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Optimal experimental design for quantitative water, fat and silicone separation using a variable projection method with 4 or 6 echoes at 3T

Jonathan K. Stelter¹, Christof Boehm¹, Stefan Ruschke¹, Maximilian N. Diefenbach^1,2, Mingming Wu¹, Kilian Weiss³, Tabea Borde¹, Stephan Metz¹, Marcus R. Makowski¹, and Dimitrios C. Karampinos¹
¹Department of Diagnostic and Interventional Radiology, School of Medicine, Technical University of Munich, Munich, Germany, ²Division of Infectious Diseases and Tropical Medicine, University Hospital, LMU Munich, Munich, Germany, ³Philips Healthcare, Hamburg, Germany

Synopsis

Patients with silicone breast implants undergoing MR mammography are examined with a water- and fat-suppressed sequence to verify the implant’s integrity. In parallel, chemical shift encoding-based water–fat separation has been recently used for quantifying breast water-fat composition to assess breast density and for extracting magnetic susceptibility maps to detect breast calcifications. In this work, a water–fat–silicone separation method is developed for a joint estimation of all three components and applied with NSA-optimized echo times to simulated single-voxel data, scanner phantom and in vivo data showing robust species separation and fat fraction mapping.

Purpose

Silicone implants are commonly used for breast augmentation or breast reconstruction after mastectomy. MRI is a sensitive method for monitoring the implant’s integrity to detect possible ruptures¹. T2-weighted turbo spin echo acquisitions employing frequency-selective water suppression and short tau inversion recovery (STIR) for fat suppression are clinically primarily used to generate silicone-only images with bright silicone signal^2,3. In parallel, multi-echo gradient echo imaging acquisitions have been also recently combined with chemical shift encoding-based water–fat separation for quantifying water–fat composition to assess breast density⁴ and for extracting magnetic susceptibility maps to detect breast calcifications^5-7. However, there is still limited knowledge on how to simultaneously separate three chemical species in the breast in the presence of water, fat, and silicone. The present work aims to develop a methodology for the joint estimation of the field-map as well as water, fat, and silicone images based on the variable projection (VARPRO) method for chemical species seperation⁸, to find optimal experiment parameters using the Cramér–Rao analysis⁹, and to demonstrate the method for Dixon acquisitions with 4 or 6 echoes in numerical simulations, in a phantom and in vivo.

Methods

Parameter estimation for three species
The water–fat voxel signal model¹⁰ was extended for silicone and its chemical shift of -4.9 ppm¹¹:
$$s(t_n)=(\rho_W+\rho_F(\sum_{p=1}^P\alpha_pe^{i2\pi f_{F,p}t_n})+\rho_Se^{i2\pi f_S t_n})e^{i2\pi \phi t_n}e^{-R_2^*t_n}$$ where $$$t_n$$$ is the echo time shift, $$$\phi$$$ is the field-map, $$$\alpha_i$$$ are the relative amplitudes for the spectral fat model for $$$i\in\{1,..,P\}$$$, $$$ f_{j}$$$ are the resonance frequencies in consideration of temperature shift effects¹² and $$$\rho_j$$$ are the complex signals of the water, fat and silicone components assuming a common transverse relaxation rate $$$R_2^*$$$.
Residuals were calculated using the VARPRO method⁸ and all local minima were extracted and inserted to a single-min-cut variable-layer graph-cut algorithm¹³ for field-mapping:
$$\{\rho_W,\rho_F,\rho_S,\phi,R_2^*\}=\operatorname*{argmin}_{\rho_W,\rho_F,\rho_S,\phi,R_2^*}\sum_{n=1}^{N_{TE}}|s(t_n)-y_n|^2$$ where $$$y_n$$$ is the measured signal for the n-th echo and $$$N_{TE}$$$ is the number of echoes.
Based on the global optimal field-map yielded by the graph-cut, the water, fat and silicone images can be computed with consideration of the $$$T_2^*$$$ decay¹⁴. Proton density fat fraction (PDFF) maps were calculated with correction for noise bias effects using magnitude discrimination^15,16.
Cramér–Rao analysis
The selection of echo times was optimized based on the Cramér–Rao analysis using the Fisher Information Matrix^9,17 to minimize the noise variance expressed by the number of signal averages (NSA)⁹.
Several water–fat–silicone-fractions were analyzed based on its noise performance in dependence on the number and spacing of echoes. For experiment optimization, the mean NSA for the magnitudes of the species was computed and the minimum value for different water–fat–silicone-fractions was compared for varying echo spacings and first echo times.
Numerical phantom
A numerical phantom (20x20x1 voxels) consisting of different fat and silicone fractions in the range of 0% to 100% with constant $$$R_2^*$$$=50 Hz was simulated based on the water–fat–silicone signal model. A constant echo spacing with ΔTE$$$\in$$${1, 1.5}ms, TE₁=1.7 ms for 4 and 6 echoes and ΔTE=2.75 ms, TE₁=1.55 ms for 6 echoes was simulated based on the results of the Cramér–Rao analysis. A ramp map was specified as field-map and Rician noise¹⁸ with SNR=100 was added.
MR measurements
A phantom composed of vials with different water–fat-fractions ([10.0,19.5,36.3,34.9,58.2]%, verified by single-voxel spectroscopy) and a silicone implant was scanned twice with a monopolar time-interleaved multi-echo gradient echo sequence¹⁹ on a clinical 3T scanner (Ingenia/Elition X, Philips Healthcare, Best, The Netherlands) with N_TE=20, ΔTE=0.45 ms, TE₁=1.7 ms, FOV=179.5x179.5x140.4 mm³ and N_TE=6, ΔTE=2.75 ms, TE₁=1.55 ms, FOV=179.5x179.5x140.4 mm³. From the scanned images, echo times were selected matching to the phantom simulations.
A breast scan of a subject with a silicone implant with N_TE=6, ΔTE=1.28 ms, TE₁=1.58 ms, FOV=384x384x192.4 mm³ using the aforementioned sequence at 3T was evaluated separately for the first 4 and all 6 echoes.

Results

For the noise performance of the three species, similar patterns were shown (Fig.1): a local maximum at ΔTE=1 ms, and local minima when the phasors of the silicone or the main fat component stay the same across TEs. In the latter case, the separated images suffered from high noise, however, the accuracy of the field-map estimate was high (Fig.3, NRMSE_{water/silicone}>10*NRMSE_field-map). The selection of ΔTE was more robust with 6 echoes than with 4 echoes if the echo spacing was in a similar range. In vivo results (Fig.5) demonstrated the feasibility of the method in separating all three species in a large field-of-view with 6 non-optimized echo times. Phantom PDFF maps (Fig.4) showed a good agreement to MRS PDFF values, but higher deviations from the MRS were measured for the larger echo spacing.

Discussion & Conclusion

Similar phasors for the species lead to low differentiation and therefore to more noise due to broadened peaks in the residual. For large echo spacings (ΔTE=2.75 ms), the distance between minima in the residual is smaller, such that field-map jumps are more probable due to the graph-cut algorithm, although high NSA was predicted.
High PDFF accuracy and low noise in the separated images were achieved for ΔTE=1 ms using 4 echoes and a stronger independence of the results on the echo spacing was observed using 6 echoes. The feasibility of the water–fat–silicone separation was also shown in vivo with non-NSA-optimized 6 echo times.

Acknowledgements

The present work was supported by the European Research Council (grant agreement No 677661, ProFatMRI). This work reflects only the authors view and the EU is not responsible for any use that may be made of the information it contains. The authors also acknowledge research support from Philips Healthcare.

References

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Figures

Figure 1: Noise performance as a function of the echo spacing ΔTE with constant TE₁ = 1.3 ms for different fat (FF=fat/(water+fat+silicone)) and silicone (SF=silicone/(water+fat+silicone)) fractions. The individual NSA for the magnitude of the three species are shown in (A) using 4 echoes, whereas the mean NSA for the magnitudes of the three species are shown in (B) for different numbers of echoes. For the echo spacings marked with a solid or dashed line, silicone or the main fat component has the same phasor position in all images, respectively.

Figure 2: Optimization of the echo times with regard to the noise performance. The mean NSA for the magnitudes of water, fat and silicone is shown in dependence on the echo spacing ΔTE and the first echo time TE₁. For each combination, the minimum value for 20x20 different silicone and fat fractions was calculated. Optimization was performed for 4 (A) and 6 (B) echoes. The circles indicate the echo times used in the phantom study and the squares indicate a typical echo time used for in vivo measurements with a large FOV. The minimum mean NSA is stated for those echo combinations.

Figure 3: Water–fat–silicone separation in a numerical phantom with SNR=100 consisting of different fat and silicone fractions. The water, fat and silicone images show noise in agreement with the NSA analysis and the characteristics of the VARPRO residuals are compared. Sequences with 4 (A, B) or 6 (C, D) echoes were evaluated with ΔTE=1 ms or ΔTE=1.5 ms. The 6-echo combination with highest NSA is shown additionally (E). The NRMSE was calculated using the whole images as region of interest. The last column shows the VARPRO residual of the voxel highlighted in the field-map column.

Figure 4: Water–fat–silicone separation in a phantom shows similar noise tendencies as in the simulations and PDFF results with low deviation to MRS PDFF. The phantom is composed of vials with different water–fat fractions and a silicone implant. Note the slightly different echo spacings compared to Figure 3. The white boxes (10x10x1 voxels) indicate the regions of interests used for evaluating the mean value ± standard deviation of the PDFF in %. Using spectroscopy, the following values were measured for the different PDFF values (from left to right): [10.0, 19.5, 36.3, 34.9, 58.2]%.

Figure 5: Water–fat–silicone separation for a breast scan shows feasible separation results with low noise after the analysis of 6 echoes. Two analyses with 4 (A) or 6 (B) echoes and ΔTE=1.28 ms were evaluated. The theoretical NSA for those echo times is stated in Figure 2. In the breast, the white box (10x10x1 voxels) indicates the region of interest used for evaluating the mean value ± standard deviation of the PDFF in %.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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