One important application of B₀ mapping is to characterise the shim fields as input for the calibration of B₀ shim systems. To that end, B₀ maps were acquired to assess the shim sensitivities and real shim fields for each shim coil. The problem with measuring strong B₀ shim fields is that B₀ inhomogeneity causes geometric distortion of the B₀ map [1,2].

In this work, we investigate distinct acquisition and post-processing strategies to sufficiently reduce geometric distortions when characterising shim fields of MRI systems.

A 9.4T Siemens Magnetom whole-body human MRI system equipped with an integrated 2nd order spherical harmonic B₀ shim system and a 16-channel transceiver array coil [3] was used for all measurements. Two second order shim terms (ZY and XY) at 4mT/m² were used for the investigation. A 3D gradient echo mapping (GRE) sequence was used based on the suggestions in [4]. The acquisition parameters were as follows: 192x192x192 resolution; 270x270x270mm FOV; TE = 4.00/4.76ms; TR = 10ms.

Two strategies were investigated; firstly, different bandwidths for the read-out gradient were used and secondly, a grid phantom was used for retrospective correction of geometric image distortions.

The read-out bandwidths used were 250Hz/pixel, 500Hz/pixel and 1300Hz/pixel. A 250mm diameter silicon oil cylindrical phantom with a plastic grid (with equidistant spacings of 15mm) was constructed (fig. 1).

For the retrospective distortion correction cross-points of the grid were marked automatically with a custom Matlab™ feature detection script. Cross-points in the cross-plane direction were then manually marked. The corrected positions of the crosspoints and their displacement were then calculated (based on the fact that the grid lines are parallel and spaced at 15mm). The mid-points of the marked cross-points were used to ensure that we took positions where the silicon oil was present (fig. 2).

The real fields were modelled by fitting a linear combination of spherical harmonic functions to the acquired B0 map for each shim term. This was done using either:

1) the entire B₀ map of the phantom (without the grid being present during the acquisition to avoid additional distortions due to magnetic susceptibility differences between grid and oil) or

2) the B₀ values at the mid-points with and

3) without position correction (with the grid inserted into the phantom during acquisition).

Maps of the modelled real field distributions were reconstructed on a 100x100x100mm FOV using the coefficients of the spherical harmonic functions.

The B₀ map acquired with 3D GRE at 1500Hz/Px read-out bandwidth without the grid was used as the reference as it shows negligible geometric distortions (fig. 1 and 3). Fig. 4 shows a slice of the XY B₀ map for using each of the three methods described above. Since it was difficult to see the differences, difference maps are shown for the same slice in fig. 5.

To evaluate the performance of the real field modelling and the impact of the retrospective geometric distortion correction difference maps between this reference and the modelled real fields were calculated for different acquisition bandwidths (as shown in fig. 6).

Fig. 3 shows the total displacement between the original and corrected mid-points for different bandwidths. The retrospective distortion correction can be seen to reduce the distance errors.

Using a retrospective distortion correction method can reduce the modelling error regardless of the read-out bandwidth (as shown in fig. 6). The improvement is more obvious when a lower bandwidth is used. However, modelling with the entire B₀ map consistently gives better results than using the retrospective correction. This is due to the fact that the reduced spatial resolution (of the mid-points) is not sufficient to capture the field.

Therefore, although using a grid-based retrospective correction technique can improve the accuracy of the modelling such that it is comparable to using the entire B₀ map, this method is more time-consuming. Furthermore, using the grid also introduces more susceptibility inhomogeneity in the B₀ maps. Therefore, a grid-free, high read-out bandwidth B₀ mapping sequence is recommended.

In conclusion, to reduce geometric distortion when measuring B₀ maps, a high bandwith for the read-out gradient is sufficient. The use of a grid phantom for retrospective correction may increase the accuracy of the modelling. However, compared to using a grid-free B0 map acquired with a high bandwidth, the reduced sampling and higher susceptibility distortion of the grid phantom may make the modelling less accurate.

Note that this study was done assuming the reference field was an accurate estimation of the actual field. The study can be improved if a more reliable method of measuring the actual field was available.