Approximated analytical characterization of the steady-state chemical exchange saturation transfer (CEST) signals

Analytical solution of the Bloch-McConnell equations for steady-state CEST Z-spectra

PURPOSE

To derive an analytic expression for the steady-state Chemical Exchange Saturation Transfer (CEST) Z-spectra of a two-pool proton-exchanging system, facilitating simulations and expedited fitting of steady-state Z-spectra.

METHOD

The analytical expression is derived by directly solving the set of Bloch-McConnell differential equations in matrix form for a two-pool exchanging system, determining water magnetization under steady-state saturation across the entire Z-spectrum. The analytic solution is compared and validated against the numerical solution of Bloch-McConnell equations under prolonged saturation. The study also explores the line shape of a CEST peak, interpolating under-sampled Z-spectra, and Z-spectral fitting in the presence of noise.

RESULTS

The derived analytic solution accurately reproduces spectra obtained through numerical solutions. Direct fitting of simulated CEST spectra with the analytical solution yields the physical parameters of the exchanging system. The study shows that the analytical solution enables the reproduction of fully sampled spectra from sparsely sampled Z-spectra. Additionally, it confirms the approximation of the CEST spectrum of a single exchanging proton species with a Lorentzian function. Monte Carlo simulations reveal that the accuracy and precision of Z-spectral fittings for physical parameters are significantly influenced by data noise. The study also derives and discusses the analytical solution for three-pool Z-spectra.

CONCLUSION

The derived analytic solution for steady state Z-spectra can be utilized for simulations and Z-spectrum fitting, significantly reducing fitting times compared to numerical methods employed for fitting CEST Z-spectra.

The exchange rate of creatine CEST in mouse brain

PURPOSE

To estimate the exchange rate of creatine (Cr) CEST and to evaluate the pH sensitivity of guanidinium (Guan) CEST in the mouse brain.

METHODS

Polynomial and Lorentzian line-shape fitting (PLOF) were implemented to extract the amine, amide, and Guan CEST signals from the brain Z-spectrum at 11.7T. Wild-type (WT) and knockout mice with the guanidinoacetate N-methyltransferase deficiency (GAMT-/- ) that have low Cr and phosphocreatine (PCr) concentrations in the brain were used to extract the CrCEST signal. To quantify the CrCEST exchange rate, a two-step Bloch-McConnell (BM) fitting was used to fit the CrCEST line-shape, B1 -dependent CrCEST, and the pH response with different B1 values. The pH in the brain cells was altered by hypercapnia to measure the pH sensitivity of GuanCEST.

RESULTS

Comparison between the Z-spectra of WT and GAMT-/- mice suggest that the CrCEST is between 20% and 25% of the GuanCEST in the Z-spectrum at 1.95 ppm between B1  = 0.8 and 2 μT. The CrCEST exchange rate was found to be around 240-480 s-1 in the mouse brain, which is significantly lower than that in solutions (∼1000 s-1 ). The hypercapnia study on the mouse brain revealed that CrCEST at B1  = 2 μT and amineCEST at B1  = 0.8 μT are highly sensitive to pH change in the WT mouse brain.

CONCLUSIONS

The in vivo CrCEST exchange rate is slow, and the acquisition parameters for the CrCEST should be adjusted accordingly. CrCEST is the major contribution to the opposite pH-dependence of GuanCEST signal under different conditions of B1 in the brain.

Chemical exchange saturation transfer imaging of creatine, phosphocreatine, and protein arginine residue in tissues

Chemical exchange saturation transfer (CEST) MRI has become a promising technique to assay target proteins and metabolites through their exchangeable protons, noninvasively. The ubiquity of creatine (Cr) and phosphocreatine (PCr) due to their pivotal roles in energy homeostasis through the creatine phosphate pathway has made them prime targets for CEST in the diagnosis and monitoring of disease pathologies, particularly in tissues heavily dependent on the maintenance of rich energy reserves. Guanidinium CEST from protein arginine residues (i.e. arginine CEST) can also provide information about the protein profile in tissue. However, numerous obfuscating factors stand as obstacles to the specificity of arginine, Cr, and PCr imaging through CEST, such as semisolid magnetization transfer, fast chemical exchanges such as primary amines, and the effects of nuclear Overhauser enhancement from aromatic and amide protons. In this review, the specific exchange properties of protein arginine residues, Cr, and PCr, along with their validation, are discussed, including the considerations necessary to target and tune their signal effects through CEST imaging. Additionally, strategies that have been employed to enhance the specificity of these exchanges in CEST imaging are described, along with how they have opened up possible applications of protein arginine residues, Cr and PCr CEST imaging in the study and diagnosis of pathology. A clear understanding of the capabilities and caveats of using CEST to image these vital metabolites and mitigation strategies is crucial to expanding the possibilities of this promising technology.

Theory of chemical exchange saturation transfer MRI in the context of different magnetic fields

Chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI) is a versatile MRI method that provides contrast based on the level of molecular and metabolic activity. This contrast arises from indirect measurement of protons in low concentration molecules that are exchanging with the abundant water proton pool. The indirect measurement is based on magnetization transfer of radio frequency (rf)-prepared magnetization from the small pool to the water pool. The signal can be modeled by the Bloch-McConnell equations combining standard magnetization dynamics and chemical exchange processes. In this article, we review analytical solutions of the Bloch-McConnell equations and especially the derived CEST signal equations and their implications. The analytical solutions give direct insight into the dependency of measurable CEST effects on underlying parameters such as the exchange rate and concentration of the solute pools, but also on the system parameters such as the rf irradiation field B1 , as well as the static magnetic field B0 . These theoretical field-strength dependencies and their influence on sequence design are highlighted herein. In vivo results of different groups making use of these field-strength benefits/dependencies are reviewed and discussed.

Average saturation efficiency filter (ASEF) for CEST imaging

PURPOSE

Endogenous CEST signal usually has low specificity due to contamination from the magnetization transfer effect and from fast exchanging labile protons with close Larmor frequencies. We propose to improve CEST signal specificity with an average saturation efficiency filter (ASEF).

METHODS

ASEF measures the difference between CEST signals acquired with similar average irradiation power but largely different duty cycles (DC), for example, a continuous wave or a high DC pulse train versus a low DC one. Simulation and Cr phantom studies were performed to evaluate the characteristics of ASEF for CEST.

RESULTS

Theoretical and simulation studies show that ASEF can suppress fast exchanging processes, with only a small loss of chemical exchange contrast for slow-to-intermediate exchange rates if the difference in DC is large. In the RF offset range of 2 to 5 ppm with an averaged saturation power of 0.8 and 1.6 microteslas, there is a mismatch of ∼0.1% to 2% in the magnetization transfer signal between saturation by continuous wave and a pulse train with DC = 15% and pulse duration of 24 ms, respectively. This mismatch can be minimized by careful selection of saturation power, pulse duration, and DC differences or by applying a small fudge factor between the 2 irradiation powers. Phantom studies of Cr confirmed that ASEF can minimize the magnetization transfer effect and reduce sensitivity to fast exchange processes.

CONCLUSION

ASEF can improve the specificity of slow-to-intermediate exchanging CEST signal with a relatively small loss of sensitivity.

Role of chemical exchange on the relayed nuclear Overhauser enhancement signal in saturation transfer MRI

PURPOSE

The pH sensitivity of chemical exchange-relayed nuclear Overhauser enhancement (rNOE) signal in a saturation transfer experiment is not fully understood and needs further investigation.

METHODS

A three-pool-exchange model was simulated assuming that the magnetization transfer between an NOE pool and water is relayed by a chemical exchange (CE) pool. The saturation transfer signals from bovine serum albumin (BSA) and egg white albumin (EWA) phantoms were measured with different pH or different D₂ O/H₂ O mixture solutions.

RESULTS

Simulation results showed that the rNOE signal is independent of the Larmor frequency of the CE pool, indicating any CE pool can effectively relay NOE magnetization. The rNOE signal is sensitive to a change of the CE pool size and/or exchange rate only if the CE becomes a rate-limiting step in the relay process. The rNOE signal from BSA phantoms showed larger pH-dependence at -3.0 ppm than those at -1.9 and -4.0 ppm. However, rNOE signals from aliphatic protons have much weaker pH-dependence than the CEST signal, suggesting that CE is unlikely the rate-limiting step and the rNOE signals in BSA are mainly relayed by fast exchanging protons. The existence of aromatic NOE was confirmed by proton spectroscopy.

CONCLUSION

The pH-sensitivity of the rNOE signal is determined by whether the CE process is a rate-limiting step in the relay. The rNOE signal has much weaker pH-sensitivity than the CEST signal in BSA proteins, which can explain the weak pH sensitivity of rNOE in vivo.

Mapping intracellular pH in tumors using amide and guanidyl CEST-MRI at 9.4 T

PURPOSE

In principle, non-invasive mapping of the intracellular pH (pH_i ) in vivo is possible using endogenous chemical exchange saturation transfer (CEST)-MRI of the amide and guanidyl signals. However, the application for cancer imaging is still impeded, as current state-of-the-art approaches do not allow for simultaneous compensation of concomitant effects that vary within tumors. In this study, we present a novel method for absolute pH_i mapping using endogenous CEST-MRI, which simultaneously compensates for concentration changes, superimposing CEST signals, magnetization transfer contrast, and spillover dilution.

THEORY AND METHODS

Compensation of the concomitant effects was achieved by a ratiometric approach (i.e. the ratio of one CEST signal at different B₁ ) in combination with the relaxation-compensated inverse magnetization transfer ratio MTR_Rex and a separate first-order polynomial-Lorentzian fit of the amide and guanidyl signals at 9.4 T. Calibration of pH values was accomplished using in vivo-like model suspensions from porcine brain lysates. Applicability of the presented method in vivo was demonstrated in n = 19 tumor-bearing mice.

RESULTS

In porcine brain lysates, measurement of pH was feasible over a broad range of physiologically relevant pH values of 6.2 to 8.0, while being independent of changes in concentration. A median pH_i of approximately 7.2 was found in the lesions of 19 tumor-bearing mice.

CONCLUSION

The presented method enables non-invasive mapping of absolute pH_i values in tumors using CEST-MRI, which was so far prevented by concomitant effects. Consequently, pre-clinical studies on pH_i changes in tumors are possible allowing the assessment of pH_i in vivo as a biomarker for cancer diagnosis or treatment monitoring.

Demonstration of fast multi-slice quasi-steady-state chemical exchange saturation transfer (QUASS CEST) human brain imaging at 3T

PURPOSE

To combine multi-slice chemical exchange saturation transfer (CEST) imaging with quasi-steady-state (QUASS) processing and demonstrate the feasibility of fast QUASS CEST MRI at 3T.

METHODS

Fast multi-slice echo planar imaging (EPI) CEST imaging was developed with concatenated slice acquisition after single radiofrequency irradiation. The multi-slice CEST signal evolution was described by the spin-lock relaxation during saturation duration (T_s ) and longitudinal relaxation during the relaxation delay time (T_d ) and post-label delay (PLD), from which the QUASS CEST was generalized to fast multi-slice acquisition. In addition, numerical simulations, phantom, and normal human subjects scans were performed to compare the conventional apparent and QUASS CEST measurements with different T_s , T_d, and PLD.

RESULTS

The numerical simulation showed that the apparent CEST effect strongly depends on T_s , T_d , and PLD, while the QUASS CEST algorithm minimizes such dependences. In the L-carnosine gel phantom, the proposed QUASS CEST effects (2.68 ± 0.12% [mean ± SD]) were higher than the apparent CEST effects (1.85 ± 0.26%, p < 5e-4). In the human brain imaging, Bland-Altman analysis bias of the proposed QUASS CEST effects was much smaller than the PLD-corrected apparent CEST effects (0.03% vs. -0.54%), indicating the proposed fast multi-slice CEST imaging is robust and accurate.

CONCLUSIONS

The QUASS processing enables fast multi-slice CEST imaging with minimal loss in the measurement of the CEST effect.

Low duty cycle pulse trains for exchange rate insensitive chemical exchange saturation transfer MRI

PURPOSE

To introduce and validate a pulse scheme that uses low duty cycle trains of π-pulses to achieve saturation that is relatively insensitive to exchange rate yet linearly dependent on labile proton concentration.

METHODS

Simulations were performed to explore the exchange rate sensitivity of π-pulse trains and continuous wave chemical exchange saturation transfer (CEST) signals. Creatine phantoms with varying pH and varying concentrations were imaged to demonstrate pH insensitivity and concentration dependence of low duty cycle π-pulse saturation.

RESULTS

Simulations show decreasing the duty cycle of π-pulse saturation decreases peak sensitivity to exchange rate, and this range of insensitivity can be tuned to different exchange rates through average B₁ power. The range of insensitivity is unaffected by changes in relaxation and magnetization transfer, while the sensitivity of CEST signal maintains linear dependence on labile proton concentration. Under B_{1, avg} = 0.48 μT, 30 mM creatine with pHs ranging between 6.36 and 8.21 exhibited CEST contrast ranging between ~6 and 11% under continuous wave and ~4% across all pHs using 10% duty cycle π-pulses. Imaging these phantoms using duty cycles of 5, 10, 25, and 50% showed decreasing pH sensitivity with decreased duty cycle. Creatine phantoms with varied concentrations and pHs reveal that π-pulse train saturation exhibited stricter correlation to concentration at lower DCs.

CONCLUSION

Low DC π-pulse train is an easy-to-implement way of providing labile proton concentration-dependent CEST MRI signal that is insensitive to exchange rate. This approach can be useful in studies where a change of chemical exchange rate may interfere with accurate assessments of physiology or pathology.