Quantification of Blood Velocity with 4D Digital Subtraction Angiography Using the Shifted Least-Squares Method

Abstract

Background and purpose: 4D-DSA provides time-resolved 3D-DSA volumes with high temporal and spatial resolutions. The purpose of this study is to investigate a shifted least squares method to estimate the blood velocity from the 4D DSA images. Quantitative validation was performed using a flow phantom with an ultrasonic flow probe as ground truth. Quantification of blood velocity in human internal carotid arteries was compared with measurements generated from 3D phase-contrast MR imaging.

Materials and methods: The centerlines of selected vascular segments and the time concentration curves of each voxel along the centerlines were determined from the 4D-DSA dataset. The temporal shift required to achieve a minimum difference between any point and other points along the centerline of a segment was calculated. The temporal shift as a function of centerline point position was fit to a straight line to generate the velocity. The proposed shifted least-squares method was first validated using a flow phantom study. Blood velocities were also estimated in the 14 ICAs of human subjects who had both 4D-DSA and phase-contrast MR imaging studies. Linear regression and correlation analysis were performed on both the phantom study and clinical study, respectively.

Results: Mean velocities of the flow phantom calculated from 4D-DSA matched very well with ultrasonic flow probe measurements with 11% relative root mean square error. Mean blood velocities of ICAs calculated from 4D-DSA correlated well with phase-contrast MR imaging measurements with Pearson correlation coefficient r = 0.835.

Conclusions: The availability of 4D-DSA provides the opportunity to use the shifted least-squares method to estimate velocity in vessels within a 3D volume.

Fig 1.

A representative phantom study demonstrates the flow calculation from 4D-DSA. A, MIP image of the reconstructed phantom with centerline (red) overlaid. B, The contrast waveform map of the voxels along the centerline. The horizontal direction is the timeframe in the 4D-DSA scan, and the vertical direction is the position along the vessel centerline. Each point in the map M(t,z) represents the signal intensity of the voxel at distance z along the centerline and at time frame t. The highlighted area is the optimized waveform region where the pulsatility is strong and consistent. TCCs of 2 selected voxels along the centerline (marked as blue and red stars on A and blue and red curves on B) are shown in C. D, The least-squares differences of these 2 signals as a function of the time-shift, in which the minimal appears at τ⁰ = 5 shown as red arrow on D is considered as the time of bolus transport from the blue voxel to the red voxel. The time-shift as a function of the centerline position was fit to a linear relation (F), where the slope is the inverse of the velocity. E, The flow profile recorded from the flow probe (downsampled to 1/30 second to correspond to the 4D-DSA timeframes). Flow measurement is the average taken between the red lines, which correspond to the optimized window shown in B. AUI indicates arbitrary unit of intensity.

Fig 2.

Linear regression between the flow probe measurements and the 4D-DSA calculations from 15 phantom studies. Evaluations have been obtained with significance levels P = 4.521E-11 for the slope and P = 0.18 for the intercept.

Fig 3.

A representative ICA study. A, The centerline positions of the ICA. B, The contrast waveform map of the voxels along the centerline. The highlighted area is the optimized waveform region for the flow calculation. C, The time-shift as a function of the centerline position was fit to a linear relation in which the slope is the inverse of the velocity.

Fig 4.

Correlation analysis between velocity estimated from 4D-DSA and measured using PC VIPR. The significance level is P = .0002.

Fig 5.

Bland-Altman analysis of 4D-DSA compared with PC VIPR.

Fig 6.

Fluctuation of the velocity estimation with a different average range. A, The flow profile recorded from the flow probe. Red lines define the starting average window. This window was gradually expanded to the purple line. The corresponding mean velocity was shown as the blue curve. A zoom-in of the green window is shown in B. Similarly, velocity calculations have been performed by gradually expanding the window coverage from yellow to purple as shown in the waveform map (C). Estimated velocity varies (D) as the window edge slides from position A toward B. AU indicates arbitrary units.