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.

Effect of chemical conjugation of L-leucine to chitosan on the dispersibility and drug release of a dry powder inhaler nanoparticle formulation

Purpose: This study investigated the effect of chemical conjugation of the amino acid L-leucine to the polysaccharide chitosan on the dispersibility and drug release pattern of a polymeric nanoparticle (NP)-based controlled release dry powder inhaler (DPI) formulation. Methods: A chemical conjugate of L-leucine with chitosan was synthesized and characterized by Infrared (IR) Spectroscopy, Nuclear Magnetic Resonance (NMR) Spectroscopy, Elemental Analysis and X-ray Photoelectron Spectroscopy (XPS). Nanoparticles of both chitosan and its conjugate were prepared by a water-in-oil emulsification – glutaraldehyde cross-linking method using the antihypertensive agent, diltiazem (Dz) hydrochloride as the model drug. The surface morphology and particle size distribution of the nanoparticles were determined by Scanning Electron Microscopy (SEM) and Dynamic Light Scattering (DLS). The dispersibility of the nanoparticle formulation was analysed by a Twin Stage Impinger (TSI) with a Rotahaler as the DPI device. Deposition of the particles in the different stages was determined by gravimetry and the amount of drug released was analysed by UV spectrophotometry. The release profile of the drug was studied in phosphate buffered saline at 37 ⁰C and analyzed by UV spectrophotometry. Results: The TSI study revealed that the fine particle fractions (FPF), as determined gravimetrically, for empty and drug-loaded conjugate nanoparticles were significantly higher than for the corresponding chitosan nanoparticles (24±1.2% and 21±0.7% vs 19±1.2% and 15±1.5% respectively; n=3, p<0.05). The FPF of drug-loaded chitosan and conjugate nanoparticles, in terms of the amount of drug determined spectrophotometrically, had similar values (21±0.7% vs 16±1.6%). After an initial burst, both chitosan and conjugate nanoparticles showed controlled release that lasted about 8 to 10 days, but conjugate nanoparticles showed twice as much total drug release compared to chitosan nanoparticles (~50% vs ~25%). Conjugate nanoparticles also showed significantly higher dug loading and entrapment efficiency than chitosan nanoparticles (conjugate: 20±1% & 46±1%, chitosan: 16±1% & 38±1%, n=3, p<0.05). Conclusion: Although L-leucine conjugation to chitosan increased dispersibility of formulated nanoparticles, the FPF values are still far from optimum. The particles showed a high level of initial burst release (chitosan, 16% and conjugate, 31%) that also will need further optimization.

Crushed tablets : does the administration of food vehicles and thickened fluids to aid medication swallowing alter drug release?

Purpose. To evaluate the influence of co-administered vehicles on in vitro dissolution in simulated gastric fluid of crushed immediate release tablets as an indicator for potential drug bioavailability compromise. Methods. Release and dissolution of crushed amlodipine, atenolol, carbamazepine and warfarin tablets were tested with six foods and drinks that are frequently used in the clinical setting as mixers for crushed medications (water, orange juice, honey, yoghurt, strawberry jam and water thickened with Easythick powder) in comparison to whole tablets. Five commercial thickening agents (Easythick Advanced, Janbak F, Karicare, Nutilis, Viscaid) at three thickness levels were tested for their effect on the dissolution of crushed atenolol tablets. Results. Atenolol dissolution was unaffected by mixing crushed tablets with thin fluids or food mixers in comparison to whole tablets or crushed tablets in water, but amlodipine was delayed by mixing with jam. Mixing crushed warfarin and carbamazepine tablets with honey, jam or yoghurt caused them to resemble the slow dissolution of whole tablets rather than the faster dissolution of crushed tablets in water or orange juice. Crushing and mixing any of the four medications with thickened water caused a significant delay in dissolution. When tested with atenolol, all types of thickening agents at the greatest thickness significantly restricted dissolution, and products that are primarily based on xanthan gum also delayed dissolution at the intermediate thickness level. Conclusions. Dissolution testing, while simplistic, is a widely used and accepted method for comparing drug release from different formulations as an indicator for in vivo bioavailability. Thickened fluids have the potential to retard drug dissolution when used at the thickest levels. These findings highlight potential clinical implications of the addition of these agents to medications for the purpose of dose delivery and indicate that further investigation of thickened fluids and their potential to influence therapeutic outcomes is warranted.

Bioactive inorganic materials/alginate composite microspheres with controllable drug-delivery ability

Alginate microspheres are considered a promising material as a drug carrier in bone repair due to excellent biocompatibility, but their main disadvantage is low drug entrapment efficiency and non-controllable release. The aim of this study was to investigate the effect of incorporating mesoporous bioglass (MBG), non-mesoporous bioglass (BG) or hydroxyapatite (HAp) into alginate microspheres on their drug-loading and release properties. X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and atomic emission spectroscopy (AES) were used to analyse the composition, structure and dissolution of bioactive inorganic materials and their microspheres. Dexamethasone (DEX)-loading and release ability of four microspheres were tested in phosphate buffered saline with varying pHs. Results showed that the drug-loading capacity was enhanced with the incorporation of bioactive inorganic materials into alginate microspheres. The MBG/Alginate microspheres had the highest drug loading ability. DEX release from alginate microspheres correlated to the dissolution of MBG, BG and HAp in PBS, and that the pH was an efficient factor in controlling the DEX release; a high pH resulted in greater DEX release, whereas a low pH delayed DEX release. In addition, MBG/alginate, BG/alginate and HAp/alginate microspheres had varying apatite-formation and dissolution abilities, which indicate that the composites would behave differently with respect to bioactivity. The study suggests that microspheres made of a composite of bioactive inorganic materials and alginate have a bioactivity and degradation profile which greatly improves their drug delivery capacity, thus enhancing their potential applications as bioactive filler materials for bone tissue regeneration.

Preparation and in vitro release of zein microparticles loaded with prednisolone for oral delivery

Zein has been proposed as a polymer for targeted-drug delivery via the oral route. Zein microparticles were loaded with prednisolone and evaluated as an oral delivery system. Microparticles were formulated using phase separation. Starting quantities of zein and prednisolone, along with the agitation method and temperature were found to significantly impact drug loading and loading efficiency. Vortex mixing produced the highest drug loading and loading efficiency. Drug release was measured in simulated conditions of the stomach and small intestine using the microparticles made with the method that best improved drug loading. In simulated stomach and small intestine conditions, prednisolone release reached almost 70 over 3 and 4h, respectively. While a clinically relevant dose may be delivered using c. 100mg of zein microparticles, prednisolone release from the microparticles indicates that they may not be suited as a controlled-or targeted-delivery system.

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.

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.

Synthesis of an erodible biomimetic hydrogel for drug delivery using native chemical ligation

Hydrogels are hydrophilic, three dimensional polymers that imbibe large quantities of water while remaining insoluble in aqueous solutions due to chemical or physical cross-linking. The polymers swell in water or biological fluids, immobilizing the bioactive agent, leading to drug release in a well-defined specific manner. Thus the hydrogels��� elastic properties, swellability and biocompatibility make them excellent formulations for drug delivery. Currently, many drug potencies and therapeutic effects are limited or otherwise reduced because of the partial degradation that occurs before the administered drug reaches the desired site of action. On the other hand, sustained release medications release drugs continually, rather than providing relief of symptoms and protection solely when necessary. In fact, it would be much better if drugs could be administered in a manner that precisely matches physiological needs at desired times and at the desired site (site specific targeting). There is therefore an unmet need to develop controlled drug delivery systems especially for delivery of peptide and protein bound drugs. The purpose of this project is to produce hydrogels for structural drug delivery and time-dependent sustained release of drugs (bioactive agents). We use an innovative polymerisation strategy based on native chemical ligation (NCL) to covalently cross-link polymers to form hydrogels. When mixed in aqueous solution, four armed (polyethylene glycol) amine (PEG-4A) end functionalised with thioester and four branched Nterminal cysteine peptide dendrimers spontaneously conjugated to produce biomimetic hydrogels. These hydrogels showed superior resistance to shear stress compared to an equivalent PEG macromonomer system and were shown to be proteolytically degradable with concomitant release of a model payload molecule. This is the first report of a peptide dendrimers/PEG macromonomer approach to hydrogel production and opens up the prospect of facile hydrogel synthesis together with tailored payload release.

Electrospraying of polymers with therapeutic molecules : state of the art

The encapsulation and release of bioactive molecules from polymeric vehicles represents the holy grail of drug and growth factor delivery therapies, whereby sustained and controlled release is crucial in eliciting a positive therapeutic effect. To this end, electrospraying is rapidly emerging as a popular technology for the production of polymeric particles containing bioactive molecules. Compared with traditional emulsion fabrication techniques, electrospraying has the potential to reduce denaturation of protein drugs and affords tighter regulation over particle size distribution and morphology. In this article, we review the importance of the electrospraying parameters that enable reproducible tailoring of the particles' physical and in vitro drug release characteristics, along with discussion of existing in vivo data. Controlled morphology and monodispersity of particles can be achieved with electrospraying, with high encapsulation efficiencies and without unfavorable denaturation of bioactive molecules throughout the process. Finally, the combination of electrospraying with electrospun scaffolds, with an emphasis on tissue regeneration is reviewed, depicting a technique in its relative infancy but holding great promise for the future of regenerative medicine.