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.

Thermal transport in graphene-polymer nanocomposites

Graphene-polymer nanocomposites have attracted considerable attention due to their unique properties, such as high thermal conductivity (~3000 W mK-1), mechanical stiffness (~ 1 TPa) and electronic transport properties. Relatively, the thermal performance of graphene-polymer composites has not been well investigated. The major technical challenge is to understand the interfacial thermal transport between graphene nanofiller and polymer matrix at small material length scale. To this end, we conducted molecular dynamics simulations to investigate the thermal transport in graphene-polyethylene nanocomposite. The influence of functionalization with hydrocarbon chains on the interfacial thermal conductivity was studied, taking into account of the effects of model size and thermal conductivity of graphene. The results are considered to contribute to development of new graphene-polymer nanocomposites with tailored thermal properties.

Effects of HNO3 molecular doping in graphene/Si Schottky barrier solar cells

Schottky barrier solar cells based on graphene/n-silicon heterojunction have been fabricated and characterized and the effect of graphene molecular doping by HNO3 on the solar cells performances have been analyzed. Different doping conditions and thermal annealing processes have been tested to asses and optimize the stability of the devices. The PCE of the cells increases after the treatment by HNO3 and reaches 5% in devices treated at 200 °C immediately before the exposition to the oxidant. Up to now our devices retain about 80% of efficiency over a period of two weeks, which represents a good stability result for similar devices.

Enhanced interfacial thermal transport across graphene–polymer interfaces by grafting polymer chains

Thermal transport in graphene-polymer nanocomposite is complicated and has not been well understood. The interfacial thermal transport between graphene nanofiller and polymer matrix is expected to play a key role in controlling the overall thermal performance of graphene-polymer nanocomposite. In this work, we investigated the thermal transport across graphene-polymer interfaces functionalized with end-grafted polymer chains using molecular dynamics simulations. The effects of grafting density, chain length and initial morphology on the interfacial thermal transport were systematically investigated. It was found that end-grafted polymer chains could significantly enhance interfacial thermal transport and the underlying mechanism was considered to be the enhanced vibration coupling between graphene and polymer. In addition, a theoretical model based on effective medium theory was established to predict the thermal conductivity in graphene-polymer nanocomposites.

Assessment of the effects of CT dose in averaged x-ray CT images of a dose-sensitive polymer gel

The signal-to-noise ratio achievable in x-ray computed tomography (CT) images of polymer gels can be increased by averaging over multiple scans of each sample. However, repeated scanning delivers a small additional dose to the gel which may compromise the accuracy of the dose measurement. In this study, a NIPAM-based polymer gel was irradiated and then CT scanned 25 times, with the resulting data used to derive an averaged image and a "zero-scan" image of the gel. Comparison between these two results and the first scan of the gel showed that the averaged and zero-scan images provided better contrast, higher contrast-to- noise and higher signal-to-noise than the initial scan. The pixel values (Hounsfield units, HU) in the averaged image were not noticeably elevated, compared to the zero-scan result and the gradients used in the linear extrapolation of the zero-scan images were small and symmetrically distributed around zero. These results indicate that the averaged image was not artificially lightened by the small, additional dose delivered during CT scanning. This work demonstrates the broader usefulness of the zero-scan method as a means to verify the dosimetric accuracy of gel images derived from averaged x-ray CT data.

Effect of covalent functionalisation on thermal transport across graphene-polymer interfaces

This paper is concerned with the interfacial thermal resistance for polymer composites reinforced by various covalently functionalised graphene. By using molecular dynamics simulations, the obtained results show that the covalent functionalisation in graphene plays a significant role in reducing the graphene-paraffin interfacial thermal resistance. This reduction is dependent on the coverage and type of functional groups. Among the various functional groups, butyl is found to be the most effective in reducing the interfacial thermal resistance, followed by methyl, phenyl and formyl. The other functional groups under consideration such as carboxyl, hydroxyl and amines are found to produce negligible reduction in the interfacial thermal resistance. For multilayer graphene with a layer number up to four, the interfacial thermal resistance is insensitive to the layer number. The effects of the different functional groups and the layer number on the interfacial thermal resistance are also elaborated using the vibrational density of states of the graphene and the paraffin matrix. The present findings provide useful guidelines in the application of functionalised graphene for practical thermal management.

Synthesis of a multimodal molecular imaging probe based on a hyperbranched polymer architecture

Molecular imaging is utilised in modern medicine to aid in the diagnosis and treatment of disease by allowing its spatiotemporal state to be examined in vivo. This study focuses on the development of novel multimodal molecular imaging agents based on hyperbranched polymers that combine the complementary capabilities of optical fluorescence imaging and positron emission tomography-computed tomography (PET/CT) into one construct. RAFT-mediated polymerisation was used to prepare two hydrophilic hyperbranched polymers that were differentiated by their size and level of branching. The multiple functional end-groups facilitated covalent attachment of both near infrared fluorescent dyes for optical imaging, as well as a copper chelator allowing binding of 64Cu as a PET radio nuclei. In vivo multimodal imaging of mice using PET/CT and planar optical imaging was first used to assess the biodistribution of the polymeric materials and it was shown that the larger and more branched polymer had a significantly longer circulation time. The larger constructs were also shown to exhibit enhanced accumulation in solid tumours in a murine B16 melanoma model. Importantly, it was demonstrated that the PET modality gave rise to high sensitivity immediately after injection of the agent, while the optical modality facilitated extended longitudinal studies, thus highlighting how the complementary capabilities of the molecular imaging agents can be useful for studying various diseases, including cancer.

Substrate, molecular structure, and solvent effects in 2D self-assembly via hydrogen and halogen bonding

Recently, halogen···halogen interactions have been demonstrated to stabilize two-dimensional supramolecular assemblies at the liquid–solid interface. Here we study the effect of changing the halogen, and report on the 2D supramolecular structures obtained by the adsorption of 2,4,6-tris(4-bromophenyl)-1,3,5-triazine (TBPT) and 2,4,6-tris(4-iodophenyl)-1,3,5-triazine (TIPT) on both highly oriented pyrolytic graphite and the (111) facet of a gold single crystal. These molecular systems were investigated by combining room-temperature scanning tunneling microscopy in ambient conditions with density functional theory, and are compared to results reported in the literature for the similar molecules 1,3,5-tri(4-bromophenyl)benzene (TBPB) and 1,3,5-tri(4-iodophenyl)benzene (TIPB). We find that the substrate exerts a much stronger effect than the nature of the halogen atoms in the molecular building blocks. Our results indicate that the triazine core, which renders TBPT and TIPT stiff and planar, leads to stronger adsorption energies and hence structures that are different from those found for TBPB and TIPB. On the reconstructed Au(111) surface we find that the TBPT network is sensitive to the fcc- and hcp-stacked regions, indicating a significant substrate effect. This makes TBPT the first molecule reported to form a continuous monolayer at room temperature in which molecular packing is altered on the differently reconstructed regions of the Au(111) surface. Solvent-dependent polymorphs with solvent coadsorption were observed for TBPT on HOPG. This is the first example of a multicomponent self-assembled molecular networks involving the rare cyclic, hydrogen-bonded hexamer of carboxylic groups, R66(24) synthon.

The synthesis and application of novel profluorescent nitroxides as probes for polymer degradation

This PhD project has expanded the knowledge in the area of profluorescent nitroxides with regard to the synthesis and characterisations of novel profluorescent nitroxide probes as well as physical characterisation of the probe molecules in various polymer/physical environments. The synthesis of the first example of an azaphenalene-based fused aromatic nitroxide TMAO, [1,1,3,3-tetramethyl-2,3-dihydro-2-azaphenalen-2-yloxyl, was described. This novel nitroxide possesses some of the structural rigidity of the isoindoline class of nitroxides, as well as some properties akin to TEMPO nitroxides. Additionally, the integral aromatic ring imparts fluorescence that is switched on by radical scavenging reactions of the nitroxide, which makes it a sensitive probe for polymer degradation. In addition to the parent TMAO, 5 other azaphenalene derivatives were successfully synthesised. This new class of nitroxide was expected to have interesting redox properties when the structure was investigated by high-level ab initio molecular orbitals theory. This was expected to have implications with biological relevance as the calculated redox potentials for the azaphenalene ring class would make them potent antioxidant compounds. The redox potentials of 25 cyclic nitroxides from four different structural classes (pyrroline, piperidine, isoindoline and azaphenalene) were determined by cyclic voltammetry in acetonitrile. It was shown that potentials related to the one electron processes of the nitroxide were influenced by the type of ring system, ring substituents or groups surrounding the moiety. Favourable comparisons were found between theoretical and experimental potentials for pyrroline, piperidine and isoindoline ring classes. Substitution of these ring classes, were correctly calculated to have a small yet predictable effect on the potentials. The redox potentials of the azaphenalene ring class were underestimated by the calculations in all cases by at least a factor of two. This is believed to be due to another process influencing the redox potentials of the azaphenalene ring class which is not taken into account by the theoretical model. It was also possible to demonstrate the use of both azaphenalene and isoindoline nitroxides as additives for monitoring radical mediated damage that occurs in polypropylene as well as in more commercially relevant polyester resins. Polymer sample doped with nitroxide were exposed to both thermo-and photo-oxidative conditions with all nitroxides showing a protective effect. It was found that isoindoline nitroxides were able to indicate radical formation in polypropylene aged at elevated temperatures via fluorescence build-up. The azaphenalene nitroxide TMAO showed no such build-up of fluorescence. This was believed to be due to the more labile bond between the nitroxide and macromolecule and the protection may occur through a classical Denisov cycle, as is expected for commercially available HAS units. Finally, A new profluorescent dinitroxide, BTMIOA (9,10-bis(1,1,3,3- tetramethylisoindolin-2-yloxyl-5-yl)anthracene), was synthesised and shown to be a powerful probe for detecting changes during the initial stages of thermo-oxidative degradation of polypropylene. This probe, which contains a 9,10-diphenylanthracene core linked to two nitroxides, possesses strongly suppressed fluorescence due to quenching by the two nitroxide groups. This molecule also showed the greatest protective effect on thermo-oxidativly aged polypropylene. Most importantly, BTMIOA was found to be a valuable tool for imaging and mapping free-radical generation in polypropylene using fluorescence microscopy.

Evaluation of polycaprolactone scaffold degradation for 6 months in vitro and in vivo

The use of polycaprolactone (PCL) as a biomaterial, especially in the fields of drug delivery and tissue engineering, has enjoyed significant growth. Understanding how such a device or scaffold eventually degrades in vivo is paramount as the defect site regenerates and remodels. Degradation studies of three-dimensional PCL and PCL-based composite scaffolds were conducted in vitro (in phosphate buffered saline) and in vivo (rabbit model). Results up to 6 months are reported. All samples recorded virtually no molecular weight changes after 6 months, with a maximum mass loss of only about 7% from the PCL-composite scaffolds degraded in vivo, and a minimum of 1% from PCL scaffolds. Overall, crystallinity increased slightly because of the effects of polymer recrystallization. This was also a contributory factor for the observed stiffness increment in some of the samples, while only the PCL-composite scaffold registered a decrease. Histological examination of the in vivo samples revealed good biocompatibility, with no adverse host tissue reactions up to 6 months. Preliminary results of medical-grade PCL scaffolds, which were implanted for 2 years in a critical-sized rabbit calvarial defect site, are also reported here and support our scaffold design goal for gradual and late molecular weight decreases combined with excellent long-term biocompatibility and bone regeneration. (C) 2008 Wiley Periodicals, Inc. J Biomed Mater Res 90A: 906-919, 2009

Enhanced human bone marrow stromal cell affinity for modified poly(L-lactide) surfaces by the upregulation of adhesion molecular genes

To enhance and regulate cell affinity for poly (l-lactic acid) (PLLA) based materials, two hydrophilic ligands, poly (ethylene glycol) (PEG) and poly (l-lysine) (PLL), were used to develop triblock copolymers: methoxy-terminated poly (ethylene glycol)-block-poly (l-lactide)-block-poly (l-lysine) (MPEG-b-PLLA-b-PLL) in order to regulate protein absorption and cell adhesion. Bone marrow stromal cells (BMSCs) were cultured on different composition of MPEG-b-PLLA-b-PLL copolymer films to determine the effect of modified polymer surfaces on BMSC attachment. To understand the molecular mechanism governing the initial cell adhesion on difference polymer surfaces, the mRNA expression of 84 human extracellular matrix (ECM) and adhesion molecules was analysed using quantitative reverse transcriptase polymerase chain reaction (qRT-PCR). It was found that down regulation of adhesion molecules was responsible for the impaired BMSC attachment on PLLA surface. MPEG-b-PLLA-b-PLL copolymer films improved significantly the cell adhesion and cytoskeleton expression by upregulation of relevant molecule genes significantly. Six adhesion genes (CDH1, ITGL, NCAM1, SGCE, COL16A1, and LAMA3) were most significantly influenced by the modified PLLA surfaces. In summary, polymer surfaces altered adhesion molecule gene expression of BMSCs, which consequently regulated cell initial attachment on modified PLLA surfaces.

Establishment of a mouse model of colitis and its use to evaluate the anti-inflammatory effects of two ghrelin peptides

Ghrelin is a gut-brain peptide hormone that induces appetite, stimulates the release of growth hormone, and has recently been shown to ameliorate inflammation. Recent studies have suggested that ghrelin may play a potential role in inflammation-related diseases such as inflammatory bowel diseases (IBD). A previous study with ghrelin in the TNBS mouse model of colitis demonstrated that ghrelin treatment decreased the clinical severity of colitis and inflammation and prevented the recurrence of disease. Ghrelin may be acting at the immunological and epithelial level as the ghrelin receptor (GHSR) is expressed by immune cells and intestinal epithelial cells. The current project investigated the effect of ghrelin in a different mouse model of colitis using dextran sodium sulphate (DSS) – a luminal toxin. Two molecular weight forms of DSS were used as they give differing effects (5kDa and 40kDa). Ghrelin treatment significantly improved clinical colitis scores (p=0.012) in the C57BL/6 mouse strain with colitis induced by 2% DSS (5kDa). Treatment with ghrelin suppressed colitis in the proximal colon as indicated by reduced accumulative histopathology scores (p=0.03). Whilst there was a trend toward reduced scores in the mid and distal colon in these mice this did not reach significance. Ghrelin did not affect histopathology scores in the 40kDa model. There was no significant effect on the number of regulatory T cells or TNF-α secretion from cultured lymph node cells from these mice. The discovery of C-terminal ghrelin peptides, for example, obestatin and the peptide derived from exon 4 deleted proghrelin (Δ4 preproghrelin peptide) have raised questions regarding their potential role in biological functions. The current project investigated the effect of Δ4 peptide in the DSS model of colitis however no significant suppression of colitis was observed. In vitro epithelial wound healing assays were also undertaken to determine the effect of ghrelin on intestinal epithelial cell migration. Ghrelin did not significantly improve wound healing in these assays. In conclusion, ghrelin treatment displays a mild anti-inflammatory effect in the 5kDa DSS model. The potential mechanisms behind this effect and the disparity between these results and those published previously will be discussed.

Vibrational spectroscopic studies of laboratory scale polymer melt processing : application to a thermoplastic polyurethane nanocomposite

A laboratory scale twin screw extruder has been interfaced with a near infrared (NIR) spectrometer via a fibre optic link so that NIR spectra can be collected continuously during the small scale experimental melt state processing of polymeric materials. This system can be used to investigate melt state processes such as reactive extrusion, in real time, in order to explore the kinetics and mechanism of the reaction. A further advantage of the system is that it has the capability to measure apparent viscosity simultaneously which gives important additional information about molecular weight changes and polymer degradation during processing. The system was used to study the melt processing of a nanocomposite consisting of a thermoplastic polyurethane and an organically modified layered silicate.

Investigation of molecular mechanisms regulating biomineralization of pearl oyster Pinctada maxima

Biomineralization is a process encompassing all mineral containing tissues produced within an organism. The most dynamic example of this process is the formation of the mollusk shell, comprising a variety of crystal phases and microstructures. The organic component incorporated within the shell is said to dictate this remarkable architecture. Subsequently, for the past decade considerable research have been undertaken to identify and characterize the protein components involved in biomineralization. Despite these efforts the general understanding of the process remains ambiguous. This study employs a novel molecular approach to further the elucidation of the shell biomineralization. A microarray platform has been custom generated (PmaxArray 1.0) from the pearl oyster Pinctada maxima. PmaxArray 1.0 consists of 4992 expressed sequence tags (ESTs) originating from the mantle, an organ involved in shell formation. This microarray has been used as the primary tool for three separate investigations in an effort to associate transcriptional gene expression from P. maxima to the process of shell biomineralization. The first investigation analyzes the spatial expression of ESTs throughout the mantle organ. The mantle was dissected into five discrete regions and each analyzed for gene expression with PmaxArray 1.0. Over 2000 ESTs were differentially expressed among the tissue sections, identifying five major expression regions. Three of these regions have been proposed to have shell formation functions belonging to nacre, prismatic calcite and periostracum. The spatial gene expression map was confirmed by in situ hybridization, localizing a subset of ESTs from each expression region to the same mantle area. Comparative sequence analysis of ESTs expressed in the proposed shell formation regions with the BLAST tool, revealed a number of the transcripts were novel while others showed significant sequence similarities to previously characterized shell formation genes. The second investigation correlates temporal EST expression during P. maxima larval ontogeny with transitions in shell mineralization during the same period. A timeline documenting the morphologicat microstructural and mineralogical shell characteristics of P. maxima throughout larval ontogeny has been established. Three different shell types were noted based on the physical characters and termed, prodissoconch I, prodissoconch 11 and dissoconch. PmaxArray 1.0 analyzed ESTs expression of animals throughout the larval development of P. maxima, noting up-regulation of 359 ESTs in association with the shell transitions from prodissoconch 1 to prodissoconch 11 to dissoconch. Comparative sequence analysis of these ESTs indicates a number of the transcripts are novel as well as showing significant sequence similarities between ESTs and known shell matrix associated genes and proteins. These ESTs are discussed in relation to the shell characters associated with their temporal expression. The third investigation uses PmaxArray 1.0 to analyze gene expression in the mantle tissue of P. maxima specimens exposed to sub-lethal concentrations of a shell-deforming toxin, tributyltin (TBT). The shell specific effects of TBT are used in this investigation to interpret differential expression of ESTs with respect to shell formation functions. A lethal and sublethal TBT concentration range was established for P. maxima, noting a concentration of 50 ng L- 1 TBT as sub-lethal over a 21 day period. Mantle tissue from P. maxima animals treated with 50 ng L- 1 TBT was assessed for differential EST expression with untreated control animals. A total of 102 ESTs were identified as differentially expressed in association with TBT exposure, comparative sequence identities included an up-regulation of immunity and detoxification related genes and down-regulation of several shell matrix genes. A number of transcripts encoding novel peptides were additionally identified. The potential actions of these genes are discussed with reference to TBT toxicity and shell biomineralization. This thesis has used a microarray platform to analyze gene expression in spatial, temporal and toxicity investigations, revealing the involvement of numerous gene transcripts in specific shell formation functions. Investigation of thousands of transcripts simultaneously has provided a holistic interpretation of the organic components regulating shell biomineralization.