One primary limitation of CEST is the quantification reproducibility, which is intrinsically challenging due to the simultaneous and competing spillover and $$$T_{1}$$$ decay effects. Recently, a new metric¹ has been proposed to eliminate these competing effects to deliver a CEST effect only quantification. However, this model is under the requirement of being in a steady state, which is difficult to satisfy in practice due to the restricting long saturation period needed (>3s). In this work, we extent this metric to transient state while eliminating the contaminating effects, and verify its performance in phantom and in vivo experiment.

Zaiss^2,3 used the Z value with a continuous wave rectangular pulse for quantification:

$$Z=\left(P_{zeff}P_{z}Z^{ini}-P_{z}\cos(\theta)\frac{R_{1}}{R_{1\rho}}\right)\exp(-R_{1\rho}t_{sat})+P_{z}\cos(\theta)\frac{R_{1}}{R_{1\rho}} (1)$$

θ is defined as $$$\theta=\tan^{-1}(\frac{\gamma B_{b}}{\Delta\omega})$$$, $$$R_{1}$$$ and $$$R_{1\rho}$$$ are reciprocal of $$$T_{1}$$$ and $$$T_{1\rho}$$$. $$$P_{z}$$$ and $$$P_{zeff}$$$ are projection factors dependent on the pulse sequence. The first part (weighted by $$$exp(-R_{1\rho}t_{sat})$$$ represents the transient effects of CEST saturation, which was neglected in previous reports [1].

As $$$R_{1\rho}=R_{1\rho}^{calib}+\sum R_{ex}$$$, in a general case we can treat influence of exchangeable solutes $$$\sum R_{ex}$$$ as a perturbation to $$$R_{1\rho}$$$. As Z in Equ.(1) is a function of $$$R_{1\rho}$$$, for small $$$R_{1\rho}$$$ it is natural that $$$\Delta R_{1\rho}=\Delta Z/\frac{\partial Z}{\partial R_{1\rho}}$$$. Under the assumption of a continuous square wave, it can be expressed as:

$$\Delta R_{1\rho}=\Delta Z/\left\{\left[\cos^{2}\theta\left(1-\exp\left(-\left(TR-t_{sat}\right)R_{1a}\right)-R_{1a}/R_{1\rho}\right)\exp\left(-R_{1\rho}t_{sat}\right)\left(-t_{sat}\right)+\cos^{2}\theta \frac{R_{1a}}{R_{1\rho}^{2}}\exp\left(-t_{sat}R_{1\rho}\right)-\cos^{2}\theta \frac{R_{1a}}{R_{1\rho}^{2}}\right]/\left(1-\exp\left(-R_{1a}TR\right)\right)\right\} (2)$$

For proper $$$\Delta Z=Z_{ref}-Z_{lab}$$$, direct water saturation could be excluded then $$$\Delta R_{1\rho}=\sum R_{ex}$$$. According to analytical solution of $$$R_{ex}$$$ [2], for high exchange rate ($$$k_{b}\gg R_{2}$$$) solutes and small $$$B_{1}$$$ ($$$\omega_{1}\ll k_{b}$$$), a simplification could be:

$$R_{ex}^{calib}=\frac{R_{ex}}{\sin^{2}\theta}\approx f_{b}k_{b}\frac{\delta\omega^{2}}{k_{b}^{2}+\Delta\omega_{b}^{2}+\omega_1^2}\approx f_{b}k_{b}\frac{\delta\omega^{2}}{k_{b}^{2}+\Delta\omega_{b}^{2}} (3)$$

Then a new transient state CEST effect metric could be defined as $$$\Delta R_{1\rho}^{calib}=\frac{\Delta R_{1\rho}}{\sin^{2}\theta}=\sum R_{ex}^{calib}$$$.

For verification of the proposed metric, CW rectangular saturation pulse followed by a SE-EPI sequence was implemented and used for CEST acquisition. Several experiments were designed to assess impacts of various experimental factors: a) phantoms with the same solutes densities and but different MnCl₂ densities (hence different relaxation times) were prepared and used to test the impacts of $$$T_{1}$$$ and $$$T_{2}$$$; b) data acquisitions with different TR (2s, 3s, 5s) and lengths of saturation (0.5s, 0.75s, 1s, 1.25s, 1.5s) were performed to test impacts of TR and $$$t_{sat}$$$; c) CEST saturations with differentmagnitudes (1uT, 1.25uT, 1.5uT, 1.75uT, 2uT, 3uT) were performed to test the impacts of $$$B_{1}$$$. In vivo data was acquired on a healthy subject with varying TR/$$$t_{sat}$$$: 2s/1.5s, 1.5s/1s, 7s/5s. The resulting CEST quantification using the proposed $$$\Delta R_{1\rho}^{calib}$$$ for phantom and in vivo data were compared to those using conventional $$${MTR}_{asym}$$$. As shown in Fig.1, for phantom 1 and 2 (Fig.1a) that have the same solutes densities (the same CEST effects) but different relaxation times, conventional were quite different; whereas $$$\Delta R_{1\rho}^{calib}$$$ were nearly identical that better reflect the underlying CEST effects. Also $$${MTR}_{asym}$$$ was also impacted by $$$B_{1}$$$ inhomogeneity (Fig.1b) leading to heterogeneous CEST quantification within the phantoms, while $$$\Delta R_{1\rho}^{calib}$$$ was not. In Fig.2, where the TR and saturation period were varied, conventional $$${MTR}_{asym}$$$ were dramatically different with different scan parameter settings, whereas $$$\Delta R_{1\rho}^{calib}$$$ measure stayed nearly unchanged as desired. In Fig.3, $$$B_{1}$$$ of the CEST saturation, which has largest impacts on conventional CEST measurement, was varied. It can be seen that for a range of $$$B_{1}$$$ used, the $$${MTR}_{asym}$$$ measure not only changed in magnitude, the location of its spectral peak was also shifted; whereas $$$\Delta R_{1\rho}^{calib}$$$ stayed fairly constant for small level of $$$B_{1}$$$ variation (<3uT), and although the magnitude level changed for larger $$$B_{1}$$$ the position of the spectral peak stayed unchanged. In in vivo experiments using different $$$TR/t_{sat}$$$
(Fig.4), it was also observed that $$${MTR}_{asym}$$$ varied considerably as compared to $$$\Delta R_{1\rho}^{calib}$$$ when $$${MTR}_{asym}$$$ is dramatically nonzero (arrowed).Conventional CEST measurement is contaminated with both competing signal sources and transient signal state, although the former may may be eliminated via proper correction^1,4 , steady state requires restrictingly long saturation period. In this work, an analytical metric for transient state that also eliminates spillover and T₁ decay effects is proposed. This metric is analytical and hence eliminates the computation burden and error in empirical fitting. In the comparison with conventional CEST measure, this metric was seen to be largely immune to variation in relaxation rates, scan parameters as well as saturation pulse magnitude, hence better reflect the underlying unchanged CEST effects in transient states. The use of this metric would be beneficial for application where quantitative measure is needed, such as in tumor grading.