MR fingerprinting for semisolid magnetization transfer and chemical exchange saturation transfer quantification

Chemical exchange saturation transfer (CEST) MRI has positioned itself as a promising contrast mechanism, capable of providing molecular information at sufficient resolution and amplified sensitivity. However, it has not yet become a routinely employed clinical technique, due to a variety of confounding factors affecting its contrast‐weighted image interpretation and the inherently long scan time. CEST MR fingerprinting (MRF) is a novel approach for addressing these challenges, allowing simultaneous quantitation of several proton exchange parameters using rapid acquisition schemes. Recently, a number of deep‐learning algorithms have been developed to further boost the performance and speed of CEST and semi‐solid macromolecule magnetization transfer (MT) MRF. This review article describes the fundamental theory behind semisolid MT/CEST‐MRF and its main applications. It then details supervised and unsupervised learning approaches for MRF image reconstruction and describes artificial intelligence (AI)‐based pipelines for protocol optimization. Finally, practical considerations are discussed, and future perspectives are given, accompanied by basic demonstration code and data.


| INTRODUCTION
Semisolid magnetization transfer (MT) and chemical exchange saturation transfer (CEST) MRI have proven to be powerful tools for detecting changes in semisolid macromolecular components (e.g., myelin sheets or membranes and lipids) and solute molecules (e.g., mobile proteins, peptides, and metabolites) in numerous disease pathologies. [1][2][3][4][5][6][7] However, most currently used imaging protocols are not able to provide quantitative measurement of tissue parameters and acquire semisolid MT and CEST-weighted images only. In addition, the observed CEST contrast is a complex overlay of contributions from different proton pools, including amide, amine, semisolid MT, and/or relayed nuclear Overhauser enhancement (rNOE), which can sometimes bias the biological interpretation of the observed signal changes. For instance, amide proton transfer (APT) imaging, a variant of CEST MRI, has shown promise in brain cancer detection, diagnosis, and treatment-response assessment. [8][9][10][11] These studies have established that increased cytosolic protein content in gliomas can cause an APT hyperintensity, as revealed by proteomics and in vivo MRS. 12,13 However, some recent preclinical 14,15 and clinical 16,17 studies of brain tumors, which observed a hyperintense tumor APT signal, demonstrated a decreased tumor amide CEST contrast after separating out the contributions to the APT signal from the semisolid MT and rNOE proton pools.
This decreased tumor amide CEST signal may be due to the significant tumor edema or due to differences in the RF saturation parameter or analysis method used. Thus, the complex nature of the CEST contrast can challenge the interpretation of the underlying disease pathology in some cases. 18 Similarly, the magnetization transfer ratio (MTR) metric conventionally used in semisolid MT imaging is influenced by relaxation effects, thus limiting the detection of the specific tissue composition. 4,19 Even worse, the weighted signals or image contrasts are highly dependent on the image acquisition parameters (e.g., TR, RF saturation powers, durations, frequency offsets, saturation labeling strategies, etc.) and data analysis methods. 20 These differences presumably contribute in part to the inconsistencies observed across studies. Consequently, the development of quantitative semisolid MT and CEST imaging methodologies could provide correct proton exchange parameter estimates, independent of the above-mentioned confounds, experimental settings, and data analysis approaches, and improve the repeatability and reproducibility of the measurements across different imaging platforms.
Currently, the semisolid MT and CEST communities have a great interest in quantifying exchangeable proton concentrations and exchange rates as surrogate biomarkers of protein/metabolite/lipid composition and intracellular pH, respectively. One of the most promising exchange quantification methods fits the CEST signals using the steady-state analytical solution of the Bloch-McConnell (BM) equations. 21 However, it requires long scan and computation times. Over the past decade, although many quantification methodologies have been developed to address the challenges discussed above, a tremendous leap in acquisition and reconstruction times was only recently made by integrating semisolid MT and CEST with MR fingerprinting (MRF). Furthermore, recent advances in deep learning provide a new paradigm for solving ill posed inverse problems in MRF reconstruction. Herein, we provide readers with an overview of semisolid MT and CEST-MRF acquisition, reconstruction, optimization, and interpretation strategies. The scope and organization of this review are described in Supporting Information Figure S1.
2 | CEST MRI BACKGROUND 2.1 | CEST-weighted imaging CEST-weighted signals are usually obtained from the Z-spectrum using an MTR asymmetry analysis at certain frequency offsets, where MTR asym is given by 3 MTR asym ¼ SðÀΔωÞ À SðþΔωÞ S 0 ¼ ZðÀΔωÞ À ZðþΔωÞ ð 1Þ S(±Δω) is the signal measured with saturation at offset ±Δω, and S 0 is a reference signal acquired without saturation. In the case of APT imaging, MTR asym is evaluated at an amide chemical shift of 3.5 ppm from the water resonance. However, due to the contribution to MTR asym from the nuclear Overhauser enhancement (NOE) effect of aliphatic protons of mobile cellular macromolecules with a chemical shift of around À3:5 ppm, including the inherent semisolid MT asymmetry, the APT signals are reduced and do not provide a clean quantification of the amide proton signal.
In addition, the fast-exchanging amine protons of glutamate, at a chemical shift of around 3 ppm, and guanidinium protons in proteins and creatine, resonating at around 2 ppm, can make contributions to the APT signal, particularly for high RF saturation power levels. Various methods were developed for separating the desired APT effects from the background semisolid MT and NOE signals. These include the three-offset approach, which estimates the MT and direct water saturation contribution using a linear approximation, 22 and its later refinement using relaxation-based direct saturation correction (DISC). 23 In a different work, a two-pool BM equation-based fitting with super-Lorentzian line shape, called extrapolated semisolid MT reference (EMR), 24,25 which subtracts the fitted semisolid MT signal from the acquired Z-spectrum, has been proposed. Furthermore, a multi-pool Lorentzian fitting analysis of the Z-spectrum can also be used to better separate the different spectral components. 26,27 Nevertheless, dilution effects on the measured APT signal from direct water and semisolid MT saturations still remain due to the non-linear contributions from the different proton pool components (water, semisolid MT, APT, and other CEST components) of the Z-spectrum, which changes with the RF saturation parameters. In addition, these approaches cannot completely disentangle the coupled parameters of exchange rate and concentration. All of the above challenges have motivated a considerable effort to develop truly quantitative CEST imaging techniques, as described below.

| Non-MRF quantitative CEST imaging
In light of the detailed review papers for CEST quantification, [28][29][30][31][32] this section aims to briefly describe the general concept underlying previous quantitative approaches and highlight the motivation to develop CEST-MRF methodology.
One of the first in vivo measurements of chemical exchange rate was performed using the water exchange spectroscopy (WEX) method for the quantification of the amide proton exchange rate from endogenous mobile proteins. 33 An exchange rate of about 30 Hz was estimated from the mixing-time evolution of the amide signal in the WEX spectrum using a simple two-pool exchange model (free bulk water and amide proton pools). Relatively long mixing times for the water labeling preparation were used in the study, limiting the detection of fast-exchanging amide protons. The amide proton concentration of approximately 72 mM was calculated by solving the two-pool-based APT ratio equation with the exchange rate estimated from the WEX spectrum. Moreover, the use of a high saturation power in the WEX experiment would increase the spillover effect of direct water saturation and semisolid MT. Therefore, the amide exchange rate and concentration reported from the WEX experiment may not necessarily be accurate for all amide protons.
Quantification of exchange rate using varying saturation power (QUESP) and saturation time (QUEST) methods were proposed to estimate the exchange rate using a simplified analytical solution of the two-pool BM equations. 34 The methods estimate and correct for spillover water saturation by applying a saturation pulse on the opposite side of water from the exchangeable protons to calculate the proton transfer ratio (PTR). However, the result may be corrupted by upfield NOE as well as semisolid MT signals for in vivo applications. In addition, the analytical solution used in QUESP/QUEST assumes complete saturation under a strong B 1 saturation power, which can significantly increase direct water saturation and semisolid MT signal contributions, and thus is less accurate for measuring fast exchange rates. Recently, refined QUESP/QUEST analytical equations were introduced for inefficient saturation conditions. 35 In addition, an empirical solution, which also considers the direct water saturation (spillover) effect, was derived. 36,37 However, this approach is sensitive to water relaxation, and requires voxel-wise mapping of the T 1 and T 2 relaxation times. 29 Finally, the acquisition of multiple Z-spectra with various saturation pulse powers and durations requires very long acquisition times, although an acceleration is feasible using multi-echo length and offset varied saturation (MeLOVARS), 38 progressive saturation for quantifying exchange rates using saturation times (PRO-UEST), 39 and a post-processing solution for quasi-steady-state (QUASS) saturation time and relaxation delays. 40 The apparent exchange-dependent relaxation (AREX) method 41 was demonstrated for measuring an inverse exchange rate (from a free bulk water proton pool to a labile proton pool) using an inverse Z-spectrum metric with known water T 1 . Using this metric, an in vivo quantification of solute concentrations can be further estimated, following the use of a phantom calibration study and by acquiring multiple Z-spectra, 42 or assuming a fixed volume fraction of the solute pool. 41 However, the simple analytical solution used for the AREX method could be a poor approximation of the full BM-equation solution at strong RF saturation and low spectral resolution (clinical field strength) conditions. 31,43 Additional prominent CEST quantification methods include omega-plots, 44,45 full BM equation fitting, 21 ratiometric analysis, 46,47 and frequency labeled exchange (FLEX). 48,49 However, these approaches are either challenging to apply in vivo, 50 require a long processing time, 51 involve exogeneous media injection, 52 or are mostly appropriate for saturating fast-exchanging protons. 49 3 | SEMISOLID MT/CEST MRF For reconstruction, a pattern-matching algorithm is used to find different tissue-type parameters against a pre-calculated dictionary (or database) from Bloch simulations with a wide range of tissue parameter combinations. The best match is then used for practically solving the inverse problem of the Bloch equations.
Originally introduced for water T 1 and T 2 relaxation, B 0 shift, and proton density quantification, MRF has gradually expanded for the quantification of additional tissue parameters, 54 such as blood flow velocity, 55 perfusion, 56 and B þ 1 . 57 Importantly, the MRF framework can be adapted to estimate multiple proton-exchange components such as semisolid MT and CEST parameters. A significant effort is currently ongoing to develop a robust, quantitative semisolid MT and CEST MRF imaging framework using pseudorandomized RF saturation and acquisition schedules, and a database matching process for reconstruction. Figure 1 shows the primary components of the semisolid MT/CEST-MRF: image acquisition, dictionary generation, reconstruction, and visualization.

| Dictionary matching for semisolid MT/CEST-MRF reconstruction
A preliminary CEST "fingerprinting-like" experiment was performed by Geades et al, 58 where a numerically simulated look up table was used to extract the NOE, amide, and semisolid MT quantitative proton volume fractions from Z-spectra acquired with three different saturation powers.
However, the simulations were performed for a very restrictive parameter space, with only eight different proton concentration values considered for each pool, a fixed proton exchange rate, and a total acquisition time of 24 min. For reconstruction of the concentration and exchange rate maps of the exchangeable proton, the experimental signal trajectories were matched to a simulated dictionary using a correlation-based metric (dot product). The estimated exchange parameters for the L-arginine phantom ( Figure 2) were shown to be in good agreement with results from the QUESP method. Although reasonable in vivo semisolid MT and amide parameter maps were obtained from a wild-type in vivo rat, this approach is limited by the use of a single acquisition schedule with a fixed frequency offset (3.5 ppm), which is sub-optimal for assessing the semisolid MT exchange parameters and separating it from the amide-related signal contribution. 15 In addition, the B 0 field inhomogeneity was not considered.
The study of Zhou et al 60 reported a CEST-MRF sequence for the quantification of creatine amine proton exchange rates in a three-pool creatine/agarose phantom, which explored methods for removing the semisolid component from the amine CEST signal at 2 ppm and correcting for B 0 inhomogeneity. Prior to the dictionary matching, the semisolid MT effects were estimated by measuring saturated signals at the opposite F I G U R E 1 General pipeline of a semisolid MT/CEST MRF experiment. (A), Initially, a pseudo-random imaging protocol is designed, where at least one acquisition parameter is being varied, to produce a set of N images. Importantly, a pre-saturation block needs to be implemented, where at least the saturation pulse power (B 1 ), duration (T sat ), or frequency offset (ω rf ) should vary, for sufficient encoding of the chemical exchange parameters. The protocol typically includes a rapid readout, e.g., using echo planar imaging or turbo spin echo, with either a fixed or varied flip angle and recovery time (  60 frequency offset (À2 ppm), upfield from the water resonance, and removed using a pre-calculated dictionary ( Figure 3). However, the estimation of semisolid MT signals from the opposite frequency offset might be biased, particularly for in vivo tissue, due to asymmetric semisolid MT and NOE contributions. To allow for retrospective correction of B 0 field inhomogeneities, the CEST-MRF image acquisition was also repeated at multiple frequency offsets. However, this prolonged the total scan time to approximately 10 min.
Conventional dictionary-matching-based MRF reconstruction methods, however, have certain challenges and limitations. First, the dictionary generation time, which is built on the numerical solution of the BM equations, is exceedingly long and may take hours, or even days, depending on the available hardware and complexity of the CEST imaging scenario. 15 Second, the reconstructed parameters are discrete, and their resolution is limited by the size of the dictionary. Third, large dictionaries with millions of entries are needed for complicated multi-pool CEST scenarios, requiring expansive computational storage. Finally, the quantitative image reconstruction may take many hours, making it infeasible for use in clinical settings, where rapid decisions must sometimes be made.
The first attempt to overcome the limitations of dictionary matching methods was demonstrated by Heo et al, 61 where the acquired MRF trajectories were fit to a multiple-pool exchange model using a non-linear least-square procedure. The dictionary-free reconstruction method was demonstrated on CEST phantoms and healthy volunteer human brains at 3 T ( Figure 4). Although the model-based fitting approach has almost unlimited tissue parameter range and precision for estimating semisolid MT and CEST parameters, it may be affected by the parameter initialization conditions and prone to local minima errors. Moreover, it still suffers from a long reconstruction time. 61 This important consideration has therefore motivated the exploration of alternative, deep-learning-based MRF reconstruction methods for fast tissue parameter quantification.
F I G U R E 4 Quantitative proton exchange parameter maps of ammonium chloride (NH 4 Cl) phantoms and a healthy human volunteer obtained using dictionary-free CEST-MRF. 61

| Deep learning for semisolid MT/CEST-MRF reconstruction
The recent improvements in deep-learning capabilities have created unique opportunities for medical imaging. While the most familiar examples include accurate pathology detection, 62 segmentation, 63 and classification 64 at the post-processing stage, an evident benefit lies in utilizing deep learning for improving image reconstruction. In addition to being able to approximate and represent complex non-linear relations, 65 a significant advantage of using deep learning compared with earlier machine-learning approaches is its ability to automatically learn and optimize the classification features, thereby reducing the need for domain expertise and manual feature selection/design. 66,67 However, the main practical limitation for using deep learning in medical imaging is the need to acquire large quantities of training data for high performance. While large databases are available for natural scene images, 68 only a few, much smaller MRI data repositories have been made publicly available (e.g., ref. 69 ). Luckily, the MRF reconstruction approach is based on artificially synthesized data, allowing the generation of data sets of any desired size. This characteristic has rendered the combination of deep learning and MRF an attractive means for rapid reconstruction of MR images, as demonstrated for water T 1 and T 2 . By feeding a fully connected neural network (FCNN) voxel-wise with MRF trajectories (acquired using a pseudorandom sequence with varied flip angles and repetition times), Cohen et al 67 were able to reconstruct water relaxation times in less than 100 ms. Can deep learning be similarly applied in the molecular imaging and semisolid MT/CEST realm?
As mentioned in Section 2.1, CEST-related signals are commonly measured from the Z-spectrum. It is therefore not surprising that the first reported combination of neural network (NN) and CEST data for quantitative exchange parameter mapping has used this intuitive signal as the input source for an artificial neural network (dubbed ANNCEST). 70 By training four ANNCESTs ( Figure 5A) with the Z-spectra generated using the BM equation, the phosphocreatine exchange parameters of the human skeletal muscle ( Figure 6B) and the B 0 /B 1 field inhomogeneities were successfully quantified in vivo. Although this approach was not originally reported as an MRF experiment, 70 the use of a simulated dictionary for the neural-network training, together with an input signal that encodes for CEST changes, allow this approach to be considered as a CEST-MRF variant.
F I G U R E 5 Supervised machine-learning architectures for semisolid MT/CEST MRF. (A), Quantification of phosphocreatine exchange parameters using an artificial NN composed of a single hidden layer. 70 The input layer was fed with Z-spectrum measurements, analogous to a CEST-MRF schedule where the varied parameter is the saturation pulse frequency offset ω rf ), and the output was either the phosphocreatine proton volume fraction (f s ), exchange rate (k sw ), B 0 , or transmit field (B 1 ). The NN had four variants that were fed with the same input but trained to output each of the four different sought-after parameters, using a simulated dictionary. (B), Brain semisolid MT exchange parameter quantification and background semisolid MT (Z ref ) contrast image synthesis, 71 using a fully connected NN. The input MRF schedule varied the saturation pulse power (B 1 ), duration (T sat ), ω rf , and the recovery time (T rec ). The output included the semisolid MT parameters, and a synthesized MT reference image at 3.5 ppm, calculated by plugging in the resulting parameters and the water T 2 values obtained from a separate protocol in the two-pool BM equations solution. (C), Sequential and deep CEST and semisolid MT quantification in the brain. 15 A semisolid MT-oriented MRF acquisition schedule, which varies ω rf and B 1 , yields 30 images that are fed voxelwise into the first NN, together with the quantitative water pool and field homogeneity maps (T 1 , T 2 , B 0 ). This NN maps the semisolid MT pool exchange parameters, which are then fed, together with the previously obtained quantitative data, into the second NN, ultimately yielding the amide proton f s and k sw While the semisolid MT pool can be treated as a spatially homogeneous proton pool in the leg muscle (as performed in the ANNCEST approach), its properties vary markedly across the brain. 72 Given that changes in semisolid MT exchange parameter values are useful for the diagnosis of several diseases (the best-known example is multiple sclerosis), 73 there is a clear motivation for developing rapid semisolid MT quantification methods. Accordingly, Kim et al 71 developed a deep-learning approach for simultaneously quantifying semisolid MT proton exchange rate, volume fraction, and transverse relaxation, as well as the water longitudinal relaxation, demonstrated in the brain of healthy volunteers at 3 T. A dynamic MRF schedule that varied the saturation pulse power, duration, frequency offset, and relaxation recovery time was used to train deep NNs ( Figure 5B). Furthermore, using the tissue parameters estimated from MRF and the acquired water T 2 relaxation, accurate semisolid MT signal intensities were able to be estimated at certain CEST frequency offsets (e.g., 3.5 ppm and À3:5 ppm for APT and NOE imaging, respectively), allowing for a clean separation of the semisolid MT and CEST signals.
There is a clear value in the ability to accurately de-bias CEST-weighted brain images from the semisolid MT and water contribution. Nevertheless, a fully quantitative and rapid estimation of the amide proton volume fraction and exchange rate would provide an ideal means for assessing the underlying molecular phenomena and pathology, as discussed in Section 2. However, for this application, there are at least three prominent compound pools involved (amide, semisolid MT, and water), whose parameters all vary simultaneously with disease progression. This complex and highly multi-dimensional parameter space imposes a considerable challenge. Accordingly, trying to employ a single NN with a single parameter encoding acquisition schedule in tumor bearing mice has resulted in very noisy and poorly discriminating parameter maps. 74 The first deep-learning-based CEST-MRF method that fully quantified these parameters in the brain disease environment was recently reported by Perlman et al. 15 The key element responsible for this progress was a sequential deep-learning pipeline ( Figure 5C), aimed to obtain both semisolid MT and amide quantitative information, while reducing the complexity of each quantification step, by relying on the results of the former. The method was explored in the context of neuro-oncology applications and was used for monitoring the treatment response of glioblastoma multiforme T A B L E 1 Literature values of the brain white/gray matter semisolid MT and amide proton volume fractions (f ss /f s ) and exchange rates (k ssw / k sw ) (GBM) bearing mice to oncolytic virotherapy (Figure 7). The translation of this method to a 3 T clinical scanner has demonstrated good agreement with previous literature reports in a healthy human volunteer (Table 1).
All the NN strategies discussed so far can be associated with the machine-learning branch of supervised learning, where labeled ground-truth information is paired to each input signal during the system's training. In the context of MRF, these data pairs are obtained via an extensive numerical dictionary generation step, which may take hours, depending on the complexity and number of pools involved in the simulated scenario and the availability of computational resources (number of CPUs/GPUs, RAM, etc.). In addition, the accuracy of the quantification is highly dependent on the model used for dictionary simulation, which is not guaranteed to accurately reflect the experimentally measured data. To address  Figure 8). Instead of presenting the NN with pairs of simulated MRF trajectories and the corresponding ground truth tissue parameters, the convolutional neural network (CNN) architecture was trained to minimize the difference between "real" experimentally acquired MRF trajectories (input) and synthesized MRF trajectories (output) by solving the BM equations. By defining the loss as the L 2 distance between the "real" MRF trajectories and the simulated counterparts, the CNN iteratively optimizes its quantification ability. The CNN in the unsupervised fashion outperformed supervised NN at lower signal to noise ratios (SNRs), in terms of robustness to noise, which could be beneficial to estimate lowconcentration CEST parameters. However, the unsupervised learning has limited generalization ability because the deep-learning framework was trained with a limited range of tissue parameter in healthy volunteers. In particular, pathological cases that include a distinctly different combination of tissue (and exchange) parameters are not expected to be accurately mapped, unless sufficiently represented in the CNN parameter optimization. While the dictionary generation required for training the NN in the supervised approach is time consuming, it could, in principle, take place only once and include a huge number of parameter combinations, potentially sufficient for many different pathologies (e.g., brain cancer, stroke, etc.).

| Optimization of MRF acquisition schedules
The ability to discriminate different exchange parameters is sensitive to the acquisition schedule used (Figure 9). Thus, it is crucial to tailor and optimize the properties of the imaging protocol for the biological imaging scenario of interest.
A basic means for understanding the influence of the acquisition parameters on the discrimination ability of CEST-MRF and for comparing different schedules is to employ a similarity-based loss metric, such as the dictionary Frobenius norm dot-product loss. 59,81,82 Intuitively, such metrics compare the correlation between different pairs of simulated signal trajectories associated with a given MRF dictionary, assuming that minimal correlation is a predictor for improved parameter discrimination ability. Using this metric, it was demonstrated that different molecular  Figure 10). 82 While similarity metrics, such as the dot product and Euclidean distance, can also serve as predictors of the encoding capability of CEST-MRF acquisition schedules, it was recently shown that an improved pH quantification prediction could be obtained by using the Cramer-Rao bound. 83 Another approach for acquisition protocol optimization is Monte Carlo simulations of noise propagation. 84 Here, a dictionary with a particular imaging protocol is repeatedly generated with random noise perturbations. As the noisy trajectories are matched to the original "clean" dictionary, the proton exchange rate and volume fraction quantification error can be calculated. Based on this strategy, a numerical evaluation predicted that a CEST-MRF schedule could be shortened by more than 60%, with only a minor decrease in reconstruction accuracy. The finding was then successfully confirmed using an experimental phantom study. 82 The main limitation of the numerical optimization strategies mentioned above is the need to calculate a particular loss (or quantification error) for each acquisition-schedule candidate. Given the very large parameter space involved in CEST-MRF, where at least five scan parameters (saturation pulse power, duration, frequency offset, readout flip angle, and repetition time) could be varied, and a huge dictionary of biophysical parameter combinations must be synthesized for each schedule, it is virtually impossible to explore all (or most) of the acquisition parameter space.
In an attempt to bypass the time-consuming dictionary generation requirement, and improve the chances of finding a global solution, a preliminary work by Cohen 85 has developed a schedule optimization network (SCONE), aiming to learn the direct functional mapping between the acquisition schedule and the corresponding reconstruction error. In the first step, a mapping from the raw dictionary signals associated with an MRF protocol to the corresponding quantitative parameters is performed, using a supervised learning approach, similar to that described in Recently, a more unified framework termed AutoCEST was developed, allowing an end-to-end automated discovery of semisolid MT/CEST MRF acquisition protocols and quantitative deep reconstruction ( Figure 11). 76 Its key component was treating each acquisition schedule parameter similarly to an NN node weight, thereby allowing its efficient optimization. To enable such optimization, the CEST saturation block was represented as a computational graph ( Figure 11B), based on the analytical solution of the two-87 or three-88 proton-pool BM equations. Next, the readout and relaxation blocks were similarly represented using the Bloch equations with a discrete-time state-space model in the rotating frame ( Figure 11C), allowing for the calculation of the expected MR signal for a randomly initialized set of acquisition parameters. These signals are then directly fed into a quantitative reconstruction network ( Figure 11D), trained to output the desired semisolid MT/CEST exchange parameters. To obtain efficient and simultaneous optimization of the acquisition and reconstruction parameters involved in deep CEST-MRF, all computational graphs were serially connected. This enables a "single-click" optimization using automatic differentiation and stochastic gradient descent.
AutoCEST was used for discovering optimized amide and semisolid MT acquisition schedules and yielded amide and semisolid MT exchange parameters in good agreement with previous reports ( Table 1).
The potential and strength of using a supervised deep-learning strategy, combined with a loss function that directly evaluates tissue quantification error for MRF schedule optimization, was recently further substantiated by Kang et al. 89 A framework for learning-based optimization of the acquisition schedule (LOAS) was developed to optimize RF saturation-encoded MRF acquisition with a minimal number of scan parameters for tissue parameter quantification ( Figure 12). The BM-based numerical phantom and in vivo studies showed that the LOAS outperforms existing indirect optimization methods, such as the Cramer-Rao lower bound 90 and interior point (IP), 81 in terms of quantification accuracy and acquisition efficiency.

| Practical considerations in semisolid MT/CEST-MRF studies
There are several practical issues to consider in the development of the semisolid MT/CEST-MRF methodologies. The performance of the MRF methods must be rigorously evaluated in terms of their accuracy, repeatability, and reproducibility across subjects, vendors, and imaging sites, and assessed with the certainty of the estimated tissue parameters.

| Accuracy
For the MRF reconstruction (or tissue parameter quantification), deep-learning NNs can be trained with a huge dataset that covers all possible combinations of tissue properties. Then, the reconstruction accuracy of the deep-learning NNs can be evaluated on a never-before-seen test dataset. Furthermore, the semisolid MT/CEST-MRF method can be demonstrated using well controlled phantoms with known proton concentration and pH. For instance, the amide proton exchange rate has a one-to-one correspondence with pH because the exchange rate of -NH groups is base catalyzed and decreases with decreasing pH. 3 Thus, an estimated proton exchange rate can be indirectly evaluated by observing signal changes at different pH values and deriving empirical calibration formulas to relate exchange rate to pH. Several important NMR and MRI methods have been developed to directly estimate proton exchange rates by measuring the temperature-dependent linewidth, fitting the Z-F I G U R E 1 2 A schematic diagram of the LOAS. Semisolid MT-MRF signals synthesized using initialized scan parameters (RF saturation power, B 1 , frequency offset, Ω, saturation time, T s , relaxation delay time, T d ), noise, and tissue parameters (Input) are fed to the FCNN. The FCNN outputs tissue parameter estimates (Output). The loss function is defined as the mean square error between the ground truths and estimated tissue parameters. The calculated loss was back-propagated with an ADAM optimizer to update the scan parameters. APT and NOE images were calculated by subtracting the synthesized semisolid MT image at 3.5 ppm from the acquired saturated image at ±3.5 ppm. Reproduced and modified with permission from Kang et al., NMR Biomed 2021:e4662. 89 spectrum with the BM equations, 21 QUESP, 34 WEX, 33 or Omega plot. 44,45 The estimation of semisolid MT and CEST parameters reported in the literature is shown in Table 1. Although the methods are promising as a reference standard, the measurement of the absolute in vivo exchange rate remains challenging and there is no widely accepted "gold standard" method regarding the measurement. To enable effective validation, previous studies performed synthetic MRI analysis ( Figure 13) to evaluate the reconstruction accuracy. Various contrast-weighted images were synthesized with the tissue parameters estimated by deep-learning semisolid MT-MRF by solving the BM equations with new RF saturation parameters and relaxation delay time (T d ). Good agreement between the synthetic and actually acquired images was found, which may guarantee stable solutions (tissue parameters) of the inverse problem of semisolid MT-MRF. In the absence of a ground truth, synthetic MRI could be useful for validation of in vivo tissue parameters and applied to CEST-MRF or other quantification methods. In addition, histology and immunohistochemistry images can be used to confirm any assumptions made based on proton exchange parameters (e.g., apoptosis, tumor/healthy tissue, total . Notably, such measurements should be carefully analyzed, as they do not directly reflect the exchangeable proton volume fraction or exchange rate.

| Repeatability and reproducibility
As in any other quantitative MRI, it is important to ensure that tissue parameters estimated from semisolid MT/CEST-MRF methods are repeatable and reproducible. 91 While a conventional MRF method has demonstrated high repeatability and reproducibility of water T 1 and T 2 relaxation times, there is unfortunately sparse literature studying the repeatability and reproducibility of semisolid MT/CEST-MRF measurements due to their relative novelty. A standardized phantom must be used to determine the repeatability for each scanner and between-scanner reproducibility.
For human studies, an interesting approach called "the traveling heads" 92 was recently introduced to improve the reproducibility of quantitative MRI. 93 The same two subjects were imaged on different scanners at multiple sites, comprising multiple repetitions at each scanner to assess inter-

| Open source for semisolid MT/CEST-MRF
One of the main drivers for widespread implementation of a new MRI technique is the availability of open-source tools. 96 Publicly available data and processing codes will facilitate reproducibility and allow research groups to quickly build upon the project, and further advance the research field. For instance, aligned with this principle, Chen et al 70

| CONCLUSIONS AND FUTURE PERSPECTIVES
The limited availability of expert-labeled clinical data and the recent developments in deep-learning methodologies have motivated the use of synthetic data for augmenting and improving the training of machine-learning models for medical imaging. 99 Within this approach, MRF lies on the extreme edge of the spectrum, as it builds solely on synthetic, physical-model-based generated signals. Therefore, the success of MRF is heavily dependent on the ability of the physical model to accurately depict the real-world measured signals. Although both the classical Bloch equations, 100 used for "conventional" water T 1 /T 2 MRF, and the BM equations, 101 used for semisolid MT/CEST MRF, were intensively investigated in the past decades, the latter contain a considerably larger number of parameters, as each of the proton pools involved contains its own transverse and longitudinal relaxation times, concentration, and exchange rates with the other pools. Therefore, as semisolid MT-MRF, and especially CEST-MRF, contain a large number of "moving parts", they are more prone to inaccuracies caused by model imperfections. An exception to the general MRF concept is the use of unsupervised learning (Section 3.2.2), which does not involve synthesized dictionaries at all. Instead, the training is performed using "real" experimentally acquired images. However, a model is still an integral part of this approach and is considered as the ground truth reference. 75 We postulate that in the future a hybrid deep-learning method, trained using both experimental and synthesized data, could reap the benefits of both worlds.
The performance of semisolid MT/CEST MRF is also expected to further improve due to "third-party" developments, stemming from each of the three parents of this technique: water T 1 /T 2 MRF; deep-learning algorithms; and classical CEST theory. In particular, water T 1 /T 2 MRF is an increasingly investigated field, 54,102 where new acquisition schemes and novel reconstruction approaches are continuously suggested and evaluated. [103][104][105] However, the unique attributes of the CEST-MRF contrast mechanism will mandate careful adaptations to any conventional MRF inspired approach and will require additional and separate research efforts.
The exponential growth in deep-learning applications and methods, and the vast international resources allocated for artificial intelligence (AI) research, are expected to keep expanding the capabilities of deep-learning-based parameter estimation. In the context of the future translation of CEST-MRF for routine clinical care, the topic of explainable AI, which is aimed at uncovering what happens "under the hood" in a deeplearning system, is of particular importance. [106][107][108] Last but not least, new investigations into the exact biophysical properties of various CEST compounds are routinely conducted, [109][110][111] and are expected to improve the accuracy of the semisolid MT/CEST MRF models. Such studies might also assist in clearing the fog of uncertainty concerning the semisolid MT/CEST quantitative ground truth. As demonstrated in Table 1, although some similarities exist between the exchange parameters obtained by various groups, there is a substantial variance for some of the exchange parameters (most strikingly seen for the amide proton exchange rate), for both MRF-based and non-MRF quantitative evaluations. This variability is likely rooted in the different model variants used by different methods (e.g., the use of the analytical or the numerical solution of the BM equations), the assumptions made regarding the biophysical environment (e.g., the number of simulated proton pools and the values of the fixed parameters), the sensitivity and discrimination ability of the particular acquisition schedule used (as discussed in Section 3.3), and the resolution/size of the dictionary/data used for image reconstruction and NN training. A related summary of the key concepts and pros and cons of each semisolid MT/CEST MRF method described throughout this review is available in Table 2.
An additional open subject in quantitative semisolid MT/CEST is the required performance. Is it sufficient to obtain a 10 mM mean squared error in estimating the compound concentration? A 20 Hz resolution for proton exchange rate estimation? A 10% mean absolute error for any parameter? Arguably, the minimal performance should allow the reasonable detection of disease and its classification into various stages/ treatment response.
The clinical imaging field is slowly but steadily transitioning to rely on quantitative instead of qualitative measures. 112 The effort in converting CEST and semisolid MT to become fully quantitative methods for obtaining molecular information could constitute an important component in this transition to quantitative MRI. Given that deep semisolid MT/CEST-MRF provides a drastically shorter scan time, a simultaneous estimation of quantitative biophysical parameters, and a simplified and objective means of analysis, we anticipate that it could play a substantial role in the efforts to make semisolid MT and CEST-MRI an integral part of the clinical imaging routine.