A random sampling pattern was obtained by rotating each spiral by a random angle and by delaying for few time steps the gradient waveforms of the different interleaves. A three-dimensional (3D) variable sampling density was obtained by designing different variable density spirals for each slice encoding. The proposed approach was tested with phantom simulations up to a five-fold undersampling factor. Fully sampled 3D dataset of a human knee, and of a human brain, were obtained from a healthy volunteer. The proposed approach was tested with off-line reconstructions of the knee dataset up to a four-fold acceleration and compared with other noncoherent trajectories.

The proposed approach outperformed the standard stack of spirals for various undersampling factors. The level of coherence and the reconstruction quality of the proposed approach were similar to those of other trajectories that, however, require 3D gridding for the reconstruction.

The variable density randomized stack of spirals (VDR-SoS) is an easily implementable trajectory that could represent a valid sampling strategy for 3D compressive sensing MRI. It guarantees low levels of coherence without requiring 3D gridding.