On the Modelling and Numerical Simulation of Non-Newtonian Blood Flow in an Aneurysm

TL;DR

This study models blood flow in cerebral aneurysms using a non-Newtonian haemorheological model, compares it with other models, and introduces stabilization techniques to improve numerical simulations at higher flow parameters.

Contribution

It introduces a haemorheological blood model based on polymer network theory and new stabilization methods for simulating blood flow in aneurysms at higher flow conditions.

Findings

Velocity profiles differ between models, with Owens and Newtonian being similar.

New stabilization techniques enable simulations at higher Weissenberg and Reynolds numbers.

The Owens model captures erythrocyte aggregation effects in aneurysm blood flow.

Abstract

Cardiovascular diseases, specifically cerebral aneurysms, represent a major cause of morbidity and mortality, having a significant impact on the cost and overall status of health care. In the present work, we employ a haemorheological blood model originally proposed by Owens to investigate the haemodynamics of blood flow through an aneurytic channel. This constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. To better understand the effect of rheological models on the haemodynamics of blood flow in cerebral aneurysms we compare our numerical results with those obtained with other rheological models such as the Carreau-Yasuda (C-Y) model. The results show that the velocity profiles for the Newtonian and the Owens models are approximately similar but differ from those of the C-Y model. In order to stabilize our numerical simulations, we propose two new stabilization techniques, the so-called N-Owens and I-Owens methods. Employing the N-Owens stabilization method enables us to capture the effect of erythrocyte aggregation in blood flow through a cerebral aneurysm at higher Weissenberg (We) and Reynolds (Re) numbers than would otherwise be possible.