Introduction

Balanced steady-state free-precession (bSSFP) signal profiles (i.e. steady-state transverse magnetization over a range of RF pulse phases) were shown to have different shapes depending on the underlying tissue composition¹. Furthermore, it was reported that asymmetries in these signal profiles indicate the presence of multiple tissue components (e.g. different types of tissue) in single voxels^2,3. The aim of this work was to develop a novel quantitative method that exploits bSSFP signal profile asymmetries for robust multi-compartment quantification (SPARCQ) and to provide a validation for voxel-wise water-fat separation and fat fraction mapping.

Methods

The prototype SPARCQ acquisition consists of multiple phase-cycled bSSFP acquisitions (N=37), with constant RF pulse phase increments equidistantly distributed according to:
$$\phi_j=\frac{2\pi}{N-1}(j-1),\;\;\;\;\;\;j=1,2,...,N\;\;\;\;\;\;\;\;\bf{(Eq. 1)}$$
For each phase cycle, k-space is acquired using a fully sampled Cartesian trajectory, with TR/TE = 3.4/1.7 ms, RF excitation angle α = 35°, an isotropic resolution of (2mm)³ and receiver bandwidth of 930 Hz/px. Magnitude and phase images are reconstructed directly on the scanner.

SPARCQ reconstruction framework. First, a complex-valued 2D dictionary of bSSFP signal profiles is constructed using Bloch simulations. The two dimensions are composed of the relaxation time ratio Λ (T1/T2) and the off-resonance frequency df (Fig. 1a). Second, an optimization algorithm is used to express each acquired signal profile (s_acq) as a weighted sum of the simulated signals in the dictionary (D) as follows: $$\hat{\bf{w}}=argmin_{\bf{w}}\parallel\bf{D}\cdot\bf{w}-\bf{s}_{acq}\parallel_{2}^{2}+\lambda\parallel\triangle w\parallel_{2}^{2},\:\:\it{subject}\:to\:\bf{w}\geq0\:\:\: \:(Eq. 2)$$ yielding a weight matrix (2D representation of $$$\hat{\bf{w}}$$$), containing information on the voxel content (Fig.1b). Distributions of Λ and df are obtained by projecting the weight matrix along its dimensions (Fig. 1c-d). Third, parameters (i.e. fractions of the components of interest and thermal equilibrium magnetization M₀) are voxel-wise extracted from the obtained spectra (i.e. distributions of weights) (Fig. 1e). Finally, M₀-weighted separated images for each component are obtained by multiplying the corresponding fraction map with the M₀ map.

Phantom experiments at 3T and 9.4T. A dedicated fat-water phantom was created⁴ composed of six 50 mL Falcon tubes with different nominal fat fractions immersed in a 3%wt agar solution (Fig. 2A). First, the exact content of each vial was determined by integrating the peak areas in high-resolution ¹H NMR spectra obtained by unlocalized spectroscopy in a horizontal-bore 9.4T magnet (Magnex Scientific, Oxford, UK) with a Direct Drive spectrometer (Agilent, Palo Alto, CA, USA). A custom-made RF hybrid probe (two 10mm diameter proton surface coils in quadrature mode) was positioned over the phantom for transmission and reception. Additionally, whole-phantom acquisitions were performed on a clinical 3T scanner (MAGNETOM Prisma^fit, Siemens Healthcare, Erlangen, Germany) using a commercially available body coil and the suggested prototype sequence. Fat fractions estimated with SPARCQ - in manually drawn circular ROIs corresponding to the six vials - at 3T were compared with gold-standard fat fractions determined via unlocalized spectroscopy at 9.4T.

Volunteer experiments were performed on the knees of six healthy volunteers on the same clinical 3T scanner using a commercially available 15-channel Tx/Rx knee coil (Quality Electrodynamics, Mayfield, OH, USA). The acquisition protocol consisted of a scan-rescan acquisition with repositioning with the suggested prototype sequence. Additionally, a Dixon acquisition was performed with a standard turbo spin echo (TSE) Dixon sequence. Parametric maps and water-fat-separated images were obtained with SPARCQ and compared with water-fat-separated images obtained with Dixon. A Bland-Altman analysis was performed on the mean fat fractions obtained with SPARCQ in five elliptical ROIs in five different tissues.

Results

In phantoms, distributions of the estimation error, i.e. difference between the voxel-wise fat fractions estimated with SPARCQ and the measured fat fractions at 9.4T in the corresponding vial are shown in Fig. 2B. For all the vials, a median error of less than 5% was obtained, with a median error <1% for vials with 0%,40% and 60% fat.

In volunteers, df spectra obtained from the weight matrix (Fig. 3) showed the expected frequency components. Parametric maps (Fig. 4A) and water-fat-separated images (Fig. 4B) showed the expected contrast between fatty and non-fatty tissues. Despite the difference in contrast in water-fat-separated images obtained with SPARCQ (M₀-weighting) and with Dixon (T2*-weighting) (Fig. 4B), SPARCQ fat and Dixon fat images were in good agreement. In water images, hyperintensities were observed in the same liquid structures. The Bland-Altmann analysis on the fat fraction maps in the scan-rescan experiment (Fig. 5) revealed very low bias b = 0.0002 and a good coefficient of repeatability CR = 0.0695.

Discussion

The SPARCQ framework provided accurate and repeatable quantification of water and fat. This may facilitate fat suppression in bSSFP acquisitions and provide useful information for various clinical applications (e.g. assessment of liver steatosis⁵ and prognosis of heart failure^6,7). The method relies on the extraction of voxel-wise Λ and df spectra from bSSFP signal profiles, suggesting the potential of SPARCQ for other multi-compartment applications. An optimization of the acquisition protocol (~33s/phase cycle) towards scan time should be considered (e.g. phase cycles reduction, compressed sensing with regularization along phase cycles^8,9) as well as strategies to increase the robustness of the algorithm (e.g. joint sparsity constraint¹⁰).

Conclusion

The SPARCQ framework was proposed as a novel quantitative method for detection of different tissue compartments, and its potential was demonstrated for water-fat separation.

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.