Susceptibility artifacts, including geometric distortion and signal dropout, result from spatial mismapping due to field perturbations, ΔB, and their spatial gradients, G = ∇B. They are most severe at high field strengths, particularly surrounding air spaces in tissue. We aimed to improve understanding of these artifacts by characterising and modelling field maps of the mouse brain at 9.4 T because susceptibility artifacts hamper high-resolution preclinical MRI at this field strength. Here, we characterised the field maps by calculating an average field map measured in several mice. In addition, a forward susceptibility model was used to simulate a modelled field map, and the measured and modelled field maps were compared.An Agilent 9.4 T VNMRS 20 cm horizontal-bore system was used to image 7 C57BL/6 ten-week-old male mice in vivo¹. Prior to imaging, the mice were secured in a cradle under anaesthesia with 1-2% isoflurane in 100% oxygen. A 72-mm-diameter birdcage radiofrequency (RF) coil was used for RF transmission and a mouse brain surface coil array (RAPID, Germany) was used for signal detection. A Multi-Echo Gradient Echo sequence was used with 12 echoes at TE₁ = 1.38 ms and ΔTE = 2.64 ms, with isotropic 150 μm voxels and 110×100×100 matrix size. The phase data from the two receive coils were combined by finding the weighted mean of the single coil phase as in Robinson et al².

We tested several methods for field map calculation. The best approach, with the least noise and no residual wraps, was to use a nonlinear fit³ of the complex (magnitude and phase) data over time in each voxel, followed by 3D spatial unwrapping (FSL Prelude)⁴ to unwrap any residual wraps.

Calculating the Average Measured Field Map: This approach was used to calculate field maps for each mouse and global field offset corrections were made by referencing to the mean value in a central region of each mouse field map. Coregistration was then performed using NiftyReg⁵: Magnitude image volumes were corrected for bias fields using N4ITK⁶. They were then coregistered using 12 degrees-of-freedom affine transformations (Figure 1). The net transformations, saved as 4x4 matrices, were applied to each corresponding field map. The voxelwise group-average of the 7 offset-corrected and coregistered field maps was then calculated.

Simulating the Modelled Field Map: A model of the underlying susceptibilities was constructed by thresholding the average magnitude image volume and assigning values⁷ for tissue (-9 ppm) and air (0.36 ppm) susceptibilities. The model was zero-padded by 100 voxels in each dimension. In an attempt to correctly model the mouse tissue susceptibility outside the imaged region, tissue susceptibility values at the edge of the imaged region were replicated along the B₀ direction to the edge of the padded field of view. This padded susceptibility model was used to compute the field map using a Fourier forward model⁸.

Comparing the Measured and Modelled Field Maps: The difference of the measured and modelled field maps was calculated. A mask of the brain region was drawn manually on the average magnitude image (1st echo). Using this mask, histograms of ΔB/B₀ were computed in the brains of the measured, modelled and difference field maps. Gradient magnitude maps were also calculated by scaling ΔB/B₀ voxelwise difference maps to give gradient maps for each direction, G_x, G_y, and G_z. The gradient magnitude was found for each voxel using: $$$|G|=\sqrt{G_x+G_y+G_z}$$$⁹.

The measured and modelled field maps (Figure 2) appear qualitatively similar, with characteristic dipoles surrounding the aural air cavities. The difference image highlights the fact that the modelled field map seems to have slightly more field perturbation immediately surrounding the aural cavities. This may reflect the additional effect of bone which was not included in the model. Histograms for the measured and modelled field maps (Figure 3) show a difference in the spread and symmetry of field values inside the brain region, possibly due to residual shimming differences. Figure 4 shows the large |G| around the aural cavities where susceptibility artifacts will be worst.The measured and modelled field and gradient maps have qualitatively similar patterns, but differ quantitatively. This is likely to be due to inaccuracies in the susceptibility model such as neglecting the susceptibility of bone and an imprecise representation of the mouse anatomy outside the imaged field of view. Work is ongoing to accurately incorporate these effects into the model. This approach could be used in future to evaluate artifact reduction techniques such as automated¹⁰, passive¹¹ or active¹² shimming and tailored RF pulses¹³ in mouse brain studies at 9.4 T.