2D spiral gradient echo

A spoiled low-flip-angle excitation is followed by one spiral interleaf. Gradient and RF spoiling suppress residual transverse coherence between repetitions. TR and flip angle primarily determine T1 weighting; off-resonance and T2* decay affect the spiral readout. Spiral SPGR supports rapid dynamic and structural imaging.

Constant-density spiral

Sixteen interleaves at a constant pitch, which sample the disc at the Nyquist spacing.

import pypulseqpp as pp
from pypulseqpp.sequences import gre_spiral2D_sequence

baseline = gre_spiral2D_sequence(
    n=192, n_shots=16, n_slices=1, te=None, tr=None, n_dummy=0
)
print(f"{baseline.num_blocks} blocks, {baseline.duration()[0]:.2f} s")

80 blocks, 0.24 s

Sequence diagram

baseline.paper_plot()

Sampling order

Each interleaf is the same spiral gradient waveform, rotated to its own angle by a rotation extension.

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

Variable density

density='dual' preserves the Nyquist spacing near the origin and increases the pitch at larger radii. The shorter readout requires a reconstruction that accounts for peripheral undersampling.

alternative = gre_spiral2D_sequence(
    n=192,
    n_shots=16,
    n_slices=1,
    density="dual",
    periphery_undersampling=2.0,
    te=None,
    tr=None,
    n_dummy=0,
)

                   blocks  duration (s)  acquisitions
constant               80          0.24            16
dual density           80          0.19            16

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