Divergence of the normalized wall shear stress as an effective computational template of low-density lipoprotein polarization at the arterial blood-vessel wall interface

Abstract

Background and objective: Near-wall transport of low-density lipoproteins (LDL) in arteries plays a relevant role in the initiation of atherosclerosis. Although it can be modelled in silico by coupling the Navier-Stokes equations with the 3D advection-diffusion (AD) equation, the associated computational cost is high. As wall shear stress (WSS) represents a first-order approximation of the near-wall velocity in arteries, we aimed at identifying computationally convenient WSS-based quantities to infer LDL near-wall transport based on the underlying near-wall hemodynamics in five models of three human arterial districts (aorta, carotid bifurcations, coronary arteries). The simulated LDL transport and its WSS-based surrogates were qualitatively compared with in vivo longitudinal measurements of wall thickness growth on the coronary artery models.

Methods: Numerical simulations of blood flow coupled with AD equations for LDL transport and blood-wall transfer were performed. The co-localization of the simulated LDL concentration polarization patterns with luminal surface areas characterized by low cycle-average WSS, near-wall flow stagnation and WSS attracting patterns was quantitatively assessed by the similarity index (SI). In detail, the latter two represent features of the WSS topological skeleton, obtained respectively through the Lagrangian tracking of surface-born particles, and the Eulerian analysis of the divergence of the normalized cycle-average WSS vector field.

Results: Convergence of the solution of the AD problem required the simulation of 3 (coronary artery) to 10 (aorta) additional cardiac cycles with respect to the Navier-Stokes problem. Co-localization results underlined that WSS topological skeleton features indicating near-wall flow stagnation and WSS attracting patterns identified LDL concentration polarization profiles more effectively than low WSS, as indicated by higher SI values (SI range: 0.17-0.50 for low WSS; 0.24-0.57 for WSS topological skeleton features). Moreover, the correspondence between the simulated LDL uptake and WSS-based quantities profiles with the in vivo measured wall thickness growth in coronary arteries appears promising.

Conclusions: The recently introduced Eulerian approach for identifying WSS attracting patterns from the divergence of normalized WSS provides a computationally affordable template of the LDL polarization at the arterial blood-wall interface without simulating the AD problem. It thus candidates as an effective biomechanical tool for elucidating the mechanistic link amongst LDL transfer at the arterial blood-wall interface, WSS and atherogenesis.

Keywords: Advection-diffusion; Atherosclerosis; Computational fluid dynamics; Near-wall transport; Topological skeleton.