Spiral FLASH

Qualitative imaging with a golden spiral FLASH (spoiled gradient echo) sequence.

Imports

import tempfile
from pathlib import Path

import matplotlib.pyplot as plt
import MRzeroCore as mr0
import numpy as np
from einops import rearrange
from mrpro.algorithms.reconstruction import DirectReconstruction
from mrpro.data import KData
from mrpro.data.traj_calculators import KTrajectoryIsmrmrd
from mrpro.operators.models import SpoiledGRE
from raw2ismrmrd.utils import combine_ismrmrd_files

from mrseq.scripts.spiral_flash import main as create_seq
from mrseq.utils import sys_defaults

/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Settings

We are going to use a numerical phantom with a matrix size of 128 x 128. To ensure we really acquire all spiral arms in the steaady state, we use a large number of dummy excitations before the actual image acquisition.

image_matrix_size = [128, 128]
flip_angle_degree = 12
n_dummy_excitations = 200

tmp = tempfile.TemporaryDirectory()
fname_mrd = Path(tmp.name) / 'spiral_flash.mrd'

Create the digital phantom

We use the standard Brainweb phantom from MRzero, but we choose the B1-field to be constant everywhere.

phantom = mr0.util.load_phantom(image_matrix_size)
phantom.B1[:] = 1.0

Create the spiral FLASH sequence

To create the spiral FLASH sequence, we use the previously imported spiral_flash script.

sequence, fname_seq = create_seq(
    system=sys_defaults,
    test_report=False,
    timing_check=False,
    n_dummy_excitations=n_dummy_excitations,
    rf_flip_angle=flip_angle_degree,
    fov_xy=float(phantom.size.numpy()[0]),
    n_readout=image_matrix_size[0],
    n_spiral_arms=int(image_matrix_size[1]),
)

Target undersampling: 1.0 -  achieved undersampling: 1.00 FOV: 0.200 (k-sapce center) - 0.200 (k-space edge)
Receiver bandwidth: 781 Hz/pixel

Current echo time = 1.195 ms
Current repetition time = 4.570 ms

Saving sequence file 'spiral_flash_200fov_128nx_128na_1ns.seq' into folder '/home/runner/work/mrseq/mrseq/examples/output'.

Simulate the sequence

Now, we pass the sequence and the phantom to the MRzero simulation and save the simulated signal as an (ISMR)MRD file.

mr0_sequence = mr0.Sequence.import_file(str(fname_seq.with_suffix('.seq')))
signal, ktraj_adc = mr0.util.simulate(mr0_sequence, phantom, accuracy=1e-1)
mr0.sig_to_mrd(fname_mrd, signal, sequence)
combine_ismrmrd_files(fname_mrd, Path(f'{fname_seq}_header.h5'))

>>>> Rust - compute_graph(...) >>>
Converting Python -> Rust: 0.00237231 s
Compute Graph
Computing Graph: 0.21284693 s
Analyze Graph
Analyzing Graph: 0.005106506 s
Converting Rust -> Python: 0.06277971 s
<<<< Rust <<<<

<ismrmrd.hdf5.Dataset at 0x7ff58b8d5370>

Reconstruct the image

We use MRpro for the image reconstruction.

kdata = KData.from_file(str(fname_mrd).replace('.mrd', '_with_traj.mrd'), trajectory=KTrajectoryIsmrmrd())
recon = DirectReconstruction(kdata, csm=None)
idata = recon(kdata)

/opt/hostedtoolcache/Python/3.12.13/x64/lib/python3.12/site-packages/mrpro/data/KData.py:166: UserWarning: No vendor information found. Assuming Siemens time stamp format.
  warnings.warn('No vendor information found. Assuming Siemens time stamp format.', stacklevel=1)

Compare to theoretical model

We can now compare the result to a simulation using the idealized signal model for spoiled gradient echo sequences. First, we need to calculate \(T2^*\) using \(1/T2^* = 1/T2 + 1/T2'\).

t2star = 1 / (1 / phantom.T2 + 1 / phantom.T2dash)

model = SpoiledGRE(flip_angle=np.deg2rad(flip_angle_degree), echo_time=kdata.header.te, repetition_time=kdata.header.tr)
idat_model = model(m0=phantom.PD, t1=phantom.T1, t2star=t2star)[0]
idat_model = idat_model.detach().abs().numpy().squeeze()
idat_model /= idat_model.max()
idat_model = np.roll(rearrange(idat_model[::-1, ::-1], 'x y -> y x'), shift=(1, 1), axis=(0, 1))

idat = idata.rss().abs().squeeze().numpy()
idat /= idat.max()

fig, ax = plt.subplots(1, 3, figsize=(15, 3))
for cax in ax:
    cax.set_xticks([])
    cax.set_yticks([])

im = ax[0].imshow(idat_model, vmin=0, vmax=1, cmap='gray')
fig.colorbar(im, ax=ax[0], label='MRzero image')

im = ax[1].imshow(idat, vmin=0, vmax=1, cmap='gray')
fig.colorbar(im, ax=ax[1], label='MRseq image')

im = ax[2].imshow(idat - idat_model, cmap='bwr', vmin=-0.1, vmax=0.1)
fig.colorbar(im, ax=ax[2], label='Difference')

relative_error = np.sum(np.abs(idat - idat_model)) / np.sum(np.abs(idat_model))
print(f'Relative error {relative_error}')
assert relative_error < 0.03

Relative error 0.024650063898768816