2D multiple gradient echo sequence. TR = 6000 ms, TE = 6 ms. The image matrix is 256×256. The number of subvoxels is 1×1×4. The total number of subvoxels is 13,572,096. The calculation time was 49.0 s using RTX 2080Ti.

 

Image intensity vs echo time:

 

Pulse sequence chart visualized by the SequenceViewer:

 

One data acquisition sequence.

 

Python source code:

from psdk import *
import numpy as np

gamma = 42.57747892 # [MHz/T]
TR = 6000.0e+3 # [us]
TE = 6.0e+3 # [us]
NR = 256 # Number of readout points
NPE1 = 256 # Number of 1st phase encoding
fov = [220.0, 220.0, 256.0] # [mm]
dwell_time = 10.0 # [us]
slice_width = 5.0 # [mm]
gx_value = 1e+6 / (dwell_time * gamma * fov[0]) # [mT/m]
gy_value = 2e+6 / (dwell_time * gamma * fov[1]) * NPE1 / NR # [mT/m]
gz_value = 1.25 / (slice_width * 1.0e-3) / gamma # [mT/m]
gx_rise_time = 300.0 # [us]
gy_rise_time = 300.0 # [us]
gz_rise_time = 300.0 # [us]
ex_pulse_width = 3200.0 # [us]
excitation_pulse_flip_angle = 90.0 # [degree]

def sinc_with_hamming(flip_angle, pulse_width, points, *, min=-2.0*np.pi, max=2.0*np.pi):
    x0 = np.arange(min, max, (max - min) / points)
    x1 = x0 + (max - min) / points
    y = (np.sinc(x0 / np.pi) + np.sinc(x1 / np.pi)) * 0.5 * np.hamming(points)
    return flip_angle * y * points / (y.sum() * pulse_width * 360.0e-6 * gamma)

with Sequence('2D multiple GRE'):

    with Block('Excitation', ex_pulse_width + 2.0*gz_rise_time):
        GZ(0.0, gz_value, gz_rise_time)
        RF(gz_rise_time, sinc_with_hamming(excitation_pulse_flip_angle, ex_pulse_width, 160), ex_pulse_width / 160)
        GZ(ex_pulse_width + gz_rise_time, 0.0, gz_rise_time)

    with Block('PhaseEncoding', NR // 2 * dwell_time + gx_rise_time * 2.5 + 920):
        GX(0.0, -gx_value, gx_rise_time)
        GY(0.0, ([gy_value * (i - NPE1 // 2) / NPE1 for i in range(NPE1)], ['PE1']), gy_rise_time)
        GY(NR // 2 * dwell_time, 0.0, gy_rise_time)
        GX(NR // 2 * dwell_time + gx_rise_time * 0.5 + 920, gx_value, gx_rise_time * 2.0)
        GZ(0.0, -gz_value * 0.5 * 3.2e+3 / (NR // 2 * dwell_time), gz_rise_time)
        GZ(NR // 2 * dwell_time, 0.0, gz_rise_time)
        
    with Block('Readout', NR * dwell_time):
        AD(0.0, NR, dwell_time)
 
    with Block('Reverse', gx_rise_time * 2.0):
        GX(0.0, ([-gx_value, gx_value], ['Echo']), gx_rise_time * 2.0)
        
    with Block('Rewinding', NR // 2 * dwell_time + gx_rise_time):
        GY(0, ([gy_value * (NPE1 // 2 - i) / NPE1 for i in range(NPE1)], ['PE1']), gy_rise_time)
        GX(NR // 2 * dwell_time - gx_rise_time * 0.5, 0.0, gx_rise_time)
        GY(NR // 2 * dwell_time, 0.0, gy_rise_time)
        
    with Main():
        with Loop('PE1', NPE1):
            BlockRef('Excitation')
            WaitUntil(TE + ex_pulse_width * 0.5 + gz_rise_time - NR // 2 * 2 * dwell_time - gx_rise_time * 2.5)
            BlockRef('PhaseEncoding')
            with Loop('Echo', 15):
                WaitFor(920)
                BlockRef('Readout')
                WaitFor(920)
                BlockRef('Reverse')
            WaitFor(920)
            BlockRef('Readout')
            WaitFor(920)
            BlockRef('Rewinding')
            WaitUntil(TR)