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

Area of Science:

• Biomedical Engineering
• Fluid Dynamics
• Medical Visualization

Background:

• Topological features like wall shear stress (WSS) fixed points in 3D vector flow fields indicate pathological blood flow in cardiovascular diseases.
• Current 2D visualizations of 4D spatiotemporal dynamics are limited by occlusion and animation dependence, hindering holistic pattern detection.

Purpose of the Study:

• To develop novel visualization strategies for depicting the 4D nature of WSS fixed points in cardiovascular flows.
• To overcome limitations of current methods in reducing occlusion and reliance on animations for detecting flow patterns.

Main Methods:

• Introduced the 'fixed-point carousel,' a novel visualization approach.
• Employed topographic mapping of the 3D aneurysm sac to preserve fixed-point distances and morphological features while mitigating occlusion.
• Arranged mapped features into a carousel model to holistically present the temporal dimension of WSS fixed points.

Main Results:

• Demonstrated the method using image-based computational fluid dynamic (CFD) models of intracranial aneurysms.
• Successfully illuminated intricate and distinct fixed-point trajectories and their interactions within the aneurysm models.
• Showcased the ability to visualize complex 4D dynamics without significant occlusion or animation.

Conclusions:

• The fixed-point carousel offers a new strategy for visualizing complex 4D flow dynamics, particularly in cardiovascular applications like intracranial aneurysms.
• This method facilitates a better understanding of volumetric flow manifolds driving pathological blood flow.
• The approach has potential applications beyond cardiovascular fluid dynamics, including other biomedical and non-biomedical fluid dynamics.