The dynamics of angioplasty: Effects of vascular bed and lesion morphology

This thesis sought to examine the influence of the vascular bed on the tissue response to endovascular stent implantation. Closed form analytic solutions were obtained for the different beds studied. Ideal arteries were considered of normal, tapered, curved, or eccentric morphology. The application of the stent boundary conditions in the appropriate defining equations produced the desired strains and stresses. It was found that even severe curvature could not produce stresses that came close to those obtained with tapered and eccentric vessels. The highest absolute stresses (circumferential) in the curved, tapered, and eccentric vessels were 38.158 kPa, 59.117 kPa, and 97.721 kPa respectively. For comparison, the stresses in 'normal' vessels are 38 kPa. Eccentric vessels produced the highest variation in stresses (66%) followed by variations in the tapered vessel (27%). In contrast blood pressure loading created far lower stresses, and shear forces from blood flow were negligible (0.63 Pa and 0.9 Pa for the aorta and renals). In the tapered bed, the maximal stress principally arose was at the smallest diameter location of the arterial wall. This corresponded to a maximum level of strain at the smallest diameter section of the tapered vessel wall (in a vessel with a monotonically decreasing diameter or in other words in a vessel with a constant taper, this corresponds to either the top or the bottom portion of the vessel). Thus, one design that alleviates this problem inputs a uniform strain, not a uniform displacement, in the arterial wall. This minimizes both the absolute stresses and the variation in axial stresses (ideally, the variation should approach zero in the 'constantstrain stent'. In conclusion, the eccentric vessel imposes far higher stresses than other vessel geometries, with the tapered geometry following close behind. The curved vessel stresses are negligible. Thesis Supervisor: Elazer R. Edelman Title: Thomas D. and Virginia W. Cabot Professor, Harvard-MIT Department of Health Sciences and Technology