Blood flow in deforming vessels

Abstract

Blood flow is most often modeled in vessels whose shape does not change over time. This approach significantly simplifies the calculations and reduces their time. Temporal vascular deformations affect blood flow patterns, the deposition of atherosclerotic plaques, the formation of aneurysms, and many other phenomena. There are two methods to consider blood vessel deformations: registration of vascular geometry by diagnostic imaging such as CT, MRI, ultrasound or the use of the fluid-structure interaction (FSI) models. The first method requires additional procedures for processing image data, and the second requires knowledge of the material properties of the vessel walls, which is a very challenging task for in vivo experiments. The article will show the method to obtain a time-varying geometry of the coronary artery based on images obtained by angioCT. Emerging difficulties arise from the use of images of different resolutions and the need to generate numerical grids of the same topology at every time step. This problem was solved by using image segmentation, smoothing the resulting 3D geometry, and projecting the numerical grid on subsequent shapes of the vessel using diffeomorphism. The simulations have been validated using measurements on a phantom. The resulting velocity fields show the locations of intense oscillations of the shear stress of the wall where the atherosclerotic plaque is deposited.