• No results found


1. INTRODUCTION 8 into the biological tissues. Development of the model requires understanding of drug release kinetics and underlying physiological phenomena governing the drug transport. Any approach used in the present work may be of application in other parts of the human body provided the system does not have major clinical complexity. The outcomes of the models under study will certainly be of some assistance for evolution of future models through the introduction of more biological complexities and different modes of drug administration depending on the objectives of the drug release phenomena adhere to the real situation.

Here, the following six research objectives with pertinent improvement at every stages of the disserta- tion are illustrated and discussed in details.

X Objective 1:

To mathematically model drug release from microparticles with combined effects of solubilisa- tion and recrystallization.

This study aims to provide a comprehensive mathematical model of drug release from micropar- ticles to the adjacent tissues. In the elucidation of drug release mechanisms, the role of math- ematical modelling has been proposed thereby facilitating the development of new therapeutic drug by a systematic approach, rather than expensive experimental trial-and-error methods. In order to study the whole process, a two-phase mathematical model describing the dynamics of drug transport in two coupled media is proposed. Drug release may be described by taking into consideration both solubilisation dynamics of drug crystallites and diffusion of the solubilised drug through the microparticles. In the coupled media, reversible dissociation / recrystallization processes take place. The model seems to point out the important roles played by the diffusion, mass-transfer and reaction parameters, which are the main architects behind drug kinetics across two layers.

X Objective 2:

To mathematically model drug release from polymeric matrix and subsequent drug transport to the biological tissue through endocytosis.

The purpose of the current study is to frame primarily an appropriate mathematical model for drug release from a porous polymeric matrix to biological tissues through endocytosis. Drug release phenomenon needs to be described by taking into account both solubilisation dynamics of solid drug and diffusion of solubilised drug through porous polymeric matrix. In the tissue medium, reversible dissociation / association together with internalization processes of drug are also involved. In order to establish the potency of the proposed model, the simulated results are to be compared with corresponding experimental data to look for any remarkable agreement so as to validate the applicability of the model considered. A quantitative analysis is also planned to be carried out through numerical simulations in order to understand the temporal behaviour of drug concentrations under various situations.

X Objective 3:

To mathematically model drug release kinetics from a degradable polymeric matrix and to carry

1. INTRODUCTION 9 out local sensitivity analysis.

The work undertaken is to concentrate on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Drug release phenomenon is to put forward by considering solubilisation dynamics of drug particles, effective diffusion of the solubilised drug through polymeric matrix along with reversible dissociation / recrystallization process. In the tissue phase, reversible dissociation / association along with internalization processes of drug are to be taken into account. This model is likely to propound the sensitivity of important drug kinetic parameters, such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which may be illustrated through local sensitivity analysis.

X Objective 4:

To have a nonlinear mathematical model of drug delivery from polymeric matrix incorporating more biological complexities.

The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tis- sue. The model embodies drug diffusion, dissolution, solubilisation, polymer degradation and dissociation / recrystallisation phenomena in the polymeric matrix accompanied by diffusion, ad- vection, reaction, internalization and specific / non-specific binding in the biological tissue. The model simulations should deal with the comparison between a drug delivery from a biodegrad- able polymeric matrix and that from a biodurable polymeric matrix. Furthermore, simulated results are to be examined and compared with corresponding existing experimental data to man- ifest the efficaciousness of the advocated model. A quantitative analysis is also in mind to be performed through numerical computation relied on model parameter values. The numerical re- sults obtained are expected to reveal an estimate of the effects of biodegradable and biodurable polymeric matrices on drug release rates. Furthermore, through graphical representations, the sensitized impact of the model parameters on the drug kinetics are to be illustrated so as to assess the model parameters of significance.

X Objective 5:

To mathematically model the liposomal drug release to tumour.

The main objective of this study is to model liposomal drug release, subsequent drug transport in solid tumour along with integrated actions of tumour cell surface and endosomal events. Gen- eralized mathematical model for liposomal drug delivery is proposed in which vital physical phenomena, such as kinetics of liposome-encapsulated drug, free drug release from liposomes, transport of both liposomal drug and free drug into the tumour compartment, plasma clearance, protein-drug interactions, drug-tumour cell receptor interactions, internalization of drug through endocytosis along with corresponding endosomal events are taken into account. Simulated re- sults are to be examined and compared with respective existing experimental data to demonstrate the potency and reliability of the proposed model. Graphical representations of time variant con-

1. INTRODUCTION 10 centration profiles are to be illustrated to understand the underlying phenomena in details. More- over, the model should speak for the sensitized impact of important drug kinetic parameters, such as advection coefficients, drug release coefficient, plasma clearance rate and internalization pa- rameters through graphical portrayals. The proposed model and the simulated results should act as a tool in designing a more effective drug delivery system for cancerous tumours.

X Objective 6:

To study stability analysis of drug dynamics model.

Here, a mathematical model of drug release from polymeric matrix and consequent intracellular drug transport is proposed and needs to be analysed. Modelling of drug release is done through solubilisation dynamics of drug particles, diffusion of the solubilised drug through the polymeric matrix in addition to reversible dissociation / recrystallization process. The interaction between drug-receptor, drug-plasma proteins along with other intracellular endosomal events are to be modelled. Furthermore, besides the stability of the proposed model, several sub-models are also proposed to study for their stability criteria. Prominence may be provided to the reduced model system having requisite relevance to the original system where Quasi Steady State Approxima- tion (QSSA) theory is utilized. For the model to be potent enough to generate appropriate pre- dictive results for drug delivery, the stability properties of equilibrium in the mathematical model are to be analysed both analytically and numerically. Numerical simulation in the embodiment of graphical representations should speak about various vital characteristics of the underlying physical phenomena along with the importance and sensitized impact of the model parameters controlling significant biological functions.