Mathematical modeling in assessing the risk of restenosis after carotid endarterectomy

Abstract

Carotid endarterectomy is the main way to combat atherosclerosis of the carotid arteries, which disrupts cerebral circulation. The generally accepted marker of atherogenesis risk are hemodynamic indices associated with near-wall shear stress. The purpose of the work is to conduct a comparative analysis of hemodynamic indices in various carotid bifurcation models. The influence of a virtual change in the geometric shape of the model in order to optimize hemodynamic indices is also being studied. On the basis of computed angiography data, carotid bifurcation models are constructed, in which critical zones of hemodynamic indices are built using computational fluid dynamics. A comparative analysis of the critical zones for different classes of models is carried out. Comparison of averaged indices for critical zones between 'normal' and post-operative groups gave more than 5-x worse results for the latter. The same results for the near-bifurcation parts of the zones give a 25% better result for postoperative models. Virtual ‘removal’ of insignificant plaques leads to a deterioration of the indices of up to 40% in the places of the plaque’s former location. The described method makes it possible to build the indices critical zones and compare them for various types of models. A technique for virtual changing the shape of a vessel (virtual surgery) is proposed. The novelty of the approach lies in the use for comparative analysis both real vessel models and hypothetical ‘improved’ virtual ones, as well in the proposed division of post-operative model’s critical zones into subzones of different genesis.