Introduction

Phase-cycled balanced Steady-State Free-Precession (bSSFP) acquisitions can be used to sample bSSFP profiles, the steady-state magnetization as function of the RF phase angle. The recently developed “Signal Profile Asymmetries for Robust multi-Compartment Quantification” (SPARCQ)^[1] framework enabled quantification of fat and water content using asymmetries^[2] in bSSFP profiles. In prior work^[1], 37 low-resolution scans were performed to sample the profile in 20min. This work aims at accelerating the SPARCQ framework and improving signal encoding to maximize the accuracy of fat-water separation with an improved resolution.

Methods

TR optimization to maximize SPARCQ sensitivity for fat-water separation
In bSSFP, the magnetization vector precesses during the repetition time TR and accumulates a precession angle $\Phi$ depending on the off-resonance frequency $f$: $$\Phi=2\pi f\text{TR}$$
Depending on TR, water ($f=0$Hz) and fat ($f=-440$Hz) signals may have the same $\Phi$ and thus overlap (Figure 1A). The bSSFP signals of water and fat as a function of $\Phi$ display a periodic behaviour^[3] (Figure 1AB) and their precession angle $\Phi$ as function of TR is wrapped into the range $[0;2\pi]$. Water and fat peaks accordingly wrap into the corresponding frequency range $[0;1/\text{TR}]$, with respective relative frequencies $f_{W,\textit{rel}}$ and $f_{F,\textit{rel}}$ such that: $$f_{rel}=\Phi_{[0;2 \pi]}/ 2\pi\text{TR}$$ The relative distance between the wrapped peaks was calculated as $\Delta f_{peak}=f_{F,\textit{rel}} – f_{W,\textit{rel}}$. The optimal TR was defined as the shortest TR which maximizes $\Delta f_{peak}$. To determine the effect of TR on fat-fraction quantification, spectra containing water and fat resonances with varying fat fractions FF were generated, then Bloch simulations^[4] were performed to obtain bSSFP profiles, with TR $\in [3;11]$ms and T1/T2 = 5. Fat fractions were extracted from the frequency spectra fitted by the SPARCQ prototype framework^[1]. The difference between simulated and estimated fat fraction was calculated.
Minimization of phase-cycled acquisitions
Simulations: The effect of reducing the amount of phase-cycles $N_{\phi}$ on SPARCQ fat-fraction estimation was tested numerically. bSSFP profiles were simulated^[4] using $f \in [-600;200]$ Hz, T1/T2 = 5, FF $\in [0;1]$ and TR = 3.41ms. After noise addition (with signal-to-noise ratio SNR $\in [1;100]$), the fat fraction was estimated with SPARCQ. The error between simulated and estimated fat fraction was calculated for $N_{\phi} \in [2;37]$.
In vivo imaging: The effect of $N_{\phi}$ reduction on fat quantification was tested in knee images of three volunteers. Phase-cycled bSSFP acquisitions were performed at a 3T clinical scanner (MAGNETOM, Prisma^fit, Siemens Healthcare, Erlangen, Germany). 72 phase-cycled scans were acquired with 5° RF phase increments and sub-sampled into 36 subsets of length $N_{\phi} \in [2;37]$. Fat fractions were estimated in each subset. 25-pixel-wide regions of interest (ROI) were selected in bone marrow, muscle, and sub-cutaneous fat compartments. Within each ROI, the mean and standard deviation of the fat fraction were computed and compared to the fully sampled acquisition. A reference, low-resolution, non-accelerated protocol^[1] was compared to the proposed protocol in one volunteer. The proposed protocol incorporated parallel imaging (GRAPPA^[5]) to further enhance the acceleration. Sequence parameters are summarized in Figure 5D.

Results

The maximum relative distance between fat and water signals occurs when $\Delta \Phi = k\pi$, $k \in ℕ$ (Figure 1C) and TR = 3.41ms. Similarly, the quantification error follows a periodic pattern (Figure 2). Regions where fat-fraction quantification fails correspond to TR values yielding a similar precession angle for water and fat, i.e. where the profiles are nearly identical. A SNR ≥ 30 resulted in a consistent estimation when $N_{\phi}$ is reduced (Figure 3). Relatively small errors were observed for 16 ≤ $N_{\phi}$ ≤ 37 (Figure 3). This was corroborated in vivo, where a consistent standard deviation within each ROI was observed when $N_{\phi}$ is reduced to 16 (Figure 4). Comparing the long low-resolution protocol with the short high-resolution protocol shows that fat fractions were the same (Figure 5). Due to a misclassification of the fat peak, a signal void can be observed in the patella for both acquisitions (Figure 5).

Discussion

The SPARCQ framework for water-fat separation is TR sensitive and optimal TRs can be chosen from the analysis of the bSSFP profiles by maximizing the relative distance $\Delta f_{peak}$. This is an important consideration for the use of slab-selective RF excitation pulses, or for changing the magnetic field strength. Agreement between numerical simulations and in vivo experiments indicates that a simple reduction to 16 phase cycles provides sufficient data for SPARCQ to resolve water and fat. Further acceleration could be achieved with compressed sensing^[6,7]. With SPARCQ a frequency spectrum is obtained in each voxel that is independent from field inhomogeneities^[1]. However, the current SPARCQ framework assigns water or fat depending on which peak is closest to on-resonance (Figure 5C). This caused the misclassification of bone marrow in the patella as water (Figure 5). Using the peak shape, in conjunction with its location, may be more suitable to classify fat and is currently being investigated.

Conclusion

The SPARCQ framework to separate and quantify water and fat was optimized in terms of TR and accelerated to a total acquisition time of 7:12min with an isotropic resolution of (1.25mm)³. Simulations and in vivo experiments demonstrated the accuracy of fat-fraction quantification with the proposed accelerated SPARCQ framework.

Acknowledgements

This study was supported by funding from the Swiss National Science Foundation (grant number PZ00P3_167871), the Emma Muschamp foundation, and the Swiss Heart foundation.