@UNPUBLISHED{publication1, title = "Drug delivery from bimaterial orthopedic implants: a mathematical approach", author = "{BERNARDES, Raquel} and {FERREIRA, Jos{\'{e}} Augusto} and {OLIVEIRA, Paula de} and {GRASSI, Mario} and {NHANGUMBE, M.}", year = "2018-10-01", abstract = "

The aim of this paper is to study a coupled model that describes drug release from a biodegradable polymeric surface, coated to a metallic device, and the evolution of a bacterial population adhering to the surface. Bacteria can cause infections, that are common events in orthopedic prosthesis, and are often responsible for rejection. A controlled drug delivery to fight bacterial adhesion is crucial in reducing infection rates. A strategy recently adopted to address the problem is to deliver therapeutic agents locally by dispersing them into polymeric implant coatings.

The mathematical model is composed by a system of three partial differential equations that describe the drug release from a biodegradable polymeric coating and by an ordinary differential equation that governs the density of a bacterial population. The link between the space-time differential system and the ordinary differential equation is defined by the mass of drug that is released by the polymeric structure at time t. Quasi-sharp estimates for the bacterial density, that give insight into its dependence on the polymeric properties and the drug characteristics, are established. Numerical experiments illustrating the behaviour of the density of bacteria, in function of the characteristics of the drug-polymeric coating system, are included.

", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }