High SNR full brain relaxometry at 7T by accelerated MR‐STAT

To demonstrate the feasibility and robustness of the Magnetic Resonance Spin TomogrAphy in Time‐domain (MR‐STAT) framework for fast, high SNR relaxometry at 7T.


INTRODUCTION
][3] The main motivation for quantitative imaging at high field (≥7T) is the additional SNR available.][11][12] Conventional quantitative MRI techniques are time-intensive as they estimate these tissue properties (T 1 , T 2 , proton-density) using multiple steady-state sequences with different sequence parameters to sensitize the sequence to a single parameter.Consequently, fast multi-parametric quantitative MRI techniques have been developed that simultaneously estimate multiple parameters from a single scan.Generally, these techniques use a transient-state sequence and a physics-based reconstruction and obtain the tissue parameters by either performing voxel-by-voxel dictionary matching on highly undersampled images (MR fingerprinting, or MRF) 9 or by directly solving for spatially resolved parameter maps from the time-domain signal (Magnetic Resonance Spin TomogrAphy in Time-domain, or MR-STAT). 13he application of fast quantitative MR techniques at high field is challenging due to an increase in B + 1 -inhomogeneities and tissue heating (SAR), which both result from the higher RF frequencies used at 7T and beyond.Here, the B + 1 -inhomogeneities lead to spatially varying biases in the parameter maps which can be mitigated by including the B + 1 as an extra parameter in the physics model.][16] An additional challenge for fast quantitative MR techniques is the high RF-power required.This originates from (i) the adiabatic inversion pulses used to improve T 1 encoding and reduce sensitivity to B + 1 , and (ii) the variable flip-angles which features large variations in flip-angle to ensure sufficient T 1 and T 2 encoding.The main approaches to limit SAR are a decrease in flip-angles or an increase in TR, which lead to a decrease in SNR of the estimated tissue parameters and longer scan times, respectively.
In this work, we demonstrate that the MR-STAT framework can be applied at high field (7T) by using a flip-angle train specifically optimized for 7T and by correcting for B + 1 -inhomogeneities using a short B + 1 -mapping scan and a TR-FOCI adiabatic inversion pulse. 17In addition, we compare the SNR(−efficiency) of MR-STAT at 7T with the existing MR-STAT implementation at 3T and show that the additional SNR at 7T can be used to shorten the MR-STAT acquisition and obtain highly accurate mapping.This is demonstrated by applying two-fold undersampling, which leads to a full brain protocol with 1 x 1 x 3 mm 3 resolution (1.5 mm slice-gap) of 3 min.This protocol was validated in a gel phantom to test the accuracy and precision of the estimated T 1 and T 2 values and five healthy volunteers were scanned to demonstrate the feasibility and robustness.

METHODS
MR-STAT enables the estimation of multi-parametric quantitative MR-maps directly from time-domain data of a single short scan.Here, the quantitative parameters are encoded into the signal by using a combination of Cartesian gradient encoding and a time-varying flip-angles during a non-balanced transient-state sequence.Quantitative parameter maps are obtained by directly and simultaneously solving for spatial localization and tissue parameters quantification in a single large-scale non-linear optimization process. 10,13

Sequence design
A typical unaccelerated MR-STAT acquisition repeats a linear phase-encoding pattern over a transient state flip-angle train where spin states are different for each phase encoding step.Spatial frequencies are sampled at the Nyquist rate and cover the equivalent of five or six full k-spaces (Figure 1).Acceleration can be achieved by skipping phase-encoding steps according to arbitrary design choices.Here, acceleration can be denoted by a factor R, similar to undersampling in conventional MR-acquisitions, which indicates the spatial frequencies omitted with respect to the unaccelerated (fully-sampled) MR-STAT sampling.The transient-state is achieved by using a series of varying RF-excitations which are preceded by an inversion pulse and are used to capture the time-domain signal needed to estimate T 1 , T 2 , and proton-density.To enable alias-free reconstruction when accelerating, we included receive coil sensitivities into the MR-STAT signal model, which enhance spatial encoding and can be obtained from a separate low-resolution scan.This leads to the following signal model: Top: A schematic depiction of the sampling scheme for the accelerated (R = 2) MR-STAT acquisition.Five k-spaces were acquired which were two-fold undersampled (indicated by the solid lines).Bottom: the BLAKJacoptimized low SAR flip-angle train.
where S n is the temporal signal from each coil and  represents the proton-density that is spatially weighed by the receive sensitivity C n of each receive coil.m denotes the spatial and temporal variation of the transverse magnetization during the MR-STAT experiments which depends on the spatial encoding and the applied RF-pulses, and MR-related parameters like T 1 , T 2 , and B + 1 that are represented by .
The BLAKJac 18 analytical framework was used to design a flip-angle train that minimizes the noise in the estimated T 1 , T 2 , and proton-density () while taking into account the phase-encoding pattern used alongside the varying flip-angles.The cost function used for the BLAK-Jac optimization contains a SAR penalty term based on the RMS flip-angle and TR which was used to optimize a flip-angle train specifically for low SAR by limiting the RMS flip-angle to 35 • (excluding the inversion pulse).This value of 35 • corresponded to the vendor defined low SAR condition for a TR of 11 ms.Furthermore, the optimization was performed for a set of eight T 1 and T 2 values which are typical for 7T brain imaging with T 1 ranging between 370 and 3300 ms and T 2 ranging between 25 and 308 ms.The resulting flip-angles and associated phase-encoding pattern can be found in Figure 1.

Sequence parameters
Data were acquired in a gel-phantom and in vivo on a 7T MR-scanner (Philips, The Netherlands) using a 32-channel receive array (Nova Medical, USA) and a two-channel transmit coil (driven in quadrature).The imaging parameters were based on a previous clinical study performed with MR-STAT at 3T, 19 albeit with a longer TR/TE to limit SAR: voxel size = 1 x 1 mm For the two-fold undersampled scans (see Figure 1 for a schematic k-space sampling), this resulted in an acquisition time of 6 s per slice and 2 ′ 42 ′′ s for the whole MR-STAT acquisition.The B + 1 -inhomogeneities were estimated using a separate, 13 s long DREAM 20 sequence with a STEAM angle of 40 degrees, a 3.5 x 3.5 x 3.5 mm 3 isotropic resolution.The resulting B + 1 map was subsequently used in the MR-STAT reconstruction.Receive coil sensitivity maps were obtained using ESPIRiT from the vendor's standard receive coil mapping scan. 21

Phantom experiments
Phantom experiments were performed on a phantom with 12 gel vials with varying T 1 and T 2 values (TO5, Eurospin II test system, Scotland).The effect of non-homogeneous B + 1 on the MR-STAT reconstruction was tested by performing reconstructions with and without the measured B + 1 -prior.In addition, a two-fold undersampled acquisition was performed to investigate the effect of acceleration on the reconstructed parameters.
Ground truth values for T 1 and T 2 were obtained by acquiring a series of inversion recovery spin-echo acquisitions (T 1 ) and single-echo spin echo acquisitions (T 2 ) at varying inversion and TEs (10 TIs between 200 and 4150 ms and 10 TEs between 20 and 520 ms).

2.4
In vivo experiments Five volunteers (three male, two female, age 26-62) were scanned using the undersampled MR-STAT acquisition to assess the in vivo repeatability and enable comparison with relevant literature findings.Informed consent was given by all volunteers in accordance with the local Institutional Review Board for all scans.To enable comparison with literature values, a gray-white matter segmentation was performed using FSL (FAST) 22,23 on synthetic T 1 -weighted images which were based on the R 1 -maps (1/T 1 ).

Comparison to 3T
In vivo and phantom data were also acquired on a 3T MR-scanner (Philips, The Netherlands) using a 15-channel receive array with identical imaging parameters except for a shorter TR and TE of 10.4 ms and 5.2 ms, respectively.A flip-angle train specifically optimized for 3T was used which also featured a flip-angle constraint of 35 degrees rms.Due to SNR-constraints, the in vivo data at 3T were acquired without undersampling while the phantom data were acquired both fully sampled (R = 1) and two-fold undersampled (R = 2).B + 1 and coil sensitivity maps were acquired similarly to the data at 7T to allow for B + 1 -correction during the reconstruction.The phantom data from 7T and 3T were used to calculate SNR-efficiency for T 1 and T 2 using 9 : Here, T n NR is the SNR for T 1 or T 2 based on the mean of the T 1 /T 2 divided by the SD over each vial.T scan is the scan time per slice in seconds.

Reconstruction
The MR-STAT reconstructions were performed on a GPU (NVIDIA, A5000) using a reconstruction algorithm written in the Julia programming language. 24This reconstruction algorithm included an EPG-simulator to compute the forward signal model and the partial derivatives with respect to the tissue parameters for the spoiled gradient sequence.For this work, the EPG simulator was adapted to include the history of inversion pulses applied to each slice before acquiring the data, an explanation on the necessity of this adaption is found in the supplementary information (Figure S1).The reconstruction also included slice-profile effects which were included by using Bloch equation simulations for 35 sub-slices equally distributed along the slice-selection direction over a range of three times the nominal slice-thickness. 25

Phantom experiments
Figure 2A shows a comparison between the reconstructed T 1 and T 2 values per vial without and with B + 1 -correction for the fully-sampled and accelerated MR-STAT acquisitions.Here, the effect of the B + 1 -correction was similar for both acquisitions.Specifically, the reconstructed T 1 values did not significantly change after correcting for B + 1 with a mean relative error of 2.9% (R = 1) and 1.7% (R = 2) with respect to the ground truth values.The reconstructed T 2 values, on the other hand, did change significantly when correcting for B + 1 as this caused the mean relative error to decrease from 33.5% (R = 1) and 30.2% (R = 2) to 4.2% (R = 1) and 4.4% (R = 2).After B + 1 -correction, both fully-sampled and undersampled data yielded similar T 1 and T 2 estimates with a mean relative difference of 1.6% for T 1 and 2.4% for T 2 .
Figure 2B shows the effect of the B + 1 -inhomogeneities on the reconstructed T 1 , T 2 , and proton-density for the gel phantom for R = 2. Here, the inclusion of the B + 1 -map in the reconstruction mainly affected the T 2 and proton-density reconstructions (Figure 2B).The artifact highlighted by the red arrows was caused by a large B 0 -inhomogeneity (∼400 Hz) at an air-water boundary, which could not be mitigated by B 0 -shimming.As such, these vials were omitted from the quantitative plots in Figure 2A.

In vivo experiments
Figure 3(A,B) shows two representative slices for two subjects at 7T (the rest of the slices and subjects can be found in Figure S2 of the supporting information).All parameter maps show a low noise level allowing for a clear distinction between gray and white matter and smaller structures like the basal ganglia (Figure 3A). Figure 3B shows a slice lower in the brain where a bias in T 2 and T 1 values was observed in the cerebellum due to a combination of a bias in the B + 1 mapping at extremely low B + 1 (<20% of the nominal B + 1 , indicated by the green arrows in Figure 3B) and B 0 inhomogeneities (yellow arrows in Figure 3B) close to the ear cavities resulting in imperfect inversion.In addition, we observed minor pulsatility artifacts in the phase-encoding direction originating from blood flow in large vessels (red arrows in Figure 3A).
Figure 3C shows the distribution T 1 and T 2 values in the gray and white matter over the whole-brain across all subjects.The peak values for the reconstructed T 1 and T 2 are summarized in Table 1.Here, the reconstructed T 1 was found to be 1092 ± 11 ms (1.0% inter-subject variation) in white matter and 1610 ± 34 ms (2.1% inter-subject variation) in the gray matter.The reconstructed T 2 varied from 28 ± 1.2 ms (4.3% inter-subject variation) in the white matter to 36 ± 1.9 ms (5.3% inter-subject variation) in the gray matter.Both the observed T 1 and T 2 values fall in the range of values reported previously in the relevant literature (Table 1). 26-30

Comparison to 3T
Figure 4A,B shows the SNR(−efficiency) for unaccelerated and accelerated MR-STAT acquisitions on a phantom at 3T and 7T. Figure 4A shows that the SNR at 7T is consistently higher than at 3T for an RMS flip-angle of 35 degree.In the Figure S4, this is shown to also hold when an RMS flip-angle of 70 degrees is used at 3T.Additionally, the SNR in T 1 at 7T was observed to not decrease for two-fold undersampling.Overall, a higher SNR-efficiency Reconstructed T 1 and T 2 values for the different subjects.Note: The values were obtained from the peak of the gray and white matter histograms.On the bottom the range of literature values for T 1 and T 2 .

Reconstructed
was observed for the MR-STAT acquisitions at 7T with a 3.1 (R = 1) and 4.1 (R = 2) times increase in SNR-efficiency for T 1 and a 2.2 (R = 1) and 2.3 times (R = 2) increase for T 2 .
Importantly, the SNR-efficiency remained relatively constant for unaccelerated and accelerated acquisitions at 3T while an increased SNR-efficiency in T 1 was observed for the accelerated scan at 7T.The in vivo 3T and 7T results in Figure 4C also highlight the increased SNR at 7T which can primarily be seen in the T 2 and proton-density maps.

DISCUSSION AND CONCLUSIONS
In this work, we demonstrated an accelerated MR-STAT acquisition at 7T that yielded high-quality quantitative parameters maps both in-vitro and for full-brain in five healthy volunteers.This was enabled by a flip-angle train that was optimized for low SAR, and for the expected T 1 and T 2 values occurring at 7T using the BLAK-Jac framework.In addition, we showed an increase in SNR-efficiency compared to MR-STAT at 3T and a reduction in the sensitivity to B + 1 variations by incorporating measured B + 1 -maps.The phantom experiments highlighted the necessity of B + 1 -correction especially for estimation of the T 2 .Specifically, the variations in B + 1 at 7T (between 50% and 150% of the nominal B + 1 ) caused a mean relative error of 30.2% in the reconstructed T 2 if not taken into account.After B + 1 -correction, this error was reduced to 4.4% (R = 2) which was primarily caused by a bias (overestimation) at higher (>100 ms) T 2 values.In addition to imperfect B + 1 , the B 0 fluctuation was also found to influence the reconstructed T 1 and T 2 values, which was caused by aliasing of signals with a larger difference in B 0 offset (>100 Hz).
In vivo, we observed residual influences of B + 1 -inhomogeneities in the cerebellum on the reconstructed parameters.Here, an underestimation of T 1 value was still observed in areas of extremely low B + 1 (<20% of the nominal B + 1 ) where the adiabatic condition for the inversion pulse was not met.Notably, these areas of low B + 1 also featured a bias in T 2 values due to a lack of T 2 encoding, which was caused by the low effective flip-angle reached in these areas.To improve B + 1 -coverage, a multi-transmit RF-coil could be used to provide a more homogeneous B + 1 (RF shimming) and more importantly to achieve high B + 1 over a larger volume. 31,32t 7T, similar T 1 and T 2 values were found across the five human subjects with a SD between 1% and 2% (WM-GM) for T 1 and 5%-6% (WM-GM) for T 2 and fit within the range of values reported previously in literature.Here, the largest variability between subjects possibly originated from variations in head sizes affecting the coil loading, which resulted in different B + 1 -profiles and slightly different RF-power used for scans.In literature, the RF-power has been identified as one of the main confounders for variability in quantitative parameter mapping, [33][34][35][36] as changes in RF-power will exacerbate magnetization transfer effects and change the effectively measured T 1 and T 2 .These effects could potentially be incorporated into the MR-STAT signal model albeit at the cost of extra computational complexity and scan time.
The accuracy of the B + 1 -map is the main limitation of the approach presented in this work.Especially at very low B + 1 (<30%), the accuracy of the DREAM sequence is limited leading to a bias in T 2 values in the cerebellum.This could be improved by using a multi-transmit setup with larger B + 1 -coverage.Alternatively, direct estimation of the B + 1 could also be considered with the MR-STAT framework by using a B + 1 -sensitive flip-angle train. 14,15,37owever, this could potentially increase scan time as more time might be needed to ensure sufficient encoding of B + 1 along with T 1 and T 2 .
Compared to MR-STAT at 3T, the phantom results showed an expected increase in SNR-efficiency when going to 7T for both T 1 and T 2 .In addition, an increase in SNR-efficiency for T 1 was observed when accelerating MR-STAT at 7T.The in vivo accelerated parameter maps at 7T showed a higher SNR when compared to fully-sampled MR-STAT at 3T.Given these results, we hypothesize that further increases in SNR-efficiency could be achieved by combining MR-STAT with a simultaneous multi-slice (SMS) approach [38][39][40] or by extending MR-STAT to 3D to yield a higher through-plane resolution while allowing for higher acceleration factors. 41n conclusion, we presented an extension of the MR-STAT to high field (7T) and showed that whole-brain coverage is possible within 3 min.The resulting quantitative parameter maps showed a low noise level and should therefore be suitable for studying disease progression and microstructure in the brain at 7T.

F I G U R E 2
Results for the phantom experiments at 7T. (A) comparison of the reconstructed quantitative values with (R = 2) and without (R = 1) acceleration and with (red) and without (blue) B + 1 -correction.(B) The reconstructed T 1 , T 2 , and proton-density maps for the accelerated MR-STAT acquisition (R = 2) showing the effect of including a measured B + 1 -map in the reconstruction.Here, the red arrows highlight vials that display an artifact originating from a large B 0 -inhomogeneity.

F I G U R E 3
Reconstructed T 1 , T 2 , and proton-density () and the measured B + 1 -map used during reconstruction for two representative slices in two subjects.(A) A central slice with relatively homogeneous B + 1 .Here, the red arrow highlights an artifact originating from blood pulsation.(B) A slice in the lower brain with inhomogeneous B + 1 and B 0 .Here, the yellow arrows point toward susceptibility artifacts caused by B 0 -inhomogeneities around the ears.The green arrows highlight a bias in T 2 values which is observed in areas of low B + 1 (<35% of the nominal B + 1 ).(C) The distribution of T 1 and T 2 values in gray and white matter across the five volunteers.

F I G U R E 4
Results for the comparison between MR-STAT at 3T vs 7T.The measured SNR (A) and SNR-efficiency (B) for T 1 and T 2 in phantom experiments which show higher SNR(−efficiency) at 7T for both R = 1 and R = 2. (C) In vivo MR-STAT reconstructions at 3T (R = 1) and 7T (R = 2) which show the increased SNR when going to 7T.The other slices of the volumes can be found in Figure S3 of the supporting information.