Rapid and accurate navigators for motion and B0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators

To develop a framework that jointly estimates rigid motion and polarizing magnetic field (B0) perturbations ( δB0$$ \delta {\mathbf{B}}_{\mathbf{0}} $$ ) for brain MRI using a single navigator of a few milliseconds in duration, and to additionally allow for navigator acquisition at arbitrary timings within any type of sequence to obtain high‐temporal resolution estimates.

and/or timing, which allows for higher temporal-resolution motion and B 0 estimates.

K E Y W O R D S
B 0 correction, motion correction, navigators, parallel imaging, reconstruction, scout

INTRODUCTION
Due to long scan times, MRI is susceptible to changes in data acquisition, causing artifacts in the reconstructed images.2][3] Although nonrigid motion is known to occur, 4 head motion is usually approximated as rigid.Similarly, B 0 perturbations (B 0 ) are often represented by a set of low-order spatial basis functions (e.g., to model respiratory-induced B 0 ), although higher-order terms exist (e.g., pose-dependent susceptibility induced B 0 ). 5,6As the higher-order terms are especially relevant at ultrahigh-field MRI, 7 this work, performed at 3 T, only considers the low-order approximation.
][9][10] For both prospective and retrospective motion and B 0 correction, estimates of these time-varying parameters are needed.2][13][14][15] As a second category, data-driven estimation methods estimate changes in motion and B 0 by fitting a motion-and B 0 -informed signal model to the acquired imaging data. 2,7,16,17As a third category, navigators are dedicated encoding blocks added to the sequence that encode relative changes in motion and/or B 0 that can be retrieved using different strategies.9][20][21] Prescan calibration approaches acquire navigator data in the presence of a range of motion and/or B 0 perturbations, which can then be matched to the acquired navigators to retrieve corresponding parameters.3][24] As a third strategy, parameters can be retrieved by matching the navigator data to a low-resolution multi-coil reference image (scout) using a model-based approach.Scout data can be acquired quickly. 25,26For the remainder of this work, navigators using a scout will be referred to as "scout-based navigators."This strategy enables motion estimation from FID signal.FID navigators are short enough so that they can replace or precede image-encoding blocks within the TR of any sequence, which is desirable to provide flexible navigator deployment.Using the idea of a scout acquisition, the SAMER approach was proposed to incorporate the scout data into a data-driven motion estimation to improve accuracy and computation time from more general k-space encodings. 27Subsequently, a "guidance-lines" trajectory (4 k-space lines placed across four TRs in the sequence) was proposed to improve robustness compared with the FID when estimating motion, while minimally affecting the sequence structure. 28lthough scout-based FID navigators have been proposed for either motion or B 0 estimation, 29 a model-based joint estimation of motion and B 0 has not been proposed yet, to the best of our knowledge.Therefore, the first aim of this work is to develop a framework to allow joint motion and B 0 estimation from a single (non-Cartesian) navigator using a separately acquired scout.
State-of-the-art scout-based navigators use a single-contrast scout, limiting their use to certain timings in a sequence in which the navigator contrast matches the scout.Hence, a second aim is to extend this concept to a quantitative scout (Q-Scout) that can predict the navigator contrast at the time of acquisition and enable navigator placement in almost any sequence and/or timing.We propose the "QUantitatively Enhanced parameter Estimation from Navigators" (QUEEN), which leverages the Q-Scout predicted navigator contrast when estimating motion and/or B 0 .
Finally, a navigator trajectory is deployed that encodes the spatial information needed to estimate motion akin to "guidance lines" navigator but is short enough in duration to fit within almost any TR, akin to an FID navigator, to allow flexible usage.Furthermore, as estimating motion and B 0 are not separate problems, a tailored navigator design is desired that allows for joint motion and B 0 estimation.
To summarize, this work's novel components include 1. QUEEN motion and B 0 estimation from navigator data with arbitrary trajectory and contrast; 2. A Q-Scout to predict the navigator contrast at the time of navigator acquisition; and 3. A tailored, fast, motion-and B 0 -sensitized navigator trajectory.

SAMER motion estimation
For volumetric encoding using array receiver coils and Cartesian sampling, the "Scout Accelerated Motion Estimation and Reduction" (SAMER) framework 27 achieves fast motion estimation from a group of k-space readouts by turning the alternating motion and image estimation of the aligned SENSE framework 30 into a single motion estimation.The latter is achieved by replacing the otherwise unknown image x in the forward signal model with a separately acquired reference image (scout): x → x s , as follows: where S are the sensitivity profiles of the coil receiver array; F is the discrete Fourier transform; T(z) is the rigid motion operator with six rigid-motion parameters z; A is the sampling mask; and y is the measured data for all coil elements.As a low-resolution scout, x s is often sufficient to estimate rigid motion, it can be acquired quickly (∼3 s) and therefore contains minimal motion artifacts.Rigid motion estimation is then formulated as the inverse problem: Whereas joint motion and image estimation methods require tailored encoding strategies (e.g., grouping 100 s of carefully placed readouts per motion estimate in DISOR-DER 17 ), the use of a scout allows for less constrained k-space encodings from which to estimate motion.For example, using only 4 k-space readout lines ("guidance lines") still allows reliable motion estimation. 28

Q-Scout-informed signal model
The SAMER framework is suited for estimating motion from a small amount of acquired k-space data that has a matching image contrast to that of the (single-contrast) scout image.Therefore, motion estimation from navigators in non-steady-state sequences, in which contrast is changing, will be limited to those navigators that are contrast-matched to the scout.For example, SAMER estimation in MPRAGE sequences will result in a single motion estimate per inversion recovery, as within-inversion signal changes are currently not modeled by x s .To overcome this, we propose the concept of a Q-Scout that predicts the time-varying navigator signal (Figure 1) x s → Q s (t).The Q-Scout should contain the information needed to predict all relevant contrast variations throughout the navigator acquisition.For example, in steady-state sequences like gradient-recalled echo (GRE), parameter estimation will benefit from modeling T 2 * and baseline B 0 in Q s (t) to accurately describe the temporal signal variation across the navigator acquisition.Analogous to the fixed-contrast scout, the Q-Scout can be acquired at a low resolution to provide accurate estimation of rigid brain motion and low-order B 0 .As such, fast quantitative imaging sequences such as MR fingerprinting (MRF) 31 and echo-planar time-resolved (EPTI) imaging 32 can be deployed to acquire quantitative maps at the required resolution in a 10-20-s timeframe.As this work proposes a novel framework with a focus on introducing individual components (e.g., Q-Scout contrast prediction), dedicated Q-Scout acquisitions have not been developed yet and a proof-of-concept alternative was used instead (see Section 3).

B 0 perturbation-informed signal model
The baseline B 0 is (or can be) known and can be modeled in Q s (t), whereas B 0 cannot.Therefore, this work models B 0 as a separate operator in the forward model.B 0 is represented using a set of solid harmonics (SH) (B 0 = Lc with SH basis L and coefficients c), where c is estimated from each navigator acquisition.The effect of B 0 (and similarly other within-navigator signal changes) is modeled using a time-segmented approach for segments n = 1 ∶ N at time t n and are incorporated in motion-and B 0 -informed signal model, as follows: where A n is the segment-dependent sampling mask; P n is the B 0 -induced phase e 2iB 0 t n = e 2iLct n ; and Q s n is the Q-Scout-predicted navigator contrast at time t n .Note that baseline B 0 is implicitly modeled in Q s n as e 2iB 0 t n .For the remainder of this work, second-order SH are considered, following previous work. 29

Motion-sensitized and B 0 -sensitized navigator design
A navigator trajectory was designed to quickly sample a k-space subset that is sufficient to estimate motion and B 0 .The spiral nonselective (SPINS) trajectory, 33 which is a type of 3D spiral-in trajectory originally designed for transmit (B 1 + )-mitigated RF excitation, is deployed in this work due to its rapid acquisition and sensitivity to rigid motion and B 0 : Arc-like sampling sensitizes signal to rotation and translation.Furthermore, in contrast to spherical-like trajectories, the SPINS trajectory can leverage the SNR at the origin while still sampling k-space features at outer radii.The B 0 sensitivity is obtained by sampling the k-space origin at the start and the end of the navigator trajectory.The SPINS trajectory k(t) was designed using Eqs.( 1)-(3) from Malik et al. 33 with = 3.5 2 π∕4 rad∕ms, v = 3.5 2 ∕4 rad∕ms, and  = 3,  = 1 2 , which were chosen after manual ad hoc parameter testing.The value of k max was set to ∕4 rad∕mm, as scout data at 4-mm isotropic resolution is used in this work.To make the start and end of the trajectory smooth, spline interpolation was performed at both edges.Finally, the navigator duration was minimized using gradient trajectory optimization with a maximum slew rate S max = 100mT∕m∕ms and a maximum gradient G max = 50mT∕m, 34 resulting in a navigator duration of 3.5 ms, which is short enough to fit in almost any TR.A 3D visualization of the trajectory is shown in Figure 1.Because the SPINS trajectory is non-Cartesian, the Fourier transform and sampling mask in Eq. ( 3) have been replaced by the non-uniform Fourier transform A n F →  n as follows:

QUEEN
Although the Q-Scout predicts the time-varying navigator signal Q s n (Figure 1), QUEEN refers to the estimation of motion and B 0 parameters as follows: (5) Motion and B 0 parameters are iteratively estimated using the Levenberg-Marquardt algorithm (see Appendix) as follows:

F I G U R E 1
In the QUantitatively Enhanced parameter Estimation from Navigators (QUEEN) framework, a low-resolution quantitative scout (Q-Scout) can be acquired using a rapid prescan to predict image contrast during navigator acquisition in any type of sequence using the sequence parameters (A) and an appropriate signal model (B).(C) Navigator contrast is included in a motion-informed and δB 0 -informed parallel-imaging model to estimate motion and δB 0 parameters (respectively z and c) using QUEEN.(D) A rapid (3.5-ms), tailored, spiral nonselective (SPINS) navigator trajectory was deployed that can flexibly be inserted in most sequences and/or timings to estimate motion and δB 0 variations, here shown for a steady-state gradient-recalled echo (E.I) and a non-steady-state MPRAGE (E.II).

METHODS
As this work contains multiple novel components, simulations and experiments aim to dissect the behavior and contribution of each component independently.Therefore, the method sections are organized in the following way: • First, Simulations 1 and 2 are performed to test the following two hypotheses: -Hypothesis 1. QUEEN joint motion and B 0 estimation are needed in the presence of B 0 perturbations, and an optimized navigator trajectory is desired; and -Hypothesis 2. Q-Scout contrast prediction is needed when performing QUEEN on multicontrast navigator data.
• Next, Experiments 1 and 2 test these hypotheses in vivo.
• Finally, Experiment 3 is performed to test the third hypothesis: -Hypothesis 3. Image artifacts from motion and B 0 can be corrected using QUEEN-estimated parameters.

Simulations: Pose experiment
Simulation 1 (QUEEN) tests Hypothesis 1 by synthesizing navigator data for a range of poses and B 0 , for both the SPINS and FID navigator.For all synthesized navigator signals, motion is estimated by either ignoring B 0 ("motion only") or joint QUEEN estimation ("motion+B 0 ").Simulation 2 (Q-Scout) tests Hypothesis 2 by synthesizing SPINS navigator data for a range of poses and signal contrasts.Motion is estimated using either the correct navigator contrast (Q-Scout) or a fixed contrast (fixed-contrast scout).Pose parameters for each pose are randomly generated from the uniform distribution ±5 mm, and δB 0 are synthetized to result in a range of −20 → 20 Hz across the head.Further details and results of the simulation can be found in Supporting Information Section 1.

In vivo: Pose experiment
Experiment 1 (QUEEN) tested Hypothesis 1 in vivo by modifying a multi-echo GRE sequence.The SPINS navigator trajectory was inserted before every image readout.The modified GRE sequence was acquired on 2 (consented) adult healthy volunteers (HV) on a 3T scanner (GE UHP; GE Healthcare, Milwaukee, WI, USA) using a 32-element adult head coil array.Additional sequence parameters were as follows: 4.77 ms between RF excitation and SPINS navigator, TE = 9.83/10.72/11.63/12.52/13.43ms, TR = 40 ms, flip angle (FA) = 20 • , 2 − mm isotropic resolution, FOV = 220 × 220 × 220 mm 3 , fat-suppressed excitation using SLfRank pulse design, 35 and acquisition time (TA) = 4 min 15 s.To obtain the navigator and the fully sampled imaging data at multiple head poses, scans were acquired with the subject holding a different static pose within each acquisition (five and seven poses, respectively, for the first and second HV).Additionally, from the second acquisition onwards, the forearms were placed on the chest as an additional source of susceptibility-induced B 0 in the head that has a spatial distribution that can be modeled using the SH basis.The validity of this hypothesis was confirmed when fitting the ground-truth (GT) B 0 with the SH basis L (see Supporting Information Figure S4).Coil sensitivities were estimated using the first echo image of the first pose by using the BART implementation of ESPIRiT. 36,37or each pose acquisition, three processing steps were performed.First, individual echo images were reconstructed using SENSE.Gradient delays were estimated using reversed-polarity reference data.Eddy current effects between odd and even echoes were corrected by removing the nonlinear temporal phase evolution between odd and even echoes.Second, a voxel-wise T 2 *, proton density (PD), and B 0 fitting was performed on all echo images using a mono-exponential fit on the magnitude images (PD and T 2 *) and the phase images (B 0 ).Finally, pose parameters with respect to the first (reference) pose were estimated from SPINS data using QUEEN by either ignoring B 0 ("motion only") or joint QUEEN estimation ("motion + B 0 ").To limit computation time, a subset of only 10 SPINS navigators with a 2-s interval were extracted from each pose.
Q-Scout information was generated by down-sampling the quantitative maps from the reference pose to 4-mm isotropic resolution.Estimated motion and B 0 parameters were compared with the GT: GT motion parameters z GT were obtained from registering the reconstructed images, and GT SH coefficients c GT were obtained by performing a weighted least-squares fit on B 0 GT as follows: where W is brain mask, and B 0 GT is obtained by subtracting the registered B 0 maps.
Experiment 2 (Q-Scout) tested Hypothesis 2 in vivo and used a modified MPRAGE sequence with an incoherent spiral-projection encoding 31 that was adopted for later reconstruction (see subsequently).Additional sequence parameters were as follows: a 8475 − ms TR between inversion times (TR long ), a dummy inversion followed by 47 inversions each containing 500 readouts with a 14.5-ms TR between readout excitations (TR short ), a 15.2-ms dead time between the inversion pulse and the first readout, a 1209.8-msrecovery time between the last readout and the next inversion pulse, TE = 1.56 ms, FA = 8 • , 1-mm isotropic resolution, FOV = 220 × 220 × 220 mm 3 , and TA = 7 min 18 s.A SPINS navigator was placed every 50th TR short to obtain navigator data throughout the entire inversion recovery, totaling 10 navigators per inversion at TI i = 1 + 50(i − 1) × TR short , where i = 1 ∶ 10.Each SPINS navigator replaced the imaging readout and was not inserted before each image readout (resulting in a small 2% loss in imaging efficiency).This sequence was acquired on 2 HVs on a 3T scanner (GE Premier) using a 48-element adult head coil array.For both HVs, five scans were acquired, with the subject holding a different static pose within each scan to get imaging and navigator data in multiple poses.For the first (reference) pose, an additional acquisition at TE = 4 ms was acquired to obtain the baseline B 0 .
To obtain the Q-Scout data in the reference pose, the time-varying image contrast Q s was directly reconstructed from the acquired imaging data to ensure synchronized Q-Scout and imaging data.Temporal volumetric Q s was estimated by using a time-resolved subspace signal model Q s ≅ , where  are the temporal basis functions and  are the corresponding volumetric coefficient maps. 38The value of  is a generated dictionary of signal evolutions for a range of T 1 /T 2 /inversion and B 1 + efficiencies using the extended phase graph framework. 39The value of  is compressed using the singular value decomposition (SVD) to five components.Using the incoherent encoding, 31  was estimated with the pics (parallel imaging and compressed sensing) implementation in BART, as follows: where S are the sensitivity profiles, and  is the nonuniform Fourier transform for the spiral-projection trajectory.Coil sensitivities were estimated by inverse-gridding the acquired data for each coil individually and performing ESPIRiT in BART.
For each pose, two processing steps were performed.First, coefficient maps α were estimated using Eq. ( 8) only to perform image registration and obtain z GT with respect to the reference pose.To reduce computational load, reconstructions were performed directly at 4-mm isotropic resolution.Registration was performed on the first coefficient map.Second, the 10 SPINS acquisitions within the inversion were extracted and used to estimate motion and B 0 parameters (with respect to the reference pose) using either a fixed-contrast scout (arbitrarily taken as TI 2 ∶ Q s = (∶, 101)) or Q-Scout-predicted contrast for each navigator i (Q s i = [∶, 1 + 50(i − 1)]).To limit computation time, a subset of only five inversion recoveries were extracted from each pose.
Because each acquisition contains both the Q-Scout imaging data and SPINS navigators, a self-consistency check was performed within each pose by predicting the SPINS navigator signal using the Q-Scout and the QUEEN signal model.A detailed analysis can be found in Supporting Information Section 2 and resulted in ad-hoc corrections to the navigator data before performing Eq. ( 6).A phase correction was performed for both experiments, and the SPINS trajectory was cropped for Experiment 2 due to signal model imperfections.

3.3
In vivo: Inter-pose motion experiment Experiment 3 (interpose image correction) evaluates the ability to use the QUEEN estimates to correct image artifacts caused by motion and B 0 .A retrospective experiment was performed by synthesizing a k-space data set y synthetic that combined k-space data from five poses into a single data set.Experiment 3.I and 3.II used data acquired in Experiments 1 (GRE) and 2 (MPRAGE), respectively.Image reconstruction was performed on y synthetic using a motion-informed and B 0 -informed signal model, as follows: Where z n and c n are the estimated motion and B 0 parameters for pose n.Equation ( 9) was solved using the MATLAB (MathWorks, Natick, MA, USA) implementation of the preconditioned conjugate gradient algorithm.Experiment 3.I used the first echo image from the multipose GRE data in HV 1.Because the GRE data were Cartesian, k-space from each pose was allocated to y synthetic by binning the first phase encoding into five linear segments.Synthesized data were reconstructed at the original 2-mm isotropic resolution in four different ways: i. "uncorrected": without motion or B 0 modeling (z n = 0, c n = 0, corresponding to SENSE); ii. "motion corrected": using motion estimates from the motion only optimization (z n = ẑnMotion only , c n = 0); iii."motion corrected, B 0 informed": using motion estimates from the motion + B 0 optimization but without incorporating the estimated B 0 into the reconstruction (z n = ẑnMotion+B 0 , c n = 0); and iv."motion + B 0 corrected": using motion and B 0 estimates from the motion + B 0 optimization ( z n = ẑnMotion+B 0 , c n = ĉnMotion+B 0 ) .
Experiment 3.II used a subset from the MPRAGE data to achieve contrast between white and gray matter.Therefore, 40 TR short around TI 3 were extracted from each pose in HV 1.Note that a window of 40 was used, as a single spiral arm per inversion would not yield enough data to reconstruct an image.Because MPRAGE data were non-Cartesian, k-space from each pose was allocated to y synthetic by binning all 47 × 40 spiral arms into five segments.Synthesized data were reconstructed at the original 1-mm isotropic resolution in three different ways, each ignoring the B 0 term in Eq. ( 9) as follows: i "uncorrected"; ii "motion corrected, fixed-contrast scout" using motion estimates from the QUEEN estimation using the fixed-contrast scout; or iii "motion corrected, Q-Scout" using motion estimates from the QUEEN estimation using the Q-Scout.
Reconstructed images x were evaluated by computing the signal to residual ratio (SRR) with respect to the reference image x ref in decibels (dB): SRR = 10 log 10 . The value of x ref is defined as the reconstructed image from y synthetic using the GT estimates in Eq. 9 (for both z n and c n ).All experiments were implemented in MATLAB.For all in vivo experiments, 10 outer iterations of Eq. ( 6) are performed, and non-rigid motion (predominantly in the neck region) was suppressed by focusing the estimation on the superior approximate two-thirds of the inferior-superior FOV. 17 This is achieved by extracting the 21 and 31 most superior elements for both coils, respectively.The element's localization was based on the centroids of the sensitivity maps.Therefore, mean absolute errors (MAEs) of the B 0 estimation in the QUEEN in vivo experiment were computed for the upper two-thirds of the inferior-superior FOV.Estimations were performed on a 46 Intel Gold 5320 2.20 GHz CPU, 305 GB RAM, in which only 10 cores and 10 GB of memory were used during job allocation using Slurm (SchedMD).The longest computation time for a single motion + B 0 estimation was about 7 min.

Simulations
Results of the simulation are shown in Supporting Information Figures S1 and S2.Simulation 2 (Q-Scout) shows that for both translation and rotation, MAE for the fixed-contrast scout is larger (>5 • ) than the uncorrected case when the navigator contrast does not match the fixed-contrast scout.Using the Q-Scout results in consistently lower residuals (< 0.1 mm and 0.1 • ).Finally, the accuracy of the Q-Scout-informed estimation has a small dependency on signal contrast, yielding highest accuracy in the case of high signal amplitude of the corresponding contrast.

In vivo: Pose experiment
Results of the in vivo pose experiments are shown in Figures 2-4.For Experiment 1 (QUEEN), Figure 2 shows the histograms of the absolute errors (referred to as "error histograms") of translation, rotation, and B 0 (Figure 2A-C  improved motion estimates.For HV 1, motion accuracy is < 0.4 mm and 0.4 • , whereas lower motion accuracy is observed in HV 2 (< 0.65 mm and 0.9 • ), which is accompanied by higher absolute pose and B 0 parameters.Temporal evolution of motion estimates within each single-pose acquisition are shown in Supporting Information Figure S5 for HV 1 and give stable estimates.The spatial map of estimated and GT B 0 is shown in Figure 3 for all poses (rows) and HVs (columns).Overall agreement is observed between the estimated and GT B 0 .However, close comparison shows residual field errors.
Results of Experiment 2 (Q-Scout) are shown in Figure 4. Bar plots containing the mean (bar) and SD (line) of the AEs are shown for both translation and rotation parameters (Figure 4.I,II) and both HVs (Figure 4A,B).Each bar plot contains the AEs for the same navigator contrasts (columns) within all inversion recoveries for both the fixed-contrast scout (blue) and Q-Scout (yellow).Motion estimates were compared with the uncorrected case on the right (red).Note that only a single bar for the uncorrected case is shown, as all navigators belong to a single static pose, assuming the same pose parameters for every contrast.Temporal evolution of motion estimates across inversions (within a single-pose acquisition from HV 1) are shown for TI 1−4 in Supporting Information Figure S6 and show stable estimation across inversions.The navigator contrast used for the fixed-contrast scout is indicated in blue.The AEs for the fixed-contrast scout estimation show strong contrast-dependent performance, with the highest error when the navigator contrast diverts from the fixed contrast, reaching even higher AEs than for the uncorrected case.When using the Q-Scout, AEs have limited contrast dependence, with all navigators achieving lower errors than the uncorrected case.The mean and SD of the AE across all poses and contrasts using the Q-Scout is 0.20 ± 0.14 mm/0.35 ± 0.3 • and 0.16 ± 0.17 mm/0.35 ± 0.44 • for HV 1 and HV 2, respectively.

In vivo: Inter-pose motion experiment
Image reconstructions for Experiment 3.I (GRE data) are shown in Figure 5, with different columns referring to reconstructions with different estimation and/or correction methods.The uncorrected reconstruction in Figure 5A shows clear image artifacts.The motion-corrected reconstruction in Figure 5B using the motion-only estimates shows similar image quality and deteriorated SRR (5.6➔4.7 dB).Using the motion estimates from the motion + B 0 estimation in Figure 5C F I G U R E 3 Experiment 1 (QUEEN): Visualization of the QUEEN δB 0 estimation.(A,B) Ground truth (GT) and estimated δB 0 are shown for the first five poses (I-IV) and for both healthy volunteers (HVs).GT δB 0 is obtained from registering the B 0 maps.An anatomical image is added on top as a reference.
shows a strong increase in image quality as well as SRR (5.6➔10.4dB).Furthermore, a reduction of image shading and ringing artifacts is observed (arrow in Figure 5B.III,C.III).When additionally correcting for the B 0 variations in Figure 5D, signal loss in Figure 5C.I (arrow) is additionally removed, and a further increase in SRR is achieved (10.4➔14.2dB).Compared with the reference reconstructions in Figure 5E.I,III, no strong visual differences are observed, although error plots in Figure 5D.II,IV show residual artifacts.Image reconstructions for Experiment 3.II (MPRAGE data) are shown in Figure 6 using the same organization as Figure 5.The uncorrected reconstruction in Figure 6A shows clear image artifacts.The motion-corrected reconstruction in Figure 6B using the fixed-contrast scout motion estimates shows slightly improved image quality and SRR (9.2➔12 dB).Using the motion estimates from the Q-Scout-informed estimation results in a strong increase in image quality (Figure 6C) as well as SRR (12➔21.7 dB).Compared with the reference reconstructions in Figure 6D, no strong visual differences are observed, although error plots in Figure 6C.II,IV show residual artifacts.

DISCUSSION
A method has been presented to estimate both rigid brain motion and B 0 perturbation (B 0 ) from navigators using pre-acquired reference data.We also propose the use of a quantitative scout (Q-Scout) instead of the conventional fixed-contrast scout.This enables contrast prediction throughout the entire acquisition and allows contrast-matched scout data for parameter estimation from arbitrary-contrast navigators.The QUEEN optimization framework was developed to jointly estimate motion Experiment 2 (Q-Scout): Bar plots of the absolute errors in translation (I) and rotation (II) for the motion estimation from in vivo acquired SPINS navigators acquired in different poses and at 10 different contrasts for healthy volunteer (HV) 1 (A) and HV 2 (B).QUEEN motion estimation is performed using a fixed-contrast scout (blue = TI 2 ) and using a contrast-matched scout predicted by the Q-Scout (yellow).Results are compared with the uncorrected case (red).

F I G U R E 5
Experiment 3 (Interpose image correction using GRE data): (A-D) Sagittal and axial view (I,III) of the different motionand δB 0 -informed reconstruction experiments.(E) Error maps with respect to the reference experiment are added below the corresponding reconstructions (II,IV).Experiments and reference reconstructions are defined based on the estimation and correction of both motion and/or δB 0 .SRR, signal to residual ratio.and B 0 from navigators with arbitrary k-space trajectory.A dedicated navigator trajectory (SPINS) was deployed that encodes the k-space information needed to robustly estimate motion and B 0 , while still being short enough (3.5 ms) to be interchangeable with most image readouts during a given TR.Conducted simulations have shown that motion and B 0 can be accurately estimated from SPINS navigator data and that the SPINS trajectory outperforms the FID navigators.Furthermore, the need for a contrast-matched scout during motion estimation was also demonstrated in simulations for navigators placed throughout an inversion recovery.In vivo experiments confirmed the ability to estimate motion and B 0 from SPINS data in a steady-state sequence, with improved performance over the conventional motion-only estimation.In vivo application of SPINS navigators within an inversion-recovery sequence provided consistent performance across all contrasts using the Q-Scout, whereas the fixed-contrast scout was limited to navigators with similar contrast.
Simulation 1 (QUEEN) in Supporting Information Figure S1 confirmed Hypothesis 1 that using the joint motion + B 0 estimation results in improved motion estimation.Although previous work achieves robust motion correction using FID in the absence of strong B 0 , 26 this work shows that in the presence of strong B 0 , FID cannot provide robust motion estimation, and tailored trajectories like SPINS improve the estimation performance.In this first proof-of-concept study, it was only feasible to test a single navigator trajectory, but there is scope to explore optimized trajectory designs.Additionally, a systematic analysis of model imperfections (e.g., gradient imperfections, 40 contribution from fat signal 41 ) and their effect on the QUEEN performance would be useful.Simulation 2 (Q-Scout) in Supporting Information Figure S2 confirmed Hypothesis 2 and shows that matching scout contrast allows for consistent and accurate motion estimation from arbitrary-contrast navigator data.MAEs remain under 0.1 mm and 0.1 • for the added noise level and a pose range of ±5 mm/ .
Experiment 1 (QUEEN) in Figure 2 confirmed Hypothesis 2 and showed overall improved motion estimation in vivo when additionally estimating B 0 in the presence of B 0 perturbations.Additionally, B 0 estimates are consistent with the separately measured GT values.In contrast to the simulations, using the motion-only estimation showed increased motion errors compared with the uncorrected case.Additionally, the MAE levels across poses and HVs of motion estimates using QUEEN is higher than in simulations (∼0.4 mm and ∼0.5 • compared with the 0.1 mm and 0.1 • ) and might not be sufficient to fully correct motion in high-resolution acquisitions.This is hypothesized to be caused by nonidealities in the forward model as well as the uncertainty in the estimated GT parameters obtained using image registration.Detailed analysis of the navigator signal (Supporting Information Figure S3) did show signal contaminations that could not be explained by the Q-Scout and motion/ B 0 -informed model.These signal contaminations could come from multiple effects: First, gradient imperfections could lead to trajectory deviations as well as B 0 variations throughout a single readout.Second, signal from fat tissue that is insufficiently suppressed by the SLfRank pulse (in vivo GRE in the QUEEN experiment) or not suppressed at all (in vivo MPRAGE in the Q-Scout experiment) will add off-resonance signal not included in the signal model.Finally, although the HVs are instructed to hold a static pose during each acquisition, within-scan subject motion could have occurred.Motion estimates across multiple navigators within an acquisition indeed showed small fluctuations, although no strong evidence exists about whether these are related to genuine within-acquisition motion or other effects.
Experiment 2 (Q-Scout) in Figure 4 confirms Hypothesis 2 in vivo, showing that using the Q-Scout to match scout contrast allows for consistent and more accurate motion estimates from arbitrary-contrast navigator data.Although choosing a later time point in the inversion recovery as the fixed-contrast scout could improve the overall baseline performance, this sequence quickly reaches a slow-recovery state with little contrast changes (after the fourth navigator).Moreover, the experiment shows the potential of the Q-Scout in a sequence in which similar contrast is not often achieved (e.g., MRF).Consistent with the observation in Experiment 1, the accuracy of the motion estimates (∼0.2 mm/0.4 • ) is lower than the ones obtained in Simulation 2, and the imperfections mentioned previously for Experiment 1 are likely to have also affected Experiment 2.
Experiment 3 (inter-pose image correction) in Figures 5 and 6 confirmed Hypothesis 3.For Experiment 3.I in Figure 5, motion correction using the motion-only estimation does not improve image quality, whereas motion correction using the motion estimation from the motion + B 0 estimation achieves clear improvements.Additionally, correcting for B 0 further improves images quality, indicating that the B 0 estimates are accurate enough to be used in image reconstruction.For Experiment 3.II in Figure 6, motion correction using the fixed-contrast scout only marginally improves image quality, whereas using the Q-Scout estimation achieves clear improvements.
As a continuation of this work, future research is needed to build these contributions into a robust motion and B 0 correction framework.First, a more in-depth analysis across a larger set of HVs of the acquired signals is needed to see how they are affected by the imperfections/nonidealities mentioned previously.Including the latter should result in higher accuracy and will allow corrected reconstructions at higher resolutions.Similarly, imperfections of the imaging data (e.g., eddy currents) induced by adding the SPINS navigator in the sequence should be verified.If problematic, existing strategies to mitigate this effect can be adopted. 28Second, as this work shows that the Q-Scout and the QUEEN framework can lead to improved motion and B 0 estimations and resulting reconstructions, the success/usefulness of such an approach will be dependent on the ability to rapidly acquire a high-quality Q-scout scan.To provide preliminary data on the feasibility of this, 3D-MRF 31 and 3D EPTI 32 acquisitions were modified to obtain low-resolution PD, T 1 , T 2 , T 2 *, and B 0 maps in 12 s.Results of these acquisitions are shown in Supporting Information Figure S7.As can be seen, promising quantitative maps can be obtained in a short timeframe.However, further optimization in the k-t trajectory design and reconstruction are likely to be required to mitigate remaining artifacts.This will form an important part of our future work in creating an optimized rapid Q-scout scan and investigating how associated model mismatches and imperfections affect the QUEEN estimation.Finally, the proposed framework should be tested in a motion experiment in which the HV is moving throughout the scan.A straightforward extension of the method could be MRF sequences in which several SPINS trajectory navigators are placed throughout the acquisition to provide high-temporal-resolution motion correction.Of course, an increased number of navigators decreases efficiency, so a balance will need to be explored.

CONCLUSIONS
We have developed a framework that jointly estimates rigid-motion parameters and B 0 from navigators.This work builds on current state-of-the-art methods by adding the joint estimation and contrast-matched scout to previously presented scout-informed estimation methods from navigators.Combining a contrast-matched scout with the proposed trajectory allows for navigator deployment in almost any sequence and/or timing, enabling higher-temporal-resolution motion and B 0 estimates.The Levenberg-Marquardt optimization in Eq. ( 6) consists of estimating the motion (z) and B 0 (c) parameters from k-space acquisitions, as follows: = argmin z L(z) (A1.1)

F I G U R E 2
Experiment 1 (QUEEN): Histograms of the absolute errors in translation (A), rotation (B), and voxel-wise δB 0 (C) for the QUEEN estimation from in vivo acquired SPINS navigators acquired in different poses and δB 0 for healthy volunteer (HV) 1 (I) and HV 2 (II).QUEEN motion estimation is performed without (blue) and with (yellow) additionally estimating δB 0 , and results are compared with the uncorrected case (red).Mean values () of each distribution are added to each error histogram.

F I G U R E 6
Experiment 3 (Interpose image correction using MPRAGE data): (A-C) Sagittal and axial view (I,III) of the different motion-informed reconstruction experiments.(D) Error maps with respect to the reference experiment are added below the corresponding reconstructions (II,IV).Experiments and reference reconstructions are defined based on the estimation and correction of motion parameters.SRR, signal to residual ratio.

Figure S3. 2 .Figure S3. 3 .
Figure S3.2.Experiment 1 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.1 (VI.D) A subset of coils (A-D) in Healthy Volunteer (HV) 1. Figure S3.3.Experiment 2 self-consistency check for spiral nonselective (SPINS) navigators and quantitative scout (Q-Scout) data: SPINS navigators acquired within the scout acquisition are compared with the forward model prediction obtained using the Q-Scout imaging data.Self-consistency checks of the magnitude (A) and phase (C) are performed with corresponding errors (B-D) for the first five poses (I-IV) in Healthy Volunteer (HV) 1.The SPINS data shown correspond to the first contrast (TI 1 ).An overlay of the errors from each pose are shown in the bottom row (VI).Figure S3.4.Experiment 2 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.3.(VI.D) A subset of coils (A-D) and contrasts (I-V) in Healthy Volunteer (HV) 1. Contrasts 1-5 correspond to the first TIs (TI 1-5 ).Figure S4.Experiment 1 (QUEEN [quantitatively enhanced parameter estimation from navigators]): Validation of the solid harmonic (SH) fitting of the B 0 between gradient-recalled echo (GRE) acquisitions (here between Poses 1 and 2 for Healthy Volunteer [HV] 1).Rows show an anatomical reference (A), the B 0 between poses obtained by subtracting registered B 0 maps (B), the SH fit (C), and the corresponding absolute error (D).A mask is applied to show tissue only.Note that the B 0 artifact in (B) and corresponding errors in (D) are related to the registration implementation using sinc interpolation.Figure S5.Experiment 1 (QUEEN): Robustness of the quantitatively enhanced parameter estimation from navigators (QUEEN) motion estimation performed on multiple spiral nonselective (SPINS) navigators within gradient-recalled echo (GRE) acquisitions (shown for Healthy Volunteer [HV] 1).A set of 10 SPINS navigators (with an interval of 2 s) are extracted for each pose acquisition and are shown in each row.Columns show the ground-truth (GT) motion estimates from image registration (A), motion estimates from the proposed "Motion + B 0 estimation" (B), and the corresponding errors (C).Errors are small despite no motion regularization being used.Note that a single GT estimate obtained for each pose (hence GT estimates in column [A]) are constant across SPINS navigators.Reconstructions of the single-pose data with and without motion correction are shown in (D) to visualize the effect of motion errors in (C) on the reconstructed images.Labels for translation (Tr) are defined for the right-left (RL), posterior-anterior (PA), and foot-head (FH) directions.Labels for rotation (Rot) are defined for rotation around the FH, PA, and RL axes.Figure S6.Experiment 2 (quantitative scout [Q-Scout]): Robustness of the quantitatively enhanced parameter

Figure S3. 4 .
Figure S3.2.Experiment 1 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.1 (VI.D) A subset of coils (A-D) in Healthy Volunteer (HV) 1. Figure S3.3.Experiment 2 self-consistency check for spiral nonselective (SPINS) navigators and quantitative scout (Q-Scout) data: SPINS navigators acquired within the scout acquisition are compared with the forward model prediction obtained using the Q-Scout imaging data.Self-consistency checks of the magnitude (A) and phase (C) are performed with corresponding errors (B-D) for the first five poses (I-IV) in Healthy Volunteer (HV) 1.The SPINS data shown correspond to the first contrast (TI 1 ).An overlay of the errors from each pose are shown in the bottom row (VI).Figure S3.4.Experiment 2 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.3.(VI.D) A subset of coils (A-D) and contrasts (I-V) in Healthy Volunteer (HV) 1. Contrasts 1-5 correspond to the first TIs (TI 1-5 ).Figure S4.Experiment 1 (QUEEN [quantitatively enhanced parameter estimation from navigators]): Validation of the solid harmonic (SH) fitting of the B 0 between gradient-recalled echo (GRE) acquisitions (here between Poses 1 and 2 for Healthy Volunteer [HV] 1).Rows show an anatomical reference (A), the B 0 between poses obtained by subtracting registered B 0 maps (B), the SH fit (C), and the corresponding absolute error (D).A mask is applied to show tissue only.Note that the B 0 artifact in (B) and corresponding errors in (D) are related to the registration implementation using sinc interpolation.Figure S5.Experiment 1 (QUEEN): Robustness of the quantitatively enhanced parameter estimation from navigators (QUEEN) motion estimation performed on multiple spiral nonselective (SPINS) navigators within gradient-recalled echo (GRE) acquisitions (shown for Healthy Volunteer [HV] 1).A set of 10 SPINS navigators (with an interval of 2 s) are extracted for each pose acquisition and are shown in each row.Columns show the ground-truth (GT) motion estimates from image registration (A), motion estimates from the proposed "Motion + B 0 estimation" (B), and the corresponding errors (C).Errors are small despite no motion regularization being used.Note that a single GT estimate obtained for each pose (hence GT estimates in column [A]) are constant across SPINS navigators.Reconstructions of the single-pose data with and without motion correction are shown in (D) to visualize the effect of motion errors in (C) on the reconstructed images.Labels for translation (Tr) are defined for the right-left (RL), posterior-anterior (PA), and foot-head (FH) directions.Labels for rotation (Rot) are defined for rotation around the FH, PA, and RL axes.Figure S6.Experiment 2 (quantitative scout [Q-Scout]): Robustness of the quantitatively enhanced parameter

Figure S4 .
Figure S3.2.Experiment 1 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.1 (VI.D) A subset of coils (A-D) in Healthy Volunteer (HV) 1. Figure S3.3.Experiment 2 self-consistency check for spiral nonselective (SPINS) navigators and quantitative scout (Q-Scout) data: SPINS navigators acquired within the scout acquisition are compared with the forward model prediction obtained using the Q-Scout imaging data.Self-consistency checks of the magnitude (A) and phase (C) are performed with corresponding errors (B-D) for the first five poses (I-IV) in Healthy Volunteer (HV) 1.The SPINS data shown correspond to the first contrast (TI 1 ).An overlay of the errors from each pose are shown in the bottom row (VI).Figure S3.4.Experiment 2 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.3.(VI.D) A subset of coils (A-D) and contrasts (I-V) in Healthy Volunteer (HV) 1. Contrasts 1-5 correspond to the first TIs (TI 1-5 ).Figure S4.Experiment 1 (QUEEN [quantitatively enhanced parameter estimation from navigators]): Validation of the solid harmonic (SH) fitting of the B 0 between gradient-recalled echo (GRE) acquisitions (here between Poses 1 and 2 for Healthy Volunteer [HV] 1).Rows show an anatomical reference (A), the B 0 between poses obtained by subtracting registered B 0 maps (B), the SH fit (C), and the corresponding absolute error (D).A mask is applied to show tissue only.Note that the B 0 artifact in (B) and corresponding errors in (D) are related to the registration implementation using sinc interpolation.Figure S5.Experiment 1 (QUEEN): Robustness of the quantitatively enhanced parameter estimation from navigators (QUEEN) motion estimation performed on multiple spiral nonselective (SPINS) navigators within gradient-recalled echo (GRE) acquisitions (shown for Healthy Volunteer [HV] 1).A set of 10 SPINS navigators (with an interval of 2 s) are extracted for each pose acquisition and are shown in each row.Columns show the ground-truth (GT) motion estimates from image registration (A), motion estimates from the proposed "Motion + B 0 estimation" (B), and the corresponding errors (C).Errors are small despite no motion regularization being used.Note that a single GT estimate obtained for each pose (hence GT estimates in column [A]) are constant across SPINS navigators.Reconstructions of the single-pose data with and without motion correction are shown in (D) to visualize the effect of motion errors in (C) on the reconstructed images.Labels for translation (Tr) are defined for the right-left (RL), posterior-anterior (PA), and foot-head (FH) directions.Labels for rotation (Rot) are defined for rotation around the FH, PA, and RL axes.Figure S6.Experiment 2 (quantitative scout [Q-Scout]): Robustness of the quantitatively enhanced parameter

Figure S6 .
Figure S3.2.Experiment 1 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.1 (VI.D) A subset of coils (A-D) in Healthy Volunteer (HV) 1. Figure S3.3.Experiment 2 self-consistency check for spiral nonselective (SPINS) navigators and quantitative scout (Q-Scout) data: SPINS navigators acquired within the scout acquisition are compared with the forward model prediction obtained using the Q-Scout imaging data.Self-consistency checks of the magnitude (A) and phase (C) are performed with corresponding errors (B-D) for the first five poses (I-IV) in Healthy Volunteer (HV) 1.The SPINS data shown correspond to the first contrast (TI 1 ).An overlay of the errors from each pose are shown in the bottom row (VI).Figure S3.4.Experiment 2 self-consistency check: The overlay of phase errors across poses from Supporting Information Figure S3.3.(VI.D) A subset of coils (A-D) and contrasts (I-V) in Healthy Volunteer (HV) 1. Contrasts 1-5 correspond to the first TIs (TI 1-5 ).Figure S4.Experiment 1 (QUEEN [quantitatively enhanced parameter estimation from navigators]): Validation of the solid harmonic (SH) fitting of the B 0 between gradient-recalled echo (GRE) acquisitions (here between Poses 1 and 2 for Healthy Volunteer [HV] 1).Rows show an anatomical reference (A), the B 0 between poses obtained by subtracting registered B 0 maps (B), the SH fit (C), and the corresponding absolute error (D).A mask is applied to show tissue only.Note that the B 0 artifact in (B) and corresponding errors in (D) are related to the registration implementation using sinc interpolation.Figure S5.Experiment 1 (QUEEN): Robustness of the quantitatively enhanced parameter estimation from navigators (QUEEN) motion estimation performed on multiple spiral nonselective (SPINS) navigators within gradient-recalled echo (GRE) acquisitions (shown for Healthy Volunteer [HV] 1).A set of 10 SPINS navigators (with an interval of 2 s) are extracted for each pose acquisition and are shown in each row.Columns show the ground-truth (GT) motion estimates from image registration (A), motion estimates from the proposed "Motion + B 0 estimation" (B), and the corresponding errors (C).Errors are small despite no motion regularization being used.Note that a single GT estimate obtained for each pose (hence GT estimates in column [A]) are constant across SPINS navigators.Reconstructions of the single-pose data with and without motion correction are shown in (D) to visualize the effect of motion errors in (C) on the reconstructed images.Labels for translation (Tr) are defined for the right-left (RL), posterior-anterior (PA), and foot-head (FH) directions.Labels for rotation (Rot) are defined for rotation around the FH, PA, and RL axes.Figure S6.Experiment 2 (quantitative scout [Q-Scout]): Robustness of the quantitatively enhanced parameter

Figure S7 .
Prototype quantitative scout (Q-Scout) acquisition: A prototype low-resolution (3-mm and 4-mm isotropic resolution) Q-Scout acquisition was developed by adjusting the gradient waveforms of an echo-planar time-resolved imaging (EPTI; A) and MR fingerprinting (MRF; B) sequence.Quantitative maps for each sequence are shown in (I)-(III).Sequence parameters for the EPTI acquisition are echo spacing = 0.64 ms, TR = 40 ms, and number of echoes = 48.Sequence parameters for the MRF acquisition are single inversion recovery followed by 500 TRs (TR = 12.5 ms, TE = 1.7 ms) with flip angles (FAs) ranging from 10 to 90 .How to cite this article: Brackenier Y, Wang N, Liao C, et al.Rapid and accurate navigators for motion and B 0 tracking using QUEEN: Quantitatively enhanced parameter estimation from navigators.Magn Reson Med.2024;91:2028-2043.doi: 10.1002/mrm.29976APPENDIX evenberg-Marquardt updates for the motion and B 0 parameters