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Triglyceride Saturation Estimation using Phase- and Amplitude-Modulated Bipolar MRI

Manuel Schneider¹, Felix Lugauer¹, Dominik Nickel², Berthold Kiefer², Sungheon Gene Kim^3,4, Linda Moy^3,4, Andreas Maier¹, and Mustafa R Bashir^5,6,7

¹Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany, ²MR Application Predevelopment, Siemens Healthcare GmbH, Erlangen, Germany, ³Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University School of Medicine, New York, NY, United States, ⁴Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, United States, ⁵Radiology, Duke University Medical Center, Durham, NC, United States, ⁶Center for Advanced Magnetic Resonance Development, Duke University Medical Center, Durham, NC, United States, ⁷Division of Gastroenterology, Department of Medicine, Duke University Medical Center, Durham, NC, United States

Synopsis

Our purpose was to develop a robust method to estimate triglyceride saturation from bipolar multi-gradient-echo MRI data. Discrepancies in amplitude and phase between even and odd echoes were addressed analytically. The method was demonstrated in abdominal (n=5 patients) and breast (n=1 volunteer) MRI data. Compared to calculating fatty acid composition parameters without modeling amplitude modulations, the proposed method reduced the intensity shift in the readout direction in the estimated parameter maps, but also led to artifacts at water/fat borders.

INTRODUCTION

Triglyceride molecules are classified based on their saturation state. This so-called “fatty acid composition” (FAC) can give insight into the pathophysiology of the metabolic syndrome^1,2, or the risk of breast cancer development³. Therefore, the FAC in fat deposits throughout the body, including liver, abdominal fat or breast tissue, is important. Spatially resolved FAC maps using chemical shift MRI, including methods applying monopolar^4-6 or bipolar^7,8 readout gradients, have been proposed. In case of a bipolar data acquisition, gradient non-linearities, eddy currents and non-ideal receiver characteristics potentially cause a discrepancy in amplitude and phase between even and odd echoes. These confounding effects have previously been addressed using an eddy-current phase parameter⁸, or by accounting for both amplitude and phase variations⁷. Our aim is to present a technique for quantifying FAC estimates by addressing phase and amplitude modulations analytically, and to show its applicability in abdominal data from n=5 patients and breast imaging data from n=1 healthy volunteer. Additionally, differences to FAC maps calculated by neglecting amplitude discrepancies⁸ are demonstrated.

METHODS

Fatty acid composition quantification: The spatial distribution of the FAC at a respective echo time $$$t_n$$$ can be quantified from bipolar, multi-gradient-echo MRI data by $$S(t_n) = \left( W + c(ndb, nmidb)F\right) \text{e}^{i 2 \pi \psi t_n} \operatorname{e}^{-R_2^{*}t_n} a_n \text{e}^{i (-1)^n \phi},$$ where $$$W$$$ and $$$F$$$ denote complex water and fat components, and $$$c(ndb, nmidb)$$$ is a multi-peak fat model^9,10, expressed by the number of double bonds (ndb) and number of methylene-interrupted double bonds (nmidb). The model accounts for the confounding factors field-map $$$\psi$$$^11,12, transverse relaxation R2*¹³, eddy-current phase $$$\phi$$$¹⁴ and amplitude modulations^14-16 $$a_n =\begin{cases}\nonumber\rho, & \text{for } n \text{ even} \\1, & \text{for } n \text{ odd.}\end{cases}$$ Fitting the multi-echo data in the least-squares sense to the signal model and performing variable projection on the linear parameters yields the non-linear functional $$$\chi^2_{\mathrm{m},1}(\psi,\phi, R_2^{*},\rho)$$$. Breaking down the contributions of even and odd echoes results in $$$\chi^2_{\mathrm{m},2}(\psi,R_2^{*},z,z^*)$$$, where the complex parameter $$z = \frac{1}{\rho} \text{e}^{i 2\phi},$$and $$$z^*$$$ is its complex conjugate. Analytical formulations for $$$z$$$ and therefore a residual $$$\chi^2_{\mathrm{m},3}(\psi,R_2^{*})$$$ are determined by evaluating $$\frac{\partial \chi^2_{\mathrm{m},2}(\psi,R_2^{*},z,z^*)}{\partial z^*}\stackrel{!}{=} 0.$$ These derivations are used to estimate the confounding factors, and then relative fractions of the saturated, mono-unsaturated and poly-unsaturated fat are calculated (see Figure 1)⁵.

Noise propagation: We analyzed the noise performance of the applied signal model for three fat fraction values (15%, 35%, 99%) using 12 simulated echoes⁸.The calculations were performed for the operating point parameters $$$\psi$$$/$$$\phi$$$ /R2*/$$$\rho$$$ = 30Hz/0.04$$$\pi$$$ rad/50Hz/1.1, and the simulated fat was assumed to be 27.1% saturated and 23.4% poly-unsaturated.

In-vivo study: In an IRB-approved study abdominal MRI data was acquired in n=5 patients scheduled for NAFLD assessment at 3T (MAGNETOM Trio a Tim system, Siemens Healthcare, Erlangen, Germany) using a spine and a six-channel body array coil with protocol 1 (Table 1). The data was processed using both the proposed and our previous approach⁸, which on some platforms showed a slight right-to-left intensity gradient in readout direction on FAC maps. Therefore, ROIs were drawn on the fat fraction maps in the subcutaneous tissue (right and left), and the difference of the mean values between the right and left ROIs was evaluated and used as a measure of parameter consistency along the readout direction.

To visualize the benefit of the analytically derived formulations, one exemplary abdominal case was additionally reconstructed by minimizing equation $$$\chi^2_{\mathrm{m},1}(\psi,\phi, R_2^{*},\rho)$$$ instead of $$$\chi^2_{\mathrm{m},3}(\psi,R_2^{*})$$$ numerically. To investigate an additional application, protocol 2 (Table 1) was used to acquire breast images of one healthy volunteer at 3T (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany) using a 16-channel AI breast coil.

RESULTS AND DISCUSSION

Results of the noise simulation are shown in Fig. 2. Compared to a signal model that neglects amplitude modulations⁸, this noise analysis shows another distinct peak in the standard deviation of the saturated component for phase shifts close to $$$\pi$$$ rad.

FAC maps calculated using the analytically derived phase and amplitude modulation parameters visually contain fewer invalid regions compared to maps estimated by minimizing $$$\chi^2_{\mathrm{m},1}(\psi,\phi, R_2^{*},\rho)$$$ for both abdominal (Fig. 3a-b) and breast imaging (Fig. 4a-b).

Compared to calculating FAC parameters without modeling amplitude modulations (Fig. 3c), the proposed approach reduced the intensity gradient along the readout direction in the 5 patients from 8.2%, 12.4% and 4.2% to 4.9%, 7.2% and 2.5% for the saturated, mono-unsaturated and poly-unsaturated components, respectively. However, accounting for amplitude modulations did not completely remove the gradients and introduced unexpected effects at water/fat edges, potentially due to intra-voxel, chemical shift and Gibbs ringing effects (see arrows).

CONCLUSION

The derived formulations led to more robust FAC quantification. Modeling amplitude modulations reduced the intensity gradient in FAC maps along the readout direction, but also led to unwanted effects at water/fat borders.

Acknowledgements

No acknowledgement found.

References

1. van Werven JR, Schreuder TC, Nederveen AJ, Lavini C, Jansen PL, Stoker J. Hepatic unsaturated fatty acids in patients with non-alcoholic fatty liver disease assessed by 3.0 T MR spectroscopy. Eur J Radiol 2010;75(2):e102–e107.

2. Flintham R, Eddowes P, Semple S, et al. Non-invasive quantification and characterization of liver fat in non-alcoholic fatty liver disease (NAFLD) using automated analysis of MRS correlated with histology. In: Proceedings of the 24th Annual Meeting of ISMRM; 2016. #0357.

3. Freed M, Storey P, Lewin AA, et al. Evaluation of breast lipid composition in patients with benign tissue and cancer by using multiple gradient-echo MR imaging. Radiology 2016;281(1):43–53.

4. Berglund J, Ahlström H, Kullberg J. Model-based mapping of fat unsaturation and chain length by chemical shift imaging - phantom validation and in vivo feasibility. Magn Reson Med 2012;68(6):1815–1827.

5. Peterson P, Månsson S. Simultaneous quantification of fat content and fatty acid composition using MR imaging. Magn Reson Med 2013;69(3):688–697.

6. Leporq B, Lambert SA, Ronot M, Vilgrain V, Van Beers BE. Quantification of the triglyceride fatty acid composition with 3.0 T MRI. NMR Biomed 2014;27(10):1211–1221.

7. Leporq B, Lambert SA, Ronot M, et al. Hepatic fat fraction and visceral adipose tissue fatty acid composition in mice: quantification with 7.0 T MRI. Magn Reson Med 2016;76(2):510–518.

8. Schneider M, Janas G, Lugauer F, et al. Accurate fatty acid composition estimation of adipose tissue in the abdomen based on bipolar multi-echo MRI. Magn Reson Med, doi: 10.1002/mrm.27557.

9. Hamilton G, Yokoo T, Bydder M, et al. In vivo characterization of the liver fat 1H MR spectrum. NMR Biomed 2011;24(7):784–790.

10. Bydder M, Girard O, Hamilton G. Mapping the double bonds in triglycerides. Magn Reson Imaging 2011;29(8):1041–1046.

11. Hernando D, Haldar J, Sutton B, Ma J, Kellman P, Liang ZP. Joint estimation of water/fat images and field inhomogeneity map. Magn Reson Med 2008;59(3):571–580.

12. Hernando D, Kellman P, Haldar J, Liang ZP. Robust water/fat separation in the presence of large field inhomogeneities using a graph cut algorithm. Magn Reson Med 2010;63(1):79–90.

13. Yu H, McKenzie CA, Shimakawa A, et al. Multiecho reconstruction for simultaneous water-fat decomposition and T2* estimation. J Magn Reson Imaging 2007;26(4):1153–1161.

14. Peterson P, Månsson S. Fat quantification using multiecho sequences with bipolar gradients: investigation of accuracy and noise performance. Magn Reson Med 2014;71(1):219–229.

15. Yu H, Shimakawa A, McKenzie CA, et al. Phase and amplitude correction for multi-echo water–fat separation with bipolar acquisitions. J Magn Reson Imaging 2010;31(5):1264–1271.

16. Delakis I, Petala K, De Wilde JP. MRI receiver frequency response as a contributor to Nyquist ghosting in echo planar imaging. J Magn Reson Imaging 2005;22(2):324–328.

17. Lugauer F, Nickel D, Wetzl J, et al. Robust Spectral Denoising for Water-Fat Separation in Magnetic Resonance Imaging. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer; 2015. p. 667-674.

Figures

Figure 1: Workflow of the proposed fatty acid quantification framework. The method applies a spectral low-rank denoising approach¹⁷ on the complex multi-echo data. Field map and transvere relaxation estimates are found using non-linear function minimization, whereas the eddy current phase and amplitude modulation parameters are addressed analytically. Then the parameter vector of interest is calculated¹⁴, and maps of the relative FAC are derived. FAC, fatty acid composition.

Figure 2: Noise propagation behavior of the proposed signal model. Plots show the lower bounds on the standard deviations in the (a) complex fat signal, the (b) saturated, (c) mono-unsaturated, and (d) poly-unsaturated fatty acid parameter with regard to noise in the input data. For low fat contents, the noise propagation performance of the parameter estimates is poor for phase shifts close to 1.3$$$\pi$$$ rad, 1.7$$$\pi$$$ rad and 2$$$\pi$$$ rad between water and the main fat peak. In areas containing mainly fat, the noise performance is similar for all phase shifts between 0.5$$$\pi$$$ rad and 2$$$\pi$$$ rad. FF, fat fraction.

Table 1: Parameters of the prototypical 2-D GRE sequence used in the in-vivo measurements for abdominal (MAGNETOM Trio a Tim system, Siemens Healthcare, Erlangen, Germany) and breast imaging (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany). The images were interpolated in k-space to a larger matrix.

Figure 3: In-vivo abdominal FAC results. Parameter maps were calculated (a) by means of minimizing $$$\chi^2_{\mathrm{m},1}(\psi,\phi, R_2^{*},\rho)$$$, (b) using the proposed approach (see workflow in Fig. 1), and (c) without modelling amplitude modulations. The difference between parmeters maps in (b) and (c)⁸ is shown in (d). FAC, fatty acid composition; PDFF, proton density fat fraction.

Figure 4: In-vivo breast FAC maps. Parameter maps were calculated (a) by means of minimizing $$$\chi^2_{\mathrm{m},1}(\psi,\phi, R_2^{*},\rho)$$$ and (b) using the proposed approach (see workflow in Fig. 1). Parameter maps of the proposed approach contain less invalid regions (outlier pixels) (see arrows) and resemble a smoother and more realistic appearance.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)

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