### 3846

On the effect of fat spectrum complexity in Dixon MR Fingerprinting
Elizabeth Huaroc1, Dominik Weidlich1, Thomas Amthor2, Peter Koken2, Manuel Baumann2, Kilian Weiss3, Marcus Makowski1, Benedikt Schwaiger4, Mariya Doneva2, and Dimitrios Karampinos1
1Department of Diagnostic and Interventional Radiology, School of Medicine, Technical University of Munich, Munich, Germany, 2Philips Research Lab, Hamburg, Germany, 3Philips Healthcare, Hamburg, Germany, 4Department of Diagnostic and Interventional Neuroradiology, Technical University of Munich, Munich, Germany

### Synopsis

Dixon Magnetic Resonance Fingerprinting (Dixon-MRF) has been emerging for achieving efficient fat suppression in body applications of MRF. Fat quantification using traditional Dixon imaging relies on a pre-calibrated proton density fat spectrum. The fat spectrum is known to be composed of different fat peaks, which have different relaxation times and are affected by J-coupling modulations. Existing Dixon-MRF methods perform water-fat separation assuming a constant pre-calibrated fat spectrum and not accounting how the complex fat spectrum varies along the MRF flip angle train. The present work proposes a framework to characterize the effect of fat spectrum complexity in Dixon-MRF.

### Purpose:

Magnetic resonance fingerprinting (MRF) enables the simultaneous acquisition of several quantitative parameters by varying acquisition parameters during the pulse sequence train(1). MRF has been increasingly used in applications outside the brain, including the prostate(2), the abdomen(3),the myocardium(4) and the breast(5). Spiral trajectories are commonly used in MRF acquisitions because of their sampling speed and large k‐space coverage. However, for the application of spiral trajectories in the body, MRF acquisitions require efficient fat suppression. Dixon Magnetic Resonance Fingerprinting (Dixon-MRF) enables water-fat separation to remove the fat-induced blurring in spiral imaging(6,7), to remove bias in water relaxometry(8,9) and to quantify the tissue fat fraction(10). Fat quantification using traditional Dixon imaging relies on a pre-calibrated proton density fat spectrum(11). However, the fat spectrum is known to be composed of different fat peaks which have different relaxation times and are affected by J-coupling modulations. Existing Dixon MRF methods perform water-fat separation assuming a constant pre-calibrated proton density (PD)-weighted fat spectrum and not accounting how the complex fat spectrum varies along the MRF flip angle train. The present work proposes a framework to characterize the effect of fat spectrum complexity in Dixon-MRF, relying on a fully-sampled multi-echo Cartesian acquisition using an MRF flip angle train excitation.

### Methods:

Fully-sampled multi-echo Cartesian MRF pulse sequence
A spoiled gradient echo MRF sequence(12)(Figure 1a) is the basis for the multi-echo acquisition and was extended by reading 16-echoes with a monopolar readout gradient (Figure 1b). The MRF flip angle train varies smoothly along all TRs (40ms) (Figure 1c). The same 2D-image is acquired for every element of the MRF flip angle train ($MRF_i$) and for every echo time ($TE_n$).
Signal modelling theory
Assuming a fat spectrum with $P$ peaks and a single $T_2^*$ decay, the signal of a fully-sampled multi-echo Cartesian MRF acquisition at $TE_n$ and after one $MRF_i$ is:
$$s\left(TE_{n},MRF_{i}\right)=W_{0}e^{i\phi_{W}}\psi\left(MRF_{i},T_{1 W},T_{2 W}\right)e^{\left(i\omega_{W}-R_{W}\right)TE_{n}}+\sum_{p=1}^{P}\alpha_{p}F_{0}e^{i\phi_{F}}_{0}\psi\left(MRF_{i},T_{1p},T_{2p}\right)e^{\left(i\omega_{p}-R_{p}\right)TE_{n}}$$
where $W_0$ and $F_0$ are the water and fat proton density signals.

Calibration of MRF-weighted fat spectrum

The framework (Figure 2) processes fully-sampled multi-echo Cartesian MRF-data and calculates maps of $T_1$, $T_2$ for water and for all fat peaks and maps for the relative fat peak weights $\alpha_p$.The multi-echo MRF signal is processed for water-fat separation using the chemical species separation (CSS) algorithm(13). CSS allows to define the MRF signal as the sum of 10 chemical species: water and 9 fat peaks at 0.90, 1.30, 1.60, 2.02, 2.24, 2.75, 4.20, 5.19 and 5.29ppm, corresponding to subcutaneous fat(14). In contrast to the PD-weighted fat spectrum approach, the proposed MRF-weighted fat spectrum approach defines the fat peaks as independent species, each with its own magnitude and phase, to account the complex fat spectrum variation across all $MRF_i$ . Since their frequencies are known and a single $R_2^*$ is considered, the problem is then solved for in total 22 unknowns(10 magnitudes, 10 phases, frequency of water and $R_2^*$). The fingerprints, $\psi$ , per species across all $MRF_i$ are assembled from the CSS results.
As a next step, every $\psi$ is matched to obtain its $T_1$, $T_2$ and $PD$ values which will form the corresponding maps of the acquired 2D-image. A dictionary was previously computed simulating signals based on the described sequence and considering $T_1$=[50:5:1700]ms and $T_2$=[10:1:300]ms.Finally, the $\alpha_p$ map of the MRF-weighted fat spectrum is calculated from the PD-maps of all fat peaks according to Eq.(2).
$$\alpha_{p}(x,y)=\frac{PD_{p}(x,y)}{\sum_{l=1}^{9}PD_{l}(x,y)}$$

Dictionary signals simulations

Signals with different fat fractions were simulated for evaluating the bias induced by using the the PD-weighted fat spectrum on synthetic data generated using the MRF-weighted fat spectrum. The fingerprints of the fat peaks and the $\alpha_p$ were averaged from a fat-ROI and water was represented by the dictionary entry with $T_1=1420$ms and $T_2=32$ms. Following Eq.(1), a 6-echoes signal is simulated and processed by using the PD-weighted fat spectrum. Dictionary matching is performed on the water and fat images for calculation of $T_1, T_2$ and $FF$.

In-vivo data simulations

The signal from a muscle-, a fat-ROI and the combination of both allow to simulate different FF from in-vivo data. Only 6 echoes were considered for analysing the bias induced by using the PD-weighted fat spectrum.

### Results:

For a fat-pixel, every fat peak matches to a unique fingerprint (Figure 3). When a signal simulated from those fingerprints was processed using the PD-weighted fat spectrum, the $T_1$ of water was underestimated while the $T_2$ was overestimated along FF (Figure 4).In-vivo simulations of partial voluming effects between muscle and fat show again the influence of the MRF flip angle train in the water-fat separation performance (Figure 5). The in-vivo water T2 maps using the PD-weighted fat spectrum show overestimation at the border between muscle and fat, which is an area with intermediate fat fraction.

### Discussion & Conclusion:

The present work shows the effect of the fat spectrum complexity in Dixon MRF and proposes a framework to extract an MRF-weighted fat spectrum. When the pre-calibrated PD-weighted fat spectrum is used, the fat spectrum complexity is ignored, the FF bias is small, but the and water relaxation times show a bias which increases as the FF increases. Therefore, a strategy incorporating the MRF-weighted fat spectrum in the Dixon-MRF processing needs to be developed.

### Acknowledgements

The present research was supported by Philips Healthcare.

### References

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3. Chen Y, Jiang Y, Pahwa S, Ma D, Lu L, Twieg MD, Wright KL, Seiberlich N, Griswold MA, Gulani V. MR Fingerprinting for Rapid Quantitative Abdominal Imaging. Radiology 2016;279(1):278-286.

4. Jaubert O, Cruz G, Bustin A, Schneider T, Lavin B, Koken P, Hajhosseiny R, Doneva M, Rueckert D, Botnar RM, Prieto C. Water-fat Dixon cardiac magnetic resonance fingerprinting. Magn Reson Med 2020;83(6):2107-2123.

5. Panda A, Chen Y, Ropella-Panagis K, Ghodasara S, Stopchinski M, Seyfried N, Wright K, Seiberlich N, Griswold M, Gulani V. Repeatability and reproducibility of 3D MR fingerprinting relaxometry measurements in normal breast tissue. J Magn Reson Imaging 2019;50(4):1133-1143.

6. Koolstra K, Webb AG, Veeger TTJ, Kan HE, Koken P, Bornert P. Water-fat separation in spiral magnetic resonance fingerprinting for high temporal resolution tissue relaxation time quantification in muscle. Magn Reson Med 2020;84(2):646-662.

7. Nolte T, Gross-Weege N, Doneva M, Koken P, Elevelt A, Truhn D, Kuhl C, Schulz V. Spiral blurring correction with water-fat separation for magnetic resonance fingerprinting in the breast. Magn Reson Med 2020;83(4):1192-1207.

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### Figures

Figure 1: Pulse sequence diagram of the multi-echo Cartesian MRF acquisition. a) Basis MRF-FISP sequence (12) with an extended -readout. b) Extended readout in detail. 16 echoes were acquired using monopolar gradients. c) The flip angle train consists on 500 flip angles. The MRF-sequence components include the flip angle, TE1=7ms and TR=40ms. The flip angle train is not modified to represent more echoes.

Figure 2: MRF-weighted fat spectrum process for considering the effect of the MRF flip angle train over the fat spectrum. A multi-echo Cartesian MRF signal is separated into 10 species which are matched to a dictionary to obtain their T1, T2 and PD maps. Based on the latest, the $\alpha_p$-map is calculated. The model considered for water-fat separation and a list of the variables are also presented. The signals dimensions are provided to clarify the effect of every step of the process on the data.

Figure 3: Fat and fat peaks fingerprints. Fat peaks labeling according to ppm and pixel of interest in a fat region. Pixel signals: fingerprint (red) and matched dictionary signal (blue) for fat from the PD-weighted water-fat separation approach for 16 echoes, fat as the sum of all species except water from the MRF-weighted water-fat separation approach for 16 echoes and fat peaks of the MRF-weighted water-fat separation approach for 16 echoes. T1 and T2 per case are shown.

Figure 4: Simulations. Water properties and FF. The water T1, water T2 and FF values of both the simulation and the result of the matching when using the PD-weighted fat spectrum approach are presented. The plots show that the PD-weighted fat spectrum method underestimates water T1 and overestimates water T2 with increasing along the FF values.

Figure 5: ROI signals from in-vivo data. Water T1, T2 and FF maps of a knee acquired with the multi-echo MRF-sequence acquisition. The first row shows the results using the PD-weighted fat spectrum and the second row the results using the MRF-weighted fat spectrum. The last row shows the water T1, water T2 and FF values of 6-echo signals simulated from ROIs with different FF using the PD-weighted water-fat spectrum. The red boxes over the first image represent examples of the mentioned ROIs.

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