Predicting dynamic, motion‐related changes in B0 field in the brain at a 7T MRI using a subject‐specific fine‐trained U‐net

Subject movement during the MR examination is inevitable and causes not only image artifacts but also deteriorates the homogeneity of the main magnetic field (B0), which is a prerequisite for high quality data. Thus, characterization of changes to B0, for example induced by patient movement, is important for MR applications that are prone to B0 inhomogeneities.


INTRODUCTION
MRI requires a spatially homogeneous-or at least temporarily stable-static magnetic field (B 0 ).For instance, in MRS, intra-voxel B 0 inhomogeneities and temporal frequency changes degrade the spectral resolution, which translates into reduced chemical specificity. 1In MRS imaging, they aggravate artifacts arising from extracranial lipid and unsuppressed water signals. 2In particular, a stable B 0 field is critical for dynamic mapping of metabolites. 3,4n fast MR imaging, B 0 inhomogeneities cause nonlinear image distortions (e.g., for EPI) or image blurring (e.g., for spiral acquisitions). 5For CEST, B 0 inhomogeneities induce frequency offsets 6 which cause systematic errors in quantification.
In vivo MRI examinations are sensitive to subject motion.Those with long MRI sequences or with many repetitions are particularly susceptible to subject motion. 7,8A change in the subject's position causes frequently not only motion artifacts directly via inconsistencies between different parts of k-space, but also indirectly via decreased homogeneity of the B 0 field by positional changes of local field perturbation caused by sources at susceptibility interfaces between the tissues with high difference of magnetic susceptibility such as brain tissue, bone tissue, and air. 9,10he latter is increasingly problematic at ultra-high-field MR scanners (B 0 ≥7T). 11o tackle those issues, several MR-based and external tracking methods have been proposed, which provide information about the change of the patient position, and some of them are able to map the change of B 0 distribution.
MR-based tracking methods consist of short MR sequences (termed navigators), which are for example based on fast gradient echo scans with EPI read-out 12 or are based on the FID signals acquired in the multi coil settings. 13Navigators are temporally interleaved with the main (parent) sequence that requires correction. 14Simple navigators can monitor subject position and more advanced volumetric navigators (vNavs) can even map changes of the B 0 field over time. 15,16However, for vNavs, the acquisition alone can be as long as 500 ms 17 and can thus not be easily inserted into the majority of sequences, especially not those with short TR (frequently <10 ms). 12impler navigators are easier to implement, do not impact the spin history and are easier to include in the parent sequence, but they can only measure global frequency drift and have limited ability to capture the spatial distribution of B 0 changes due to subject movement. 9inally, self-navigation allows motion to be monitored, for example, based on repeated resampling of the k-space center via the parent sequence.Self-navigation does not require additional scans, but reduces the SNR efficiency of most sequences and has limited or no ability to characterize B 0 field changes, depending on the contrast of the main sequence. 18xternal tracking methods use additional hardware.Their advantage over navigators is that motion (detected for example by optical tracking 19,20 ) or changes of the B 0 field (detected for example by NMR probes 21 ) are acquired independently from the MR scanner and are, thus, compatible with every sequence.However, optical or similar tracking systems do not provide information about B 0 field changes.NMR probes are a hardware solution that can track the B 0 changes up to second order of spherical harmonics inside of the subject brain. 22,23While optical tracking is already established as a clinically approved commercial product, an NMR probe system is a highly specialized and costly piece of equipment that is not generally supplied as part of an MRI system.
An approach that combines the benefits of external motion tracking (i.e., independence from the parent sequence, highly accurate tracking with high temporal resolution) with that of internal navigators (i.e., accurate dynamic volumetric B 0 mapping) without their disadvantages, is, thus, highly desirable.Ideally, it would allow improved real-time (or retrospective) correction of both motion and B 0 instabilities.
In recent years, deep learning methods have proved to be successful in uncovering hidden patterns in image data, which can be leveraged to solve complex problems, provided that sufficient training data are available. 24For MRI methods, the image reconstruction 25 as well as the segmentation 26 and many other problems 27 potentially can be overcome by deep learning-based methods.
In this study, we, therefore, propose a neural network (NN) approach to predict changes of the B 0 field within the brain from observed changes of the head position and orientation.

Proposed approach
A U-net is used to predict a B 0 map from the following input: (i) anatomical MRI at the initial position, (ii) initial B 0 map, and (iii) head pose change at a certain time point described via six degrees of freedom.The B 0 maps are predicted for each known head position/time point.The U-net is trained using the data of 11 volunteers and then further fine-trained for each volunteer in the testing dataset using the acquired B 0 -maps of six head positions for each particular volunteer to include subject-specific information and, thus, improve the B 0 -prediction (i.e., mitigate issues with generalizability due to relatively small training dataset).The training dataset is augmented by the physics-driven augmentation.The spherical harmonics up to second order of the shimming system are randomly scaled and added to both B 0 maps of each instance in the training dataset.
The whole proposed method therefore would include the measurement of an anatomical MRI sequence, and a prescan including B 0 -scans for up to six head positions to refine the general network for each specific subject in a short training (∼1 min), while the subject is in the scanner and before any B 0 -sensitive sequences are performed.The fine-trained U-net is then used to predict the B 0 -changes caused by motion, which can be used to correct the data (i.e., in the future on the fly to perform real-time correction).The following subsections provide details about the proposed approach.

Experimental data
All measurements were carried out on a 7T Magnetom+ MR Scanner (Siemens Healthineers, Erlangen, Germany) with a 32-channel head coil (Nova Medical, Wilmington, MA).A total of 15 healthy volunteers (11 males and 4 females) were included in this study.The study was approved by the Ethics Committee of the Medical University of Vienna and written informed consent was obtained from all volunteers.
The B 0 maps were acquired at 30 random head positions per volunteer.All volunteers were asked to change their head positions randomly, to cover the possible range within the head coil.The first head position was identical to that for the MP2RAGE scans.At each head position, two sequences for B 0 mapping were run: (i) 2D multi-echo gradient echo (GRE) sequence with nominal resolution of 1.9 × 1.

Experimental data for physics-driven augmentation
In a separate experiment, measurements with a spherical phantom were used to map the first-and the second-order spherical harmonics of the shimming system of the 7T Magnetom+ MR Scanner via the same multi-echo GRE sequence described above.B 0 shimming was performed using the standard automatic shim procedure and the initial B 0 map was measured.The current amplitudes for each spherical harmonic term were manually altered four times from its initial B 0 shim setting in a linear fashion (−100, −50, 50 and 100 μT/m n , where n is the order of the spherical harmonic).After each modification, another B 0 map was acquired.These data were later used for data augmentation in the NN training.

Pre-processing of experimental data
For each head position, B 0 maps were calculated from the GRE sequence and the EPI-based sequence.GRE-based B 0 maps were calculated from the magnitude and phase images coil combined by ASPIRE, 29 and phase unwrapped using ROMEO. 30B 0 maps from the 2TE-EPI sequence were calculated as Hermitian inner product. 31GRE-based B 0 maps were acquired in high spatial resolution with multiple TE to estimate B 0 inhomogeneity.For the NN training, GRE-based B 0 maps were considered the ground truth.Low spatial resolution EPI-based B 0 maps are equivalent to the dual-echo navigators, which can be used to estimated B 0 inhomogeneity in the dead time of the parent sequence. 15P2RAGE data were transformed to different head positions using FLIRT from the FSL toolbox 32 by applying transformation matrices from the co-registration of the first position to the other positions using the magnitudes of the first echoes.MP2RAGE datasets were also used to calculate brain masks (BET, FSL toolbox 32 ), which were transformed in the same way as described above.
Spherical harmonics of the first and the second order of the shimming system (i.e., X, Y, Z, XY, ZY, Z2, ZX, X2-Y2) 11 were characterized using the five B 0 maps with different shim current amplitudes.The measured B 0 field associated with each shim term was fitted with the respective analytical spherical harmonic function 33 by a nonlinear curve fitting solver in Matlab. 34he training dataset consisted of the 319 instances from 11 volunteers.Each instance contained the input: (i) anatomical MRI (i.e., T1-weighted MP2RAGE) at the initial position, (ii) B 0 map at initial position, and (iii) the same anatomical MRI, but after applying the 6DoF transformation to the new position.The transformation matrices calculated from the co-registration were used.The output consisted of the B 0 map at the new position.
Augmentation of the training dataset was performed during each epoch of the network training by adding the same, randomly-scaled spherical harmonic B 0 fields to both input and output B 0 maps of one instance.The spherical harmonics are normally used for B 0 shimming of the volume-of-interest.Thus, that data augmentation is physically meaningful since the changes of the B 0 -maps with motion should not depend on the B 0 shimming, and by adding spherical harmonics B 0 fields, the acquisition of the same volunteer under different shimming conditions is simulated.
The test dataset consisted of the data of four volunteers.The pre-processing was similar to that performed on the training dataset.

Architecture and training of NN
All calculations were performed on a DGX station equipped with Tesla V100 GPU cards (Nvidia, Santa Clara, CA, US).The PyTorch DL framework 35 was used.The U-net architecture was used 36 because of the ability to extract features from the input data at different spatial resolutions which are later used in the decoder part of the network to form a prediction.The network had four levels, with the encoder part at each level containing two 3D convolution layers each followed by the leakyRelu activation.The spatial resolution was decreased with a max-pooling layer by a factor of two.The bottom of the U-net consists of two 3D convolution and one 3D transposed convolution layers, each followed by leakyRelu activation.The decoder part, at each level, consists of two 3D transposed convolution each followed by leaky Relu.The spatial resolution was increase by a trilinear interpolation by factor of 2. All convolutional layers had a kernel size of 5 in all three spatial dimensions and convolutions were performed with a stride of one.The skipped connection was performed as a concatenation of features from the encoder part to the features of the same spatial resolution in the decoder part.At the end, 3D convolution was performed with a kernel size of one.The architecture is depicted in Figure 1.
The training was performed for 2000 epochs with a mini batch of 10.The Adam optimizer was used with a learning rate of 1e-5 and weight decay of 1e-7.For each epoch during the training, the order of the training dataset was randomly permuted and each instance was augmented by the randomly scaled spherical harmonics.The mean-squared error of the unwrapped B 0 map and the prediction formed a loss function.

Fine-training to specific subject
The U-net trained on the training dataset was fine-trained to each subject with a very short training (50 epochs).The first 6 head positions from all volunteers in the test dataset were separated for the fine-training and the 23 head positions were kept for evaluation.The Adam optimizer was used with learning rate of 1e-6, and weight decay of 1e-7.

Evaluation
The accuracy of the subject-specific, fined-trained U-net (NN-FT) was compared to three approaches: (i) no-correction (NC), for which the B 0 map was not updated and directly compared to the initial head position without The 3D U-net architecture used in the study.The input to the network has three features: (i) B 0 map of the initial position, (ii) anatomical reference of the initial position, and (iii) anatomical reference of a new position.The output has one feature: a B 0 map of the new position.any rotation or translation; (ii) prediction of NN, which was not fine-trained (NN); (iii) EPI-based approach (EPI), in which the B 0 maps were measured at the new position with a navigator-like sequence set up.The B 0 maps of all four approaches were compared against the ground truth data (GRE-based B 0 maps) and residua maps, as a difference between a B 0 maps of particular method to the ground truth, were calculated.
The B 0 maps and the residua maps were compared qualitatively.The quantitative analysis was performed using the absolute values of residua maps within the brain mask.For each head position in the testing dataset, median and interquartile range (IQR), as the difference between the 75th and 25th percentile, were calculated of the difference to the ground truth.Boxplots of these values were created, which summarize the approach overall performance on the test dataset.
The fine-training of the NN for a specific subject was analyzed in terms of the required minimum number of head positions used for fine-training training and the number of epochs.Fine-training was tested with three, four, five, and six head positions and in each case the fine-training was performed for 50 epochs.The number of epochs was tested with six head positions and 5, 10, 20, 35, 50, 75, 100, 150, and 200 epochs were tested.The quantitative analysis was run over the residua maps of each fine-training test in the same fashion as describe above.

Accuracy of network prediction
The qualitative comparison of B 0 maps of four approaches and their residua to the ground truth B 0 maps is depicted along with the anatomical references in Figures 2-4, for three representative cases: a mild rotation in the axial plane (Figure 2), a strong rotation in the axial plane (Figure 3), and a rotation in the sagittal plane (Figure 4).The results are presented in three orthogonal planes.The residua maps of the NC approach depict the effect of patient movement on the homogeneity of the B 0 field.In Figures 3 and 4, the residua maps clearly depict the gradient of error.In the sagittal planes, a high amplitude hotspot of error is visible in the frontal lobe in all three figures.The gradients of error in the residua maps are not visible for the EPI-based approach; however, in the sagittal plane in Figures 2 and 4, the small hotspot of error is still visible.For the NN-FT, it is not the case.
Quantitative comparison of overall performance of the four approaches is depicted in Figure 5.The medians and the IQRs of the absolute values of residua maps are compared.The EPI approach as well as NN-FT yield lower absolute residua compared to the NC approach.For the NC approach, the median of the median of the absolute residua was 7.59 Hz, while for the EPI approach it was significantly lower, 3.48 Hz (p-value ≪0.0001), as well as for NN-FT, 3.45 Hz (p-value ≪0.0001).There was no significance difference between the EPI approach and the NN-FT (p-value = 0.69).
For the NC approach the median of the IQR of the absolute residua was 10.94 Hz, which was significantly higher compared to the other three approaches: 8.37 Hz (p-value = 2.21e − 5) for NN, 4.82 Hz (p-value ≪0.0001) for EPI approach, 4.48 Hz (p-value ≪0.0001) for NN-FT.The NN-FT results are significantly lower than the NN (p-value ≪0.0001).There was no significant difference between NN-FT and the EPI approach (p-value = 0.57).
A quantitative comparison of methods for one volunteer is depicted in Figure 6.A total of 23 head positions are evaluated.Boxplots of absolute residua maps for each method at each head position are plotted.For the NC approach and the NN, the medians of absolute residua are above 5 Hz in all cases.For the EPI approach and the NN-FT, the medians in all case are Comparison of B 0 maps at a new head position along with anatomical reference images and B 0 maps at the initial position, which are displayed for three orthogonal planes.A case of mild rotation in the sagittal plane is depicted.An arrow in the axial plane points to the gradient of B 0 inhomogeneities.Arrows in the sagittal plane point to the residual error of hotspots in the frontal lobe in the case of the EPI-based method, which is compensated by subject-specific fine-trained NN.The B 0 maps for three correction approaches [i.e., (i) EPI-based approach (EPI), (ii) predicted B 0 map from not fine-trained NN (NN), and (iii) predicted B 0 map from subject-specific fine-trained NN (NN-FT)] are compared with the ground truth B 0 maps.The residua to the ground truth B 0 map at the new position are shown below each estimated B 0 map together with the RMS error metric for the given residua map.below 5 Hz.Moreover, the average of upper quartiles is 5.58 Hz for the EPI approach and 5.19 Hz for the NN-FT.

Analysis of fine-training procedure
Quantitative results of the fine-training evaluation are depicted in Figure 7 in terms of number of epochs and in Figure 8 for the number of brain volumes used for the fine-training.The effect of using a different number of epochs for the fine-training was evaluated in a range between 5 and 200 epochs.In Figure 7, section A, a trend of decreasing of the median of the absolute median residua can be observed in a range between 5 and 50 epochs.In a range between 50 and 200 epochs, the difference in the median values were not observed.
The IQR metric followed the same trend, as shown in Figure 7, section B. Only in the range between 5 and 50 epoch of fine-training, the values were decreasing.For the fine-training, which lasted longer than 50 epochs, there were no differences compared to the case of 50 epochs of the fine-training.
The number of volumes used for the fine-training were compared in a range of three to six brain volumes.There were no major differences for the median of the absolute median residua, depicted in Figure 8, section A, nor for the IQRs of the absolute median residua, depicted in Figure 8, section B.

DISCUSSION
This work demonstrates the proof-of-principle for a method to predict motion-induced B 0 changes via a NN Comparison of the medians (section A) and the IQRs (section B) of the residua maps between four tested approaches and the ground truth for the test dataset.The approaches are: no-correction (NC), prediction by the non-fine-trained NN (NN), EPI-based B 0 mapping (EPI), and prediction by the fine-trained NN (NN-FT).
from any available rigid-body head motion logs (e.g., obtained from external motion tracking), an initial B 0 map and an initial anatomical image.The prediction of the B 0 maps was carried out with a U-net trained with the experimentally acquired and augmented data of 11 volunteers.For each volunteer in the test dataset, the network was fine-trained with a small number of subject-specific data and a limited number of epochs.The performance of the network was compared with three other approaches using a test dataset of four volunteers.
B 0 (as well as B1) inhomogeneities can cause severe artifacts in reconstructed images.8][39][40][41][42] Such calibration methods typically require a specific calibration scan at the beginning of each MRI acquisition protocol to correct the apparent inhomogeneities of the B 0 field.The results are then used to set the B 0 correction terms for the following sequences.In case of subject movement, the B 0 field is changing, but the correction terms are not updated, which is analogous to the no-correction approach in our manuscript.Repeated B 0 mapping throughout the acquisition protocol is therefore necessary to account for any temporal instability (e.g., patient movement related B 0 changes).vNavs-typically interleaved with the main (parent) sequence-are able to provide dynamic B 0 estimates, but would often increase the total scan time, lower the SNR-per-unit-time efficiency, or alter the image contrast in an unacceptable way. 16Another option is to use FID-based navigators which utilize multi-channel sensitivity profiles to estimate directly the coefficient of the shim settings. 43,44he FID-based navigator takes only 4 ms to acquire; however, it requires sensitivity profiles that are stable with respect to the measured object, which means that mainly B 0 changes non-originated from motion are detected.In some specific cases (e.g., fMRI), the B 0 maps can be calculated from the phase of single-echo EPI sequences.Some of those methods require modification to the sequence which may not be desirable, such as jittering the TE, 45 and it has been shown that even for an approach which uses unmodified, single-echo EPI, 46 careful consideration of eddy currents and appropriate corrections are necessary. 47Our NN approach has similar accuracy to those methods but is more flexible, in that it is expected to be applicable to fast imaging with non-Cartesian readouts (such as spiral and wave).It is also capable of predicting the change of the B 0 with high temporal resolution without measuring extra data during the subsequent sequences in the particular volunteer's MRI acquisitions.If motion information can be acquired externally, for example by optical tracking or directly from the MR data, no sequence parameter changes are necessary for our proposed NN method, which relies only on an accurate knowledge of the transformation matrices describing the rigid-body motion.The fine-training procedure depends on the limited number of subject-specific data, which can be acquired at the beginning of the MR investigation protocol.
In recent years, deep learning methods have been applied in the reconstruction of MRI data, 27 mainly assuming that the acquired k-space data are artifact-free.A small number of methods have been proposed which reduce or remove some artifacts arising from B 0 inhomogeneities but this is, to the best of our knowledge, the first which directly predicts B 0 map inhomogeneities.In the context of distortions in EPI images caused by B 0 inhomogeneities, deep-learning-based methods have been proposed to directly predict distortion free images. 48,49nother deep-learning based approach was designed to compensate for the artifact due to B 0 fluctuations arising from respiration in multi-slice GRE by predicting the phase error term from the corrupted images. 50In contrast, our approach is less direct, but more flexible.

F I G U R E 6
Quantitative results of one volunteer.The boxplots of the absolute B 0 residua to the ground truth for four tested approaches at 23 head positions are presented.No-correction (NC), prediction by not fine-trained NN (NN), EPI-based B 0 mapping (EPI), and prediction by fine-trained NN (NN-FT) are compared.The fine-training was performed with 6 brain volumes in 50 epochs.
We have used subject-specific fined-trained NN to predict B 0 maps.In general, this NN-FT approach outperformed NN (i.e., without fine-training) and the NC approach.The results of NN-FT are similar to those obtained with the EPI approach.The NC method yielded the highest medians of B 0 residua as well as IQRs.The B 0 residua maps shows the left-right gradient of error in the axial and the coronal plane.The sagittal plane frequently shows error hotspots in the frontal lobe.Those effects are in agreement with a previously published analysis. 51he NN approach, at some test positions yielded slightly better results compared to the NC approach.The quantitative comparison showed improvement in the medians and the IRQs of B 0 residua maps.From the investigation of methods per single head position, the NN had similar performance for each position, no matter how severe the error of the NC approach was.The residua maps of the NN shows a reverse gradient of the error compared to the NC approach.However, the B 0 maps themselves have similar features compared to the NN-FT.The main difference is in their magnitude.
NN-FT results were similar to those with the EPI approach in several investigations.The B 0 maps of both methods are comparable to the ground truth.Their B 0 maps residua did not contain the left-right gradient and the frontal lobe hotpot, which are typical B 0 inhomogeneities originating from subject movement.Quantitative results showed the same results for the median and IQRs of the absolute B 0 map residua in the overall comparison of the methods as well as in the comparison of methods per head volume.
The EPI approach and the fine-training required acquisition of additional subject-specific data.However, while the EPI approach acquires data during the whole scan, the data for fine-training are only acquired at the beginning of the MR protocol as a prescan.Once the network is fine-trained for a specific subject, only the tracking of movement is required.These motion logs could be acquired via several internal or external methods. 12The one most independent from the MR acquisitions, and hence the most versatile, is optical tracking, in which information about the movement is sampled at a very high temporal rate up to 80 Hz. 20 Another approach with minimal interference to the MR acquisition is to use navigators based on highly-undersampled kSpace, 52 which takes only 2.3 ms to detect the rigid-body movement.
Acquiring subject-specific additional data (e.g., as prescan) for the MRI reconstruction is common practice for conventional methods.For example, the parallel imaging method GRAPPA requires ACS lines to reconstruct the missing kSpace points. 53Similarly, SENSE requires measured coil sensitivity profiles to disentangle aliased MRI images. 54Subject-specific NN were also proposed by Akçakaya et al. 55 to perform MRI reconstructions.
Our investigation of the subject-specific NN fine-training suggested that the amount of the additional training datasets can be as little as three volumes.The amount of head positions used for training were investigated and no significant differences were shown in the range from three to six datasets.However, there were no special instruction for the fine-training data.Further optimization could, thus, lead to improved results.The fine-training computation should be performed for a sufficient time, however after some point the improvement is saturated.In our case, 50 epochs (which took approximately 1 min without any specific optimization) were sufficient for the fine-training with the three head positions (would take ∼3 min), but further optimization should allow to reduce this well below 1 min.

Limitations and outlook
The paper presents a proof-of-principle, and there are many details that can be improved.The training dataset was created from only 11 volunteers.For each volunteer, only B 0 maps at 30 positions were acquired, and although the distribution of test and training data was similar, more data on a much more diverse group of subjects (e.g., different head sizes) will be necessary to achieve optimal results.It is possible that the performance gap between the fine-trained and the original NN will starting to close, when we train the network with a substantially larger amount of training data, as this will automatically improve the generalizability.To achieve accurate B 0 maps, we acquired five closely spaced echoes with quite a long TR, unwrapped phase data with a robust method 30 and combined data over echoes according to consensus best practice. 56Methodical work shows, however, that, although GRE-based B 0 mapping is the most robust approach among feasible alternatives, 57 discrepancies nonetheless exist between GRE-based B 0 maps acquired with different TR, TEs, flow compensation and gradient polarity. 58As such, they do not represent ground truth values (other than in the narrow context of learning), and improved methods may be proposed.This study demonstrates the ability of our method to reproduce the B 0 maps of the type used in training.We expect that, if those were to be improved in accuracy, they would be equally well reproduced by our 3D U-net approach.
The training dataset was augmented by a physics-driven concept employing spherical harmonics.This augmentation, thus, simulates only the differences in the B 0 shimming of the volume-of-interest.However, the number of head positions remained unchanged.Also, other augmentation approaches and tests on generalizability should be considered.The subject-specific fine-training was performed with six volumes in 50 epochs.
The fine-training volumes were acquired with the same multi-echo GRE sequence as GT B 0 maps with acquisition time of 59 s.In the future, the acquisition time can be further optimized, for example, by reducing the number of echoes or replacing GRE sequence with EPI-based sequence to speed up the acquisition of subject-specific training data.No special instruction were given, which can be improved by a tailored process of fine-training sampling for a given coil.
Future research should involve a combination with external motion tracking hardware and evaluating the benefits for B 0 -and motion-sensitive MRI sequences.Optical tracking could provide updates of the patient position with temporal resolution up to 85 Hz.Another possibility is to combine our approach with the FID navigators.The FID navigators could extract the information about the subject movement, which would be an input for our approach.Currently, the proposed method requires calibration sampling, acquired with the same GRE-sequence as was used for training dataset, for the fine-training and short training.After that the input to the NN consist of anatomical images, the initial B 0 map from the beginning of the measurement protocol, and information of the rigid movement.The prediction of the B 0 map is completely independent from the MR scanner.Thus, the valuable information about the change of the B 0 map due to subjects movement, which is usually available only from lengthy volumetric navigators, could be predicted with the same temporal resolution as is available from rigid-body motion logs.In the future, these predicted B 0 maps could even be used for real-time updating both the MRI volume and the B 0 shim parameters together during the acquisition of the MR data.This can ultimately lead to significantly improved data quality for a range of B 0 -sensitive MRI methods.

CONCLUSIONS
This paper presents the proof-of-principle implementation of a new deep learning-based and subject-specific approach to predicting the change of the B 0 maps due to patient movement.Results were compared to the ground truth and the established EPI-based navigator approach.
Our results suggest that the prediction of B 0 maps is feasible and highly accurate.In combination with external tracking, a considerable improvement in data quality of B 0 -sensitive MRI methods could be expected.

E 2
Comparison of B 0 maps at a new head position along with anatomical reference images and B 0 maps at the initial position, which are displayed for three orthogonal planes.A case of mild rotation in the axial plane is depicted.Arrows point to the hotspots of B 0 inhomogeneities.The B 0 maps for three correction approaches [i.e., (i) EPI-based approach (EPI), (ii) predicted B 0 map from not fine-trained NN (NN), and (iii) predicted B 0 map from subject-specific fine-trained NN (NN-FT)] are compared with the ground truth B 0 maps.The residua to the ground truth B 0 map at the new position are shown below each estimated B 0 map together with the RMS error metric for the given residua map.F I G U R E 3Comparison of B 0 maps at a new head position along with anatomical reference images and B 0 maps at the initial position, which are displayed for three orthogonal planes.A case of strong rotation in the axial plane is depicted.An arrow in the axial plane points to the left-right gradient of B 0 inhomogeneities.An arrow in the sagittal plane points to the B 0 inhomogeneities hotspot in the frontal lobe.The B 0 maps for three correction approaches [i.e., (i) EPI-based approach (EPI), (ii) predicted B 0 map from not fine-trained NN (NN), and (iii) predicted B 0 map from subject-specific fine-trained NN (NN-FT)] are compared with the ground truth B 0 maps.The residua to the ground truth B 0 map at the new position are shown below each estimated B 0 map together with the RMS error metric for the given residua map.

7
Quantitative comparison of the number of epochs for fine-training on the test dataset.A range of epochs was between 5 and 200.The results of fine-training (NN-FT) are plotted alongside other three methods: No-correction (NC), EPI-based B 0 mapping (EPI), and prediction by non-fine-trained NN (NN).(Section A) Comparison of the medians of absolute residua maps.(Section B) Comparison of the IQRs of the absolute residua maps.

8
Quantitative comparison of the number of volumes for fine-training on the test dataset.The range of used volumes was between three and six.The results of fine-training (NN-FT) are plotted alongside other three methods: No-correction (NC), EPI-based B 0 mapping (EPI), and prediction by not fine-trained NN (NN).(Section A) Comparison of the medians of absolute residua maps.(Section B) Comparison of the IQRs of the absolute residua maps.