Katsumi Kose^{1} and Ryoichi Kose^{1}

This study proposes a simple and accurate dictionary creation method for MR fingerprinting using a fast Bloch image simulator. A typical MR fingerprinting sequence based on a FISP sequence and a numerical phantom were used for dictionary generation. Cartesian and spiral readout gradients were used for the Bloch image simulation of the numerical phantoms. MR fingerprinting parameter maps obtained by pattern matching with the dictionaries generated by the proposed method demonstrated validity and usefulness of the method. The proposed method is simple and useful for creation of accurate dictionaries in MR fingerprinting.

A
FISP-based MRF sequence^{3} consisted of 1000 TR units was designed for
the Bloch image simulator. The TR unit consisted of a selective-excitation
pulse (hamming-windowed sinc: ±2π, 3.2ms duration) with unbalanced slicing
gradient and a variable-density spiral readout gradient (TE=3ms, 7.47ms
sampling window, 5µs dwell-time) with 0-th moment compensation. FA was varied
as sinusoidal function of 0~π for the TR_index of 0~200, 250~450, 500~700, and
750~950, and the maximum of the FA was π/4, π/2, π/4, and π/2. To enhance the
T1 contrast, an inversion pulse was applied 100ms before the acquisition. The
spiral trajectory was designed for 256×256 image matrices with 256mm square FOV
to fill the k-space using the 48 segments separated by 7.5°
rotation angle. In the MRF sequence, the rotation angle of the trajectory was
incremented by 120°, 120°, 127.5°, 120°, 120°, 127.5° … to
utilize the sliding window reconstruction. The MRF dictionary was acquired with
the 48 repetitions of the MRF sequence with increasing the rotation angle by
7.5° (full
spiral-sampling). For comparison, Cartesian sampling (TE=3ms, 1.28ms sampling
window, 5μs dwell-time) MRF sequence was also used for dictionary calculation.

Figure
1A-C shows a relaxation-time phantom that simulated ten cylindrical containers
filled with materials having identical PD, T_{1} from 228 to 1666ms, and T_{2} from
37 to 150ms. Figure 1D-F shows a dictionary phantom filled with materials
having identical PD and all possible combinations of relaxation times. In the
dictionary phantom, T_{1} varied from 100 to 1000 by 10ms steps, from 1000 to 2000
by 20ms steps, and from 2000 to 5000 by 100ms steps, and T_{2} varied from 10 to
200 by 2.5ms steps and from 200 to 500 by 25ms steps. 9,219,072 and 13,464,000
isochromats were used for the Bloch image simulations of the numerical phantoms.

Figure 2A shows the 280th image of the relaxation-time phantom acquired with the one-shot MRF sequence and reconstructed from three consecutive signals. The temporal changes of the pixel values at the center of the cylindrical samples are shown in Figure 2B. The abrupt changes were caused by reconstruction noise. The simulation time for the one-shot MRF sequence was 137 seconds.

Figure 3 shows images selected from the image series of the dictionary phantom acquired with the full MRF sequences. The simulation times for the dictionaries were 5.89 and 2.75 h. No noticeable artifacts were seen in the image by Cartesian sampling, whereas remarkable reconstruction noise appeared in that by the spiral sampling. However, reconstruction noise was almost removed by the LPF. Therefore, we used the image dataset obtained from the Cartesian-sampling and the low-pass filtered image dataset obtained from the spiral sampling for the dictionary matching.

Figure
4 shows temporal changes in the image intensity of the MRF dictionaries.
Although two dictionary datasets presented almost the same changes, remarkable
intensity decrease in shorter T_{2} entries for the spiral sampling
dictionary was observed.

Figures
5 show matching results for the relaxation-time phantom datasets and the two
dictionaries, deviation maps from true values, and correlation plots for T_{1} and
T_{2}. The Cartesian dictionary was used in A and C and the spiral dictionary was
used in B and D. The Cartesian sampling MRF image dataset and the full
spiral-sampling MRF image dataset were used in A and B. The one-shot
spiral-sampling MRF image dataset was used in C and D. Figure 5A clearly shows
that the deviation in T_{1} and T_{2} was caused by the lack of resolution of the
dictionary entries. Figure 5B shows that the deviation in T_{1} and T_{2} was caused
by reconstruction noise as well as the lack of the resolution. In Figures
5C-5D, the deviation in T_{1} and T_{2} were mostly caused by the reconstruction
noise but the matching result for 5D was better than that for 5C, which demonstrated
the shorter T_{2} effect on the spiral trajectory.

Bloch image simulation for a FISP-based MRF sequence clarified a difference between trajectories used for the data-acquisition.

In conclusion, Bloch image simulations successfully reproduced the MRF process and the proposed method is a simple and accurate method for dictionary generation in MRF.

[1] Ma D, Gulani V, Seiberlich N, Liu K, Sunshine JL, Duerk JL, Griswold MA. Magnetic Resonance Fingerprinting. Nature 2013;495:187–192.

[2] Weigel M. Extended phase graphs: Dephasing, RF pulses, and echoes - pure and simple. J. Magn. Reson. Imaging. 2015;41:266-295.

[3] Jiang Y, Ma D, Seiberlich N, Gulani V, Griswold MA. MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout. Magn Reson Med 2015;74:1621–1631.

[4] Kose R, Kose K. BlochSolver: A GPU-optimized fast 3D MRI simulator for experimentally compatible pulse sequences. J Magn Reson 2017;281:51-65.

[5] Kose R, Setoi A, Kose K. A fast GPU-optimized 3D MRI simulator for arbitrary k-space sampling. Magn Reson Med Sci, accepted for publication, September 9th, 2018.

A-C.
Proton density, T_{1}, and T_{2} maps of a numerical phantom
with various sets of relaxation times in the cylindrical containers (Φ35mm, 110mmL).
The proton density is constant and T_{1} (ms) and T_{2} (ms)
combinations are (228, 47), (368, 56), (446, 72), (486, 51), (669, 71), (794,
84), (813, 37), (977, 88), (1227, 146), and (1666, 150). Backgrounds of the T_{1}
and T_{2} maps are filled with their average values. D-F. Proton
density, T_{1}, and T_{2} maps of a numerical phantom for the
MRF dictionary. The phantom size is 170 mm wide, 90 mm high, and 110 mm
deep.

A.
The 280th image of the relaxation time phantom reconstructed from three contiguous
spiral shot signal data acquired with the one-shot MR fingerprinting sequence. B.
Image intensity measured at the centers of the S01, S02, and S10 samples
plotted against TR_index.

A.
The 280th image of the MR fingerprinting dictionary acquired with the Cartesian readout
MR fingerprinting sequence. RGB image (left) and its bird eyes view (right). B.
The 280th image of the MR fingerprinting dictionary acquired with the full spiral
sampling MR fingerprinting sequence. RGB image (left) and its bird eyes view
before and after the low-pass image filtering.

A,
B. T_{1} and T_{2} dependences of the temporal change of the MR
fingerprinting dictionary acquired with the Cartesian sampling MRF sequence. C,
D. T_{1} and T_{2} dependences of the temporal change of the MR
fingerprinting dictionary acquired with the full spiral sampling MR fingerprinting
sequence.

Matching
results (T_{1}, T_{2}, and proton density maps) for image
datasets of the relaxation time phantom and the two dictionaries, deviation
maps from the true values, and correlation plots of designed and measured
values for T_{1} and T_{2}. The Cartesian dictionary was used
for the matching in A and C and the spiral dictionary was used for the matching
in B and D. The Cartesian sampling MR fingerprinting image dataset and the full
spiral sampling MR fingerprinting image dataset were used in A and B. The
one-shot spiral sampling MR fingerprinting image dataset was used for C and D.