Exploring Helical Flow Topology in Coronary Arteries through a Complex Networks-Based Approach

The role of hemodynamics in vascular physiopathology has been widely elucidated through the increasingly detailed modeling of cardiovascular flow. In recent studies, the beneficial role of helical flow in the onset of cardiovascular diseases and its physiological significance was verified. However, the spatiotemporal evolution of spiral blood flow and its level of organization in dynamically correlated structures were not largely examined. The proposed study aims to bridge this gap applying the complex networks (CNs) theory to ten swine-specific hemodynamic models of left anterior descending (LAD) coronary artery. The complexity of arterial flow was schematized through nodes and links and studied applying the characteristic CNs metrics. Starting from available computational fluid dynamics (CFD) data, correlations between the nodal time-histories, defined in the grid points of the CFD volume mesh, of the bulk flow descriptor kinetic helicity density (Hk), were computed. Then, spatial networks were built establishing one topological link between two time-histories correlated above a chosen threshold. Typical CNs metrics were adapted at the case study and the derived information was analyzed and synthesized using both qualitative and quantitative tools. In particular, the networks formalism allowed to identify dynamically correlated helical flow patterns and their persistence length inside the investigated vascular domain. Moreover, the topological nature of the H_k-based networks was exploited to quantify the compactness/dispersion of the correlations between the temporal behavior of helical structures. The findings of this study confirm the flow arrangement in helical counter-rotating structures in the coronary arteries and prove that such structures are all correlated in terms of dynamical behavior. It emerges that the counter-rotating patterns tend to be distributed all along the length of the LAD models, with no significant topologically isolated structures. In addition to that, it was found that the topological dispersion of the correlations between helical flow structures is negatively correlated with the well-established helical rotation balance descriptors, introduced in previous studies. The used approach allows to identify fluid structures with similar dynamical evolution and it represents an alternative method to comprehend vascular physiopathology.