Stents have proven very effective in opening the lumens of blocked and diseased arteries, leading to an increased quality of life for thousand of patients. Due to their success, stents have grown into a $1.5 billion dollar industry, but unfortunately still suffer from failure rates of 20–30% in the first year. Many of these failures can be traced back to restenosis or thrombosis of the stented arteries, a problem which conventional self-expanding or balloon-expanded stents have not proved effective in combating. Mathematical and experimental research shows that stents create adverse flow conditions and increase the stresses found around the implants, and trials of designs intended to reduce these effects have proven effective in combating restenosis. The goal of this research was to investigate mathematically design considerations for an improved stent that can reduce these negative effects. This was accomplished through the construction of a onedimensional numerical model for the fluid mechanics of the artery that was implemented using FEA and a combination of WENO and Runge-Kutta methods. The output from this model was compared with solutions from the literature and with in-vitro experimental results. Based on these tests it was concluded that the model accurately predicted the behavior of the pressure waves in a vessel. These numerical models were then used to evaluate several proposed designs. The pressure wave reflection was found to be controlled entirely by the design of the stent ends; mid-length variations in stent compliance provided no change in the model behavior. Also, a region of gradual transition between the low stiffness of the artery and the increased stiffness of the stent, while useful for reducing wall stresses, proved ineffective in reducing the magnitude of the reflected pressure waves. The best design for minimizing pressure wave reflection was found to be one that minimized total stent length.

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