Modelling chemistry and biology after implantation of a drug-eluting stent. Part I: Drug transport

Drug-eluting stents have been used widely to prevent restenosis of arteries following percutaneous balloon angioplasty. Mathematical modelling plays an important role in optimising the design of these stents to maximise their efficiency. When designing a drug-eluting stent system, we expect to have a sufficient amount of drug being released into the artery wall for a sufficient period to prevent restenosis. In this paper, a simple model is considered to provide an elementary description of drug release into artery tissue from an implanted stent. From the model, we identified a parameter regime to optimise the system when preparing the polymer coating. The model provides some useful order of magnitude estimates for the key quantities of interest. From the model, we can identify the time scales over which the drug traverses the artery wall and empties from the polymer coating, as well as obtain approximate formulae for the total amount of drug in the artery tissue and the fraction of drug that has released from the polymer. The model was evaluated by comparing to in-vivo experimental data and good agreement was found

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

One dimensional Saint-Venant system

On étudie certaines solutions explicites du système d'équations de Saint-Venant, que l'on obtient en prescrivant une hauteur d'eau, et en calculant la bathymétrie qui convient. Cette méthode, introduite par McDonald, est adaptée à divers termes de friction

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

Some design considerations for polymer-free drug-eluting stents : a mathematical approach

In this paper we provide the first model of drug elution from polymer-free arterial drug-eluting stents. The generalised model is capable of predicting the drug release from a number of polymer-free systems including those that exhibit nanoporous, nanotubular and smooth surfaces. We derive analytical solutions which allow us to easily determine the important parameters that control the drug release. Drug release profiles are provided, and we offer design recommendations so that the release profile may be tailored to achieve the desired outcome. The models presented here are not specific to drug-eluting stents and may also be applied to other biomedical implants that use nanoporous surfaces to release a drug