Transformer Enabled Half Z‑spectrum Sampling B₀ Inhomogeneity Correction for GluCEST and NOE MRI

Abstract

Purpose. Chemical Exchange Saturation Transfer (CEST) MRI relies on multiple saturation offsets to correct B₀ inhomogeneity-induced quantification errors at the cost of a prolonged scan time. We previously developed a deep learning-based method for B₀ inhomogeneity correction in Glutamate-weighted CEST (GluCEST) using a parsimonious number of Z-spectrum offset images, which can significantly reduce scan time and provide better correction quality. In this study, we propose a Transformer-based model that achieves B₀ correction using only downfield Z-spectrum offset images, further reducing scan time by about 50%. Methods. B₀ correction was performed separately for the positive and negative sides of the Z-spectrum using reduced saturation offset acquisitions. We constructed distinct Swin transformer networks for each side, training them to learn the nonlinear mapping from a limited number of GluCEST images at various frequencies on the positive side to the specific 3 ppm points where GluCEST peaks. A similar methodology was applied to NOE CEST imaging, optimizing each network to effectively handle the unique characteristics of each spectrum side. Results. The Transformer-based models significantly outperformed the previous deep learning methods both visually and quantitatively. By limiting inputs to only the positive Z-spectrum offsets, we achieved a 50% reduction in data acquisition time compared with previous deep learning approaches while maintaining B₀ inhomogeneity correction accuracy. Conclusion. Efficient B₀ inhomogeneity correction in GluCEST and NOE MRI can be achieved by using a select number of offset images from the downfield Z-spectrum, reducing the acquisition time by over 80%. The proposed transformer-based model demonstrates superior performance over traditional convolutional neural networks, offering a robust and efficient solution for performing CEST MRI in clinical practice.

1. Introduction

Chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI) is a noninvasive technique for measuring regional exogenous and endogenous molecules with high spatial resolution compared to magnetic resonance spectroscopic imaging. CEST MRI relies on selectively saturating the exchangeable protons of specific molecules to be measured using radio frequency (RF) pulses at their resonance frequencies and then detecting changes in the bulk water signal resulting from the transfer of saturation through chemical exchange processes. Any deviation from the desired saturation frequency will reduce the saturation efficiency and increase signal contaminations from molecules with similar resonant frequency, resulting in molecular quantification errors. , These errors, however, are inevitable due to the unavoidable magnetic field (B₀) inhomogeneity, which is more severe at higher field strengths and varies by spatial location. To correct for these B₀ inhomogeneities, a standard approach is to acquire multiple CEST-weighted images across a range of frequency offsets, relative to the water saturation frequency. Based on the estimated CEST signal at the different nominal offsets (the prescribed offset + field inhomogeneity), a Z-spectrum can be estimated at each voxel so that a corrected CEST signal at the desired nominal offset can be estimated from the Z-spectrum through data interpolations. − A practical issue is that acquiring CEST images at a series of offset frequencies substantially prolongs the total scan time, which is multiplied by the number of offsets to be sampled. Extremely long scan time can lead to patient discomfort and increase the risk of head motion. , Significantly reducing the total acquisition time without affecting CEST quantification represents an urgent need. Meanwhile, there is a need to improve the signal-to-noise ratio (SNR) since the CEST signal is much smaller than the background signal. However, simultaneously meeting these goals is analytically insurmountable.

To address challenges in Glutamate-weighted CEST (GluCEST) MRI, we developed a deep learning algorithm, DL-B₀CEST (originally tested as DL-B₀GluCEST). This method significantly accelerates the imaging process and enhances the signal-to-noise ratio (SNR), reducing scan time by approximately 50% without compromising the quality of the B₀ inhomogeneity correction. DL-B₀CEST’s effectiveness relies on a hierarchical arrangement of numerous nonlinear models tailored to fit the low-dimensional Z-spectrum and incorporates image-based nonlocal feature extraction to minimize sporadic noise.

The aim of this study was to further reduce the CEST imaging time by using only downfield Z-spectrum offset images for correcting B₀ inhomogeneity. This approach simplifies the imaging process by concentrating on positive offset images, which consist mainly of the background signal and CEST contrast. Through mathematical operations, we can effectively separate the CEST contrast from the background, exploiting the smooth, low-dimensional nature of both sides of the Z-spectrum as documented in CEST literature. This setup facilitates a machine learning-based model capable of predicting upfield Z-spectrum images from downfield images, employing techniques akin to those in computer vision and medical imaging. By focusing solely on downfield images, we eliminate the need for acquiring upfield (negative offset) images, thereby streamlining the process even further.

Initially, the conventional convolutional neural network (CNN)-based approach demonstrated suboptimal performance in metabolite-specific CEST and Nuclear Overhauser Effect (NOE) MRI applications. , , . In this paper, we introduce a model based on the Swin Transformer, , specifically optimized for both NOE and GluCEST MRI, utilizing only downfield Z-spectrum images. By using the Swin Transformer, the new half Z-spectrum based CEST imaging acceleration and reconstruction model offers a robust and efficient solution for a wider array of CEST-based applications, achieving high correction accuracy while further reducing the imaging times.

In this paper, we present several significant contributions: 1) We have explored the capability of learning a nonlinear transformation from a limited selection of downfield offset images to images at both positive and negative resonance frequencies; 2) We have significantly enhanced the efficiency of DL-B₀CEST, achieving over an 80% reduction in acquisition times compared to conventional methods; 3) We have showcased the superior performance of transformer models over a traditional convolutional neural network (CNN) model, particularly in managing complex and limited imaging data.

2. Method

Chemical Exchange Saturation Transfer

Images were acquired on seven healthy volunteers (6 males, 1 female) with an average age of 45.0 ± 14.5 years (age range: 28 to 66 years). All subjects were imaged with written informed consent under an approved University of Pennsylvania Review Board protocol. MR imaging was performed on a 7T system (Magnetom Terra, Siemens, Erlangen, Germany) using a single-channel transmit/32-channel receive phased-array head coil (Nove Medical, Wilmington, MA, USA). Twenty-nine GluCEST scans were collected from the seven subjects. Twenty scans were used as the training data sets, and nine scans were used as the test sets.

Data acquisition employed a single slice GluCEST sequence, positioning the axial slice 3 to 4 mm above the corpus callosum. Consistent slice placement across sessions was ensured using an in-house developed coregistration program. The imaging parameters included a gradient-echo readout with TR/TE of 7.4 and 3.5 ms, a readout flip angle of 10°, two averages, and a single shot TR of 8000 ms. The scans featured a slice thickness of 5 mm, an in-plane resolution of 1 × 1 mm², and a matrix size of 256 × 256. CEST signal preparation involved a series of 99.8 ms Hanning-windowed saturation pulses, separated by 0.2 ms gaps, with a B_1,RMS of 3.06 μT and a total saturation duration of 800 ms. The saturation flip angle was set at 3772°. Frequency offsets were acquired from ±1.8 to ±4.2 ppm, with additional offsets of ±20 and ±100 ppm gathered for calculating the magnetization transfer ratio (MTR) map. B₀ inhomogeneity was assessed at the same imaging slice using a WASSR sequence. WASSR images were captured from ±0 to ±1 ppm (step size 0.1 ppm) with a saturation pulse of B1rms = 0.29 μT and a duration of 200 ms, employing the same imaging parameters. A K-mean clustering algorithm with three segments (gray matter, white matter, and CSF) was utilized to analyze the MTR map. GluCEST contrast was determined by the signal difference between the upfield and downfield 3 ppm GluCEST images, normalized by the upper field GluCEST image. This calculation process can be described by the following equation:

$$GluCES{T}_{asym(\mathrm{\Delta }\omega =3ppm)}=\frac{M_{sat(-3ppm)}-M_{sat(3ppm)}}{M_{sat(-3ppm)}}\times 100$$

where M _sat(±3ppm) are the magnetizations obtained with saturation at Δω = ±3 ppm offset from the water resonance which need to be interpolated from the acquired data at different off-resonance positions due to the inhomogeneity of B₀.

In addition, another data set was collected as the NOE CEST data set. , The NOE CEST MRI protocol involved a modified turbo FLASH sequence with a gradient echo readout. The data set includes 27 scans from 11 subjects. The sequence parameters were TR/TE = 3.9/1.79 ms and a shot TR of 6 s. Three shots were taken per image, with a B1rms of 0.72 μT and a saturation duration of 3 s. Frequency offsets were acquired from −5 to +5 ppm in increments of 0.2 ppm, and a 100 ppm offset was recorded for MTR normalization. The scan encompassed 12 slices each with a 1 mm slice thickness and a 1 × 1 mm² in-plane resolution.

$$NO{E}_{MTR(\mathrm{\Delta }\omega =-3.5ppm)}=\frac{M_{sat(-100ppm)}-M_{sat(-3.5ppm)}}{M_{sat(-100ppm)}}\times 100$$

In the earlier B₀ correction models that employed deep learning techniques, , a Wide Deep Super-Resolution (WDSR) network was utilized. In our current approach, we have adopted the Swin Transformer to model GluCEST and NOE-weighted CEST separately. Each model is designed to output channels for specific offsets, specifically ±3 ppm for GluCEST as well as −3.5 and −100 ppm for NOE.

DL-Based B₀ Correction and CEST Quantification

Figure shows a schematic diagram of the proposed method called DL-B₀CEST-HS (half spectrum). For GluCEST, the input is a variable number of downfield offset images and the B₀ inhomogeneity map. The same interpolation block of the original DL-B₀CEST was used to get a roughly corrected saturation image to be fed into the next block for finer processing. The middleware block contains two sub-DL networks: one for predicting the Z-spectrum sample at +3 ppm; the other for −3 ppm. The two subnetworks shared the same input. Both subnetworks employed the same configuration as displayed in Figure , utilizing the Swin Transformer network. , Similarly, the outputs for the NOE CEST are specifically at −3.5 and −100 ppm, respectively.

1.

Flowchart of the CEST estimation process via deep learning.

2.

Network architecture of the proposed B₀ correction Swin transformer network.

Network Architecture

The architecture of the network is depicted in Figure , where the Swin Transformer Unet serves as the backbone model, providing an advanced framework for feature extraction and analysis. While the Swin Transformer model brings innovative capabilities to the table, its performance is comparable to that of traditional CNN models previously used in the B₀ correction. The network consists of three primary modules: shallow feature extraction, Unet feature extraction, and image synthesis. Together, these modules ensure robust processing and accurate calculation of MTR CEST images. The hyperparameters of the Swin Transformer are listed in Table .

1. Hyperparameters of Swin Transformer.

Hyperparameter	Value
Input Image Size	224 × 224
Patch Size	4 × 4
Window Size	7 × 7
Embedding Dimension	96
Number of Heads	3
Number of Layers	4
MLP Ratio	4
Dropout Rate	0.1
Stochastic Depth Rate	0.1
Shift Size	3
Optimizer	ADAM
Learning Rate	1e-4
Batch Size	16
Weight Decay	0.05

The shallow feature extraction module employs a single 3 × 3 convolution layer to capture essential low-frequency details such as color, shape, and texture from the input CEST images. These preliminary features are further refined by the UNet feature extraction module, specifically designed to extract high-level and multiscale deep features critical for accurate diagnostics. This enhancement is achieved through three Swin Transformer Blocks (STBs), each containing eight Swin Transformer Layers (STLs). Detailed descriptions of the STBs and STLs will be provided in a subsequent section. To complete the feature extraction phase, another 3 × 3 convolution layer is used to synthesize the final CEST images, effectively mapping the features to both the positive and negative resonant frequencies.

In the UNet feature extraction module, Swin Transformer Blocks (STBs) are used in place of traditional convolutional layers, as depicted in Figure (a). The Swin Transformer Layer (STL), which adapts the foundational Transformer layer originally developed for natural language processing, forms the core of this module. STLs are organized in pairs to serve dual functions: one layer is dedicated to window multihead self-attention (W-MSA) and the next to shifted-window multihead self-attention (SW-MSA). This arrangement includes a cyclic shift approach, diverging from typical Transformer architectures. Such a modification not only boosts computational efficiency but also preserves essential attributes of convolutional networks, including translation invariance, rotation invariance, and a consistent correlation between the receptive field size and the number of layers. This innovative structure optimizes the processing power and effectiveness of feature extraction in imaging applications.

3.

(a) Swin Transformer Block (STB) which has 8 Swin Transformer Layers (STL) in our experiments. (b) The structure of the STL.

Network Training

For the GluCEST study, of 29 scans, 20 were designated for training, and 9 were designated for testing. In the DL-B₀CEST-HS model, input pairs at 2.4, 2.8, 3, 3.4, and 3.8 ppm were utilized. Each scan, originally at a resolution of 256 × 256, was reshaped to 224 × 224 to conform to the model’s required input size. The training was conducted over 300 epochs with a batch size of 16. The ADAM optimizer was employed with an initial learning rate of 0.0001. More details of the hyperparameters are listed in Table . All deep learning experiments were performed using the Pytorch framework on an Ubuntu 20.04 system equipped with an NVIDIA GTX 2080ti graphics card. For the NOE study, 18 out of the 27 scans were allocated for training, with the remaining configurations identical with those used in the GluCEST study.

Evaluations

We employed the previously proposed WDSR model as a benchmark. Both the WDSR and our proposed model (Swin) are image-based. Drawing inspiration from the pixel model outlined in this paper, we also developed two pixel-based models for benchmarking. The first model, Pixel-v1, adheres to the same framework as the image-based models, processing the positive and negative sides separately before calculating the CEST MTR. The second model, Pixel-v2, directly maps the input images to the CEST MTR values.

Network performance was evaluated with the structural similarity index (SSIM), peak signal-to-noise ratio (PSNR) and mean absolute error (MAE). SSIM is a perceptual metric that quantifies image quality degradation as perceived changes in structural information. SSIM is used for measuring the similarity between two images. It is a full reference metric that requires two images from the same image capturea reference image and a processed image. The metric PSNR is an expression for the ratio between the maximum possible value (power) of a signal and the power of distorting noise that affects the quality of its representation. Because many signals have a very wide dynamic range (ratio between the largest and smallest possible values of a changeable quantity), the PSNR is usually expressed in terms of the logarithmic decibel scale. MAE is a statistical metric used to quantify the accuracy of predictions or estimates by measuring the average magnitude of errors between the predicted values and actual values. It is a model accuracy metric that computes the absolute differences between predicted and actual observations, averaging these absolute errors over the data set. Higher SSIM, PSNR and low MAE indicate better image reconstruction quality. Table demonstrates the formulas.

2. Formulas and Descriptions of SSIM, MSE, and PSNR Metrics.

3. Results

Traditionally, the total scan times for the GluCEST and NOE sequences in our protocol are 3:45 and 10:36 min, respectively. By using only 5 offset images for deep learning reconstruction, the estimated scan times can be substantially reduced to approximately 0:44 min for GluCEST 3:45×(5/26) and 1:01 min for NOE 10:36×(5/52).

Visually, a couple of experiments were conducted to predict the GluCEST maps of all 7 subjects from the testing set. Figure shows an example from two representative subjects. Based on the CEST maps, the reconstruction outcomes are comparable between the pixel-based and image-based models. The error maps indicate that the image-based models performed slightly better in the regions of the angular gyrus compared to the pixel-based models. Notably, for both subjectsparticularly the second onethere were noticeable discrepancies in the region of the cingulate cortex.

4.

GluCEST_asym maps of two representative subjects from the GluCEST data set, calculated by using different deep learning methods (from left to right: Reference, Pixel-v1, Pixel-v2, WDSR, and SWIN). For each subject, the top row shows the reconstructed GluCEST_asym maps, and the bottom row displays the corresponding error maps relative to the reference. The reference maps were obtained using the conventional method.

For the NOE_MTR data set, the differences between models are more evident as shown in Figure . The two pixel-based models managed to roughly maintain the basic structural integrity compared with the reference, though finer details were lost. Regarding the image-based models, the Swin model significantly outperformed the WDSR model. The Swin model successfully preserved all of the details in the reconstructions, whereas the WDSR model occasionally confused patterns from different slices.

5.

NOE_MTR maps of two representative subjects on the NOE CEST data set calculated by using different deep learning methods (from left to right: Reference, Pixel-v1, Pixel-v2, WDSR, and SWIN). For each subject, the top row shows the reconstructed NOE_MTR maps, and the bottom row displays the corresponding error maps relative to the reference. The reference maps were obtained by using the conventional method.

The quantitative metrics align with the visual results for both the GluCEST and NOE CEST data sets. As shown in Table , for the GluCEST data set, the image-based models slightly outperform the pixel-based models across all three metrics. The WDSR model achieves the best SSIM and MAE scores, matching the Swin model in terms of highest PSNR. For the NOE data set, as illustrated in Table , the Swin model significantly surpasses the other models in all three metrics, demonstrating its superior performance, whereas the WDSR model exhibits the worst results.

3. All Deep Learning Based Methods Were Compared with the Reference Quantitatively Using SSIM, PSNR and MAE on the GluCEST Data Set.

GluCEST data set	Pixel v1	Pixel v2	WDSR	SWIN
SSIM	0.8226	0.8285	0.8540	0.8333
PSNR	19.43	20.83	21.23	21.23
MAE	0.59	0.58	0.28	0.33

4. All Deep Learning-Based Methods Were Compared with the Reference Quantitatively Using SSIM, PSNR and MAE on NOE Data Set.

NOE data set	Pixel v1	Pixel v2	WDSR	SWIN
SSIM	0.7310	0.7412	0.5546	0.8925
PSNR	19.17	19.71	16.23	25.36
MAE	3.19	3.02	4.18	1.39

Figure demonstrates the scatter regression plots for testing data in GluCEST (the first row) and NOE CEST (the second row) of different models, respectively. Each red dotted line denotes a voxel of the CEST MTR map. The x-axis represents the reference, and the y-axis represents the predicted value. The green dashed line was the linear regression fitting based on those points, and the blue dashed line was the golden standard that prediction equals ground truth, which means the smaller the angle between the green and blue lines, the better the performance of the prediction models. In line with the quantitative and visual results, the two image-based models performed slightly better than the two pixel-based models in the GluCEST data set. On the other hand, for the NOE data set, the Swin model performs better than other models.

6.

Scatter plots comparing the performance of different models (Pixel-v1, Pixel-v2, WDSR, and SWIN) against the reference on the GluCEST (top) and NOE CEST (bottom) data sets. Each data point represents the CEST contrast intensity of a voxel at a fixed spatial location with the reference value on the x-axis and the model prediction on the y-axis. The green line indicates the linear regression fit of the data points, while the blue line represents the identity line corresponding to perfect agreement. The coefficient of determination (R²) is reported below the title of each plot.

Additionally, we calculated the R-squared (R²) value for each model across both data sets. For the GluCEST data set, the WDSR model achieved the highest R² value (≈0.631) compared to the other models. In the NOE CEST data set, the Swin model demonstrated the strongest reference-versus-predicted value correlation (R² ≈ 0.768), indicating its superior ability to predict NOE CEST accurately.

4. Discussion

The conventional approach to correct the B₀ inhomogeneity of CEST data is an image synthesis task, which relies on pixelwise interpolation. However, the deep learning-based approach employs nonlinear image prior modeling. In contrast, the deep learning method leverages a convolutional neural network trained end-to-end on a large set of images, allowing the model to learn optimal parameters through iterative updates and capture complex spatial relationships beyond pixelwise interpolation. The receptive fields in the network enable the model to extract features to capture the full characteristics of the image structures. Every data point at any position contributes to the prediction for the entire image instead of a pixel-by-pixel calculation. Since every image has a stable spatial pattern, the brain structure information can be utilized during the training process. This allows us to use spatial information to compensate for potential temporal information loss, which makes our deep learning-based approach much more efficient than traditional approaches.

In our previous DL based CEST MRI B₀ inhomogeneity correction work, we showed that a sparse sampling paradigm is sufficient to reconstruct the full Z-spectrum. The success of that work is attributed to the overall smoothness of the Z-spectrum and the use of spatial information (across different neighboring voxels) to compensate for the frequency domain information (the frequency offset saturations). The same rationale suggests the possibility of using the sparsely sampled half Z-spectrum to reconstruct the entire Z-spectrum. Even though it was assumed that the MT and DS effects were symmetrical about the water frequency initially to predict the CEST signal, the manifold learning process was not determined on the assumption in practice. The symmetrical signal of the MT and DS effects on upfield and downfield Z-spectrum can perfectly translate the physical interpretation of the CEST saturation that includes CEST, MT and DS effects. Nevertheless, the nonlinear mapping was ultimately learned from real data sets, and the results presented in this paper clearly demonstrate the feasibility of this approach.

Given the limited performance of existing models for B₀ inhomogeneity correction on the NOE data set, we proposed leveraging the Swin Transformer to enhance model performance. Additionally, we introduced a pixel-based model as a baseline for comparison to our proposed image-based model. While no significant performance differences were observed across models on the GluCEST data set, the Swin model emerged as the preferred choice for the NOE CEST data set, demonstrating superior effectiveness over other methods. The results indicate that model training for the GluCEST data was comparatively more straightforward, likely due to the consistency introduced by acquisition at a single scanning position. In contrast, the NOE data set was acquired at two distinct positions, introducing greater variability and thereby increasing the difficulty of learning a consistent mapping between input and output. This is reflected in the lower MAE values observed for GluCEST (0.28–0.59) relative to those for the NOE data set (1.39–4.18).

The varying performances across the two data sets highlight the distinct capabilities of the CNN and Transformer frameworks. In simpler tasks like GluCEST, where the imaging is consistently done at the same position across all subjects, both frameworks exhibit a comparable performance. However, in more complex scenarios, such as the NOE CEST data set, which involves scanning multiple slices at different positions and has a limited number of training samples, the Transformer framework significantly outperforms the conventional CNN approach. This suggests that Transformers may be better suited for handling complexities and variations in data, especially when training samples are restricted.

Reviewing the original network outputs, even WDSR demonstrates the ability to learn the mapping from the downfield and upfield reference effectively. As shown in Figure , the output images at −100 ppm and −3.5 ppm closely resemble the reference. However, when the equation is applied to compute the NOE_MTR maps, the discrepancies become substantial. The subtraction of signals at these two frequencies reduces the signal intensity to only 5–10% of the original, making it highly sensitive to small variations, which can lead to significant errors. In this scenario, Transformer-based models continue to perform well, further validating the robustness of the framework.

7.

Separate results of −100 ppm, −3.5 ppm, and CEST MTR from the WDSR model on the NOE CEST data set (from left to right).

We also trained a single model using both the GluCEST and NOE CEST data sets to evaluate its ability to handle multiple data sets simultaneously. As shown in Figure , qualitatively, the Swin Transformer effectively managed both data sets, whereas the WDSR model struggled to distinguish patterns from different training samples. However, even for the Swin model, the quantitative performance remained lower than those of models trained and tested separately. As a result, we did not include this approach in a formal comparison. Nevertheless, with a sufficiently large training data set, we anticipate that a joint model could achieve performance comparable to that of individually trained models.

8.

NOE MRI maps of two representative subjects on the NOE data set.

Another potential limitation is that the GluCEST data used for training and validation lacked B₁ correction, leaving the impact of B₁-corrected inputs on the model performance uncertain. In contrast, the NOE data set incorporated partial B₁ correction via dielectric padding, allowing the model to account to some extent for B₁ inhomogeneity.

5. Conclusion

This study presents key advancements in deep learning-based B₀ inhomogeneity correction for CEST imaging. We demonstrated the ability to learn nonlinear transformations from limited downfield offset images to predict both positive and negative resonance frequencies. Additionally, our approach significantly reduces acquisition time by over 80% compared with conventional methods. Furthermore, Transformer-based models, particularly the Swin Transformer, outperformed traditional CNNs in handling complex and data-limited scenarios. While challenges remain in optimizing joint training and improving quantitative performance, our findings highlight the potential of deep learning to enhance CEST imaging efficiency and accuracy.

The authors declare no competing financial interest.

Published as part of Chemical & Biomedical Imaging special issue “AI for Chemical and Biomedical Imaging”.