Multi‐parametric liver tissue characterization using MR fingerprinting: Simultaneous T1, T2, T2*, and fat fraction mapping

Quantitative T1, T2, T2*, and fat fraction (FF) maps are promising imaging biomarkers for the assessment of liver disease, however these are usually acquired in sequential scans. Here we propose an extended MR fingerprinting (MRF) framework enabling simultaneous liver T1, T2, T2*, and FF mapping from a single ~14 s breath‐hold scan.


| INTRODUCTION
Non-alcoholic fatty liver disease (NAFLD) is highly prevalent worldwide (25%) and is associated with many hepatic and extra-hepatic diseases creating an increasingly large clinical and economic burden. 1 In the Western and industrialized countries, NAFLD is one of the main causes of cirrhosis and highly prevalent in patients with hepatocellular carcinoma the main causes of liver-related deaths. 2 Pathogenesis of NAFLD can be subdivided into four stages, which are progressively characterized by fat accumulation, inflammation (nonalcoholic steatohepatitis, or NASH), and potentially leading to irreversible fibrosis (cirrhosis), hepatocellular carcinoma, or other life-threatening complications. 2 Liver biopsy remains the current reference standard for diagnosing and staging NAFLD; however, they are invasive, costly, and potentially hazardous. Liver biopsies are also prone to sampling errors and suffer from inter-rater variability (with agreement of diagnostic category reported at 0.61 3 ).
Quantitative MRI parametric mapping is rapidly emerging as a non-invasive approach for the assessment of fatty liver disease. Quantitative MRI has been applied successfully to map spatially hepatic lipid content using proton density fat fraction (PDFF), 4,5 hepatic iron content using T * 2 6 and to detect fibrosis and inflammation using T 1 , T 2 7 and elastography. 8 Multi-parametric quantitative MRI has shown to provide valuable diagnostic and prognostic information by jointly monitoring the different pathophysiologies of the disease. 9,10 These multiple scans are usually performed sequentially during separate breath-holds, 9 thus leading to long scan times, patient fatigue, and potentially mis-registered parameter maps. Joint parameter mapping has been proposed to map liver T * 2 and PDFF simultaneously 11 and more recently to map liver T 1 , T 2 , and M 0 , 12 with both methods accounting for inter-parametric dependencies. The first method fits multiple echo images to a multi-peak water-fat signal model with T * 2 decay 13,14 while the latter uses MR fingerprinting (MRF) 15 to generate multiple parametric maps from a highly undersampled acquisition with dynamically varying contrasts. Recent works combining water-fat imaging and MRF have been proposed to map water-specific T 1 and T 2 and fat fraction (FF) 16,17 simultaneously to further reduce inter-parametric biases and overall scan time.
Here, we propose to jointly map T 1 , T 2 , T * 2 , and FF for comprehensive liver tissue characterization. This is achieved by extending our previous work on 3-echo Dixon cardiac MRF 17 to a 9-echo gradient rewound echo (GRE) acquisition and graphcut method 18 for estimation of B 0 and T * 2 and water-fat separation. To the best of our knowledge, this is the first time that liver T 1 , T 2 , T * 2 , and FF are simultaneously quantified in a single acquisition. The proposed framework was evaluated in phantoms against spin echo T 1 and T 2 and 12-echo GRE (PDFF and T * 2 ) reference measurements, and in 12 subjects against MOLLI, T2-GRASE, and 12-echo GRE. Preliminary clinical feasibility is shown in four patients.

| METHODS
The proposed framework combines (1) a nine-echo GRE acquisition; (2) a B 0 and B 1 insensitive acquisition scheme using fixed repetition time (TR), gradient spoiling, low flip angles (FA), and magnetization preparations; (3) an undersampled reconstruction with temporal compression and patch-based low-rank tensor regularization; (4) a graphcut based method for estimation of B 0 , T * 2 and water-FFs; (5) a dot-product matching step; and (6) an FF estimation step from the relative proton density (M 0 ) images. Details of the framework are described below.

| Acquisition
The proposed liver MRF acquisition (Figure 1) consists of a nine-echo, golden angle radial (~111°) GRE acquisition with bipolar readouts and varying inversion recovery (IR) and T 2 preparation (T2prep) pulses. 17 The acquisition scheme includes T2 preps with four adiabatic refocusing pulses 19 and varying durations, noted as T2prepX, and hyperbolic hypersecant IR pulses with varying inversion delays, noted as TIY, where X and Y are durations in ms. A total of 12 magnetization preparations followed by data acquisition are applied during a single breath-hold scan of 13.9 s with the following pattern: TI12, no preparation (noPrep), T2prep40, T2prep80, T2prep160, TI300, noPrep, T2prep40, T2prep80, T2prep160, TI12, noPrep. The data acquisition block consists of varying low FAs (9 linear ramp-up radiofrequency [RF] pulses from 5° to 15° followed by 26 fixed 15° RF pulses 20 ), 35 TRs, bandwidth 746 Hz/pixel, nine echoes per TR, TR/echo time 1 [TE1]/ΔTE = 20/1.5/2 ms leading to 700 ms data acquisition blocks. Acquisition blocks are spaced regularly every 1.2 s allowing for recovery (varying between ~200-500 ms) before the next magnetization preparation module. A fixed TR, low FAs, and 4π gradient spoiling along slice selection were used to reduce the sensitivity to B 0 and B 1 inhomogeneities. 20

| Image reconstruction
MRF time-series reconstruction was performed using a multi-contrast patch-based high-order low-rank reconstruction (HD-PROST) 23  Given a water (W ′ ) and a set of fat (F ′ k ) compartments timeseries, 14,26,27 the reconstructed singular images at echo i, can be written as: Δf l t i are the water and fat (or combined fat compartments) singular images, Δf l is the known difference in precession frequency between water and fat compartment l, Δf B0 is the precession frequency difference induced by B 0 field inhomogeneities and t i is the echo time i. A graphcut scheme 18 is used to solve for B 0 , T * 2 and water-fat separation using a pre-defined six-peak fat model. 28 First singular images of all echo times are used for B 0 and T * 2 estimation. The resulting maps are subsequently used to separate the other singular images by pseudo inverse 29 into water and fat. This model ignores the different T 1 and T 2 values 28 of the fat peaks which can lead to varying signal peak weights during the MRF acquisition. The impact of this simplified model was investigated in simulations.

| T 1 , T 2 , and FF maps
The water and fat singular images are then matched (using dot-product) to a previously generated MRF dictionary (with fixed TE = 0 + ms) to obtain the water-and fat-specific T 1 , T 2 , and relative M 0 maps. The dictionary was generated using the extended phase graph formalism, 30 including slice profile 31 (1) The proposed nine-echo liver MRF acquisition consists of 12 acquisition modules (700 ms) (5 shown here) with different IR and T 2 preparation pulses (and recovery times ~200-500 ms) performed in a single ~14 s breath-hold scan. (B) Images are reconstructed using dictionary-based temporal compression and low-rank patch-based regularization (HD-PROST). The signal from the nine echoes is separated into water and fat components. (C) B 0 and T * 2 maps are estimated during the separation of the signals. Water-and fat-specific T 1 , T 2 and M 0 maps are obtained through dot product matching to a previously generated MRF dictionary, whereas FF is estimated from the water and fat M 0 maps (51 points along the slice profile) and inversion efficiency 20 corrections. The dictionary contained signal evolutions corresponding to combinations of T 1 and T 2 of interest (ie, [50:10:1400, 1430:30:1600, 1700:100:2200, 2400:200:3000] ms for T 1 and [5:2:80, 85:5:150, 160:10:300, 330:30:600] ms for T 2 as well as the standardized T 1 /T 2 phantom 32 reference values. The FF map is estimated from the water and fat M 0 and phase images (for noise bias correction 17,33 ).

| Experiments
Experiments were performed on phantoms and 2 cohorts of subjects. Cohort 1 (12 subjects, 7 females; age: 31 ± 4 years; body mass index [BMI]: 23.9 ± 3.5 kg/m 2 ) underwent the proposed liver MRF and conventional techniques. Cohort 2 (four subjects, one female; age: 56 ± 13 years; BMI: 27.9 ± 4.0 kg/m 2 ) underwent only the proposed liver MRF during a clinically referred scan. Cohort 2 had large BMI > 25 kg/m 2 or previously diagnosed liver iron overload. All experiments were approved by the Institutional Review Board and written informed consent was given by all participants before scanning. Acquisitions were performed on a 1.5T Ingenia MR scanner (Philips Healthcare, The Netherlands).
Preliminary experiments investigated the number of echoes necessary for T * 2 mapping in phantom (Supporting Information Text S1, which is available online) and the performance of the framework in numerical simulations (Supporting Information Text S2 and Figure S1).

| Phantom study
Acquisitions were performed on a standardized T 1 /T 2 phantom (T1MES) with 0% fat 32 and on a water-fat phantom built in-house. The standardized T 1 /T 2 phantom was used to validate the water T 1 and T 2 measurements against T 1 inversion recovery spin echo (IRSE) and T 2 multi-echo spin echo (MESE). The reference T 1 and T 2 methods do not consider fat suppression/separation thus only the phantom with 0% fat was used to validate the T 1 and T 2 measurements avoiding biases due to incomplete fat suppression. FF and T * 2 measurements were performed in the standardized phantom and water-fat phantom and validated against a reference 12-echo GRE. The reference PDFF and T * 2 maps were obtained using the same graph cut method, 18 fat model, and noise bias correction 33 as described for the proposed nine-echo liver MRF. Acquisition and mapping parameters for all reference sequences are included in Supporting Information Table S1.
Scan parameters for the proposed liver MRF were described in the Acquisition section, remaining parameters were: field of view (FOV) = 496 × 496 mm 2 , 2 × 2 mm 2 resolution, 8 mm slice thickness.

| In vivo study
The proposed liver MRF T 1 , T 2 , T * 2 , and FF maps were validated against reference T 1 MOLLI (5(3)3), T2-GRASE, and 12-echo GRE (T * 2 and PDFF), respectively, in cohort 1. Acquisition parameters for all conventional sequences are included in Supporting Information Table S1. All acquisitions were performed in transversal orientation under breath-hold at end-expiration.
The same liver MRF acquisition was performed on cohort 2 to show preliminary feasibility of the approach in a clinical setting.

| Analysis
Regions of interest (ROIs) were manually drawn in each vial of the phantoms. Coefficients of determination, lines of best fit and biases are reported for each parameter map in comparison to their corresponding reference measurements.
For each subject, CX.Y (cohort X, subject number Y), ROIs were manually drawn in the liver (in four different areas of the liver avoiding blood vessels, the median value is reported), posterior muscle, subcutaneous fat, and the spleen. Mean measurements and range in 11 subjects with no history of liver disease (C1.1-10) or benign hemangioma (C1.11) are reported for all parameters for the proposed liver MRF and the corresponding conventional maps. C1.12 has been previously diagnosed with mild liver steatosis. Mean values, range, mean bias, 95% (±1.96 SD) confidence intervals (CI), and coefficients of determination are used to compare the measurement methods for cohort 1. A paired t-test was performed to test for statistically significant differences (P < .05) between the proposed liver MRF and conventional measurements.

| Preliminary studies
T * 2 maps of the preliminary phantom acquisition (standardized T 1 /T 2 and water/fat phantoms) obtained using the first 3, 6, 9, or 12 echoes for map estimation are shown in Supporting Information Figure S2A. Bland Altmann plots (Supporting Information Figure S2B) and maps show large bias of T * 2 estimation when using only the first 3 echoes, and small bias but noisy measurements when using 6 echoes. Maps obtained using the first 9 echoes compare qualitatively and quantitatively well with the ones obtained using all 12 echoes, albeit enabling shorter TR and thus scan time. The T * 2 map obtained using the first 9 echoes of the 12-echo MRF acquisition presented a mean bias of 1.4 ms when compared to the reference T * 2 map obtained from a conventional 12-echo GRE scan.
Numerical simulations of the proposed framework led to accurate (<1%) liver T * 2 and B 0 estimation and ensuing water T 1 , water T 2 , and FF estimation despite the simplified model used for water-fat separation (Supporting Information Figure  S3), although overestimation of subcutaneous fat T * 2 was observed. Simulated errors in the estimation of B 0 before water-fat separation caused significant errors in FF maps (>9%) and low errors in water T 1 or T 2 maps (<20 ms and <1 ms respectively) (Supporting Information Figures S4 and S5). Errors in T * 2 did not show an effect in the subsequent T 1 , T 2 , and FF estimation.

| Phantom study
Water T 1 , water T 2 , FF, and T * 2 maps for the proposed MRF approach (Supporting Information Figure S6) are quantitatively compared to T 1 IRSE, T 2 MESE, and T * 2 and FF (12-echo GRE) reference maps (Figure 2A). Correlation plots with lines of best fit show high coefficients of determination for water T 1 and water T 2 (standardized phantom only, 0% fat) (r 2 > 0.99) and for FF and T * 2 (standardized and water-fat phantoms) (r 2 > 0.97). Biases were measured at −15 ms, −4.7 ms, 1.9 ms, and −0.5% for T 1 , T 2 , T * 2 , and FF respectively. The bias for short T 2 s (0.73 ms) was smaller than for T 2 s outside the range of interest (T 2 > 80 ms).

| In vivo study
Water T 1 , water T 2 , FF, and T * 2 ROI measurements for the proposed liver MRF in subjects C1.1-12 are compared to conventional techniques ( Figure 2B) showing high coefficients of determination (r 2 > 0.93) for all parameters. Water T 1 and T 2 measurements were not performed in the subcutaneous fat ROI due to its low water content.
Liver F I G U R E 2 (A) Phantom correlation plots comparing water T 1 and water T 2 (standardized T 1 /T 2 phantom, 0% fat) and FF and T * 2 (standardized T 1 /T 2 and water-fat phantoms) measurements obtained from the proposed 9-echo liver MRF and from reference IRSE (T 1 ), MESE (T 2 ), and 12-echo GRE (T * 2 /FF) scans. (B) In vivo correlation plots comparing the proposed 9-echo liver MRF approach to conventional MOLLI (T 1 ), T2GRASE (T 2 ), and 12-echo GRE (T * 2 /FF) scans. Liver (median over four ROIs), anterior muscle, spleen, and subcutaneous fat (for T * 2 and FF estimation only due to its low water content) measurements were performed in cohort 1 (12 subjects) and subcutaneous fat are reported in Supporting Information Table S2 in comparison to the conventional methods and literature values [34][35][36] when available. Fat-specific T 1 and T 2 are reported for the subcutaneous fat ROI. Boxplots showing T 1 , T 2 , FF, and T * 2 mean, median, interquartile, SD and outliers obtained with the proposed liver MRF and conventional sequences are included in Figure 3 for subjects C1.1-12. Biases and CI (bias [CI]) observed with the proposed liver MRF in comparison to conventional methods for all ROIs combined (excluding subcutaneous fat for water T 1 and T 2 measurements due to its low water content) were 110 ms [23; 200]  , and FF respectively) with statistically significant differences for T 1 , T 2 , and T * 2 . Water T 1 , water T 2 , FF, T * 2 , and B 0 maps for the proposed liver MRF are shown for two subjects in comparison to the corresponding conventional mapping techniques (Figure 4). An elevated liver FF was measured in subject C1.12 at 10.3% with the proposed approach and 9.2% with conventional PDFF ( Figure 4A). Subject C1.11, with a previously diagnosed benign hemangioma (ie, abnormal mass of small blood vessels), is shown in Figure 4B. Water T 1 , water T 2 , T * 2 , and FF in the hemangioma were measured at 1603 ms, 112 ms, 80 ms, and 1.2% with the proposed liver MRF and 1469 ms, 163 ms, 71 ms, and −0.2% with conventional methods respectively.

| DISCUSSION
A nine-echo MRF approach is proposed for multi-parametric and simultaneous T 1 , T 2 , T * 2 , and FF liver tissue characterization in a single 14 s acquisition. The proposed approach relies on the reconstruction of a transient signal sampled for different echo times. The echo sampling allows for T * 2 and B 0 estimation and separation of the transient signal into a water and fat fingerprints. The fingerprints can then be used for MRF dictionary matching to obtain water and fat T 1 , T 2 , and relative M 0 maps, whereas FF can be estimated from the water and fat M 0 maps. Compared to previous water-fat MRF F I G U R E 3 Boxplots showing T 1 , T 2 , T * 2 and FF measurements mean (+), median (__), interquartile range (IQR) (box), Tukey whiskers and remaining outliers (•) obtained in cohort 1 (12 subjects, C1.1-12) for liver, muscle, spleen, and subcutaneous fat for proposed 9-echo liver MRF and conventional (Conv) methods (ie, MOLLI, T2-GRASE, and 12-echo GRE T * 2 and PDFF). Statistically significant differences (paired t-test) in mean measurements are indicated with * (P < .05) and are shown for each body organ. Please note that water T 1 and water T 2 are reported for the liver, muscle and spleen ROIs with the proposed MRF approach, whereas fat T 1 and fat T 2 are reported for subcutaneous fat. Numerical mean and full range values for C1.1-11 (with no history of liver disease) are reported in Supporting Information Table S2 | 2631 JAUBERT ET Al. works using multi-peak fat models, 16,17,37 in this work T * 2 decay is included in the signal model (Equation 1) to improve water and fat separation and additionally map T * 2 for liver iron content assessment. Dictionary-based methods 37,38 could be investigated for single step FF, water and fat T 1 and T 2 , T * 2 , and B 0 estimation; however, this may lead to challenging dictionary sizes while relying on single voxel information. Chemical shift based approaches 18,39 usually enforce B 0 field smoothness for robust estimation and water-fat separation. Previously proposed water-fat MRF works have used these approaches 16,40,41 but mapped less parameters and required an additional (separately acquired) B 1 map.
Phantom experiments show high coefficients of determination between the proposed approach and reference measurements for the T 1 , T 2 , T * 2 , and FF ranges of interest. Good agreement of the B 0 maps ( Figure 4) and low FF errors compared to those observed in simulations suggest accurate B 0 estimation. Sequence modifications might be necessary if the tissue of interest has long T 2 and T * 2 . Biases with respect to conventional and literature values were observed in vivo. These are expected for a few reasons: (1) Magnetization transfer effects in biological tissues and flow are expected to bias MRF 42-44 as well as conventional 45 measurements.
(2) In vivo conventional mapping present their own biases and are suboptimal references (eg, MOLLI has a tendency to underestimate T 1 46,47 and T2-GRASE to overestimate T 2 when compared to T2-prep bSSFP 48 ). Moreover, previously proposed MRF approaches 17,20,49 have shown overestimation of T 1 when compared to MOLLI and underestimation of T 2 compared to conventional scans in vivo. (3) Acquisitions were performed sequentially during separate breath-holds leading to potentially mis-registered MRF and conventional measurements. (4) Fat model simplifications led to overestimation of T * 2 in subcutaneous fat in simulations and in vivo. Despite these biases, good correlations were obtained in vivo between the proposed approach and conventional techniques. The proposed approach requires shorter scan time and fewer breath-holds while keeping similar resolutions as those proposed in recent multi-parametric 50 and NAFLD clinical studies. [51][52][53] Additionally, it provides inherently F I G U R E 4 Proposed nine-echo liver MRF water T 1 , water T 2 , T * 2 , FF, and B 0 compared to T 1 (MOLLI), T 2 (T 2 GRASE) , T * 2 , PDFF, and B 0 (12-echo GRE) maps acquired in three separate breath-holds for two subjects. (A) Subject C1.12 presented slightly elevated hepatic fat content, measured at 10.3% with the proposed liver MRF and 9.2% with the conventional method. (B) Subject C1.11 presented a previously diagnosed hemangioma, which is visualized in the parametric maps (white arrow on T 1 maps). Water T 1 , water T 2 , T * 2 , and FF in the hemangioma were measured at 1603 ms, 112 ms, 80 ms, and 1.2% with the proposed liver MRF and 1469 ms, 163 ms, 71 ms, and −0.2% with the corresponding conventional methods co-registered maps ensuring mapping of the same slice of the liver for all parameters and enabling pixel-wise multi-parametric measurements.
Water-fat separation and T * 2 corrections do not correct for the effect of iron content on T 1 and T 2 measurements directly as seen in subject C2.4 ( Figure 5); however, additional corrections could be incorporated to better correlate results with biopsy fibrosis scores in the presence of iron overload. 54 This would require simulating multiple compartments and magnetization transfer effects 44 while making strong model assumptions. 54 Further investigation of the precision (reproducibility) and accuracy of this framework in clinical settings is still needed.

| CONCLUSION
A multi-echo MRF framework is proposed for fast and simultaneous quantitative multi-parametric liver tissue characterization. Co-registered parametric maps (water T 1 , water T 2 , T * 2 , and FF) are acquired in a single breath-hold (13.9 s). The proposed approach was validated in phantoms showing good correlation with reference measurements. The feasibility of the proposed approach was evaluated in vivo in 16 subjects. Future investigation in patients with liver disease is now warranted.

ACKNOWLEDGMENTS
This work was supported by the following grants: (1) EPSRC EP/P032311/1, EP/P001009/1 and EP/P007619/1, (2)  GG has been supported by a research fellowship from the European Association of Cardiovascular Imaging. We acknowledge the use of the Fat-Water Toolbox (http://ismrm. org/works hops/FatWa ter12 /data.htm) for some of the results shown in this article.

F I G U R E 5
Proposed nine-echo liver MRF water T 1 , water T 2 , T * 2 , FF and B 0 maps acquired in a single breath-hold in three patients with large BMI and one with iron overload. An elevated hepatic fat content of 15.25%, 12.45%, and 18% was measured for subjects C2.2, C2.3, and C2.4 respectively. Subject C2.4 presented abnormally low water T 1 , water T 2 , and T * 2 consistent with previously diagnosed elevated hepatic iron content