illustrates two 2-pool exchange models with different exchange rate and labile proton concentration. Specifically, shows concentrated CEST agents undergoing slow chemical exchange with bulk water; while represents the counter scenario where dilute CEST agents undergoing faster chemical exchange with bulk water. Our study aims to investigate whether exchange rate and labile proton concentration can be simultaneously determined by CEST MRI, hence, develops more quantitative CEST MRI.
Illustration of two representative CEST systems, a) 2-pool exchange model that depicts relatively concentrated CEST agents undergoing slow chemical exchange, b) shows the case of dilute CEST agents undergoing faster interaction with bulk water.
shows how CEST MRI contrast varies with RF power when exchange rate and labile proton concentration is varied by comparing the empirical solution with numerical simulation. shows CEST MRI contrast for three representative exchange rates, 30 (up triangle), 75 (down triangle) and 150 (square) s−1
, for a representative concentration of 1:1000. It is important to note that empirical solution (solid lines) overlapped with numerical simulation, indicating that although not directly derived from 2-pool exchange model, the empirical solution is sufficiently accurate to describe slow and intermediate chemical exchange processes. The CEST MRI contrast initially increases with RF power, while it decreases when RF power is too strong, leading to an optimal RF power at which CEST MRI contrast reaches maxima. The optimal RF power was extrapolated and shown in dashed line. In addition, the optimal RF power is plotted as a function of exchange rate in , with circles, solid line and dash dotted line represent numerical simulation, solution from Eq. 1
and estimation from Eq. 2
, respectively, which are all in good agreement. It shows that the optimal RF power strongly varies with chemical exchange rate. In addition, zig-zag behavior of optimal RF power was observed, which can attributed to finite step increase of RF power in numerical simulation. Specifically, RF power was varied 0.06 µT per step, and for a narrow range of exchange rate, optimal RF power becomes undistinguishable within 0.06 µT. In contrast, depicts the RF power dependence of CEST contrast as a function of labile proton concentration. Three representative concentrations of 1:2000 (up triangle), 1:1000 (down triangle), and 1:500 (square) were simulated, for a representative exchange rate of 75 s−1
. The optimal RF power (dashed line) was overlaid in . The optimal RF power is plotted as a function of labile proton concentration in , which showed that the optimal RF power remains the same despite four folds increase in labile proton concentration.
Fig. 2 a) CEST MRI contrast was simulated as a function RF power for three exchange rates, 30, 75 and 150 s−1 at a labile proton content of 1:1000. The up triangle, down triangle and square markers denote numerical simulation, while the line represent (more ...)
CEST MRI contrast, however, is very complex. It depends on not only exchange rate and labile proton concentration; it also varies with chemical offset and relaxation parameters. Thereby, it is important to elucidate how such factors affect optimal RF power. Specifically, three representative chemical offsets of 450, 700 and 1400 Hz were explored, which correspond to amide proton offset of endogenous cerebral proteins/peptides (3.5 ppm) at field strengths of 3, 4.7 and 9.4 Tesla, respectively (). It shows that change of chemical offset did not alter the finding that optimal RF power strongly depends on exchange rate, while nearly independent of labile proton concentration. The observation that optimal RF power increases with chemical offset for both cases can be attributed to the fact that spillover effect is smaller at larger chemical offset, hence, resulting in an increase in the optimal RF power. In fact, for the same range of exchange rates, the increase in optimal RF power confers a broader dynamic range of optimal RF power for experimental test. In addition, CEST MRI contrast was simulated for three representative bulk water T1w of 1, 1.5 and 2s, while its T2w was kept at 60 ms (). The optimal RF power decreases at longer T1w, consistent with the finding that less RF power is needed to compete with slower longitudinal relaxation. Moreover, bulk water T2w effect was also evaluated by varying T2w from 100, 60 and 40 ms, for a T1w of 1.5 s (). The result showed that optimal RF power is larger at longer T2w, which can be attributed to less spillover effects when bulk water spectrum is relatively sharp. Moreover, RFP CEST MRI was also studied as a function of labile proton relaxation time. Because our study investigates long CW RF irradiation, very little change was observed for three T1s of 1, 1.5 and 2 s (data not shown). Similarly, optimal RF power had minimally dependence on labile proton relaxation rates when three T2s of 20, 15 and 10 ms were evaluated (data not shown). As such, our results showed that although optimal RF power varies with chemical offset and to a far lesser extent, relaxation parameters, the dependence of optimal RF power upon exchange rate and labile proton concentration remains the same (i.e., optimal RF power increases with exchange rate but is nearly independent of labile proton concentration).
Fig. 3 evaluation of the dependence of optimal RF power upon chemical offset and relaxation rates for the case of dominant change in exchange rate (Figs 3a, c and d) and the case of labile proton concentration effect (Figs 3b, d and f). Specifically, Figs 3a (more ...)
Our results suggested that optimal RF power is sensitive to chemical exchange rate, while nearly independent of labile proton concentration. As such, optimal RF power may serve as a sensitive parameter that allows quantification of CEST system. Specifically, chemical exchange rate may be first estimated from optimal RF power by finding the exchange rate, whose corresponding optimal RF power is equal to the derived optimal RF power following Eq. 2
. Labile proton concentration can then be estimated by the empirical solution (Eq. 1
). A flow chart of the proposed CEST quantification procedure is shown in .
We further tested whether labile proton concentration and exchange rate can be simultaneously determined by the proposed technique. Two CEST systems were examined. In the first case, chemical exchange rate was varied at a fixed labile proton concentration, while for the second case, labile proton concentration effect was studied for a given exchange rate. Specifically, for the first case, labile proton concentration was assumed to be 1:1000, while the exchange rate was varied from 1 to 150 s−1, mimicking dominant pH change. As suggested in the flow chart (), exchange rate was first derived from optimal RF power, and labile proton concentration was subsequently calculated based on CEST MRI contrast and the derived exchange rate. showed exchange rate and labile proton concentration estimated from RFP CEST MRI, respectively, for the first case of dominant difference in chemical exchange rate. The derived exchange rate (ksw_RFP) closely correlated with simulated exchange, and can be described by a linear function, ksw_RFP=1.47 ksw - 9.46 (, dash dotted line). While adding a quadratic term seemed to better represent the data, with ksw_RFP=0.0027 ksw2 +1.06 ksw + 0.83 (, dash line), the linear fitting provided reasonable description of the results. In addition, the labile proton content was found to be 1:1175 ± 103, in comparison to the simulated value of 1:1000 (). For the second case, the labile proton concentration was varied from 1:2000 to 1:500 for a representative chemical exchange rate of 75 s−1, representing the scenario of dominant change in CEST agent concentration. We followed the same procedure as shown in The optimal power was found to be 0.98 µT, which corresponds to a chemical exchange rate of ksw_RFP=98 s−1, for the simulated exchange rate of 75 s−1. The labile proton concentration was then derived as fRFP=0.82 f. In sum, numerical simulation confirmed our theoretical derivation and showed that the CEST MRI system can be reasonably characterized by probing RF power dependence of CEST MRI, in particular, the optimal RF power. Future experimental evaluation of the proposed quantitative CEST MRI technique is needed to test its practicability and sensitivity, prior to its routine use.
Fig. 5 Evaluation of the inverse problem that whether exchange rate and labile proton concentration effect can be simultaneously determined from the optimal RF power. For the first case, exchange rate was varied between 1 and 150 s−1, while the labile (more ...)