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

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.

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.

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.

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