A framework for comparing vascular hemodynamics at different points in time

Computational simulations of blood flow contribute to our understanding of the interplay between vascular geometry and hemodynamics. With an improved understanding of this interplay from computational fluid dynamics (CFD), there is potential to improve basic research and the targeting of clinical care. One avenue for further analysis concerns the influence of time on the vascular geometries used in CFD simulations. The shape of blood vessels changes frequently, as in deformation within the cardiac cycle, and over long periods of time, such as the development of a stenotic plaque or an aneurysm. These changes in the vascular geometry will, in turn, influence flow within these blood vessels. By performing CFD simulations in geometries representing the blood vessels at different points in time, the interplay of these geometric changes with hemodynamics can be quantified. However, performing CFD simulations on different discrete grids leads to an additional challenge: how does one directly and quantitatively compare simulation results from different vascular geometries? In a previous study, we began to address this problem by proposing a method for the simplified case where the two geometries share a common centerline. In this companion paper, we generalize this method to address geometric changes which alter the vessel centerline. We demonstrate applications of this method to the study of wall shear stress in the left coronary artery. First, we compute the difference in wall shear stress between simulations using vascular geometries derived from patient imaging data at two points in the cardiac cycle. Second, we evaluate the relationship between changes in wall shear stress and the progressive development of a coronary aneurysm or stenosis.