Modelling diffusion from drug eluting stents in compressed arterial tissue

Coronary artery disease is atherosclerosis of the coronary arteries that results in blockages or narrowing of the arterial wall, is caused by the accumulation of lipid-laden atherosclerotic plaque. Drug eluting stents were developed to essentially replace their bare metals stent predecessors, in an effort to combat the effect of restenosis following angioplasty. However, the incidence of late stent thrombosis after drug eluting stent implantation has become a major issue in post percutaneous coronary intervention patient care. Recent clinical follow up reviews have indicated the need for therapeutic drug delivery in the early time periods post procedure, in an effort to inhibit smooth muscle cell proliferation. A key element in determining the therapeutic success of a drug eluting stent is an in depth understanding of the physical factors that affect the mass transport of anti-proliferative drug species to the injured region of the arterial wall. Current studies focus mainly on stent design, coatings and deployment techniques; however, few studies address the issue of the physics three dimensional mass transport in the arterial wall. There is a dearth of adequate validated numerical mass transport models that simulate the physics of diffusion dominated drug transport in the arterial wall whilst under compression. A novel experimental setup from a previous body of work was adapted and an expansion of that research was carried out in an effort to validate Fick’s 2nd law in three-dimensional form for diffusion dominated mass transport. Firstly this study developed new methods in characterising the mass transport properties of a porous media such as the porosity and tortuosity. Secondly the study developed a more sensitive method for measuring the concentration of the species by relating induced colour changes on the porous media by diffusing species to percentage concentration. Consequently, it revalidated mass transport in the radial direction and the results highlight the need for an evaluation of the governing equation for transient diffusive mass transport in a porous media, in its current form, to be further explored. This study investigated more efficient numerical modelling methods such as modelling the internal diffusion of drug species in the polymer coating of a drug eluting stent in one dimensional form where it can be applied to both two and three dimensional models. Further model reduction strategies were developed where it was found that a 2D stent strut model could adequately represent a 3D model by appropriately accounting for the missing dimension. It was shown that boundary condition selection has a key influence on the outcomes of numerical predictions in terms of therapeutic drug delivery to the arterial wall where care and justification must be exercised when assigning such conditions. A key factor that has been shown to influence drug transport in the arterial wall is compression yet many studies chose to neglect its presence from geometries while other studies do include it but do not account for its repercussions on transport properties at such regions therein. This study developed mathematical models to represent the influence that compression has on therapeutic drug delivery in the arterial wall. A deductive method was employed to estimate the radial tortuosity of the arterial wall and a sensitivity analysis was conducted on possible longitudinal tortuosity based on reported evidence from literature which states that the arterial wall has an anisotropic ultra-structure. The first phase of numerical models focussed on modelling the effect that compression has on drug transport in an isotropic arterial ultra-structure and the second phase expanded the mathematical model to account for these bi-directional transport properties of an anisotropic arterial ultra-structure. Additional numerical models that were developed within this study focussed on assessing the influence of a host of physical factors that may either facilitate or impede therapeutic drug delivery from the unit cell of an idealised drug eluting stent into the depth of the arterial wall. Finally, the mathematical and numerical modelling methods were applied to a commercially available drug eluting stent in an effort to test the efficacy of such modelling methods. In addition to this, a supplementary study was conducted to compare the efficacy of a patented drug eluting balloon design (developed from separate research project) to a traditional design that is currently on the market. It was found the utilising the principle of variable compression can significantly increase the spatial distribution of therapeutic levels of drug in the arterial wall. This study contributed advancements to research in both experimental and numerical approaches. A full characterisation of an anisotropic porous media was experimentally conducted along with a more sensitive concentration measurement technique. While the numerical prediction does not fully correspond to the experimental results it does indicate the need for future work to be conducted on assessing the validity of Fick’s 2nd law and its applicability in mathematically representing mass transport in a porous media