Rigid real-time prospective motion-corrected three-dimensional multiparametric mapping of the human brain

Purpose: To develop a rigid real-time prospective motion-corrected multiparametric mapping technique and to test the performance of quantitative estimates. Methods: Motion tracking and correction were performed by integrating single-shot spiral navigators into a mul- tiparametric imaging technique, three-dimensional quantiﬁcation using an interleaved Look-Locker acquisition sequence with a T2 preparation pulse (3D-QALAS). The spiral navigator was optimized, and quantitative mea- surements were validated using a standard system phantom. The eﬀect of motion correction on whole-brain T1 and T2 mapping under diﬀerent types of head motion during the scan was evaluated in 10 healthy volunteers. Finally, six patients with Parkinson’s disease, which is known to be associated with a high prevalence of motion artifacts, were scanned to evaluate the eﬀectiveness of our method in the real world. Results: The phantom study demonstrated that the proposed motion correction method did not introduce quantitative bias. Improved parametric map quality and repeatability were shown in volunteer experiments with both in-plane and through-plane motions, comparable to the no-motion ground truth. In real-life validation in patients, the approach showed improved parametric map quality compared to images obtained without motion correction. Conclusions: Real-time prospective motion-corrected multiparametric relaxometry based on 3D-QALAS provided robust and repeatable whole-brain multiparametric mapping.


Introduction
Multiparametric mapping enables the acquisition of multiple tissue properties for the non-invasive and objective characterization of biological tissues in a single acquisition. While conventional contrast-weighted images are mainly used for visual assessments, quantitative multiparametric mapping allows for an assessment based on absolute physical quantities, which has the potential to allow for more objective clinical decision-making ( Seiberlich et al., 2022 ). Several rapid multiparametric mapping techniques have been thoroughly researched ( Deoni et al., Abbreviations: 3D, three-dimensional; 3D-QALAS, interleaved Look-Locker acquisition sequence with T2 preparation pulse; CV, coefficient of variation; FOV, field of view; LOA, limits of agreement; MRI, magnetic resonance imaging; SpNav, spiral navigator pulse sequences TE, echo time; TR, repetition time; VOI, volume of interest. Fig. 1. Schematic overview of a real-time prospective motion-corrected multiparametric relaxometry with a three-dimensional (3D) quantification using an interleaved Look-Locker acquisition sequence with a T2 preparation pulse sequence. (a) Pulse sequence diagram of the prospective motion-corrected multiparametric mapping. Five acquisitions were performed at equal time intervals of 1 s. Spiral navigator pulse sequences were inserted into wait times after 3D segmented data acquisition blocks 3-5. Extended Kalman filter motion correction was performed after the three spiral navigators. (b) Three orthogonal two-dimensional single-shot spiral navigator pulse sequences for image-based motion tracking. SpNav, spiral navigator; Acq, acquisition; EKF, extended Kalman filter. maps. Moreover, the artifacts in the quantitative maps may present different visual characteristics from those typically observed in contrastweighted images. The difficulty of recognizing image degradation on quantitative mapping by visual inspection may result in suboptimal patient management based on incorrect tissue parameters. Thus, it is advantageous to make the acquisition robust to patient motion, especially for patients where movement is anticipated, such as those with movement disorders and dementia.
In conventional magnetic resonance imaging (MRI), various strategies have been proposed to address patient motion during the scan ( Godenschweger et al., 2016 ). One strategy is to acquire redundant data required to perform fitting in anticipation of rejecting motion-corrupted images during a quality control step of the processing; however, this increases the scan time and decreases measurement efficiency, while the retrospective correction may introduce image distortions or artifacts due to interpolation. One effective approach to compensate for participant motion is real-time prospective motion correction, guiding the real-time adjustment of the imaging pulse sequence by tracking participant motion during the scan ( Maclaren et al., 2013 ;Tisdall et al., 2012 ;White et al., 2010 ). Prospective motion correction techniques have already been reported to be useful in conventional structural brain imaging ( Brown et al., 2010 ;Tisdall et al., 2012 ;Watanabe et al., 2016 ).
Despite the emerging potential of multiparametric imaging, only a few studies have reported a motion correction technique for multiparametric imaging ( Cruz et al., 2019 ;Mehta et al., 2018 ;Xu et al., 2019 ). These techniques are based on retrospective motion correction, mainly in two-dimensional (2D) settings. Furthermore, few studies have reported 3D motion-corrected multiparametric mapping ( Callaghan et al., 2015 ;Kurzawski et al., 2020 ), which enables highresolution imaging with whole-brain coverage. This study aimed to develop a real-time prospective motion-corrected multiparametric relaxometry method based on 3D quantification using an interleaved Look-Locker acquisition sequence with T2 preparation pulse (3D-QALAS) ( Fujita et al., 2020 ;Kvernby et al., 2014 ), and to test the performance of its quantitative estimates. We hypothesized that the proposed method will reduce the bias and variance in brain T1 and T2 values induced by participant motion. After optimizing the technique using a phantom, we evaluated the effect of motion correction on various movements in healthy participants. Finally, we evaluated the effects of motion correction in patients to establish a mapping technique that is reliable in clinical settings.

Pulse sequence development
We integrated a real-time prospective motion tracking and correction technique for the original 3D-QALAS sequence ( Fig. 1 ). The 3D-QALAS sequence obtains five image contrasts using a 3D gradient echo sequence, each acquired with segmented Cartesian k-space sampling ( Kvernby et al., 2014 ). Five acquisitions were performed at an equal time interval of 900 ms. The first acquisition was performed after a T2 preparation pulse. The second and subsequent acquisitions were performed during T1 relaxation after an inversion pulse. The data collection used the 3D Cartesian sampling acquisition in a segmented manner with a centric radial fan-beam trajectory. Each point in k-space (Ky, Kz) was sorted by its distance from the center of the k-space and azimuthal angle, grouping the steps of the encoding into multiple blades. Sampling points were close within each blade, thereby making the trajectory immune to eddy current artifacts.
For prospective motion tracking, three orthogonal 2D single-shot spiral navigator pulse sequences (SpNav) were inserted into the wait times in the original 3D-QALAS acquisition . The reconstructed images of the three spiral navigators were input to the extended Kalman filter algorithm ( Kalman, 1960 ) for tracking and correcting translations and rotations in the x-z coordinate system, under the assumption that the head can be regarded as a rigid body. For motion tracking, multiple reference navigators were acquired to isolate the effect of head motion by mitigating the change in image contrast due to T1 recovery between three spiral navigators. In other words, the SpNav had three different reference images that were acquired at the beginning of the scan . Motion estimation was performed with respect to each reference. To focus the extended Kalman filter estimation on the brain itself, areas of the head that often move non-rigidly, such as the jaw and neck, were masked out. The acquisition time of one SpNav image is approximately 15 ms, and the total acquisition time for all three images is 45 ms. We assumed that there is practically no body motion in a time window as short as 45 ms; thus, the effect of the ordering of the three planes could be ignored. The acquisition coordinate system of the pulse sequence was updated in real-time such that the frequency, phase, and slice encoding axes of the image volume were always consistent with respect to the current head position. Partialreacquisitions were performed when the k-space inconsistency exceeded a preset threshold. Details of the SpNav and correction procedures can be found in a previous study .

Spiral navigator optimization
To optimize the flip angle of spiral acquisition used for SpNav, numerical simulations and a phantom experiment were performed to eval-uate the effect of signal saturation caused by the spiral navigations. Both the QALAS and navigator read-outs are based on spoiled gradient-echo acquisitions. The effect of each RF pulse with a flip angle causes the longitudinal magnetization Mz to decrease with a factor cos( ). We implemented the RF pulse shown in Fig. 1 and simulated the behavior of transverse and longitudinal magnetization in a voxel using the Bloch equation. The time course of magnetizations was simulated with T1 and T2 values of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) in the literature ( Drake-Perez et al., 2018 ;Wansapura et al., 1999 ). The effect of the navigator pulse was investigated by comparing the signal characteristics with and without its presence. To estimate the additional estimation error associated with the estimated T1 and T2 values that were caused by a given navigator flip angle, T1 and T2 values were obtained voxel-wise from the five sampling points using exponential fitting. The relative T1 and T2 errors were calculated for each navigator flip angle. To evaluate the effect of signal saturation via Sp-Nav on the image volume, the flip angle of SpNav was optimized with cylindrical phantoms designed to mimic the spin relaxation properties of WM (T1, 588 ms; T2, 79 ms), GM (T1, 808 ms; T2, 99 ms), and CSF (T1, 4061 ms; T2, 1639 ms). The initial position of the spiral navigator was automatically computed from the 24 axial spiral images acquired at the beginning of the scan. A navigator slice thickness of 10 mm was used to emphasize the saturation effect caused by SpNav. Flip angles of 0, 3, 10, and 30 °were tested for parameter optimization.

Phantom validation experiment
To evaluate the effects of signal saturation caused by spiral navigators on quantitative mapping, we first evaluated the quantitative accuracy of the proposed technique on an International Society of Magnetic Resonance in Medicine/National Institute of Standards and Technology (ISMRM/NIST) system phantom ( Keenan et al., 2016 ). To evaluate the effect of spiral navigation scans on quantitative mapping, the NIST/ISMRM system phantom was scanned ten times in an interleaved manner both with and without motion correction ( i.e. , 10 sets both with and without spiral scans). The phantom was kept in a room at a temperature of 20 °C. Since the NIST/ISMRM system phantom consists of liquid-filled spheres, it was set on the scanner at least 30 min before the scan to minimize the effect of motion on the quantification. A spherical volume of interest with a diameter of 10 mm was set in the middle of the spheres with an inner diameter of 15 mm. The mean values were recorded in the spheres covering the typical physiological range of T1 (300-1400 ms) and T2 (50-300 ms) values for human brain tissues. The T1 and T2 values of the clinically relevant range obtained with spiral navigators were compared to those obtained without them. The imaging parameters of this motion-corrected sequence were identical to those of the original 3D-QALAS sequence except for the insertion of spiral navigators.

In vivo validation experiment
Data were collected with the approval of the institutional review board, and all participants provided written informed consent before the scan. This study included 10 healthy volunteers (3 females and 7 males; mean age ± standard deviation [SD], 31.9 ± 11.0 years; age range, 22-63 years). None of the participants had a history of major neurological or psychiatric disorders or cognitive impairments. The thresholds for partial-reacquisitions were empirically set to an L2 norm ( i.e. , the square root of the sum of squares of the range of movement) of ≥ 1 mm or degree in the motion measures between acquisitions . This threshold was set based on (i) the resolution of the navigator image and that of the 3D-QALAS imaging, and (ii) a previous study ( Brown et al., 2010 ). The volunteers were first instructed to remain as still as possible and were scanned with and without motion correction. Next, to assess the effect of motion correction on different head motions, the volunteers were instructed to move in two different ways: (1) sideto-side shaking (producing in-plane motion) and (2) nodding (producing through-plane motion). The volunteers were instructed to intentionally move their heads whenever they heard a buzzer, which was pressed every 30-60 s by a scanner operator. For each head motion type, scanning was performed with and without motion correction. The entire process was then repeated, for a total of ten scans (no motion for two scanning sequences, plus two motion types × two scanning sequences × scanrescan). The order of the scans was permuted for each participant. The participants were blinded to the order of the scans, and the scanning order was counterbalanced across the participants. As a measure of the magnitude of participant motion for each scan, the L2 norm of the range of motion (minimum to maximum) in translation and rotation was computed across scans of both motion types with and without motion correction for each participant. The participants used earplugs instead of headphones and used a standard pillow provided by the scanner manufacturer.
Quantitative T1 and T2 values were estimated for each brain subregion on the maps with and without prospective motion correction. A widely used automated brain segmentation algorithm, FIRST, implemented in FMRIB Software Library software version 6.0.4 ( Patenaude et al., 2011 ), was used to segment brain regions, and these masks were used to obtain regional T1 and T2 values for each scan. The default structures of FIRST were used. We did not use FreeSurfer, another widely used brain segmentation software, because the reconstruction was expected to fail in the case of data with motion artifacts. Since FIRST and other automated brain segmentation software are designed for use with T1-weighted images, synthetic T1-weighted images with post-processed TR of 650 ms and TE of 10 ms were used as inputs for brain segmentation. Since the acquired maps are inherently coaligned, the segmentation on the synthetic T1-weighted images could be readily used as masks for T1 and T2 maps to obtain regional T1 and T2 values. The bilateral values were averaged for subsequent analyses. These regional values obtained with the proposed approach were compared with reference values defined as values acquired with standard 3D-QALAS without head motion and motion correction. Two scans were conducted for each type of motion to assess the repeatability of the quantitative values. The CV was calculated for each condition (combination of the type of motion and presence of motion correction) and plotted against the degree of motion.
To evaluate qualitative image quality, a neuroradiologist (K.K. with 11 years of experience) rated the T1 and T2 maps visually on a 4-point Likert scale as follows: 1 = poor, 2 = fair, 3 = good, and 4 = excellent. All T1 and T2 maps from all participants, regardless of motion correction, were pooled as a single dataset for visual evaluation. The rater was blinded to the motion type and motion correction. To visualize the differences of the quantitative maps, difference maps (maps without motion correction minus those with motion correction) were calculated after registering them using the FSL flirt function ( Jenkinson et al., 2002 ).

Validation in patients with movement disorders
Real-life validation was designed to assess the overall performance of the proposed framework for reducing any motion artifacts in clinical scans under realistic conditions. This study included six patients with Parkinson's disease (four females and two males; mean age, 71.3 ± 8.5 years; age range, 61-83 years; Mini-Mental State Examination, 28.3 ± 1.6; Hoehn and Yahr stage, 3.0 ± 0.6). Patients with Parkinson's disease have difficulty in generating intentional movement and preventing involuntary movements, such as bradykinesia, tremor, and levodopa-induced dyskinesia, and are known to show a high prevalence of motion artifacts in standard MRI examinations ( Mangia et al., 2013 ). Data were collected with the approval of the institutional review board, and all participants provided written informed consent before the scan. The patients were instructed to remain as still as possible during the scan. Each patient was scanned with and without prospective motion correction with identical imaging settings used in the healthy volunteer scan. Since unintentional body movements were expected to occur more often in the latter stage of the MRI scans, the order of the scans was counterbalanced across participants. Brain segmentation was performed as described in the section on healthy volunteers.

Statistical analyses
R version 3.3.0 (R Core Team, 2016). R: Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https:// www.R-project.org/ ) with the tidyverse package was used for all statistical analyses ( Wickham et al., 2019 ). For each anatomical region, scan-rescan repeatability was assessed by the coefficient of variation (CV), which is defined as the ratio of the SD to the mean ( i.e. , lower CV indicates higher repeatability). Bland-Altman plots were generated to assess the agreement between repeated measurements across brain regions. The limits of agreement (LOA) were defined as the mean ± 1.96 × SD of the difference between the scan and rescan values.
We hypothesized that using motion correction would increase the accuracy (decrease difference from the reference) of quantitative values using those without head motion as reference. To test this hypothesis, we calculated a variable for each observation. To avoid repeated measurements being included in the same testing, we (i) independently evaluated nodding and side-byside, and (ii) used the average value of scan-rescan to exclude the withinsubject repeated measures in the statistic. The above variable was used to conduct the paired Wilcoxon signed-rank test with a null hypothesis of 0. Further, the squared differences from the reference values were compared between the images with and without motion correction using the paired Wilcoxon signed-rank test with a null hypothesis of 0 using the following variable: This test corresponded to a testing difference in SDs with and without motion correction, ignoring the mean difference in two measurements.
We also hypothesized that using motion correction would increase scan-rescan repeatability (decrease scan-rescan variance). To test this hypothesis, the within-participant CV was calculated for each motion type for each metric. These CVs were pooled across participants and the distribution of these CVs using motion correction and without motion, the correction was tested with paired Wilcoxon signed-rank test.
The Wilcoxon signed-rank test was used to compare the Likert scores between images obtained with and without prospective motion correction. The distribution of the magnitude of translation and rotation between scans performed with and without motion correction was compared with Wilcoxon signed-rank test. Results were considered significant if P-values were below the significance threshold (0.05 divided by the total number of testing) after applying the Bonferroni method for multiple-comparison correction. The significance threshold for adjusted P-values was set at 0.05.

Data availability statement
Source codes for the quantitative evaluation of T1 and T2 maps are available at https://doi.org/10.5281/zenodo.5385899 . The acquisition data is not openly available due to restrictions imposed by the administering institution on the privacy of clinical data.

Spiral navigator optimization
In numerical simulations, the time course of magnetizations of the WM and GM using a spiral navigator of 3°showed almost complete overlap with those of 0° (Fig. S1). On the other hand, the simulation showed that minimal signal saturation occurs even at 3°for tissues with very long T1 and T2 values, as demonstrated in the CSF. The simulated errors associated with the estimated T1 and T2 values acquired with different navigator flip angles are shown in Table S1. The simulations showed that the errors associated with the estimated T1 and T2 values acquired with a 3°navigator flip angle were less than 0.9%, except the long T2 value (simulation of T2 = 400 ms) showing an error of 1.6%. The signal saturation effect caused by spiral navigation on source image 4 is shown in Fig. S2. A flip angle of 3°caused no observable signal saturation artifact on the source images in the 3D-QALAS and produced a similar signal profile to that without spiral navigation. Signal saturation was observed on the phantom acquired with flip angles of 10°and 30° (  Fig. S2). Other acquisitions ( i.e. , source images 1-3 and 5) of the 3D-QALAS also showed the same effect. Hence, a flip angle of 3°was used in subsequent analyses.

In vitro validation experiment
The results from the NIST/ISMRM phantom scans are shown in Fig. 2 . Across a wide range of T1 values (approximately between 300 and 1400 ms), values obtained using 3D-QALAS with and without spiral navigation varied by less than 4%. The T1 and T2 values acquired with motion correction showed a strong linear relationship (R 2 = 0.9990 for T1 and R 2 = 0.9992 for T2) with those without ( Fig. 2 ). The 95% LOA for T1 and T2 ranged from − 2.6 to 2.0 ms and − 3.8 to 0.9 ms, respectively. Table S2 shows the L2 norm of the participant's motion for each type of scan. Wilcoxon signed-rank tests revealed no significant difference in the magnitude of translation and rotation between scans performed with and without motion correction ( P < 0.001). The average number ± SD of partial-reacquisitions in the motion-corrected scans was 10.8 ± 5.4 and 8.1 ± 4.4 for in-plane and through-plane motion, respectively. Fig. 3 shows representative T1 and T2 maps of the brain along with the estimated motion plot obtained from a healthy volunteer with intentional side-to-side (in-plane) motion with and without motion correction. Fig. 4 shows representative T1 and T2 maps of the brain along with the estimated motion plot obtained from a healthy volunteer with intentional nodding (through-plane) motion with and without motion correction. The proposed method effectively improved the motion robustness of both motion types. Supporting Information Videos S1 and S2 contain examples in animated Graphics Interchange Format illustrating the through-time spiral navigation data for cases with side-to-side and nodding motions. Fig. 5 shows the accuracy of regional T1 and T2 values of the brain acquired with head motion with and without motion correction. The regional values obtained in the moving brain with motion correction were significantly closer to those obtained in the brain without head motion, compared to the values in the moving brain obtained without motion correction, except for the T1 values in the through-plane motion (T1, P = 0.0019 and P = 0.074 for in-plane and through-plane motion, respectively; T2, Ps < 0.001 for both in-plane and through-plane motions). The difference in quantitative values between those with head motion with motion correction and the reference ( i.e. , no head motion without motion correction) was calculated to be T1, 2.6 ± 1.9%, and 5.0 ± 6.7% for with and without motion correction, respectively; T2, 2.0 ± 2.0% and 2.9 ± 2.2% for with and without motion correction, respectively. Bland-Altman plots of the T1 and T2 values with and without motion correction shown. (c) Bland-Altman plots show the bias introduced by motion correction. The dotted lines represent the agreement limit, which was defined as the mean difference ± 1.96 × SD of the difference between the measurements with and without motion correction.   . 4. Comparison of images with and without correction on a volunteer with intentional through-plane motion. Representative motion tracking and quantitative maps of a healthy volunteer with intentional throughplane ( "nodding ") head motions. The head motion was rigidly tracked in three translational and three rotational directions. (a) Motion tracking time curve of translations and rotations in the x-z coordinate system. (b) T1 and T2 maps acquired with the proposed method and those without motion correction, as well as subtraction maps are shown.

Fig. 5.
Quantitative T1 and T2 measurements in volunteers with head motion. Effect of motion correction on regional quantitative values in automatically segmented volumes of interest using FIRST. Box plots representing the accuracy of regional quantitative values with motion both with and without motion correction compared with scans without motion as references. Regional quantitative values scanned with head motion with motion correction showed closer values to those obtained without head motion than without motion correction, indicating a higher accuracy.
are presented in Fig. 6 for all measurements of all participants. For both side-to-side and nodding motions, relaxation time estimates using motion correction reduced the scan-rescan variance. Quantitative values acquired with motion correction showed smaller LOA than those without motion correction. Fig. 7 shows the repeatability of regional T1 and T2 values obtained from the brain with head motion acquired with and without motion correction. The mean regional CVs with and without motion correction were 1.4% and 2.7% for T1 and 1.2% and 2.1% for T2, respectively. Significant differences in CV were observed in-plane motion for both T1 and T2 ( P < 0.001 and P = 0.002 for T1 and T2, respectively) but not in through-plane motion ( P = 0.142 and 0.089 for T1 and T2, respectively). Compared to the values without motion correction, the CVs with motion correction were lower by 48% and 41% on average for T1 and T2, respectively. Regarding the motion type, the CVs with motion correction were lower compared to the values without motion correction by 48% and 38% for side-to-side and nodding motions, respectively. Importantly, the CVs for the values with motion correction remained small even when the participant exhibited large motions during the scans, while the CVs for the values without motion correction became larger with larger motions ( Fig. 8 ). One subject presented a relatively large CV ( > 10%) in the T2 values associated with less-extreme motion. However, this was due to a mis-segmentation of the brain structure, rather than the malfunctioning of the motion-correction technique.
The qualitative image quality of motion-corrected T1 and T2 maps were both significantly superior to the maps without motion correction ( P values < 0.001 for all combinations of motion type and metrics [ i.e. , T1 and T2], Table 1 ).

Validation in clinical patient scans
The magnitude of patient motion is summarized in Table S3. There was no significant difference in the magnitude of translation and rotation between scans performed with and without motion correction (P values of 0.54 and 0.36 for translation and rotation, respectively). Fig. 6. Quantitative T1 and T2 measurements in volunteers with head motion. Effect of motion correction on regional quantitative values in automatically segmented volumes of interest using FIRST. Bland-Altman plots representing the bias of relaxation times in participants with motion acquired with and without motion correction compared with scans without participant motion acquired without motion correction as references. Data points with motion correction are closer to zero than those without, indicating a smaller variance achieved by motion correction. The solid lines indicating the means of the differences show the bias introduced by the motion correction technique. The dashed lines at ± 1.96 standard deviations from the mean show the limit of agreement. Fig. 7. Repeatability of T1 and T2 measurements in volunteers with head motion. Effect of motion correction on regional quantitative values in automatically segmented volumes of interest using FIRST. Coefficients of variation (CV) were calculated for each scan-rescan set. CVs represent the repeatability of the scans. For both T1 and T2, within-participant CVs were smaller, indicating higher repeatability in motion-corrected scans than in those without motion correction in most of the regions. One patient required one partial-reacquisition with an extra scan time of approximately 5 s using the motion correction technique, whereas the others required no rescans. Examples of T1 and T2 maps for two patients with Parkinson's disease are shown in Figs. 9 and 10 , respectively. An example of results with less extreme motion is shown in Fig.  S3. Acquisitions with and without motion correction showed similar L2 norm values for both patients, indicating that the image quality improvement between the maps was due to motion correction, rather than to different magnitudes of motion during the scan. The other patients showed only small magnitudes of motion and are not shown. Note that no partial-reacquisition was required (the motion was corrected solely by updating the gradient) in the patient shown in Fig. 10 , but the image quality was better with motion correction. The results from the experi-ments on patients once again demonstrated the overall effectiveness of the motion correction for reducing head motion artifacts under real-life conditions.

Discussion
In this study, a motion-robust multiparametric mapping technique was proposed and validated in a standardized phantom, healthy volunteers with intentional head motion, and patients with movement disorders. The proposed approach integrates interleaved spiral navigator scans into 3D-QALAS for real-time image-based position tracking and rigid motion correction. Our results indicate that the proposed Fig. 8. Scatter plots of CV against motion metrics. The CVs were calculated for the scanrescans, and the motion metric is the mean of the sum of the translation/rotation during the scans used to calculate CVs. Note that the red points (without motion correction) tend to show larger CVs with larger degrees of motion metric, while the blue points (with motion correction) show smaller values even for large participant motions. CV, coefficient of variation. Fig. 9. Comparison of images with and without motion correction on a representative patient. Quantitative T1 and T2 maps from a patient with a movement disorder, demonstrating the ability to correct for real-life patient head motion. (a) Motion-tracking time curve of translations and rotations in the x-z coordinate system. (b) T1 and T2 maps acquired with the proposed method and those without motion correction. (Top row) axial maps, (middle row) sagittal maps, (bottom row) coronal maps. Zoom views are shown on the right for each orientation. Motion correction required one partial reacquisition (corresponding to an additional 5 s of acquisition time). The L2 norm of translation and rotation were 6.0 mm and 6.8°for motion-corrected images, respectively, whereas translation and rotation were 7.1 mm and 8.0°without motion correction, respectively. Zoom views are shown on the right for each orientation. Motion correction did not require any extra partial-reacquisitions in this participant. The L2 norm of translation and rotation were 3.5 mm and 7.1 °during acquisition with motion correction, respectively, whereas the corresponding values during acquisition without motion correction were 2.5 mm and 5.2 °, respectively. method can improve the repeatability of T1 and T2 values and reduce bias compared with values acquired without motion correction and improve qualitative image quality. The proposed prospectively motioncorrected 3D mapping method yielding multiple 3D volumetric maps could significantly improve scan workflow, productivity, and information provided and would be feasible in neuroimaging studies and clinical settings.
The proposed motion-correction technique was validated against various motion types (translation and rotation) with different magnitudes. When motion correction was applied, not only was the CV improved (reduced) in almost all regions but the T1 and T2 values were closer to those obtained without motion. The proposed method was more effective at correcting side-to-side (in-plane) motions than nodding (through-plane) motions (CV improvement of 48% and 38%, respectively). In principle, prospective motion correction cannot evaluate the extent to which motion has occurred during the scan from the reconstructed data. This is because the spatial encoding performed by the gradients and radiofrequency pulses is adjusted according to the participant motion to maintain the coordinate system of the scan, and the reconstructed images do not contain the information of the participant motion. Since the motion of the participant cannot be the same in every scan, it can be difficult to distinguish the effect of the prospective motion correction technique on image quality from the effect of varying amounts of participant motion across scans. To overcome this issue, as well as to counterbalance the acquisition ordering in all participants, we tracked the head position even during the scan without motion correction (using spiral navigators but disabling correction). This allowed us to quantify the amount of motion with and without motion correction and to separate the effect of the correction technique from the effect of head movement.
Although the effect of coil sensitivity on the quantitative values could not be fully addressed in this study, we assume that this effect on the parameter estimates is minimal considering that: (1) Since the B0 field is more homogeneous in the head than in other parts of the body, the change in B0 due to body movement is expected to be smaller. (2) The parallel imaging we used is a data-driven reconstruction that estimates k-space weighting factor from the neighboring points to interpolate kspace data that is not acquired. Our approach may be preferable to image-based reconstruction such as SENSE due to its relative motion insensitivity. Also, the parallel imaging technique is used in cardiac and abdominal scans where there is large motion, such as that corresponding to breathing and the heartbeat. In particular, the use of multi-parametric mapping in cardiac imaging is increasing in clinical settings, providing reliable quantitative mapping. Finally, (3) the difference in quantitative values between those with head motion with motion correction and the reference ( i.e., no head motion without motion correction) was calculated to be 2.6 ± 1.9% and 2.0 ± 2.0% for T1 and T2, respectively, in the experiments in scans of healthy volunteers ( Fig. 5 ). This shows the robustness of our technique to the effect of motion, presumably including its effect on the B0 field. Even though regions with large susceptibility inhomogeneity may show relatively large changes in B0 due to head displacement, this is inevitable in most prospective motion correction techniques, as well as in retrospective motion correction techniques.
Retrospective correction requires preset redundant data acquisition to acquire motion information, which increases the imaging time ( Anderson et al., 2013 ;Pipe, 1999 ). This redundant data acquisition is performed regardless of the magnitude of participant motion; thus, the fixed imaging time makes it easy to manage scan scheduling for routine clinical examination. In contrast, the total acquisition time is increased unnecessarily even when there is no motion. Severe motion can cause signal distortion, which cannot be corrected retrospectively. Furthermore, it could be problematic when the reconstructed images turn out to be of poor quality after completing the imaging acquisition or after the patient has left the scanner. In comparison, prospective acquisition, including our proposed method, constantly updates the information in k-space so that the most consistent data can be acquired at any point in time, regardless of when the imaging is completed ( Brown et al., 2010 ;White et al., 2010 ). In our approach, the scan time was maintained by inserting navigators into the inherent wait time of the 3D-QALAS. Rescans were performed for imaging segments with unacceptable motion over a preset threshold, which is a reasonable trade-off to ensure a more reliable measurement with a minor increase in acquisition time, instead of repeating the entire scan. In our study, the extended partial-reacquisition time using the proposed approach in Parkinson's disease was 0-5 s for whole-brain mapping. It is noteworthy that motion during the scan could occur in any patient ( e.g. , sneezing or falling asleep), including cooperative participants. Furthermore, the maximum amount of partial-reacquisition time could be prescribed based on the desired trade-off between the degree of motion correction and additional partial-reacquisition time, depending on the expected amount of motion.
There are few studies on motion-corrected whole-brain multiparametric mapping. A previous study ( Kecskemeti and Alexander, 2020 ) used 3D motion-corrected whole-brain T1 mapping and demonstrated highly reproducible T1 values (CV of 0.8-2.0% for subcortical regions), even in children without anesthesia who moved during the scan. This was comparable with our study, which showed CVs of 1.4% and 1.2% for regional T1 and T2 values, respectively. Another study ( Cruz et al., 2019 ) developed rigid motion-corrected MR fingerprinting for wholebrain T1 and T2 mapping in 2D. Their technique improved the parametric map image quality and accuracy compared to approaches without motion correction. One study reported a multiparametric mapping of the whole brain in 3D using an optical imaging system to capture and correct participant motion ( Callaghan et al., 2015 ). They reported that the CV in cortical subregions showed improvements of 11-25% in scans with participant motion. Although improvement in the metric depends on the magnitude of the motion, our approach showed an average improvement of 48% and 41% for T1 and T2, respectively (our results may be overestimated because the volunteers showed severe motion during scans). Although optical imaging systembased motion detection and correction is a promising approach, it requires installation and modification of the imaging hardware ( e.g. , optical capture system, cables, and processing unit). Our approach offers a prospective motion-corrected multiparametric mapping of the whole brain with high resolution (1.0 mm isotropic), without any hardware modifications.
The higher repeatability and accuracy (defined as closeness to values obtained without participant motion) shown in the in vivo study indicates that 3D-QALAS combined with a prospective-motion correction may serve as an improved neuroimaging tool and robust clinical imaging technique. In a previous study on automated measurement of brain structure, the presence of artifacts reduced the number of rejected scans by 15.8% among 129 patients with Alzheimer's disease, and the most common artifacts affecting approximately half of the rejected scans were motion artifacts ( Holland et al., 2009 ). Reducing rejections of scans due to motion and lower variability in quantitative measurements has a positive effect on the statistical power of detecting differences using brain imaging. In addition, exclusion of scans with motion artifacts may introduce a selection bias in those populations with a high prevalence of participant motion were excluded. For example, cognitive decline may be associated with participant motion during the scan, which could lead to the exclusion of populations with low cognitive function from the analysis. Using our proposed method may not only increase the number of acceptable quality examinations in imaging studies but also lower the selection bias due to image quality degradation caused by participant motion.
One limitation of this study is that since our method is a prospective motion correction technique, it is practically impossible to replicate the same participant motion between scans. However, this is unavoidable when using prospective motion correction techniques and applies to other, previous studies. To address this problem, we performed motion tracking during all acquisitions, even during acquisitions without motion correction, which allowed us to demonstrate the small differences in motion between scans acquired with and without correction. Another limitation of the proposed prospective motion correction approach is that a large portion of the k-space may need to be re-acquired when severe motion is constant, resulting in extended imaging time. However, these situations are rare, and the rescan strategy is robust against occasional large movements. The proposed sequence combining 3D-QALAS and spiral navigations is a gradient-intensive sequence that may cause heating of the gradient system throughout the scan, potentially leading to bias in the measured quantitative values. However, this could be the case concerning most of the rapid multiparametric techniques. For the current sequence, when the gradient coil or gradient amplifier heating is a concern due to gradient duty cycle limits, the TR of the main 3D-QALAS sequence is extended based on the hardware limitation of the MRI scanner, but the TR of the spiral navigator remains the same. Moreover, quantitative values obtained with and without spiral navigations were stable in the NIST/ISMRM phantom ( Fig. 2 ) and healthy volunteers ( Fig. 5 ), which verifies that our method is robust concerning the potential heating of the gradient system. Tissues with extremely long T1 and T2 values ( e.g. , CSF) may not be reliable because 3D-QALAS is not designed to measure CSF in the first place, and also because SpNav may cause slight signal saturation as the numerical simulations demonstrated. Fourth, we used FIRST to segment and obtain regional T1 and T2 values in this study, but not any other software or manual segmentation validation. We did not use FreeSurfer, another widely used brain segmentation software, because the reconstruction often failed with data without motion correction. Fifth, since our method is an image-based motion tracking system, although very rare, noise may be detected as small movements. However, as shown in Fig. 8 , we did not observe any worsening of the CVs in subjects with less extreme motion when using the motion correction technique. Finally, we tested our method only on a particular patient cohort. Future studies focusing on children and patients with dementia will be of interest.
In conclusion, the prospective motion-corrected 3D-QALAS technique demonstrated highly reproducible T1 and T2 values, even in clinical patients who involuntarily moved during scan acquisition. The proposed motion correction did not introduce a large bias in the quantitative values obtained in phantoms and improved the accuracy and repeatability of multiparametric maps in volunteer experiments with both in-plane and through-plane motions.

Conflict of interest and source of funding
Naoyuki Takei, Dan Rettmann, and Suchandrima Banerjee are currently employed at GE Healthcare. This work was supported by Japan Agency for Medical Research and Development (Grant No.: JP19lk1010025h9902); JSPS KAKENHI (Grant Nos.: 19K17150, 19K17177, 19K17244, 18H02772, and 18K07692); Health, Labor and Welfare Policy Research Grants for Research on Region Medical; a grant-in-aid for special research in subsidies for ordinary expenses of private schools from The Promotion and Mutual Aid Corporation for Private Schools of Japan; and Brain/MINDS beyond program from Japan Agency for Medical Research and Development (Grant Nos.: JP19dm0307024 and JP19dm0307101).

Role of the funding source
The funding agencies had no role in study design; in the collection, analysis, and interpretation of data; in the writing of the report; and in the decision to submit the article for publication.

Data availability statement
Source codes for the quantitative evaluation of T1 and T2 maps are available at https://doi.org/10.5281/zenodo.5385899 . The acquisition data is not openly available due to restrictions imposed by the administering institution on the privacy of clinical data.