To develop a method of rapid B0 field estimation for robust and accurate B0 field shimming, which is insensitive to the eddy currents.Chemical shift based fat suppression techniques as well as spectroscopic applications do not work well without proper B0 shimming. 3D gradient echo (GRE) sequences acquiring a pair of in-phase echoes were proposed and widely used to measure the B0 map¹, in which the common effects of non-static field induced by eddy currents² lead to inaccurate shimming. We propose a robust method of rapid B0 field map estimation, with a single calibration scan in which a full gradient polarity reversal is used to estimate the influence of eddy currents, before the sub-sequential in-vivo mapping scans and the eddy current induced error correction in the post-processing.Fig.1(a) depicts a routine GRE dual-echo sequence for raw (uncorrected) B0 field mapping, with the so called “fly-back” unipolar gradient readouts to reduce phase inconsistencies due to effects such as gradient delay and eddy currents. Phase difference of the two echoes is the B0 field plus the eddy currents induced field B_eddy encoded over the echo time difference ΔTE. As well known, the polarity of B_eddy will be flipped if all of the applied field gradients are reversed, as shown in Fig.1(b). The phase difference between images acquired in the two parts of the calibration scan can be written as$$\Delta\phi_{positive}={\gamma}B_{0}\Delta{TE}+{\gamma}B_{eddy}\Delta{TE}{\hspace{4cm}}(1)$$ $$\Delta\phi_{negative}={\gamma}B_{0}\Delta{TE}-{\gamma}B_{eddy}\Delta{TE}{\hspace{4cm}}(2)$$ From which B_eddy can then be calculated as $$B_{eddy}=(\Delta\phi_{positive}-\Delta\phi_{negative})/2\gamma\Delta{TE}\hspace{3.3cm}(3)$$In a given MR scanner, the eddy currents patterns are determined by the hardware material and structure, and system tuning including the eddy currents compensation (ECC), while the fast varying field changes form the patients are basically negligible. Thus, the B_eddy field distribution measured on a regular sphere phantom in the calibration scan, and later extrapolated onto the full imaging volume can be considered the same as in the in-vivo shimming. The eddy currents calibration combining sequences in Fig.1(a) and Fig.1(b) runs once, before running the actual B0 mapping sequence in Fig.1(a) in vivo. The B_eddy map calculated through (1)–(3) then goes through a 3D phase unwrapping algorithm³, decomposed into 0^th and higher spatial order terms, while in general the 3^rd order and above are negligible. Surface fitting with quadratic basis function is thus generally enough to obtain smooth eddy currents induced field maps over the full imaging space B’_eddy. Finally, the extrapolated and refined B’_eddy estimation is applied to correct the raw B0 field maps for shimming$$B_{0}=(\Delta\phi_{positive}-{\gamma}B_{eddy}\Delta{TE})/\gamma\Delta{TE}\hspace{3.9cm}(4)$$The B0 mapping sequences and the processing procedure were implemented on an Alltech EchoStar 1.5T scanner (AllTech Medical Systems, Chengdu, China). Fig.2(a) shows the center slice of a measured 3D B_eddy distribution on a 190mm sphere water phantom. The sequence parameters were TR/TE1/TE2/θ=13.4ms/4.5ms/9.0ms/20°, with a 320mm cubic FOV and a matrix size of 32x32x32, zero-filled to 64x64x64. The ECC was turned off to make the comparisons more obvious. Fig.2(b) shows the B’_eddy correction map from Fig.2(a) through phase unwrapping and quadratic fitting, with the 0^th term discarded as it does not affect shimming. To validate the method’s effectiveness, a proton density (PD) weighted FSE sequence with chemical shift selective (CHESS) fat saturation pre-pulse was acquired for pelvic imaging. The imaging parameters were TR/TE=1800/27ms, ETL=5, FOV380x300mm, acquisition matrix size316x188, and 6mm slice thickness. Only the sequence in Fig.1(a) run in-vivo for shimming, with a partial Fourier ratio of 0.85 in the both phase encoding (PE) and the slice encoding (SE) directions. The total duration of shimming is about 10 seconds. Fig.3 shows the resulting images after applying the shimming results, with (a) and without (b) corrections of the B’_eddy map. Fat signal in Fig.3(a) was almost fully saturated, while in Fig.3(b) there are residue non-saturated fats and unintended water suppression from the insufficiently homogeneous B0 distribution.

The proposed calibration method with full gradient polarity reversal estimates the eddy currents induced field distribution with reasonable accuracy, in practical situations from our experiences. It was found that with matching calibration and shimming sequence parameters, the B’_eddy patterns stay essentially the same. Moreover, translations of the shimming FOV do not change the gradient waveforms, so that the B’_eddy map is not changed. Therefore, multiple shimming protocols with changing shimming volume definitions can share the same B’_eddy correction map. In summary, the proposed B0 mapping procedure provides an eddy currents insensitive method without increasing the in-vivo shimming time from the normal mapping methods. This also reduces errors from motion induced phase changes because of the relatively short mapping time.