A Hybrid Lagrangian-Eulerian Solver for Non-Newtonian Arterial Flow with Vessel Compliance

Abstract

Cardiovascular disease remains the leading cause of global mortality, and while current clinical tools offer valuable information needed in their diagnosis, they predominantly assess arterial risk through structural behaviour rather than hemodynamic criteria. This project aims to develop a hybrid computational fluid dynamics solver by coupling the Lattice Boltzmann Method (LBM), Smoothed Particle Hydrodynamics (SPH), and a three element Windkessel lumped parameter model to simulate non-Newtonian blood flow in compliant arterial geometries. The solver is to be validated against analytical methods (such as Poiseuille flow) and complex emergent behaviour (such as the Von Karman vortex), all while being applied to fictional, yet clinically plausible case studies, one of which being a 74.6% carotid artery stenosis case. The solver was able to produce accurate and physical results for the fictional case studies (e.g. peak velocity amplification of 17.4x, maximum wall shear stress of 30.36 Pa, and a trans-stenotic pressure drop of 35.78 mmHg; all are consistent with clinical thresholds). While the solver proved to be accurate and viable as it is, it is limited by its 2D nature, the use of linear spring compliance for the vessel walls, and the Windkessel pressure clamping, each of which were addressed accordingly.