3D magnetic resonance fingerprinting with quadratic RF phase

Abstract

Purpose:

To implement 3D magnetic resonance fingerprinting (MRF) with quadratic RF phase (qRF-MRF) for simultaneous quantification of ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, $\Delta {\mathrm{B}}_0$, and ${\mathrm{T}}_2^{\ast }$.

Methods:

3D MRF data with effective undersampling factor of 3 in the slice direction were acquired with quadratic RF phase patterns for ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, and ${\mathrm{T}}_2^{\ast }$ sensitivity. Quadratic RF phase encodes the off-resonance by modulating the on-resonance frequency linearly in time. Transition to 3D brings practical limitations for reconstruction and dictionary matching because of increased data and dictionary sizes. Randomized singular value decomposition (rSVD)-based compression in time and reduction in dictionary size with a quadratic interpolation method are combined to be able to process prohibitively large data sets in feasible reconstruction and matching times.

Results:

Accuracy of 3D qRF-MRF maps in various resolutions and orientations are compared to 3D fast imaging with steady-state precession (FISP) for ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ contrast and to 2D qRF-MRF for ${\mathrm{T}}_2^{\ast }$ contrast and $\Delta {\mathrm{B}}_0$. The precision of 3D qRF-MRF was 1.5-2 times higher than routine clinical scans. 3D qRF-MRF $\Delta {\mathrm{B}}_0$ maps were further processed to highlight the susceptibility contrast.

Conclusion:

Natively co-registered 3D whole brain ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, ${\mathrm{T}}_2^{\ast }$, $\Delta {\mathrm{B}}_0$, and QSM maps can be acquired in as short as 5 min with 3D qRF-MRF.

1 ∣. INTRODUCTION

Magnetic resonance fingerprinting^1,2 (MRF) is a flexible framework for quantitatively mapping multiple tissue properties and system parameters simultaneously. It is flexible because many properties can be encoded in MRF signal evolutions with varying patterns of sequence parameters and with additional modules (${\mathrm{T}}_1$, ${\mathrm{T}}_2$ prep, diffusion, etc.). Beyond the traditional ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ mapping, MRF has been extended to map more diverse contrasts such as diffusion,^3,4 flow,⁵ ASL,^6,7 magnetization transfer (MT),⁸ CEST,⁹ and ${\mathrm{T}}_2^{\ast }$.^10-14${\mathrm{T}}_2^{\ast }$ contrast is particularly important in characterization of Alzheimer’s,^15,16 Huntington’s,^17,18 and Parkinson’s^19-21 disease because of modulation of iron content in various deep brain structures and for healthy aging.²² In the case of ${\mathrm{T}}_2^{\ast }$ mapping with MRF, there have been different approaches to include ${\mathrm{T}}_2^{\ast }$ weighting into the MRF framework for 2D. Rieger et al¹⁰ harnessed the native ${\mathrm{T}}_2^{\ast }$ contrast of EPI for MRF by varying the flip angle (FA), TE, and TR for a series of EPI readouts. Hong et al¹³ combined blocks of FISP MRF for ${\mathrm{T}}_1∕{\mathrm{T}}_2$ sensitivity and multi-echo spoiled gradient echo (GRE) blocks for off-resonance and ${\mathrm{T}}_2^{\ast }$ sensitivity. The additional z-shimming scheme compensates for through-slice field inhomogeneity and enables accurate ${\mathrm{T}}_2^{\ast }$ matching in the case of poor shimming. Wang et al¹² showed in 2D that MRF sensitivity to ${\mathrm{T}}_2^{\ast }$ could be introduced by the addition of quadratically varied RF phase, effectively sweeping on-resonance excitation frequency linearly in time. The MRF sequence was made sensitive to off-resonance ($\Delta {\mathrm{B}}_0$) in this regard and frequency dispersion inside a voxel was simulated in the dictionary with Lorentzian distributions around $\Delta {\mathrm{B}}_0$ with varying width, where the width of the distribution was denoted by $\Gamma$. ${\mathrm{T}}_2^{\ast }$ can be calculated from ${\mathrm{T}}_2$ and $\Gamma$. In a similar fashion, Körzdörfer et al¹⁴ mapped frequency dispersion by assuming a Gaussian distribution and mapping the off-resonance with an MRF sequence combined of FISP, TrueFISP, and FLASH blocks.

In this work, we extend the previous work¹² and move 2D qRF-MRF framework to 3D for larger FOV coverage, higher through plane resolution and shorter scan times. Sequence parameters were tailored to 3D acquisition for sensitivity to all the properties of interest. On the reconstruction and matching side, the practical limitations that already exist for 2D become prohibitive when moving to such a high dimensional acquisition. Our previous 3D reconstructions used compression in time domain with singular value decomposition (SVD)²³ to be able to fit data into physical memory. However, even calculating the SVD of qRF-MRF dictionary with 4 property dimensions (${\mathrm{T}}_1$, ${\mathrm{T}}_2$, $\Delta {\mathrm{B}}_0$, and $\Gamma$) was limited by memory. To overcome this limitation, randomized SVD (rSVD)²⁴ was chosen. The dictionary was also undersampled uniformly in the tissue property dimension and the high resolution was brought back with quadratic interpolation.²⁵

The accuracy of 3D qRF-MRF is analyzed with phantom experiments and reference mapping techniques. ${\mathrm{T}}_2^{\ast }$ maps from 2D qRF-MRF were compared with GRE in the previous work.¹² Here, 3D qRF-MRF maps are compared to 2D qRF-MRF and 3D FISP MRF²⁶ in vivo. On the post-processing side, the new 3D sequence is also compared to its standard clinical protocol counterparts in terms of precision. It is demonstrated that local field inhomogeneities are encoded in $\Delta {\mathrm{B}}_0$ maps and resemble GRE phase maps processed for QSM. Additional QSM processing of 3D qRF-MRF $\Delta {\mathrm{B}}_0$ maps reveal susceptibility contrast that may be used for further clinical diagnoses.

2 ∣. METHODS

2.1 ∣. Data acquisition

A 3D bSSFP sequence with partition encoding in the slice direction was modified from Ma et al.²⁶ The 3D implementation allows undersampling in z-direction with encoding of multiple partitions in 1 repetition of the FA/TR/PH cycle of the sequence. A gel phantom with 10 vials of varying ${\mathrm{T}}_1$ and ${{\mathrm{T}}_2}^1$ was scanned with 3D qRF-MRF (1 in Table 1) and standard mapping techniques. Standard ${\mathrm{T}}_1$ mapping used a 2D inversion recovery spin-echo sequence with 6 different inversion times (30/100/500/1000/2000/3900 ms), TRs (6030/6100/6500/7000/8000/9900 ms), and scan times (393/398/424/457/520/644 s) and the same following acquisition parameters: FOV = 300 × 150, 128 × 64 matrix size. ${\mathrm{T}}_2$ was fit from 6 2D spin-echo scans with varying echo times (TE = 20/40/60/100/200/400 ms), TRs (6020/6040/6060/6100/6200/6400 ms), and scan times (393/394/395/398/405/418 s). FOV and matrix size were the same as ${\mathrm{T}}_1$ mapping scans. Three sets of 3D qRF-MRF in vivo data were collected with a 20 channel head/neck coil on a 3T Siemens Skyra system from a volunteer after obtaining informed consent with Institutional Review Board approval. The acquisition parameters are listed in Table 1. All 3D data sets have an undersampling factor of 3 in the partition encoding direction and 3s gap after each partition for ${\mathrm{T}}_1$ recovery. The third qRF-MRF data set was interpolated to 192 slices with 0.8 mm isotropic resolution. Interpolation was done by zero-filling in k-space for individual MRF image series before dictionary matching. At each time point 1 of the 48 (rotated by 7.5° with respect to each other) heavily undersampled (by 24 at the center and by 48 at the edge of k-space) spiral trajectories is acquired. The spiral index is updated at each time point with the bit-reverse order. A single slice 2D qRF-MRF and 3D FISP data matching the FOV of 3D qRF-MRF data were obtained for comparison.

TABLE 1.

Acquisition parameters for MRF data sets

	FOV (mm3)	Resolution (mm)	Number of slices	Acquisition time
3D qRF-MRF No. 1	300 × 300 × 120	1.2 × 1.2 × 5	24	5 min 30 s
3D qRF-MRF No. 2	300 × 300 × 144	1.2 × 1.2 × 3	48	11 min
3D qRF-MRF No. 3	300 × 300 × 154	Acquired: 1.2 × 1.2 × 1.6, resampled to: 0.8 isotropic	Acquired: 96, resampled to 192	22 min
2D qRF-MRF	300 × 300 × 5	1.2 × 1.2 × 5	1	38.7 s
3D FISP MRF	300 × 300 × 144	1.2 × 1.2 × 3	48	5 min

The RF phase (PH) was varied in time with the following quadratic functions: PH (n) = −1.42 * n² + 180n, n ≤ 126, and PH(n) = 1.34 * n² + 180n, 127 ≤n≤293, within each block of 293 time points, and repeated 12 times for a total of 3516 time points. The sweep of the off-resonance frequency separates spins with different off-resonance frequencies in time (Figure 1B). With the slightly different sweep rates within one 293 time point block, the on-resonance frequency is at 0, −1/(4*TR), −1/(2*TR), and 1/(4*TR) at the end of each block of 879 time points (Figure 1A), which starts with an inversion pulse. This scheme was selected to more incoherently distribute ${\mathrm{T}}_1$ encoding from the inversion pulses among the different off-resonance frequencies. The FA pattern (Figure 1C) was selected for ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, and ${\mathrm{T}}_2^{\ast }$ sensitivity based on our experience and previous investigations. This FA pattern used a recurring block of 879 time points, following each inversion pulse, which is repeated 4 times. The high FA portions of the sequence and the inversion pulses increase the sensitivity to ${\mathrm{T}}_1$. Low FAs and the smooth transitions to high FAs are necessary for ${\mathrm{T}}_2$ and $\Gamma$ encoding. The sensitivity of the selected FA pattern over the tissue properties is illustrated in the Supporting Information Figure S1 by looking at the variance between dictionary entries. TR was fixed to 11 ms.

FIGURE 1.

(A) Linear change of resonance band over time with quadratic RF phase. With TR = 11 ms, please note the periodicity of 1/TR = 90.909 Hz. (B) Two dictionary entries with equivalent ${\mathrm{T}}_1∕{\mathrm{T}}_2$ and different off-resonance frequencies are plotted. They differ from each other through all the time points. (C) Same FA block of 879 time points is repeated 4 times. All the repeated blocks start with an inversion pulse

2.2 ∣. Reconstruction and dictionary matching

With the 3D encoding framework,²⁶ 1 interleaved partition effectively encodes multiple partitions simultaneously. This brings the flexibility to compress the data before reconstruction for faster and uniform processing. When k-space data are projected onto an individual singular vector, the resulting sampling density is over the Nyquist rate and therefore, can be considered to be fully sampled. As shown by McGivney et al,²³ the k-space sampling pattern is the same for each singular vector and therefore, the same nonuniform fast Fourier transform (NUFFT) can be applied to all rank images or volumes. However, calculating the SVD of the whole qRF-MRF dictionary is prohibitively long and does not fit into physical memory. To overcome this, rSVD²⁴ was run on a dictionary with a smaller pool of tissue properties and parameter values that span the whole space. By checking the cumulative energy of singular values, an appropriate cut-off (200 with >0.9999 of the whole energy) was selected. Therefore, in this work only 200 subspace volumes were reconstructed and matched to a compressed dictionary.

The qRF-MRF dictionary was formed by first constructing a dictionary with a range of ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, and $\Delta {\mathrm{B}}_0$ values and then, convolving with a range of Lorentzian distributions over the $\Delta {\mathrm{B}}_0$ dimension with the width described by $\Gamma$. The matched $\Gamma$ property describes the full-width-at-half-max frequency dispersion in a voxel around the center frequency depicted by the matched $\Delta {\mathrm{B}}_0$. ${\mathrm{T}}_2^{\ast }$ is calculated after dictionary matching:

$$\frac{1}{T{2}^{\ast }}=\frac{1}{T2}+\pi \Gamma .$$ (1)

The dictionary was simulated based on the Bloch equations with the FA/TR/PH described above for the following range of values and step sizes with the notation (start:step:end): ${\mathrm{T}}_1$ (in ms), 10:10:90,100:20:1000, 1020:40:1500, 1550:100:2000, 2050:200:3000; ${\mathrm{T}}_2$ (in ms), 2:4:10, 15:10:150, 160:20:200, 250:100:500; $\Delta {\mathrm{B}}_0$ (in Hz), −50:2:50; $\Gamma$ (in Hz), ε:0.15:0.75, and then, increasing with the natural exponential function with exponent varied as −0.2877:0.1906:3.69. The step sizes selected were twice the desired step size in each dimension to further reduce the computational workload of 3D qRF-MRF. The compressed signal evolutions were matched to this compressed coarse dictionary to obtain the coarse tissue property maps. Following this, the relatively low resolution (in the tissue property dimension) was rectified with quadratic interpolation.²⁵ This was performed by recognizing that the inner product function around the matched dictionary entry follows a quadratic curve. To exploit this, a quadratic function was fit with the neighboring entries in all 4 tissue property dimensions (81 combinations in total) and the new maximum along the fitted curve was taken as the new dictionary match. Combining all of these factors, the size of the compressed dictionary was 3.2 GB after having been effectively compressed by a factor of ~281 with undersampling in the tissue property dimension (by 16) and compression in time (by 3516/200).

2.3 ∣. Post-processing

To demonstrate the value of qRF-MRF, 2 analyses were carried out. In the first analysis, the precision of qRF-MRF was compared to routine clinical weighted acquisitions. The acquisition parameters of the clinical protocols are listed in Table 2. The accuracy of qRF-MRF was tested with the phantom experiment and the comparison to FISP MRF provided a qualitative comparison in vivo. In the case of precision, the focus was on testing the sensitivity to noise using a bootstrapping analysis as has been used previously.^1,27 The same qRF-MRF data were reconstructed 15 times after adding reshuffled noise. For a meaningful comparison, weighted images were synthesized from the qRF-MRF maps and the SD over 15 reconstructions was taken as the precision metric. The same analysis of repeated reconstruction with added noise was applied to standard weighted clinical routine scans of MPRAGE for ${\mathrm{T}}_1$ comparison, turbo spin-echo (TSE) for ${\mathrm{T}}_2$ comparison and GRE for ${\mathrm{T}}_2^{\ast }$ comparison. The precision values were corrected for both voxel size and square root of acquisition time for all the protocols. Mean values over white matter ROIs are reported.

TABLE 2.

Clinical protocol parameters

	FOV (mm3)	Resolution	Acquisition time	TR/TE (ms)	FA
MPRAGE	230 × 230 × 307	1.2 × 0.75 × 1.2	255 s	2200/2.12	9°
TSE	300 × 300 × 144	1.2 × 1.2 × 3	161 s	10000/103	150°
GRE	300 × 262 × 144	1.2 × 1.2 × 3	155 s	28/20	15°

The second analysis explores the possibility of using $\Delta {\mathrm{B}}_0$ maps for QSM. Publicly available standard QSM processing tools were used to analyze the high resolution 3D qRF-MRF data set with interpolated 0.8 mm isotropic resolution. QSM analysis included Laplacian unwrapping with STI Suite,²⁸ removal of background phase with Laplacian background value (LBV),²⁹ 3D polynomial fit to remove ${\mathrm{B}}_1$ effects, dipole kernel estimation, and 2 QSM inversions: truncated k-space division (TKD)³⁰ and (fast nonlinear susceptibility inversion) FANSI with TV regularization.³¹ QSM processing was done in MATLAB (The MathWorks, Natick, MA) with the tools available from https://martinos.org/~berkin.

3 ∣. RESULTS

The phantom experiment results are presented in Figure 2. The mean ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ values from manually drawn ROIs show good agreement between 3D qRF-MRF and reference measurements. A comparison of 2D qRF-MRF with a similar slice from 3D qRF-MRF and 3D FISP is illustrated in Figure 3. ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ property maps of 3D qRF-MRF is similar to 3D FISP, but slightly different from 2D qRF-MRF (Figure 3A,B). For the additional tissue properties, 2D qRF-MRF and 3D qRF-MRF (Figure 3C-E) are also compared. In Figure 4, multiple representative slices of 3D FISP and 3D qRF-MRF (both with 5-mm slice thickness) show good agreement for ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ (Figure 4A,B). qRF-MRF-specific property maps over the same slices are in Figure 4C-E. Air–tissue interfaces are responsible for the wrapping of $\Delta {\mathrm{B}}_0$, inflated $\Gamma$, and extremely low ${\mathrm{T}}_2^{\ast }$ in the frontal regions. Whole brain ${\mathrm{T}}_2^{\ast }$ maps can be seen in Figure 5 for 3D qRF-MRF with 3-mm slice thickness.

FIGURE 2.

The mean ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ of the 10 vials from the phantom are calculated over 4 × 4 voxel ROIs from the center of the vials. X-axes denote relaxation times from the standard measurements. Y-axis denotes the relaxation times of the standard measurement (red) and the 3D qRF-MRF (yellow) ROIs. The reference line is the line of identity (connecting the standard ROIs with slope = 1) and it visually aids the comparison between qRF-MRF and the standard measurements. There’s good agreement for ${\mathrm{T}}_1$ and in general for ${\mathrm{T}}_2$ with a slight deviation for the long ${\mathrm{T}}_2$ values

FIGURE 3.

2D versus 3D comparison. (A) ${\mathrm{T}}_1$ and (B) ${\mathrm{T}}_2$ maps are compared for 2D qRF-MRF, 3D qRF-MRF, and 3D FISP for 5-mm slice thickness. 2D ${\mathrm{T}}_1$ is underestimated compared to 3D FISP and 3D qRF-MRF. The anatomic contrast of $\Delta {\mathrm{B}}_0$ for 2D and 3D qRF-MRF is noteworthy. $\Gamma$ and ${\mathrm{T}}_2^{\ast }$ maps are in (D) and (E), respectively. Please note the residual artifacts in 3D qRF-MRF pointed by the white arrows

FIGURE 4.

3D comparison for qRF-MRF and FISP (5-mm thick 24 slices). Four representative slices for (A) ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ maps point to overall good agreement between qRF-MRF and FISP. In (B) the other qRF-MRF maps over the same slices are plotted. ${\mathrm{T}}_2^{\ast }$ color map is the same as ${\mathrm{T}}_2$ but the scale is adjusted to highlight the available contrast. Please note the residual artifacts in 3D qRF-MRF pointed by the white arrows

FIGURE 5.

Sagittal ${\mathrm{T}}_2^{\ast }$ (in ms), off-resonance (in Hz), and $\Gamma$ (in Hz) maps from the 48 slice 1.2 × 1.2 × 3 mm resolution 3D qRF-MRF data set. Gray color map and the scale was chosen to demonstrate the typical ${\mathrm{T}}_2^{\ast }$ contrast

The precision of qRF-MRF and routine clinical protocols are reported in Table 3. Higher values for all contrasts show that qRF-MRF is more robust to noise compared to clinical protocols. Figure 6 shows 2 slices of $\Delta {\mathrm{B}}_0$ maps before and after quadratic interpolation. The low spatial resolution is improved with quadratic interpolation and the underlying anatomic contrast of $\Delta {\mathrm{B}}_0$ is revealed. Output of each QSM analysis pipeline step and the resulting susceptibility maps from the 2 inversion algorithms are shown in Figure 7.

TABLE 3.

Precision of qRF-MRF and standard clinical protocols

Precision	${\mathbf{T}}_1$	${\mathbf{T}}_2$	${\mathbf{T}}_2^{\ast }$	$\Delta {\mathbf{B}}_0\mathbf{SD}$
qRF-MRF	108	117	148	0.0315 Hz
Standard clinical	56 (MPRAGE)	51 (TSE)	90 (GRE)

The same data sets were reconstructed for 15 times after adding noise. Precision is calculated as the ratio of the mean reconstruction and the SD over 15 reconstructions and corresponds to SNR per unit time in conventional image analysis. For all sequences, the precision values are normalized by the square root of the relative scan time with respect to 3D qRF-MRF. In the case $\Delta {\mathrm{B}}_0$, only SD is reported.

FIGURE 6.

Effect of quadratic interpolation shown on 2 representative slices. Low resolution (left) because of the matching with the coarse dictionary blurs underlying contrast between tissues. High resolution is recovered after quadratic interpolation (right)

FIGURE 7.

Output of each individual step in the QSM processing pipeline is illustrated. Wraps, in the frontal part of the brain because of the wide band of frequencies, are removed with the unwrapping step. Once the bulk main field inhomogeneity in the background is removed, the susceptibility contrast starts to appear. ${\mathrm{B}}_1$ correction removes the additional inhomogeneity around the cerebellum, the top and the center of the brain. The results of the 2 dipole kernel inversion algorithms are at the bottom of the figure. As expected, truncated k-space division introduces some noise and FANSI with regularization smooths the susceptibility maps

4 ∣. DISCUSSION

The 3D implementation of qRF-MRF differs from 2D qRF-MRF in several aspects. The initial 2D implementation consisted of 2 separate types of acquisition blocks; a TrueFISP block with alternating 0/180° RF phase for ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ sensitivity, and quadratic RF phase block with $\Gamma$ encoding. The TrueFISP block suffered signal dropouts associated with the strong gradients at the air tissue interfaces in the frontal lobes of the brain. By avoiding TrueFISP blocks and instead using continuously updated quadratic RF phase blocks with additional inversion pulses in 3D, ${\mathrm{T}}_1$, and ${\mathrm{T}}_2$ maps are free from such artifacts (Figure 4A). $\Delta {\mathrm{B}}_0$ maps still have residual wrapping and $\Gamma$ maps tend to have the highest value for $\Gamma$ in those regions to compensate for the large variation in the signal response in these areas (Figure 4B). These could further be mitigated with a short TR implementation of qRF-MRF, which would widen the on-resonance band.

The 3D qRF-MRF reconstruction and matching was made possible by rSVD and quadratic interpolation. With rSVD, 3D FISP MRF reconstruction can be reduced to as low as 25 subspace images. However, the qRF-MRF dictionary has 2 additional dimensions ($\Delta {\mathrm{B}}_0$ and $\Gamma$) bringing increased variance and therefore, requires more singular values for accurate compression. Two hundred singular values were experimentally verified to be sufficient for accurate rSVD compression of the qRF-MRF dictionary. Using more than 200 singular values increases the processing requirements for reconstruction and dictionary matching with a negligible effect on accuracy or precision. The computational overhead was also curbed with reduction in size of the tissue property dimension of the dictionary by undersampling each of ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, $\Delta {\mathrm{B}}_0$, and $\Gamma$ property dimensions by a factor of 2. Quadratic interpolation not only restored the effects of this undersampling, but also provided continuous resolution in the tissue property dimension. The SD of $\Delta {\mathrm{B}}_0$ over repeated reconstructions and the high anatomic contrast seen in Figure 6 exemplifies the value of quadratic interpolation. It could be that the large step size is forcing the signal evolutions to be matched to the same dictionary entries over repeated reconstructions with noise, hence, the low SD (~1.5% of the dictionary step size) for $\Delta {\mathrm{B}}_0$ in Table 3. However, the high resolution is recovered (Figure 5) after quadratic interpolation pointing to an accurate match. Other interpolation approaches with reduced dictionary size have been proposed.³²

${\mathrm{B}}_1$ transmit inhomogeneity affects MRF accuracy, especially ${\mathrm{T}}_2$. It could be considered as another dimension in the dictionary³³ even though qRF-MRF data were not observed to be affected by ${\mathrm{B}}_1$ possibly because of the lower FAs compared to 3D FISP MRF. It will add greater complexity to the reconstruction and dictionary matching steps. However, this is a question of computing resources rather than methods development. Future research will consider either mapping ${\mathrm{B}}_1$ directly by encoding into the sequence or correcting for it with external measurements.

The higher precision observed for qRF-MRF in Table 3 comes from the higher magnetization level obtained in qRF-MRF as compared to conventional acquisitions. Additionally, the through-time encoding of off-resonance with frequency sweep and quadratic interpolation after dictionary matching makes the off-resonance maps stable and precise. As a result, $\Delta {\mathrm{B}}_0$ maps have high anatomic contrast that resembles the phase maps used for QSM processing. The possibility of QSM analysis on qRF-MRF $\Delta {\mathrm{B}}_0$ maps was explored with standard QSM tools. The effect of each processing step can be followed in Figure 7. After unwrapping and background field removal, the susceptibility-like contrast is revealed. The contrast is not as sharp as typically available with QSM data. The 2 dipole kernel inversion algorithms produce expected results. FANSI tends to over smooth and TKD might be amplifying noise. All the QSM processing was done using the default settings for each step. Optimization of the processing pipeline or even implementation of new tools tailored for qRF-MRF data will be explored in future work.

One advantage of QSM from qRF-MRF data is the possibility to start the QSM processing from an intermediate stage. One does not need to optimize for TE, efficiently combine coil data, fit multi-echo series, and even unwrap phase. qRF-MRF comes with perfectly co-registered ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, and ${\mathrm{T}}_2^{\ast }$ maps that would reduce the problems associated with registration. The anatomic information could be beneficial for some of the iterative QSM deconvolution algorithms that rely on anatomical data. Recent MPRAGE-based mapping techniques bring similar advantages with co-registered ${\mathrm{T}}_1$, ${\mathrm{T}}_2^{\ast }$, and susceptibility maps. Metere et al³⁴ combined multi-echo and MP2RAGE at 7T achieving slightly shorter acquisition (19 min vs 22 min) and similar results to separately acquired multi-echo and MP2RAGE data. They also showed that the ME-MP2RAGE sequence has high precision when inversion and TEs are carefully selected. Caan et al,³⁵ again at 7T, showed that a faster acquisition (17 min) is possible with a multi-echo readout for only the second inversion. A recent paper³⁶ also compared QSM with MPRAGE phase and GRE phase in a deep brain segmentation study on a healthy cohort, concluding that QSM from GRE is still superior but QSM from MPRAGE can improve segmentation performance with the co-registered ${\mathrm{T}}_1\mathrm{w}$ image.

Brain structures that benefit from ${\mathrm{T}}_2^{\ast }$ contrast imaging are usually small in size and call for high spatial resolution imaging. To achieve high isotropic resolutions (~1 mm) with a clinically feasible scan time the 3D qRF-MRF sequence has to be accelerated. The current implementation has an undersampling factor of 3 in the slice direction that could be the possible limit of the 20 channel coil used for the study. In fact, there are residual artifacts that appear in the central slices of 3D qRF-MRF maps because of the limited coil sensitivity information (depicted by the arrows in Figures 3 and 4). One could consider reducing the uniform undersampling factor to 2, which would further extend the scan time, or applying non-uniform undersampling with a nominal undersampling factor of 3 and keep the scan time feasible. An example with different undersampling strategies is provided in Supporting Information Figure S2. The other option is shortening the sequence. Whereas the current RF phase was based off prior implementation,¹² faster sweep of the RF phase can be considered, but care must be considered to avoid possible interference from RF spoiling or loss of property sensitivity. Fewer time points per partition can also help reduce scan time but it might affect the accuracy of dictionary matching. The interplay between all the sequence variables and the possible options for acceleration needs to be considered and tested with controlled experiments in future work.

5 ∣. CONCLUSION

MRF with quadratic RF phase was implemented in 3D with a design of sequence parameters simultaneously sensitive to all tissue properties. The complexity of large data and dictionary sizes was circumvented with rSVD-based compression and quadratic interpolation. Accuracy and precision of 3D qRF-MRF was comparable with standard techniques. The first example of MRF-based QSM was shown with simple processing, bringing additional value to MRF framework. QSM from qRF-MRF is free and comes with co-registered ${\mathrm{T}}_1$, ${\mathrm{T}}_2$, ${\mathrm{T}}_2^{\ast }$, and $\Delta {\mathrm{B}}_0$ maps. In conclusion, 3D qRF-MRF can go beyond previous MRF implementations and open the door for new analyses with the novel and rich information available in ${\mathrm{T}}_2^{\ast }$ and $\Delta {\mathrm{B}}_0$ maps.

Supplementary Material

supplementary file

FIGURE S1 Sensitivity of the sequence over the tissue properties is illustrated by keeping all the tissue properties the same except 1. In (B), multiple dictionary entries with ${\mathrm{T}}_2=45\mathrm{ms}$, $\Delta {\mathrm{B}}_0=-10\mathrm{Hz}$, $\Gamma =0.15\mathrm{Hz}$, and ${\mathrm{T}}_1$ varied between 0 to 3000 ms are plotted with the blue-yellow color map. The variance of dictionary entries, plotted in red, represents where dictionary entries with different ${\mathrm{T}}_1$ differ from each other the most. In case of ${\mathrm{T}}_1$, it can be seen that high FA portions of the sequence (highlighted in yellow) provide sustained variance. (C) ${\mathrm{T}}_1=800\mathrm{ms}$, $\Delta {\mathrm{B}}_0=-10\mathrm{Hz}$, $\Gamma =0.15\mathrm{Hz}$, and ${\mathrm{T}}_2$ varied between 0 to 500 ms. For ${\mathrm{T}}_2$, low FAs (highlighted in orange) contribute more for the separability. (D) ${\mathrm{T}}_1=800\mathrm{ms}$, ${\mathrm{T}}_2=45\mathrm{ms}$, $\Delta {\mathrm{B}}_0=-10\mathrm{Hz}$ and $\Gamma$ varied between 0 and 30 Hz. $\Gamma$ sensitivity is dependent on ${\mathrm{T}}_2$ sensitivity and also suffers from high FAs

FIGURE S2 A single slice from a 3D qRF-MRF and matching FOV 3D FISP data are plotted. qRF-MRF data were acquired fully sampled and reconstructed in 3 different ways. Fully sampled reconstruction represents the reference for comparison. Retrospective reconstruction with uniform undersampling mimics the acquisition strategy presented in the main body of the manuscript where 1 partition out of 3 partitions was uniformly acquired. In the case of non-uniform undersampling, in the partition dimension, center of k-space was fully sampled and the edges of k-space were undersampled with acceleration factors higher than 3. The nominal undersampling factor is 3 when all the partitions are considered for the non-uniform undersampled case. In other words, uniform and non-uniform undersampled data would have the same total scan time. When compared to fully sampled data, it can be seen that the artifacts (depicted by the arrows) are because of the type of undersampling rather than the nominal undersampling factor

Additional Supporting Information may be found online in the Supporting Information section.