In this thesis we analyze simple compartment models for percutaneous drug absorption including transdermal drug delivery, in which a delivery device is fastened adhesively to the surface of the skin, and topical drug delivery, in which a drug is spread across the skin as a paste. We have used these models to gain a better understanding of factors that influence the time it takes the drug to enter the blood stream.
Prior to our mathematical modeling, we present a literature review reviewing background information on percutaneous drug absorption along with the approaches that have been used to model the phenomena and relevant experimental work.
In our first mathematical model the skin is viewed as a single compartment. This assumption leads to a system of two ordinary differential equations representing the concentrations of drug in the skin and the delivery device.
Expanding on the single compartment model, we investigate double and triple compartment models in which the skin is modelled as two and three layers respectively. These models better account for the physical barrier created by the skin which delays the drug from entering the bloodstream.
The compartment models have also been extended to investigate the reapplication of a delivery device. In a single application a delivery device is attached to the skin, and then removed after a particular amount of time. In the reapplication of a delivery device, the vehicle is removed after a particular time, and then a new vehicle is attached to the skin.
Finally, as a result of our literature survey and our investigation into compartment models, we suggest areas for future work which extends the models considered here.
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