Single-breath-hold 3D abdominal metabolic MRI enables label-free diagnosis of liver cancer

Domain: biology
Published: 2026-03-31
Editorial outcome: major_revision

Abstract
Chemical exchange saturation transfer (CEST) MRI could detect proteins/peptides, creatine, glucose, and glycogen by labeling their exchangeable amide, amine, and hydroxyl groups respectively, via frequency-selective RF pulses. Without the need for contrast agents or specialized hardware, CEST can be conveniently integrated into existing clinical MR protocols. However, its abdominal application is limited by long scan time (> 5 min) and susceptibility to respiratory motion (60%-70% successful scan rate). We develop an ultra-fast 3D CEST MRI approach using spatial-spectral encoding (SSE), enabling a full spectral scan of whole-liver 3D images within a single breath-hold. SSE-CEST employs an efficient z-ω encoding pattern by applying a saturation gradient, followed by a data-driven spatial spectral reconstruction based on the low-rankness of CEST spectra.

SSE-CEST is comprehensively evaluated in glycogen phantoms, ex vivo porcine liver, healthy volunteers and patients. Single breath-hold SSE-CEST largely improves successful rate, with a correlation of 0.95 between two repeated scans. SSE-CEST enables the detection of multi-metabolite changes in the liver and pancreas after an overnight fasting, and the dynamic mapping of hepatic glucose metabolism during an oral glucose test. For liver cancer patients, SSE could differentiate active lesions from post-treatment necrosis, featuring superior in-slice spatial resolution and motion-stabilized images. SSE-CEST MRI potentially could facilitate the diagnosis and patient management for liver and other abdominal diseases.

Introduction
The liver, the largest gland in the human body, plays vital metabolic roles, including food digestion, glycogen storage, and the synthesis and secretion of proteins, fats, and vitamins. Altered liver metabolism is linked to various chronic and acute diseases, such as cancers, diabetes, glycogen storage diseases, and other metabolic disorders, affecting one third of the global population1.

Magnetic resonance imaging (MRI) is a powerful non-invasive tool for managing liver disease patients, allowing precise localization and functional evaluation of both focal and diffuse lesions2. Additionally, MR spectroscopic methods, including 1H-MRS3, 13C-MRS4,5 and 31P-MRS6, have shown promise in revealing liver metabolic functions including fat characterization, glycogen and glucose metabolism, and mitochondrial functions. However, these MRS methods either have low sensitivity or require specialized agents and hardware, which hinders their clinical application. Recently, a label-free metabolic MRI technique, called chemical exchange saturation transfer (CEST), has demonstrated the capability of detecting tissue endogenous glycogen7,8, protein content9 and creatines10. Besides, dynamic MRI of glucose metabolism can be obtained following oral or intravenous glucose uptake11.

As a convenient add-on to routine MR protocols, CEST has demonstrated substantial values in the diagnosis and prognosis of glioma patients12,13, and has become an FDA-approved product. These values include tumor differentiation and grading14, identifying gene mutations15, and monitoring treatment response16. However, the application of CEST in abdominal imaging has been significantly limited, due to the prolonged scan time and susceptibility to respiratory motion17. Only two clinical studies have been published, displaying low scan success rates (~60–70%) and inconsistencies among observers and studies18,19,20.

As a spectral-based method, CEST-MRI requires multiple well-aligned images at a series of saturation frequencies (ω), for field correction and signal quantification. CEST acquisition for each ω typically takes 4–6 seconds, involving second-long saturation RF pulse for labeling certain types of protons and transferring their signals to water for amplification, followed by image readout at water frequency. To acquire CEST images from both amide (mobile proteins and peptides) and hydroxyl (glycans) groups21, tens of saturation ω’s are required, leading to minute-long scan time. Therefore, the technique is not reliable for abdominal exams, easily corrupted by image misalignment or by readout artifacts. By using respiratory triggers22,23 or data-inherent rhythms24, free-breathing liver CEST techniques have been developed and tested on healthy subjects. But their clinical applications are still hindered by non-neglectable image misalignment among respiratory cycles, as well as the severely-prolonged scan time (> 5 minutes) 25,26.

Ideally, a single-breath-hold 3D abdominal CEST sequence is preferred for both scan efficiency in clinical settings and improved image quantification. Herein, we propose a spatial-spectral encoding (SSE) metabolic MRI technique that enables super-fast abdominal CEST within a single breath-hold. The SSE method is inspired by ultra-fast CEST-spectral (UFZ) acquisition, which simultaneously applies a gradient field with the saturation RF pulse. UFZ enables fast scanning of a tube27, a selected voxel28, or a 10 mm-thick slab29, but it fails to resolve 3D spatial distribution as effectively as conventional multi-slice or 3D sequences.

When expanding each slice of CEST dataset along the voxel dimension, a z-ω plane formed with a single UFZ scan corresponding to a diagonal line (Fig. 1). To efficiently sample the z-ω plane and thereby resolve spatial-spectral information, we designed a 'diagonal' acquisition trajectory composed of multiple UFZ scans. Next, based on the low-rankness of CEST spectra, voxels within a slice or adjacent slices were grouped together for spectral feature extraction, achieving customized spectral reconstruction of each slice. The efficient acquisition strategy of multiple z-ω encodings, combined with data-driven CEST-spectral interpolation for each slice, makes SSE a revolutionary technique for CEST metabolic MRI in clinical settings. Within a single breath-hold, SSE acquires high-quality 3D images at multiple frequency offsets targeting amides, amines, and hydroxyls, and also allows fine quantitative images, including APTw, GlucoCEST, and Lorentzian-fitted images. Furthermore, the high in-slice resolution allows recognition of small lesions in the liver or kidneys, as well as small organs such as the pancreas and spleen.

Results
Imaging framework. Super-fast 3D spatial-spectral encoding CEST (SSE-CEST) MRI is accomplished through two steps: the z-ω encoding step during acquisition and the z-ω decoding step during reconstruction (Fig. 1). To rapidly acquire multiple saturation frequencies, we adopted a z-ω encoding sequence, which applies a field gradient along the z-dimension (Gsat) during the saturation RF pulse. This results in a z-dependent saturation frequency (ω) for different slices, corresponding to a diagonal line in the z-ω plane (Fig. 1a,b).

ω(z) = γGsat∙z+ω0 (1)

By varying either the center frequency ω0 or Gsat, efficient traversal and sampling of the z-ω plane is achieved through multiple z-ω encodings arranged in a designated pattern (e.g., parallel, radial, diamond) (Fig. 1c). In the reconstruction step, we grouped voxels within each slice and adjacent slices to extract spectral features via Singular Value Decomposition (SVD). Due to the low-rank nature of CEST spectra, a slice-specific interpolation is performed using these features, i.e., spectral basis functions (Fig. 1d,e, Supplementary Fig. 1.1). Noted that SSE-CEST reconstruction utilized the same Partial Separable theory as in the MRSI accelerations30, the spatial resolution does not be affected, even when grouping voxels on adjacent slices for augmentation of sampled ω (each slice presents loosely-sampled and distinct ω (Supplementary method 1). Without any truncation, the image sets can be accurately resolved by poly-nominal fitting the spectral bases and transforming the voxel dimension back to 2D slices (Fig. 1f,g). For human abdominal protocol, we acquire only 10 or 11 z‑ω lines plus S0 within a single breath-hold (18–21 s), enabling 3D CEST images with a fine-spectral of 121 saturation frequency offsets (>11 spectral interpolation).

Ex-vivo porcine liver: flexibility to z-ω acquisition patterns. SSE-CEST was first validated on an ex-vivo scan of porcine liver, with three distinct z-ω acquisition patterns tested: parallel, diamond, and radial (Fig. 2a1-a3). The three patterns under a B1 of 0.7 μT are as follows: parallel (4 minutes 14 seconds, 30 z-ω lines); diamond (4 minutes 22 seconds, 31 z-ω lines); radial (2 minutes 38 seconds, 18 z-ω lines). In contrast, the conventional CEST acquisition without z-ω encoding took 11 minutes 58 seconds with 88 ∆ω values (Fig. 2a4). Three types of contrast maps were obtained by a Lorentzian Difference (LD) analysis (Supplementary methods, Supplementary Table 1), including amide CEST, glycogen NOE and aliphatic NOE (Fig. 2b1-b4). At the bottom of each SSE-CEST contrast map, Bland-Altman analysis revealed its consistency with that acquired using the conventional method, with all three patterns exhibiting acceptable 95% limits of agreement (parallel ≤ [-2.58%, 1.37%], diamond ≤ [-2.36%, 1.15%], radial ≤ [-2.63%, 2.14%] as quantitatively listed in Supplementary Table 1.2, n = 69, the number of liver ROIs (8×8 square) within the displayed slice). When compared with the conventional methods, none of the SSE-CEST contrast maps displayed statistically significant biases (p > 0.05, n = 69, same as above) except for aliphatic NOE with radial pattern (Supplementary Fig. 2.1).

Spectral consistency was further validated through averaged Z spectra and the substitute LD spectra within a ROI (Fig. 2d), where parallel and diamond patterns achieved exceptional spectral reproducibility, outperforming radial pattern (Z-spectra: parallel RMSE = 0.69%, diamond RMSE = 0.67%, radial RMSE = 1.94%; LD spectra: parallel RMSE = 0.59%, diamond RMSE = 0.54%, radial RMSE = 1.47%, Fig. 2c1-c3). SSE-CEST demonstrated well spatial reconstruction with vessel details for all acquired slices, as shown on the raw ST images at 3.5 ppm, -1.2 ppm and 1.2 ppm, respectively. (Supplementary Fig. 2.2) Bland-Altman analysis also suggested high agreement with the conventional method and minimal variance across slices (Supplementary Fig. 2.3; n=21 slices, one ROI per slice at the location indicated in Fig. 2d).

Quantitative evaluations using glycogen phantoms. Glycogen phantoms with various concentrations, dissolved in 1% Agar, were scanned for quantitative assessment. As CEST spectral profile changes with saturation B1, we acquired a lower B1 for measuring the relayed-NOE from macromolecular glycogen (0.7 μT, Fig. 3) and a higher one for enhancing the hydroxyl CEST signals on glycans (2 μT, Supplementary Fig. 3.1).

The glycogen-NOE maps derived from 0.7µT SSE-CEST show consistency among slices (represented slices. #9, 11, 13, Fig. 3b,c), revealing linear correlation with the glycogen concentrations (Fig. 3d, n=21 slices, mean±std, r=0.95). Averaged Z-spectra per tube in slice 11 (Fig. 3e) illustrated concentration-dependent profiles, with the marked points indicating ×8 under-sampling of SSE-CEST. Although distinct saturation frequencies were sampled on each slice, the reconstructed Z-spectra of SSE-CEST were almost identical for the same tube (Supplementary Fig. 3.2). LD spectra extracted from raw Z-spectra further displayed cleaner glycogen-NOE spectral peaks (-0.5 to -2 ppm) and hydroxyl signals (0.5 to 2 ppm) on a quantitative manner (Fig. 3g).

SSE-CEST demonstrated high-fidelity reconstruction when compared with full-sampled conventional CEST, as suggested by the scattering plots and the Bland-Altman plots in Fig. 3g,h (0.7 µT), Supplementary Fig. 3.1 (2 µT) (all with n = 126, 6 tubes X 21 slices, glycogen NOE signals: r=0.97, p<0.0001, mean difference 0.25%, 2 µT ST(1.2 ppm) and ST(-1.2 ppm), both with r = 0.98, p <0.0001), and Supplementary Fig. 3.5. Slice-by-slice comparison of SSE-CEST and conventional CEST ST images demonstrated spatial consistency and correlation with glycogen concentration. (Supplementary Fig. 3.3, 3.4).

Single-breath-hold 3D abdominal CEST MRI in healthy volunteers. On ten healthy volunteers, we demonstrated a parallel SSE-CEST MR protocol within a single breath-hold (18-21 seconds, B1 = 2 µT). By collecting 11 parallel z-ω lines, SSE-CEST enabled reconstruction of 41-slice saturation images across 121 frequencies, achieving 44-fold (11-fold spectral interpolation multiplied by 2x2-acceleration upon parallel imaging) acceleration compared with conventional fully-sampled approach (Fig. 4a). By acquiring an additional reference without saturation (S0), SSE-CEST could directly output the ST maps (ST = 1-S(Δω)/S0), reflecting contrasts from amides from mobile proteins/peptides (3.5 ppm), hydroxyls on glycans (1.2 ppm),and the relayed NOE from macromolecular aliphatic protons (-3.5 ppm)8,31. Noted that SSE-CEST utilized a Dixon-type readout with capability of water-fat separation and B0 maps, readily providing B0-corrected images without fat contaminations. The B0-corrected APTw images as used in clinical glioma diagnosis were also obtained (MTRasym @3.5 ppm, Fig. 4b,c,f)13. Consecutive scan-rescan data showed high repeatability of SSE-CEST, with 24 out of the 40 contrast images exhibiting a correlation of >0.99 between the two scans and only one contrast map showing low correlation (Fig. 4b). All 40 evaluated contrast maps displayed low mean squared error between two repeats (Fig. 4c APTw<0.1% for all subjects). Pearson correlation and the Bland-Altman analysis from average liver signal from all ten subjects further suggested the reliability of SSE-CEST. (Supplementary Fig. 4.2, r=0.95 for ST@1.2 ppm , r=0.96 for ST@3.5 ppm). For one of the subjects, the multi-metabolite ST images, the APTw images and B0 maps of the entire liver are displayed in three orthogonal slices, overlaid on a high-resolution T1w images (Fig. 4d,e). The single-breath-hold 3D SSE-CEST protocol provides excellent repeatability and capability of multi-modality fusion, towards a robust metabolic MRI tool in clinic.

Overnight fasting: multi-metabolite, multi-organ MRI. The SSE-CEST MRI was evaluated in a fasting experiment involving five healthy volunteers. Each subject underwent an initial scan at 2-hour after a full dinner and was re-scanned after a 12-hour fast. Each scan involved three single-breath-hold SSE protocols, which are Zpos (0.7 µT), Zneg (0.7 µT) and Z (2 µT), each with 11 parallel z-ω lines plus S0 (Supplementary Table 1, Fig. 5.1, same protocol in tumor patients). For SSE-CEST using a saturation B1 of 0.7 µT, three types of contrast were calculated, including Amide CEST, Glycogen NOE and Aliphatic NOE. Whereas for SSE-CEST of 2 µT, the APTw maps and the glycan-CEST maps were obtained using asymmetric MTR analysis. Fig. 5a,b displayed the five contrast maps from one of the subjects, revealing notable signal drops post overnight fasting in amide CEST and glycogen NOE (~1/3), as also denoted in the LD spectra of a liver ROI (Fig. 5c). When comparing all 205 slices acquired from 5 subjects acquired post-meal and post-fasting, all five contrast maps displayed significant difference (Fig. 5d). To further eliminate the changes in water relaxation, another R1ρ-based quantification method was also performed, validating the signal drops of glycogen NOE and of amide CEST (Supplementary Fig. 5.5). The multi-offset ST images also displayed significant signal drops post fasting, with the high-quality motion-free images allowing for easy recognition of major vessels and the multiple organs including spleen, pancreas, kidney. (Supplementary Figs. 5.6-5.7). Noted the 2 µT SSE-CEST images may present lower SNR than the 0.7 µT ones when offsets getting closer to water, suggesting the benefit of using a smaller B1, with lower contaminations from non-CEST background signals.

Dynamic Glucose Imaging for Oral Glucose Tolerance Test (OGTT). To demonstrate the utility of SSE-CEST for dynamic spatial-spectral characterization of biological systems after administration of exogenous agents, we conducted an OGTT Experiment in five healthy human volunteers11,32-34. Each volunteer underwent repeat SSE-CEST scans until 51 minutes after glucose uptake, and a pre-administration baseline scan was also acquired (Fig. 6a). SSE-CEST present a unique advantage of full-spectral capture, allowing for monitoring the spectral profile over time and making the CEST data more interpretable and reliable. Fig. 6b compared Z-spectra and derived MTRasym spectra acquired the baselines and at 51 minutes post take-up, with the largest changes observed at ~ 2.1 ppm similar to previous findings in brain34. For a representative subject, Fig. 6c presents dynamic glucose images quantified via MTRasym (2.1 ppm) and the corresponding time course of signals within liver voxels; signals rose consistently until ~30 min after oral glucose administration and were maintained through the final scan (51 min). Whereas the upward trend of T2 values is less obvious, only displaying < 6 ms (mean T2 = 101.9 ms) changes of mean signals with a larger standard deviation, presumably due to less specificity and the single-slice acquisition we used. For all five subjects, liver MTRasym maps showed consistent signal increases within 15 minutes post-administration, with low inter-voxel variability across parenchymal voxels; (Supplementary Fig. 6.1). The time course also varied among subjects, possibly due to differences in individual digestion times after oral administration. Nevertheless, images acquired at all time-points displayed well-alignment, clearly depicting the pancreas. These evidences suggested SSE-CEST allows for rapid capture of the dynamics post administration of exogeneous agents, with good spatial-spectral performance.

Assessment in patients with focal lesions. We further evaluated SSE-CEST in patient with Hepatocellular Carcinoma (HCC). Two types of lesions were included in this study: active HCC lesions and necrotic lesions after treatment. Fig. 7a,b show representative images from a patient who presents both active HCC and necrotic lesions 4 months post-treatment, as characterized on routine clinical contrast-enhanced images. Three SSE-CEST scans were acquired (Zpos-0.7 μT, Zneg-0.7 μT and Z-2 μT), each within a single breath-hold (Supplementary Table 1, Fig. 5.1). Visually, the active HCC lesion showed marked hyper-intensity on all three 0.7 μT LD maps (i.e., amide CEST, aliphatic NOE and glycogen-related NOE), indicating elevated levels of mobile proteins and altered macromolecular environment. The detailed spectra allowed further contrast interpretation and quality control, with the spectral bottom all centered at 0 ppm (Supplementary Fig. 7.4). In contrast, the necrotic lesion appeared hypo-intense across all CEST contrasts. All 41 slices of APTw and 0.7 μT ST(3.5ppm) images demonstrated SSE-CEST's robust spatial reconstruction, revealing the complete lesion distribution. (Supplementary Figs. 7.2-7.3).

Interestingly, the APTw maps from 2 μT SSE-CEST did not show as obvious hyper-intensity contrast as those on 0.7 μT images.

Quantitative analysis corroborated these observations (Fig. 7c,d). When comparing active HCC to necrotic tissue, the 0.7 μT LD signals for amide CEST, glycogen NOE, and aliphatic NOE were all significantly higher in HCC (p=0.0066, p=0.0052, and p=0.0052, respectively). Similarly, compared to adjacent normal liver, active HCC exhibited significantly elevated LD signals for aliphatic NOE (p=0.000019) and amide CEST (p=0.0013). In contrast, none of the 2 μT MTR asymmetry metrics showed significant differences in these comparisons. This discrepancy may be attributed to the inherent property of asymmetry analysis: both the +3.5 ppm (amide) and -3.5 ppm (aliphatic NOE) pools can yield saturation effects. Their concurrent elevation in HCC might lead to substantial cancellation upon subtraction, thereby attenuating the sensitivity of the asymmetry metric (APTw) despite of genuine metabolic differences. These results demonstrate that the LD contrasts from the 0.7 μT acquisition offer superior specificity for differentiating active HCC from necrotic or normal tissue, underscoring the value of multi-B1, spectrally-resolved assessment with SSE-CEST. To clinically evaluate the detection of focal lesions using SSE‑CEST, two radiologists independently contoured lesions on the ST maps in 21 patients while blinded to other imaging results. Inter‑reader agreement was excellent (Cohen’s kappa = 0.89). The lesion detection rates were as follows: for active HCC lesions (n=11), 100% and 90.9% for the two readers; for treated necrotic lesions (n=12), 100% and 100% for the two readers. These detection rates align with the expected visibility of different tissue types on metabolic images and support the clinical reliability of SSE‑CEST for lesion assessment. This analysis revealed excellent inter-reader agreement (Cohen's kappa = 0.89) and demonstrated clinically meaningful detection rates that logically correlated with expected metabolic activity: for active HCC lesions (n=11), 100% and 90.9% for the two readers; for treated necrotic lesions (n=12), 100% and 100% for the two readers; while benign lesions including cysts and hemangiomas (n=22) exhibited lower rates of 45.5% and 50% for the two readers. These detection rates align with the expected visibility of different tissue types on metabolic images and support the clinical reliability of SSE‑CEST for lesion assessment.

To validate metabolic specificity, we compared SSE-CEST with 18F-FDG PET/CT in an HCC patient showing a PET hot spot 10 months post-treatment (Fig. 8). SSE-CEST contrast maps acquired 3-week after PET scan revealed matched hyper-intense regions (red arrows) on three representative axial slices. The SSE-CEST maps included the amide-specific LD contrast at 3.5 ppm acquired with a low saturation power (B1 = 0.7 μT), reflecting mobile protein/peptide content, and the glucose-weighted ST contrast at 2.1 ppm acquired with a higher power (B1 = 2 μT). Both contrasts also display adjacent necrotic regions (white arrows). This agreement with PET/CT and Gd-enhance MRI suggest the potential of SSE‑CEST for ‘label-free’ non-radiative way in monitoring treatment response.

Methods
Acquisition and reconstruction

Single readout of 3D images with saturation-gradient. Similar to the UFZ sequence, we employ a saturation labeling strategy by simultaneously applying a z-direction gradient with frequency-selective saturation RF pulse centered at ∆ω. This allows simultaneous acquisition of spatial and spectral information in a single 3D volume. The relationship between the spatial location and the frequency offset is defined in Eq.(1). To achieve faster readouts, a 3D single-shot Turbo-field-echo (TFE) readout was employed, with k-space ordering processing from lower to higher frequencies. The proposed framework incorporates 3-echo Dixon readout to separate water and fat signal and obtain a B0 map. A z-ω encoding block and a readout block constitute a single imaging unit.

Multiple readouts with designated z-ω trajectory. To recovery the 4D tensor, the imaging unit is repeated multiple times. The 3D data from a single imaging unit constitutes a 3D plane in x-y-z-ω space, of which the location in 4D space was determined by Gsat and ω0. The repeated acquisition with varied Gsat and ∆ω forms a specific z-ω trajectory. Especially, if Gsat is fixed to 0, this imaging protocol are identical to the conventional CEST sequence. Notice, the multiple readouts were completed in a single breath-hold in our implementation.

4D CEST-spectra reconstruction with z-ω decoding. Reconstruct of the 4D CEST-spectra is achieved using a z-ω decoding strategy that exploits the anatomical and spectral similarity within a single slice or adjacent slices (Nadj = 0, 1, 2, …). B0-correction was performed immediately after the interpolation step, using the Dixon-derived B0 map. Consider the zth slice with m voxels and n acquired frequency offsets:

Ωz = [ω1(z) ,ω2(z) ,⋯,ωn(z) ] (2)

Due to the existence of z-ω encoding gradient, the two adjacent slices sample distinct frequency offsets:

Ω(z−1) = [ω1(z−1) ,ω2(z−1) ,⋯,ωn(z−1) ] ,Ω(z+1) = [ω1(z+1) ,ω2(z+1) ,⋯,ωn(z+1) ]

s.t.|ωk(z−1) −ωk(z) | = |ωk(z+1) −ωk(z) | = γ|Gsat|∆z, k = 1,2,⋯,n (3)

For zth slice, the unresolved raw signal could be expanded into a matrix of n X m, 𝐒𝐳, where n is the number of z-ω encodings and m is the voxel numbers. To combine slices with distinct sampled Ω, we initialized a unified zero matrix of size m × Nfull (the number of fully-sampled ω with 0.1 ppm interval), and filled the acquired values in corresponding ω position. Taking Nadj = 3(using one adjacent slice on each side), we pack signals from three consecutive slices as 𝐒raw = [𝐒z−1 𝐒𝐳 𝐒z−1] to extract the spectral basis, with a matrix format in below:

𝐒raw = [𝐒z−1 𝐒𝐳 𝐒z−1] =

[sω1,1(z−1) ⋯ sω1,m(z−1) 0 ⋯ 0 0 ⋯ 0
0 ⋯ 0 sω1,1(z) ⋯ sω1,m(z) 0 ⋯ 0
0 ⋯ 0 0 ⋯ 0 sω1,1(z+1) ⋯ sω1,m(z+1)
⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ ⋮ (4)
sωn,1(z−1) ⋯ sωn,m(z−1) 0 ⋯ 0 0 ⋯ 0
0 ⋯ 0 sωn,1(z) ⋯ sωn,m(z) 0 ⋯ 0
0 ⋯ 0 0 ⋯ 0 sωn,1(z+1) ⋯ sωn,m(z+1)]

Performing SVD to 𝐒raw, resulting in 𝐒raw = 𝐔∙𝚺∙𝐕′ , where U is the spatial coefficient matrix, 𝚺 is the diagonal matrix of singular values in descending order, 𝐕 is the right singular matrix, with the matrix form of

[vω1,1(z−1) 0 0 ⋯ vωn,1(z−1) 0 0
0 vω1,1(z) 0 ⋯ 0 vωn,1(z) 0
0 0 vω1,1(z+1) ⋯ 0 0 vωn,1(z+1)
𝐕 = ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ (5)
vω1,n(z−1) 0 0 ⋯ vωn,n(z−1) 0 0
0 vω1,n(z) 0 ⋯ 0 vωn,n(z) 0
0 0 vω1,n(z+1) ⋯ 0 0 vωn,n(z+1)]

Note that the submatrix of V, 𝐯(𝐳) = [𝑣𝛺(𝑧),1 ,𝑣𝛺(𝑧),2 ,⋯,𝑣𝛺(𝑧),𝑛], is the spectral basis matrix of the zth slice. Due to the anatomical and similarity of the adjacent slices, we assume that 𝐯(𝐳−𝟏),𝐯(𝐳),𝐯(𝐳+𝟏) are three submatrices of 𝐯𝐟𝐮𝐥𝐥(𝐳) , that derived from the fully-sampled spectra of 0.1ppm. Thus, the denser spectral bases of the zth slice can be approximated by combining 𝑣(𝑧−1), 𝑣(𝑧), and 𝑣(𝑧+1):

[vω1,1(z−1) vω1,2(z−1) ⋯ vω1,n(z−1)
vω1,1(z) vω1,2(z) ⋯ vω1,n(z)
vω1,1(z+1) vω1,2(z+1) ⋯ vω1,n(z+1)
𝐕𝐂 = ⋮ ⋮ ⋱ ⋮ (6)
vωn,1(z−1) vωn,2(z−1) ⋯ vωn,n(z−1)
vωn,1(z) vωn,2(z) ⋯ vωn,n(z)
vωn,1(z+1) vωn,2(z+1) ⋯ vωn,n(z+1)]

As seen, grouping Nadj adjacent slices could resolve a combined spectral bases matrix, VadjC, enabling Nadj-fold spectral sampling rate.

min‖𝐌∙(𝐔𝐕𝐂 𝐓 −𝐒𝐜𝐨𝐫𝐫)‖ 2 (7)
U 2

where U is the spatial coefficient matrix, 𝐒𝐜𝐨𝐫𝐫 is the B0-corrected signal of the zth slice, with each voxel shifted by its B0-drift value along ω-axis, and M is a binary matrix that describes the acquired offsets after B0 correction. After minimizing Eq. (7) using gradient decent algorithm, the reconstructed SSE value can be calculated by:

𝐒𝐫𝐞𝐜𝐨𝐧 = 𝐔𝐕𝐂 𝐓 (8)

where 𝐒𝐫𝐞𝐜𝐨𝐧 is the reconstructed S-value matrix of the zth slice. For slices located on the edge of FOV, adjacent slices were selected only on the single side within the FOV. For these slices, sampling rate of spectral bases decreased due to less adjacent slices.

Ex vivo validation of SSE-CEST

Porcine liver experiments. A whole, fresh porcine liver (never frozen) was procured from a commercial slaughterhouse and underwent MR scan within four hours post-mortem. The liver was placed in a glass box during MR scanning. MR protocol for porcine liver consists of sequences of four z-ω trajectories: (1) ‘parallel’ pattern (30 encodings). ∆ω(ppm)|Gsat (mT/m) was: -1560|0, -10|-0.1, -8|-0.1, -7|-0.1, -6|-0.1, -5|-0.1, -4.5|-0.1, -4|-0.1, -3.5|-0.1, -3|-0.1, -2.5|-0.1, -2|-0.1, -1.5|-0.1, -1|-0.1, -0.5|-0.1, 0|-0.1, 0.5|-0.1, 1|-0.1, 1.5|-0.1, 2|-0.1, 2.5|-0.1, 3|-0.1, 3.5|-0.1, 4|-0.1, 4.5|-0.1, 5|-0.1, 6|-0.1, 7|-0.1, 8|-0.1, 10|-0.1; (2) ‘diamond’ pattern (30 encodings). ∆ω(ppm)|Gsat (mT/m) was: -1560|0, -10|-0.1, -10|0.1, -7|-0.1, -7|0.1, -5|-0.1, -5|0.1, -4|-0.1, -4|0.1, -3|-0.1, -3|0.1, -2|-0.1, -2|0.1, -1|-0.1, -1|0.1, 0|-0.1, 0|0.1, 1|-0.1, 1|0.1, 2|-0.1, 2|0.1, 3|-0.1, 3|0.1, 4|-0.1, 4|0.1, 5|-0.1, 5|0.1, 7|-0.1, 7|0.1, 10|-0.1, 10|0.1; (3) ‘radial’ pattern (18 encodings). ∆ω(ppm)|Gsat (mT/m) was: -1560|0, -6|-0.6, -6|0.6, -4|-0.4, -4|0.4, -2|-0.2, -2|0.2, -1|-0.1, -1|0.1, 0|0, 1|-0.1, 1|0.1, 2|-0.2, 2|0.2, 4|-0.4, 4|0.4, 6|-0.6, 6|0.6; and (4) conventional CEST pattern (88 frequency offsets), in which saturation encoding gradient was turned off, but more frequency offsets: -1560, -10:0.5:-5.5, -4.95:0.15:4.95, and 5.5:0.5:10 ppm. The MR protocol was repeated at three saturation power: 0.7 μT (3.5s), 1 μT (3.5s) and 2 μT (1.75s). The 3D single-shot turbo-field-echo (TFE) readout parameters were: shot interval of 8000 ms, TE of 1.5/3.0/4.5 ms, flip angle of 15°, TR of 10 ms, SENSE of 2  1, resolution of 2  2  5.84 mm3, FOV of 230  115  61 mm3, echo train length of 302. The scan time for the conventional CEST protocol (scheme 4) was 11 minutes and 58 seconds, while the scan times of three SSE-CEST patterns are: parallel (4 minutes 14 seconds, 30 z-ω lines); diamond (4 minutes 22 seconds, 31 z-ω lines); radial (2 minutes 38 seconds, 18 z-ω lines). B0 maps were calculated from three-point Dixon readouts. Data from schemes 1-3 were compared with the conventional CEST data (scheme 4) using Bland-Altman analysis, to evaluate the consistency of the SSE-CEST with the gold-standard method.

Glycogen phantom experiments. The phantom comprises six 50-mL tubes, each containing oyster glycogen (Sigma-Aldrich, G8751) dissolved in PBS (pH 7.4) at concentrations of 0 mM, 6.25 mM, 12.5 mM, 25 mM, 50 mM, and 100 mM. For SSE-CEST protocol, Gsat was fixed to -0.1 mT/m, and frequency offsets (a total of 30) were: -1560, -10, -8, -7, -6, -5, -4.5, -4, -3.5, -3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 7, 8, and 10 ppm. For conventional CEST protocol, frequency offsets (a total of 88) were: -1560, -10:0.5:-5.5, -4.95:0.15:4.95, and 5.5:0.5:10 ppm. The 3D TFE readout parameters were: shot interval of 10000 ms, TE of 1.03 ms, flip angle of 10°, TR of 5 ms, SENSE of 2  1, resolution of 2  2  3 mm3, FOV of 157  157  61 mm3, echo train length of 402.

Data analysis. For porcine liver, the reconstructed images were additional corrected for B0-inhomogeneity using the lowest point as water frequency (Self B0-correction), and ST images were obtained by 1-Z along the entire frequency dimension (-10 to 10 ppm, resolution 0.1 ppm). LD images were calculated for amide (3.5 ppm), glycans (-1.2 ppm), and aliphatic (-3.5 ppm). For a clarified visualization, an 8  8 window was used to down-sample the ST images from matrix 64  128 to 8  16. A non-zero array was generated for each contrast with each acquisition trajectory after averaging the values in each voxel and removing zeros from the voxels. Afterwards, Bland-Altman analysis was used to test the consistency of spatial performance between the z-ω acquisition trajectories and the conventional one for all the contrasts. The data was evaluated using bias (mean ± std) and 95% Limits of Agreement. To test statistical significance, normal distribution of all arrays was tested first. Then Mann Whitney tests were performed between the z-ω acquisition trajectories and the conventional one for all the contrasts. For spectral evaluation, a representative ROI was selected from the down-sampled T1-weighted image in the same slice. Averaged CEST-spectra were calculated within this ROI for all the trajectories. Root mean square error (RMSE) along the whole CEST-spectra between three z-ω acquisition trajectories and the conventional one was calculated to verify the spectral accuracy.

For glycogen phantom, LD-0.7μT images of glycogen phantoms 1.2 ppm and -1.2 ppm were generated. For comprehensive statistics and better SNR, values within each tube in each slice were averaged, generating 6  11 matrixes for LD 1.2 ppm and ST -1.2 ppm, respectively. Linear regression associated with Pearson correlation was used to evaluate the relationship between LD values and glycogen concentration. Each data presented as mean ± SD represented data of a tube from all slices. To verify the consistency between our method and the gold standard, linear regression associated with Pearson correlation was performed on all the 66 points.

In vivo validation of SSE-CEST

Human participants

In vivo MRI experiments on healthy volunteers were performed at the Center for Biomedical Imaging Research, Tsinghua University, approved by the Institutional Review Board of Tsinghua University. Patient scans were performed at Beijing Tsinghua Changgung Hospital, approved by the Institutional Review Board of Beijing Tsinghua Changgung Hospital. All participants provided written informed consent before MRI scans.

MRI protocols. All MR experiments were conducted on 3-Tesla Philips Ingenia CX scanners (Philips Healthcare, Best, The Netherlands), using a 16-channel body coil and a 16-channel posterior coil as receivers. For all subjects, two parallel-type CEST labeling schemes were implemented: (1) B1 of 2μT, saturation time of 0.4s, 12 saturation encodings with frequency offset of -1560, -6, 6, -4.8, 4.8, -3.6, 3.6, -2.4, 2.4, -1.2, 1.2, 0 ppm. Shot interval was 1472 ms. Gsat was fixed to -0.1 mT/m. (2) B1 of 0.7 μT, saturation time of 0.8s, 11 saturation encodings, with frequency offset of -1560, -9, -6, -5, -4, -3, -2, -1, 0, 1.5, 3 ppm for the NOE contrast acquisition (Zneg), and with frequency offset of -1560, 9, 6, 5, 4, 3, 2, 1, 0, -1.5, -3 ppm for the CEST contrast detection (Zpos). Shot interval was 1871 ms. Gsat was fixed to -0.1 mT/m. The Dixon-type 3D turbo-field-echo (TFE) readouts were employed (Supplementary Fig. 4.1): voxel size=4.5 × 4.5 × 2.9 mm3, field of view (FOV) = 320 × 288 × 150 mm3, flip angle (FA)=8°, repetition time (TR)=2.9 ms, echo time (TE)=0.77/1.27/1.77 ms, echo train length=350. Each sequence was performed in single breath-hold.

Repeatability test. Ten healthy volunteers were recruited (eight males and two females; age of 24.8 ± 3.3 years), and scanned twice using MRI protocols above. Repeatability of SSE-CEST was evaluated using Pearson’s correlation coefficients, and Bland-Altman analysis.

Fasting experiments. Data were acquired in five subjects (four males and one female; age of 24.2 ± 1.5 years). For each subject, two scans were performed: (1) a post-meal scan on the evening (20:00), which was performed 2 hours after a full dinner, and (2) a post-fasting scan in the following morning (08:00), which was performed after overnight fasting (~12 h after the post-meal scan). Participants have been instructed to have nothing to eat or drink other than water in the intervening period. Data from the two scans were reconstructed and post-processed independently. Differences between the post-meal scan and the post-fasting scan were measured using two-sided Student’s t-tests.

Oral glucose test. Five healthy volunteers (four males and one female; age of 24.8 ± 1.92 years) were recruited for oral glucose test experiments. Each subject underwent an MRI scan that begins at 7:30 a.m. after overnight fasting. The MRI scan consists of four stages: (1) Before OGT: a pre-scan and an SSE-CEST. (2) OGT: the subject drank 300ml of sugar water, in which 75g of anhydrous glucose was dissolved. (3) After OGT (0-21 minute): a pre-scan and six repeated SSE-CEST, with time interval of five minutes. (4) After OGTT (26-51 minute): a pre-scan and six repeated SSE-CEST, with time interval of five minutes. A total of 13 SSE-CEST data was acquired and reconstructed. ST signal at 2 ppm, MTR asymmetry signal at 2 ppm, and line-width of CEST-spectrum were plotted over time.

Liver patients. Twenty-one patients with focal liver lesions were prospectively enrolled, comprising 8 benign lesions and 12 hepatocellular carcinomas (HCCs). Among the HCC cohort, 11 were post-treatment. One HCC patient was excluded from statistical analysis due to protocol deviation for technical validation.

Two radiologists (Y.Y. and B.Z.) independently contoured lesions on CEST images; perilesional normal parenchyma served as control regions on the same slice. Lorentzian difference (LD) and magnetization transfer ratio (MTR) asymmetry values were quantified by averaging voxels within each ROI.

Data Analysis

Data reconstruction and CEST quantification was performed in MATLAB R2021b on a workstation. The reconstruction time was ~260 seconds. The CEST images and spectra were quantified by calculating MTR asymmetry (MTRasym), Saturation Transfer values (ST), and Lorentzian Difference (LD), as defined by the following equations:

MTRasym = (S(-ωCEST)−S(ωCEST))/S0 (9)

ST = 1− S(ωCEST)/S0 (10)

LD = ZLFCEST −ZexpCEST (11)

where ωCEST is the frequency offset, S(ωCEST) is the saturation image at ωCEST, S0 is the reference image at -1560 ppm, ZLFCEST is the fitted Lorentzian line-shape, and ZexpCEST is the acquired CEST-spectrum.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work describes a new MRI acquisition technique for chemical exchange saturation transfer (CEST). CEST is a type of\nMRI contrast that is more specific for detecting molecular signals compared to other more conventional MRI scans such as\nT1 and T2 weighted imaging, and magnetization transfer contrast (MTC). CEST MRI has the potential to improve clinical\ncare by elucidating the underlying mechanisms of several diseases, including cancer. The work presented here shows\nsubstantial improvement in the acquisition by acquiring a whole Z-spectrum within a single-breathhold which is important for\nimaging organs in the abdomen. Still, it is hard to judge the quality of the data using the new method via the analysis\nmethods used here. As mentioned, CEST aims to specifically detect molecules. Acquiring a full Z-spectrum in this sense is\nimportant because it allows for the separation of different signal contributions using multiple-pool modeling approaches. The\nanalysis methods used in this manuscript often report the signal change of water (ST) which contains much larger\ncontributions from water relaxation and immobile macromolecules, thus confounding the specific signals from solute\nmolecules. If the ST signal is sufficient, other approaches are already available for reporting this in a single breath hold. I\nbelieve the work is of interest to the readers of this journal and I would recommend publication after major revisions to the\ndata analysis methods used to quantify reproducibility and CEST signal. Specific comments are listed below.\n1. Since the focus of this paper is on CEST, which aims to extract Z-spectral peaks from background signals (e.g., MTC and\ndirect water saturation), I believe the ST metric shouldn't be used. In Figure 2, the regional contrast from amides and\nglycogen is very similar which indicates larger contributions from water properties and MTC. Can the authors quantify the\nseparate signals using multiple-pool fitting or background curve fitting via R1rho theory? Additionally, for validation, can the\nauthors compare their maps with other non MR techniques?\n2. In the difference spectra shown in Figure 2c, f, i:, it is clear that the z-omega pattern does affect Z-spectral features. The\nBland-Altman plots shown in Figure S7 are comparing whole Z-spectra which are primarily determined by water properties\nand MTC. CEST signals tend to be much smaller (approx 1-3%). It would be more important to compare extracted CEST\nsignals with the different sampling schemes.\n3. In Figure 2, it was determined that a parallel trajectory was the most reproducible. Can the authors explain why this was?\nIs it possible that it is due to only the frequency offset being changed with no changes in the gradient?\n4. In Figure 3, and similar to before, I think it is incorrect to use the ST metric to characterize the glycan and glycogen\nsignals. Background fitting or multiple-line fitting should be used.\n5. What is causing the variation in contrast across the slices and within the tubes in Figure 3? I am assuming the mixture is\nhomogeneous.\n6. The methods section states that human experiments were performed using either 2 uT or 0.7 uT. The 2uT results shown\nin Figures 4 and 5 show that almost 90% of the signal was saturated at 1.2/-1.2 ppm. What did the 0.7 uT results look like?\nDid they have higher SNR? Also, it is unclear what is being reported on at these frequencies.\n7. It is sometimes difficult to follow the signals reported and what they are meant to represent. For instance, for healthy\nvolunteers, amides are at 3.5 ppm, amines from 2-3 ppm, and hydroxyls from 0.6 to 2 ppm. In the subsequent results\ninvolving fasting, signals are reported at 3.5, 2, 1.2, -1.2, and -3.5 ppm. Is 2 ppm supposed to be amines or hydroxyls? In the\nglucose ingestion experiments, MTRasym is reported in the main document and also linewidth in the supplementary. The\nparameters keep on changing throughout the paper and are hard to follow. I would like to see a consistent parameter used\nand one that is as specific to the molecular origin of the contrast.\n8. In Figure 5, there is a statistically significant signal change for ST(3.5ppm) bit not APTw. Does this indicate the changes\nare mostly due to changing water parameters?\n9. Comparing the results in Figure 6, and Part 7 of the supplementary, it is not clear if the time course in Figure 6b is\nreproducible across the five subjects. I suspect the SNR is insufficient to measure changes due to glucose ingestion. In\naddition, given the relatively slow time course of glucose signal changes, is this rapid imaging technique suitable for this\napplication?\n10. Similar to Figure 5, there is a significant difference in the ST(3.5ppm) results but no significance in the APTw. Are the\nresults due to changes in water parameters or MT instead of a CEST effect?\n11. In some figures, it is not clear how many adjacent slices/points where used in the SVD. Using adjacent slices in SVD\nrequires anatomical similarity. For heterogeneous regions (e.g., liver lesions) how would this affect the results?\nOther comments:\n12. In the supplementary, can you please describe how the resolution is calculated in z-omega space?\n13. There is inconsistent use of delta omega (e.g., Figure 1d and Eq. 1)\n14. I assume the total scan time is calculated by the number of saturation encodings multiplied by the shot interval. Based on\nthe methods, this will mean a scan time of approximately 20 seconds. Can the authors clarify this?", "reviewer_2": "This is very interesting research, combining UFZ and low rank tensor-based reconstruction to achieve super-fast abdominal\nCEST imaging within a single breath-hold. The study was well-planned, including optimization of different z-ω encoding\npatterns, validation in glycogen phantoms, and in vivo studies in healthy subjects, fasting, glucose tolerance tests, and\nhepatic carcinoma patients (both HCC and necrotic lesions). Imaging framework is well presented, manuscript is very well\nprepared, and results are convincing. This technique has great potential of making CEST imaging feasible in the abdomen.\nI have a few questions:\n• The major technical innovation is z-ω encoding, allowing x11 acceleration. It relies on interpolation of the spectral basis\nfrom adjacent slices, assuming the CEST signals are similar. It could be ok for normal subjects or diffuse disease but may\nhave problems when there are metabolite concentration variations or focal disease. Zcorr was solved directly from the\ninterpolated spectral basis without further refinement. The reliability of this approach needs to be rigorously tested.\n• Are saturation times of 0.4 and 0.8s sufficient for the CEST signal to reach steady state? Usually 2-4s are used for\ncontinuous saturation.\n• There was discrepancy between phantom and in vivo studies. In human studies, B1 = 2 uT with 0.4 s saturation and B1 =\n0.7 uT with 0.8 s saturation, with TFE shot intervals of 1472/1871 ms. By contrast, in phantom studies, 0.7 uT (3.5 s), 1 uT\n(3.5 s), and 2 uT (1.75 s) were used with a TFE shot interval of 8 s. It would have been helpful if they had included phantom\nexperiments using the same parameters as in vivo, and compared them with a conventional CEST spectrum."}, "author_response": "We would like to thank the reviewers and editors for their time and insightful comments. We’re\nvery appreciated that the reviewers gave us very positive feedbacks, considering our work “show\nsubstantial improvement in the acquisition … which is important for imaging organs in the abdomen”,\n“very interesting research”, “… results are convincing”, “has great potential of making CEST imaging\nfeasible in the abdomen.” Building on the reviewers' constructive guidance, we substantially\nrefined our data analysis and reliability validations. Three key improvements include:\n1. Quantitative analysis confirms the full-spectral, motion-stabilized benefits of SSE-CEST:\nReplaced previous less-specific ST images in the main text with the extracted CEST imaging (except\nFig. 4, used for repeatability), with five contrast maps defined consistently throughout; Statistical plots\nhave been updated to match (revised Figs. 2, 3, 5, 6, 7, Supplementary Table 1, Supplementary\nMethods 2, 3).\n2. Reliability validated in phantoms and in ex vivo porcine liver: Since in vivo scans lack\nmotion-free gold standard, we have comprehensively compared SSE-CEST with the conventional\nCEST, in ex vivo porcine liver and in phantoms (re-prepared phantoms by dissolving glycogen in agar\nto mimic human tissue). All-slice images and reconstruction errors for 1-21 slice groups are now\nsupplied (Supplementary Figs. 2.1-2.3, 3.1-3.5).\n3. Spatial-spectral performance in volunteers and in patients: we now supply detailed\nspectra, whole-volume images and grouped-slice comparisons (revised Figs. 5, Supplementary Figs.\n5.1-5.7, 7.1-7.5). Retrospective data enable direct matching of SSE-CEST images to 18F-FDG-PET\nhotspots (Fig. 8), and prospective high-resolution acquisition in a further patient confirms the ability\nfor focal-lesion detection (Supplementary Fig. 7.6).\nWe have also sharpened the discussion and reordered the Supplementary Information to mirror\nthe main-text experiments, reinforcing reliability and quantification. We believe the ultra-fast motion-\nstabilizing SSE-CEST will significantly advance the diagnosis for liver cancer and other abdominal\ndiseases, offering a label-free, clinical-accessible metabolic MRI solution.\nThe detailed corrections and responses to the reviewers' comments are listed below point-by-point."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have done a commendable job addressing my previous comments. I feel that the changes make the research\nmuch stronger and it is suitable for publication a minor edit.\n1. The broad direct water saturation line is not Lorentzian in nature and thus is probably the major reason for the poor fits in\nSupplementary Figures 5.1-5.3. Perhaps the authors can briefly mention in the Discussion or Section 5 of the supplementary\nthat Gaussian lineshapes or multiple lineshape fitting may improve the specificity of the signal extracted.", "reviewer_2": "All my comments have been satisfactorily addressed. Congratulations on this important work!"}, "author_response": "We sincerely thank the Editors and Reviewers for accepting our paper in principle. We have\nrevised the manuscript to address all editorial requests (detailed in the attached Author Checklist), with\nthe remaining comment from reviewer 1 responded below.\nReviewer 1\nThe authors have done a commendable job addressing my previous comments. I feel that the changes\nmake the research much stronger and it is suitable for publication.\na minor edit: The broad direct water saturation line is not Lorentzian in nature and thus is probably\nthe major reason for the poor fits in Supplementary Figures 5.1-5.3. Perhaps the authors can briefly\nmention in the Discussion or Section 5 of the supplementary that Gaussian lineshapes or multiple\nlineshape fitting may improve the specificity of the signal extracted.\nAuthor Response:\nWe agree that refined quantification strategies should be discussed. Two edits have been made as below.\nWe have added in the Discussion that “Finally, our single Lorentzian approximation for water\nsaturation at 0.7 μT overlooks line broadening and magnetization transfer effects that become prevalent\nat higher B₁ amplitudes. Extension to Gaussian, Voigt, or multi-pool lineshapes is warranted to ensure\nfidelity across diverse saturation conditions and tissue types.” (The last two senescence’s in the\nlimitation part)\nFurthermore, we added descriptions in the supplement methods (the last paragraph in\nSession 2): “Noted this model neglects water line broadening and the distortions due to\nmagnetization transfer contributions, therefore may cause inaccurate quantification for diverse tissue\ntypes and/or larger saturation B1 field. Nevertheless，owing to the highly-efficient spectral\ninterpolation and motion-stabilizing of SSE-CEST，other refined fitting strategies could be integrated\nin future— including Gaussian, Voigt, or multi-component Lorentzian schemes — combined with\nmachine-learning (Chen, 2023) or deep-learning (Chen, L 2020, Glang, Deshmane et al. 2020).”"}]

Decision letter