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Chemical exchange saturation transfer (CEST) MRI is an emerging imaging technique capable of detecting dilute proteins/peptides and microenvironmental properties, with promising in vivo applications. However, CEST MRI contrast is complex, varying not only with the labile proton concentration and exchange rate, but also with experimental conditions such as field strength and RF irradiation scheme. Furthermore, the optimal RF irradiation power depends on the exchange rate, which must be estimated in order to optimize the CEST MRI experiments. Although methods including numerical fitting with modified Bloch-McConnell equations, quantification of exchange rate with RF saturation time and power (QUEST and QUESP), have been proposed to address this relationship, they require multiple-parameter non-linear fitting and accurate relaxation measurement. Our work here extended the QUEST algorithm with ratiometric analysis (QUESTRA) that normalizes the magnetization transfer ratio (MTR) at labile and reference frequencies, which effectively eliminates the confounding relaxation and RF spillover effects. Specifically, the QUESTRA contrast approaches its steady state mono-exponentially at a rate determined by the reverse exchange rate (kws), with little dependence on bulk water T1, T2, RF power and chemical shift. The proposed algorithm was confirmed numerically, and validated experimentally using a tissue-like phantom of serially titrated pH compartments.
Chemical exchange saturation transfer (CEST) MRI is an emerging imaging technique that holds great promise for in vivo applications to image dilute CEST agents and microenvironmental properties (1–5). For instance, amide proton transfer (APT) imaging, a variant of CEST MRI, can detect exchangeable amide protons from endogenous mobile proteins and peptides, and has been explored as a means to assess tissue acidosis during acute ischemic stroke, characterize mobile protein/peptide content in cancerous tissue and quantify myelination in brain white matter (6–13). Additionally, exogenous diamagnetic CEST (DIACEST) and paramagnetic CEST (PARACEST) agents are being developed as novel probes for molecular imaging (14–17). However, CEST MRI contrast is complex. In addition to labile proton concentration, exchange rate and chemical shift, the experimentally obtainable CEST MRI contrast also varies with magnetic field strength, RF irradiation scheme, power and duration as well as bulk water T1 and T2 (18). As such, it is very important to delineate the CEST agent properties (exchange rate and labile proton concentration) from the effects of experimental parameters in order to properly optimize the design of CEST agents and quantify experimental measurements (19,20).
Both analytical solutions and numerical simulations have been developed to describe CEST MRI contrast (18,21–27). Particularly, the optimal RF saturation power and experimentally obtained CEST MRI contrast strongly depend on the exchange rate of labile proton groups, which is often pH-dependent (8,28). In fact, several methods have been established to estimate the exchange rate from CEST MRI experiments, including direct numerical fitting of the CEST spectrum with modified Bloch-McConnell equations, quantifying exchange rate with saturation time and power (QUEST and QUESP), and omega plot (18,21,29,30). Particularly, the QUEST algorithm is relatively simple to use. However, several issues must be addressed to improve its accuracy. First, the QUEST solution requires accurate measurement of the intrinsic longitudinal relaxation rate (R1w) so that exchange rate can be calculated from the experimentally derived apparent relaxation rate. Hence, a small measurement error in R1w may introduce sizeable error in ksw. In addition, the simplistic time-dependent solution assumes no concomitant direct RF saturation, which may not be negligible (31–33). Whereas the precision of QUEST solution can be improved with the use of numerical solution, it still requires independent relaxation measurement and extensive simulation. As such, it is helpful to develop a simplified yet reasonably accurate quantitative algorithm for calibrating CEST MRI.
Our study extended the concept of QUEST algorithm with ratiometric analysis (QUESTRA). Specifically, given that label and reference scans are subject to approximately equal relaxation recovery and RF spillover effects, we postulated that such effects could be normalized by analyzing the ratio of magnetization transfer ratio (MTR) at label and reference frequencies. We showed that the QUESTRA contrast approaches its steady state mono-exponentially by a rate of the reverse exchange rate (kws). As such, the proposed QUESTRA algorithm greatly simplifies the conventional QUEST analysis, which may in turn improve its precision and reproducibility. Here, our study first evaluated the QUESTRA algorithm with a 2-pool exchange model, which confirmed good agreement. We also examined the QUESTRA solution as a function of bulk water T1, T2, RF power and labile proton chemical shift, showing significantly less variation than the conventional QUEST analysis. Furthermore, the proposed QUESTRA algorithm was experimentally validated using a Creatine-gel CEST phantom of serially titrated pH; the derived exchange rate revealed a base-catalyzed exchange relationship, consistent with previous findings and simulation (34).
CEST MRI can be quantified as the percentage signal decrease due to RF irradiation, similar as the magnetization transfer (MT) MRI. We have MTR=1-I(Δω,ω1)/I0, where I(Δω,ω1) is the image intensity with RF irradiation, with ω1 (ω1=γB1, where γ is the gyromagnetic ratio and B1 is the RF irradiation field strength) and Δω being its amplitude and offset, respectively, and I0 is the control scan without RF irradiation. Thus, we have MTRref=1-Iref/I0 for the reference CEST scan (Δω=-Δωs), and MTRlabel=1-Ilabel/I0 for the label scan (Δω=Δωs). In addition, CEST contrast (CESTR) is often calculated by an asymmetry analysis, being CESTR=(Iref- Ilabel)/I0.
CEST MRI has often been described using a 2-pool exchange model. It has been shown that in the simplistic case, involving instantaneous saturation of labile protons and no direct RF saturation, CESTR can be described by (26,29),
where CESTRss is the steady state CESTR, r1w_app is the apparent relaxation time, and Ts is the saturation time. When RF spillover effects are negligible, we have r1w_app=R1w+fs*ksw. However, it is necessary to point out that in the presence of sizeable RF spillover effects, the exchange rate estimated with Eq. 1 is susceptible to non-negligible errors. To address this, the proposed QUESTRA method investigates the relative rate by which MTRlabel and MTRref approach their steady state. Specifically, we have
where MTRlabel_ss and MTRref_ss are the steady state MTR for the label and reference scans, respectively. The chemical exchange rate can be solved as
CEST MRI was simulated using the classic 2-pool exchange model in Matlab (Mathworks, Natick MA) (21,24). We assumed a long repetition time (TR) so both spins are at equilibrium states before RF irradiation. We chose representative bulk water T1 and T2 of 2 s and 100 ms, and labile protons of 1 s and 15 ms, respectively. In addition, we assumed a representative ksw of 100 s−1, Δωs of 2 ppm with its fs being 1:1000. We serially varied Ts from 0.5 to 3 s in 11 steps, and simulated Z-spectrum from −5 to 5 ppm for each Ts. The steady state was obtained with a long Ts of 15 s. CEST asymmetry was calculated, being CESTR= (Iref- Ilabel)/I0=MTRlabel-MTRref.
We also studied the precision of the proposed QUESTRA technique by repeating the simulation for a typical range of T1w, T2w, B1 and Δωs. Briefly, we assumed a representative ksw of 100 s−1 and fs of 1:1000. In addition, we assumed T1w=2 s, T2w=100 ms, T1s= 1s, T2s=15 ms, B1=2 µT, Δωs= 2 ppm for a representative field strength of 4.7 T, while a single parameter was varied independently each time to assess its effect upon the precision of the QUEST and QUESTRA solutions. Specifically, four parameters were varied: T1w from 0.5 to 4 s (Fig. 3a); T2w from 50 to 200 ms (Fig. 3b); B1 from 0.5 to 5 µT (Fig. 3c) and Δω from 0.5 to 5 ppm (Fig. 3d). In addition, we compared QUEST and QUSTRA solutions for a range of chemical exchange rate from 10 to 150 s−1 for two representative B1 amplitude of 1 and 2 µT, as well as an “optimal” RF irradiation amplitude estimated from ksw (i.e., B1=ksw/ 2πγ) (18,21).
We prepared a multi-pH CEST gel phantom composed of creatine and low gelling point (LGP) agarose (34). Briefly, we added 1% agarose to phosphate-buffered saline (PBS) solution doped with a trace amount of CuSO4· 5H2O (Sigma Aldrich, St Louis, MO). The mixture was microwave-heated, and immersed in a waterbath at 50°C. We added creatine to the gel solution until it reached a final concentration of 50 mM, then serially titrated its pH to 5.99, 6.45, 7.0, 7.24 and 7.55 (EuTech Instrument, Singapore), and transferred the solution at each pH into separate centrifuge tubes. Afterward, the tubes were sealed and inserted into a phantom holder. Finally, a central tube and the phantom holder were filled with 1.25% gel to position and fix the Creatine-gel tubes.
Fig. 1 illustrates the QUESTRA CEST MRI pulse sequence, which includes a long relaxation recovery delay (Tr), and a continuous wave (CW) RF saturation module of adjustable duration (Ts) and image readout (Ti). Ti is typically negligible when compared with Tr and Ts. All images were acquired at 4.7 T (Bruker Biospec, Billerica, MA), with single-shot spin-echo (SE) echo planar imaging (EPI) (slice thickness = 10 mm, field of view (FOV) = 76 × 76 mm, bandwidth=200 kHz). The image matrix was 64 × 64, and Tr/TE=12 s/28 ms, respectively, and Ts was serially varied at 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 6 and 12 s (NA=2). We also varied the RF amplitude from 2, 2.5, 3 to 4 µT, with the label and reference offset being ±1.9 ppm (375 Hz at 4.7T). The CEST spectrum was obtained with five Ts values of 0.5, 1, 1.5, 3, 6 s for all four RF power levels (±600 Hz per 25 Hz, Tr/TE=12 s/28 ms, NA=2). Moreover, T1 and T2 maps were obtained with inversion recovery (seven inversion intervals (TI) from 0.1 to 7.5 s, Tr/TE=12 s/25 ms, NA=2), and fast RF enforced steady state (FRESS) SE EPI (six TEs from 30 to 150 ms, TR=12 s, NA=2) (35). A B0 map was obtained with asymmetric SE (ASE) MRI, with echo time shifted by 1, 3, 5 and 7 ms (TR/TE=12s/28 ms, NA=2). In addition, a B1 map was obtained using the double-angle method (TR/TE=12s/28 ms, NA=2, α=60° and 120°)(36).
Fig. 2 shows simulated Ts-dependent CEST spectra and compares the conventional QUEST solution (Eq. 1) with the proposed QUESTRA solution (Eq. 3). CEST spectra are shown in Fig. 2a, with three representative Ts of 0.5, 1 and 3 s, for an RF amplitude of 1 µT. Z-spectral signal persistently decreased at longer Ts, approaching the steady state. Fig. 2b shows Ts-dependent MTRlabel, MTRref and CESTR in circle, square and triangle markers, respectively. Fig. 2c shows the natural log of normalized MTRlabel, MTRref and CESTR contrast, which increased linearly with Ts. The slope was obtained with least-square linear fitting, being 0.69 s−1 and 0.92 s−1 for MTRlabel and CESTR, respectively. We used the simplistic estimation of exchange rate (i.e., ksw=(r1w-R1w)/fs), which was found to be 190 s−1 and 419 s−1 for MTRlabel and CESTR, respectively. Note that the exchange rates were significantly higher than the simulated exchange rate of 100 s−1. In addition, the slope for the reference scan (MTRref) was 0.61 s−1, slightly higher than the endogenous R1w of 0.5 s−1. In comparison, the QUESTRA analysis (Eq. 3) increased linearly with Ts, and its slope was found to be 0.078 s−1, corresponding to an exchange rate of 78 s−1, which was in reasonable agreement with the simulated value of 100 s−1 (Fig. 2d).
We also examined the reproducibility of the proposed QUESTRA algorithm by varying T1w, T2w, B1 and Δωs, and compared the QUESTRA and QUEST results (Fig. 3). As shown in Fig. 3a, while the conventional QUEST solution significantly overestimated the exchange rate when T1w was varied, with the normalized exchange rate (i.e., ksw_fit/ksw_sim) ranging from 5.2 to 5.4, the QUESTRA solution was 0.83. The QUESTRA solution also outperformed the QUEST analysis when T2w was varied, with the normalized QUEST solution being from 2.8 to 9.4, while the QUESTRA analysis ranging from 0.90 to 0.91 for (Fig. 3b). Interestingly, both the QUEST and QUESTRA solutions showed sizeable dependence on the RF irradiation amplitude. The normalized exchange rate obtained from the QUEST solution ranged from 0.79 to 9.72, while the QUESTRA solution increased from 0.51 to 0.90 (Fig. 3c). It is important to note that although the QUESTRA solution was sensitive to RF power, it quickly plateaued when an intermediate RF power level was used. For instance, the normalized QUESTRA solution was between 0.88 and 0.90 for irradiation RF amplitude beyond 1.5 µT. This is in contrast to the QUEST analysis, which showed no apparent plateaus with respect to RF power. Similarly, QUESTRA solution also yielded more accurate calibration of the exchange rate when the chemical shift offset was varied from 0.5 to 5 ppm. Fig. 3d shows that whereas the QUEST solution ranged from 1.6 to 15.4, the QUESTRA solution showed excellent agreement with the simulated exchange rate, with the normalized exchange rate of 0.81 to 0.93. It is important to note that the precision of QUEST solution improved at large chemical shift due to its reduced RF spillover effects, consistent with that of McMahon et al (29). Therefore, our simulation confirmed that the QUESTRA solution augmented the QUEST analysis, which provided improved calibration of exchange rate for a relatively broad range of relaxation and experimental parameters.
Fig. 4 compares QUEST and QUESTRA solutions as a function of exchange rate. The exchange rate obtained with the QUEST solution significantly deviated from the simulated value (Fig. 4a). The QUEST solution can be described by a linear regression ksw_fit =−0.0024*k2sw + 1.04*ksw + 72.5 s−1 at 1 µT and ksw_fit = −0.001*k2sw + 1.02*ksw + 273.5 s−1 at 2 µT. When a variable RF power was used to match the exchange rate (B1=ksw/(2πγ)), the QUEST solution also significantly overestimated the exchange rate, particularly at high exchange rate (21). The relationship can be described with a second-order polynomial function, ksw_fit = 0.030*k2sw + 1.76*ksw −11.4 s−1. It is important to note that for the QUEST analysis, knowledge of the exact T1w was assumed. In comparison, QUESTRA solution showed very good agreement with the simulated exchange rate (Fig. 4b). Specifically, for a fixed RF amplitude of 1 µT, we had ksw_fit=−0.0024*k2sw + 1.04*ksw - 1.5 s−1, R2=0.69. In addition, we had ksw_fit=−0.0024*k2sw + 1.01*ksw - 1.4 s−1, R2=0.94 for B1=2 µT. For the case of variable RF power level, ksw_fit=−0.0013*k2sw + 1.07*ksw - 4.1 s−1, R2=0.93, with very little change from that of 2 µT. Interestingly, the results showed that QUEST and QUESTRA solutions had approximately equal slope yet very different offset. This is caused by RF spillover effect in the QUEST analysis, which can be reasonably corrected by the proposed QUESTRA solution. In addition, it is important to note that because the QUESTRA solution does not require relaxation measurement, it is relatively simple to implement.
We evaluated the QUESTRA algorithm using a tissue-like pH phantom imaged at 4.7 Tesla. Fig. 5 a shows a representative CESTRasym map of the multiple pH Creatine-gel phantom, obtained with B1=2 µT and Ts of 3 s. Note that the central tube, containing only gel, did not display notable CEST contrast (< 1%), while the CESTR for the Creatine-gel compartments increased with pH. Interestingly, given the relatively small chemical shift of Creatine amine protons, the CEST contrast decreased with RF power, indicating severe RF spillover effects (Fig. 5b). In addition, very little difference was found in T1 and T2. Specifically, T1 was 2.84±0.02, 2.81±0.01, 2.81±0.01, 2.81±0.01, 2.81±0.01, 2.79±0.01 s for the central gel, Creatine-gel compartments of pH 5.99, 6.45, 7.0, 7.24 and 7.55, respectively; T2 measurements for each of these same compartments were 85.0±2.8, 105.6±6.4, 102.3±5.2, 96.6±6.3, 93.6±4.4, 88.1±3.6 ms. T2 was shorter for the central gel compartment due to its higher gel concentration (1.25% vs. 1%). Furthermore, both B0 and B1 field maps were reasonably homogeneous, with typical B0 inhomogeneity within 3 Hz and normalized B1 field variation within 6%.
Fig. 6a shows CEST spectra obtained with representative Ts of 0.5, 1, 1.5, 3 and 6 s (B1=2 µT), which decreased at longer RF saturation time, approaching the steady state. Fig. 6b shows the MTRlabel and MTRref for pH of 7.55 (B1=2 µT), as a function of Ts, with the dashed line indicating the least squares fit using Eq. 1. It shows that MTR from the label scan was persistently higher than that of reference scan, suggesting sizeable CEST MRI contrast. Fig. 6 c shows -ln(QUESTRA), derived from numerical fitting of Fig. 6b, as a function of Ts, which increased linearly with Ts (B1=2 µT). The central gel compartment had negligible CEST contrast, with a slope of 0.0026 s−1, suggesting that the label and reference scans approach steady state at the same rate. The QUESTRA solution nearly overlapped for pH at 7.24 and 7.55, indicating that an RF amplitude of 2 µT was not strong enough to delineate the exchange process, consistent with Fig. 4b. Moreover, Fig. 6 d shows the estimated reverse exchange rate (kws), with the QUEST analysis (squares) and the proposed QUESTRA (circles), obtained under four RF amplitude levels of 2 (blue), 2.5 (green), 3 (red) and 4 µT (cyan). Both solutions indicated faster exchange at higher pH, consistent with base-catalyzed amine proton exchange. It is important to note that the exchange rate derived from the QUEST solution varied strongly with RF power level. In comparison, the QUESTRA solution yielded very little change with RF power level, and hence provides more reproducible estimation of chemical exchange rate. However, the exchange rate derived by the QUESTRA solution showed sizeable increase with RF power at high pH (e.g. 7.55), suggesting relatively fast chemical exchange. We described the QUESTRA solution (B1=4 µT) using a base-catalyzed chemical exchange formula (i.e., k=k0+kb·10pH-pkw), where pKw is the negative log of the water ion product, k0 and kb are the spontaneous and base-catalyzed chemical exchange rates, respectively. We found k0=0.04 s−1, kb=0.148 s−1, and pkw=6.93; the fitting was reasonably good with an R2 of 0.98.
In this study we developed a QUESTRA algorithm for quantitative CEST MRI that is simple to use yet provides reasonably accurate estimation of the reverse chemical exchange rate. Our results showed that QUESTRA analysis had little dependence on T1, T2, and chemical shift of labile protons, provided that the RF irradiation field was reasonably strong. In comparison, the QUEST analysis requires accurate calibration of intrinsic bulk water relaxation rate, which may be somewhat challenging in the presence of RF irradiation. In addition, Trott and Palmer have shown that relaxation during RF irradiation is governed by the relaxation rate in the rotation frame (R1wρ) instead of intrinsic relaxation rate (R1w) (32). Because the simplified QUEST analysis uses R1 instead of R1_rho, it may lead to an overestimation of the exchange rate in the presence of non-negligible RF spillover effects. Therefore, accurate measurement of T1ρ is needed in order to improve the precision of QUEST solution. This is consistent with our observation that the QUEST solution increased with RF power, suggesting severe T1ρ contamination (Fig. 4a and Fig. 6d). Therefore, the proposed QUESTRA algorithm provided a simple yet effective strategy to correct for such confounding factors.
It is known that ksw is closely associated with CEST contrast via simplistic CEST contrast (f*ksw/(R1w+f*ksw)), labeling coefficient and RF spillover effect. Particularly, the labeling coefficient is strongly dependent on ksw (not kws), and such dependence may not be clearly shown if kws is used. While on the other hand, QUESTRA solution is the reverse bulk water exchange rate (kws) and ksw was not calculated (Fig. 6). This is so because simultaneous estimation of both labile proton exchange rate and fraction concentration is somewhat challenging. For instance, we have shown that by probing the RF power dependence of CEST MRI contrast, the exchange rate can be first estimated, allowing calculation of fraction concentration (23). Additionally, this may also be delineated by numerical fitting of the CEST spectra obtained under multiple RF power or field strength. Nevertheless, by accurately calibrating the reverse chemical exchange rate, the proposed QUESTRA solution may augment the commonly used simplistic CESTR asymmetry and QUEST analysis, particularly, for in vivo applications. For instance, it has been assumed that for endogenous APT MRI the amide proton concentration undergoes minimal change immediately after ischemia (6,8). In addition, applied to image cancerous tissue, APT MRI often assumes the labile proton content change dominates tissue pH variation (37).
It is necessary to note that numerical solution may improve the precision of QUEST analysis. In addition, numerical fitting with the modified Bloch-McConnell equations can also quantify CEST contrast. However, such numerical solutions require multi-parametric non-linear fitting and somewhat difficult to use routinely. In addition, it requires accurate relaxation measurement and extensive simulation, which can be time consuming. In addition, the RF field has to be carefully calibrated. Here, we showed that QUESTRA solution is relatively simple to use yet provides fast yet reasonably accurate measurement of kws, with little dependence on T1, T2, B1 and chemical shift.
It is important to note that additional technical developments are needed before we can routinely apply the proposed QUESTRA technique. Our phantom study had very good field homogeneity (i.e., B0 and B1), and field inhomogeneity correction was not necessary. However, in cases where field inhomogeneity is not negligible, additional image data may have to be acquired, hence, potentially extending the total scan time (38,39). In addition, we have recently proposed a unevenly segmented RF irradiation scheme for fast CEST MRI, which includes a long RF saturation pulse to generate the CEST steady state, with short secondary pulses to maintain the steady state for signal average and multi-slice acquisition (40). It remains very interesting to extend our evaluation of how the QUESTRA algorithm may be combined with fast multi-slice acquisition strategies (40,41). Moreover, the QUESTRA method may be somewhat challenging to apply, in its current form, to elucidate CEST agents of multiple overlapped labile proton groups (17,21,24). Furthermore, concomitant RF irradiation effects including semisolid macromolecular magnetization transfer (MT) and nuclear overhauser effect (NOE) have to be considered for in vivo CEST applications (13,42).
We have developed a simplified QUESTRA solution for quantifying CEST MRI contrast. The QUESTRA solution can reasonably compensate the relaxation and RF irradiation spillover effects, and is significantly less sensitive to confounding parameters including T1, T2, RF irradiation power and chemical shift than the conventional QUEST solution. The proposed method has been validated experimentally using a tissue-like Creatine-gel phantom, which confirmed the base-catalyzed Creatine amine proton chemical exchange.
This study was supported in part by grants from AHA/SDG 0835384N, NIH/NIBIB-1K01EB009771, NIH/NINDS-1R21NS061119, NIH/NCRR-P41RR14075 and Genzyme-Partners Healthcare Initiative Translational Grant. The author would like to thank Ms. Nichole Eusemann for her editorial assistance.