Spiral Blurring Correction with Water-Fat Separation for Magnetic Resonance Fingerprinting in the Breast

PURPOSE: Magnetic Resonance Fingerprinting (MRF) with spiral readout enables rapid quantification of tissue relaxation times. However, it is prone to blurring due to off-resonance effects. Hence, fat blurring into adjacent regions might prevent identification of small tumors by their quantitative T1 and T2 values. This study aims to correct for the blurring artifacts, thereby enabling fast quantitative mapping in the female breast. METHODS: The impact of fat blurring on spiral MRF results was first assessed by simulations. Then, MRF was combined with 3-point Dixon water-fat separation and spiral blurring correction based on conjugate phase reconstruction. The approach was assessed in phantom experiments and compared to Cartesian reference measurements, namely inversion recovery (IR), multi-echo spin echo (MESE) and Cartesian MRF, by normalized root mean square error (NRMSE) and standard deviation (STD) calculations. Feasibility is further demonstrated in-vivo for quantitative breast measurements of 6 healthy female volunteers, age range 24-31 years. RESULTS: In the phantom experiment, the blurring correction reduced the NRMSE per phantom vial on average from 16% to 8% for T1 and from 18% to 11% for T2 when comparing spiral MRF to IR/MESE sequences. When comparing to Cartesian MRF, the NRMSE reduced from 15% to 8% for T1 and from 12% to 7% for T2. Furthermore, STDs decreased. In-vivo, the blurring correction removed fat bias on T1/T2 from a rim of about 7-8 mm width adjacent to fatty structures. CONCLUSION: The blurring correction for spiral MRF yields improved quantitative maps in the presence of water and fat.


Introduction
Quantitative Magnetic Resonance Imaging (qMRI) offers an vendor independent imaging contrast, which promises the identification and classification of lesions based on their intrinsic tissue properties 1,2 .
Moreover, quantitative image data represents an optimal input for post processing, such as machine learning methods 3 . The tissue relaxation times T1 and T2 are intrinsic tissue parameters that underlie the contrast formation of the clinically used qualitative, i.e., contrast weighted, MR images. However, the acquisition of quantitative parameter maps has not yet widely found its way into clinical practice, mainly due to long scan times.
In breast imaging, previous reports suggest that qMRI can help to determine the response to neoadjuvant chemotherapy 4-6 (namely, decreased T2 values are reported for responders) as well as to distinguish invasive ductal carcinoma from healthy tissue 7 or between different types of lesions 8,9 . Moreover, if the observed differences prove to be significant, a fast quantitative breast imaging protocol may be of interest in contrastagent free breast screening.
Magnetic Resonance Fingerprinting (MRF) is a fast sequence that measures several quantitative markers at a time 10,11 from an image series with varying acquisition parameters such as flip angles, repetition times and RF phases. The measured signal evolution in every voxel is compared to a dictionary of simulated signal evolutions, which permits to select the best-matching quantitative parameters. MRF allows for highly efficient parameter estimation, as the MRF signal is acquired during transient state while making use of high undersampling during readout in each TR interval. Up to a certain undersampling factors / for long enough MRF sequences, correct identification of the underlying tissue properties is possible as long as the resulting undersampling artifacts distribute in a noise-like manner around the true signal evolution [11][12][13] . Spiral readout is often preferred for MRF because of its sampling speed and large k-space coverage 14 .
However, spiral sampling results in blurred images for off-resonant spins. This effect becomes especially important if the field of view (FOV) does not only contain aqueous tissues, but also fat, of which the main spectral peak presents an average chemical shift of about -3.5 ppm with respect to the resonance frequency of water 15 . In consequence, fat signal that has blurred into adjacent voxels obscure the contours of tissues as well as the presence of adjacent structures of interest, such as small tumors. A conjugate phase reconstruction (CPR) allows correction for off-resonance induced blurring artefacts in spiral images 16 . Yet, CPR requires knowledge about the spatial off-resonance distribution. A different approach that circumvents fat blurring is suppression of the fat signal, e.g. by fat saturation techniques 17 . Fat-saturated MRF was recently presented in the abdomen as well as in female breast 7,18 . However, fat saturation techniques may not always yield complete suppression of the fat signal over the entire FOV, especially at higher field strengths and/or in breast MRI protocols that involve larger FOVs to cover both breasts such as the axial 4 bilateral imaging protocols used for breast cancer screening. In the female breast anatomy, the fat signal may provide diagnostic information as well. For instance, keeping the fat signal in T2-weighted images (and rather not suppressing it) permitted the distinction of benign from malignant tumors in such lesions that showed enhancement during dynamic contrast enhanced MRI 19 .
In this work, we extend MRF by a Dixon water-fat separation approach 20 , which allows to correct for the fat blurring. The presented method does not require the separate acquisition of an off-resonance map. It is inspired by the approach of Boernert et al. 21 , who combined a 3-point Dixon method with CPR on fully sampled spiral images. CPR can equally deblur undersampled MRF data 22,23 . In both cases, the authors characterized the off-resonance map in a separate scan before computing the CPR of the individual, undersampled images. Preliminary results on fat blurring-corrected MRF with water-fat separation were recently presented [24][25] . Very recently, alternative MRF methods estimating water T1 and T2/water T1 and fat T1 as well as the fat signal fraction were proposed 26,27 . However, the breast anatomy has not yet been addressed.
We thus propose 2D blurring-corrected MRF with Dixon water-fat separation in the female breast, where both aqueous fibroglandular tissue as well as fatty tissue are present. Thereby, quantitative parameter maps of the relaxation times in the breast as well as the off-resonance map are obtained.

5
Methods CPR for spiral off-resonance blurring correction Spiral MRI is prone to off-resonance artifacts. Deviations ∆ from the water proton resonance frequency may result from the spatial inhomogeneity of the main magnetic field, i.e., due to local differences in magnetic susceptibility, or from the chemical shift of a tissue, as in the case of fat. If a spin distribution ( ) is subject to any type of spatially varying off-resonance frequency ∆ ( ), the MR signal can be written as For reconstruction, the spiral signal S(t) is commonly interpolated onto a Cartesian k-space grid prior to Fourier transformation into the image space 28  Here, ( ) is the inverted spiral k-space trajectory ( ), i.e., a map that indicates the time at which a kspace location = ( , ) is reached. Numerical implementation of the CPR comprises the following steps: (1) compute ( ) from the gradient shapes, (2) transform the blurred image ( ) into k-space, (3) demodulate each pixel of location = ( , ) at the corresponding off-resonance frequency ∆ ( ).
Step (3) can be accelerated by demodulating ( ) with an array of discrete, evenly spaced off-resonance frequencies 30

MRF-Dixon with spiral deblurring
To correct for off-resonance blurring in MRF, we combined spiral MRF with a 3-point Dixon water-fat separation and CPR deblurring. For superposing signal fractions of water and fat in the same voxel, the resulting voxel signal ( ) = ( ) + ( ), acquired at TE, may be written as Here, is a constant receiver offset-phase. For simplicity, we use a single peak fat model, although fat exhibits multiple spectral components. In three-point Dixon methods, three complex images First, the off-resonance map is retrieved from the undersampled MRF data. Temporal averages over each of the three MRF trains are calculated, which highly reduces the undersampling induced aliasing artifacts that are present in the individual images: The mean off-resonance map ∆ = 2 • ∆ • arg [5] is calculated and phase unwrapping is applied to ∆ if phase jumps are present within the breast. Phase unwrapping was implemented as a region-growing algorithm 15 . The unwrapped off-resonance map is then  Table 1. Hence, the fat signal was deliberately blurred using equation [2] with ∆ = −∆ and spiral k-  Table 2. For MRF-Dixon scans, a square FOV of 430 mm size with voxels of (1.92 × 1.92 × 5) mm 3 was selected. As in the simulation study, we utilized a constant TR of 20 ms and the train of 500 flip angles 32 depicted in Figure 1(a), preceded by a 180° inversion pulse. Echo times (TE1/TE2/TE3) = (4.61/6.92/9.23) ms were set for the three MRF trains, corresponding to in-phase/out-of-phase/in-phase readout at 1.5 T. The delay time in between the MRF trains was set to = 7.5 s to allow for complete relaxation of the magnetization in breast tissues. A single spiral interleaf of uniform sampling density (acquisition window Tacq=7ms) was acquired in each TR interval, corresponding to an undersampling factor of R = 20. Between successive TR intervals, the k-space trajectory was rotated by 18 degrees. The transmit field (B1 + ) inhomogeneity over the slice was measured in a separate Cartesian 3D sequence using the actual flip angle technique 33 . The MRF-Dixon dataset was deblurred based on the above-described approach. To compare between different sampling strategies, Cartesian MRF data was further acquired with TE=4.61 ms. To retrieve T1 and T2 parameter maps, a dictionary with approximately 300.000 normalized entries was calculated. B1 + inhomogeneity was included in the dictionary as a multiplicative correction factor fB1+ in front of the flip angle train. The dictionary resolution is specified in Table 1. To reconstruct T1 and T2 maps, the measured signal evolution in every voxel was first normalized to a complex magnitude of 1 and then compared to the subset of dictionary entries with fB1+ closest to the measured B1 + of that voxel. The best matching dictionary entry was selected based on the maximum inner product between dictionary entry and measured signal evolution 10 . To evaluate the effect of CPR deblurring on the matching results, matching was equally performed to the first MRF-train without any correction for blurring, equal to the standard MRF measurement and matching procedure 10 .
All Cartesian reference scans were acquired with a reduced FOV of 80% in right-left direction to shorten the overall scan time. An additional SENSE factor of 1.5 was intrinsically applied in the scanner reconstruction to avoid fold-over artifacts, e.g. from the arms in the breast scans.
Here, i={1,2}. "A" stands for either the Standard MRF or the MRF-Dixon measurement, while "B" stands for either the IR/MESE or the Cartesian MRF measurement.

In-vivo breast scans
Breast MR scans were acquired of six female healthy volunteers after informed consent, with age and ACR breast density as stated in Table 3. The breasts were immobilized in cranio-caudal direction.
As in the phantom, an undersampled spiral MRF-Dixon sequence was acquired (R=20). In order to verify the robustness of our MRF-Dixon acquisition in-vivo to undersampling artifacts and hence the quality of the parameter maps, a fully sampled MRF measurement (R=1) was performed for 3 out of the 6 volunteers.

In-vivo breast scans
As an example for the breast scans, we present the full dataset for one volunteer. Further results are available in the Supporting Information Figures S1 and S2.
Deblurring and water-fat separation

Discussion and Conclusions
This work addresses the blurring problem in spiral MRF for water and fat by a three-point Dixon approach.
Three fingerprint trains of different echo time permit both water-fat separation and deblurring without requiring a separate off-resonance map. Thereby, an accurate measurement of the relaxation times of small features by spiral MRF becomes possible in regions that are else compromised by the overlapping, blurred fat signal.
In the simulation study, we first investigated the resulting bias on T1 and T2 near a fatty structure, depending on the spiral acquisition time. In the phantom validation experiments, we observed smaller NRMSE values between MRF-Dixon and Cartesian reference relaxation times than between Standard MRF and the reference. We equally see this improvement when calculating the NRMSEs with respect to Cartesian MRF.
It should be underlined that the latter comparison judges the effect of our blurring correction best, as the spiral and Cartesian MRF sequences were employing equal acquisition parameters apart from the signal readout. The difference in long T2 values between MRF and MESE measurements is likely attributable to increased diffusion effects in the MRF sequence 35 . However, we do not expect such large T2 in breast tissues 36 . We therefore conclude that the validation of the MRF sequence was relevant with respect to the intended application.
For the in-vivo breast scans, the deblurring approach via CPR resulted in blurring-free mean water and fat signals. The effect of deblurring was most prominent for the fat signal, as the scanner's resonance frequency usually adjusts close to the water resonance frequency. Retrospectively, the successful deblurring justifies using the mean off-resonance map during CPR, despite minor differences to the Cartesian Dixon map.
Deblurring further permitted an improved feature delineation in both the T1 and the T2 maps. The quantitative maps of the undersampled MRF-Dixon measurement agreed well with those of the fully sampled one, despite the 20-fold acceleration. Next to the phantom measurements, this is an important indicator for the stability of our MRF-Dixon sequence in the presence of undersampling. We suggest that such a comparison should be made each time that an MRF sequence is changed, especially if the amount of acquired information is decreased, e.g. when reducing the number of TR intervals or the voxel sizes.
Future effort will comprise removal of the streak artifacts, which are supposedly due to wrong registration of signal in the presence of heart movement and through-plane blood flow. While for Cartesian sampling the in-flowing blood results in coherent ghosts along the phase-encoding direction 37 the spiral readout, bearing a continuously changing phase-encoding direction, smears such signal around the source of flow in a spiral-looking manner. A solution to this problem might lie in presaturation of signal in the heart region.
A different strategy may be to increase the signal-to-noise ratio (and thus to decrease the importance of flow artifacts) during reconstruction, such as by compressed sensing 38 or matrix completion methods 39 .
We corrected the presented MRF-Dixon measurements for in plane B1 + inhomogeneity. Slice profile effects were not corrected during MRF matching; however, we employed an RF pulse shape with a time-bandwidth product of 10.2 that minimizes slice profile effects. B1 + correction proved to remove the large intra-breast inhomogeneity of the T2 values 40 . MRF is known to be prone to B1 + inhomogeneity 41 , as the dictionary reconstruction relies on exact knowledge of the flip angle train. Admittedly, a faster B1 + mapping method would be preferred for future MRF exams.
In-vivo, differences were present between the relaxation times in the MRF and the reference maps. The MRF and reference pulse sequences differed in the employed gradients and RF pulse shapes, which complicates their direct comparison. Slice profile effects and imperfect inversion pulses [42][43] , diffusion 35,45 and magnetization transfer effects 46,47 are confounding factors affecting both MRF and reference relaxation measurements to different degrees, which can explain the differences in the relaxation time maps. In addition, fat has multiple spectral components with different relaxation times. This may lead to different apparent relaxation times for different sequences. These discrepancies are a problem yet to be solved by qMRI, which we cannot remedy by our deblurring approach alone.
Three separate MRF trains of different echo time are demonstrated here as a proof of principle that the approach works. Although we were still able to acquire a single slice in less than a minute, prolonged scan times will be of concern for volumetric acquisitions which are of relevance for breast imaging. Acceleration can be achieved by performing only a two-point Dixon water-fat separation with an additional phaseunwrapping step 48     As a first step, the mean off-resonance map is computed from the temporal averages of the in-phase MRF trains (TE1, TE3). With the mean off-resonance map, a 3-point Dixon water-fat separation is conducted for each TR interval. A blurred water MRF train and a blurred fat MRF train are obtained, which are subsequently deblurred by CPR. By calculating the temporal average over the deblurred water and fat MRF train, we obtain a mean water and a mean fat image. In a last step, the deblurred water and fat data are recombined and subjected to the MRF matching process. In result, deblurred T1 and T2 maps are obtained.