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.

Elevated concentration of TNF-a induces trophoblast differentiation in mouse blastocyst outgrowths

Elevated expression of tumour necrosis factora (TNF-a) is associated with adverse pregnancy outcome. This study has examined the expression of TNF-a and its receptors (TNF-Rs) by mouse blastocysts and blastocyst outgrowths from day 4 to 9.5 of pregnancy and investigated the effects of elevated TNF-a on the inner cell mass (ICM) and trophoblast cells of blastocyst outgrowths. RTPCR demonstrated TNF-a mRNA expression from day 7.5 to 9.5, TNF-R1 from day 6.5 to 9.5 and TNF-R2 from day 5.5 to 7.5 of pregnancy, and in situ hybridisation revealed the trophoblast giant cells (TGCs) of the early placenta as the site of TNF-a expression. Day 4 blastocysts were cultured in a physiologically high concentration of TNF-a (100 ng/ml) for 72 h to the outgrowth stage and then compared to blastocysts cultured in media alone. TNF-a-treated blastocyst outgrowths exhibited a significant reduction in ICM cells (mean € SD 23.90€10.42 vs 9.37€7.45, t-test, P<0.0001) with no significant change in the numbers of trophoblast cells (19.97€8.14 vs 21.73€7.79, t-test, P=0.39). Within the trophoblast cell population, the TNF-a-treated outgrowths exhibited a significant increase in multinucleated cells (14.10€5.53 vs 6.37€5.80, t-test, P<0.0001) and a corresponding significant decrease in mononucleated cells (5.87€3.60 vs 15.37€5.87, t-test, P<0.0001). In summary, this study describes the expression of TNF-a and its receptors during the peri-implantation period in the mouse. It also reports that elevated TNF-a restricts ICM proliferation in the blastocyst and changes the ratio of mononucleated to multinucleated trophoblast cells. These findings suggest a mechanism by which increased

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Airborne particulate matter at a bus station : concentration levels and governing parameters

Traffic emissions are an important contributor to ambient air pollution, especially in large cities featuring extensive and high density traffic networks. Bus fleets represent a significant part of inner city traffic causing an increase in exposure to general public, passengers and drivers along bus routes and at bus stations. Limited information is available on quantification of the levels, and governing parameters affecting the air pollution exposure at bus stations. The presented study investigated the bus emissions-dominated ambient air in a large, inner city bus station, with a specific focus on submicrometer particles. The study’s objectives were (i) quantification of the concentration levels; (ii) characterisation of the spatio-temporal variation; (iii) identification of the parameters governing the emissions levels at the bus station and (iv) assessment of the relationship between particle concentrations measured at the street level (background) and within the bus station. The results show that up to 90% of the emissions at the station are ultrafine particles (smaller than 100 nm), with the concentration levels up to 10 times the value of urban ambient air background (annual) and up to 4 times the local ambient air background. The governing parameters affecting particle concentration at the station were bus flow rate and meteorological conditions (wind velocity). Particle concentration followed a diurnal trend, with an increase in the morning and evening, associated with traffic rush hours. Passengers’ exposure could be significant compared to the average outdoor and indoor exposure levels.

A pilot study on the effect of indoor particle sources on indoor particle concentration in residential houses

Characterization of indoor particle sources from 14 residential houses in Brisbane, Australia, was performed. The approximation of PM2.5 and the submicrometre particle number concentrations were measured simultaneously for more than 48 h in the kitchen of all the houses by using a photometer (DustTrak) and a condensation particle counter (CPC), respectively. From the real time indoor particle concentration data and a diary of indoor activities, the indoor particle sources were identified. The study found that among the indoor activities recorded in this study, frying, grilling, stove use, toasting, cooking pizza, smoking, candle vaporizing eucalyptus oil and fan heater use, could elevate the indoor particle number concentration levels by more than five times. The indoor approximation of PM2.5 concentrations could be close to 90 times, 30 times and three times higher than the background levels during grilling, frying and smoking, respectively.

Determination of particle concentration in the breathing zone for four different types of office ventilation systems

Many factors affect the airflow patterns, thermal comfort, contaminant removal efficiency and indoor air quality at individual workstations in office buildings. In this study, four ventilation systems were used in a test chamber designed to represent an area of a typical office building floor and reproduce the real characteristics of a modern office space. Measurements of particle concentration and thermal parameters (temperature and velocity) were carried out for each of the following types of ventilation systems: a) conventional air distribution system with ceiling supply and return; b) conventional air distribution system with ceiling supply and return near the floor; c) underfloor air distribution system; and d) split system. The measurements aimed to analyse the particle removal efficiency in the breathing zone and the impact of particle concentration on an individual at the workstation. The efficiency of the ventilation system was analysed by measuring particle size and concentration, ventilation effectiveness and the Indoor/Outdoor ratio. Each ventilation system showed different airflow patterns and the efficiency of each ventilation system in the removal of the particles in the breathing zone showed no correlation with particle size and the various methods of analyses used.

On-road ultrafine particle concentration in the M5 East road tunnel, Sydney, Australia

The human health effects following exposure to ultrafine (<100nm) particles (UFPs) produced by fuel combustion, while not completely understood, are generally regarded as detrimental. Road tunnels have emerged as locations where maximum exposure to these particles may occur for the vehicle occupants using them. This study aimed to quantify and investigate the determinants of UFP concentrations in the 4km twin-bore (eastbound and westbound) M5 East tunnel in Sydney, Australia. Sampling was undertaken using a condensation particle counter (CPC) mounted in a vehicle traversing both tunnel bores at various times of day from May through July, 2006. Supplementary measurements were conducted in February, 2008. Over three hundred transects of the tunnel were performed, and these were distributed evenly between the bores. Additional comparative measurements were conducted on a mixed route comprising major roads and shorter tunnels, all within Sydney. Individual trip average UFP concentrations in the M5 East tunnel bores ranged from 5.53 × 104 p cm-3 to 5.95 × 106 p cm-3. Data were sorted by hour of capture, and hourly median trip average (HMA) UFP concentrations ranged from 7.81 × 104 p cm-3 to 1.73 × 106 p cm-3. Hourly median UFP concentrations measured on the mixed route were between 3.71 × 104 p cm-3 and 1.55 × 105 p cm-3. Hourly heavy diesel vehicle (HDV) traffic volume was a very good determinant of UFP concentration in the eastbound tunnel bore (R2 = 0.87), but much less so in the westbound bore (R2 = 0.26). In both bores, the volume of passenger vehicles (i.e. unleaded gasoline-powered vehicles) was a significantly poorer determinant of particle concentration. When compared with similar studies reported previously, the measurements described here were among the highest recorded concentrations, which further highlights the contribution road tunnels may make to the overall UFP exposure of vehicle occupants.

Velocity and Concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller. Both the mean axial velocity profile and the mean concentration profile showed self-similarity. Further, the stand deviation growth curve was linear. The effects of propeller speed and dye release location were also investigated.

Biotribological assessment for artificial synovial joints : the role of boundary lubrication

Biotribology, the study of lubrication, wear and friction within the body, has become a topic of high importance in recent times as we continue to encounter debilitating diseases and trauma that destroy function of the joints. A highly successful surgical procedure to replace the joint with an artificial equivalent alleviates dysfunction and pain. However, the wear of the bearing surfaces in prosthetic joints is a significant clinical problem and more patients are surviving longer than the life expectancy of the joint replacement. Revision surgery is associated with increased morbidity and mortality and has a far less successful outcome than primary joint replacement. As such, it is essential to ensure that everything possible is done to limit the rate of revision surgery. Past experience indicates that the survival rate of the implant will be influenced by many parameters, of primary importance, the material properties of the implant, the composition of the synovial fluid and the method of lubrication. In prosthetic joints, effective boundary lubrication is known to take place. The interaction of the boundary lubricant and the bearing material is of utmost importance. The identity of the vital active ingredient within synovial fluid (SF) to which we owe the near frictionless performance of our articulating joints has been the quest of researchers for many years. Once identified, tribo tests can determine what materials and more importantly what surfaces this fraction of SF can function most optimally with. Surface-Active Phospholipids (SAPL) have been implicated as the body’s natural load bearing lubricant. Studies in this thesis are the first to fully characterise the adsorbed SAPL detected on the surface of retrieved prostheses and the first to verify the presence of SAPL on knee prostheses. Rinsings from the bearing surfaces of both hip and knee prostheses removed from revision operations were analysed using High Performance Liquid Chromatography (HPLC) to determine the presence and profile of SAPL. Several common prosthetic materials along with a novel biomaterial were investigated to determine their tribological interaction with various SAPLs. A pin-on-flat tribometer was used to make comparative friction measurements between the various tribo-pairs. A novel material, Pyrolytic Carbon (PyC) was screened as a potential candidate as a load bearing prosthetic material. Friction measurements were also performed on explanted prostheses. SAPL was detected on all retrieved implant bearing surfaces. As a result of the study eight different species of phosphatidylcholines were identified. The relative concentrations of each species were also determined indicating that the unsaturated species are dominant. Initial tribo tests employed a saturated phosphatidylcholine (SPC) and the subsequent tests adopted the addition of the newly identified major constituents of SAPL, unsaturated phosphatidylcholine (USPC), as the test lubricant. All tribo tests showed a dramatic reduction in friction when synthetic SAPL was used as the lubricant under boundary lubrication conditions. Some tribopairs showed more of an affinity to SAPL than others. PyC performed superior to the other prosthetic materials. Friction measurements with explanted prostheses verified the presence and performance of SAPL. SAPL, in particular phosphatidylcholine, plays an essential role in the lubrication of prosthetic joints. Of particular interest was the ability of SAPLs to reduce friction and ultimately wear of the bearing materials. The identification and knowledge of the lubricating constituents of SF is invaluable for not only the future development of artificial joints but also in developing effective cures for several disease processes where lubrication may play a role. The tribological interaction of the various tribo-pairs and SAPL is extremely favourable in the context of reducing friction at the bearing interface. PyC is highly recommended as a future candidate material for use in load bearing prosthetic joints considering its impressive tribological performance.

Nanoparticle melting as a Stefan moving boundary problem

The melting of spherical nanoparticles is considered from the perspective of heat flow in a pure material and as a moving boundary (Stefan) problem. The dependence of the melting temperature on both the size of the particle and the interfacial tension is described by the Gibbs-Thomson effect, and the resulting two-phase model is solved numerically using a front-fixing method. Results show that interfacial tension increases the speed of the melting process, and furthermore, the temperature distribution within the solid core of the particle exhibits behaviour that is qualitatively different to that predicted by the classical models without interfacial tension.