Johannes Breitling^{1}, Steffen Goerke^{1}, Jan-Eric Meissner^{1}, Andreas Korzowski^{1}, Patrick Schuenke^{1}, Mark E. Ladd^{1}, and Peter Bachert^{1}

In this study, we
propose a novel approach to determine the steady-state of CEST experiments
without the application of prolonged saturation periods. This is achieved by
numerically calculating the steady-state from a measurement with a reduced
saturation period (in the order of the water proton T_{1}). This may
allow quantitative CEST measurements, capable of providing information about pH
and metabolite concentrations, in a reasonable and clinical relevant time
frame.

During a pulsed CEST experiment (Fig. 1a) the initial Z-magnetization
Z_{init} can be assumed to mono-exponentially decay – via the so-called
transient-state Z – towards the steady-state $$$Z^{ss}_{pulsed}$$$
with the
effective decay rate R_{1ρ,pulsed} (Fig. 1b)^{4,5}. $$Z(Δω)=Z^{ss}_{pulsed}+(Z_{init}-Z^{ss}_{pulsed})e^{t_{sat}·R_{1ρ,pulsed}} [1]$$ $$$Z^{ss}_{pulsed}$$$ itself depends on
R_{1ρ,pulsed} according to $$Z^{ss}_{pulsed}=\frac{R_{1w}(1-DC+\cos\theta\cdot DC)}{R_{1\rho,pulsed}} [2]$$ with the tilt angle of the effective field $$$\theta=\tan^{-1}(\omega_{1}/\Delta\omega)$$$. This mathematical relation can be exploited to
reduce the number of unknown parameters in Eq.1. For a known Z_{init},
this allows determining $$$Z^{ss}_{pulsed}$$$ from Z for an
arbitrary saturation time. Solving Eq. 2 for the denominator and insertion in
Eq. 1 yields Z as function of
$$$Z^{ss}_{pulsed}$$$. $$Z(Δω)=Z^{ss}_{pulsed}+(Z_{init}-Z^{ss}_{pulsed})e^{t_{sat}·R_{1w}(1-DC+\cos\theta\cdot DC)/Z^{ss}_{pulsed}} [3]$$ Eq.
3 cannot be solved analytically for
$$$Z^{ss}_{pulsed}$$$. However since Z is
a strictly monotonously increasing function of $$$Z^{ss}_{pulsed}$$$, a numerical calculation
can be applied. This calculus requires Z and Zinit for each
frequency offset
$$$\Delta\omega$$$. In addition, B_{0},
B_{1} and T_{1w} have to be determined once. Z_{init} can
be estimated pixelwise by the preceding measurement according to
$$$Z_{init,i+1}=P_1\cdot Z_{i}+P_0$$$, where
P_{1 }and
P_{0} are determined in a calibration
with the same sequence timings.
All MR measurements were performed on a 7T
whole-body scanner (Siemens Healthineers, Germany). Pre-saturation was obtained
by either 60 or 700 Gaussian-shaped pulses (mean B_{1} = 0.5µT, t_{p} = 15ms, duty
cycle = 60%) leading to a saturation time of t_{sat} = 1.5s and 17.5s respectively.
B_{0} and B_{1} were obtained using the WASABI approach^{6}
and T_{1w} with a saturation recovery sequence. Quantitative relayed
nuclear Overhauser effect (rNOE)-CEST images were calculated using the apparent
exchange-dependent relaxation rate (AREX)^{5} with a 5-pool Lorentzian
fit analysis.

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