Zhengguo Tan1, Dirk Voit1, Jost M Kollmeier1, Martin Uecker2,3, and Jens Frahm1,3
1Biomedizinische NMR, Max-Planck-Institute for Biophysical Chemistry, Göttingen, Germany, 2Department of Diagnostic and Interventional Radiology, University Medical Center Göttingen, Göttingen, Germany, 3DZHK (German Center for Cardiovascular Research), Göttingen, Germany
Synopsis
To achieve dynamic water/fat separation even in
the presence of rapid physiological motions and large magnetic field
inhomogeneities, this work presents a multi-echo multi-spoke radial FLASH
sequence and a model-based non-linear inverse reconstruction. Asymmetric echoes are
integrated into the sequence to shorten echo times. A spatial-smoothness
constraint on field inhomogeneity maps is developed to counteract local minima in
the non-convex inverse problem.
Introduction
Water/fat separation based on proton water/fat
chemical shift in multi-gradient-echo acquisitions1,2,3 has been of
great interest in scientific research and clinical diagnostics. Due to the use of multiple echoes, however, it suffers from poor temporal
resolution. Secondly, the successful separation of water and fat requires an accurate estimation of the B0 field inhomogeneity. Existing joint estimation
techniques4,5 rely on proper initialization via region growing6, which is
not applicable to dynamic imaging. To overcome these limitations, this work
aims at developing: (1) an undersampled asymmetric-echo multi-echo radial FLASH
sequence and (2) a model-based reconstruction technique with a
spatial-smoothness regularization on B0 field map.Methods
Figure
1 illustrates the multi-echo multi-spoke radial FLASH sequence and its corresponding
k-space trajectory, where an echo asymmetry 75% is integrated to shorten TE and TR7. To achieve optimal coverage of k-space, radial
spokes with the same TE are uniformly distributed in k-space, and the
incremental angle between frames is empirically chosen as Golden angle (68.75o).
The
signal model is:
$$F_{j,l} (x) = P_l \mathcal{F} \{ (W + F \cdot z_l) \cdot e^{i 2\pi f_{B0} \text{TE}_l \cdot c_j} \} \; \text{with} \; x = (W, F, f_{B0}, c_1, ... c_N)^T$$
Here, $$$P_l$$$ and $$$\mathcal{F}$$$ are the sampling pattern for the $$$l$$$th echo and 2D FFT, respectively. The unknown $$$x$$$ consists of water ($$$W$$$), fat ($$$F$$$), B0 field inhomogeneity (off-resonance) frequency ($$$f_{B0}$$$), and coil sensitivity maps ($$$c_j$$$). The fat modulation8 follows $$$z_l = \sum_{p=1}^{6} a_p \cdot e^{i 2\pi f_p \text{TE}_l}$$$. To jointly estimate all unknowns, the cost function is
$$\Phi(\hat{x}) = \text{argmin}_{\hat{x}} \left \| y - F(T\hat{x}) \right \|_2^2 + \alpha \left \| \hat{x} \right \|_2^2 \; \text{with} \; x = T\hat{x} $$
$$$y$$$ is the gridded k-space data without roll-off corrections. The weighting matrix is $$$T = \mathcal{F}^{-1} \Big(1 + w \cdot \left \| \vec{k} \right \| \Big)^{-h}$$$, with $$$w=11$$$ and $$$h=18$$$ for the B0 field map, $$$w=880$$$ and $$$h=16$$$ for coil sensitivity maps, while an identity matrix ($$$T=I$$$) is applied onto water and fat maps. $$$\vec{k}$$$ is a 2D Cartesian grid matrix. Although weaker than coil sensitivity maps, the weighting on the B0
field map enforces spatial smoothness and assures
accuracy. This cost function is minimized by the iteratively regularized
Gauss-Newton method9 with automatic scaling10 for water and fat, while the
scaling for the B0 field map is kept as 1.5 to warrant convergence. The reconstruction starts with $$$W=F=1$$$, $$$f_{B0}=0$$$, and $$$c_j=0$$$, while the initialization for the following frames is set as the estimate
from the preceding frame damped by 0.9 to enforce temporal continuity.
Data acquisitions were performed on a 3T scanner (Magnetom Prisma,
Siemens Healthineers, Erlangen, Germany) with an 18-channel body matrix coil. Acquisition
parameters were: 8o FA, standard shimming, 1560 Hz/Px bandwidth, 320 x 320 mm2 FoV, 200 x 200 matrix size, 1.6 x 1.6 x 6 mm3 spatial resolution, and 40 ms temporal resolution with 9 RF excitations per frame and TR = 4.43 ms, TE = 1.26/2.66/3.69 ms.
In addition, a whole-body scan with the
built-in 2-channel body receiver coil was conducted. The volunteer was pulled
through the isocenter from the lower leg to the head. Acquisition parameters
were: 16o FA, tune-up shimming, 1200 Hz/Px bandwidth, 448 x 448 mm2 FoV, 320 x 320 matrix size, 1.4 x 1.4 x 10 mm3 spatial resolution, and 50 ms temporal resolution with 9 RF excitations per frame and TR = 5.54 ms, TE = 1.54/3.12/4.70 ms. This
scan covers the whole body within only 40 s. To accompany with rapid change of anatomies from slice to
slice, a real non-negative constraint is applied on water and fat maps during
image reconstructions.
Results
Figure
2 shows results of a static phantom using the proposed acquisition and joint
estimation techniques. The reconstruction is able to capture fast varying B0
field inhomogeneity across the FoV. Moreover, temporal B0 field inhomogeneity
variations in the presence of abdominal breathing are well resolved (see Figure
3). When imaging the beating heart, the proposed method again accurately separates
water and fat in different sections and for all cardiac phases (see Figure 4).
In the experiment where the volunteer was pulled through the isocenter, the field
inhomogeneity changes rapids along with anatomy, as depicted
by the selected slices in Figure 5. Discussion and Conclusion
B0 field homogeneity is affected by various
factors, e.g., shimming, tissue composition, and motions. Therefore, accurate
estimation of dynamic field inhomogeneity maps is crucial for the successful separation
of water and fat. The proposed sequence and joint estimation reconstruction provide a practical solution to
time-resolved water/fat separation at a temporal resolution of 40 ms.Acknowledgements
The authors would like to thank Dr. Arun Joseph, Olkesandr Kalentev, Klaus-Dietmar Merboldt, and Thomas Michaelis for their help on the experiments.References
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