Myung-Ho In^{1}, Uten Yarach^{1}, Daehun Kang^{1}, Ek Tsoon Tan^{2}, Erin M Gray^{1}, Nolan K Meyer^{1}, Joshua D Trzasko^{1}, Yunhong Shu^{1}, John Huston^{1}, and Matt A Bernstein^{1}

This study reports a novel gradient nonlinearity (GNL) calibration approach using DIADEM (Distortion-free Imaging Approach with a Double Encoding Method) diffusion imaging. Unlike standard diffusion-weighted echo-planar-imaging (DW-EPI), DIADEM is free from DW-EPI distortions. This allows GNL calibration with a uniform phantom, since confounding effects between DW-EPI and GNL-induced distortions in the calibration are separated. Direct bias correction could be applied to the corresponding in-vivo data from the DIADEM scans, which results in reliable quantitative diffusion imaging. The feasibility was successfully demonstrated in phantom and in-vivo on a compact 3T system.

Introduction

Gradient-nonlinearity (GNL) induces not only geometric distortion in MR imaging, but also spatially‐dependent intensity bias in gradient-encoded signals, including quantitative diffusion values such as fractional anisotropy (FA) and apparent diffusion coefficient (ADC)Theory and Methods

Presuming
sufficiently high SNR, the applied *b*-value
in a diffusion scan can be estimated as^{8}:

b=ln(S_{0}/S_{b})/D, (1)

where
D, S_{0}, and, S_{b}
are the diffusion coefficient, the non-diffusion-weighted (DW) image, and the DW
image, respectively. In an isotropic diffusion phantom filled with water or
agar (to minimize bulk motion), the diffusion coefficient, D, is assumed to be
spatially and directionally invariant. When the diffusion coefficient is known,
the bias map, C, for any applied DW gradient can be simply calculated by^{9}:

C=|b|/|b_{0}|=sqrt(tr(b^{2}))
/|b_{0}|, (2)

where
b_{0} is the ideal b-value
requested for the imaging. Rather than the correction during the
diffusion-tensor-imaging (DTI) scalar calculation, intensity correction of
individual DW image allows to use existing diffusion analysis tools without any
modification and can be is achieved by^{10}:

S_{b,corr}=S_{0}exp((C-1)/C)×S_{b}exp(1/C).
(3)

Two healthy
volunteers were imaged under an IRB-approved protocol on the compact 3T^{11} using
an 8-channel coil (Invivo, Gainesville, FL) and concomitant field compensation^{12,13}. A calibration scan from a uniform agar gel phantom was also obtained. Each
DIADEM dataset was acquired with 7 and 14 shots, respectively for the in-vivo
and phantom calibration scans, which resulted in a total scan time of 3:02 and 6:04, respectively.
The GNL-caused
bias maps were measured by Eq. 2 based on the images from non-DW and DW-DIADEM
data in the SW-PE dimension. To normalize the bias map, a value assumed to be ideal
(i.e. C=1) at the isocenter was chosen without direct measurement of the
diffusion coefficient in phantom. After the proposed GNL bias correction in Eq.
3, GNL-induced geometric distortion correction was performed using the vendor
provided algorithm. Finally, DTI scalars were calculated using FSL^{14}. The results
were also compared with those obtained from the GNL bias correction method using
a 10^{th}-order spherical harmonic model (SHM) determined via EM
simulation^{1,2}.

Results and Discussion

Strong GNL-induced bias was observed in both the FA and ADC maps without correction on the compact 3T system (Fig. 1). The non-uniformity effects were more pronounced, especially at regions far away from the isocenter. Although the GNL bias correction was effective for both the high-order SHM and the proposed calibration approaches, the error was further reduced by the proposed approach, as shown in the histograms of FA and ADC (Fig. 2). While reliable bias correction was still possible using the proposed approach even in the regions far from the isocenter, the spatial non-uniformity errors can still be observed in results from the previously described approach (Fig. 2). Due to the bias, in the color-coded FA maps, green and blue colors were more apparent, respectively in the inferior and superior regions of the brain without correction (yellow arrows in Fig. 3). These were effectively resolved after GNL correction. No noticeable differences between two approaches were observed in in-vivo results. Given these results, and the relative simpler calibration using the phantom compared to using the standard GNL phantoms, the results are encouraging.1. Tan ET, Marinelli L, Slavens ZW, King KF, Hardy CJ. Improved correction for gradient nonlinearity effects in diffusion‐weighted imaging. JMRI 2013;38(2):448-453.

2. Tao AT, Shu Y, Tan ET, Trzasko JD, Tao S, Reid R, Weavers PT, Huston J, Bernstein MA. Improving apparent diffusion coefficient accuracy on a compact 3T MRI scanner using gradient non-linearity correction. JMRI 2018; doi: 10.1002/jmri.26201.

3. In MH, Posnansky O, Speck O. High-resolution distortion-free diffusion imaging using hybrid spin-warp and echo-planar PSF-encoding approach. Neuroimage. 2017;148:20-30. doi: 10.1016/j.neuroimage.2017.01.008.

4. Huang KC, Cao Y, Baharom U, Balter JM. Phantom-based characterization of distortion on a magnetic resonance imaging simulator for radiation oncology. Phys Med Biol. 2016;61(2):774-90.

5. Gunter JL, Bernstein MA, Borowski BJ, Ward CP, Britson PJ, Felmlee JP, Schuff N, Weiner M, Jack CR. Measurement of MRI scanner performance with the ADNI phantom. Med Phys. 2009 Jun; 36(6):2193-205.

6. Weavers PT, Tao S, Trzasko JD, Shu Y, Tryggestad EJ, Gunter JL, McGee KP, Litwiller DV, Hwang KP, Bernstein MA. Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging. MRI 2017;38:54-62.

7. Tao S, Trzasko, J, Gunter J, Weavers P, Shu Y, Huston J, Lee SK Tan E, Bernstein MA. Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system. Phys Med Biol. 2017; 21(62):N18-N31.

8. Stejskal EO, Tanner JE. Spin diffusion measurements: spin echoes in the presence of time-dependent field gradient. J Chem Phys. 1965;42:288–292

9. Bammer, R., Markl, M., Barnett, A., Acar, B., Alley, M., Pelc, N., Glover, G., Moseley, M., Analysis and generalized correction of the effect of spatial gradient field distortions in diffusion‐weighted imaging. MRM 2003; 50, 560-569.

10. Malyarenko DI, Ross BD, Chenevert TL. Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements. MRM 2014;71(3):1312-1323.

11. Foo TK, Laskaris E, Vermilyea M, Xu M, Thompson P, Conte G, Van Epps C, Immer C, Lee SK, Tan ET. Lightweight, compact, and high-performance 3 T MR system for imaging the brain and extremities. MRM 2018. doi: 10.1002/mrm.27175.

12. Tao S, Weavers PT, Trzasko JD, Shu Y, Huston J 3rd, Lee SK, Frigo LM, Bernstein MA. Gradient pre-emphasis to counteract first-order concomitant fields on asymmetric MRI gradient systems. MRM 2017;77(6):2250-2262. doi: 10.1002/mrm.26315.

13. Weavers PT, Tao S, Trzasko JD, Frigo LM, Shu Y, Frick MA, Lee SK, Foo TKF, Bernstein MA. B0 concomitant field compensation for MRI systems employing asymmetric transverse gradient coils. MRM 2017; doi:10.1002/mrm.26790

14. FSL package, https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSL

Figure 1. FA and
ADC maps at three different locations along inferior-superior direction without
(No Corr.) and with GNL correction using the spherical harmonic model (SHM) and
the proposed calibration approaches (Cal.). Note that the image scale for each
FA and ADC map is equal and the image intensity inhomogeneity directly reflects
the GNL-induced bias.

Figure 2. Histograms
of FA (left) and ADC (right) in the entire phantom mask volume without (No
Corr., blue-colored line) and with GNLC using the spherical harmonic model (SHM,
red-colored line) and the proposed calibration approaches (Cal., green-colored
line).

Figure 3. Gray
scaled and color-coded FA maps without and with GNL correction. Yellow arrows
indicate more apparent FA bias as gray and color scale. The Imaging
parameters were: TR/TE = 3668/50ms, partial Fourier of 5/8 and 7/8 in the EPI
phase-encoding (PE) and the spin-warp (SW) PE dimension, 36 slices, slice
thickness = 4 mm, total readout bandwidth = ±250 kHz, FOV = 220×220 mm^{2},
matrix size for acquisition/reconstruction = 256×280/256×256, in-plane
acceleration = 3, echo spacing (effective) = 632(210.8) µs, one b-value = 0,
and six b-value = 1000s/mm^{2}. The image resolution is 0.86×0.86×4 mm^{3}.