Learning‐based motion artifact correction in the Z‐spectral domain for chemical exchange saturation transfer MRI

Abstract

Purpose

To develop and evaluate a physics‐driven, saturation contrast‐aware, deep‐learning‐based framework for motion artifact correction in CEST MRI.

Methods

A neural network was designed to correct motion artifacts directly from a Z‐spectrum frequency (Ω) domain rather than an image spatial domain. Motion artifacts were simulated by modeling 3D rigid‐body motion and readout‐related motion during k‐space sampling. A saturation‐contrast‐specific loss function was added to preserve amide proton transfer (APT) contrast, as well as enforce image alignment between motion‐corrected and ground‐truth images. The proposed neural network was evaluated on simulation data and demonstrated in healthy volunteers and brain tumor patients.

Results

The experimental results showed the effectiveness of motion artifact correction in the Z‐spectrum frequency domain (MOCO_Ω) compared to in the image spatial domain. In addition, a temporal convolution applied to a dynamic saturation image series was able to leverage motion artifacts to improve reconstruction results as a denoising process. The MOCO_Ω outperformed existing techniques for motion correction in terms of image quality and computational efficiency. At 3 T, human experiments showed that the root mean squared error (RMSE) of APT images decreased from 4.7% to 2.1% at 1 μT and from 6.2% to 3.5% at 1.5 μT in case of “moderate” motion and from 8.7% to 2.8% at 1 μT and from 12.7% to 4.5% at 1.5 μT in case of “severe” motion, after motion artifact correction.

Conclusion

The MOCO_Ω could effectively correct motion artifacts in CEST MRI without compromising saturation transfer contrast.

1. INTRODUCTION

Saturation transfer MRI (ST‐MRI) is an important molecular MRI technique that enables imaging of exogenous or endogenous compounds containing exchangeable protons or molecules. ¹ , ² , ³ Typically, target exchangeable protons in tissue molecules are saturated using an off‐resonance RF pulse, and the saturation is transferred to the surrounding free bulk water protons through direct chemical exchange (CEST), dipolar coupling, or multiple‐step relayed proton exchange, the so‐called relayed nuclear Overhauser enhancement effect (rNOE), resulting in an observable reduction of the water signal. ⁴ , ⁵ , ⁶ The degree of water signal attenuation provides an indirect measurement of the molecular species with exchangeable protons, in a manner related to their concentration and exchange rate. The ability to use these water signal changes to image the biochemical change in tissue offers advantages in understanding the disease mechanisms at the molecular level and assessing treatment responses. For instance, amide proton transfer (APT) imaging that targets endogenous mobile proteins and peptides in tissue has been successfully used to image higher protein content in brain tumors ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² and acidic pH level (which has a one‐to‐one correspondence to exchange rate) in ischemic stroke lesions. ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰

CEST MRI often assesses a so‐called Z‐spectrum, generated by measuring the normalized water signal intensity as a function of saturation frequency offset under varied RF saturation settings, which is time‐consuming and, therefore, vulnerable to artifacts from subject motion. ²¹ Motion induced during k‐space sampling causes spin dephasing or non‐ideal magnetization evolution, resulting in blurring and ghosting effects on saturation‐weighted images. In addition, motion between image acquisitions misaligns a series of saturation‐weighted images. However, intensity‐based motion correction approaches used in conventional MRI are often not applicable to CEST MRI because (1) its signal intensity or contrast changes along a frequency offset dimension; (2) saturation‐weighted images particularly close to the water resonance have very low SNR and little signal information available for motion correction; (3) the choice of a reference image among different saturation‐weighted images highly influences the performance of motion correction; and (4) the saturation pattern varies spatially because of B₀ or B₁ inhomogeneities. In addition, the magnitude of motion artifacts is often comparable with target CEST signal contrast (on the order of 1%), and therefore, the intensity‐based registration algorithms would fail to distinguish CEST signals from motion artifacts. Previously, several retrospective motion correction techniques for CEST MRI have been proposed. The issue of the contrast variation in saturation‐weighted images across frequency offsets was addressed using the low‐rank approximation of the Z‐spectral images (LRAZ). ²² However, the selection of tuning regularization parameters is challenging to balance the contribution of the low‐rank and sparse components. Another previous study used a two‐step robust principal component analysis and principal component analysis (RPCA‐PCA) approach to separate saturation‐weighted images from coarse and fine motion effects, which was demonstrated with 2D preclinical CEST images. ²³ A 3D motion correction method was proposed to use the weighted averaging of motion parameters to mitigate artifacts near the water resonance. ²⁴ However, it was computationally expensive because of the iterative registration algorithm. In addition to the above post‐acquisition motion correction methods, a prospective motion correction with volumetric navigators could be used to capture subject position and coil sensitivity, enabling real‐time corrections of motion during acquisition. ²⁵ , ²⁶ , ²⁷ , ²⁸ However, updating gradients and RF pulses to ensure excitation and acquisition of the same FOV and re‐acquiring k‐space data add extra scan time, which may be undesirable for clinical studies. Optimizing motion correction is especially desirable for patient populations prone to generate more motion artifacts in the scanner, such as brain tumor patients who have poor performance status.

In this study, a deep‐learning neural network was designed to learn motion effects directly from the Z‐spectrum frequency domain (Ω) rather than the image spatial domain. A saturation‐contrast‐specific loss function was added to preserve CEST or APT contrast, as well as to enforce image alignment between motion‐corrected and ground‐truth image domains. This learning‐based motion artifact correction in the frequency offset domain (MOCO_Ω) was evaluated on numerical phantoms, healthy volunteers, and brain tumor patients, and compared with existing methods, such as learning‐based motion correction in the spatial domain (MOCO_xyz), mutual information‐based motion correction (MI), ²⁹ LRAZ, and RPCA‐PCA techniques.

2. METHODS

2.1. Image acquisition

In vivo experiments were approved by the local institutional review board and written, and informed consent was obtained from participants. Seven adult healthy volunteers (four males, three females; mean age, 36.1 ± 9.5) and seven brain tumor patients with glioblastoma (six males, one female; mean age, 50.3 ± 12.7) were scanned using an RF saturation‐encoded multi‐shot turbo spin echo (TSE) sequence with a 32‐channel coil array for signal reception at 3 T (Achieva dStream, Philips Healthcare). Two‐channel parallel RF transmission via a body coil enabled pseudo‐continuous RF saturation beyond the 50% duty‐cycle of a signal RF amplifier. The imaging parameters of the TSE sequence were taken from a previously established protocol ³⁰ , ³¹ : TR/TE = 6500 ms/ 6 ms; FOV = 212 × 192 × 36 mm³; spatial resolution = 1.8 × 1.8 × 4 mm³; turbo factor = 174; and slice sampling factor = 1.4. For compressed sensing acceleration (fourfold), a variable density sampling pattern with a centric elliptical k‐space ordering was used in the two phase‐encoding directions (k_y‐k_z) of the 3D acquisition. The saturation‐weighted images were acquired using parallel RF transmission‐based continuous RF saturation block pulses with frequency offsets of 80, 60, 40, 30, 20, 10, and 8 ppm for semisolid magnetization transfer contrast (MTC) and ± 3, ±3.5, and ± 4 ppm for APT and rNOE measurements, an RF saturation strength of 1 μT or 1.5 μT, and RF saturation durations of 1.5 s for healthy volunteers and 2 s only for tumor patients. The relaxation delay time for healthy volunteers and tumor patients was 2.5 s. An additional unsaturated (S₀) image was acquired for signal normalization. B₀ inhomogeneity effects were corrected using the water saturation shift referencing method. ³²

2.2. Motion simulation

For supervised learning with ground‐truth rigid‐body motion trajectories, “clean” (motion‐free) saturation‐weighted images were used to simulate motion‐corrupted images. The clean images were chosen by estimating motion parameters using statistical parametric mapping (SPM12, Wellcome Department of Cognitive Neurology). In the SPM, six motion parameters (including three‐dimensional translation and rotation parameters) of an affine “rigid‐body” transformation were estimated by minimizing the sum of squared differences between each successive image and a reference image (e.g., S₀) iteratively. The selection criteria were that the sum of motions in the x, y, and z directions would be less than 1.5 mm and the sum of motions in the pitch, yaw, and roll directions would be less than 0.1° individually at all frequency offsets. For simulation, six motion parameters were randomly chosen from the range of ±2 mm translation in each direction and ±1° for rotation angles corresponding to the x, y, and z‐directions (θ_x, θ_y, and θ_z). Three dimensional saturation‐weighted images at each frequency offset, I (x, y, z)_Ω, were translated and rotated as follows:

$$[x,y,z,1]\to [x+\partial x,y+\partial y,z+\partial z,1],$$ (1)

$$I{(z^{\prime },y^{\prime },z^{\prime })}_{\mathrm{\Omega }}=\mathbf{M}\cdot I{(x,y,z)}_{\mathrm{\Omega }},$$ (2)

where M is a transformation matrix, which is a dot product of the translation matrix T and rotation matrix R. The transformation matrix M can be defined as follows:

$$\mathbf{M}=\mathbf{T}\cdot \mathbf{R},$$ (3)

$$\mathbf{T}=\left[\begin{array}{cccc}1& 0& 0& t_x\\ 0& 1& 0& t_y\\ 0& 0& 1& t_z\\ 0& 0& 0& 1\end{array}\right],$$ (4)

$$\mathbf{R}={\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{x}}}\cdot {\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{y}}}\cdot {\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{z}}}.$$ (5)

Where

$${\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{x}}}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos {\mathrm{\theta }}_x& -\sin {\mathrm{\theta }}_x& 0\\ 0& \sin {\mathrm{\theta }}_x& \cos {\mathrm{\theta }}_x& 0\\ 0& 0& 0& 1\end{array}\right],$$

$${\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{y}}}=\left[\begin{array}{cccc}\cos {\mathrm{\theta }}_y& 0& \sin {\mathrm{\theta }}_y& 0\\ 0& 1& 0& 0\\ -\sin {\mathrm{\theta }}_y& 0& \cos {\mathrm{\theta }}_y& 0\\ 0& 0& 0& 1\end{array}\right],$$

$${\mathbf{R}}_{{\mathbf{\theta }}_{\mathit{z}}}=\left[\begin{array}{cccc}\cos {\mathrm{\theta }}_z& -\sin {\mathrm{\theta }}_z& 0& 0\\ \sin {\mathrm{\theta }}_z& \cos {\mathrm{\theta }}_z& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right].$$

In addition, subject motion during k‐space sampling may result in missing k‐space samples and local violations of the Nyquist theorem, leading to additional artifacts, such as blurring, ringing, or ghosting in the reconstructed image. The motion‐corrupted k‐space data was simulated by combining various segments of k‐space data for different motion patterns (Figure 1). Randomly translated (I′_x, I′_y) and rotated images (I′_θ) were Fourier‐transformed (F) to create k‐space data. The motion effect corrupted k‐space data by changing the sampled k‐space trajectory (m₁, m₂, m₃) and accumulating additional phases in each k‐space sample. Next, inverse Fourier transform (F⁻¹) was performed to obtain final motion‐corrupted images, I^k (x′, y′, z′)_Ω in the image space:

$$\begin{array}{cc}& I^{\mathrm{k}}{(z^{\prime },y^{\prime },z^{\prime })}_{\mathrm{\Omega }}\\ & =F^{-1}\left[m_1\times F\left(I_{z^{\prime }}\right)+m_2\times F\left(I_y^{\prime }\right)+m_3\times F\left(I_{\mathrm{\theta }}^{\prime }\right)\right].\end{array}$$ (6)

FIGURE 1.

An illustration of the deep‐learning‐based motion artifact correction framework for CEST MRI. Motion artifacts were simulated by modeling 3D rigid‐body motion and readout‐related motion during k‐space sampling. Next, motion‐corrupted Z‐spectra were normalized by an unsaturated image (S₀). The motion artifact correction network (MOCO_Ω) learned motion effects directly from a Z‐ spectrum frequency domain. The deep learning‐extrapolated semisolid magnetization transfer reference (DeepEMR) network estimated Z_ref (± 3.5 ppm) signals for MTC, APT^#, and rNOE^# images. Z^m (Ω), Z^mf (Ω), and Z^moco (Ω) indicate motion‐corrupted (m), motion‐free (mf), and motion artifact‐corrected (moco) Z‐spectra, respectively. APT^#, free water pool + semisolid macromolecule pool for APT; MTC, magnetization transfer contrast; rNOE^#, free water pool + semisolid macromolecule pool) for relayed nuclear Overhauser enhancement.

2.3. Neural networks

2.3.1. MOCO_Ω

The proposed motion artifact correction network (MOCO_Ω) in the frequency domain consisted of two 1D convolutional layers followed by a flattening operation and five fully connected dense layers (Figure S1). The convolutional layers had 256 filters (f) and 1 × 3 kernel size (k) with a stride (s) of 1. A batch normalization was applied to the convolutional layers. Intermediate dense layers had 256 neurons (n). At the output, the last dense layer had 15 neurons to match the length of the Z‐spectrum. The hidden convolutional and dense layers had a ReLU activation function, whereas the output dense layer had a sigmoid activation function. Motion‐corrupted Z‐spectra, Z^m, were fed to the MOCO_Ω network, which output the motion‐corrected Z‐spectra, Z^moco (Figure 2). The learning of MOCO_Ω can be expressed as follows:

$${\mathrm{\theta }}_1^{\prime }=\underset{{\mathrm{\theta }}_1}{\arg \min }\left({\mathrm{E}}_{Z_{\mathrm{m}}˜P\left(Z_{\mathrm{m}}\right)}\left[{‖{\mathrm{\Phi }}_{{\mathrm{\Omega }}_i}\left(Z^{\mathrm{m}}|{\mathrm{\theta }}_1\right)-Z_{\mathrm{mf}}‖}_2\right]\right),$$ (7)

where ${\mathrm{\Phi }}_{\mathrm{\Omega }}\left(Z^{\mathrm{m}}|{\mathrm{\theta }}_1\right):Z^{\mathrm{m}}(\mathrm{\Omega })\to Z^{\text{moco}}(\mathrm{\Omega })$ is a neural network with trainable parameters (θ₁) and Z^mf are motion‐free Z‐spectra. ${\mathrm{E}}_{Z_{\mathrm{m}}˜P\left(Z_{\mathrm{m}}\right)}[.]$ is an expectation operator with respect to the motion‐corrupted Z‐spectra (Z^m) and belong to the data distribution P (Z^m). Another deep‐learning neural network for semisolid MTC signal estimation, a so‐called deep learning‐extrapolated semisolid magnetization transfer reference (DeepEMR) network, ³³ was incorporated within the training loop of MOCO_Ω to preserve saturation contrast. The DeepEMR outputs semisolid MTC signal intensities at ±3.5 ppm, Z_ref (±3.5 ppm), as reference signals (free water pool + semisolid macromolecule pool) for APT (APT^#) and rNOE (NOE^#) signal calculations. The DeepEMR network was trained with ground‐truth Z‐spectra simulated from Bloch‐McConnell equations. The learning of the DeepEMR network is defined as follows:

$${\mathrm{\theta }}_2^{\prime }=\underset{{\mathrm{\theta }}_2}{\arg \min }\left({\mathrm{E}}_{Z˜P(Z)}\left[{‖{𝒩}_{{\mathrm{\Omega }}_i}\left(Z|{\mathrm{\theta }}_2\right)-Z_{\mathrm{ref}}‖}_2\right]\right),$$ (8)

where ${𝒩}_{{\mathrm{\Omega }}_i}\left(Z|{\mathrm{\theta }}_2\right):Z\left({\mathrm{\Omega }}_i\right)\to Z_{\mathrm{ref}}\left({\mathrm{\Omega }}_j\right)$ is a neural network with trainable parameters (θ₂) and Z_ref denotes ground‐truth reference signal at Ω (e.g., +3.5 ppm and − 3.5 ppm for APT and rNOE imaging, respectively). In the motion artifact correction scheme, Z^mf was fed to a pre‐trained DeepEMR network, which output motion artifact‐free Z_ref ($Z_{\mathrm{mf}}^{\mathrm{ref}}$) and Z^moco was fed to a pre‐trained DeepEMR network, which output motion artifact‐corrected Z_ref ($Z_{\mathrm{moco}}^{\mathrm{ref}}$) for Loss₂. The data consistency loss (Loss₁) was calculated between Z^mf and Z^moco as follows:

$${ℒ}_1={‖Z^{\mathrm{mf}}\left({\mathrm{\Omega }}_i\right)-{\mathrm{\Phi }}_{{\mathrm{\Omega }}_i}\left(Z^{\mathrm{m}}|{\mathrm{\theta }}_1\right)‖}_2,$$ (9)

FIGURE 2.

Overall pipeline for the proposed motion artifact correction in the frequency offset domain (MOCO_Ω) approach. Loss₁ was calculated between motion artifact‐free and motion artifact‐corrected Z‐spectra (Z^mf vs. Z^moco), whereas Loss₂ was calculated between motion artifact‐free and motion artifact‐corrected Z_ref signals at 3.5 ppm, estimated by the deep learning‐extrapolated semisolid magnetization transfer reference (DeepEMR) (Z_ref ^mf [3.5 ppm] vs. Z_ref ^moco [3.5 ppm]). Acquired data points are indicated by asterisks in red color, whereas estimated Z_ref (3.5 ppm) signals are indicated by asterisks in black. The network architecture details of MOCO_Ω are provided in Figure S1. Note that simulated Z‐spectra and Z_ref signals were used for illustrative purposes. The experimentally measured Z‐spectra and Z_ref signals, both before and after motion artifact correction, are presented in Figure S2.

In addition, the biophysical loss function of mean absolute error between $Z_{\mathrm{mf}}^{\mathrm{ref}}$ and $Z_{\text{moco}}^{\mathrm{ref}}$ (Loss₂) was minimized:

$${ℒ}_2=\left|{𝒩}_{{\mathrm{\Omega }}_i}\left(Z^{\mathrm{mf}}|{\mathrm{\theta }}_2^{\prime }\right)-{𝒩}_{{\mathrm{\Omega }}_i}\left({\mathrm{\Phi }}_{{\mathrm{\Omega }}_i}\left(Z^{\mathrm{m}}|{\mathrm{\theta }}_1\right)|{\mathrm{\theta }}_2^{\prime }\right)\right|.$$ (10)

The total loss was computed by summing the two loss values:

$${\mathrm{ℒ}}_{\text{total}}={\mathrm{ℒ}}_1+{\mathrm{ℒ}}_2.$$ (11)

Similar to the training process, the MOCO_Ω network required 1D Z‐spectra as input during the testing phase. All CEST images were processed in a voxel‐by‐voxel fashion. The acquired saturation‐weighted images were vectorized and stacked together along a frequency‐offset dimension before feeding into the MOCO_Ω network. After motion artifact correction, the output Z‐spectra were stacked into a 4D (3D image + frequency offset dimension) image matrix.

The Adam optimizer was used to train the networks with a learning rate of 10⁻⁵. All the experiments were implemented on a Linux workstation (32‐core, 3.75‐GHz AMD processor, and 512 GB of memory) with an NVIDIA RTX A6000, 48GB GPUs system via TensorFlow (version 1.12.0).

2.3.2. MOCO_xyz

The MOCO_Ω network was compared with a MOCO_xyz, which performs spatial alignment of saturation‐weighted images, followed by readout‐related motion correction. The cascaded MOCO_xyz approach consisted of an image alignment network at stage‐1 and a readout‐related motion artifact correction network at stage‐2 (see Figure S3 for details). Combined field extraction ³⁴ and spatial transformer networks ³⁵ were used for image alignment, whereas a residual learning‐based U‐net (Res‐Unet) ³⁶ was used to reduce motion artifacts that occurred during k‐space sampling. The design of the Res‐Unet architecture was inspired by a deep neural network used for brain segmentation.

2.3.3. Training and testing dataset

Approximately 5 million and 0.5 million Z‐spectra extracted from five healthy volunteers and five brain tumor patients, respectively, were used for training and validation. For testing, saturation‐weighted images acquired from one healthy volunteer and one tumor patient was used, where motion artifacts were retrospectively simulated. Furthermore, the neural networks were prospectively (without motion simulation) tested on a healthy volunteer who was instructed to move their head, neck, and legs during MRI scanning and on a brain tumor patient who showed motion artifacts on MR images. The severity of motion effects was evaluated by estimating motion parameters using the SPM12 (see Figure S4). In addition, to evaluate the benefit of using a saturation‐contrast‐specific loss function (Loss₂) in the neural network, Bloch‐McConnell equations‐based numerical phantoms were constructed, and saturation contrast errors caused by motion were calculated. A three‐pool exchange model, including free bulk water (w), semisolid MTC (m), and amide (s) proton pools, was considered for the Bloch‐McConnell simulation with the same scan parameters as those used in the in vivo study. The semisolid macromolecular pool size ratio and the amide proton pool size ratio (relative to free water pool size) were varied from 12% to 2% and 0.22% to 0.02%, respectively, whereas other tissue parameters were fixed: the exchange rate of the MTC and APT to the water were 15 Hz and 200 Hz, respectively, and T₁ and T₂ relaxation times of water were 1.4 s and 80 ms, respectively. ³⁷ Motion artifacts were encoded in the numerical phantoms.

The motion artifact correction performance of the neural network was evaluated and compared against existing motion correction approaches with well‐established evaluation metrics, such as root mean squared error (RMSE), peak SNR (PSNR), and structural similarity index measure (SSIM) metrics on the testing dataset.

2.4. Image processing

For APT^# and rNOE^# imaging, a conventional CEST ratio (CESTR) metric was calculated by subtracting the MT ratio (MTR = 1 – S_sat/S₀ = 1 – Z, where S_sat and S₀ are the signal intensities measured with and without RF saturation, respectively) of the reference signal (Z_ref) from that of the label signal (Z_lab), ¹⁴ , ³⁸ as follows:

$$\text{CESTR}=\frac{S_{\mathrm{ref}}-S_{\mathrm{lab}}}{S_0}=Z_{\mathrm{ref}}-Z_{\mathrm{lab}},$$ (12)

where S_ref and S_lab are the reference and label signal intensities, respectively, and Z_ref and Z_lab are the corresponding signal intensities normalized by S₀. For Z_ref signal calculation, the EMR method can be used by solving an inverse two‐pool Bloch‐McConnell equation with a super‐Lorentzian line‐shape, based on the nonlinear least squares fitting approach. ³⁹ , ⁴⁰ Recently, a DeepEMR method was developed to overcome the inherent limitations (e.g., computational cost and local minima) of the iterative fitting approach, ³³ which was adapted in this study for the estimation of Z_ref at ±3.5 ppm.

3. RESULTS

The utility of the biophysical loss (Loss₂) function in MOCO_Ω was evaluated with a head‐shaped numerical phantom (Figure 3 and Figure S5). In addition, the numerical phantom was designed to assess the ability of the MOCO_Ω to differentiate motion artifact signals from true CEST or APT signals. The APT^# signal intensities calculated by subtracting Z_ref (3.5 ppm) from Z_lab (3.5 ppm) signals are increased in counterclockwise direction (from 7 o'clock position). As shown in Figure 3, both MOCO_Ω with and without the Loss₂ function could restore severely motion‐corrupted images. However, the MOCO_Ω with the saturation‐contrast‐specific loss function (${\text{MOCO}}_{\mathrm{\Omega }}^{\mathrm{L}1+\mathrm{L}2}$) outperformed the MOCO_Ω without the Loss₂ (MOCO_Ω ^L1) in terms of the quantification accuracy. The Z_lab (3.5 ppm), Z_ref (3.5 ppm), and resulting APT^# signals were well preserved from MOCO_Ω with the saturation‐contrast‐specific loss function, compared to ground‐truth, motion‐free images. The mean absolute errors of the Z_ref (3.5 ppm) from MOCO_Ω with and without the saturation‐contrast‐specific loss function, compared to ground‐truth were 1.4% and 2.5%, respectively. These results underscore the efficacy of the biophysical loss function in the MOCO_Ω by demonstrating robust performance in motion artifact correction with minimal impact on true CEST signals.

FIGURE 3.

Evaluation of motion artifact correction in the frequency offset domain (MOCO_Ω) networks trained to minimize L₁ only or L₁ (for motion artifact correction) + L₂ (for saturation transfer contrast) loss functions using numerical phantoms. Ground‐truth (GT) images were obtained from three‐pool Bloch‐McConnell equations. Motion artifacts were simulated in GT images and then corrected using the MOCO_Ω network with L₁ only or L₁ + L₂ loss functions.

The MOCO_Ω method was compared with the existing motion artifact correction methods (Figure 4). The MOCO_Ω showed improved performance against the other motion correction methods, by achieving an RMSE of 2.6% and an SSIM of 97.5% on the test dataset (Table 1). From the deep‐learning‐based motion correction networks in the spatial domain (MOCO_xyz), the motion‐corrected images appeared to be processed with a low‐pass filter because of convolutional kernels on the images. The signal intensity profiles along the frequency offset for MOCO_Ω were consistent with the intensity profile of the reference, whereas the other methods showed higher errors because of remaining motion artifacts (Figure 4B). In terms of computational efficiency, the MOCO_Ω outperformed all existing methods, for example, 6.5‐fold faster than the MI that was the fastest approach among the tested methods. As a validation step, the MOCO_Ω was applied to human brain images with various degrees of motion artifacts (not simulated). In the same imaging session, three image acquisitions were performed to obtain reference (very little motion), moderate, and severe motion‐corrupted images from a healthy volunteer, as shown in the motion parameter estimations (translation and rotation in the top row of Figures 5 and 6). The images with moderate (Figure 5) and severe (Figure 6) motion artifacts showed substantial improvements in quality after MOCO_Ω processing, although some residual errors were still observed in the artifact‐corrected image. With MOCO_Ω, RMSE values improved from 4.3% to 3.9% for the moderate motion and from 7.5% to 4.3% for the severe motion, whereas there was no significant improvement in the image quality with the RPCA‐PCA method. The severe motion artifacts subsequently influenced the MTC (3.5 ppm), APT^#, and rNOE^# image qualities (Figure 7). As expected, motion artifacts are most prominent at contrast edges, for instance, the border between gray and white matter and around the sulcus and ventricles. After motion artifact correction with MOCO_Ω, the average RMSE improved from 4% to 2% for MTC (3.5 ppm) and from 8% to 3% for APT^# and rNOE^# images (Table 2). The MOCO_Ω was further applied to a tumor patient (glioblastoma, IDH‐wild‐type, MGMT methylation) without motion‐related simulations (Figure 8). Although no reference images are available to quantify improvement in the quality of the images, the MOCO_Ω restored the fine structure of the brain and preserved the tumor contrast very well, particularly in the ring‐shaped gadolinium enhancement area and peritumoral edema area (hyperintense on fluid attenuated inversion recovery).

FIGURE 4.

Comparative analysis of several motion artifact correction methods, including MI, LRAZ, RPCA‐PCA, MOCO_xyz, and MOCO_Ω approaches. Motion simulations were performed on motion‐free (Ref) saturation‐weighted images. (A) Examples of the motion artifact corrections with saturation‐weighted images at 20 ppm. (B) Corresponding error images between Ref and motion artifact‐corrected images across the frequency offset (Ω = 80, 60, 40, 30, 20, 10, 8, ±4, ±3.5, and ± 3 ppm) and x‐axis, profiled by a red‐colored dashed line (A). LRAZ, low‐rank approximation of the Z‐spectral images; MI, mutual information‐based motion correction; MOCO_Ω, motion artifact correction in the frequency offset domain; MOCO_xyz, motion correction in the spatial domain; Ref, reference; RPCA‐PCA, robust principal component analysis and principal component analysis.

TABLE 1.

Comparison of the performance of motion artifact correction methods (MI, LRAZ, RPCA‐PCA, MOCO_xyz, and MOCO_Ω).

	Method
	Input	MI	RPCA‐PCA	LRAZ	MOCOxyz	MOCOΩ
RMSE (%)	7.1 ± 1.5	6.1 ± 0.7	4.8 ± 0.4	5.0 ± 0.4	5.3 ± 0.7	2.6 ± 0.3
PSNR	27.4 ± 1.7	28.6 ± 0.9	30.7 ± 0.6	30.3 ± 0.6	29.7 ± 0.5	36.0 ± 1.0
SSIM (%)	94.6 ± 0.8	94.4 ± 0.6	95.8 ± 0.4	95.5 ± 0.5	95.1 ± 0.5	97.5 ± 0.5

Note: The motion artifact simulated images were fed as the input to the motion correction methods. The mean RMSE, PSNR, and SSIM were calculated between motion artifact‐free and motion artifact‐corrected saturation‐weighted images. The test dataset included images from one healthy volunteer and one tumor patient with nine slices.

Abbreviations: LRAZ, low‐rank approximation of the Z‐spectral images; MI, mutual information‐based motion correction; MOCO_Ω, motion artifact correction in the frequency offset domain; MOCO_xyz, motion correction in the spatial domain; PSNR, peak SNR; RMSE, root mean squared error; RPCA‐PCA, robust principal component analysis and principal component analysis; SSIM, structural similarity index measure.

FIGURE 5.

Assessment of the RPCA‐PCA and MOCO_Ω approaches in human brains with moderate motion artifacts. The upper figures display estimated motion parameters (3D translation and rotation). The motion artifact‐corrected images and corresponding error images are shown. With MOCO_Ω, the image quality improvement is reflected by a decrease in root mean squared error (RMSE) (from 4.3%–3.9%). Signal profiles for Ref and motion artifact‐corrected images, along with the corresponding error profiles, are displayed, across the red dashed line and the cross (x), respectively. MOCO_Ω, motion artifact correction in the frequency offset domain; Ref, reference; RPCA‐PCA, robust principal component analysis and principal component analysis.

FIGURE 6.

Comparison of the RPCA‐PCA and MOCO_Ω approaches in human brains with severe motion artifacts. The improvement in image quality is reflected by a decrease in root mean squared error (RMSE) (from 7.5%–4.3%) with MOCO_Ω. Signal profiles for both the Ref and motion artifact‐corrected images, along with their corresponding error profiles, are shown across the red dashed line and the cross (x), respectively. MOCO_Ω, motion artifact correction in the frequency offset domain; Ref, reference; RPCA‐PCA, robust principal component analysis and principal component analysis.

FIGURE 7.

Testing on real motion‐corrupted CEST data using MOCO_Ω. The impact of motion was notably pronounced in MTC, APT^#, and rNOE^# images. The MOCO_Ω effectively mitigated artifacts induced by severe motion, while preserving saturation contrast. Note that the MTC signals at 3.5 ppm (= 1 – Z_ref [3.5 ppm]) were estimated by the deep learning‐extrapolated semisolid magnetization transfer reference (DeepEMR) network. APT^#, free water pool + semisolid macromolecule pool for APT; MOCO_Ω, motion artifact correction in the frequency offset domain; MTC, magnetization transfer contrast; rNOE^#, free water pool + semisolid macromolecule pool) for relayed nuclear Overhauser enhancement.

TABLE 2.

Evaluation of the MOCO_Ω method on actual motion artifacts.

	RMSE (%)
	Moderate motion		Severe motion
	B1 = 1 μT	B1 = 1.5 μT	B1 = 1 μT	B1 = 1.5 μT
MTC (3.5 ppm)
Motion	2.6 ± 0.1	3.2 ± 0.0	4.4 ± 0.2	6.3 ± 0.3
MOCOΩ	2.3 ± 0.1	2.2 ± 0.0	2.1 ± 0.2	2.0 ± 0.0
APT#
Motion	4.7 ± 1.8	6.1 ± 0.9	8.7 ± 1.8	12.7 ± 2.0
MOCOΩ	2.1 ± 0.4	3.4 ± 0.4	2.7 ± 0.4	4.5 ± 0.6
rNOE#
Motion	4.3 ± 1.5	6.3 ± 0.9	9.6 ± 1.5	13.0 ± 1.8
MOCOΩ	2.2 ± 0.4	3.5 ± 0.4	3.0 ± 0.4	4.6 ± 0.6

Note: A healthy volunteer was instructed to perform various degrees of motion during the scan. RMSE metrics were calculated with minimal motion reference images (motion‐free). Data is displayed as mean ± SD.

Abbreviations: APT^#, free water pool + semisolid macromolecule pool for APT; MOCO_Ω, motion artifact correction in the frequency offset domain; MTC, magnetization transfer contrast; RMSE, root mean square error; rNOE^#, free water pool + semisolid macromolecule pool) for relayed nuclear Overhauser enhancement.

FIGURE 8.

Example images from a representative brain tumor patient (glioblastoma, IDH‐wildtype, MGMT methylation) before and after motion artifact correction (MOCO_Ω). The head motion resulted in discontinuities mainly at the border between white matter and gray matter, peritumoral edema, and at the ring‐enhancing left thalamic lesion, particularly seen in APT^# and rNOE^# images. The artifacts were removed from the motion‐corrected images without degrading the diagnostic image quality. APT^#, free water pool + semisolid macromolecule pool for APT; MOCO_Ω, motion artifact correction in the frequency offset domain; rNOE^#, free water pool + semisolid macromolecule pool) for relayed nuclear Overhauser enhancement.

4. DISCUSSION

A deep‐learning‐based motion artifact correction method for CEST imaging was developed and validated in numerical phantoms and in vivo data. The effect of motion artifacts in the image spatial domain can be observed as a change in the signal intensity of the Z‐spectra. Therefore, the proposed motion artifact correction (MOCO_Ω) was performed along the frequency offset direction rather than in the spatial image domain, reliably providing high spectral quality for subjects with mild‐to‐pronounced movements. The addition of the biophysical loss function in the deep‐learning architecture indeed preserved saturation transfer contrast, and the motion artifact correction negligibly affected the diagnostic properties of the APT in tumors.

Existing motion correction approaches, including MI, LRAZ, and RPCA‐PCA, reduce motion‐induced image misalignment between saturation‐weighted images acquired along the frequency offset. ²² , ²³ , ²⁴ , ²⁹ These approaches rely on the assumption that no motion occurred during the k‐space sampling. However, this assumption does not hold for a long 3D readout (or TSE shot duration). Motion during the k‐space sampling can produce inconsistencies between the effective readout directions for different k‐space lines, resulting in ghosting or blurring. In this study, more realistic motion simulations were performed by applying 3D image misalignment between dynamic scans and sampling misalignment in k‐space. Similar to other motion correction methods in brain MRI, ⁴¹ , ⁴² rigid motion was assumed in this study, rather than non‐rigid motion commonly considered in cardiac and abdominal MRI.

Typically, deep‐learning‐based motion artifact correction approaches almost exclusively occur in the spatial image domain. However, the proposed motion artifact correction (MOCO_Ω) was performed along the frequency direction rather than in the spatial image domain, reliably providing high image quality for mild‐to‐pronounced subject movements. Compared to the deep‐learning‐based motion encoding and resolving method in the spatial image domain (MOCO_xyz), the MOCO_Ω significantly improved the quality of reconstruction images. Note that MOCO_xyz consisted of 2D convolutional layers because of a lack of volumetric CEST data for training and validation. However, a single slice of a subject had ˜40 k Z‐spectra, resulting in ˜5.5 million Z‐spectra in total. Therefore, a sufficient amount of training data helped prevent the MOCO_Ω model from overfitting to the training data and the training of the model successfully converged for given Z‐spectra data. Although MOCO_Ω significantly reduced the error between the reference and motion‐corrupted images, demonstrating robust performance, it could not completely eliminate the errors, leaving some residual artifacts. Although MOCO_Ω was trained on simulated motion patterns, testing on real clinical data introduces a gap, as patient‐specific motion patterns can vary significantly, and accurately replicating these patterns in simulations is inherently challenging. Furthermore, complex 3D volumetric motion patterns were converted to simplified 1D motion patterns in Z‐spectra, which aided intuitive and straightforward learning of motion artifacts. The calculation time of the MOCO_Ω was approximately 39 s for an image matrix of 256 × 256 × 15 × 16, which was slightly slower than that of the MOCO_xyz (17 s). However, the deep‐learning‐based motion artifact correction approaches outperformed the conventional MI approach (˜123 s), in terms of computation efficiency.

We observed that the APT^# and NOE^# images exhibited similar contrast at relatively higher B₁ with pseudo‐continuous RF saturation. This finding is consistent with previous studies, which have reported homogenous MTR_asym (3.5 ppm) (= APT^#–rNOE^#) in most normal brain tissue, ¹⁰ , ¹¹ , ³³ , ⁴³ suggesting that APT^# and rNOE^# images exhibit similar contrasts. However, at low B₁, distinct differences in the strength dependencies of the APT^# and rNOE^# signals were clearly observed. ³³ , ⁴³ These differences arise from the different signal origins, amide protons (NH) from mobile proteins and peptides versus aliphatic protons (CH₃, CH₂, CH) from mobile proteins, metabolites, and lipids, as well as their corresponding exchange rates. In addition, the sensitivity of the CEST signal to T₁ relaxation time varies with RF saturation strength. ³⁸ , ⁴⁴ , ⁴⁵ T₁ effects are less pronounced at higher B₁, but become more significant at lower B₁. In this study, T₁ relaxation is expected to influence both APT^# and rNOE^# imaging. Quantitative CEST imaging techniques could help disentangle the contributions of CEST proton concentration and exchange rate from water relaxation effects, therefore, providing a clearer interpretation of the imaging results. ³¹ , ⁴⁶ , ⁴⁷ , ⁴⁸ , ⁴⁹

The training dataset was generated by extracting Z‐spectra from different regions of the brain of healthy volunteers and tumor patients, acquired with different RF saturation times. Therefore, the variability in the training dataset helped effective learning of motion artifacts on Z‐spectra so that the MOCO_Ω model yielded high‐fidelity motion artifact correction on unseen Z‐spectra acquired at 1 μT during the testing phase (Figure 7). It is important to note that the proposed MOCO_Ω reduced artifacts caused by motion rather than correcting for it. The MOCO_Ω functions as a denoising method for Z‐spectra, which is particularly evident at the boundaries of tissue compartments (e.g., white matter, gray matter, and cerebrospinal fluid, see Figure S6) as the network does not incorporate any spatial information. Nevertheless, the MOCO_Ω outperformed motion correction approaches based on spatial information because of factors such as dynamic contrast changes, inherent low signal intensity, limited signal information available for motion correction, and other factors described in the Introduction. In addition, the MOCO_Ω network was specifically trained for the acquisition protocol outlined in Section 2.1, which limits its generalizability to different acquisition parameters that may affect the amplitude and lineshape of Z‐spectra. Therefore, the training dataset should be prepared based on the acquisition parameter values, and the neural network should be trained accordingly. However, the advantage of learning from 1D Z‐spectra information enables the MOCO_Ω network to effectively reduce motion artifacts in different organs. In this work, only tumor‐related applications were tried out, the effectiveness of the MOCO_Ω model could be improved by training the neural network with other pathological cases. Given the limited number of volunteers and patients in this study, multiple‐pool Bloch simulations offer an alternative way to supplement the dataset with broader variations in tissue parameter values. Combining measured Z‐spectra with simulated Z‐spectra could provide diverse data features, thereby enhancing the robustness and generalizability of the MOCO_Ω. In addition to expanding the training dataset, self‐supervised learning techniques could offer another promising direction for motion artifacts correction. These approaches would allow the model to refine its motion correction capabilities using real‐world motion data, reducing dependency on simulated reference images and potentially further improving motion correction performance.

5. CONCLUSIONS

A saturation transfer contrast‐aware neural network was developed for motion artifact correction in CEST MRI. The network effectively learned and mitigated the impact of motion artifacts on the Z‐spectra. Our study demonstrated the superiority of the MOCO_Ω approach against existing registration‐based motion correction approaches performing in the spatial domain. The MOCO_Ω method substantially improved the quality of saturation‐weighted images and could potentially improve acquisition in motion‐prone populations, such as brain tumor patients with poor performance status or be used even for motion‐susceptible abdominal or fetal MRI.

FUNDING INFORMATION

National Institutes of Health, Grant/Award Numbers: R01EB029974, R01NS112242, R01EB034978, and P41EB031771.

Supporting information

Figure S1. The network architecture consists of convolutional operations, flattening and dense layers used in motion correction framework (Figure 2).

Figure S2. Measured Z‐spectra and Z_ref signals, before and after motion artifact correction, for a selected voxel in the white matter (WM) region. The Z‐spectra before motion correction are denoted as Z^m (Ω), while after motion artifact correction, they are denoted as Z^moco (Ω), respectively.

Figure S3. (A) A two‐stage image spatial motion correction network (MOCO_xyz) consisted of image spatial alignment at stage 1 and readout‐related motion artifact correction at stage 2. (B) A field extraction network (FEN) and spatial transform network (STN) for image alignment across frequency offsets. Motion‐free and motion‐corrupted images were concatenated and fed (input size = 256 × 256 × 2) to the FEN. The initial layer featured 64 filters, a systematic reduction in image size by a factor of two was performed on the encoder‐side, accompanied by a doubling of filter numbers. Conversely, on the decoder‐side, the image size was systematically increased, while the filter numbers were decreased by a factor of two. The inclusion of skip connections resulted in a decoder‐side image depth that was 2x that of the corresponding encoder‐side image depth, as the encoded image was concatenated with the decoded image. The STN received the deformation field (DF) as the input and estimated motion parameter matrix at the output. Within the STN network architecture, the DF underwent max pooling, two convolutional layers, a flattened layer, and two dense layers, culminating in an output dense layer with six neurons. Grid sampling and interpolation were performed with the help of estimated motion parameters to obtain the corrected aligned image. (C) A residual learning‐based U‐net (Res‐Unet) for readout‐related motion artifact correction. The initial layer was comprised of 16 filters, with a systematic doubling of filter numbers and simultaneous reduction in image size by a factor of two on the encoder‐side, while on the decoder‐side, there was a systematic decrease in filter numbers corresponding to an increase in the size of the image by a factor of two. Residual learning was integrated at every layer of the U‐net architecture.

Figure S4. An illustration of motion parameters estimated from 3D CEST data acquired from a representative healthy volunteer at different frequency offsets. (A) Estimated motion parameters from reference data. The acquired images were assumed to be motion‐free images if motion parameters remained within the threshold limit (Section 2.2). (B) Estimated motion parameters in the presence of moderate motion artifacts and (C) severe motion artifacts.

Figure S5. Evaluation of MOCO_Ω w/ and w/o L₂ (saturation transfer contrast specific) loss. (A) Comparison of GT Z_ref vs. the Z_ref obtained after motion correction, using MOCO_Ω with L₁ only and with L₁ + L₂. (B) Difference between GT and the motion correction using MOCO_Ω with L₁ only and with L₁ + L₂.

Figure S6. Evaluation of the MOCO_Ω network at tissue interfaces. The MOCO_Ω network demonstrated its ability to eliminate motion‐induced errors (A) during a single CEST acquisition at 8 ppm (B) during several image acquisitions at higher frequency offsets (80, 60, 40, 30, and 20 ppm). However, when motion occurred (C) during additional image acquisitions, particularly at lower frequency offsets (80, 40, 20, 8, 3.5, 3, −3.5, −4 ppm) and (D) frequency offsets (10, 8, 4, 3.5, 3, −3, −3.5, −4 ppm), the MOCO_Ω was able to reduce motion‐induced errors but struggled to estimate averaged values at the tissue interfaces due to the lack of spatial information. The ground truth (GT) images were simulated from three‐pool Bloch‐McConnell equations.

Singh M, Mahmud SZ, Yedavalli V, et al. Learning‐based motion artifact correction in the Z‐spectral domain for chemical exchange saturation transfer MRI . Magn Reson Med. 2025;94:331‐345. doi: 10.1002/mrm.30440