The combined effect of wall shear stress topology and magnitude on cardiovascular mass transport

Abstract

Cardiovascular disease typically initiates at the vessel wall where near-wall transport of certain biochemicals influences disease initiation and progression. Wall shear stress (WSS) influences these transport processes in a complex manner. WSS magnitude and the shear force exerted on the endothelial cells determine the biochemical flux at the vessel wall. In addition, it has been recently shown that Lagrangian WSS structures (topological features) influence near-wall transport in high Schmidt and Peclet numbers. In this study, the influence of WSS topology and magnitude on surface concentration patterns in shear-dependent biochemical transport problems was explored in a coronary artery stenosis and a carotid artery model. Shear-enhanced and shear-reduced biochemical flux boundary conditions were defined at the wall and surface concentration patterns were obtained by solving the advection-diffusion-reaction equation using the finite element method. Surface concentration patterns were demonstrated to depend on a competition between WSS topology and magnitude. A threshold point was identified where WSS topology determined surface concentration patterns for flux equations closer to homogeneous flux, whereas WSS magnitude dominated surface concentration once the wall flux was sufficiently heterogeneous and strongly dependent on shear stress. Finally, nitric oxide (NO) transport was investigated as an example of an important biochemical with shear-enhanced flux at the vessel wall. It was shown that NO transport was close to the identified threshold where WSS topology and magnitude both influenced surface concentration. This study shows that WSS could potentially be used as a powerful parameter to predict qualitative surface concentration patterns without the need to solve numerically challenging cardiovascular mass transport problems.