Toward an accurate estimation of wall shear stress from 4D flow magnetic resonance downstream of a severe stenosis

Abstract

Purpose: First, to investigate the agreement between velocity, velocity gradient, and Reynolds stress obtained from four-dimensional flow magnetic resonance (4D flow MRI) measurements and direct numerical simulation (DNS). Second, to propose and optimize based on DNS, 2 alternative methods for the accurate estimation of wall shear stress (WSS) when the resolution of the flow measurements is limited. Thirdly, to validate the 2 methods based on 4D flow MRI data.

Methods: In vitro 4D MRI has been conducted in a realistic rigid stenosed aorta model under a constant flow rate of 12 L/min. A DNS of transitional stenotic flow has been performed using the same geometry and boundary conditions.

Results: Time-averaged velocity and Reynolds stresses are in good agreement between in vitro 4D MRI data and DNS (errors between 2% and 8% of the reference downsampled data). WSS estimation based on the 2 proposed methods applied to MRI data provide good agreement with DNS for slice-averaged values (maximum error is less than 15% of the mean reference WSS for the first method and 25% for the second method). The performance of both models is not strongly sensitive to spatial resolution up to 1.5 mm voxel size. While the performance of model 1 deteriorates appreciably at low signal-to-noise ratios, model 2 remains robust.

Conclusions: The 2 methods for WSS magnitude give an overall better agreement than the standard approach used in the literature based on direct calculation of the velocity gradient close to the wall (relative error of 84%).

Keywords: 4D flow MRI; Reynolds stress; direct numerical simulation; stenotic transitional flow; wall shear stress.