General patterns and asymptotic dose in the design of coated stents

Stents are used in interventional cardiology to keep a diseased vessel open. New stents are coated with a medicinal agent to prevent early reclosure due to the proliferation of smooth muscle cells. It is recognised that it is the dose of the agent that effectively controls the growth. This paper focusses on the asymptotic behaviour of the dose for general families of coated stents under a fixed ratio between the coated region of the stent and the targeted region of the vessel and set therapeutic bounds on the dose. It generalises the results of Delfour, Garon and Longo for stents made of a sequence of thin equally spaced rings to stents with an arbitrary pattern. It gives the equation of the asymptotic dose for a normal tiling of the target region using the theory of tilings, patterns and motifs on a cylinder.