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.

Influence of surface chemistry of mesoporous alumina with wide pore distribution on controlled drug release

The crucial role of the drug carrier surface chemical moeities on the uptake and in vitro release of drug is discussed here in a systematic manner. Mesoporous alumina with a wide pore size distribution (2-7 nm) functionalized with various hydrophilic and hydrophobic surface chemical groups was employed as the carrier for delivery of the model drug ibuprofen. Surface functionalization with hydrophobic groups resulted in low degree of drug loading (approximately 20%) and fast rate of release (85% over a period of 5 h) whereas hydrophilic groups resulted in a significantly higher drug payloads (21%-45%) and slower rate of release (12%-40% over a period of 5 h). Depending on the chemical moiety, the diffusion controlled (proportional to time(-0.5)) drug release was additionally observed to be dependent on the mode of arrangement of the functional groups on the alumina surface as well as on the pore characteristics of the matrix. For all mesoporous alumina systems the drug dosages were far lower than the maximum recommended therapeutic dosages (MRTD) for oral delivery. We envisage that the present study would aid in the design of delivery systems capable of sustained release of multiple drugs.

Synthesis and characterization of magnetic FexOy@SBA-15 composites with different morphologies for controlled drug release and targeting

Magnetic functionalization of the ordered mesoporous SBA-15 (SiO2) aggregate blocks and rice grain-like particles were realized by using a sol-gel method, resulting in the formation of FexOy@SBA-15 composite materials. The X-ray diffraction (XRD), N-2 adsorption/desorption, and transmission electron microscopy (TEM) results show that these composites conserved ordered mesoporous structure after the formation of FexOy nanoparticles in the pores and on the outer surface of SBA-15. It was confirmed by the XRD and X-ray photoelectron spectroscopy (XPS) analysis that the FexOy generated in these mesoporous silica hosts is mainly composed of gamma-Fe2O3. Magnetic measurements reveal that these composites possess superparamagnetic properties at 300 K. The saturation magnetization of these composites increased with the increasing loading amount of gamma-Fe2O3. These composites, which possess high surface area and high pore volume, show magnetic response sufficient for drug targeting in the presence of an external magnetic field.

Synthesis of biodegradable thermo- and pH-responsive hydrogels for controlled drug release

Novel intelligent hydrogels composed of biodegradable and pH-sensitive poly(L-glutamic acid) (PGA) and temperature sensitive poly(N-isopropylacrylamide-co-2-hydroxyethyl methacrylate) (PNH) were synthesized and characterized for controlled release of hydrophilic drug. The influence of pH on the equilibrium swelling ratios of the hydrogels was investigated. A higher PNH content resulted in lower equilibrium swelling ratios. Although temperature had little influence on the swelling behaviors of the hydrogels, the changes of optical transmittance of hydrogels as a function of temperature were marked, which showed that the PNH part of hydrogel exhibited hydrophobic property at temperature above the lower critical solution temperature (LCST). The biodegradation rate of the stimuli-sensitive hydrogels in the presence of enzyme was directly proportional to the PGA content. Lysozyme was chosen as a model drug and loaded into the hydrogels.

RAFT controlled synthesis of graphene/polymer hydrogel with enhanced mechanical property for pH-controlled drug release

A pH-sensitive, mechanically strong and thermally stable graphene/poly (acrylic acid) (graphene/PAA) hydrogel was prepared via reversible addition fragmentation transfer (RAFT) polymerizations in the presence of a cross-linking agent. The RAFT agent was covalently coupled onto graphene basal planes via an esterification reaction, with benzoic acid functionalities pre-attached on graphene with its aryl diazonium salt precursor. AFM and SEM analysis revealed the successful preparation of single layered graphene sheets and graphene/polymer hydrogels with pH controlled porous structures. Attenuated total reflection infrared (ATR-IR) and thermogravimetric analyzer (TGA) verified the successful stepwise preparation of graphene/PAA hydrogel. This graphene/PAA hydrogel was pH-sensitive and more mechanically elastic than the PAA hydrogel prepared without graphene. The pH sensitivity of the hydrogel was further utilized for controlled drug release. Doxorubicin was chosen as a model drug and loaded into the hydrogels. The drug loading and release experiment indicated that this hydrogel can be used to efficiently control drug release in the intestine environment (pH = 7.4), better than release in a more acidic environment.© 2013 Elsevier Ltd. All rights reserved.

Modeling a system of phosphated cross-linked high amylose for controlled drug release. Part 2: Physical parameters, cross-linking degrees and drug delivery relationships

High amylose cross-linked to different degrees with sodium trimetaphosphate by varying base strength (2% or 4%) and contact time (0.5-4 h) was evaluated as non-compacted systems for sodium diclophenac controlled release. The physical properties and the performance of these products for sodium diclophenac controlled release from non-compacted systems were related to the structures generated at each cross-linking degree. For samples at 2% until 2 h the swelling ability, G' and eta* values increased with the cross-linking degree, because the longer polymer chains became progressively more entangled and linked. This increases water uptake and holding, favoring the swelling and resulting in systems with higher viscosities. Additionally, the increase of cross-linking degree should contribute for a more elastic structure. The shorter chains with more inter-linkages formed at higher cross-linking degrees (2%4h and 4%) make water caption and holding difficult, decreasing the swelling, viscosity and elasticity. For 2% samples, the longer drug release time exhibited for 2%4h sample indicates that the increase of swelling and viscosity contribute for a more sustained drug release, but the mesh size of the polymeric network seems to be determinant for the attachment of drug molecules. For the 4% samples, smaller meshes size should determine less sustained release of drug. (C) 2008 Elsevier B.V. All rights reserved.

Controlled Drug Release from Ureasil-Polyether Hybrid Materials

Flexible, transparent, and insoluble urea-cross-linked polyether-siloxane hybrids presenting a tunable drug delivery pattern were prepared using the sol-gel method from PEO (poly(ethylene oxide)) and PPO (poly(propylene oxide)) functionalized at both chain ends with triethoxysilane. Different polyether chain lengths were used to control the urea/siloxane (named ureasil) node density, flexibility, and swellability of the hybrid network. We herein demonstrate that the drug release from swellable hydrophilic ureasil-PEO hybrids can be sustained for some days, whereas that from the unswellable ureasil-PPO hybrids can be sustained for some weeks. This outstanding feature conjugated with the biomedically safe formulation of the ureasil cross-linked polyether-siloxane hybrid widens their scope of application to include the domain of soft and implantable drug delivery devices.

Modeling a system of phosphated cross-linked high amylose for controlled drug release. Part 1: Synthesis and polymer characterization

High amylose was cross-linked with sodium trimetaphosphate (STMP) using 2% and 4% solutions of NaOH at room temperature with reaction contact times of 0.5, 1, 2 and 4 h. The different polymers obtained were analyzed by FT IR, C-13 and P-31 solid state NMR, SEM and C, H and P elemental analysis. The results were used to propose a two-stage mechanism for phosphate incorporation, the first being kinetically controlled. (C) 2008 Elsevier Ltd. All rights reserved.

Development of organic-inorganic polymeric film formers for controlled drug release and wound care

Film forming polymeric systems represents a new and unexplored technology of systems forskin or wounds protection and for controlled drug release. The aim of this work was to study the use of polymeric organic-inorganic ureasil-polyether hybrids synthesized by the sol-gel process as film forming system containing silver sulfadiazine as model drug. The film formationtime can be controlled by changing the precursor/catalyst ratio used during the step of hydrolysis and condensations. The results showed that the precursor/catalyst proportion influences both the visual characteristics and time required to form the film. The precursor/catalyst ratio equal to 20.8 m/v was considered ideal due to promote the homogeneous and transparent film formation in less than 5 minutes. The release profile of sulfadiazine is dependent on the characteristics of the matrixes: matrix more hydrophobic as ureasil-POP provided a slowed released mainly due to the low swelling of the matrix. The more hydrophilic ureasil-POE matrix presents a large capacity to swell and favors the faster release of the drug. The set of results showed the possibility of future use of these systems for treating wounds caused by burns.

A novel graphene nanodots inlaid porous gold electrode for electrochemically controlled drug release

A uniform graphene nanodots inlaid porous gold electrode was prepared via ion beam sputtering deposition (IBSD) and mild corrosion chemistry. HRTEM, SEM, AFM and XPS analyses revealed the successful fabrication of graphene nanodots inlaid porous gold electrode. The as-prepared porous electrode was used as π-orbital-rich drug loading platform to fabricate an electrochemically controlled drug release system with high performance. π-orbital-rich drugs with amino mioety, like doxorubicin (DOX) and tetracycline (TC), were loaded into the graphene nanodots inlaid porous gold electrode via non-covalent π-π stacking interaction. The amino groups in DOX and TC can be easily protonated at acidic medium to become positively-charged NH3(+), which allow these drug molecules to be desorbed from the porous electrode surface via electrostatic repulsion when positive potential is applied at the electrode. The drug loading and release experiment indicated that this graphene nanodots inlaid porous gold electrode can be used to conveniently and efficiently control the drug release electrochemically. Not only did our work provide a benign method to electrochemically controlled drug release via electrostatic repulsion process, it also enlighten the promising practical applications of micro electrode as a drug carrier for precisely and efficiently controlled drug release via embedding in the body.

Controlled swollen and drug release from urea-cross-linked polyether/siloxane hybrids

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Controlled systemic release of interleukin-12 after gene electrotransfer to muscle for cancer gene therapy alone or in combination with ionizing radiation in murine sarcomas

Background: The present study aimed to evaluate the antitumor effectiveness of systemic interleukin (IL)-12 gene therapy in murine sarcoma models, and to evaluate its interaction with the irradiation of tumors and metastases. To avoid toxic side-effects of IL-12 gene therapy, the objective was to achieve the controlled release of IL-12 after intramuscular gene electrotransfer. Methods: Gene electrotransfer of the plasmid pORF-mIL12 was performed into the tibialis cranialis in A/J and C57BL/6 mice. Systemic release of the IL-12 was monitored in the serum of mice after carrying out two sets of intramuscular IL-12 gene electrotransfer of two different doses of plasmid DNA. The antitumor effectiveness of IL-12 gene electrotransfer alone or in combination with local tumor or lung irradiation with X-rays, was evaluated on subcutaneous SA-1 and LPB tumors, as well as on lung metastases. Results: A synergistic antitumor effect of intramuscular gene electrotransfer combined with local tumor irradiation was observed as a result of the systemic distribution of IL-12. The gene electrotransfer resulted in up to 28% of complete responses of tumors. In combination with local tumor irradiation, the curability was increased by up to 100%. The same effect was observed for lung metastases, where a potentiating factor of 1.3-fold was determined. The amount of circulating IL-12 was controlled by the number of repeats of gene electrotransfer and by the amount of the injected plasmid. Conclusions: The present study demonstrates the feasibility of treatment by IL-12 gene electrotransfer combined with local tumor or lung metastases irradiation on sarcoma tumors for translation into the clinical setting. Copyright © 2009 John Wiley & Sons, Ltd.

Role of surface chemistry in modulating drug release kinetics in titania nanotubes

Surface chemistry and the intrinsic porous architectures of porous substrates play a major role in the design of drug delivery systems. An interesting example is the drug elution characteristic from hydrothermally synthesised titania nanotubes with tunable surface chemistry. The variation in release rates of Ibuprofen (IBU) is largely influenced by the nature of the functional groups on titania nanotubes and pH of suspending medium. To elucidate the extent of interaction between the encapsulated IBU and the functional groups on titania nanotubes, the release profiles have been modelled with an empirical Hill equation. The analysis aided in establishing a probable mechanism for the release of IBU from the titania nanotubes. The study of controlled drug release from TiO2 has wider implication in the context of biomedical engineering. (C) 2014 Elsevier B.V. All rights reserved.

High-amylose carboxymethyl starch matrices for oral sustained drug-release : in vitro and in vivo evaluation

Les amidons non modifiées et modifiés représentent un groupe d’excipients biodégradables et abondants particulièrement intéressant. Ils ont été largement utilisés en tant qu’excipients à des fins diverses dans des formulations de comprimés, tels que liants et/ou agents de délitement. Le carboxyméthylamidon sodique à haute teneur en amylose atomisé (SD HASCA) a été récemment proposé comme un excipient hydrophile à libération prolongée innovant dans les formes posologiques orales solides. Le carboxyméthylamidon sodique à haute teneur en amylose amorphe (HASCA) a d'abord été produit par l'éthérification de l'amidon de maïs à haute teneur en amylose avec le chloroacétate. HASCA a été par la suite séché par atomisation pour obtenir le SD HASCA. Ce nouvel excipient a montré des propriétés présentant certains avantages dans la production de formes galéniques à libération prolongée. Les comprimés matriciels produits à partir de SD HASCA sont peu coûteux, simples à formuler et faciles à produire par compression directe. Le principal objectif de cette recherche était de poursuivre le développement et l'optimisation des comprimés matriciels utilisant SD HASCA comme excipient pour des formulations orales à libération prolongée. A cet effet, des tests de dissolution simulant les conditions physiologiques du tractus gastro-intestinal les plus pertinentes, en tenant compte de la nature du polymère à l’étude, ont été utilisés pour évaluer les caractéristiques à libération prolongée et démontrer la performance des formulations SD HASCA. Une étude clinique exploratoire a également été réalisée pour évaluer les propriétés de libération prolongée de cette nouvelle forme galénique dans le tractus gastro-intestinal. Le premier article présenté dans cette thèse a évalué les propriétés de libération prolongée et l'intégrité physique de formulations contenant un mélange comprimé de principe actif, de chlorure de sodium et de SD HASCA, dans des milieux de dissolution biologiquement pertinentes. L'influence de différentes valeurs de pH acide et de temps de séjour dans le milieu acide a été étudiée. Le profil de libération prolongée du principe actif à partir d'une formulation de SD HASCA optimisée n'a pas été significativement affecté ni par la valeur de pH acide ni par le temps de séjour dans le milieu acide. Ces résultats suggèrent une influence limitée de la variabilité intra et interindividuelle du pH gastrique sur la cinétique de libération à partir de matrices de SD HASCA. De plus, la formulation optimisée a gardé son intégrité pendant toute la durée des tests de dissolution. L’étude in vivo exploratoire a démontré une absorption prolongée du principe actif après administration orale des comprimés matriciels de SD HASCA et a montré que les comprimés ne se sont pas désintégrés en passant par l'estomac et qu’ils ont résisté à l’hydrolyse par les α-amylases dans l'intestin. Le deuxième article présente le développement de comprimés SD HASCA pour une administration orale une fois par jour et deux fois par jour contenant du chlorhydrate de tramadol (100 mg et 200 mg). Ces formulations à libération prolongée ont présenté des valeurs de dureté élevées sans nécessiter l'ajout de liants, ce qui facilite la production et la manipulation des comprimés au niveau industriel. La force de compression appliquée pour produire les comprimés n'a pas d'incidence significative sur les profils de libération du principe actif. Le temps de libération totale à partir de comprimés SD HASCA a augmenté de manière significative avec le poids du comprimé et peut, de ce fait, être utilisé pour moduler le temps de libération à partir de ces formulations. Lorsque les comprimés ont été exposés à un gradient de pH et à un milieu à 40% d'éthanol, un gel très rigide s’est formé progressivement sur leur surface amenant à la libération prolongée du principe actif. Ces propriétés ont indiqué que SD HASCA est un excipient robuste pour la production de formes galéniques orales à libération prolongée, pouvant réduire la probabilité d’une libération massive de principe actif et, en conséquence, des effets secondaires, même dans le cas de co-administration avec une forte dose d'alcool. Le troisième article a étudié l'effet de α-amylase sur la libération de principe actif à partir de comprimés SD HASCA contenant de l’acétaminophène et du chlorhydrate de tramadol qui ont été développés dans les premières étapes de cette recherche (Acetaminophen SR et Tramadol SR). La modélisation mathématique a montré qu'une augmentation de la concentration d’α-amylase a entraîné une augmentation de l'érosion de polymère par rapport à la diffusion de principe actif comme étant le principal mécanisme contrôlant la libération de principe actif, pour les deux formulations et les deux temps de résidence en milieu acide. Cependant, même si le mécanisme de libération peut être affecté, des concentrations d’α-amylase allant de 0 UI/L à 20000 UI/L n'ont pas eu d'incidence significative sur les profils de libération prolongée à partir de comprimés SD HASCA, indépendamment de la durée de séjour en milieu acide, le principe actif utilisé, la teneur en polymère et la différente composition de chaque formulation. Le travail présenté dans cette thèse démontre clairement l'utilité de SD HASCA en tant qu'un excipient à libération prolongée efficace.