Four-Dimensional Visualization of Topological Fixed Points in Pulsatile Cardiovascular Flows

Topological features of time-dependent, three-dimensional (3D) vector flow fields, such as wall shear stress (WSS) fixed points, are considered surrogates of pathological blood flow dynamics in cardiovascular diseases. Fixed-point visualizations are typically constrained to two-dimensional (2D) spaces, yet they aim to display complex spatiotemporal (four-dimensional (4D)) dynamics. There is a need for visualization strategies to reduce occlusion and reliance on animations to allow the detection of holistic flow patterns. Using intracranial aneurysms as a use case, we present the fixed-point carousel, a novel approach to visually depicting the "4D" nature of WSS fixed points via (1) topographic mapping of the 3D aneurysm sac to overcome occlusion while preserving fixed-point distances and sac morphological features; and (2) arranging these into a carousel model to present with temporal dimension holistically. Examples are presented for image-based computational fluid dynamic (CFD) models of intracranial aneurysms, illuminating the intricate and distinct fixed-point trajectories and interactions, a necessary step toward understanding the volumetric flow manifolds that drive them for this and other cardiovascular-and potentially nonbiomedical-fluid dynamics applications.