The overall duration of acquiring a Nyquist sampled 3D dataset can be significantly shortened by enhancing the efficiency of $$$k$$$-space sampling. This can be achieved by increasing the coverage of $$$k$$$-space for every trajectory interleave. Further acceleration is possible by making use of advantageous undersampling properties.
This work presents a versatile 3D centre-out $$$k$$$-space trajectory, based on Jacobian elliptic functions (Seiffert's spiral). The trajectory leads to a low-discrepancy coverage of $$$k$$$-space, using a considerably reduced number of read-outs compared to other approaches. Such a coverage is achieved for any number of interleaves and therefore even single-shot trajectories can be constructed. Simulations and in-vivo studies compare Seiffert's spiral to the established 3D Cones approach.