3D stack-of-stars spin echo

A slab-selective excitation and 180-degree refocusing pulse form one spin echo, followed by a radial spoke with Cartesian partition encoding. Spoilers suppress unwanted coherence between repetitions. TE and TR determine T2 and longitudinal recovery weighting. Stack-of-stars spin echo supports motion-robust 3D structural imaging.

Nyquist angular sampling

The Nyquist set of spoke angles at every partition.

import pypulseqpp as pp
from pypulseqpp.sequences import se_stack_of_stars3D_sequence

baseline = se_stack_of_stars3D_sequence(n=96, n_z=8, te=None, tr=None, n_dummy=0)
print(f"{baseline.num_blocks} blocks, {baseline.duration()[0]:.2f} s")

9664 blocks, 16.53 s

Sequence diagram

baseline.paper_plot()

Sampling order

The spokes of every partition, over the three k-space axes.

pp.plot.plot_kspace(baseline, color_by="shot")

Angular undersampling

Retaining one spoke angle in four reduces the number of repetitions fourfold while preserving samples at each partition’s k-space origin.

alternative = se_stack_of_stars3D_sequence(
    n=96, n_z=8, ry=4, te=None, tr=None, n_dummy=0
)

                   blocks  duration (s)  acquisitions
Nyquist              9664         16.53          1208
ry = 4               2432          4.16           304

pp.plot.plot_kspace(alternative, color_by="shot")