transfer pricing. These are the rules that govern the cross-border prices of goods, services and other transactions entered into between related parties. This paper is Part 2 of the seminar presented on transfer pricing and international tax issues which are particularly relevant to the wine industry. The predominant focus of Part 2 is to discuss four key areas likely to affect international expansion. First, the use of the available transfer pricing methodologies for international related party transactions is discussed. Second, the affects that double tax agreements will have on taking a business offshore are considered. Third, the risks associated with aggressive tax planning through tax information exchange agreements is reviewed. Finally, the paper predicts future ‘trip-wires’ and areas to ‘watch out for’ for practitioners dealing with clients operating in the international arena.

Numerical simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

A closed-form approximation for pricing temperature-based weather derivatives

This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If the deviations of daily temperatures from their expected values are modelled as an Ornstein-Uhlenbeck process with timevarying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records are a particularly poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.

Metrological performances of a diffusion charger particle counter for personal monitoring

Airborne particles have been shown to be associated with a wide range of adverse health effects, which has led to a recent increase in medical research to gain better insight into their health effects. However, accurate evaluation of the exposure-dose-response relationship is highly dependent on the ability to track actual exposure levels of people to airborne particles. This is quite a complex task, particularly in relation to submicrometer and ultrafine particles, which can vary quite significantly in terms of particle surface area and number concentrations. Therefore, suitable monitors that can be worn for measuring personal exposure to these particles are needed. This paper presents an evaluation of the metrological performance of six diffusion charger sensors, NanoTracer (Philips Aerasense) monitors, when measuring particle number and surface area concentrations, as well as particle number distribution mean when compared to reference instruments. Tests in the laboratory (by generating monodisperse and polydisperse aerosols) and in the field (using natural ambient particles) were designed to evaluate the response of these devices under both steady-state and dynamics conditions. Results showed that the NanoTracers performed well when measuring steady state aerosols, however they strongly underestimated actual concentrations during dynamic response testing. The field experiments also showed that, when the majority of the particles were smaller than 20 nm, which occurs during particle formation events in the atmosphere, the NanoTracer underestimated number concentration quite significantly. Even though the NanoTracer can be used for personal monitoring of exposure to ultrafine particles, it also has limitations which need to be considered in order to provide meaningful results.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.