Three-dimensional multi-parameter brain mapping using MR fingerprinting

Abstract The purpose of this study was to develop and test a 3D multi-parameter MR fingerprinting (MRF) method for brain imaging applications. The subject cohort included 5 healthy volunteers, repeatability tests done on 2 healthy volunteers and tested on two multiple sclerosis (MS) patients. A 3D-MRF imaging technique capable of quantifying T 1 , T 2 and T 1ρ was used. The imaging sequence was tested in standardized phantoms and 3D-MRF brain imaging with multiple shots (1, 2 and 4) in healthy human volunteers and MS patients. Quantitative parametric maps for T 1 , T 2 , T 1ρ , were generated. Mean gray matter (GM) and white matter (WM) ROIs were compared for each mapping technique, Bland-Altman plots and intra-class correlation coefficient (ICC) were used to assess repeatability and Student T-tests were used to compare results in MS patients. Standardized phantom studies demonstrated excellent agreement with reference T 1 /T 2/ T 1ρ mapping techniques. This study demonstrates that the 3D-MRF technique is able to simultaneously quantify T 1 , T 2 and T 1ρ for tissue property characterization in a clinically feasible scan time. This multi-parametric approach offers increased potential to detect and differentiate brain lesions and to better test imaging biomarker hypotheses for several neurological diseases, including MS.


Introduction
The utility of MRI mapping techniques quantifying voxel-wise relaxation times for multiple contrast mechanisms such as T 1 , T 2 , or T 1ρ have been shown in a number of neurological conditions [1][2][3][4] . Despite their utility, they have not made their way to clinical protocols. A chief reason for this may be the typical extended scanning time needed to run the individual mapping sequences.
While T 1 and T 2 mapping have been developed decades earlier 5,6 , T 1ρ contrast is a newer contrast mechanism which refers to the spin-lattice time constant in the rotating frame. It represents the decay of the transverse relaxation time in the presence of a spin-lock radiofrequency eld 7 . T 1ρ contrast has been shown to be sensitive to lower frequency range (KHz) interactions between free water and complex macromolecules 8, 9 . T 1ρ mapping has been widely implemented to quantify proteoglycan loss in cartilage 9 , with clinical applications demonstrated in multiple sclerosis (MS) 2,10 , Alzheimer's 11,12 and stroke 13 .
Newer, non-invasive multi-parameter MRI techniques [14][15][16] offering quantitative measures of key parameters can enable measurements to be collected within clinically feasible scan times. MR ngerprinting (MRF) offers a novel paradigm that allows simultaneous quantitative mapping of useful MRI parameters in a relatively short time 17 . The utility of MRF has been shown in several pilot studies with applications in brain [17][18][19][20] , heart 21 , musculoskeletal and vascular applications 22,23 .
MRF uses a different approach from conventional MRI, using a single imaging sequence to assess multiple tissue parameters such as T 1 and T 2 , and therefore rapidly acquire ngerprint-like signal evolutions. A simulated dictionary is generated with combinations of possible signal evolutions. The acquired signal ngerprints are then pattern-matched to the pre-de ned simulated dictionary to generate voxel-wise quantitative parameter maps for each parameter encoded into the acquisition. Current MRF implementations typically quantify T 1 and T 2 simultaneously. Based on a previous implementation, a 3D-MRF method capable of quantifying T 1 , T 2 and T 1ρ was developed 22,24 .
The goal of this study was to develop a 3D-MRF technique, capable of quantifying T 1 , T 2 and T 1ρ for brain imaging applications, and to explore its feasibility for quantitative multi-parameter characterization in MS patients.

Results
Results from the phantom study are shown in gure 1. Figure 1(a) shows a picture and a schematic of the T 1 spheres in the NIST phantom, the sub-gure below that shows the T 1 maps reconstructed from 1-, 2-, 4-and 8-shots overlaid over the anatomical axial slice through the T 1 spheres. The bar-graph at the bottom of Figure 1(a) shows the mean and standard deviation for each sphere comparing the reference method for T 1 , and the corresponding results from 1, 2, 4, and 8 shots. The range of values for T 1 in the spheres was from 200-2500 ms, with the bar plot showing excellent agreement with the reference technique represented by a general trend of reduced standard deviation for each ROI with increasing number of shots. The T 2 range was 0-600 ms, also showing similar excellent agreement. At the top of the range (>250 ms) there some variation of estimated T 2 values between reference and multiple shots. The T 1ρ range was lower from 0-450 ms, with the estimated values at the higher values (>200 ms) showing greater variability among the shots and with the reference technique. Increasing number of shots reduces the variability in each ROI, with 4 and 8 shots showing the least variability. While there is great agreement even with one shot, variability in estimated parameters increase with lowest shots (1 shot) and at higher end of the ranges for T 1 , T 2 and T 1ρ . Figure 2 shows a comparison of multi-parameter maps for 2 exemplary control subjects for 1-, 2-and 4shots obtained using 3D-MRF, highlighting the ability of the technique to generate 3D, contiguous and simultaneous parameter maps for T 1 , T 2 and T 1ρ . The SNR using 1 shot was 6.45 ± 1.6, using 2 shots was 8.3 ± 1.9 and using 4 shots was 11.4 ± 2.1. Figure 3(a) shows representative ROIs drawn in the GM and WM in healthy subjects. Figure 3(b) shows mean T 1 values, gure 3(c) shows T 2 values and gure 3(d) shows T 1ρ values obtained from the GM and WM ROIs in the control subjects with 1-, 2-, and 4-shots. The T 1 , T 2 and T 1ρ values showed more variation in the GM compared to the WM, with the variability reducing with increased shots. The results from 2 shots were comparable to that of 4 shots. Table 1 summarizes the results from the control subjects using 1-, 2-and 4-shots.  Table 2 show the intra-class correlation coe cient (ICC) in the WM and GM ROIs for 1-, 2-and 4-shots. The results show that for 2-and 4-shots show the highest correlations. From these results, the 3D-MRF acquisition using 2 shots was considered optimal taking into consideration a clinically feasible imaging time (~12 min), SNR, noise characteristics, and accuracy, and was subsequently used for imaging in MS patients.
The results of the 3D-MRF imaging in a representative MS patient is shown in gure 4. The top row ( Figure 4(a)) shows standard non-contrast clinical FLAIR imaging in the MS patient. The 4 slices shown each contain lesions in the WM, and are highlighted in the images with the blue circles. Additional contralateral ROIs (red ROIs) were drawn on the opposite brain hemisphere from the lesion. Figure 4 show for each slice, the calculated T 1 map, T 2 map and T 1ρ map in the MS patient. Figure 5 shows the results of 3D-MRF imaging on two MS patients. Figure 5(a-d) shows results of an MS patient with chronic lesions (the same lesions were noted on MR scans for the past decade for this patient) and gure 5(e-h) shows results from an MS patient with actively enhancing lesions. Figure 5(a) and 5(c) shows T 1 and T 2 imaging using the standard non-contrast clinical imaging protocol. The T 2 imaging shows the presence of MS lesions. Figure 5  shows standard clinical imaging that shows the presence of a lesion, and gure 5(f) shows the results from the 3D-MRF. The identi ed lesions are marked with black ROIs and the contralateral ROI is shown in blue. Comparison of T 1 , T 2 and T 1ρ on the lesion side and the contralateral side shows signi cant differences. The bar graphs in Figure 5(h) show the signi cant differences between lesion ROIs and contralateral NAWM ROIs for T 1 (P=0.006), T 2 (P=0.020), and T 1ρ (0.016).   Table 3 shows the comparison of lesion ROIs, the contralateral NAWM ROI and control subjects ROI in similar brain locations as the lesion. For the MS patient with chronic lesions, the NAWM values compared to healthy controls are consistently and signi cantly higher (T 1 (P=0.026), T 2 (P=0.038), and T 1ρ (0.036)).
For the MS patient with newly enhancing lesions, the NAWM values are trending higher for all parameters but are signi cantly higher for only for T 1ρ (T 1 (P=0.07), T 2 (P=0.48), and T 1ρ (P=0.012)). Supplementary information Table S1 shows the differences between chronic lesion ROI in Patient 1 (T 1 , T 2 , and T 1ρ ) vs the newly enhancing lesion ROIS in Patient 2 (T 1 , T 2 , and T 1ρ ). The quantitative parameter values for chronic lesions are clearly trending higher than the newly enhancing lesion ROIs. A detailed study investigating additional MS patients is needed to draw statistical inferences in MS patients.

Discussion
In this study, we have demonstrated the use of MRF to acquire simultaneous 3D multi-parameter maps, quantifying T 1 , T 2 , T 1ρ in the brain, in a clinically feasible time and explored the possibility of extending it to MS applications for quantitative tissue characterization.
Multi-parameter mapping has been gaining popularity recently due to a number of advantages it offers 17,[25][26][27] . First, it allows to encode simultaneously multiple important parameters into a single imaging sequence. This allows the parameters to be automatically co-registered, and quanti ed simultaneously. Second, time and cost savings as a result of a single shorter scan. Individual mapping sequences are time consuming, and can take in excess of 40 min to complete. In comparison, the 3D-MRF implemented here can complete the acquisition in much less time (12 min for 2 shots). In a clinical setting, reduced time for scans will result in cost savings, and is desirable. Third, current diagnostic clinical scans and protocols for MS are not quantitative, and establishing quantitative metrics and better tissue characterization will give deeper insights into the mechanistic aspects of the disease at the clinical and sub-clinical level.
A number of recent developments allow quanti cation of T 1 , T 2 , T 2 * , diffusion 28 , perfusion and vascular parameters 29 . A majority of the approaches using MRF are 2D multi-slice acquisitions. The 2D-MRF acquisition is susceptible to through plane motion, and takes longer to acquire. The 3D-MRF acquisition used here achieves better imaging e ciency, allows contiguous coverage, and eliminates through plane motion. Another approach called MR multi-tasking uses simultaneously acquired multi-parametric data using a low rank tensor model to generate parameter maps, has shown preliminary feasibility for MS imaging 17 .
The estimated MRF parameters for T 1 , T 2 and T 1ρ were within the expected range reported in literature 2,12,20,30,31 . T 1ρ was consistently higher than reported T 2 values with comparable ranges. The T 1 values for WM and GM were in similar ranges compared to literature 12,31 . There were some systematic biases however. There is some variability of values in repeatability studies from the Bland-Altman studies. This may be due to imaging sequence imperfections, or experimental variability. From the in vivo multi-shot data, two trends can be seen from going from data acquired with 1-shot to 4-shots. There is increased SNR and reduced variability among the ROIs in the brain. While the errors from single-shot data have more errors, the differences from 2-shot and 4-shot are small enough to use 2-shots for brain imaging, given the advantage of time-savings.
MRI has been the standard of care for diagnostic imaging in MS since 2001 32 . MS is a complex in ammatory, demyelinating disease affecting the central nervous system (CNS) 32 . Diagnosis of MS requires evidence of disease progression in space and over time, as well as ruling out other disorders mimicking similar clinical pro les 32,33 . Adding to this complexity in MS is the di culty of classifying lesions and staging the disease in a spectrum ranging from active demyelination, mixed active and inactive demyelination to completely inactive demyelination stages [34][35][36] . Furthermore, focusing only on visible focal lesions have shown to have poor correlations with disease progression 34 , and diffuse subclinical effects are reported on NAWM and normal appearing gray matter (NAGM) too 32,37 .
In this study, the NAWM values (for T 1 ,T 2 , and T 1ρ ) in the chronic MS patient were signi cantly higher than control subject WM ROIs. Several previous studies have reported similar ndings 2,10,17,38 . The differences in NAWM values and controls may be due to a number of factors including axonal degeneration, in ammatory processes, myelin content reduction, and blood brain barrier leakage 39 . A highlight of this study is the use of T 1ρ mapping in addition to T 1 and T 2 mapping. T 1ρ mapping on its own has been used for MS applications in a number of studies 2,10,17 . T 1ρ as a contrast is sensitive to chemical exchange and lower frequency interactions and has been shown to be a sensitive indicator to lower frequency interactions between extra-cellular water and complex macromolecules 40 . In this study we noted signi cant differences between T 1ρ values within the lesion and NAWM, as well as higher values in the NAWM compared to T 1ρ values in control subjects. T 1ρ may be able to detect GM demyelination too which is a more subtle change due low myelin content 41,42 .
This study shows the results from two types of MS patients, a long-time diagnosed MS patient with many chronic lesions, and a newly diagnosed patient with recently enhancing lesions. The chronic MS lesions show increased values for T 1 , T 2 and T 1ρ compared to newly enhancing lesions (Supplementary   information Table S1), suggesting the potential to discriminate chronic and active enhancing lesions There are several future improvements that are possible to increase the coverage and resolution of 3D-MRF which will increase the utility and robustness in a clinical setting. The current 3D implementation is a stack-of-stars implementation, with Cartesian sampling in the kz-dimension, resulting in fold-over aliasing artifacts along the edge slices. Using a true 3D acquisition (along the kz dimension too) will eliminate this artifact, and result in improved usable coverage in the brain 43 . Further improvements can be made to T 1ρ spin-lock durations, by optimizing the TSL durations using a method such Cramer-Rao lower bound (CRLB) 44 or improved sub-space reconstruction methods 45 . This will reduce and optimize the number of TSL segments required and allow increased coverage. Finally, Deep Learning approaches to image reconstruction can replace the compute intensive o ine reconstruction methods 46,47 to offer near real-time construction, which will have a big clinical impact.
This study has the following limitations. The major drawback is the coverage of the 3D-MRF for brain imaging. For MS applications, full brain coverage at high resolution is desired. While we achieve 1 mm inplane resolution, more work is required to improve the through-plane resolution, and extend coverage to whole brain. This study shows a demonstration showing feasibility of quantitative 3D-MRF multiparameter mapping in only two MS patients. Larger studies in MS applications with this technique are warranted to explore the feasibility in MS diagnosis and monitoring.

Study Design
This prospective study was approved by the New York University Grossman School of Medicine institutional review board (IRB), was health information portability and accountability act (HIPAA) compliant and all methods were performed in accordance with the IRB guidelines and regulations. All recruited MS patients and healthy volunteers provided written informed consent.

MRF Sequence Design and Dictionary Construction
The 3D implementation of the MRF sequence is able to quantify four parameters: T 1 , T 2 , T 1ρ and B 1 +.
The 3D-MRF sequence was based on a previous 2D implementation 48 and was extended to encode T 1ρ , in addition to the original T 1 , T 2 and B 1 parameters for musculoskeletal applications 24,49,50 . The 3D-MRF sequence timing diagram is shown in gure 7. A 10 ms adiabatic inversion pulse was used for inversion. This is followed by 3 modules. The rst module consists of two FISP segments that encode for T 1 /T 2 , consisting of 250 slab-selective RF excitations. The rst FISP segment has ip angle varying from 0° to 20° and the second FISP segment has ip angles varying from 0° to 60°. A 50 ms delay is used between the two segments to recover magnetization. The second module of the sequence is used to encode T 1 /B 1 +, consists of 2 FLASH segments. It uses similar RF excitations and FA variation as the FISP module. The third module encodes for T 1ρ . A T 1ρ preparation pulse with variable duration (6 pulses with spin-lock duration varying from 2-45 ms) followed by 125 RF excitations for each spin lock pulse, with FAs ranging from 0° to 20°. Golden angle radial readouts following each RF excitation were used with center out readout in the kz dimension. At the end of the readouts for each spin-lock pulse, a 500 ms magnetization recovery delay is used. The T 1ρ preparation pulse uses balanced RF pulses to account for B 1 inhomogeneities. It uses a hard 90 y pulse to ip the magnetization to the transverse plane. This is followed by 4 balanced alternating phase spin-lock pulses are applied. Two 1 ms, 180 hard refocusing pulses are used (180 +x , 180 -x ) to account for B 0 inhomogeneities.
To increase SNR and k-space coverage, additional data with additional shots (n shots) were acquired by adding an offset angle (180°/n) at the beginning of each train. The 3D-MRF imaging sequence (Figure 7) with 1 shot took 6 minutes, 2 shots took 12 min, 4 shots took 24 minutes, and 8 shots took 48 minutes.
All the algorithms were implemented in MATLAB (MathWorks, Natick, MA, USA). Extended phase graph simulations were performed to compute a dictionary of simulated MR ngerprints 51 with a T 1 range of 50-3000 ms, T 2 range of 2-200 ms, and a T 1ρ range of 2-200 ms in steps of 6%. The acquired data, as well as the simulated dictionary, were compressed using singular value decomposition (SVD) to speed up dictionary matching 52 , which was performed o ine. An iterative dictionary pattern matching algorithm was used to produce quantitative maps of proton density, T 1 , T 2 , T 1ρ and B 1 .

Phantom Study
The 3D-MRF sequence was tested on a standardized ISMRM/NIST phantoms with published T 1 and T 2 values for 14 spheres 53 . 3D-MRF data were obtained using 2, 4, 6 and 8 shots were obtained on a clinical MR scanner (Prisma 3T, Siemens Healthineers, Erlangen, Germany) using a vendor provided 20-channel receive only, birdcage head coil. Reference imaging sequences used for T 1 -mapping was a 3D spoiled gradient recalled echo sequence, for T 2 -mapping was a 3D spin echo sequence as described in the reference 54 , and for T 1ρ -mapping a custom 3D-T 1ρ mapping sequence 4 was used. The speci c parameters used for each sequence compared are shown in table 1.
To compare the calculated parameters for the number of shots with the reference values regression and Bland-Altman analysis were performed for T 1 , T 2 and T 1ρ values. Supplementary information gures S1, S2, and S3 show the results for T 1 , T 2 and T 1ρ , respectively.

In-vivo Study
The study was approved by the institutional review board (IRB). To test the e ciency and errors in multiple shot acquisition schemes for neuro-imaging applications, we tested the 3D-MRF imaging on control subjects. Five control subjects (3 males, 2 females, 27±3 years) were recruited following informed consent, and in accordance with our IRB guidelines. They underwent brain imaging with the 3D-MRF imaging sequence at 1, 2 and 4 shots. To test repeatability, two subjects were scanned another time (~ a week later), and regression and Bland-Altman plots of the rst scan and the repeat scan were performed. Intra-class correlation coe cients were calculated to quantify agreement between the scans. Manual regions of interest were drawn in the gray matter (GM) and white matter (WM) of the brain in all control subjects to quantify the variability of parameter estimation among the shots.
To test the 3D-MRF for MS applications, two MS patients (1 male, 63 years and 1 female, 29 years) with MS-diagnosed lesions were recruited following informed consent in order to assess the feasibility in detecting subtle pathological changes in normal appearing white matter (NAWM) and differentiating MS lesions. They underwent brain imaging with no contrast administration using the 3D-MRF sequence at 2 shots, followed by routine clinical imaging protocol without contrast of the whole brain consisting T 1 -MPRAGE for T 1 contrast, and FLAIR imaging for T 2 contrast. Manual ROIs were drawn around the identi ed WM lesions and contralateral hemispheres with NAWM.

Statistical Analysis
For the phantom experiments, the mean and standard deviation of the ROIs drawn for each sphere across multiple slices was calculated. Regression and Bland-Altman analysis was performed to assess the agreement of multi-shot data with reference mapping techniques.
For the in-vivo control subjects, the mean and standard deviations in the manual ROIs drawn (The GM ROIs were drawn in the Insula and WM ROIs were drawn in the frontal lobe for all the subjects) across the subjects were calculated for 1, 2 and 4 shots. Test-retest reliability was assessed using regression plots, and Bland-Altman analysis. For each parameter, the intra-class correlation coe cient was calculated as : For the MS patients, manual ROIs drawn around WM lesions in the two patients were compared against contralateral sides and in ROIs drawn corresponding WM locations in the control subjects. Paired twotailed Student T-tests were used to assess the difference in relaxation times between MS-lesion ROIs and NAWM or comparable WM regions in control subjects. A p-value of less than 0.05 was considered signi cant.

Conclusion
In conclusion, this study demonstrated the use of a 3D-MRF technique that is able to quantify T 1 , T 2 and T 1ρ for brain imaging applications in a clinically feasible time, and explored the feasibility of quantitative multi-parameter characterization in MS patients.

Declarations
Grant Support: This study was supported by NIH grants R21-AR075259-01A, R01 AR076328, R01 AR076985, and R01 AR068966, and was performed under the rubric of the Center of Advanced Imaging Innovation and Research (CAI 2 R) at the NYU Grossman School of Medicine and NIBIB Biomedical Technology Resource Center (NIH P41 EB017183).

DATA AVAILABILITY
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.  Comparison of shots in vivo. The gure shows exemplary T 1 , T 2 and T 1ρ maps in two healthy controls at 1x1x3 mm 3 resolution for 1, 2 and 4 shots. The SNR improves signi cantly from 1 to 4 shots, at the cost of increased acquisition time. Two shots deemed as a suitable balance between SNR and clinically feasible time was used for scanning MS patients.   Pulse timing diagram of 3D-MRF sequence. The 3D-MRF sequence consists of an IR pulse, followed by a FISP module with two segments to encode for T 1 /T 2 , a FLASH module with two segments to encode for T 1 /B 1 , and a T 1ρ module to encode T 1ρ . To increase SNR and k-space coverage, additional shots (n shots) were acquired by adding an offset angle (180°/n) at the beginning of each train. The 3D sequence uses readouts acquired in a center-out stack-of-stars in the kz dimension.

Supplementary Files
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