Purpose

A key challenge in CE-parameters (fractional concentration f_b, exchange rate k_b and transversal relaxation rate R_2b) quantification approaches is the occurrence of CEST peak overlap. This means the CEST signal representing targeted solute may be crucially interfered by unknown CEST solutes with adjacent resonance frequencies. The interference can lead to biased quantification results. In current quantification approaches, the signal from the unknown solutes is neglected (e.g. QUESP¹ and ANN-CEST²) or linearly approximated (e.g. QUCESOP³) in the model setup. However, it remains uncertain whether severe peak overlap happens, if the model used is appropriate, and whether the quantification result is reliable. In this work, we proposed a generalized QUCESOP(gQUCESOP) method with the peak overlap evaluation by comparing the root mean squared error(RMSE) calculated by the fitting algorithm with that estimated using the noise ratio.

Theory

CEST data is acquired using continuous-wave saturation pulse with various saturation offset Δω and amplitude B1, resulting in a matrix of Z-values $$$\tilde{Z}\left(\Delta\omega_{i},B_{1j}\right)$$$ (i=1,2,…m, and j=1,2,…n). Following the QUCESOP method³, once calculating the corresponding $$$\widetilde{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$ using the $$$R_{1\rho}$$$ relaxation model, a linear approximation is introduced:
$$R_{1\rho}\left(\Delta\omega_{i},B_{1j}\right)=R_{1\rho}^{water}\left(\Delta\omega_{i},B_{1j}\right)+R_{ex}\left(\Delta\omega_{i},B_{1j}\right)+q_{1j}\Delta\omega_{i}+q_{2j}$$
Then $$$\widetilde{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$ can be fitted to obtain the unknown parameters. Root-mean-square error (RMSE) would be obtained with the acquired $$$\widetilde{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$ and the synthesized $$$\widehat{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$ values calculated using the fitted parameters:
$$RMSE=\sqrt{\{\sum_{i=1}^{m}\sum_{j=1}^{n}[{\delta}R_{1\rho}(\Delta\omega_{i},B_{1j})]^{2}\}/(mn)}$$
where $$$\delta R_{1\rho}(\Delta\omega_{i},B_{1j})=\widetilde{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)-\widehat{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$. If the standard deviation of the δZ (measurement error of each Z-value) distribution, σ_Z, has been estimated, each standard deviation of $$${\delta}{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)$$$, $$${\sigma}_{R_{1\rho},i,j}$$$, could be calculated according to the $$$R_{1\rho}$$$ relaxation model. $$$[{\delta}{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)]^{2}$$$ follows a chi-square distribution with a mean of $$${\sigma}_{R_{1\rho},i,j}^{2}$$$ and a variance of $$$2{\sigma}_{R_{1\rho},i,j}^{4}$$$. In addition, each $$$[{\delta}{R_{1\rho}}\left(\Delta\omega_{i},B_{1j}\right)]^{2}$$$ in independent. If the model for fitting is accurate, the RMSE should have a mean value (RMSE_ref) and a standard deviation (ΔRMSE_ref) as:
$$RMSE_{ref}=\sqrt{\{\sum_{i=1}^{m}\sum_{j=1}^{n}{\sigma}_{R_{1\rho},i,j}^{2}\}/(mn)}$$
$${\Delta}RMSE_{ref}=\sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n}(2{\sigma}_{R_{1\rho},i,j}^{4})}/[2\sqrt{mn\times{\sigma}_{R_{1\rho},i,j}^{2}}]$$
Therefore, a t-test could be conducted to compare the RMSE and RMSE_ref±ΔRMSE_ref. If the RMSE is statistically greater than RMSE_ref, it indicates potential illlness with the model, suggesting a significant CEST peak overlap and unreliable fitted results.

Method

In the simulation, a targeted solute with δω_b=2.65ppm, f_b=0.0005, k_b=200s^-1 and R_2b=50s^-1 was set. Additionally, a ghost solute with various f_g, k_g, R_2g and offset δω_g was added. Assuming B₀=9.4T, T₁=2.0s, T₂=0.2s and σ_Z=0.003. Z-values were generated with Δω between 2.3-3.0ppm, B₁ between 0.4-1.6μT, saturation time of 1.5s and TR=2.0s and then used to fit the CE-parameters. Moreover, RMSE was calculated to assess its potential for indicating peak overlap.

In phantom experiment, two phantoms containing “phosphocreatine(PCr) +creatine” and “PCr+ATP” with pH=7.4 were prepared. Peak of the PCr at +2.65ppm or +1.95ppm was treated as the targeted solute. In the in vivo experiment, the PCr peak at +2.65ppm from rats’ skeletal muscles was also quantified. CEST images were acquired with SE-EPI sequnce. Each image was scanned multiple times for averaging and σ_Z evaluation. The scan parameters and fitting algorithm were nearly identical to those used in simulation, while for the PCr peak at +1.95ppm, Δω values varied between 1.7 to 2.2ppm. Considering the k_b range of the PCr peak, the upper bound was set to 400s^-1 in the fitting algorithm. Methods for B₀, B₁, T₁ and T₂ maps were consistent with those in our previous report³.

Result and Discussion

Simulation demonstrated that RMSE is an effective indicator of both peak overlap and the reliability of the fitting results(Fig. 1). With δω_g is distant from δω_b, RMSE is nearly identical to RMSE_ref. It agrees with the mild peak overlap and accurate fitted CE-parameters. When δω_g is close to δω_b, RMSE increases significantly that indicating a severe peak overlap, and fitted CE-parameters exhibit substantial bias. Nevertheless, RMSE fails to distinguish two peaks with an identical offset and similar k_b and R_2b values; “summed” f_b and “averaged” k_b would be likely obtained in this situation.

Creatine(+1.95ppm) and APT(+2.10ppm) are known to significantly overlap to the PCr peak at +1.95ppm, but have minimal impact on the signal of the PCr peak at +2.65ppm. Therefore, as indicated by RMSE/RMSE_ref, CE-parameters of the PCr peak at +2.65ppm are accurate, but those of the PCr peak at +1.95 ppm are biased(Fig. 2). In the skeletal muscle tissue, the RMSE/RMSE_ref of the PCr signal validate the reliability of the fitted CE parameters. The quantification result of PCr(+2.65ppm) aligns with the finding of previous reports^2,3(Fig. 3).

Conclusion

The gQUCESOP method could evaluate the peak overlap condition of the targeted CEST solute and quantify the corresponding CE-parameters. This method would be beneficial for assessing the reliability of the CE parameter quantification results in scenarios with potential disturbance from other uninterested CEST solutes, especially in the in vivo conditions.

Acknowledgements

This work was supported by the New Teachers’ Research Program of Tianjin University of Traditional Chinese Medicine (XJS2022116), Tianjin Municipal Education Commission Scientific Research Program (2022KJ162), National Key R&D Program of China 2022YFC3602500, 2022YFC3602503 and National Natural Science Foundation of China (NSFC) (Nos. 82071914). The authors thank the National Center for Protein Sciences at Peking University in Beijing, China, for assistance with the MRI data acquisition and data analyses.