Hodge decomposition of wall shear stress vector fields characterizing biological flows

Area of Science:

• Biomedical Engineering
• Computational Fluid Dynamics
• Medical Imaging Analysis

Background:

• Wall shear stress (WSS) analysis is crucial for understanding aortic blood flow dynamics.
• Existing methods may not fully capture complex flow patterns influenced by aortic geometry.
• A new decomposition technique is needed to differentiate physiological and pathological blood flow.

Purpose of the Study:

• To introduce a discrete boundary-sensitive Hodge decomposition for WSS vector field analysis in aortic blood flow.
• To investigate the components of WSS and their relation to flow characteristics.
• To assess the method's ability to distinguish between healthy and diseased aortic conditions.

Main Methods:

• Developed a discrete boundary-sensitive Hodge decomposition based on Hodge-Morrey-Friedrichs decomposition.
• Applied the method to simulated phantom geometries (duct, idealized aorta) to analyze WSS components.
• Conducted a comparative analysis of WSS in patients with coarctation of the aorta (CoA) before/after treatment and healthy controls.

Main Results:

• The decomposition successfully separated WSS into gradient, co-gradient, and three boundary-induced harmonic fields.
• Distinguished inlet-driven harmonic flow from topology-induced harmonic circulations.
• Demonstrated significant differences in WSS patterns between CoA patients and controls, and pre/post-treatment.

Conclusions:

• The proposed Hodge decomposition offers a novel approach to WSS analysis in aortic blood flow.
• It effectively differentiates harmonic flow components and identifies geometric influences.
• The method provides a new basis for WSS-based classification of pathological and physiological blood flow, particularly in conditions like CoA.