Definition of new hemodynamic descriptors based on wall shear stress divergence in carotid bifurcations

Cardiovascular diseases are a major cause of health problems and death in developed countries. Atherosclerosis is the most predominant form of vascular disease and consists in lipid accumulation in the wall of large- and medium-sized arteries. It is associated with systemic risk factors, but disturbed haemodynamics and complex vessel geometry play a localizing role in atherosclerotic plaque formation. The prevailing theory recognizes low and oscillatory wall shear stress (WSS) acting on the endothelial layer as indices of disturbed flow that promote atherosclerosis progression. Contradictory findings and an unsatisfying co-localization of low/oscillatory WSS with atherosclerotic lesions however encouraged the investigation of different WSS features that correlate with disease initiation and progression. So, temporal multidirectionality of WSS has recently been proposed as a pro-atherogenic factor. Aim of this thesis was to introduce new hemodynamic wall parameters (HWPs) able to distinguish among tensile, compressive and uniform shear stresses acting on the endothelial cells. The direction of WSS could influence the morphology and the biology of endothelial cells, increasing the permeability to atherogenic particles under the endothelium and altering the balance between pro- and anti-atherosclerotic signals. However, none of the existing HWPs can capture the spatial directionality of WSS. For this purpose, HWPs based on WSS divergence were proposed: Positive WSS Divergence (DivP), Negative WSS Divergence (DivN) and Oscillatory WSS Divergence Index (ODI). The divergence of WSS can measure the tendency of WSS vector field to converge toward or diverge from a point. More in detail, a positive divergence identifies a source-arranged field, that results in an expansion of the vessel wall, whereas a negative divergence highlights a WSS field with a sink configuration, that causes a compression of the endothelium. So, the proposed divergence-based descriptors allow an evaluation of WSS vector field direction throughout the cardiac cycle. ODI was defined as an index that quantifies the oscillations of WSS direction between the source and sink configurations.The divergence of WSS vector field takes into account both the magnitude and the direction of WSS. So, to evaluate the WSS directionality only, neglecting the variations in WSS magnitude, it was considered the divergence of the normalized WSS. It was computed as the sum of the spatial derivatives of the normalized WSS components in each triangle of the surface meshes.The divergence-based HWPs were computed on the luminal surfaces of forty-six models of right carotid bifurcations acquired from healthy people. Then, a co-localization analysis of the divergence-based descriptors with the established HWPs was carried out through a visual examination of the critical surface areas and a systematic quantification, by means of similarity indices, of the spatial overlapping of surface areas exposed to disturbed flow, as defined by each HWP. Surface areas mainly exposed to negative divergence resulted to be more concentrated around the bifurcation expansion. DivN pointed out regions characterized by sink-arranged WSS field, it moderately co-localized with HWPs that indicate blood stagnation, high near-wall residence time of particles and uniaxial oscillatory WSS. Regions predominantly exposed to positive divergence were mainly located at the bifurcation apex. DivP pointed out multidirectional source-arranged WSS vector field. ODI co-localized with HWPs that identify surface areas exposed to uniaxial highly oscillating WSS, flow reversal regions, high residence time regions and recirculation zones. The potential correlation between the directional changes of WSS that the proposed divergence-based HWPs can identify and atherosclerotic lesion appearance needs to be checked.