2D echo-planar imaging

A slice-selective excitation is followed by alternating readout gradients and phase-encode blips that acquire multiple Cartesian lines in one echo train. Spoilers suppress residual transverse coherence between repetitions. Off-resonance phase accumulates during the train and produces geometric distortion along the phase-encode axis. EPI supports rapid structural imaging and functional MRI.

Single-shot acquisition

Every phase-encode line is acquired after one excitation. Echo-train length equals the number of acquired lines and determines the accumulated off-resonance phase across k-space.

from pypulseqpp.sequences import epi2D_sequence

diagram = epi2D_sequence(
    n_x=64,
    n_y=48,
    n_slices=1,
    n_shots=1,
    n_dummy=0,
    fat_saturation=True,
    tr=None,
)
single = epi2D_sequence(n_x=96, n_y=96, n_slices=1, n_shots=1, n_dummy=0)
print(
    f"{diagram.num_blocks} blocks, {diagram.duration()[0] * 1e3:.1f} ms, "
    f"TE {diagram.get_definition('TE')[0] * 1e3:.2f} ms"
)

58 blocks, 50.6 ms, TE 22.14 ms

Sequence diagram

diagram.paper_plot()

Segmentation and in-plane acceleration

Segmentation and in-plane acceleration both reduce echo-train length. n_shots interleaves the lines over several excitations, so every line is still acquired. ry skips lines within one excitation and requires a parallel-imaging reconstruction for the omitted lines. Off-resonance \(\Delta f\) adds a phase of \(2\pi \Delta f\, \mathrm{esp}\) per echo spacing \(\mathrm{esp}\). This phase is linear in \(k_y\) and displaces the image along the phase-encode axis by \(\Delta f \cdot \mathrm{esp} \cdot N_\mathrm{etl}\) pixels, where \(N_\mathrm{etl}\) is the echo-train length. Both segmentation and acceleration reduce \(N_\mathrm{etl}\) and therefore the displacement.

segmented = epi2D_sequence(n_x=96, n_y=96, n_slices=1, n_shots=3, n_dummy=0)
accelerated = epi2D_sequence(n_x=96, n_y=96, n_slices=1, ry=3, n_dummy=0, n_acs_y=0)

designs = {"1 shot": single, "3 shots": segmented, "ry = 3": accelerated}

            echoes  trains  per train   TE (ms)  scan (ms)  px per Hz
1 shot          96       1       96.0     55.94      108.3      0.100
3 shots         96       3       32.0     23.46      131.6      0.035
ry = 3          32       1       32.0     23.44       43.1      0.035

Echo traversal

The ordinate gives the phase-encode line acquired at each echo index. A single shot traverses the axis one line at a time. A segmented acquisition traverses it in steps of n_shots, each shot starting one line further on. An accelerated acquisition traverses it once in steps of ry.

Which lines are acquired

Segmentation and acceleration produce the same train length from different sets of lines: the segmented acquisition acquires every line, the accelerated acquisition one line in three.

Functional MRI time series

Repeated frames form an fMRI time series. The acquisition below uses eight slices in four multiband groups. REP identifies the volume and SLC identifies the group; acquisition times are the start times of the ADC blocks in the sequence.

fmri = epi2D_sequence(
    n_x=64,
    n_y=64,
    n_slices=8,
    multiband=2,
    n_frames=4,
    n_shots=1,
    n_dummy=0,
    fat_saturation=False,
    tr=1.0,
)
labels = fmri.evaluate_labels(evolution="adc")