# A mathematical model to simulate controlled drug release in last generation stents

A team of researchers of the Department of Mathematics of the Faculty of Sciences of the University of Coimbra, in collaboration with the Cardiology Department of the Coimbra University Hospital Centre (CHUC, Covões), developed a mathematical model that simulates controlled drug release from last generation stents, also called Drug-Eluting Stents (DES), which is a tool that can have an impact in interventional cardiology.

Drug-Eluting Stents, also known as pharmacological stents, are medical devices used in unclogging arteries. The difference between DES and traditional stents is the fact that DES’ metallic structure is coated by a polymer embedded with a proliferation inhibiter drug. Once the stent is inserted in the target artery, the drug is released, preventing, or at least hindering, the restenosis of the blood vessel. The behaviour of DES, that is, the release throughout time of the drug onto the arterial vessel wall is determined by a complex combination of phenomena that depends on the properties of the polymer, the properties of the drug and the clinical framework of the patient, namely, the clinical status of the target vessel wall.

The model, developed by the team of the Centre of Mathematics of the University of Coimbra (CMUC), composed by researcher José Augusto Ferreira, Maria Paula Oliveira and Jahed Naghipoor, in collaboration with Lino Gonçalves from the Cardiology Department of CHUC, allows to consider parameters that characterise the clinical framework of the patient, such as, the viscosity of the blood and the geometry and composition of the atherosclerotic plaque. Once the clinical framework is personalized and defined, the set of equations that are the backbone of the model simulate the distribution of the drug, during the period of time following the stent deployment, as well as some characteristics of the blood flow in the target deployment area, for each patient. The output of the model can provide an important tool in the clinical decision making process, opening the possibility of defining therapeutic strategies to fight restenosis.

The mathematical modelling of the in vivo coupling of a stent and an arterial vessel, turned out to be a highly challenging task. This difficulty lied on the fact that several interdependent phenomena were taken into account, such as the degradation properties of the polymeric coating, the drug kinetics on the polymeric matrix, its diffusion on the vessel wall and the influence of physiological properties of the vessel wall. «The success of the developed work lies on the close collaboration between the team of mathematicians and cardiologist Lino Gonçalves » states José Augusto Ferreira.

This collaboration between the team of mathematicians of CMUC and the Department of Cardiology of CHUC, developed in the framework of the ECMI Special Interest Group on Advancing the Design of Medical Stents, shows that translational research can escape the traditional “from bench to bedside” approach and motivate alternative strategies that link equations and patients.