Water-fat imaging (WFI) relies on solving a highly nonlinear system with many local minima [1]. In a standard complex-based water-fat signal model, the fieldmap is the most important non-linear parameter. A poor initial estimation for the fieldmap leads to converging to local minima, causing the infamous water-fat swaps (i.e. the water and the fat signal in a voxel are assigned the wrong way) and making the water and fat images diagnostically useless. The fieldmap initialization has been previously addressed by primarily imposing constraints on the smoothness of the fieldmap [2,3,4]. The fieldmap contains many sequence-, hardware- and object-dependent physical contributions. A recent work proposed the use of the object-based information of the B₀ field to improve the fieldmap estimation [5]. However, results were shown primarily at 1.5T and without considering the effect of the imperfections of the main magnetic field and the gradients produced by the shim coils. Purpose of the present work is to develop a method that considers all three contributions, the inhomogeneities of the main magnetic field, the magnetic field produced by the shim coils and the field produced by the object inside the scanner, for improving the estimation of the fieldmap in WFI and to test this method with large FOV data at 3T.

Theory

Assuming these three main contributions the fieldmap writes

$$f_B=\Delta f_{\text{mag}}+\Delta f_{\text{shim}}+\Delta f_{\chi},\quad\quad(1)$$

Given the coefficients $$$C^F_{\ell m}$$$ of the expansion in spherical harmonics $$$Y_{\ell m}$$$ up to order $$$L$$$, the first two contributions in Equation (1) can be determined by $$$F=\sum_{\ell=1}^{L} \sum_{m=-\ell}^{\ell}C^F_{\ell m}Y_{\ell m}(r,\phi,\theta)$$$, where $$$F$$$ either stands for the inhomogeneities of the main magnetic field $$$\Delta f_{\text{mag}}$$$ or the shimfield $$$\Delta f_{\text{shim}}$$$. $$$\Delta f_{\chi}$$$ represents the object-based fieldmap that is computed by

$$\Delta f_{\chi}=\frac{\gamma}{2\pi}\left[\mu_0(d\ast M)+\frac{2\mu_0}{3}M\right],\quad\quad(2)$$

where the first term is a convolution of the magnetization distribution $$$M$$$ with the dipole-kernel $$$d=\left[(3\cos^2\theta-1)/4\pi|r|^3\right]_{r\neq 0}$$$ and DC offset $$$d(r=0)=0$$$. The second term in Equation (2) is the Lorentz sphere correction [6,7]. In the approximation of small susceptibility

$$M=\frac{1}{\mu_0}\chi\left(B_0+\frac{2\pi}{\gamma}\left(\Delta f_{\text{mag}}+\Delta f_{\text{shim}}\right) \right).$$

A crude estimate of the object-based susceptibility map $$$\chi$$$ is obtained by applying a threshold of 5% to the maximum intensity projection of the magnitude images across echoes and assigning an average tissue susceptibility of -8.42ppm to the above-threshold regions and $$$\chi_{\text{air}}$$$=0.36ppm to regions below threshold. The convolution term in Equation (2) is solved similar to the Fast FieldMap Estimation (FFME) in [8].

In Vivo Measurements

Coronal scans of the cervical region of 10 subjects were performed on a 3T scanner (Ingenia, Philips Healthcare) with a standard WFI protocol: 3D multi gradient echo flyback sequence, 3 echoes, TR=5.4ms, TE1=1.06ms, ΔTE=1.6ms, FOV=480x480x224 mm³. All scans were performed once using the standard shim option with the shim volume covering the whole FOV and once without any shimming.

Water-Fat Imaging

Before passing the complex image data to a standard water-fat separation algorithm [3], the contributions in Equation (1) were demodulated as depicted in Figure 1. The standard WFI was also enhanced by the previous method [5] and compared to our proposed approach.

Water and fat images from the standard separation show three types of swaps: "Riffle", many thin elliptic swapped regions near the edges of the FOV, swaps surrounding the neck and total or partial brain swaps. Figure 2 shows phase images for every echo after each demodulation step and corresponding intermediate water-fat images for one dataset that suffers from all three types of observed swaps that could be fully resolved by the proposed method. Figure 3 shows how many datasets have water-fat swaps with the standard WFI methods [3], the method from [5] and the proposed method, (example results for comparison in Figure 4).All images showed riffles that were completely demodulated by the proposed method and did not appear in the WFI output. Swaps in the brain and neck region were mostly resolved in the shim off case, which was not the case with the previous method [5]. In cases where both the standard WFI with and without the proposed method failed, high shim values, especially for spherical harmonics varying along the direction of the slab selection, could corrupt the original source images. The "corrupted" source images make a proper water-fat separation impossible, which was observed in phantom scans with manually set shim values. The inclusion of B₀ inhomogeneities and the shimfields greatly improved the water-fat separation.In conclusion, a novel method considering the three most prominent magnetic field contributions was proposed for improving the fieldmap estimation in WFI, which showed significant improvements in datasets acquired with large-FOV in the cervical region at 3T.