Accelerated 4D-flow MRI with 3-point encoding enabled by machine learning

Abstract

Purpose: To investigate the acceleration of 4D-flow MRI using a convolutional neural network (CNN) that produces three directional velocities from three flow encodings, without requiring a fourth reference scan measuring background phase.

Methods: A fully 3D CNN using a U-net architecture was trained in a block-wise fashion to take complex images from three flow encodings and to produce three real-valued images for each velocity component. Using neurovascular 4D-flow scans (n = 144), the CNN was trained to predict velocities computed from four flow encodings by standard reconstruction including correction for residual background phase offsets. Methods to optimize loss functions were investigated, including magnitude, complex difference, and uniform velocity weightings. Subsequently, 3-point encoding was evaluated using cross validation of pixelwise correlation, flow measurements in major arteries, and in experiments with data at differing acceleration rates than the training data.

Results: The CNN-produced 3-point velocities showed excellent agreements with the 4-point velocities, both qualitatively in velocity images, in flow rate measures, and quantitatively in regression analysis (slope = 0.96, R² = 0.992). Optimizing the training to focus on vessel velocities rather than the global velocity error and improved the correlation of velocity within vessels themselves. The lowest error was observed when the loss function used uniform velocity weighting, in which the magnitude-weighted inverse of the velocity frequency uniformly distributed weighting across all velocity ranges. When applied to highly accelerated data, the 3-point network maintained a high correlation with ground truth data and demonstrated a denoising effect.

Conclusion: The 4D-flow MRI can be accelerated using machine learning requiring only three flow encodings to produce three-directional velocity maps with small errors.

Keywords: 4D-flow; deep learning; machine learning; phase-contrast.

FIGURE 1

Velocity (shown only for L/R‐component in cm/s), difference from the 4‐point ground truth, and maximum intensity projection (MIP) of the PC‐MRA images of 4‐point velocity from standard reconstruction (4 pt) and 3‐point (3 pt) velocities produced by trained neural network using only three flow encodings. The 3‐point velocities were trained with the following loss function weights: magnitude image (3pt_mag), complex difference image (3pt_CD), and uniform velocity weighting (3pt_vel), in which the inverse of the velocity frequency was used to distribute the weight evenly across all velocities before magnitude weighting. The velocity error is shown as the difference from the 4‐point velocity. The velocity images qualitatively demonstrate the subtle denoising of the 3‐point velocities within the static tissue, which become reduced as the training improved (from top to bottom), while the PC‐MRA images show little changes. In all cases, there is excellent agreement between 4‐point and 3‐point images

FIGURE 2

Scatter plots between 4‐point velocities and 3‐point velocities, shown for different trainings in which the loss function was weighted by the magnitude image (A), complex difference image (B), and uniform velocity weighting (C). As the training increased weighting within vessels (from A to C), the scatter plots showed the slope reaching closer to 1 and increasingly correlated data points taking thinner distributions. The values of the slope, correlation, and root mean square errors are tabulated in Table 1

FIGURE 3

Scatter plots comparing flow (left), maximum velocity (middle), and mean velocity (right) between 4‐point and 3‐point flow encodings. In all cases and in all vessels examined, there were excellent correlations between the two methods. Similar to the velocity correlations, there is a slight underestimation of flow parameters in 3‐point compared to 4‐point

FIGURE 4

Representative streamlines comparing 4‐point (4 pt) and 3‐point (3 pt) with 6× additional acceleration and without additional acceleration (1×). The 3‐point flow encoded images are in good agreement with 6× and 1× additional acceleration as compared to the 4‐point without additional acceleration. The 4‐point with additional acceleration shows greater streamline and velocity heterogeneity and a greater disagreement with the unaccelerated reference

FIGURE 5

RMSE, correlation analysis slope, and R ² as a function of additional acceleration for 4‐point and 3‐point velocity encoded images (all derived from the same data). All values were computed in segmented vessels. The 3‐point encoding is effective even at high accelerations and even produces lower RMSE and higher correlations compared to 4‐point at the same acceleration. The 3‐point flow encoding does produce a lower velocity value 4‐point and the underestimation increases with additional acceleration