Water–fat Dixon cardiac magnetic resonance fingerprinting

Purpose Cardiac magnetic resonance fingerprinting (cMRF) has been recently introduced to simultaneously provide T1, T2, and M0 maps. Here, we develop a 3‐point Dixon‐cMRF approach to enable simultaneous water specific T1, T2, and M0 mapping of the heart and fat fraction (FF) estimation in a single breath‐hold scan. Methods Dixon‐cMRF is achieved by combining cMRF with several innovations that were previously introduced for other applications, including a 3‐echo GRE acquisition with golden angle radial readout and a high‐dimensional low‐rank tensor constrained reconstruction to recover the highly undersampled time series images for each echo. Water–fat separation of the Dixon‐cMRF time series is performed to allow for water‐ and fat‐specific T1, T2, and M0 estimation, whereas FF estimation is extracted from the M0 maps. Dixon‐cMRF was evaluated in a standardized T1–T2 phantom, in a water–fat phantom, and in healthy subjects in comparison to current clinical standards: MOLLI, SASHA, T2‐GRASE, and 6‐point Dixon proton density FF (PDFF) mapping. Results Dixon‐cMRF water T1 and T2 maps showed good agreement with reference T1 and T2 mapping techniques (R2 > 0.99 and maximum normalized RMSE ~5%) in a standardized phantom. Good agreement was also observed between Dixon‐cMRF FF and reference PDFF (R2 > 0.99) and between Dixon‐cMRF water T1 and T2 and water selective T1 and T2 maps (R2 > 0.99) in a water–fat phantom. In vivo Dixon‐cMRF water T1 values were in good agreement with MOLLI and water T2 values were slightly underestimated when compared to T2‐GRASE. Average myocardium septal T1 values were 1129 ± 38 ms, 1026 ± 28 ms, and 1045 ± 32 ms for SASHA, MOLLI, and the proposed water Dixon‐cMRF. Average T2 values were 51.7 ± 2.2 ms and 42.8 ± 2.6 ms for T2‐GRASE and water Dixon‐cMRF, respectively. Dixon‐cMRF FF maps showed good agreement with in vivo PDFF measurements (R2 > 0.98) and average FF in the septum was measured at 1.3%. Conclusion The proposed Dixon‐cMRF allows to simultaneously quantify myocardial water T1, water T2, and FF in a single breath‐hold scan, enabling multi‐parametric T1, T2, and fat characterization. Moreover, reduced T1 and T2 quantification bias caused by water–fat partial volume was demonstrated in phantom experiments.


| INTRODUCTION
Quantitative parametric mapping has been increasingly incorporated into clinical cardiovascular MR examinations to provide objective myocardial tissue characterization 1 of both focal and diffuse diseases, including assessment of fibrosis, inflammation, 2 and edema. 3 Several mapping methods, including MOLLI, 4 SASHA, 5 T 2 -prepared bSSFP, 3 and T 2 -GRASE, 6 have been proposed to measure myocardial T 1 and T 2 independently. Conventionally, T 1 and T 2 mapping acquisitions are performed in several separate 2D scans, at different slice positions, and under breath-holding, potentially leading to mis-registration between the different acquisitions 7,8 and ultimately contributing to considerable patient fatigue (contributing to the several tens of breath-holds required in a conventional clinical cardiac protocol). Furthermore, these mapping techniques typically rely on simplified exponential relaxation models to estimate T 1 and T 2 values and, in general, do not account for system imperfections.
To accelerate parameter mapping in cardiac MR, joint relaxometry techniques have been proposed to estimate T 1 and T 2 simultaneously, relying on magnetization preparation with varying T 1 and T 2 weightings and combined relaxometry models. [9][10][11] These methods reduce the total number of breathholds and produce co-registered T 1 and T 2 maps. An alternative approach for efficient joint T 1 and T 2 tissue mapping is magnetic resonance fingerprinting (MRF). 12 MRF uses a highly undersampled transient state acquisition scheme with varying acquisition parameters that causes the signals from different tissues to have a unique signal evolution or fingerprint. Matching the measured MR signal response to a previously generated dictionary of fingerprints allows MR tissue identification and parameter estimation. Fingerprints are designed as a function of multiple tissue parameters and therefore several quantitative parameters can be simultaneously reconstructed from the same single acquisition, without the need of relying on simplified relaxation models.
In particular, cardiac MRF (cMRF) 13,14 has been recently introduced for mapping myocardial T 1 , T 2 , and M 0 during a single breath-hold scan. Different to conventional MRF, cMRF acquisition uses variable magnetization preparation with interleaved inversion recovery (IR) and T 2 preparation (T 2 prep) pulses to increase sensitivity to T 1 and T 2 parameters. 13 Furthermore, the cMRF approach does not acquire data continuously: ECG-triggering with a short acquisition window (<250 ms) is used to minimize cardiac motion, whereas breath-holding (<20 s) is needed to minimize respiratory motion, therefore limiting the total effective acquisition time to ~4 s. Additionally, the dictionary of fingerprints needs to be recomputed for each subject to account for heart rate variability. cMRF has shown promising results in comparison to conventional T 1 and T 2 mapping techniques and has the potential to be extended to map other clinically relevant parameters. 14 In addition to T 1 and T 2 mapping, fat characterization plays an important role in evaluating cardiovascular disease. Cardiac fat has been shown to carry important diagnostic information to characterize lipomatous metaplasia, 15 which has high prevalence and prognostic value in patients with myocardial infarction. 16,17 Moreover, water and fat partial volume is a known source of error in parametric mapping, 18 and previous works have explored simultaneous T 1 and fat imaging to reduce partial volume effects and quantify epicardial fat volumes. 19 Therefore, the extension of cardiac MRF to enable additional fat fraction (FF) quantification and partial volume correction is desired.
Multi-compartment 20,21 and water-fat [22][23][24][25][26] MRF approaches have been recently proposed for static body parts such as knee, liver, breast, upper thigh, and whole-body. There are several challenges in extending such methods for cardiac applications. For one, these approaches require longer acquisition times, ranging from 10-24 s of continuous acquisition per slice, making them incompatible with the requirements of cardiac imaging, i.e., short effective scan times ~4 s to enable clinically feasible breath-holding (~15 s). In previous approaches to enable water-fat MRF, additional parameters such as B 0 and/or B 1 needed to be included in the dictionary for correction. The correction was achieved in earlier water-fat MRF works using separate acquisitions to obtain the field maps 25,26 or adding the additional parameters as part of the dictionary matching step. [22][23][24] Both techniques significantly increase the dictionary size (and corresponding computation time) without providing additional diagnostic information. Since cardiac MRF requires subject-specific dictionaries, shortening dictionary computation times is essential to maintain feasible reconstruction times.
In order to address the limitations of previously introduced techniques for cardiac imaging, in this work, we propose a 3-point Dixon cardiac MRF (Dixon-cMRF) framework to enable simultaneous water-specific T 1 , T 2 , and M 0 myocardial mapping and fat fraction (FF) estimation from a single breath-hold scan, while potentially reducing T 1 and T 2 biases caused by water-fat partial volume. This is achieved by synergistically combining and extending previously proposed approaches to satisfy the requirements of cardiac MRF imaging. The proposed Dixon-cMRF framework integrates (1) a 3-echo gradient-echo golden angle radial readout to enable short TRs and reduced fat blurring (as opposed to spiral readouts previously used in cardiac MRF); (2) a B 0 and B 1 insensitive cMRF acquisition scheme, 27 avoiding the acquisition of additional B 1 and B 0 maps (that would require additional breath-holds and would be prone to mis-registration errors) or adding B 1 and B 0 as parameters in the dictionary (that would highly increase the dictionary size and computational time); (3) a patch-based multi-contrast low-rank tensor reconstruction 28 to recover the highly undersampled time series images for each echo, satisfying scan times constraints; and (4) a chemical shift-based method 29 to separate the water and fat time series in the compressed temporal domain before independent water and fat MRF matching, avoiding the generation of large dictionaries. The proposed Dixon-cMRF framework was evaluated in a standardized T 1 /T 2 phantom, a water-fat phantom, and healthy subjects. In vivo results were qualitatively and quantitatively compared to conventional SASHA, MOLLI, and T 2 -GRASE mapping in 10 subjects and 6-point Dixon proton density fat fraction (PDFF) in 3 of these subjects.

| Acquisition
The proposed Dixon-cMRF consists of a 15-heartbeat ECGtriggered golden angle radial (~111°) gradient rewound echo (GRE) acquisition with varying inversion and T 2 preparation pulses (Figure 1). Inversion pulses are applied every 5 heartbeats with delays of [10,300,10] ms, whereas T 2 preparations with TEs of [No T 2 prep, No T 2 prep, 40, 80, 160] ms are repeated 3 times over the 15 heartbeats. Additional contrast encoding is provided with the flip angle pattern composed of a linear ramp-up of 20 RF pulses from 5° to 30° followed by a fixed 30° flip angle. 27 Low flip angles, fixed TR and gradient spoiling were used to reduce the signal's sensitivity to B 0 and B 1 inhomogeneities. 27,30 Excitations were performed using a short asymmetrical sinc pulse with F I G U R E 1 Proposed Dixon-cMRF framework. (A) A 3-echo gradient echo golden radial acquisition is ECG-triggered to acquire k-space data at the mid-diastolic cardiac phase for 15 heartbeats (i.e., ~15 s). Magnetization preparation includes inversion pulses every 5 heartbeats (with inversion delays of 10, 300, and 10 ms, respectively) and variable T 2 preparation modules (no T 2 preparation, no T 2 preparation, 40, 80, and 160 ms repeated over 15 heartbeats). (B) The 3 echoes are reconstructed as separate time series from which a B 0 map estimate and water-fat separated time series are obtained. (C) After a matching step, water-and fat-specific T 1 , T 2 , and M 0 maps and fat fraction can be extracted a time bandwidth product of 3. Three echoes are sampled using bipolar gradients within each TR.

| Image reconstruction
HD-PROST, 28 a recently introduced multi-contrast, patchbased, high-order, low-rank reconstruction, is used to highly accelerate the proposed Dixon-cMRF acquisitions while still providing high quality maps. Dictionary-based global temporal compression of the MRF time-series 31,32 is exploited through singular value decomposition (SVD), to reduce undersampling artefacts in the images. This so-called low rank inversion (LRI) approach 32 replaces the reconstruction of the whole MRF time-series xʹ by the reconstruction of a reduced number R of singular images. These singular images are a low rank approximation of the MRF time-series and are obtained by projecting the time series onto a subspace identified through SVD of the dictionary. They are defined as x = U H R x � where the columns of U R are the truncated (to rank R) left singular vectors of the dictionary matrix D. LRI reconstruction is formulated as the following optimization problem where F is the Fourier transform operator, k is the undersampled k-space data, A is the sampling operator, and C are the coil sensitivity maps. The singular images x estimated with this method can still present remaining undersampling artefacts and lead to noisy parametric maps. HD-PROST 28 reconstruction proposes to further exploit local (within a patch), non-local (between patches in a neighborhood), and spectral (between contrasts) redundancies through high-order low-rank regularization. 33,34 HD-PROST reconstructs the multi-contrast Dixon-cMRF singular images x i for each echo i, by jointly solving where P b (·) is the operator that assembles a third order tensor  b for the patch centered on voxel b by concatenating the K most similar patches along the non-local similarity dimension (similar patches within a neighborhood), and the R contrasts reconstructed along the spectral dimension (singular images), whereas λ is the corresponding parameter promoting low-rank regularization.

| Water/fat separation
Considering a water (W′) and a set of fat (F ′ k ) compartments time-series, 35,36 the reconstructed singular images at echo i, can be written as Δf k t i are the temporally compressed water and fat (or combined fat compartments) time series, Δf k is the difference in precession frequency between water and fat compartment k, Δf B0 is the precession frequency difference induced by B 0 field inhomogeneities, and t i is the echo time i.
The temporally compressed signal formulation in Equation 3 leads to the same water-fat separation problem as for conventional (non-MRF) multi-echo Dixon acquisitions. 35,36 Therefore, the MRF water-fat separation problem can be solved in the compressed temporal domain given an initial B 0 estimation. A single B 0 map can be obtained from the first singular images of each echo, which have high SNR ratios. The initial B 0 estimation is performed using a multiseed region growing scheme from 3-point data and then used for water-fat separation 29 using a pre-defined 6-peak fat model 37 without accounting for T * 2 decay.

| Feature extraction
The Dixon-cMRF dictionary was simulated for a range of T 1 /T 2 values using the extended phase graph (EPG) formalism. 38 The subject-specific dictionary was generated using the simultaneously recorded ECG signal, to account for varying acquisition times resulting from intra-and inter-subject heart rate variations. For higher mapping accuracy, the EPG simulation includes a slice profile correction with 51 isochromats 39 and a Bloch simulation of the inversion efficiency , where r is the magnitude of the magnetization vector. Maps are extracted through dot product matching between the dictionary D in the compressed domain and the water-fat separated time series, W and F, to obtain water-fat-specific T 1water/fat , T 2water/fat , and M 0water/fat maps. Dixon-cMRF FF maps are estimated from the MRF M 0 maps as 40 where e j w and e j f are the initial water and fat phase and are estimated for each pixel as the mean phase from the portion of the MRF water and fat signals with positive longitudinal magnetization. Single echo T 1 , T 2 , and M 0 maps, similar to conventional cMRF, are obtained by matching the 1st, 2nd, or 3rd Dixon-cMRF reconstructed echo to the same dictionary for comparison purposes.

| Experiments
Dixon-cMRF was evaluated in a standardized T 1 /T 2 phantom, an in-house built water-fat phantom, and in vivo in 10 healthy subjects ( The echo images were reconstructed using HD-PROST (Equation 2). The reconstruction parameter values were chosen empirically based on those used in Bustin et al 28 and are listed in Supporting Information Figure S1. A reduced patch size of 5 × 5 was used here because of the lower resolution of Dixon-cMRF compared to the MRF scans reported in Bustin et al. 28 The rank R = 6 was selected based on the decay of the singular values from the dictionary (Supporting Information Figure S2A). The number of ADMM iterations was selected based on the convergence of the algorithm (Supporting Information Figures S2B and C).
Dixon-cMRF reconstruction was performed in MATLAB (The MathWorks, Natick, MA) and took ~3 h, including 2.5 h for dictionary generation, 27 min for HD-PROST reconstruction, 0.3 s for water-fat separation, and 3.2 s for matching of the water and fat time series on a Linux workstation with 8 Intel Xeon E5-2687W (3.1 GHz) and 252 GB RAM.

| Water-fat phantom study
A water-fat phantom was built in-house with 6 vials composed of a mix of different concentrations of a water solution and peanut oil, 1 vial of distilled water and agar (2%), and 1 vial of exclusively peanut oil. The peanut oil was chosen as it has a similar spectrum to the one found in the triglyceride protons present in human fat tissues. 42 The water solution contained 43 mM sodium dodecyl sulfate (SDS), 43 mM sodium chloride, and 0.3 mM gadobenate dimeglumine (MultiHance, Bracco, Milan, Italy) as described in Hines et al 43 and agar (2%) for solidification.
A proton density fat fraction (PDFF) reference measurement was made using a 6-echo Dixon GRE sequence. Acquisition parameters included: Cartesian read-outs with fly-back, 6 echoes with TR/TE1/ΔTE = 13.7/1.3/2 ms, flip angle (FA) = 5°, BW = 1085 Hz/pixel, resolution = 2 × 2 mm, and slice thickness = 8 mm. The reference PDFF estimation uses the same pre-defined 6-peak fat model as used in the proposed Dixon-cMRF. 37 A graph cut scheme was considered for B 0 estimation, 44 and T * 2 decay and noise bias correction 40 were included for accurate PDFF estimation.
Dixon-cMRF measurements were performed with the same acquisition parameters as in the standardized T 1 /T 2 phantom study. Reference T 1 IRSE and T 2 MESE water scans were acquired with the same acquisition parameters as in the standardized T 1 /T 2 phantom study but with binomial 1331 water excitation pulses to compare with Dixon-cMRF water T 1 and T 2 maps. SASHA, MOLLI, and T 2 -GRASE sequences were also acquired to compare the performance of conventional techniques in the presence of water-fat partial volume. Acquisition parameters for SASHA included: TE/TR = 1.19/2.4 ms, SENSE factor = 2, BW = 1085 Hz/pixel, FA = 70°, 9 saturation times ~120:60:650 ms and an infinity image, and acquisition time = 10 s. Acquisition parameters for MOLLI (5(3)

| In vivo study
In vivo acquisitions were performed under a single breathhold of ~15 s with the same parameters used for the phantom experiments in short-axis orientation. Conventional SASHA, MOLLI, and T 2 -GRASE maps were acquired sequentially with Cartesian readouts and the same FOV, resolution, and slice thickness as Dixon-cMRF in all subjects. Additionally, PDFF reference measurement was made using a 6-echo Dixon GRE sequence in 3 of 10 subjects. SASHA, MOLLI, and T 2 -GRASE acquisition parameters were as described in the water-fat phantom study. Six-point Dixon acquisition and reconstruction parameters were the same as those used for the water-fat phantom experiment but with SENSE factor = 2 and acquisition time ~10 s. Dixon-cMRF time series images were reconstructed using HD-PROST. Additionally, LRI, LRI with locally lowrank and Wavelet regularization (SLLR), 45 and HD-PROST reconstructions were performed in a representative healthy subject for comparison purposes.

| Analysis
T 1 and T 2 values were measured in region of interests (ROIs) for the phantoms and in vivo experiments. Mean values within the ROI were used to assess accuracy whereas the SD within the ROI (spatial variability) was considered as an indication of the mapping precision in phantom 46 and used as a surrogate for precision in the healthy myocardium measurements. 10 Accuracy of T 1 and T 2 water Dixon-cMRF was assessed in the standardized T 1 /T 2 phantom study through lines of best fit, determination coefficient, and normalized RMSE (NRMSE) with respect to reference IRSE and MESE measurements. Dixon-cMRF FF estimation was compared to the reference PDFF measurement in the water-fat phantom study and in 3 healthy subjects through determination coefficients and maximum error. Rigid registration between the PDFF and Dixon-cMRF FF maps was performed previous to the analysis of the in vivo data. In vivo T 1 and T 2 measurements were performed in the septum, and using the 6 AHA cardiac segments model, compared against MOLLI, SASHA, and T 2 -GRASE. A 2-tailed Student's t test with Bonferroni correction (resulting threshold P-values were P T1 < 0.025 and P T2 < 0.05 for T 1 and T 2 measurement methods, respectively) was performed on the mean and spatial variability septum measurements to test for statistically significant differences between the methods. Dixon-cMRF FF was measured in the septum for all subjects and additionally in 2 separate pericardial (pericardial 1 and pericardial 2) and 1 subcutaneous fat ROIs for the 3 subjects that underwent PDFF experiments.
In vivo Dixon-cMRF water T 1 and T 2 maps and conventional MOLLI, SASHA, and T 2 -GRASE maps were qualitatively assessed by an expert (R.H.) with 1 year of expertise in cardiac T 1 and T 2 mapping using a 4-point scoring system: 1, uninterpretable maps; 2, poor map quality (blurred edges, noise, and residual artefacts); 3, acceptable map quality (mildly blurred edges, mild noise, and residual artefacts); and 4, excellent map quality (sharply defined myocardium wall, neglectable residual artefacts). A Wilcoxon signed rank test with Bonferroni correction (P T1 < 0.025 and P T2 < 0.05) was performed to test for statistically significant differences between the scores.
Water and fat T 1 and T 2 Dixon-cMRF values within a partial volume mask were compared to those obtained with single echo cMRF for each of the 3 echoes to investigate any potential water-fat partial volume bias. The locations of the pixels surrounding the heart affected by water-fat partial volume, to define the mask, were extracted using the Dixon-cMRF fat fraction map (FF ϵ [0.3; 0.7]).

| Standardized T 1 /T 2 phantom study
Dixon-cMRF results obtained on the standardized T 1 /T 2 phantom are summarized in Figure 2. Dixon-cMRF water T 1 and T 2 values are in good agreement with the spin-echo reference values and those estimated with single echo cMRF (echo 1). Lines of best fit with slopes a T1 = 0.975/0.990 and a T2 = 0.972/1.008, intercepts of b T1 = 5.8/3.6 ms and b T2 = 2.5/2.5 ms, and high determination coefficients (both R 2 > 0.99) with respect to the reference values were obtained for single echo cMRF (echo 1) and water Dixon-cMRF, respectively. NRMSE over all vials were measured with single echo cMRF and water Dixon-cMRF maps at 1.9% and 1.4% for T 1 measurements and 3.6% and 5.4% for T 2 measurements, respectively. In Supporting Information Figure S3, a good water-fat separation is observed visually in both water and fat M 0 maps as well as a smooth off-resonance map.

| Water-fat phantom study
Reference PDFF measurements for the water-fat phantom are shown in comparison to Dixon-cMRF FF estimation in Figure 3A and B. A high determination coefficient of R 2 = 0.999 was obtained between both measurements, with a maximum NRMSE of 2.1% (observed at very low FF). Dixon-cMRF water and fat T 1 and T 2 measurements are shown in Figure 3C and D in comparison to water-excited spin echo and single echo cMRF (echo 1) measurements. The corresponding maps are shown in Supporting Information Figure S4. High determination coefficients were observed between water Dixon-cMRF and the reference values (excluding the fat only vial) with R 2 = 0.999 and R 2 = 0.992 for T 1 and T 2 , respectively. A maximum error with respect to references in the presence of water-fat partial volume was measured at 100 ms and 3 ms for T 1 and T 2 , respectively. Water and fat Dixon-cMRF T 1 Figure S5A and to single echo cMRF for each of the 3 echoes in Supporting Information Figure S5B. A dependency of the original cMRF measurement on the echo time selected in the presence of water fat partial volume was observed. Echo 1, which is closest to out-of-phase (2 ms), provided particularly poor matches in the presence of water-fat partial volume.

| In vivo study
Dixon-cMRF water T 1 and T 2 maps and FF estimation obtained with LRI, SLLR, and HD-PROST reconstructions are shown in Supporting Information Figure S6. Results show remaining noise-like artefacts in the unregularized LRI maps, whereas regularized SLLR and to a greater extent HD-PROST provided excellent quality water T 1 and water T 2 maps (scored 4 for HD-PROST) as well as visually good FF maps.
Water-fat separation of the compressed Dixon-cMRF time-series (singular images) are shown for a representative healthy subject in Figure 4. The resulting water and fat T 1 and T 2 Dixon-cMRF maps are shown in Figure 5. A zoom-in region around the heart shows that Dixon-cMRF recovers myocardium wall T 1 and T 2 information in the presence of fat partial volume in comparison to single echo cMRF (arrows). Dixon-cMRF water T 1 and T 2 maps and FF estimation for 5 other subjects are shown in Supporting Information Figure S7.
Dixon-cMRF water T 1 and T 2 maps are shown in Figure 6 in comparison to MOLLI, SASHA, T 2 -GRASE, and single echo cMRF (echo 1). Comparable results are observed with all methods, however, the proposed Dixon-cMRF provides additional FF estimation. Dixon-cMRF water and fat M 0 images and FF map are shown in Figure 7 together with the 6-point Dixon PDFF reference. The absolute difference image between the PDFF and Dixon-cMRF FF maps is also included ( Figure 7C).
Qualitative map quality median scores of 2, 3, and 3.5 were obtained for SASHA, MOLLI, and Dixon-cMRF water T 1 , respectively, and of 3 and 4 for T 2 -GRASE and Dixon-cMRF water T 2 , respectively. The difference between scores were not significant between Dixon-cMRF T 1 and MOLLI (P = 0.125), whereas MOLLI (P = 0.002) and Dixon-cMRF T 1 (P = 0.002) were both scored significantly better than SASHA. Dixon-cMRF T 2 was also scored significantly better than T 2 -GRASE (P = 0.0156). The distribution of the map quality scores for each mapping technique is shown in Supporting Information Figure S8. Dixon-cMRF water T 1 , T 2 , and FF septum measurements (mean and spatial variability) are shown in Figure 8 for all subjects, in comparison to measurements from SASHA, MOLLI, and T 2 -GRASE. The average T 1 septum measurements using SASHA, MOLLI, and the proposed water Dixon-cMRF T 1 were 1129 ± 38 ms, 1026 ± 28 ms, and 1045 ± 32 ms, respectively. The average T 2 measurements for T 2 -GRASE and the proposed water Dixon-cMRF T 2 were 51.7 ± 2.2 ms and 42.8 ± 2.6 ms, respectively. The bias between the mean of Dixon-cMRF T 1 and T 2 measurements was −84 ms and −8.9 ms with respect to SASHA and T 2 -GRASE, respectively, differences were statistically significant in both cases (P < 0.0001). The average Dixon-cMRF septum FF value was 1.3 ± 3% across all subjects. In the septum, Dixon-cMRF water T 1 mapping achieved lower spatial variability (49 ms) than MOLLI (60 ms) and SASHA (113 ms), whereas Dixon-cMRF water T 2 mapping spatial variability (4.6 ms) was similar to T 2 -GRASE (4.9 ms). Dixon-cMRF FF spatial variability in the septum was 3.9%. Regional 6-segment T 1 and T 2 mean measurements and spatial variability across all subjects are shown in Figure 9 for the proposed Dixon-cMRF water T 1 and T 2 , in comparison to MOLLI, SASHA, T 2 -GRASE and single echo cMRF (echo 1).

F I G U R E 5 Dixon-cMRF in a representative healthy subject. (A) Good image quality and water-fat separation is seen on the whole FOV of
the 1st singular images leading to good quality water and fat T 1 and T 2 maps. (B) Comparison of Dixon-cMRF and single echo cMRF (echo 1) in a zoomed region around the heart. Myocardium wall recovery with Dixon-cMRF in both T 1 and T 2 maps in regions with water-fat partial volume is indicated by the white arrows. Additional water-and fat-specific M 0 can be estimated with Dixon-cMRF to obtain a fat fraction map F I G U R E 6 Comparison of water Dixon-cMRF, single echo cMRF (echo 1), and conventional MOLLI, SASHA, and T 2 -GRASE maps for a representative healthy subject PDFF and the Dixon-cMRF FF measurements for 4 ROIs (pericardial 1, pericardial 2, subcutaneous fat, and septum) are shown in Supporting Information Table S1 and Figure S9 for the 3 subjects that underwent PDFF acquisition. Good agreement was observed between the reference PDFF and the Dixon-cMRF FF measurements (R 2 > 0.98), with a maximum absolute difference of 5.8% FF observed for low fat fractions.
The water-fat partial volume mask used to compare water and fat Dixon-cMRF and single echo cMRF (for each echo) T 1 and T 2 values in the presence of partial volume is shown Figure 10A for a representative healthy subject. The distribution of the corresponding measurements within the mask are shown in Figure 10B for the same healthy subject and in Figure 10C for all subjects. The 2 compartments of water and fat are clearly separated for the proposed Dixon-cMRF. Mean water T 1 and T 2 values, for the pixels within the partial volume mask, were 1174 ms and 60.9 ms, respectively, whereas mean values for single echo cMRF for each of the 3 echoes were: echo 1 T 1 /T 2 = 537/80.1 ms, echo 2 T 1 /T 2 = 549/89.3 ms, and echo 3 T 1 /T 2 = 541/90.6 ms.

| DISCUSSION
A novel 3-point Dixon cardiac MRF framework was proposed to enable simultaneous water-and fat-specific T 1 , T 2 , and M 0 mapping of the heart and fat fraction estimation in a single ~15s breath-hold scan per slice. This is achieved by extending cardiac MRF using a 3-echo radial acquisition, a water-fat separation of the MRF time series images in the compressed temporal domain and the recently introduced multi-contrast HD-PROST reconstruction.

| T 1 and T 2 quantification
T 1 and T 2 quantification with the proposed Dixon-cMRF framework was validated in a standardized T 1 /T 2 phantom.
Accurate water T 1 and T 2 values were obtained with the proposed approach in comparison to spin echo-based reference values (R 2 > 0.99, NRMSE T1 = 1.4% and NRMSE T2 = 5.4%). A slice profile correction was included in the dictionary to obtain accurate measurements (for T 2 especially) when using short pulses. 27,39 A Bloch simulation of the inversion efficiency was also included, 27 impacting mainly the T 1 measurements. To limit the impact of B 1 inhomogeneities, adiabatic inversions 47 and refocusing pulses in the T 2 preparation prepulses 48 were used, with the maximum excitation flip angle 27 limited to 30°. To extend the pattern from single echo to 3-echo Dixon encoding, the TEs were chosen based on a previously reported Cramer-Rao lower bound (CRLB) optimization. 49 However, improvements may be possible, because this CRLB optimization was performed considering a single peak model, no T * 2 decay, and no signal variations due to MRF.
F I G U R E 9 Regional T 1 and T 2 assessment of the different mapping techniques. T 1 (top) and T 2 (bottom) mean values and spatial variability reported for each segment as average measurements over 10 subjects. The value in the central segment represents the average over all segments. Average measurements/spatial variability for Dixon-cMRF water T 1 and T 2 were 1032/55 ms and 42.1/5.5 ms, respectively. Overall Dixon-cMRF presented lower spatial variability than MOLLI and SASHA measurements but higher than T 2 -GRASE measurements Dixon-cMRF water T 1 and T 2 maps were judged as being of good or excellent quality (score of 3 or more) in all the healthy subjects in this study. In vivo Dixon-cMRF water T 1 values were slightly higher than those measured with MOLLI but lower than SASHA, which is consistent with previously reported results for cMRF, 27 whereas Dixon-cMRF water T 2 values were lower than T 2 -GRASE measurements. Discrepancies between previously reported T 2 values for different T 2 mapping methods (T 2 -GRASE vs. T 2 prep bSSFP) and field strengths (1.5T vs. 3T) 50 hinders further analysis of this bias. However, myocardium measurements previously reported for cardiac MRF 13,27 seem to be in the lower end of existing literature values. Magnetization transfer and diffusion have previously been shown to cause considerable biases in MRF [51][52][53] and might be the source of the remaining biases seen in the in vivo measurements. T 1 , T 2 , and M 0 measurements in the blood are also susceptible to flow as blood entering and leaving the imaging slice could not be accurately modeled. Validation of Dixon-cMRF water T 1 and T 2 measurements in the presence of water-fat partial volume could not be performed in vivo because of unavailability of robust water T 1 and T 2 reference mapping techniques, therefore this validation was performed on a water-fat phantom, as discussed below.

| Water-fat separation and fat fraction estimation
Effective water-fat separation was obtained with the proposed Dixon-cMRF in the water-fat phantom ( Figure 3) and in vivo (Figures 4 and 5) experiments. High determination coefficients (R 2 > 0.99 in the phantom and R 2 > 0.98 in vivo) were observed between the FF map estimated with the proposed approach and the reference PDFF map, with maximum errors obtained at very low FF values. In vivo septum average FF was measured at 1.3% that is in agreement with reference literature values (~1%). 54 A limitation of the proposed Dixon-cMRF approach is that T * 2 decay is not accounted for in the water-fat separation model. The signal loss because of T * 2 decay can be accounted for as a proportion of the signal coming from an off-resonant fat compartment. This effect has been previously shown to impact FF estimation especially at low FF values and short T * 2 . 43 Negative fat fraction values were estimated in very low fat fraction areas in 2 subjects and in the phantom. The lack of T * 2 correction 55 and phase errors 56 could be the main sources of these errors and will be investigated in future works. Extending the proposed approach to obtain additional T * 2 mapping could provide more accurate FF values and T * 2 quantification, which is relevant in the diagnosis and treatment monitoring of myocardial iron overload. 57 Recently, a 3-echo GRE MRF acquisition with considerably longer acquisition times was proposed for brain imaging, obtaining additional T * 2 and T ′ 2 maps. 58 Clinical recommendations are to acquire 8 echoes from 2-18 ms for cardiac T * 2 mapping, 59 therefore longer and more numerous TEs would be necessary with Dixon-cMRF to successfully map these parameters, and therefore further investigation to enable T 1 , T 2 , T * 2 , and FF maps in a single breath-hold scan is needed.

| Water T 1 -T 2 bias correction from
water-fat partial volume Dixon-cMRF was able to recover the T 1 and T 2 of the water and fat compartments in the water-fat partial volume phantom, achieving more accurate results than those obtained with conventional mapping techniques (Supporting Information Figure S5A). Water Dixon-cMRF T 2 values were in good agreement with the water-selective spin echo reference (maximum error = 3 ms), whereas a consistent overestimation was observed for Dixon-cMRF T 1 measurements in comparison to water T 1 IRSE. The Dixon-cMRF water T 1 values with or without water-fat partial volume were all consistent, whereas water T 1 IRSE measurements presented larger variations depending on the vials. In this study, water selective spin echo measurements were considered as reference measurements (because of the unavailability of a better gold standard), however, these measurements could be affected by remaining fat signals if the water selective pulse fails to fully suppress the different fat compartments. Additionally, the discrepancy between the reference water IRSE and Dixon-cMRF T 1 measurement ( Figure 3C) for the distilled water vial (with the highest T 1 value, outside of the range of interest for cardiac imaging) indicates that either the water IRSE (with maximum TI of 3000 ms) and/or the Dixon-cMRF water measurement may not be able to map accurately very long T 1 values, therefore further validations for very long T 1 are needed.
Single echo cMRF behaved differently depending on the echo time in the presence of water-fat partial volume in the phantom experiment (Supporting Information Figure S5B). Similar observations were made in vivo by studying pixels within a water-fat partial volume mask, showing the dependency of the cMRF measurements on the echo time in zones affected by water-fat partial volume. The first echo (closest to out-of-phase: TE = 2 ms) was shown to provide inaccurate T 1 and T 2 values in zones with water-fat partial volume in both phantom and in vivo experiments. The water-fat separation used in the proposed Dixon-cMRF allows to recover the T 1 and T 2 for the 2 (water and fat) compartments with observable wall recovery in water maps.
Good quantitative correspondences were observed in vivo between single echo cMRF (echo 1) and water Dixon-cMRF T 1 and T 2 measurements in the septum (+7 ms and −0.2 ms bias for T 1 and T 2 measurements, respectively). A slightly lower spatial variability was observed in the water Dixon-cMRF maps compared to single echo cMRF (echo 1) with an average spatial variability for Dixon-cMRF and single echo cMRF of 55 ms and 67 ms, respectively, for T 1 , and of 5.5 ms and 6.7 ms for T 2 . This decrease in spatial variability was likely because of the SNR increase when combining the 3 echoes to obtain the water images.

MRF techniques
Dixon-cMRF uses a water-fat separation of the MRF time series before dictionary matching of the water and fat compartments. Recently proposed dictionary-based water-fat separation 22,23 could also be potentially applied to cardiac MRF, however, these methods significantly increase the dictionary size, require longer acquisition times than Dixon-cMRF, and do not map T 2 relaxation times, which makes it impractical for cardiac applications. Other works on chemical shift-based approaches for MRF fat fraction estimation 24,25,60 rely on long spiral readouts where water and fat deblurring will be necessary because of the long readouts. The advantage of the proposed Dixon-cMRF over these techniques for cardiac imaging lies in its relatively short scan time, low sensitivity to nuisance parameters such as B 1 and B 0 , and the use of short radial readouts (1.15 ms) leading to the fast acquisition of 3 echoes in the same TR with minimal blurring. Therefore, no extra field map acquisitions are necessary and the dictionary size remains unchanged compared to single echo cMRF. This is relevant in the context of cMRF where field maps would be acquired in separate breath-holds leading to longer scan sessions and possible mis-registration. A simplified analysis for solving the same problem using a dictionary-based water-fat separation 23 leads to 4 additional parameters in the dictionary (fat fraction, B 0 , T 1 fat, and T 2 fat). Considering the same discretization as in Cencini et al 23 (dictionary 1), the 6D dictionary would have N ff = 10, N B0 = 168, N T1fat = 7, and for Dixon-cMRF an added N T2fat = 7 number of entries for FF, B 0 , T 1 fat, and the additional T 2 fat dimension, respectively. The dictionary size would therefore be multiplied by ~82,000 leading to ~10 9 entries, 8500 days for dictionary computation (assuming linear increase of the computational complexity with the number of entries), and 36 h for matching (using an exhaustive search) with our current MATLAB implementation. In comparison, Dixon-cMRF takes 2.5 h for dictionary computation, 0.3 s for water-fat separation, and 3.2 s for matching of water and fat.
Compared to previous works on both cMRF 13,27 and water-fat MRF, 23,24 Dixon-cMRF reached higher acceleration rates to accommodate to the timing restrictions of cardiac MRI (ECG triggering, <200 ms acquisition window, and ~15 heartbeat breath-holds) and multi-echo Dixon imaging (acquisition of multiple echoes leading to longer TRs). The acquisition window of previously proposed cardiac MRF 13 was 240-280 ms (16 heartbeats acquisition), which may lead to residual bias and artefacts because of cardiac motion. In this study, the acquisition window of Dixon-cMRF was considerably shorter (188 ms leading to an effective scanning time of 2.82 s with 15 heartbeats acquisition) and similar to the clinical MOLLI sequence (180 ms). 4

| Study limitations and future work
Potential clinical applications for Dixon-cMRF include, beside myocardial tissue characterization, patient populations where the detection of fat infiltration, 16 volume quantification of pericardial 61 and epicardial 19 fat, and fat fraction values are of interest. An exemplary application is for patients with prior myocardial infarction, where detection of fat infiltration 16 has high prognostic value and slight changes in acquisition parameters, such as the TE, might lead to potentially wrong diagnosis (depending on the bias induced by phase difference between fat and water). 18 Dixon-cMRF may allow to specifically identify whether the parameter variation is because of fat infiltration or another pathophysiology. In this study, only a small number of healthy subjects with no fat infiltration were acquired, spatial variability was used as a surrogate for precision, and no reference for the cardiac in vivo water specific T 1 and T 2 measurements was available. Further validation of the proposed Dixon-cMRF technique in the presence of fat infiltrations (i.e., in patients with cardiovascular disease) will be investigated in future studies.
Finally, in this study, Dixon-cMRF was performed without contrast agent injection. Acquiring Dixon-cMRF both pre-and post-contrast may allow to obtain additional extra cellular volume maps. The extension of Dixon-cMRF to successfully map those additional parameters for global myocardial health assessment 14 will be investigated in future work.

| CONCLUSION
Dixon-cMRF allows for simultaneous co-registered quantification of myocardial water T 1 , water T 2 , and fat fraction in a single breath-hold scan, enabling multi-parametric T 1 , T 2 , and fat characterization. Moreover, reduced T 1 and T 2 quantification bias caused by water-fat partial volume was demonstrated in phantom experiments. Dixon-cMRF has been successfully demonstrated in phantoms and healthy subject experiments. Clinical validation of this approach in patients with cardiovascular disease is now warranted.
iterations for the same subject. (C) The resulting water T 1 and T 2 maps at different ADMM iterations showing the stability of the proposed Dixon-cMRF reconstruction. A dictionary rank threshold of 6 (<3% of the first singular image) and 6 ADMM iterations were used for HD-PROST reconstruction in this study FIGURE S3 Dixon-cMRF T 1 /T 2 phantom experiment. The standardized T1mes phantom was acquired together with 2 bottles of oil. (A) Water M 0 , fat M 0 , and B 0 maps showing successful separation of water and fat signals. (B) Dixon-cMRF water-specific and single echo cMRF (echo 1) T 1 and T 2 maps. Because the fat signal is well-suppressed, the water maps match to noise in the fat bottles FIGURE S4 Water-fat partial volume phantom T 1 , T 2 , and FF measurements. Dixon-cMRF maps show good qualitative correspondence with reference water selective IRSE, water selective MESE, and 6 echo PDFF scan, whereas single echo cMRF (echo 1) measurements seems to map inconsistently in vials affected by water-fat partial volume as also shown in Figure 3 and Supporting Information Figure S5B FIGURE S5 Water-fat partial volume phantom experiment. (A) Comparison of water-and fat-specific Dixon-cMRF T 1 to conventional SASHA and MOLLI (left), and waterand fat-specific Dixon-cMRF T2 to T2-GRASE (right). Conventional methods are unable to accurately estimate T 1 or T 2 for either of the 2 (water and fat) compartments. (B) Comparison of water-and fat-specific Dixon-cMRF and single echo cMRF for each of the 3 independent echo measurements. T 1 and T 2 measurements in the presence of partial volume varies depending on the echo time because of different contributions of fat and water. In particular, echo 1 that is closest to out-of-phase, provides particularly poor matches in the presence of water-fat partial volume FIGURE S6 Comparison of non-regularized LRI reconstruction (left), regularized using locally low rank and Wavelet priors (SLLR) 45 (middle), and reconstructed using HD-PROST (using high order low rank regularization). LRI shows remaining noise-like artefacts that can be removed using SLLR and HD-PROST. Although both provide good quality results, HD-PROST maps seem slightly sharper as shown by the black arrows FIGURE S7 In vivo Dixon-cMRF water T 1 , water T 2 , and fat fraction maps for 5 additional healthy subjects. High quality (score superior or equal to 3) water T 1 and T 2 maps were consistently obtained for all subjects FIGURE S8 Map quality evaluation of T 1 (left) and T 2 (right) mapping techniques according to a 4-point scale (1 = uninterpretable maps to 4 = excellent map quality). Reported median scores are 2, 3, and 3.5 for SASHA, MOLLI, and Dixon-cMRF water T 1 , respectively, and 3 and 4 for T 2 -GRASE and Dixon-cMRF water T 2 , respectively. All Dixon-cMRF water maps were of acceptable or excellent quality (score superior or equal to 3) and obtained equal or higher scores than their conventional counterpart SASHA, MOLLI, and T 2 -GRASE maps in this study. Image scores of the proposed method were significantly better when compared to SASHA (*P < 0.025) and T 2 -GRASE (*P < 0.05). The difference in scores with MOLLI was not statistically significant (P = 0.07) FIGURE S9 Comparison between Dixon-cMRF fat fraction and proton density fat fraction measured in 4 ROIs (2 separate pericardial regions, subcutaneous fat, and septum) for 3 healthy subjects. High determination coefficient R 2 = 0.9885 was measured TABLE S1 Mean proton density fat fraction (PDFF) and Dixon-cMRF fat fraction (FF) measured in 2 separate pericardial (pericardial 1, pericardial 2), septum, and subcutaneous fat ROIs in 3 healthy subjects (corresponding to the values plotted in Supporting Information Figure S9). Spatial variability of the measurement in the septum and subcutaneous fat, where homogeneous regions are expected, are also reported as a surrogate for precision. Pericardial ROIs were chosen in heterogeneous regions with varying water-fat partial volume, and therefore spatial variability would not be indicative of precision and therefore not reported here. Good agreement (R 2 = 0.9885) was observed between the 2 methods and maximum absolute difference was measured at 5.8%