BLUE RIBBON POSTER IMAGING: Numerical Evaluation of Hemodynamic-Derived Quantities Using the Meshless Method: An Application to Wall Shear Stress.
Abstract
Purpose
Accurate evaluation of near-wall hemodynamic metrics, i.e. wall shear stress (WSS), time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI), is critical for understanding vascular disease progression. These indices depend on spatial derivatives of velocity and pressure fields, which are challenging to compute robustly on complex arterial geometries. We describe a new meshless strong-form method based on Discretization-Correction Particle Strength Exchange (DC PSE) for accurate computation of spatial derivatives of unknown field functions in arterial blood flow simulations.
Methods
The proposed method operates directly on scattered point clouds without the need for a predefined connectivity (mesh). Spatial derivatives are approximated using PSE operators augmented with discretization correction terms enforcing polynomial consistency and significantly reducing truncation errors on irregular nodal distributions. The method is formulated in strong form and integrated within an incompressible Navier-Stokes solver for pulsatile blood flow. Near-wall derivative reconstruction is handled consistently using one-sided corrected operators, enabling direct evaluation of velocity gradients at the arterial wall. Hemodynamic indices, instantaneous WSS, TAWSS, and OSI, are computed from the reconstructed gradients over the cardiac cycle. The method is applied on a benchmark flow case, and on an ascending and descending aorta.
Results
Numerical experiments on idealized and patient-specific arterial geometries demonstrate that DC PSE achieves high-order accuracy for first- and second-order spatial derivatives on highly irregular point sets. DC PSE produces smooth and physically consistent WSS fields, with improved stability and reduced numerical noise compared to conventional meshless collocation and uncorrected PSE approaches.
Conclusion
The proposed DC PSE meshless strong-form method provides an accurate and robust framework for computing spatial derivatives of unknown fields in arterial blood flow simulations. Its ability to reliably evaluate hemodynamically important derived quantities such as WSS-based hemodynamic indices on complex geometries makes it a promising tool for computational hemodynamics and cardiovascular research.