IDEAL (Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares) is an efficient approach for separation of fat and water (F/W) MRI signals¹. IDEAL algorithms achieve high accuracy by modeling F/W jointly with the magnetic field inhomogeneity (field map, FM) and, for gradient echo sequences, $$$T_2^*$$$ decay. Yet, IDEAL must contend with inherent uncertainties arising from the competing sources of off-resonance (i.e., fat chemical shift and field inhomogeneity). The associated local minima of the nonlinear objective function, when trapped into, may lead to significant errors (e.g., F/W swaps). To reduce these errors, the algorithms typically exploit FM smoothness assumption², which may fail in case of significant field inhomogeneities. Theoretically, these errors may be also minimized by supplying the algorithms with an adequate FM prior; however, FM pre-estimation from IDEAL images is again confronted by fat interference. Here, we present a novel method to increase IDEAL robustness which exploits a phenomenon of absence of magnetization transfer (MT) effect in fat to attain fat-insensitive FM pre-estimation.

As demonstrated recently^3,4, off-resonance MT saturation does not have a detectable effect on the fat signal when applied far from on-resonance (offset frequency $$$\Delta$$$>2.5 kHz⁵) to avoid direct saturation. This insensitivity is due to absence of efficient mechanisms to transfer magnetization from fat to either water or tissue macromolecular (protein/membrane phospholipid) protons³. Simultaneously, the pulse attenuates water via MT exchange between saturated tissue macromolecules and water protons. Let’s assume that all parameters affecting fat (e.g., repetition time TR, excitation flip angle) are kept the same between two scans acquired without and with MT saturation. Then, the complex-valued subtraction of corresponding images $$$S_n^{off}$$$, $$$S_n^{on}$$$ at $$$n^{th}$$$ echo time $$$t_n$$$ creates MT-attenuated images without fat signal (Fig. 1):

$$S_{W,n}=S_n^{off}-S_n^{on}=(1-A_{MT})We^{-t_n/T_2^*}e^{i\phi t_n}$$

Here, $$$A_{mt}$$$ is MT attenuation, W is water signal, and $$$\phi$$$ is FM. As the fat signal is eliminated, FM can now be robustly calculated in MT-attenuated tissues from $$$S_{W,n}$$$ using standard phase difference methods⁶ and approximated in the whole object using interpolation-based estimation.

All experiments were performed on a 3.0T GE MR750 (Waukesha, WI). Full-resolution IDEAL scan was followed by low-resolution MT-IDEAL in which MT pulse was positioned in place of later echoes to maintain same TR=23ms (Fig. 2). Other parameters included: 1) IDEAL: TE=[1.5 3.3 5.0 6.7 8.4 10.2 11.9 13.6]ms, 192x160 matrix; 2) MT-IDEAL: TE=[1.5 3.3 5.0]ms, 8-ms, 600 dgr Fermi-shaped MT pulse, $$$\Delta$$$=3 kHz, 192x16 matrix). MT-IDEAL images were subtracted from resolution-matched IDEAL images to yield $$$S_{W,n}$$$ MT-based FM estimation included calculation of phase difference $$$angle[S_{W,3} \cdot conj(S_{W,2})]$$$ , phase unwrapping⁶ and nonlinear interpolation/smoothing. (The first echo was not included to avoid its prominent phase errors⁷). The interpolation-based refinement was implemented as a moving local 2D quadratic fit⁸ weighted by MT-attenuated image $$$|S_{W,2}|$$$ serving as a measure of confidence of the input FM values. The phase-difference processing was also applied directly to IDEAL data without MT IDEAL subtraction to FM prior without fat correction with proposed fat-free MT-based FM. All FMs were used to initialize both standard (non-regularized) IDEAL¹ and IDEAL with FM smoothness regularization².Figure 3 demonstrates that initialization of non-regularized IDEAL with the proposed MT-based FM resolves F/W swaps observed for default zero-valued initialization. Figure 4 shows that initializing regularized IDEAL by MT-based FM significantly improves accuracy of F/W separation when field variations are significant. FM obtained without MT IDEAL subtraction does not improve separation confirming that proposed MT-based fat correction is critical to obtain prior FM estimate of sufficient accuracy. The proposed method improves robustness of IDEAL by enabling FM pre-estimation without fat interference. In scenarios with moderate inhomogeneity, our approach improves F/W separation even without computationally demanding FM smoothness regularization (Fig. 3). As MT-based FM initialization facilitates convergence to the correct minima of the objective function, it may improve F/W estimation in suboptimal imaging conditions such as significant field inhomogeneities (Fig. 4) and non-uniform/non-optimized echo spacing. Our approach leads to moderate scan time increase (~10%). This overhead may be reduced in protocols using GRAPPA⁹ to 5% and 2.5% for 2x and 4x accelerations, correspondingly, if the extra MT-IDEAL scan is utilized for GRAPPA calibration thereby avoiding acquisition of fully sampled k-space center of IDEAL dataset. Ou­r method relies on existence of MT-sensitive tissues, which are naturally abundant in human body (e.g. brain, muscles, collagen-containing tissues, liver). We found that interpolation/smoothing processing yields FM estimate in MT-insensitive tissues (fat, fluids) sufficiently accurate for efficient initialization of IDEAL algorithms. Alternatively, the MT-based FM prior can be incorporated into probabilistic IDEAL framework¹⁰ or can be used for initialization of seed areas in region growing algorithms¹¹.