A CEST signal quantification method for non-steady state

Yi Wang^{1}, Bing Wu^{2}, Yang Fan^{2}, and Jia-Hong Gao^{1}

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 $$$\Delta R_{1\rho}^{calib}=\frac{\Delta R_{1\rho}}{\sin^{2}\theta}=\sum R_{ex}^{calib}$$$.

1. Moritz Zaiss, Junzhong Xu, Steffen Goerke et al., Inverse Z-spectrum analysis for spillover-,MT-, and T1-corrected steady-state pulsedCEST-MRI – application to pH-weightedMRI of acute stroke, NMR Biomed. 2014; 27(3): 240-252

2. Moritz Zaiss, Peter Bachert, Chemical exchange saturation transfer (CEST) andMR Z-spectroscopy in vivo: a review of theoreticalapproaches and methods, Phys. Med. Biol. 2013; 58(22): 221-269

3. Moritz Zaiss, Peter Bachert, Exchange-dependent relaxation in the rotatingframe for slow and intermediate exchange –modeling off-resonant spin-lock and chemicalexchange saturation transfer, NMR Biomed. 2013; 26(5): 507-518

4. Junzhong Xu, Moritz Zaiss, Zhongliang Zu et al., On the origins of chemical exchange saturationtransfer (CEST) contrast in tumors at 9.4 T, NMR Biomed. 2014; 27(4): 406-416

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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