Metal implants disrupt standard MRI sequences, producing images with significant artifacts. Although recently developed methods reduce many artifacts, reliable fat suppression near metal remains challenging, especially for contrast-enhanced imaging. The ability to use the Dixon technique close to metal would enable or improve applications such as contrast-enhanced detection of tumours, inflammation or scar tissue.

For the three-point Dixon technique to succeed near metal, correctly estimating the phase shift due to B0 field inhomogeneities is necessary [1]. Existing techniques can fail as the phase varies rapidly near the boundary of the implant. We propose a new technique in which the phase is estimated incrementally using a set of 1D paths around the boundary.

The gradient of the B0 field variation increases as the distance to the implant boundary decreases. The phase is therefore more difficult to estimate close to the implant. Our method unwraps the phase at the outer regions of a 2D slice first and proceeds inwards over a set of enveloping paths, ending at the implant boundary.

The phase along a closed 1D path which circumnavigates the implant can be represented by a Fourier series. Figure 1 shows the simulated B0 field variation near a titanium hip replacement [2, 3]. Two possible paths are superimposed. Figure 2 shows the field variation along the paths with a Fourier series fitted to each.

A set of suitable paths is obtained by dilating the shape of the implant in steps and identifying the boundary pixels after each step. The wrapped phase at the pixels along each path is extracted. It is assumed that the measured phase along the outermost path is slowly varying and can be unwrapped. An $$$N$$$th-order Fourier series is fitted to the unwrapped phase. The coefficients of the Fourier series, $$$\alpha_N$$$, are adjusted to minimise the objective function

$$H = \sum_{r = 1}^{D} \left[W\left\{\phi_w(r) - W\left\{F_{\alpha_N}(r)\right\}\right\}\right]^2$$

where $$$\phi_w$$$ is the wrapped phase data at point $$$r$$$ on the parameterised path. $$$F_{\alpha_N}(r)$$$ is the Fourier series representation of the unwrapped phase estimate, $$$W\left\{\cdot\right\}$$$ is the wrapping operator and $$$D$$$ is the number of pixels on the path. This ensures consistency between the rewrapped estimated phase and the wrapped data. By adjusting the Fourier coefficients instead of the phase at each pixel, only $$$2N + 1$$$ parameters are estimated.

The phase estimation works inwards by the following steps:

1. The unwrapped phase estimate at each pixel on the next path in is mapped from the closest pixel on the adjacent outer path.

2. An $$$N$$$th-order Fourier series is fitted to the unwrapped phase on the new path. This is the initial unwrapped estimate.

3. The Fourier coefficients are adjusted to minimise the objective function, and the new unwrapped estimate is calculated.

4. Steps 1-3 are repeated for each path until the path closest to the boundary of the object is reached.

The phase at pixels which do not belong to any path is estimated using 2D interpolation.

Data were obtained using a phantom containing a titanium hip replacement suspended in agar gel and surrounded by three vials of peanut oil. 2D-FSE images were acquired using the three-point Dixon technique at 3T (matrix size: 384x136, FOV: 300x210 mm, 16 slices with 3 mm thickness, TR: 3400ms, TE: 10ms, echo train length: 16, readout bandwidth: 125 kHz). The implant geometry was obtained using a white light scanner.

Figure 3 shows the fat-only and water-only images calculated using a minimum-norm phase unwrapping method [4]. The phase estimation has failed close to the implant, as indicated by the fat and water swaps. The discontinuity at the implant boundary causes errors to propagate throughout the image. This can be improved by using a weighted phase unwrapping method [4], with the fat-only and water-only images shown in Fig. 4. The phase inside the implant boundary is given a weighting of zero, so it does not influence the final result. However, the phase estimation has failed in regions with rapid field variation.

Figure 5 shows the images calculated using the method described here. The fat has been successfully separated from water near the implant boundary. Residual intensity variation remains due to artifacts such as through-plane distortion.

The proposed technique has succeeded in suppressing fat near the boundary of a titanium hip replacement phantom. Future work will focus on better methods for generating the paths circumnavigating the implant and assessing global convergence of the objective function [5].