| Summary: | The controlled drug delivery in drug eluting stents exerts an important influence in decreasing restenosis in intravascular stenting. These stents are coated with drug to avoid the re-narrowing of the arterial wall. The drug is directly associated with the original bare metal stents. Drug eluting stents have plus point of a flexible time delivery of a curative drug to the neighboring arterial tissue. It treats the required injuries efficiently having negligible systemic drug interaction. This thesis aims to develop a mathematical model for describing the procedure of drug distribution from stent coating and from arterial wall. For this purpose, a mathematical model of two phase is presented to simulate the transportation of drug between coating and arterial tissue. This two-phase model explores the impact of non-dimensional parameters such as solid liquid mass transfer rate , ratio of accessible void volume to solid volume and Peclet number on drug release and mass concentrations from coating and tissue layers. For better understanding a 2D mathematical model of biodurable stent coating is developed, where the intravascular distribution of drug from an implanted drug eluting stent in arterial wall is simulated. The model integrates reversible drug binding and diffusion of drug in the stent coating. The arterial wall and coating drug diffusivities are examined for the impact of arterial drug uptake and drug release in the coating. The diffusion coefficient of drug , the diffusion coefficients of wall , , and strut embedment play an important role to regulate the drug release. Moreover, a 3D model of mass concentrations and drug release from the cross section of artery is investigated. The impact of advective and diffusive velocities is explored and these forces can be used to control the mass concentrations of drug. FEM and FDM is used for spatial and temporal discretization of model equations. The sequential and parallel algorithms are developed for numerical simulations. Furthermore, the motivation for using GPU accelerators with CUDA is explained to handle computational complexities. A hybrid CPU/GPU algorithm for the proposed models is designed and satisfactory results for parallel performance indicators such as; speedups Sp, temporal performance Tp, efficiency Ep and effectiveness Fp are obtained. The CN method gives better sequential results because it has less RMSE than GD and BD methods. However, the BD method gives good results for parallel indicators because it involves less computation than GD and CN methods. The sequential and parallel performance of BM method is better as compared to NM and PM methods. The BM method has least RMSE for both sequential and parallel algorithms. The parallel performance indicators Sp, Tp, Ep and Fp for BM method gives better performance than the other methods. Therefore, it is a superior method than the NM and PM methods. Hybrid algorithms are more efficient in large-scale problem simulations as shown in parallel performance results. The governing models in this research provide the basis of a design tool for studying and calculating drug distribution in coating and arterial wall in the application of stent-based drug delivery. The models propose in this research are used for monitoring purpose and to determine drug release, mass transport, visualization and observation. The simulations support to offer a good perception into the potential effects of different parameters such as γ1, e1, Pe, Dc, Dw, Dwx, Dwy and strut embedment can affect the efficiency of drug release.
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