The effect of wall shear stress topology and magnitude on mass transport in atherosclerosis

Atherosclerosis is the major form of cardiovascular disease. The near-wall transport of certain biochemicals and cells influences atherosclerosis. Wall shear stress (WSS) contributes to these transport processes in a complex manner. It has been recently shown that Lagrangian WSS structures, topological features hidden in WSS vector field, govern near-wall transport in high Schmidt and Peclet number flows. Furthermore, the endothelial cells sense and respond to WSS magnitude, which determines the biochemical flux at the vessel wall. Shear-enhanced and shear-reduced biochemical flux boundary conditions were considered at the vessel wall in a coronary artery stenosis and carotid artery model. The advection-diffusion-reaction equation was solved to study biochemical transport. The intertwined relationship between WSS topology, WSS magnitude, and biochemical surface concentration was revealed. A threshold was identified in the wall flux model where WSS topology governed surface concentration patterns when the flux was closer to a homogeneous flux, whereas WSS magnitude determined surface concentration when the flux was sufficiently heterogeneous. Our results shed light on the important, yet complicated role that WSS plays in shear-dependent cardiovascular mass transport problems.