Mathematical modelling of NABD release from endoluminal gel paved stent

Coronary restenosis consists of the partial/total re-occlusion of the artery lumen following percutaneous transluminal angioplasty (PTCA). In order to match this pathology, PTCA is followed by the implantation of rigid scaffolds (stent or coated stent) aimed to contrast the most important mechanical (coronary wall elastic recoil and late remodelling) and biological (smooth muscle cells iper-proliferation) factors leading to restenosis. In the light of the clinical problems recently arisen about the use of traditional coated stents, this paper proposes a theoretical study to comprehend the release kinetics of novel anti-proliferative drugs, i.e. nucleic acid based drugs (NABD), complexed with the proper delivery agent (DA). The release of NABD-DA is supposed to occur from a double gel layer adhering to coronary wall and embedding the stent. The proposed mathematical model assumes that diffusion, convection and cellular internalisation/metabolism are the leading mechanisms ruling drug spreading in the coronary wall. In addition, stent void fraction, positioning (totally embedded or totally out of the coronary wall) and continuous or discontinuous character of the gel layer are other three important model parameters. In order to generalise the results, stent geometry is idealised as a series of not connected, equally spaced, rings positioned in the stented zone. In correspondence of stent strut, drug transport cannot occur. The most important outcomes of this study are that, in the usual void fraction range (0.7-0.9), stent presence does not sensibly affect NABD-DA release kinetics. In addition, whereas stent positioning in the continuous gel configuration (totally embedded or totally out of coronary wall) is not very important, in the discontinuous case, it becomes relevant. Finally, this study evidences that a proper mixture of NABD complexed with different (in dimensions and kind) DA can ensure an almost constant NABD coronary concentration for several months, as requested by clinical observations.