Estimating the irreversible pressure drop across a stenosis by quantifying turbulence production using 4D Flow MRI

Figure 1. Comparison between CFD and 4D Flow MRI simulation at 75% stenosis with Re = 4000. (a) Time-averaged velocity field, (b) laminar viscous stress, and (c) Reynolds stress component along XY direction. Reynolds stress component along XY direction indicates where and are velocity fluctuations along the X and Y axes, respectively. X and Y are normalized by the upstream diameter (D = 14.6 mm). Principal flow direction is toward the positive X direction. The voxel size for MRI simulation was 1 mm. X and Y-axis are depicted in the bottom panel. Z-axis is the through plane direction.

Figure 2. Effects of spatial resolution on turbulence production. (a) CFD, (b) MRI simulation at 1 mm, (c) 1.6 mm, and (d) 2.4 mm. Results shown for CFD and simulated MRI at 75% stenosis at Re = 4000. Principal flow direction is toward the positive X direction.

Figure 3. Comparison between total turbulence production from CFD and corresponding 4D Flow MRI simulation. (a) Correlation of turbulence production between CFD and MRI simulation, (b) enlarged view of plot (a,c) Bland-Altman plot of total turbulence production, and (d) enlarged view of plot (c). Each data point is the total sum of the turbulence production. The spatial resolution for MRI simulation was set to 1 mm. Black solid line in (a and b) indicates unity. Red solid line in (a and b) indicate the regression lines, which was estimated considering all data points with different stenosis severity and PSD. The solid and dashed lines in (c and d) represent mean ± 1.96 SD.

Figure 4. Effects of spatial resolution on the quantification of total turbulence production. (a) Correlation of total turbulence production between CFD and MRI simulation, (b) enlarged view of plot (a,c) Bland-Altman plot of total turbulence production, and (d) enlarged view of plot (c). Black solid line in (a and b) indicates unity. Red solid line in (a and b) indicates the regression line, considering all spatial resolutions. The solid and dashed lines in (c and d) represent mean ± 1.96 SD.

Figure 5. Effects of signal noise on quantification of turbulence production. (a) Effects of signal noise on turbulence production powerdensity at 75% stenosis at Re = 4000. X and Y are normalized by the upstream diameter (D = 14.6 mm). Principal flow direction is toward the positive X direction. The voxel size for MRI simulation was 1 mm. (b) The effects of signal noise on normalized turbulence production power density. Each data point is the mean of ten repetitions at each SNR. SD were not presented for clarity. SD are described in Supplementary Table S2.

Figure 6. Comparison between the measured irreversible pressure drop across the stenosis and predicted pressure drop based on turbulence production. (a) Correlation between irreversible pressure drop between CFD and MRI prediction at 1 mm spatial resolution, (b) Bland-Altman plot. (c) effects of spatial resolution on the correlation between irreversible pressure drop estimates derived from CFD and MRI, and (d) Bland-Altman plot of irreversible pressure drop between CFD and MRI prediction for spatial resolutions 1.0–3.0 mm (c). Black and red solid lines in (a and c) indicate the unity and regression lines, respectively. The solid and dashed lines in (c and d) represent mean ± 1.96 SD.

Figure 7. In vitro demonstration of 4D Flow MRI based turbulence production quantification for estimating the irreversible pressure drop across the stenotic channel. (a) Velocity field with corresponding peak velocity (vvc) and measured irreversible pressure drop. (b) turbulence production power density and measured irreversible pressure drop. Lower panel of (b) depicts a schematic of the 75% constriction channel used in the demonstration and the accompanying turbulence development. (c) comparison of pressure drop estimates based on turbulence production, simplified and extended Bernoulli equations. Black, red, and blue solid lines in (c) indicate the regression lines between the measured and predicted pressure drop using turbulence production, simplified Bernoulli, and extended Bernoulli methods, respectively. The black dashed line indicates the unity. Right panel of (c) describes the correlation and agreement between the measurement and the predicted values.