Chaotic velocity fluctuations caused by turbulent blood flow create fluctuations in the shear stress acting on the vascular wall. This is referred to as turbulent wall shear stress (tWSS) and may cause vascular remodeling and increased endothelial cell turnover [1]. The purpose of this work was to explore the use of MR-estimated near-wall turbulent kinetic energy (TKE) for the assessment of tWSS.

In disturbed or turbulent flows, the WSS can be separated into a mean and a fluctuating component using Reynolds decomposition: $$$WSS = \overline{WSS}+WSS'$$$ . WSS' describes the variation of WSS due to fast chaotic variations in velocity. The standard deviation of WSS is a measure of the turbulent WSS (tWSS). 4D flow MRI permits estimation of velocity fluctuation intensity and turbulent kinetic energy (TKE) [2,3]. TKE dissipated near the wall represents a large proportion of the kinetic energy lost near the vascular wall. Therefore, this study assessed the relationship between near-wall TKE and tWSS.

Time-resolved velocity data of non-pulsatile turbulent flow was obtained using the large eddy computational fluid dynamics (CFD) simulations for a patient-derived aortic coarctation (CoA) geometry and an aortic stenosis (AS) geometry [4,5]. Two physiological flow conditions were simulated per geometry. This high-resolution flow data was used as input for simulated PC-MRI measurements and also served as ground truth.

The time-resolved velocity data was used to simulate PC-MRI measurements at three voxel sizes (1, 2, 2.5 mm isotropic) using methods described previously [6,7]. The VENC was set to 1.5 m/s. Partial volume effects at the wall were incorporated into the simulation by modelling the vessel wall as having zero velocity and the same MR signal amplitude as the lumen.

Near-wall TKE estimation was performed for wall voxels by calculating the mean TKE from voxels inside a predefined maximum radius. In order to avoid voxels that have severe overlap with the wall, any voxel that was immediately adjacent to the wall was excluded. The maximum sampling radius from the centre of the wall voxel was 5.5 mm for 1 mm volumes, 7 mm for 2 mm volumes, and 8.75 for 2.5 mm volumes.

Linear regression analysis was used to assess agreement between the MR-estimated near-wall TKE and the true near-wall TKE from CFD. Linear regression was used to assess the relationship between near-wall TKE and tWSS. All regressions had their intercepts fixed to zero, and are reported as slope +/- standard error (SE). A p-value < 0.001 was considered significant.

Linear regression showed a strong correlation between MR-estimated near-wall TKE values and the true near-wall TKE from CFD. Across all models, the mean slope was 1.05 +/- 0.06, with an average R² of 0.90 +/- 0.01. Figure 1 shows representative correlations for the CoA and AS models.

Visual inspection of the estimated near-wall TKE against ground truth tWSS shows that the regions of high near-wall TKE correspond to regions of high tWSS in both the CoA and AS (Figure 2, Figure 3). In both the CoA and AS, the region with highest tWSS and near wall TKE is seen immediately downstream of the constricted region. Linear regression analysis showed strong correlations between near-wall TKE and tWSS (Table 1). In general, R² values were greater than 0.75, except in the CoA with low Reynolds number. All slopes were significantly different from zero.

MR-estimated near-wall TKE correlates strongly with tWSS in models of aortic coarctation and stenosis. The relationship between near-wall TKE and tWSS remains linear with respect to spatial resolution, in contrast to methods which approximate the velocity gradient for WSS estimation. Unfortunately, as yet there is no established link between TKE to tWSS and therefore no procedure to estimate the absolute value of tWSS using TKE. As such, only relative maps of tWSS can be generated using near-wall TKE. However, the resulting maps have strong visual correspondence to the CFD-derived ground truth in all cases. The slope of the regression line appears to decrease as voxel size increases, and a similar trend with respect to Reynolds number is seen. However, more models must be used to investigate these trends.

The possibility to identify regions of elevated tWSS opens new pathways for understanding pathologically driven vascular remodelling, damage to endothelial cells, and plaque rupture.