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

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%).

A Novel Estimation Approach of Pressure Gradient and Haemodynamic Stresses as Indicators of Pathological Aortic Flow Using Subvoxel Modelling.

OBJECTIVE: The flow downstream from aortic stenoses is characterised by the onset of shear-induced turbulence that leads to irreversible pressure losses. These extra losses represent an increased resistance that impacts cardiac efficiency. A novel approach is suggested in this study to accurately evaluate the pressure gradient profile along the aorta centreline using modelling of haemodynamic stress at scales that are smaller than the typical resolution achieved in experiments. METHODS: We use benchmark data obtained from direct numerical simulation (DNS) along with results from in silico and in vitro three-dimensional particle tracking velocimetry (3D-PTV) at three voxel sizes, namely 750  µm, 1 mm and 1.5 mm. A differential equation is derived for the pressure gradient, and the subvoxel-scale (SVS) stresses are closed using the Smagorinsky and a new refined model. Model constants are optimised using DNS and in silico PTV data and validated based on pulsatile in vitro 3D-PTV data and pressure catheter measurements. RESULTS: The Smagorinsky-based model was found to be more accurate for SVS stress estimation but also more sensitive to errors especially at lower resolution, whereas the new model was found to more accurately estimate the projected pressure gradient even for larger voxel size of 1.5 mm albeit at the cost of increased sensitivity at this voxel size. A comparison with other methods in the literature shows that the new approach applied to in vitro PTV measurements estimates the irreversible pressure drop by decreasing the errors by at least 20%. CONCLUSION: Our novel approach based on the modelling of subvoxel stress offers a validated and more accurate way to estimate pressure gradient, irreversible pressure loss and SVS stress. SIGNIFICANCE: We anticipate that the approach may potentially be applied to image-based in vivo, in vitro 4D flow data or in silico data with limited spatial resolution to assess pressure loss and SVS stresses in disturbed aortic blood flow.