Fast and accurate frequency mapping in the presence of strong magnetic field inhomogeneities, e.g. as experienced at ultra-high fields, near prominent susceptibility variations, such as tissue-air interfaces, or in the proximity of implants, typically generates severe phase ambiguities using contemporary multi-echo B0-mapping schemes. Here, we make use of sequentially shifted echo times in combination with a balanced SSFP readout scheme to provide an unconstrained echo-spacing for accurate and fast broadband B0 mapping with a matrix pencil approach that does not require dedicated phase unwrapping methods.

Similar to the work of Scheffler [1], we make use of balanced SSFP for fast frequency mapping, but use sequentially shifted echo times instead of a multi-echo readout scheme (see Fig. 1). The echo-spacing, $$$\Delta$$$TE, enters as an unconstrained parameter, and can be adapted to fit the needs; e.g. a $$$\Delta$$$TE of 1 ms mitigates phase ambiguities up to 1kHz, whereas a $$$\Delta$$$TE of 0.1ms offers a sensitivity range up to 10kHz. For B0 mapping, n acquisitions were performed with echo times, TE(i)=TE(1)+ix$$$\Delta$$$TE, where i = 0,1,…,n-1, and the local frequency is then retrieved from the data by a rank-1 matrix pencil approach [2].

Broadband B0 mapping was evaluated in a long cylindrically shaped aqueous phantom (T2/T1 ~ 1) and on a hip prosthesis immersed in a tissue-mimicking doped gel (T2/T1 ~ 0.1). To this end, the following imaging parameters were used: flip angle: 10° (hard pulse of 100us duration), $$$\Delta$$$TE = 100us; n = 10 scans (sampling duration = 900us). The phantom was scanned in 3D with 2mm isotropic resolution, whereas the hip prosthesis was scanned with an isotropic resolution of 4mm, 2mm, and 1.3mm. Other imaging parameters were: for the 4mm iso scan (approx. 30 sec scan time): 64x64x24, BW = 2298 Hz/Pixel, TR = 2.28 ms, TE = 0.69, 0.79, … , 1.59 ms; for the 2mm iso scan (approx. 3 min scan time ): 128x128x40, BW = 2298 Hz/Pixel, TR = 2.88 ms, TE = 0.99, 1.09, … , 1.89 ms; for the 1.3mm iso scan (approx. 10 min scan time): 192x192x80, BW = 1736 Hz/Pixel, TR = 3.39 ms, TE = 1.24, 1.34, … , 2.14 ms. No filtering of the data, and no acceleration, such as parallel imaging or partial Fourier, was used. All scans were performed at 3T using the body coil for signal transmission and reception.

First, the spectral resolution of the BFM-SSFP approach was investigated on a proper phantom (see Fig. 1a). Generally, the B0-map appears smooth; no discretization is visible. As a result, the spectral resolution appears to be limited only by signal-to-noise (SNR) and appears to be in the range of Hertz. It is interesting here to note that the MP has a much higher spectral resolution as compared to a simple Fourier analysis, for which the spectral resolution is given by 1/(nx$$$\Delta$$$TE) > 1kHz.

Generally, banding becomes a major issue with balanced SSFP; especially in the combination with the presence of severe perturbations in the homogeneity of the magnetic field. To this end, the phantom was detuned with a linear gradient, and prominent bands appear (see Fig. 1b). Nevertheless, expect for the loss in SNR, banding represents no issue for B0-mapping and the frequency can be accurately resolved throughout.

Finally, broadband frequency mapping was tested in the proximity of a hip prosthesis (see Fig. 3). Widespread banding artifacts even in combination with a TR as short as 2 ms attest the presence of severe local field inhomogeneities. Indeed, deviation from the on-resonance frequency roughly up to +4kHz and down -3kHz are observed. Surprisingly, no drop-offs are visible, even in the very close proximity of the implant.

We have introduced a new method for fast broadband frequency mapping with balanced SSFP that does not require phase unwrapping methods and offers a compelling spectral resolution and sensitivity range. The method may be of special interest for engineering and material studies, at ultra-high fields, or for temperature monitoring near metallic implants.