Assessment of MRF for Simultaneous T₁ and T₂ Quantification and Water-Fat Separation in the Liver at 0.55T

Abstract

Object:

The goal of this work is to assess the feasibility of performing MRF in the liver on a 0.55T scanner, and to examine the feasibility of water-fat separation using rosette MRF at 0.55T.

Materials and Methods:

Spiral and rosette MRF sequences were implemented on a commercial 0.55T scanner. The accuracy of both sequences in T₁ and T₂ quantification was validated in the ISMRM/NIST system phantom. The efficacy of rosette MRF in water-fat separation was evaluated in simulations and water/oil phantoms. Both spiral and rosette MRF were performed in the liver of healthy subjects.

Results:

In the ISMRM/NIST phantom, both spiral and rosette MRF achieved good agreement with reference values in T₁ and T₂ measurements. In addition, rosette MRF enables water-fat separation and can generate water- and fat- specific T₁ maps, T₂ maps, and proton density images from the same dataset for a spatial resolution of 1.56×1.56×5mm³ within the acquisition time of 15s.

Conclusion:

It is feasible to measure T₁ and T₂ simultaneously in the liver using MRF on a 0.55T system with lower performance gradients compared to state-of-the-art 1.5T and 3T systems within an acquisition time of 15s. In addition, rosette MRF enables water-fat separation along with T₁ and T₂ quantification with no time penalty.

Introduction

MR Fingerprinting (MRF) is an efficient multi-parametric mapping method [1]. MRF employs a flexible sequence structure with variable acquisition parameters, and retrieves tissue properties by matching the acquired signal timecourse to a predefined dictionary which describes a large set of possible signal evolutions based on Bloch equations. MRF has been shown to enable accurate quantification of tissue properties such as relaxation times in a variety of organs including brain [1, 2], heart [3, 4], abdomen [5–8], breast [9], and prostate [10, 11].

While most MRI scanners used in the clinic are 1.5T and 3T, low field systems (<1T) have recently been explored for conventional diagnostic applications. Low-field MRI systems may offer efficient imaging due to shorter T₁ times, longer T₂/T₂* times, potentially improved B₀ and B₁ field homogeneity, and lower cost compared to clinical 1.5T and 3T scanners [12]. However, the lower SNR inherent at lower field and caused by limited coil channels on lower cost systems compared to state-of-the-art 1.5T and 3T systems may pose challenges for clinical MRI scans. Multiple averages may be required to maintain SNR, resulting in long acquisition times. Multi-parametric mapping techniques such as MRF which enable maps or images to be generated even in the absence of high signal levels may serve as an efficient imaging method on low cost and/or low field systems. Furthermore, the information about several tissue properties, including relaxation times may assist in disease diagnosis, and could even be used to generate contrast weighted images retrospectively, reducing scan time.

In order to transfer MRF techniques to low field systems, alterations to the original acquisition may be required due to the differences between high field and low field systems. For example, T₁ and T₂ values vary with B₀ field strength. Tailoring the MRF pulse sequence accordingly for specific tissue types at a specific field strength may be beneficial to compensate for SNR loss. The effects of confounding factors such as off-resonance and B₁ may be reduced at low field due to potentially better field homogeneity, which might affect the choice of data sampling trajectory shape and duration, flip angles, and the parameters modeled in a dictionary. Such investigations have been performed using 3D MRF sequences on a 0.55T system [13] and a 0.35T system [14] for T₁ and T₂ quantification in the brain. Recently, an MRF-based method called OPTIMUM also achieved T₁, T₂, T₂*, B₀ and B₁⁺ quantification in musculoskeletal applications at 0.1T [15]. However, assessment of MRF on low field systems in the abdomen is limited.

Abdominal imaging may be challenging at low fields (<1T). For example, the robust fat suppression required by abdominal imaging may be difficult at lower field strength. For instance, when using fat suppression techniques based on different resonance frequencies of fat and water, the much smaller chemical shift of fat at lower fields compared to 1.5T and 3T requires a narrow spectral profile for spectrally selective pulses to suppress fat while leaving water signals untouched. Additionally, field inhomogeneity and susceptibility effects in the large imaging volume required by abdominal imaging also lead to spectral line broadening for both water and fat, making robustness of the spectral selective pulses challenging. For another category of fat suppression techniques which use inversion pulses to null fat, shorter T₁ of fat at low field may limit the readout duration. Alternatively, water-fat separation techniques such as the Dixon method can be used. However, acquisition times may be longer on low field systems due to low SNR and the requirement of long echo times. It has been shown that water-fat separation can be embedded in the MRF framework using rosette trajectories in cardiac applications [16] taking advantage of the off-resonance signal suppression property of rosette trajectories [17]. Rosette MRF can be used to generate water T₁ and T₂ maps along with a proton density image with fat suppression, and vice versa, from the same dataset.

The goal of this work is to 1) assess the feasibility of performing MRF in the liver on a commercial 0.55T scanner; 2) compare T₁ and T₂ measurements made with MRF in the liver at 0.55T to values previously reported using clinically standard techniques; and 3) examine the feasibility of water-fat separation using rosette MRF at low field.

Materials and Methods

Trajectory and Sequence Design

Two MRF sequences using spiral and rosette trajectories, respectively, were implemented on a commercial 0.55T scanner (MAGNETOM Free.Max, Siemens Healthineers, Erlangen, Germany). The lower maximal gradient amplitude and slew rate of this scanner (15mT/m and 40mT/m/ms) were accommodated when designing the spiral and rosette trajectories. The variable density spiral trajectory (Figure 1a,b) was designed to fully sample the center 50% of k-space with 12 arms and the edge of k-space with 24 arms for a FOV 300×300mm² and matrix size 192×192. Each arm has a readout duration of 11.9ms. The rosette trajectory (Figure 1c,d) was designed for the same FOV and matrix size, as well as fat signal suppression at 0.55T (−80Hz). One arm of the trajectory consists of 5 lobes with a readout duration of 9.97ms. A total of 179 arms evenly distributed over 360 degrees were used to guarantee that the Nyquist criterion was satisfied throughout k-space.

Fig. 1.

One arm of the measured spiral (a,b) and rosette (c,d) trajectories used in the MRF sequences. The six zero-crossings of the 5-lobe rosette trajectory are labeled using black circles in (d).

For both spiral and rosette MRF, 1000 time points were acquired using a FISP readout following an inversion pulse with inversion time of 21ms [2]. The flip angles were sinusoidally ramped up to 70 degrees (Figure 2). The TR/TE were set to 15ms/1.6ms for spiral MRF and 13ms/1.6ms for rosette MRF. The TE for rosette MRF was defined as the time of the first zero-crossing of the rosette trajectory; the following five zero-crossings occurred at 3.69 ms, 5.62 ms, 7.55 ms, 9.48 ms, and 11.57 ms. The trajectory was rotated by the nearest arm to the golden angle rotation among the 24 and 179 arms for spiral and rosette, respectively, to mimic a golden angle acquisition. The total acquisition time was 15s/13s during a breath-hold for spiral/rosette MRF. In-plane resolution was 1.56×1.56mm², and slice thickness was 5mm for all phantom and in vivo experiments.

Fig. 2.

Flip angles used in this study follow a sinusoidal pattern up to the maximum of 70 degrees.

Reconstruction

The MRF dictionary incorporating slice profile imperfection correction and inversion pulse efficiency correction was generated using Bloch equation simulations [18]. The dictionary resolution, denoted by min:step:max, was [10:5:500, 510:10:2000, 2050:50:3000] ms for T₁ in the liver; [10:10:90, 100:20:2000, 2050:50:3000] ms for T₁ in phantoms; [4:0.5:80, 82:2:100, 105:5:125, 130:10:300, 350:50:500] ms for T₂ in the liver; [2:2:8, 10:5:100, 110:10:300, 320:20:1500] ms for T₂ in phantoms. The dictionary was compressed along the time dimension using singular value decomposition (SVD); a threshold was set to preserve 99.9% of the signal energy, resulting in the first four singular values retained [19].

The MRF k-space data were projected to the same subspace derived from SVD of the dictionary, resulting in four coefficient images corresponding to the largest four singular values. Images were generated from the k-space data using the NUFFT [20]. Both spiral and rosette trajectories were measured using the method described in [21] and the measured trajectories were used in the gridding process to mitigate the effects of eddy currents. While aliasing artifacts are already greatly reduced in the four coefficient images compared to the time series images resulting from each single TR, a low rank reconstruction was performed before pattern matching to further reduce aliasing artifacts and improve SNR in the coefficient images [22–25]. The low rank reconstruction was solved iteratively as a constrained minimization problem described in the following equation:

$${\min }_x{‖y-Fx‖}_2^2+{\lambda }_1{R}_1\left(x\right)+{\lambda }_2{R}_2\left(x\right)$$ [1]

where y is the acquired MRF k-space data; F is the operator including sampling trajectory, NUFFT, coil sensitivity maps, and projection to the subspace derived from SVD of the dictionary; x is the coefficient images. $l_1$-TV and locally low rank regularizations in the spatial dimensions were denoted by $R_1$ and $R_2$ in the equation, respectively. In this study, in order to balance data consistency and noise suppression, ${\lambda }_1$ and ${\lambda }_2$ were chosen to be 0.05 and 0.002 for spiral data and 0.08 and 0.008 for rosette data after evaluating a few in vivo datasets reconstructed with different values. Pattern matching was performed between the coefficient images after low rank reconstruction and the compressed dictionary to generate the final T₁ and T₂ maps and proton density image.

For rosette MRF data, fat images were also generated by demodulating the acquired data at the fat frequencies using a 6-peak fat model [26, 27] and then reapplying the low rank reconstruction process as described above. Note that a different fat spectrum calibrated for peanut oil [26] was used for the phantom data in this study. Additionally, B₀ correction was performed on both water and fat coefficient images by demodulating the k-space data at a series of frequencies and combining pixels demodulated at the true resonance frequency according to a self-derived B₀ map as described in [16]. Low rank reconstruction (described above) was performed at each of the demodulating frequency during the B₀ correction process. In the current study, the range of demodulating frequencies was set from −40Hz to 40Hz with a step size of 5Hz, which was sufficient for all in vivo and phantom datasets according to the B₀ maps. The resultant B₀ corrected and low rank reconstructed coefficient images (one set for water and one set for fat) were matched to the compressed dictionary to generate the final T₁ and T₂ maps, and proton density images. Note that B₀ correction was not performed on the spiral MRF data due to the lack of a co-registered B₀ map.

Simulations

To evaluate the spectral response of the rosette trajectory, images of a numerical circular phantom were simulated at off-resonance frequencies from 0 to 500 Hz with a step size of 5 Hz. Signal intensities were measured in all images. The ratio of the signal intensity at 80Hz (the frequency of the most significant fat peak at 0.55T) and 0Hz was calculated as an indicator of the efficacy of fat suppression using this trajectory. Furthermore, fat signal suppression was evaluated using the 6-peak fat model [26]. Residual off-resonance signals at chemical shifts of [−3.80, −3.40, −2.60, −1.94, −0.39, 0.60] ppm were weighted by their corresponding amplitudes of [0.087 0.693 0.128 0.004 0.039 0.048] and then added together to calculate the final residual fat signal amplitude.

To evaluate the effects of flip angles on MRF signals, simulations were performed in a digital liver phantom using the rosette MRF sequence structure and acquisition parameters. The ground truth T₁ and T₂ values in the liver were set to 405 ms and 68 ms, respectively, to mimic the physiological values in the liver at 0.55T. The flip angle train as shown in Figure 2 was scaled to reach a maximal flip angle of 70, 50, and 30 degrees. Complex noise was added to the simulated k-space data. The standard deviation of the noise in all cases was set to 1.5% of the maximal k-space signal magnitude in the 70 degrees MRF acquisition. Low-rank reconstruction was used to generate the final T₁ and T₂ maps. SNR of the resulting T₁ and T₂ maps was calculated as the averaged signal intensity in a region-of-interest (ROI) in the liver divided by the standard deviation in an ROI in the background. The mean and standard deviation of T₁ and T₂ values in the ROI in the liver were also calculated and compared to ground truth.

Unlike spiral trajectories, the 5-lobe rosette trajectory used in this study has a rotational symmetry of 72 degrees (i.e. 360 degrees divided by 5). To investigate the effects of the rotation angle of the 5-lobe rosette trajectory between TRs on image quality, simulations were performed in the digital liver phantom described above using the rosette MRF sequence with different rotation schemes. The golden mean of 360 degrees (i.e. 360–360/1.618=137.5 degrees as used for in vivo and phantom scans in this study) was compared with the golden mean of 72 degrees (i.e. 72/1.618=44.5 degrees). Note that no noise was added to the simulated k-space data in this simulation in order to isolate the effects of undersampling artifacts and noise. T₁ and T₂ maps were generated by both direct pattern matching and iterative low-rank reconstruction. Root mean square error (RMSE) was calculated as averaged pixel-wise difference between the results and the ground truth divided by the ground truth.

Phantom Experiments

The accuracy of these low-field MRF methods for T₁ and T₂ quantification was validated in the ISMRM/NIST system phantom. Both the ISMRM/NIST phantom and the water/oil phantom (see below) were scanned in an axial orientation at 0.55T using a 12-channel head coil. Gold standard reference values were acquired using inversion recovery spin-echo and single-echo spin-echo methods, and MRF data were collected using both the spiral and rosette MRF approaches. ROIs in each vial in the T₂ layer of the phantom were drawn manually. The mean and standard deviation in T₁ and T₂ values within physiological range for each ROI were compared to reference values using a linear regression test.

The efficacy of rosette MRF in water-fat separation was demonstrated in a two-compartment water/oil phantom with one vial of peanut oil (Kraft Heinz, IL, US) and one vial of water doped with Gadolinium (MultiHance, Bracco Inc, NJ, US). Spiral MRF was also performed on this phantom for comparison. ROIs in each vial were drawn manually and the water- and oil-specific T₁ and T₂ values measured by spiral MRF and rosette MRF were calculated.

In vivo Experiments

Sixteen healthy subjects without history of hepatic disease were scanned after obtaining written informed consent in this IRB-approved study. One subject was found to have substantial visceral fat and excluded from the healthy subject cohort in the later analysis. A transverse slice in the liver was acquired with a 6-channel body array and a 15-channel spine array using the proposed spiral and rosette MRF sequences. Three ROIs in the liver excluding blood vessels were drawn manually, and the mean and standard deviation in T₁ and T₂ values were calculated. A student’s t-test was used to compare T₁ and T₂ measurements using rosette MRF and spiral MRF. Significant difference was considered with P<0.05.

Results

Simulation Data

The spectral response of the rosette trajectory obtained from simulation studies is shown in Figure 3a. The residual signal intensity at 80Hz (the frequency of the most significant fat peak at 0.55T) as compared to the on-resonance (0Hz) signal intensity is 6.2%. The corresponding images of the numerical phantom at 0Hz and 80Hz are shown in Figure 3b,c. When using the 6-peak fat model, residual fat signals from all six peaks are 18.0% as compared to the on-resonance signal intensity.

Fig. 3.

The spectral response of the 5-lobe rosette trajectory. Off-resonance signals at 80Hz are suppressed by 93.8% (a). Images of the numerical phantom at 0Hz (on-resonance) and at 80Hz (the frequency of the most significant fat peak at 0.55T) are shown in (b,c).

In the digital liver phantom, a comparison of the T₁ and T₂ maps generated using maximal flip angles of 70, 50, and 30 degrees and the ground truth are shown in Supplementary Figure 1. Supplementary Table 1 shows the T₁ and T₂ values in the liver, and SNR of the T₁ and T₂ maps for each flip angle train. A higher SNR was observed both visually and according to the SNR measurement with higher maximal flip angles. The smaller standard deviation of the T₁ and T₂ values in the liver also indicates a lower noise level with when the maximal flip angle is set to 70 degrees.

The T₁ and T₂ maps generated using different trajectory rotation angles compared with the ground truth maps are shown in Supplementary Figure 2. Using the golden mean of 72 degrees (i.e. 44.5 degrees) results in slightly higher RMSE compared to the approach used in this study (i.e. rotation angle of 137.5 degrees) without low rank reconstruction. However, low rank reconstruction effectively improves the image quality and reduces RMSE for both approaches, resulting in RMSE of 0.7~0.8% for T₁ map and ~0.5% for T₂ maps for both rotation schemes.

Phantom Data

In the ISMRM/NIST system phantom, T₁ and T₂ measurements using spiral and rosette MRF were in good agreement with the reference values (Figure 4). For T₁ measurements, the slope of the best-fit line was 1.006 for spiral MRF and 1.001 for rosette MRF with both R²>0.99. For T₂ measurements, slope of best-fit line was 0.91 for spiral MRF and 0.86 for rosette MRF with R²>0.99 for both.

Fig. 4.

T₁ and T₂ measurements in the T₂ layer of the ISMRM/NIST phantom using spiral MRF (a) and rosette MRF (b) at 0.55T have a good agreement with reference values acquired using inversion recovery spin-echo for T₁ and single-echo spin-echo for T₂.

In the water/oil phantom, T₁ maps, T₂ maps, and water and oil proton density images are shown in Figure 5. While the maps and image generated using spiral MRF exhibits blurring artifacts in the oil vial (Figure 5 top row), rosette MRF enables effective water-fat separation (Figure 5 middle and bottom rows). Note that noisy measurements in the oil compartment in rosette MRF water maps and vice versa (indicated by red arrows in Figure 5) are expected and indeed desired due to off-resonance signal suppression. Water- and oil- specific T₁ and T₂ values measured by spiral and rosette MRF are summarized in Table 1. Spiral and rosette measurements agree well for both water and oil; the oil T₁ and T₂ values are also comparable with in vivo fat tissue T₁ and T₂ values at 0.55T in the literature [12].

Fig. 5.

Results in the water/oil phantom. T₁ maps, T₂ maps and proton density (PD) images generated using spiral MRF (top row) and rosette MRF (middle & bottom rows). A cropped FOV of 100×100 mm² is displayed. Note that noisy measurements in the oil compartment in rosette MRF water maps and vice versa (indicated by red arrows) are expected due to off-resonance signal suppression.

Table 1.

Water and oil specific T₁ and T₂ measurements in the water/oil phantom at 0.55T.

Method	Water T1 (ms)	Water T2 (ms)	Oil T1 (ms)	Oil T2 (ms)
Spiral MRF	733.0 ± 24.6	76.2 ± 4.7	163.1 ± 12.8	105.0 ± 8.9
Rosette MRF	716.7 ± 30.2	75.2 ± 6.6	175.5 ± 20.1	107.6 ± 10.3

Healthy Subjects

Representative T₁ and T₂ maps, and proton density images acquired using spiral MRF and rosette MRF in a healthy subject are shown in Figure 6. A summary of the averaged T₁ and T₂ values in fifteen healthy subjects measured by spiral MRF and rosette MRF compared with literature values is shown in Table 2. T₁ values measured by spiral and rosette MRF are comparable, and both are 25~30ms higher than literature values measured by MOLLI. While rosette MRF shows a trend of higher T₂ values than spiral MRF measurements, no significant difference was observed between spiral MRF and rosette MRF measurements for either T₁ or T₂. Both T₂ measurements are lower than literature values measured using T₂prep-bSSFP. The mean and standard deviations of T₁ and T₂ measurements in each subject are shown in Figure 7. Averaged standard deviations of T₁ and T₂ in all subjects are lower in spiral MRF (33.9 ms and 6.9 ms) compared with rosette MRF (39.3 ms and 8.1 ms), indicating slightly higher noise level in the rosette maps.

Fig. 6.

Representative T₁ and T₂ maps, and proton density (PD) images in the liver in a healthy subject acquired using spiral MRF (top row) and rosette MRF (middle row for water & bottom row for fat) at 0.55T. In-plane resolution was 1.56×1.56mm²; slice thickness was 5mm.

Table 2.

Averaged T₁ and T₂ values in the liver of 15 healthy subjects at 0.55T measured using spiral and rosette MRF compared with literature values.

Method	T1 (ms)	T2 (ms)
Spiral MRF	359.9 ± 26.4	45.2 ± 4.8
Rosette MRF	367.7 ± 23.5	47.5 ± 4.0
Literature [8]	339	66

Fig. 7.

Individual T₁ and T₂ values in the liver of 15 healthy subjects acquired using spiral MRF and rosette MRF at 0.55T.

Figure 8 shows the 16th subject, who had a BMI of 29.2 and was found to have substantial visceral fat based on the MR images obtained in this study. While blurring artifacts were observed in the spiral maps and images due to the large amount of fat, rosette MRF was able to obtain water/fat maps and images without blurring. The T₁ and T₂ values measured using spiral MRF in this subject are 326.7 ± 49.3 ms and 42.7 ± 8.9 ms. The corresponding rosette measurements are 348.9 ± 53.4 ms and 46.6 ± 11.4 ms. Note that T₁ and T₂ values of this subject are excluded from Table 2 and Figure 7.

Fig. 8.

T₁ and T₂ maps, and proton density (PD) images in the liver in an obese subject acquired using spiral MRF (top row) and rosette MRF (middle & bottom rows) at 0.55T. Visceral fat causes blurring in spiral maps and images; while water maps and images with effective fat suppression (and vice versa) were achieved using rosette MRF.

Discussion

This study demonstrates the feasibility of MRF for simultaneous T₁ and T₂ quantification in the liver at 0.55T, despite the lower field strength and lower gradient performance. Both spiral and rosette MRF achieved good image quality in a single ~15s breath-hold using a low-rank reconstruction. Moreover, rosette MRF enables T₁ and T₂ maps, and images of separated water and fat components with no penalty in acquisition time. In the current study, higher T₁ and lower T₂ values measured by MRF were observed compared with previous reports in the literature, measured by MOLLI and T₂prep-bSSFP [12]. This trend is consistent with previous findings in cardiac MRF at 1.5T and 3T [16, 28], as well as MRF studies in the liver at 3T [5]. In this work, slice profile imperfection and inversion pulse efficiency were included in the dictionary, which was shown to increase the accuracy of MRF T₁ and T₂ measurements [18].

However, the confounding factors not accounted for in the dictionary such as magnetization transfer may still play a role in mismatches between measurements. Studies exploring the effects of a variety of confounding factors have been performed at 1.5T and 3T [18, 29, 30]. Their effects on the accuracy of T₁ and T₂ quantification at low field systems remain to be further investigated. One limitation of the current study is the lack of clinically standard T₁ and T₂ measurements in the liver for comparison, due to the lack of availability of these techniques on this specific 0.55T scanner. Therefore, even though the accuracy of MRF measurements in the NIST/ISMRM phantom was validated in this study, its accuracy in vivo remains to be investigated in further studies with a larger cohort of healthy subjects undergoing MRF measurements and conventional T₁ and T₂ mapping methods at 0.55T.

Compared with clinical 1.5T and 3T systems, the 0.55T scanner used in this study has limited gradient strength and slew rate, but these constraints can be compensated by the use of a much longer readout compared to higher fields. The readout duration of the spiral used here was 11.9ms at 0.55T, compared to 2.9ms deployed in the abdominal MRF study at 3T [5]. Higher flip angles were also used at 0.55T to compensate for SNR loss due to the lower B₀ strength (Supplementary Figure 1 & Supplementary Table 1). We were able to achieve good image quality using low rank reconstruction with an even higher spatial resolution compared to the study at 3T (1.6×1.6×5mm³ at 0.55T vs. 1.9×1.9×5mm³ at 3T). The finer spatial resolution would be helpful to reduce partial volume effects and thus potentially enable more accurate quantification of liver tissue properties. In the livers of healthy subjects, T₁ measured in the current study is ~50% shorter and T₂ is 48%~55% longer than those reported at 3T [5]. For abdominal scans, an advantage of low field systems is the large bore size (80cm in this work) which might be beneficial to image obese patients (Figure 8).

Compared with other research into low field water-fat separation and fat fraction quantification [31–34], this study is unique in that it takes advantage of the inherent water-fat separation property of the rosette trajectory. Unlike the commonly used Dixon and IDEAL methods which involve multi-echo acquisitions and signal model fitting for water-fat imaging [35–37], one “interleaf” of the rosette trajectory serves as multi-echo acquisition, and water and fat images can be generated in parallel simply by shifting the demodulation frequency of the k-space data rather than solving a non-linear fitting problem. The design criterion of the rosette trajectory was to make fat signals fall into the “null band” of the spectral response (Figure 3a), which was determined primarily by the readout duration. The duration between consecutive zero-crossings of the trajectory (i.e. echo spacing) was a result of a combination of factors such as gradient amplitude and slew rate, desired FOV and spatial resolution, etc. In order to compensate for SNR loss at low field, simple dictionary matching was replaced with low rank reconstruction for both spiral and rosette MRF. The reconstruction time for an in vivo spiral and rosette dataset is around 30 min and 4~5 hours, respectively, using MATLAB (Mathworks, MA, USA) on a workstation with 128GB RAM. The much longer reconstruction time for rosette MRF is due to B₀ correction on top of low rank reconstruction. Emerging deep learning techniques may assist with image denoising at low field and to accelerate data reconstruction [38, 39].

A 6-peak fat model was used to generate the fat T₁ and T₂ maps and proton density images in this study. When a 6-peak instead of a single-peak fat model was considered, the level of suppression of fat signals decreased because some fat peaks fall into the “passband” of the spectral response. Nevertheless, differences in the fat T₁ and T₂ maps and proton density images generated using the single-peak against the 6-peak fat model are almost negligible in both water/oil phantoms and in vivo (data not shown here), most likely due to the relatively small amplitudes of the other five fat peaks. However, for future studies focusing on proton density fat fraction (PDFF) quantification, a comparison between the single-peak and a 6-peak fat model could be performed.

For MRF studies using spiral trajectories, a common strategy is to rotate the trajectory by a golden angle (a golden mean of 360 degrees) between consecutive repetitions to achieve incoherent aliasing artifact distribution. Rosette trajectories might require a different strategy due to their rotational symmetry. Simulations in the current study show that using a rotation angle of 44.5 degrees does not outperform a rotation angle of 137.5 degrees between TRs for the 5-lobe rosette. Moreover, aliasing artifacts are greatly reduced in both rotation schemes using advanced reconstruction methods such as low-rank reconstruction. However, optimization of the rotation angle is worth investigating depending on the number of lobes and the shape of the rosette trajectory.

Finally, in addition to the T₁ and T₂ maps, a single MRF scan also has the potential to provide contrast weighted images retrospectively. Any desired T₁- and/or T₂- weighted image could be computed based on the T₁ and T₂ maps without the need to spend scan time acquiring them. Although the current study focused on T₁ and T₂ mapping, MRF framework could potentially enable quantification of other tissue properties simultaneously. For example, T₂* and fat fraction mapping could be of interest in hepatic disease diagnosis and the measurement of these properties has been shown to be feasible along with T₁ and T₂ mapping in the liver at 1.5T [6] as well as 0.55T [40]. The current study employed a 2D MRF sequence in the liver. However, a large volume coverage is often desired in abdominal imaging. One possible approach could be simultaneous multi-slice imaging which has been shown feasible by modulating the phase of the signals within the MRF framework in the brain [41] and heart [22]. Simultaneous multi-slice acquisition is also possible by taking advantage of the spectral filtering property of rosette trajectories [42]. A free-breathing 3D acquisition may also be possible using the rosette trajectory, which could greatly improve SNR due to a much larger imaging volume and improve patient comfort by removing the requirement of breath-holds.

Conclusions

This study shows that it is feasible to measure T₁ and T₂ simultaneously in the liver using MRF on a commercial 0.55T system with lower performance gradients within an acquisition time of 15s. In addition, water-fat separation can be achieved along with T₁ and T₂ quantification with no time penalty using rosette MRF.