QUESP and QUEST revisited – fast and accurate quantitative CEST experiments
Spectroscopy‐based methods have been proposed for measuring the exchange rates of slowly exchanging systems 18; however, they are not suitable for fast exchange rate quantification due to severe line broadening. In contrast, it is possible to provide a quantification for experiments in this regime with CEST, and data can be interpreted by the Bloch‐McConnell (BM) differential equations that incorporate parameters such as free precession, excitation and relaxation, as well as the exchange between different spin pools 20.
McMahon et al. were the first to develop an MRI‐compatible method to measure exchange rate based on exploiting the influence of saturation time and saturation power on signal intensity 21. Using a simplified solution of the BM equations as described in the work of Zhou et al. 22, McMahon et al. calculated exchange rates by changing either the labeling efficiency (by the saturation pulse power) or the saturation time 21, and compared their results with the fitting of the BM differential equations in time, which forms a gold standard for quantification of CEST 24.
The existing analytical solutions that describe these experiments are well suited for calculation of exchange rates, as long as a strong labeling is achieved. “Strong labeling” means in this context that the saturation amplitude is larger than the exchange rate (γB1 > kb); thus, the magnetization of the CEST pool is close to 0 during irradiation, and the CEST effect is maximized as well as the labeling efficiency α, which approaches 1.
In this work we show that weak labeling (γB1 < kb, α < 0.5), as well as nonequilibrium initial magnetization conditions, may result in inaccurate quantification of exchange rates if the existing analytical solutions are used. Therefore, we focused on this issue and derived analytical quantification of exchange rate using varying saturation power (QUESP) and quantification of exchange rate using varying saturation time (QUEST) formulas based on the equivalence of the spin‐lock theory to CEST experiments 25. The derived equations were applied to a system with large chemical shifts, in which direct water saturation is negligible. We show that these formulas agree with the original QUESP/QUEST equations for strong labeling; furthermore, they extend the convergence interval for weak labeling. In addition to QUESP, we apply the similar Ω‐plot method, which reformulates QUESP to a linear regression problem 27 using the same data. For the experimental validation of our formulas, we used paramagnetic CEST (paraCEST) agents 28 for the following reasons. First, these agents induce large shifts for exchanging protons, simplifying the theory (direct saturation does not have to be taken into account).