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[Truncated abstract] In this thesis we develop various numerical tools for estimating unknown parameters that characterise the diffusion property of a polymeric drug device in controlled drug delivery. Two types of fluid systems are considered in this work: the rotating fluid system and the flow-through fluid system. Based on the consideration of effects from the initial burst and boundary layer phenomena, three mathematical models are developed for the parameter estimation problem. They are the basic model (BM), initial burst model (IB) and boundary layer model (BL). The latter two models can also be combined to form the initial burst and boundary layer model (IB+BL). In these models, up to four unknown parameters need to be determined. These are the diffusion coefficient in the initial burst phase, diffusion coefficient after the initial burst, width of the boundary layer and the time of the initial burst. We first develop analytical solutions for the diffusion process of a drug from a spherical device to a finite external volume. In these solutions, we assume that the container of the system is spherical and concentric with the spherical device. The formula for the ratio of the mass released in a given time interval and the total mass released in infinite time is also derived for both BM and IB models. We then propose an optimisation approach to the estimation of the parameters based on a nonlinear least-squares method and the developed analytical solutions. A new observer approach method is developed for the parameter estimation problems. In this approach, we construct estimators for the unknown effective diffusion coefficients characterising the diffusion process of a drug release device using a combination of state observers from the area of adaptive control and the developed drug diffusion models. We show that the constructed systems are asymptotically stable and the estimators converge to the exact diffusion coefficients. An algorithm is proposed to recursively compute the estimators using a given time series of a release profile of a device. The numerical results show that this approach is much faster than the conventional least squares method when applied to the test problems. We then present a full numerical approach to the estimation of effective diffusion coefficients of drug diffusion from a device into a container in a flow-through fluid system. Compared to the rotating fluid system considered earlier, this system has a source and a sink condition due to a fluid flowing through the system at a constant rate. In this approach we first formulate the drug delivery problem as an initial boundary value problem containing the diffusion equation. We then propose a continuous nonlinear least-squares problem containing the system as a constraint to estimate the unknown parameters. The nonlinear optimisation problem is discretised by applying a finite volume scheme in space and an implicit time stepping scheme to the equation system, yielding a finite-dimensional nonlinear least-squares problem. Finally, we extend the full numerical technique to three dimensions for estimating effective diffusion coefficients of drug release devices in both rotating and flow-through fluid systems. The 3-dimensional full numerical technique is crucial for solving the parameter estimation problems in their real 3D geometries...
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An introductory but detailed treatise which includes some 1,000 references and solved examples and end-of-chapter problems, making it useful to both students and practitioners. The pharmokinetics, pharmacodynamics, and biological and biopharmaceutical parameters pertinent to each route of administra
Nowadays, advanced controlled drug delivery systems have been attracted the pharmaceutical research studies. As several experiments have to be done for pharmaceutical approaches, mathematical modeling becomes important. Mathematical modeling of drug release provides better understanding of controlled drug delivery system and would help to optimize the system without huge number of expensive experiments. Diffusion is the predominant transport phenomena of the drug delivery systems. Therefore, optimizing the parameters related to diffusional mass transport, such as diffusion coefficient and porosity, would be the essential key to get better controlled drug release profile. One of the challenges of controlled drug delivery systems is the initial burst, which decreases the effective lifetime of drug and would cause toxicity. This challenge has been solved by using a coating layer to control the drug release. Regarding to this issue, promising modeling results have been shown in this study and all the modeling data have been fitted with available experimental set of data. The mathematical modeling results in a partial differential equation. The analytical solution for the simplified equation is provided in this study. However, the boundary condition for the outer layer is complicated and the solution for the real problem would be available by using numerical methods. Finite difference method provided the numerical solution to the real problem and MATLAB software facilitate the process of solving the equation numerically.
Provides solutions for two- and three-dimensional linear models of controlled-release systems Real-world applications are taken from used to help illustrate the methods in Cartesian, cylindrical and spherical coordinate systems Covers the modeling of drug-delivery systems and provides mathematical tools to evaluate and build controlled-release devices Includes classical and analytical techniques to solve boundary-value problems involving two- and three-dimensional partial differential equations Provides detailed examples, case studies and step-by-step analytical solutions to relevant problems using popular computational software
The goal of every drug delivery system is to deliver the precise amount of a drug at a pre-programmed rate to the desired location in order to achieve the drug level necessary for the treatment. An essential guide for biomedical engineers and pharmaceutical designers, this resource combines physicochemical principles with physiological processes to facilitate the design of systems that will deliver medication at the time and place it is most needed.
Demand for better reliability from drug delivery systems has caused designers and researchers to move away from trial-and-error approaches and toward model-based methods of product development. Developing such models requires cross-disciplinary physical, mathematical, and physiological knowledge. Combining these areas under a single cover, Under
Exploring how to apply in vitro/in vivo correlations for controlled release dosage forms, Bioavailability of Drug Delivery Systems: Mathematical Modeling clearly elucidates this complex phenomena and provides a guide for the respective mathematical modeling. The book introduces mathematical modeling methods for calculating the profiles of plasma le
Numerical analysis of matter transfer is an area that pharmacists find difficult, but which is a technique frequently used in preparing controlled drug release and oral dosage forms. This book provides clear and straightforward information enabling the reader to carry out numerical analysis of matter transfer - a vital processs when looking at the formulation of oral dosage forms with controlled drug release. The drug is dispersed in a polymeric matrix either biodegradable or not, the basis of which is the transfer of the liquid and the drug through dosage form. Information on this diffusion is found either through mathematical treatment when the problem is simple, or through numerical analysis for more complex problems. Professor Vergnaud demonstrates and clarifies these, modelling the process of drug delivery by using numerical analysis and computerization. A simulation of the process is provided, together with a determination of the effects of all parameters, and the author uses both mathematical and numerical models to predict the preparation of new dosage forms able to fulfil specific conditions.
Published in 1983: Volume 2 deals with critical analyses of various test methodologies of polymeric implants, including their acute and chronic toxicological evaluation.