Longitudinal wall shear stress evaluation using centerline projection approach in the numerical simulations of the patient-based carotid artery

In this numerical study, areas of the carotid bifurcation and of a distal stenosis in the internal carotid artery are closely observed to evaluate the patient’s current risks of ischemic stroke. An indicator for the vessel wall defects is the stress exerted by blood on the vessel tissue, typically expressed by the amplitude of the wall shear stress vector (WSS) and its oscillatory shear index. To detect negative shear stresses corresponding with reversal flow, we perform orientation-based shear evaluation. We investigate the longitudinal component of the wall shear vector, where tangential vectors aligned longitudinally with the vessel are necessary. However, resulting from imaging segmentation resolution of patients’ computed tomography angiography scans and stenotic regions, the geometry model’s mesh is non-smooth on its surface areas and the automatically generated tangential vector field is discontinuous and multi-directional, making an interpretation of our orientation-based risk indicators unreliable. We improve the evaluation of longitudinal shear stress by applying the projection of the vessel’s centerline to the surface to construct smooth tangential field aligned longitudinally with the vessel. We validate our approach for the longitudinal WSS component and the corresponding oscillatory index by comparing them to results obtained using automatically generated tangents in both rigid and elastic vessel modeling and to amplitude-based indicators. We present the major benefit of our longitudinal WSS evaluation based on its directionality for the cardiovascular risk assessment, which is the detection of negative WSS indicating persistent reversal or transverse flow. This is impossible in the case of the amplitude-based WSS.