Numerical methods for the estimation of effective diffusion coefficients and other parameters of controlled drug delivery systems

[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.