The Wall Shear Stress Vector: Methods for Characterising Truly Disturbed Flow

Abstract

Haemodynamic stresses acting on the arterial wall may play an important role in the initiation and development of atherosclerosis, and in particular are likely to explain its focal occurrence. Computational fluid dynamic (CFD) simulations of blood flow in arteries have been widely used to investigate this relation and a variety of metrics have been derived to link flow characteristics with lesion prevalence [1]. Although the initial focus was on the magnitude of the time-averaged wall shear stress (TAWSS), an oscillatory shear index (OSI) was subsequently introduced “to describe the shear stress acting in directions other than the direction of the temporal mean shear stress vector” [2]. Biological evidence suggests that flow without a definite direction, in contrast to shear with a clear direction (whether resulting from steady or pulsatile flow), causes sustained molecular signaling of pro-inflammatory and proliferative pathways [3]. Although the OSI has frequently been used to quantify the extent of disturbed flow, we emphasise that no singular metric can fully characterise the flow environment; in particular, we and other research groups [4] note that OSI and other similar metrics are unable to distinguish between simple uniaxial flows (which can be purely forward flowing or reversing) and multi-directional flows, which we term “truly disturbed”. We propose a new method that has this potential, and which complements existing metrics. The new method may help investigations of the importance of flow directionality.