Didi Chi^{1}, Yasmin Blunck^{1,2}, Rebecca Glarin^{2}, Catherine E. Davey^{1,2}, Daniel Staeb^{3}, and Leigh A. Johnston^{1,2}

^{1}Department of Biomedical Engineering, University of Melbourne, Parkville, Australia, ^{2}Melbourne Brain Centre Imaging Unit, University of Melbourne, Parkville, Australia, ^{3}MR Research Collaborations, Siemens Healthcare Pty Ltd, Melbourne, Australia

A Field-Mapping-Embedded (FME) EPI sequence is proposed in which the map is acquired during EPI acquisition without increasing scan time, using phase-encoded phase correction navigators. Results from in vivo experiment demonstrate accurate measurement and robust geometric distortion that performs favourably in comparison with existing techniques that require additional scans.

The current study proposes a Field-Mapping-Embedded (FME) EPI sequence, which enables measurement of $$$\Delta{B_0}$$$ map concurrently with the EPI acquisition. The FME-EPI technique exploits existing phase correction (PC) lines for N/2 ghosting correction

The FME-EPI sequence uses conventional PC scans (3 non-phase encoded echoes at the beginning of each EPI readout train) to correct for N/2 ghosting across each N-volume time-series (Figure 1a). For the remaining image volumes, variable phase encoding gradients are added before and after the PC lines in each slice (Figure 1b,c). To facilitate the multi-band acquisition, the slice rephasing gradient is alternated every second measurement to introduce a FOV/2 CAIPIRINHA

After reordering the phase-encoded PC scans (Figure 1b), complex images at three echo times ($$$I_{{TE}_1}$$$, $$$I_{{TE}_2}$$$, $$$I_{{TE}_3}$$$) are reconstructed by slice-GRAPPA

$$$I_{{TE}_1}$$$ and $$$I_{{TE}_3}$$$ are used for calculating $$$\Delta\varphi_{31}$$$,

$$\Delta\varphi_{31} = \angle{\sum_{ch}I_{{TE}_3} \cdot I^{*}_{{TE}_1}}$$ The three complex images are used to find $$$\varphi_0$$$: $$\Delta\varphi_{2,1}(x,y,\Delta TE) = \gamma \Delta B_0(x,y)\Delta TE + ax + b^{\prime}_1 = \angle{\sum_{ch}I_{{TE}_2} \cdot I^{*}_{{TE}_1}}$$ $$\Delta\varphi_{3,2}(x,y,\Delta TE) = \gamma \Delta B_0(x,y)\Delta TE - ax - b^{\prime}_2 = \angle{\sum_{ch}I_{{TE}_3} \cdot I^{*}_{{TE}_2}}$$

The linear phase shift $$$ax$$$ and constant phase offset $$$b^{\prime}_1$$$, $$$b^{\prime}_2$$$ are estimated by linear fit of the phase data ($$$\Delta \varphi_{21}$$$, $$$\Delta \varphi_{32}$$$) along the readout direction

Fast phase-unwrapping is achieved using Herráez et al’s method

Phase-unwrapped local field variation ($$$\Delta\varphi_{31,\text{unwrapped}}$$$) and overall phase offset ($$$\varphi_0$$$) are considered in $$$\Delta{B_0}$$$ map calculation: $$\Delta{B_0}(x,y)=\frac{\Delta\varphi_{31,\text{unwrapped}} - \varphi_0}{2\gamma\Delta{TE}}$$

Voxel displacement shift maps (VDM) are calculated by $$\text{VDM}(x,y) = \gamma\Delta{B_0}(x,y)\cdot \Delta{TE}_{\text{eff}}, \Delta{TE}_{\text{eff}}=\frac{\Delta{TE}}{R}$$ where $$$N$$$ is the matrix size and $$$R$$$ is the in-plane acceleration factor.

Distortion correction is implemented by resampling the distorted image along the phase-encoding direction by linear interpolation based on VDM: $$I(x,y^\prime) = I(x,y + \text{VDM}(x,y))$$

A healthy volunteer (female, aged 26, written consent obtained) was scanned on an investigational 7T whole-body MRI scanner (Magnetom 7T plus, Siemens Healthcare, Erlangen, Germany) using an 8Tx-32Rx head-coil (Nova Medical Inc. USA). Multiband FME-EPI was acquired: TE/TR=33/1700ms, resolution=1.8mm-isotropic, phase-encoding direction=AP, R=2, MB-factor=4, 84 slices, $$$\Delta{TE}$$$=0.6ms, 119 measurements). Two conventional EPI time-series with the same timing parameters and both phase-encoding directions were also acquired. A double gradient-echo sequence (TE1/TE2=3.3/4.4ms, resolution=4mm-isotropic, number of slices=40) was acquired for $$$\Delta{B_0}$$$ comparison purposes. MP2RAGE T1-w images were acquired for anatomical reference (TI1/TI2=700/2700ms, TE/TR=1.93/4500ms, resolution=1mm-isotropic).

Time-course SNR ($$$\frac{\mu}{\sigma_t}$$$) and image SNR were calculated for conventional EPI and FME-EPI data. Brain extraction was performed using BET

$$$\Delta{B_0}$$$ maps calculated using FME-EPI compare favourably with the double echo sequence (Figure 3) and are of the same FOV and resolution as the EPI readout, thus requiring no realignment or resampling to match the image data.

The FME-EPI distortion correction is more accurate than FUGUE, particularly in the frontal lobe (Figure 4, 1st-2nd row). Compared to TOPUP, FME-EPI distortion correction does not contain the artifacts evident around the ventricles from which TOPUP commonly suffers (Figure 4, 3rd-4th row).

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Figure 1: FME-EPI sequence: a) For the first three measurements, PC lines are acquired at the center of k-space similar to conventional EPI; b) From fourth volume onwards, PC lines are phase-encoded to enable on-the-fly $$$\Delta{B_0}$$$ mapping; c) FME-EPI sequence diagram with red lines representing the phase-shifted PC scans and corresponding slice rephasing gradients, black lines representing EPI readouts.

Figure 2 1st row: SNR maps of a conventional EPI time-series (mean ($$$\pm\sigma$$$) after brain extraction $$$186.39\pm109.69$$$). 2nd row: SNR maps of the FME-EPI time-series (mean ($$$\pm\sigma$$$) after brain extraction $$$181.27\pm103.39$$$). 3rd row: tSNR maps of a conventional EPI (mean ($$$\pm\sigma$$$) after brain extraction $$$25.94\pm14.25$$$).4th row: tSNR maps of the FME-EPI time series (mean ($$$\pm\sigma$$$) after brain extraction $$$25.29\pm13.56$$$).

Figure 3 $$$\Delta B_0$$$ maps obtained by a) FME-EPI and b) the double-echo sequence.

Figure 4 comparison of different distortion correction methods: Column 1) Distorted EPI images, 2) TOPUP, 3) FUGUE, 4) the proposed FME-EPI method.

DOI: https://doi.org/10.58530/2022/1099