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 the blood is exerting on the surrounding vessel tissue, expressed standardly by the amplitude of the wall shear stress vector (WSS) and its oscillatory shear index. In contrast, our orientation-based shear evaluation detects negative shear stresses corresponding with reversal flow appearing in low shear areas. In our investigations of longitudinal component of the wall shear vector, tangential vectors aligned longitudinally with the vessel are necessary. However, as a result of stenosed regions and imaging segmentation techniques from patients' CTA scans, 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 the orientation-based risk indicators unreliable. We improve the evaluation of longitudinal shear stress by applying the projection of the vessel's center-line to the surface to construct smooth tangetial field aligned longitudinaly 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 as well as to amplitude based indicators. The major benefit of our WSS evaluation based on its longitudinal component for the cardiovascular risk assessment is the detection of negative WSS indicating persitent reversal flow. This is impossible in the case of the amplitude-based WSS.