Motion‐corrected 23Na MRI of the human brain using interleaved 1H 3D navigator images

To evaluate the feasibility of motion correction for sodium (23Na) MRI based on interleaved acquired 3D proton (1H) navigator images.


INTRODUCTION
Sodium ( 23 Na) MRI has been established as a noninvasive technique to determine the tissue sodium concentration in the human brain, and numerous studies have revealed new metabolic information for many diseases such as stroke, 1 tumors, 2,3 or multiple sclerosis. [4][5][6] Due to the important role of sodium in the metabolism of human cells, 23 Na MRI is used as a versatile tool in biomedical research. 5,7,8 Although improved hardware capabilities and increased magnetic field strengths have established 23 Na MRI in clinical research, 9 the considerably lower in vivo concentrations, fourfold lower gyromagnetic ratio, and very fast relaxation compared to proton ( 1 H) MRI still cause substantial restrictions in clinical research applications. To reach a reasonable SNR and a spatial resolution of about 2.5-3.5 mm, acquisition times of about 10-15 min are necessary. 10,11 Furthermore, for every patient additional scan time is usually required for adjustment measurements as well as for anatomical 1 H MRI scans, which are used in the image postprocessing (e.g., partial volume correction 12 ). Over such long scan times, at least small motion of the head is very likely to occur and can lead to quantification errors, 10 which may, if unnoticed, result in false clinical conclusions. Furthermore, repeating scans due to motion artifacts is costly. 13 To correct such inaccuracies resulting from head motion, a method that does not prolong scan time and that does not depend on additional devices is desirable. Whereas many approaches have been suggested for 1 H MRI, 14 for 23 Na MRI of the brain, only Lu et al. proposed a 3D 23 Na navigator-based retrospective motion correction, which uses a second echo with lower spatial but higher temporal resolution. 10 However, as a result of the intrinsically low SNR of 23 Na MRI and the fast signal decay, the proposed 8 mm isotropic spatial resolution is only sufficient to correct for relatively large motion amplitudes, and the temporal resolution of about 1 min further limits the correction capabilities. To improve both the spatial and temporal resolution of the navigator images and therefore the precision of the motion correction, performing 1 H acquisitions instead of 23 Na could be a promising approach due to the considerably higher MR signal.
Interleaved or simultaneous dual-nuclear MR acquisitions, where data of two different nuclei are acquired within the same sequence, have been performed at different magnetic field strengths, recently even at modern 3 Tesla clinical systems without the need of hardware modification. 15,16 At 7 Tesla human scanners, however, interleaved dual-nuclear MRI has always been conducted on research systems using additional hardware modifications 17,18 or a special software interface developed by the user. 19 With the recent generation of clinically approved 7 Tesla platforms, interleaved MRI measurements have also been enabled by the manufacturer, which has been demonstrated recently with interleaved 31 P/ 1 H MR spectroscopy. 20 The purpose of this work was to introduce an improved retrospective motion-correction method for 23 Na MRI by interleaving it with 1 H 3D navigator imaging. This was accomplished without applying any hardware modification and without the need of additional acquisition time.

METHODS
All measurements were conducted on a whole-body 7 Tesla MR system (Magnetom Terra, Siemens Healthcare, Erlangen, Germany) with multinuclear capability using a dual-tuned 23 Na/ 1 H head RF coil (RAPID Biomedical, Rimpar, Germany), which consists of a dual-tuned 23 Na/ 1 H quadrature transmit-receive birdcage coil and an additional 32 channel receive-only array for 23 Na MRI. In vivo measurements were performed on six healthy volunteers (4 males, 2 females, 27 ± 7 years) who provided written informed consent before being scanned. The study was approved by the local ethical review board.

Interleaved 23 Na/ 1 H density-adapted 3D radial projection pulse sequence
The motion-correction MRI measurements were conducted using a density-adapted 3D radial projection (DA3DRAD) pulse sequence, 21 which was adapted to allow for interleaved dual-nuclear acquisition with different acquisition parameters for 23 Na and 1 H. The sequence scheme is shown in Figure 1. First, the 23 Na signal is excited and acquired. The idle time before the next 23 Na excitation pulse is then used to acquire 1 H MRI data.

F I G U R E 1
Scheme of the interleaved 23 Na/ 1 H sequence. During every 23 Na repetition time TR 23Na , the acquisition of one 23 Na projection is followed by the acquisition of N 1 H MRI projections with a repetition time of TR 1H such that the complete 23 Na recovery time is used. Both nuclei are excited using rectangular RF pulses with pulse lengths and flip angles of TP 23Na and FA 23Na for 23 Na and TP 1H and FA 1H for 1 H. The signal of both nuclei is acquired by a DA3DRAD readout (TE 23Na /TE 1H and readout duration TRO 23Na /TRO 1H for 23 Na/ 1 H). Every readout is followed by a rewinder gradient. Additionally, a spoiler gradient is used to dephase the remaining 1 H magnetization by 2π per voxel 1 H, hydrogen; 23 Na, sodium; DA3DRAD, density-adapted 3D radial projection projections (28 1 H projections per 23 Na projection), nominal spatial resolution (2.5 mm) 3 for 23 Na and 1 H, and 3D golden-angle projection scheme 22 for 23 Na and 1 H. The 23 Na parameters were adapted from a measurement protocol currently used in clinical studies at our institution.
All images were reconstructed offline using a custom-written MatLab script (MatLab, MathWorks, Natick, MA). The reconstruction was based on re-gridding on a Cartesian grid after density compensation using a Kaiser Bessel kernel with width 4.0 and a twofold oversampling. To increase the SNR and avoid Gibbs' ringing artifacts, a Hamming filter was applied. 23,24 The images were finally obtained by a Fast Fourier Transform of the k-space data, which were zero-filled to a spatial resolution of (1 mm) 3 . Due to the acquisition with a 3D golden-angle projection scheme, an arbitrary number of projections could be used for image reconstruction. 22 The multichannel data were combined using an adaptive combination reconstruction. 25,26

Evaluation of multinuclear acquisition interactions
To evaluate a potential influence of the 1 H navigator acquisitions on the quality of 23 Na MRI, measurements of a spherical phantom (7.5% agarose gel, 100 mmol/L NaCl solution) were conducted. For the single-nuclear comparison measurement, reference data from each individual nucleus were acquired by running the interleaved sequence with either the 1 H or the 23 Na RF power and readout gradients turned off, without changing any of the other parameters (sequence parameters in subsection 2.2). In the following, images acquired with the interleaved dual-nuclear pulse sequence are labeled DA3DRAD IL when signals of both nuclei were excited and acquired, and DA3DRAD 23Na /DA3DRAD 1H when only the 23 Na or 1 H signal was excited and measured. The SNR was calculated using one signal region of interest (signal intensity higher than 35% of the maximum signal intensity) and one noise region of interest (signal intensity lower than 15%/5% of the maximum signal intensity for 23 Na/ 1 H) in the image. 27

Navigator images and motion correction
The navigator images were all co-registered to the first one (I 1 ) using the realign function in SPM12 (Wellcome Trust Centre for Neuroimaging, London, UK) assuming rigid-body motion. The estimated transformation parameters for the translation and (1) of every navigator image I i were then used to directly correct the k-space data of the corresponding 23 Na projections acquired during the same time. First, the rotation was performed by rotating the 23 Na k-space locations and afterward the translation was achieved by applying a phase shift of the 23 Na k-space samples Thereby, S i denotes a 23 Na complex-valued k-space sample acquired during the same time as the navigator image I i , and k S i is the corresponding k-space location. The motion-corrected 23 Na image was then obtained by reconstructing the corrected k-space data.

In vivo motion-correction measurements
To demonstrate the capacity of the proposed motion-correction method, 23 Na/ 1 H interleaved MRI measurements (sequence parameters in subsection 2.2) were performed on a total of six healthy volunteers. For every volunteer, two scans were performed with different motion during the measurement. The motion pattern and intensity were up to the volunteers and not further specified. All 23 Na data sets were reconstructed with and without applying the motion correction, and the images were normalized to the mean signal intensity in a central region of interest in the vitreous humor of the eyes. 28 To demonstrate the benefits of the motion correction, the consistency between the two scans of each volunteer was evaluated for the uncorrected as well as for the motion-corrected images by subtracting the two images after registration and visualizing the distribution of the differences in a histogram. Furthermore, the SD was calculated for the distributions of the uncorrected and corrected images to quantify the improvements.
Additionally, in order to find the optimal number of projections for navigator image registration for the chosen spatial resolution of (2.5 mm) 3 , for two volunteers the described approach was repeated for navigator image data sets reconstructed out of 700, 1400, 2800, and 3500 projections, which correspond to a temporal resolution of 3, 6, 12, and 15 s, respectively. These values result from the chosen parameters (7000 23 Na projections, 28 1 H projections per 23 Na projection) because they provide integer values for the corrected 23 Na projections per navigator image.

Hardware and sequence evaluation
The results of the interleaved sequence evaluation are shown in Supporting Information Figure S1. The 23 Na comparison measurements did not reveal any relevant influence of the additional 1 H acquisitions on the 23 Na image quality. Also, 23

In vivo motion-correction measurements
Despite the relatively low SNR of the images acquired with the 1 H birdcage of the dual-tuned 23 Na/ 1 H head RF coil (see Supporting Information Figure S2), for both volunteer measurements conducted in order to find the optimal number of projections for navigator image registration, the motion correction improved the consistency between the two scans for all evaluated 23 Na images reconstructed using different numbers of projections. The results are shown in Figure 2 (volunteer 1) and Supporting Information Figure S3 (volunteer 2). In both cases, the best consistency between the two scans was achieved with navigator images reconstructed out of 1400 projections. Therefore, in the following, this number of projections was used for the reconstruction of each 3D navigator image data set in all volunteer measurements. This leads to one navigator image data set every 6 s and 140 3D navigator image data sets in total during the interleaved 23 Na/ 1 H MR acquisition. As a result, every single 1 H navigator image data set was used to correct the corresponding 50 consecutive 23 Na projections acquired during the same time.
Exemplary results of the determined motion parameters as well as the 23 Na images with and without motion correction and the differences between uncorrected and corrected images are shown in Figure 3 for volunteer 3 and in Figure 4 for volunteer 4. Furthermore, the distributions of the differences between the uncorrected and

F I G U R E 3
Exemplary measurement results of volunteer 3 for the two consecutive scans (scan 1 (A) and scan 2 (B)). All 23 Na images were normalized to the mean signal intensity in a central region of interest in the vitreous humor. In scan 2, clearly stronger movements were detected. In both cases, differences between the uncorrected and corrected image are visible. Especially for scan 2, the correction clearly improved the image quality and reduced motion artifacts. Furthermore, the difference between the uncorrected and the corrected images of both cases respectively were significantly reduced.

F I G U R E 4
Exemplary measurement results of volunteer 4 for the two consecutive scans (scan 1 (A) and scan 2 (B)). All 23 Na images were normalized to the mean signal intensity in a central region of interest in the vitreous humor. In scan 2, clearly stronger movements were detected. For scan 1, hardly any differences between the uncorrected and corrected image are visible. For scan 2, the correction clearly improved the image quality and reduced all kinds of motion artifacts as signal blurring and wrongly depicted anatomical structures. Furthermore, the difference between the uncorrected and the corrected images of both scans respectively were significantly reduced corrected images of the consecutive scans for all examined volunteers are presented in Figure 5. In all cases, the interleaved motion-correction approach reduced the differences between the uncorrected and the corrected 23 Na images, which proves the increased image accuracy. In the measurements, motion of different intensity and characteristic were detected-abrupt as well as continuous movements. Especially for scans including strong movements with translations of up to 5 mm and rotations of up to 10 • , which showed clear motion artifacts, the image quality was significantly improved, and the corrected images did not exhibit obvious artifacts such as washed-out anatomical structures anymore (in particular, see Figure 4B).

DISCUSSION
In this work, a retrospective motion-correction method for 23 Na MRI, based on interleaved acquired 3D 1 H navigator images, was implemented. The navigator images were obtained without any hardware or software modification as well as without time penalty. The additional 1 H acquisitions did not affect the image quality of 23 Na MRI. The presented approach corrected motion of different characteristics and intensities. For all examined volunteers, it reduced differences between two consecutive scans and therefore improved the 23 Na MR image quality. For strong and abrupt movements persisting during the whole scan, parts of the motion artifacts, especially signal blurring, still remained in the corrected image. For continuous motion during the entire scan and for single strong abrupt movements, no obvious motion artifacts were observed in the corrected images. For all volunteers, apart from general signal blurring, all clear motion artifacts were removed from the images. Thus, the correction may prevent the necessity to repeat measurements. In this study, the spatial resolution of the 1 H navigator images was chosen identical to the 23 Na resolution to get high spatial accuracy in the registration process. If the focus is more on the temporal resolution, the navigator acquisition time could be shortened by using lower 1 H spatial resolutions. This tradeoff between spatial and temporal resolution can always be adapted to the specific needs of the study. With the parameters of this study, one navigator data set was used to correct only 0.7% of the acquired 23 Na projections. This should result in sufficient correction capability for most types of motion, like occasional abrupt or continuous positional changes of the head.
Different methods to correct periodical movements such as cardiac 29,30 or respiratory 31 motion exist for 23 Na MRI. However, these are not suited for correction of aperiodic motion such as motion of the head. Retrospective motion correction of random head movements for 23 Na MRI has only been performed by Lu et al. 10 using a second 23 Na echo with a long TE and was therefore mainly based on the 23 Na CSF signal. Due to the significantly higher 1 H MR signal compared to 23 Na, the proposed interleaved 23 Na/ 1 H approach, as applied in this work, provides a more than elevenfold higher temporal resolution while increasing the spatial resolution of the navigator images by a factor of ∼32 compared to Lu et al. 10 The potential for motion correction is thereby clearly improved. Because a DA3DRAD acquisition with repeated sampling of the k-space center is used for 23 Na MRI, a self-navigated motion-correction approach, as it is known for 1 H MRI 32 , would be another possibility based on 23 Na MRI, which, however, also does not reach the potential of the interleaved 23 Na/ 1 H method due to the significantly lower SNR and the resulting lower spatial and temporal resolution (see Supporting Information Figure S4).
The 1 H navigator data were acquired using a DA3DRAD readout scheme with a golden-angle projection scheme, which offers some beneficial properties. The excitation and acquisition of the 23 Na signal take about 12 ms (i.e., 3 TR 1H ) with the sequence parameters used. Therefore, the 1 H acquisition had to be segmented, and thus no uniform steady state is reached. Although this influenced the contrast of the 1 H navigator images, no artifacts deteriorated the image quality for reliable image registration because the different intensities are distributed over the whole k-space due to the golden-angle projection scheme. 22 Non-segmented 1 H acquisition (e.g., TR 1H > 12 ms) is unfavorable because this would reduce the number of 1 H projections by at least a factor of 3, resulting in accordingly lower temporal resolution of the navigator images. To reach a uniform steady state for 1 H, simultaneous acquisition of 23 Na and 1 H would be a possibility, 18,33 which, however, requires additional hardware and therefore limits applicability. Furthermore, due to the golden-angle projection scheme, the temporal resolution of the navigator image data sets can even be adapted retrospectively, depending on the needs of the study. This has also been of advantage for showing the feasibility of the interleaved method because different parameters and approaches could have been evaluated retrospectively using the same dataset.
Despite these advantages, the 1 H acquisition strategy has not been further optimized and may be improved in order to reach higher spatial or temporal resolution of the 1 H navigator image data sets. Further improvements of the temporal resolution could be achieved by using a sliding-window reconstruction, which is often used for example in myocardial imaging. 34 Because this method, however, does not generally lead to improvements for

F I G U R E 5
Distributions of the differences between the uncorrected and corrected images of the two scans for all six examined volunteers. The SD of the distribution of the uncorrected 23 Na images lies between 2.3% and 6.96%, depending on the motion characteristic of the two scans. For all volunteers, the motion correction reduced the SD of the distribution of the corrected 23 Na images and therefore improved the image quality by increasing the consistency between two consecutive scans the presented application (see Supporting Information Figure S5) without specific further optimization, this may be investigated in future work. Furthermore, other methods already used in 1 H retrospective motion-correction approaches for improving navigator data could be tested. Improvements may, for example, be achieved by using other 1 H excitation strategies such as fat navigators, 35,36 by using k-space sampling trajectories optimized for fast imaging such as EPI 37 or by additionally taking into account projection moments of the 1 H data. 32,38 However, due to the predetermined timing of the 23 Na acquisition and the additional SAR contribution in combination with the reduced quality of the 1 H channel of dual-tuned RF coils compared to RF coils commonly used in 1 H motion-correction studies, the applicability may be limited. In particular, the single channel constraint in our setting, which is a common restriction of dual-tuned RF coils, does not allow for parallel imaging techniques, and multichannel coils might diminish the accuracy of projection moment estimation. 32 The proposed method in this work is expected to work with all kinds of dual-tuned RF coils, for example independent of the number of 1 H channels and the resulting homogeneity.
A disadvantage of the interleaved 23 Na/ 1 H method is the need for a dual-tuned RF coil. Even though 23 Na MRI with RF coils comprising an additional 1 H channel benefit from advantages with localizer and adjustment measurements, single-resonant 23 Na RF coils 39 or dual-tuned X-nuclei RF coils (e.g., 23 Na/ 35 Cl RF coil 40 ) are often used, for which our approach is not applicable. Furthermore, interleaved measurements lead to a higher SAR. Even though this did not influence the choice of the acquisition parameters in the current 23 Na MRI protocol, it may be a limiting factor for other studies using inversion recovery 41 or triple-quantum filtered 42 23 Na MRI that typically have higher SAR.
Our work successfully demonstrates the feasibility of the presented motion-correction approach on a typical subject group size for current technical development MR studies. 43 Because the signal intensities were normalized to vitreous humor, relative deviations of the normalized signal intensity could be derived that should correspond to relative concentration deviations. However, for conclusions about the actual improvement in quantitative accuracy in future clinical 23 Na MRI studies, which will also depend on the characteristics of the examined pathology, quantitative measurements including crucial postprocessing steps for concentration determination such as correction of the coil sensitivity 44 and partial volume correction 12 are required. Our method is particularly promising for applications in studies on patients with neurological disorders such as multiple sclerosis because motion is typically a limiting factor in these cohorts. 45

CONCLUSION
We successfully demonstrated the feasibility of retrospective motion correction in 23 Na brain MRI using interleaved acquired 1 H navigator images. The approach neither affected the 23 Na image quality nor elongated the scan time. Especially regarding the advances in 23 Na spatial resolutions with higher field strength, the presented results are promising for improving image quality in future 23 Na MRI studies.

SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website. FIGURE S1. The 23 Na images of the DA3DRAD IL sequence were compared to the ones acquired with the DA3DRAD 23Na sequence (A) and the 1 H images to the ones of the DA3DRAD 1H sequence (B). All images were individually normalized to the maximum signal intensity of the data set. The mean differences over the whole phantom were (−0.3 ± 1.9) % of the maximum signal value for 23 Na and (−0.06 ± 0.12) % for 1 H. Therefore, in both cases no relevant deviation was observed. FIGURE S2. The dual-tuned 23 Na/ 1 H head RF coil is optimized for 23 Na MRI measurements and the included 1 H quadrature Tx/Rx birdcage so far has only been used for localizer measurements and for performing B 0 -shims based on 1 H. 44 To evaluate the quality of the 1 H quadrature Tx/Rx birdcage, single-nuclear 1 H in vivo measurements of a healthy volunteer were performed using the dual-tuned 23 Na/ 1 H as well as an 1Tx/32Rx 1 H head RF coil (Nova Medical, Wilmington, MA, USA) which is a commercial, frequently used 7 T brain RF coil. 46 These measurements were conducted using a common DA3DRAD sequence with, apart from the pause due to the 23 Na acquisition, parameters identical to those of the DA3DRAD 1H sequence: TR = 3.9 ms, TP = 1.5 ms, TE = 1.3 ms, TRO = 1 ms, FA = 6 • , 3500 1 H projections, nominal spatial resolution 2.5 mm isotropic, 3D golden angle projection scheme. Furthermore, 1 H MRI measurements of a spherical phantom (7.5% agarose gel, 100 mmoL/L NaCl solution) were used to compare the SNR of both RF coils. The SNR was calculated using a ROI in the image and an additional noise scan. 27 The comparison of the 1Tx/32Rx 1 H head RF coil and the 1 H birdcage of the dual-tuned 23 Na/ 1 H head RF coil clearly showed that the image quality of the latter was lower, as expected. Over the whole agarose gel phantom, the 1Tx/32Rx 1 H RF coil provided a five-fold higher SNR than the dual-tuned 23 Na/ 1 H RF coil. In the in vivo measurements, the image quality of the 1Tx/32Rx 1 H RF coil is mainly restricted by undersampling artifacts and not by the SNR for all considered numbers of projections. In contrast, in the images acquired with the 1 H channel of the dual-tuned 23 Na/ 1 H RF coil undersampling artifacts are strongly superimposed by noise. FIGURE S3. Results of the motion correction for volunteer 2 using 700, 1400, 2800 and 3500 projections for the reconstruction of the 1 H 3D navigator image data sets. Exemplary navigator images for the different numbers of projections are presented in (A) to get a visual impression of the image quality. Furthermore, for each number of projections the distribution of the differences between the uncorrected as well as between the corrected images are shown (B). The motion correction improved the consistency between the two scans for all evaluated numbers of projections. The best results were achieved for navigator image data sets reconstructed out of 1400 consecutive projections. FIGURE S4. As a DA3DRAD acquisition with repeated sampling of the k-space center is used for 23 Na MRI, a self-navigated motion correction approach which uses low spatial resolution image data sets with higher temporal resolution reconstructed out of the central part of the k-space. Such a self-navigation was evaluated for volunteer 2 and volunteer 3 and compared to the results of the interleaved 23 Na/ 1 H method. The spatial resolution of the navigator images was empirically chosen to be 10 mm and for the temporal resolution with 6 s (50 23 Na projections per image) the same value as for the interleaved method was used. The reconstruction, co-registration, and evaluation have been done in exactly the same way as for the interleaved 23 Na/ 1 H method. The determined motion parameters for the second scan of volunteer 3 are shown for the self-navigated approach (A) as well as the interleaved 23 Na/ 1 H approach (B). The translation values of the self-navigated method are clearly noisier compared to the interleaved method, especially in H-F-direction. Furthermore, the rotations were not detected properly for the self-navigation and clear deviation compared to the interleaved method can be seen. Furthermore, the distribution of the differences between the uncorrected as well as between the corrected images are shown for the self-navigated and for the interleaved motion correction for volunteer 2 (C, D) and volunteer 3 (E, F). For both volunteers, the self-navigated approach performs clearly worse than the interleaved 23 Na/ 1 H method. FIGURE S5. The 1 H navigator data was acquired using a density-adapted 3D radial projection pulse sequence 21 with a 3D golden-angle projection scheme. 22 As this allows for the reconstruction of an image out of an arbitrary number of consecutively acquired projections, the 1 H navigator data also allow for a sliding window approach to determine the motion parameters. This was evaluated for volunteer 3 and the results were compared to the motion correction method without using the sliding window. Like for the motion correction without sliding window, 1400 consecutive projections were used for the reconstruction of one single 3D navigator image data set. The window step size was chosen to be 350 projections. This leads to 557 3D navigator image data sets in total during the interleaved 23 Na/ 1 H MR acquisition. The reconstruction of the motion corrected 23 Na images and their evaluation was done in