Synopsis

To correct the distortion in EPI due to field inhomogeneity, an image-based method for estimating the field map from the distorted EPI image has been proposed. However, this method suffers from long computation times. Our purpose was to improve an image-based method in terms of the computation time. Whereas the previous method synthesized EPI image in k-space requiring a lot of execution of FFT, our method synthesized EPI image in the image-domain. Our method reduced the computation time in the almost same NRMSE in previous method. Our results suggest that our improved method was able to perform a reasonable estimation of the field map.

INTRODUCTION

METHODS

Our basic idea to estimate the field inhomogeneity map in EPI is to reproduce the distorted EPI image based on MR imaging physics. We used a T1WI as reference image, whose histogram was changed so as to match the histogram of measured EPI image using histogram specification.⁴ T₂ value in each voxel was estimated from the reference image. Our method synthesizes the distorted image to match the measured EPI image through the generation process of EPI image according to a single-shot EPI k-space trajectory and field inhomogeneity using an iterative conjugate gradient algorithm. In previous method, the computation time was long, because the EPI images were synthesized in k-space and FFT was executed more than a dozen times in each iteration³. To reduce the computation time, our method synthesized EPI image in the image-domain. To synthesize the distorted EPI image, an MR signal was calculated on a voxel-by-voxel basis using the estimated T₂ value and field inhomogeneity ΔB. The MR signal in the presence of field inhomogeneity ΔB is given by

$$$I(x,y,\Delta B)=\sum_{u=0}^{M-1} \sum_{v=0}^{N-1} A(u,v)\cdot exp(-\frac{TEeff}{T2(u,v)})\cdot sinc (\pi (x-u-\frac{\Delta B(u,v)}{\Delta x \cdot Gx})) \cdot sinc (\pi (y-v-\frac{\Delta B(u,v)}{\Delta y \cdot Gy}))$$$

where Δx and Δy are pixel spacing in x and y direction, respectively, Gx is the gradient in the x direction, and Gy = G_bτ /Δty (G_b is the average blip gradient in the y direction during the duration τ, and Δty is the time intervals between adjacent points in the phase-encoding directions). The field inhomogeneity map ΔB was estimated by minimizing the least-square cost function using the synthesized EPI image and the measured EPI image. The spin echo (SE) EPI and T1WI data of a healthy volunteer were acquired using a 1.5-tesla clinical scanner (Magnetom, Symphony, Siemens) with an 8-channel phased-array coil. The SE EPI data was obtained by a single-shot EPI pulse sequence (FOV: 230 mm, TR=8600ms, TE=119ms, 128×128 in-plane resolution, 3 mm thickness). Three dimensional T1WI covering the same area in EPI was obtained by MPRAGE sequence (FOV: 230 mm, TR=2090ms, TE=3.93ms, TI=1100ms, FA=15°, 256×256 in-plane resolution, 1 mm thickness). To evaluate the performance of both methods, we used the normalized root mean square error (NRMSE) between the measured EPI and synthesized EPI by those methods.

RESULTS and DISCUSSION

CONCLUSION

Acknowledgements

References

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2. Hutton C, Bork A, Josephs O, et al. 2002. Image distortion correction in fMRI: A quantitative evaluation. Neuroimage 16:217-240.

3. Kumazawa S, Yoshiura T, Honda H. 2015. Image-based estimation method for field inhomogeneity in brain echo-planar images with geometric distortion using k-space textures. Concept Magn Reson B. 45:142-152.

4. Coltuc D, Bolon P, Chassery JM. 2006. Exact histogram specification. IEEE Trans Image Process. 15:1143-1152.