Introduction

RF spoiled gradient echo sequences (SPGR) are widely used for fast T₁ weighted imaging and fast T₁ mapping [1,2]. The SPGR sequences are quite attractive from a viewpoint of computer simulation of the imaging process because the coherence of the nuclear magnetization is apparently broken between TRs but has an important role for the image contrast. In this study, we performed fast Bloch-Torrey simulation and experiments for the SPGR sequences and demonstrated the importance of the molecular diffusion for the image contrast.

Materials and Methods

We used a home built 1.5 T MRI system consisting of a horizontal bore (280 mm) superconducting magnet, a second-order shim coil, an insertable gradient coil set, a transmit-receive birdcage coil, and a digital MRI console (MRTechnology, Tsukuba, Japan). A cylindrical phantom consisting of three small cylindrical PET bottles stored in an acrylic container filled with baby oil was used. The PET bottles were filled with CuSO₄ water solution with different densities, whose T₁ (~T₂) were about 114, 244, and 351 ms, respectively. The cylindrical phantom was imaged with 3D SPGR sequences (TR/TE = 20ms/6ms, FA = 30°, image matrix = 256×256×32, bandwidth = 50 kHz, FOV = (64 mm)³). The RF pulse phase φ was changed as φ=n(n + 1)Φ/2, where n is the number of the RF pulse in the SPGR sequence and Φ (phase shift base angle) was changed from 0 to 359 degree by one degree step. The SPGR sequences were simulated using the Bloch equation for 256×256×32 voxel images and simulated using the Bloch-Torrey equation for one voxel magnetization. The number of subvoxels was 1-129 for the Bloch equation and 8-128 for the Bloch-Torrey equation. The effect of the isotropic molecular diffusion was calculated using the second order spatial derivative of the nuclear magnetization along the readout direction. The Bloch simulation was performed using a GPU optimized MRI simulator [3] with two GPU boards (GeForce GTX1080).

Results

Figure 1 shows cross-sections selected from 3D image datasets calculated using the SPGR sequence (Φ = 117°) when the number of subvoxel was changed. Considerable stripe artifacts were observed when the number of subvoxels was small but disappeared when it exceeded 65. Figure 2 shows cross-sections selected from 3D image datasets (a) experimentally acquired and (b) calculated with 65 subvoxels. The image contrast at Φ=117° was nearly identical between the experiment and the simulation but that at Φ=120° and 180° was different. Figure 3 shows image intensity of each part of the cylindrical phantom acquired with the SPGR sequences plotted against Φ. While the image intensity measured for the calculated image datasets shown in Fig.3(b) showed many distinct peaks, that measured for the acquired image datasets shown in Fig.3(a) showed only a few small peaks except that of the baby oil. Figure 4 shows molecular diffusion effects calculated for one voxel using the Bloch-Torrey equation. Figure 4(a) shows image intensity of the CuSO₄ doped water (T₁ = T₂ = 351 ms, D = 0.00316 mm²/s (water at 35°C)) calculated for the SPGR sequences when the number of subvoxels was changed. While the peak height decreased with the increased number of subvoxels, the shapes of the peaks with 64 and 128 subvoxels were identical. Figure 4(b) shows image intensity of the doped water calculated for the SPGR sequences with 64 subvoxels when the diffusion constant was changed. This graph clearly demonstrates that the peak height decreased with the increase of the diffusion constant. Figure 5 shows signal intensity of each part of the cylindrical phantom calculated for the SPGR sequences (a) without (b) and with the molecular diffusion effect using the Bloch-Torrey equation. These graphs clearly demonstrate that the experimental results for the SPGR sequences were reproduced by the diffusion effect.

Discussion

The result that more than 65 subvoxels were required to describe the motion of the nuclear magnetization in the SPGR sequences as shown in Fig.1 demonstrates the presence of the transverse coherence over a few tens of TR periods as suggested by the EPG theory [4]. The result that more than 64 subvoxels were required to describe the molecular diffusion effect as shown in Fig.4(a) is caused by the same mechanism. In conclusion, the image contrast in the SPGR sequences can be reproduced by the Bloch-Torrey simulation with adequate number of subvoxels determined by the coherent length of the nuclear magnetization.

Acknowledgements

This work is supported by Japan Science and Technology Agency.

References

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