Mathematical Analysis of Some Models for Drug Delivery

This thesis is concerned with the mathematical modelling of controlled drug release from a number of delivery systems. There are two major strands to the work: (i) modelling release from affinity-based systems, and, (ii) modelling release from thermoresponsive films. A model that is related to the affinity models is also considered, and used to evaluate the effect of reversible binding on drug release in vivo. In Chapter 1, the topic is introduced by briefly discussing some commonly used drug delivery systems and the mathematical models that have been developed to describe them. In Chapters 2 and 3, two affinity-based delivery systems composed of modified fibrin matrices are analysed. The model equations are reduced, and the non-dimensional parameters governing the release rate identified. For both models, a parameter regime that minimises the passive leakage of growth factor from the system is found. In Chapter 4, a reaction-diffusion model for drug redistribution in tissue is considered, and some generic problems to evaluate drug penetration and persistence in tissue are analysed. In Chapter 5, a model for pulsatile drug release from the thermoresponsive polymer poly(N-isopropylacrylamide) is developed. Theoretical pulsatile release profiles are compared with experimental profiles generated by colleagues working at the National Centre for Biomedical and Engineering Sciences, and the correspondence between theory and experiment is found to be good. In Chapter 6, a mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delivery system based on a thermoresponsive polymer and a cooling device, and it is found that the system may be realised for realistic parameter values and materials. Finally, in Chapter 7, an evaluation of the modelling work of the thesis is presented, and strengths and weaknesses of some of the models are identified