Physics-guided multi-dimensional scan optimization and quasi-steady-state reconstruction to enhance CEST MRI sensitivity efficiency and quantification accuracy

Abstract

Chemical exchange saturation transfer (CEST) MRI has become increasingly utilized for detecting dilute labile protons and characterizing microenvironment properties. However, the CEST MRI effect is only a few percent, and there is a need for a systematic approach to optimize scan parameters for sensitive and accurate CEST quantification. We propose multi-dimensional adjustments of key parameters such as the repetition time (TR) and RF duty cycle to optimize CEST MRI sensitivity per unit of time and utilization of quasi-steady-state (QUASS) reconstruction to recover the full CEST effect during postprocessing. Our work herein derived the CEST effect based on the generalized spin-lock CEST model and determined the interdependency of the optimal RF duty cycle and TR, showing the optimal TR decreases with the RF duty cycle but plateaus beyond 60-80%. The accuracy of the solution was validated with both numerical simulations and CEST MRI experiments on a dual pH creatine gel phantom. The desired equilibrium CEST effect was further reconstructed with the QUASS algorithm from the optimized CEST MRI scan. In summary, our study establishes a workflow for CEST MRI scan optimization and postprocessing analysis, providing a framework to boost both the sensitivity of CEST MRI scans and the accuracy of CEST quantification. This approach holds promise for future in vivo validation and translation.

Introduction

Chemical exchange saturation transfer (CEST) MRI has emerged as a molecular imaging approach to detect tissue properties [1-5], complementing routine structural and relaxation scans. It has increasingly been adopted in imaging protein and metabolic changes in the tumor [6-11] and acidosis in acute ischemia [12-21]. Despite the signal amplification strategy via the saturation transfer, a typical CEST MRI effect is limited to a few percent or less, particularly when detecting dilute tissue metabolites. As such, it is important to optimize the CEST MRI scan for peak sensitivity. It is worth noting that CEST MRI has complex dependencies on scan parameters, including repetition time, RF saturation amplitude and duration, and image flip angle [22-26]. It has been shown that CEST benefits from RF saturation optimization, so the saturation efficiency and RF spillover effect can be balanced. A relatively modest RF saturation amplitude will allow the detection and quantification of multiple partially overlapping CEST signals commonly observed in vivo. For example, careful selection of RF power levels could provide desired tissue contrast [27, 28]. Also, the exchange rate and labile proton ratio can be determined simultaneously from techniques such as the power and omega plot analyses [29-33] and ratiometric analysis [34-37]. On the other hand, there is much less work to systematically optimize scan parameters such as the repetition time (TR) and RF duty cycle [38]. Whereas the CEST MRI effect increases with the repetition and saturation times, there is a burden on the total scan time and RF energy deposition [25, 39]. Although a modest repetition time likely maximizes the CEST effect efficiency, the magnitude of the obtainable CEST effect would have been underestimated. As such, it is critical to develop a framework not only to optimize CEST MRI acquisition but also to reconstruct the desired equilibrium CEST effect that jointly supports sensitive and accurate CEST measurement.

Our study aimed to address this optimization and quantification challenge by combining the generalized spin-lock CEST model that describes the CEST signal evolution and the quasi-stead-state (QUASS) approach that reconstructs the equilibrium CEST signal [40]. Specifically, we derived the transient CEST solution using the rotating frame spin-lock model, calculated the sensitivity per unit of time (i.e., SNR efficiency), and determined the relationship between the RF duty cycle and optimal TR, under which the SNR efficiency peaks. To validate these theoretical derivations, we simulated the impact of repetition time and RF duty cycle on the creatine CEST MRI effect using Bloch-McConnell equations. The optimal RF duty cycle and TR values at which sensitivity peaks were determined numerically and validated against the analytical solution. In addition, we analyzed CEST scans on a creatine gel phantom with a serially varied TR and RF duty cycle [25]. We evaluated the sensitivity of QUASS CEST MRI to test the theoretical predictions of optimal scan conditions. In summary, our study demonstrated a workflow for CEST MRI scan optimization and quantification, enabling data acquisition at peak sensitivity efficiency and reconstruction of desired equilibrium CEST MRI signals in postprocessing.

Theory

The saturated signal intensity can be described by the spinlock model in the rotating frame [41, 42]. Specifically, the normalized reference ($I^{-}$) and label ($I^{+}$) signals are given as

$$\frac{I^{\pm }(\eta ,TR,R_{1w},R_{1\rho }^{\pm },B_1,\Delta \omega )}{I_0(\eta ,TR,R_{1w})}=\frac{(1-e^{-R_{1w}\cdot (1-\eta )\cdot TR})e^{-R_{1\rho }^{\pm }\cdot \eta \cdot TR}+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^{\pm }}\left(1-e^{-R_{1\rho }^{\pm }\cdot \eta \cdot TR}\right)}{1-e^{-R_{1w}\cdot TR}}$$ (1)

, in which, $R_{1w}$ is the tissue longitudinal relaxation rate, $R_{1\rho }$ is spinlock rate, which is $R_{1\rho }=R_{1w}co{s}^2\theta +R_{2w}si{n}^2\theta +\sum R_{ex}$ and $\theta =\mathrm{atan}(\frac{\gamma \cdot B_1}{\Delta \omega })$, in which $\gamma$ is the gyromagnetic ratio, with ${\mathrm{B}}_1$ and $\Delta \omega$ being the RF saturation amplitude and offset, respectively. In addition, $\eta$ is the CEST RF saturation duty cycle, and we have $Ts=\eta \cdot TR$ and $Td=(1-\eta )\cdot TR$, with Ts and Td being the RF saturation time and relaxation delay, and TR is the repetition time. The CEST effect has been commonly calculated using asymmetry analysis, and we have

$$MT{R}_{asym}=\frac{(1-{\mathrm{e}}^{-{\mathrm{R}}_{1\mathrm{w}}\cdot \text{Td}})\left({\mathrm{e}}^{-{\mathrm{R}}_{1\rho }^{-}\cdot \text{Ts}}-{\mathrm{e}}^{-{\mathrm{R}}_{1\rho }^{+}\cdot \text{Ts}}\right)+\frac{{\mathrm{R}}_{1\mathrm{w}}{\cos }^2\theta }{{\mathrm{R}}_{1\rho }^{-}{\mathrm{R}}_{1\rho }^{+}}\left({\mathrm{R}}_{1\rho }^{+}(1-{\mathrm{e}}^{-{\mathrm{R}}_{1\rho }^{-}\cdot \text{Ts}})-{\mathrm{R}}_{1\rho }^{-}\left(1-{\mathrm{e}}^{-{\mathrm{R}}_{1\rho }^{+}\cdot \text{Ts}}\right)\right)}{1-e^{-R_{1w}\cdot TR}}$$ (2)

Because the scans can be repeated to improve the total sensitivity, the CEST signal per unit of time should be optimized. It has been shown that the CEST sensitivity efficiency is proportional to the asymmetry normalized by the square root of repetition time (i.e., $\propto \frac{MT{R}_{asym}}{\sqrt{TR}}$) [39]. The optimal TR can be solved by nulling the derivative of MTR asymmetry efficiency against TR (Please see the appendix for detailed derivations), being

$$\frac{\partial \left(\frac{MT{R}_{asym}}{\sqrt{TR}}\right)}{\partial \text{TR}}\propto \begin{array}{c}\hfill 2\cdot (1-e^{-R_{1w}\cdot TR})\cdot \left[\begin{array}{c}\hfill R_{1w}\cdot \left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)(Td\cdot e^{-R_{1w}\cdot Td}+Ts\cdot co{s}^2\theta )\hfill \\ \hfill -Ts\cdot (1-e^{-R_{1w}\cdot Td})\left(R_{1\rho }^{-}{e}^{-R_{1\rho }^{-}\cdot Ts}-R_{1\rho }^{+}{e}^{-R_{1\rho }^{+}\cdot Ts}\right)\hfill \end{array}\right]\hfill \\ \hfill -[1+e^{{-R}_{1w}\cdot TR}(2R_{1w}\cdot TR-1)]\left[\begin{array}{c}\hfill (1-e^{-R_{1w}\cdot Td})\cdot \left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)\hfill \\ \hfill +\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^{+}{R}_{1\rho }^{-}}\left(R_{1\rho }^{+}-R_{1\rho }^{-}+R_{1\rho }^{-}{e}^{-R_{1\rho }^{+}\cdot Ts}-R_{1\rho }^{+}{e}^{-R_{1\rho }^{-}\cdot Ts}\right)\hfill \end{array}\right]\hfill \end{array}$$ (3)

It is worth noting that the optimal $\eta$ and TR from Eq. 3 not only depend on each other but also depend on ${\mathrm{R}}_{1\mathrm{w}}$ and $R_{1\rho }^{\pm }$, as well as $\theta$, and therefore, $B_1$ and $\Delta \omega$.

Methods

Simulation

We simulated a representative 2-pool CEST MRI with Bloch-McConnell equations in MATLAB (MathWorks, Natick MA). The CEST MRI sequence includes a relaxation recovery time (Td), followed by CEST RF saturation (Ts) and readout. We assumed the readout time was negligible when compared to relaxation and saturation times, for example, when using echo planar imaging (EPI) readout. We simulated the guanidino proton exchange at 1.9 ppm, with a typical labile proton fraction ratio of 1:1000 and exchange rate of 250 s⁻¹ at a slightly acidic pH of about 6 [43]. The labile protons T₁ and T₂ were set to be 1 s and 20 ms, with the bulk water T₁ and T₂ being 2.5 s and 55 ms, similar to phantom measurements. The TR was varied from 1 to 10 times of T₁ in increments of 0.25, and RF duty cycles ranged from 20% to 80% in increments of 10%. A very long TR was chosen to allow both Td and Ts to reach up to five times T₁, ensuring that both relaxation and saturation transfer reach their equilibrium states independently.

Phantom

A dual pH gel-creatine phantom was prepared for the experiment [25]. Briefly, we added 2% agarose to phosphate-buffered saline solution doped with a trace amount of CuSO4^· 5H2O (Sigma Aldrich, St Louis, MO). The mixture was heated to boiling temperature and immersed in a water bath at 46°C. Creatine was added to reach a concentration of 50 mM, followed by titration to pH values of 5.8 and 6.5. The agarose gel mixture was then transferred into two concentric tubes and solidified overnight at room temperature before MRI experiments.

MRI

Images were acquired using a 4.7 Tesla small-bore magnet (Bruker Biospec, Billerica, MA) employing a routine CEST EPI sequence (slice thickness = 10 mm, field of view = 76 x 76 mm, bandwidth = 200 kHz) with an image matrix of 64 by 64, as reported previously [25]. To determine the optimal scan conditions, we performed the 3-point CEST MRI scan (normalization control scan without RF saturation and two saturated scans at ±1.9 ppm, B₁=0.75 μT). The RF saturation time and relaxation delay were adjusted according to the TR and RF duty cycle. TR was varied from 2 to 10 s, for each TR, the RF duty cycle was varied from 20% to 80% in increments of 10%. We chose two signal averages after two dummy scans. Also, a Z-spectrum was acquired from −3 to 3 ppm at intervals of 0.25 ppm (TR=6.5 s, Td/Ts=3.5 s/3 s, and B₁=0.75 μT). Additionally, T₁ and T₂ maps were obtained with inversion recovery times ranging from 0.25 to 5 s (Recovery time = 6.5 s) and spin echo EPI with three separate echo times of 30, 60, and 90 ms.

Data Analysis

T₁ and T₂ were obtained using least-squares fitting of the inversion signal recovery and transverse relaxation functions, respectively. The B₀ inhomogeneity was determined from the Z-spectrum, which was deemed sufficiently centered and homogeneous [44]. The CEST effect was calculated as the MT asymmetry between normalized reference and label scans ($MT{R}_{asym}=\frac{I(-1.9ppm)-I(+1.9ppm)}{I_0}$), and the sensitivity was calculated as $SNR=\frac{MT{R}_{asym}(pH=6.5)-MT{R}_{asym}(pH=5.8)}{\sqrt{{(\sigma (pH=6.5)}^2+\sigma {(pH=5.8)}^2)∕2}}$, with $\sigma$ being the standard deviation within each pH compartment. In addition, CEST sensitivity efficiency was calculated as $SN{R}_{put}=\frac{SNR(\eta ,TR)}{\sqrt{TR}}$. Furthermore, the QUASS reconstruction was based on previously published work [45].

Results

Figure 1 shows the simulated CEST signal evolution for four representative RF duty cycles (100% (Fig. 1a), 75% (Fig. 1b), 50% (Fig. 1c), and 25% (Fig. 1d)) with a typical TR twice of T₁. The control signal without RF saturation, as well as the reference (−1.9 ppm) and label (1.9 ppm) signals, are plotted in cyan, red, and blue colors, respectively. Although the CEST signal continues (black) to increase throughout RF saturation, its rate of increase diminishes as it approaches a plateau, suggesting the existence of an optimal TR and RF duty cycle that balances the build-up and magnitude of the measurable CEST effect. Thus, systematic evaluation and optimization are necessary to enhance CEST signal sensitivity per unit of time.

Figure 1.

Simulation of the repetition time and RF duty cycle impact on guanidyl (1.9 ppm) CEST MRI using a representative 2-pool CEST model. a) Simulated control, reference, and label signals and the CEST effect (x 3 for visualization) for TR twice of T₁, RF duty cycle of 100%. b) Signal evolution for RF duty cycle of 75%. c) Signal evolution for RF duty cycle of 50%. d) Signal evolution for RF duty cycle of 25%.

The CEST effect was calculated as MT asymmetry between ±1.9 ppm. Figure 2a shows the CEST effect increase with the TR and RF duty cycle, and the equilibrium CEST effect is achieved when both are the largest, as expected. However, the gain in the CEST effect becomes incrementally less efficient at long TR and high RF duty cycles. Figure 2b plots the CEST effect per unit of time, which shows the advantage of choosing a modest TR that balances saturation transfer and the total scan time. Not surprisingly, the CEST SNR efficiency increases with the RF duty cycle monotonically under a given TR. Figure 2c plots the optimal RF duty cycle and TR from the numerical simulation (cross markers) and the analytical solution (Eq. 3), matching exceedingly well. Whereas the optimal TR decreases with the RF duty cycle, the gain in TR reduction becomes minimal for the RF duty cycle beyond 60-80%. In addition, the optimal conditions for reference (dashed-dotted line in gray) and label (dashed line in black) scans were calculated (Eq. A.9), sandwiching the optimal TR and RF duty cycle line for MTR_asym. This observation is expected because the label scan has a higher spinlock relaxation rate than the reference scan.

Figure 2.

Evaluation of CEST MRI as functions of repetition time and RF duty cycle. a) CEST effect, calculated from MT asymmetry, as a function of repetition time and RF duty cycle. b) CEST effect efficiency (per unit of time), calculated from MT asymmetry, as a function of repetition time and RF duty cycle. c) The optimal TR under which CEST effect efficiency peaks is plotted as a function of the RF duty cycle.

Figure 3 shows the apparent Z (Figure 3a) and asymmetry (Figure 3b) spectra from the two pH compartments. While Z-spectra largely overlapped, there was a notable signal difference at 1.9 ppm due to the guanidino CEST effect. In addition, B₀ field inhomogeneity was minimal, being −1 ± 3 Hz across the image due to the use of high-order shimming. The Lorentzian fitting was applied to quantify the guanidino CEST effect. The apparent CEST effect was 4.0% ($R_{1\rho }^{-}$(−1.9 ppm) being 0.45 $s^{-1}$ and $R_{1\rho }^{+}$(+1.9ppm) being 0.47 $s^{-1}$) and 11.2% ($R_{1\rho }^{\pm }$ being 0.45 and 0.51 $s^{-1}$), for pH of 5.8 and 6.5, respectively. In comparison, the QUASS Z (Figure 3c) and asymmetry (Figure 3d) spectra showed elevated CEST effects, as evidenced by a more pronounced contrast at 1.9 ppm. The QUASS CEST effect was 5.2% ($R_{1\rho }^{\pm }$ being 0.46 $s^{-1}$ and 0.49 $s^{-1}$) and 13.4% ($R_{1\rho }^{\pm }$ being 0.47 $s^{-1}$ and 0.55 $s^{-1}$), for pH of 5.8 and 6.5, respectively. Notably, there were little T₁ and T₂ differences. T₁ was 2.43 ± 0.04 s and 2.44 ± 0.04 s for pH compartments of 5.8 and 6.5, respectively, with their T₂ being 56 ± 1 ms and 54 ± 1 ms.

Figure 3.

The Z-spectral signal and Lorentzian fitting of the dual agarose-pH phantom. a) The apparent Z-spectra from two pH compartments, together with the Lorentzian fitting. b) The apparent CEST asymmetry spectra and the Lorentzian fitting. a) The QUASS Z-spectra from two pH compartments, together with the Lorentzian fitting. b) The QUASS CEST asymmetry spectra and the Lorentzian fitting.

Figure 4 shows the experimentally determined CEST sensitivity (Figure 4a) and sensitivity efficiency (Figure 4b) from the dual-pH phantom as functions of the RF duty cycle and TR. Similar to simulation findings (Figure 2), the CEST MRI sensitivity increases with the RF duty cycle and TR. The CEST sensitivity efficiency, however, increased with the RF duty cycle, but it peaked at a modest TR. The optimal RF duty cycle and TR were solved using the spinlock relaxation rates, the bulk water T₁ measurement, and the B₁ level, according to Eq. 3. Figure 4c plots the optimal TR and RF duty cycle determined experimentally (squares and circles), which agreed reasonably well with the theoretical prediction. It shows the optimal TR was about 2.5 times the phantom bulk water T₁ for a typical RF duty cycle of 60%, which is about 6 s. Figure 5a shows three apparent CEST images obtained under TR of 2, 6, and 10 s for an RF duty cycle of 60%, and the magnitude of the CEST effect increased with TR due to the prolonged saturation transfer process. Figure 5b shows the corresponding QUASS CEST images, which showed similar magnitudes of CEST effect across TR but clearly different SNR. The contrast-to-noise ratio between the two pH compartments was 5.0, 11.9, and 13.7 for TR of 2, 6, and 10 s, respectively, with the SNR efficiency calculated as 3.5, 4.9, and 4.3, peaking around 6 s.

Figure 4.

Evaluation of CEST MRI as functions of repetition time and RF duty cycle in a dual agarose-pH phantom. a) Phantom CEST MRI contrast-to-noise ratio (CNR) as a function of repetition time and RF duty cycle. b) Phantom CEST MRI CNR efficiency as a function of repetition time and RF duty cycle. c) The optimal TR for each RF duty cycle under which CEST effect efficiency peaks is plotted, together with the prediction from Eq. 3.

Figure 5.

CEST MRI images under three representative TR at a typical RF duty cycle of 60%. a) The apparent CEST images, calculated from asymmetry analysis, for TR of 2, 6, and 10 s, under an RF duty cycle of 60%. b) The QUASS CEST images, calculated from asymmetry analysis, for TR of 2, 6, and 10 s, under an RF duty cycle of 60%.

Discussion

This study developed a framework for the optimization of key CEST MRI parameters, including repetition time and RF duty cycle, and the solution was confirmed with both numerical simulation and phantom experiments. In addition, we showed that the desired equilibrium CEST effect could be reconstructed from the scans obtained under optimal conditions, hence yielding highly sensitive and accurate CEST MRI.

The derivation showed that the optimal TR and RF duty cycle depend on each other, as expected. This interdependence is because, at a higher RF duty cycle, the same saturation time can be achieved at a slightly shorter repetition time. However, their relationship is non-linear because the time constants appear in the exponent and square root. In addition, while the gain in repetition time shortening is substantial with an increase in the RF duty cycle initially, such gain becomes minimal as the RF duty cycle is beyond 60-80%. This pattern is apparent from Figure 1, which shows that while a high RF duty cycle always produces a higher CEST effect, the initial gain in the CEST effect was slow and, hence, not efficient for generating the CEST effect. This recognition could bear significance for CEST scans at ultrahigh fields such as 7 Tesla scanners due to a substantially elevated specific absorption rate (SAR). For example, the RF duty cycle could be determined based on the SAR limit, and the optimal TR can be predicted based on the estimated tissue properties. Under such a scenario, it could be more relevant to deploy the QUASS postprocessing to correct the underestimated CEST effect due to not sufficiently long RF saturation. In addition, whereas our current study optimizes the CEST sensitivity per unit of time, other target functions can be chosen for optimization, including CEST sensitivity per unit of RF energy deposition.

The optimized TR was divided by T₁ for normalization because T₁ provides a good time scale for CEST MRI. During the relaxation delay, the signal recovers towards the equilibrium state following the classical T₁ recovery. While the signal transits towards the equilibrium CEST effect following the spinlock relaxation rate ($R_{1\rho }=R_{1w}co{s}^2\theta +R_{2w}si{n}^2\theta +\sum R_{ex}$), it is reasonably close to the bulk water longitudinal relaxation rate under the condition of modest RF power levels. The optimal scan condition depends on the equilibrium spinlock relaxation rate (i.e., $R_{1\rho }$) because it reflects the underlying genuine coupling rate, which is higher than those measured using not sufficiently long relaxation and saturation times. For demonstration, we also simulated and predicted the optimal TR and RF duty cycle for representative CEST MRI measurement of creatine and amide signals at neutral pH (i.e., 7.0), given the substantial interest in them [46-48], under two representative RF levels of 0.75 and 2 μT at 3 (Fig. 6a) and 7 T (Fig. 6b). The creatine concentration and exchange rate were measured to be 8 mM and 810 s⁻¹ by Khlebnikov et al. [43]. The mobile amide concentration and exchange rate were 60 mM [49] and 100 s⁻¹, with the exchange rate between published values from different groups [12, 50-53]. The optimal TR decreases with the RF duty cycle, as expected. Overall, the optimal TR is lower at 3T than 7 T due to a higher spinlock relaxation rate because of the proximity of CEST and bulk water signals. For the same reason, the optimal TR for guanidino CEST is less than that for amides. Also, it is worth noting that the optimal condition depends not only on the labile group of interest but also on the partially overlapping CEST and background semisolid macromolecular signals [54]. Such complexity can be accounted for using the analytical derivation, provided the equilibrium exchange properties are known.

Figure 6.

The predicted optimal TR as a function of the RF duty cycle at two typical field strengths. a) Optimal TR against RF duty cycle for guanidino and amide signals at neutral pH under two typical B₁ levels of 0.75 and 2 μT at 3 T. b) Optimal TR against RF duty cycle for guanidino and amide signals at neutral pH under two typical B₁ levels of 0.75 and 2 μT at 7 T.

It is helpful to consider the potential gains in maximizing CEST sensitivity per unit of time, using phantom data as an example. If we use the scan time with TR = 2 seconds as a reference, the scan times needed to achieve the same SNR would be 1, 0.5, and 0.7 for TR values of 2, 6, and 10 seconds, respectively. Under optimal sensitivity efficiency conditions, the scan time can be significantly reduced. The improved SNR could also enable enhanced spatial resolution in CEST MRI. Moreover, the magnitude of the CEST effect can be accurately recovered using QUASS reconstruction. It is important to note that optimization can become complex in the presence of significant field inhomogeneity, as the estimation of the spin-lock relaxation rate depends on the RF saturation amplitude and offset, which may be inaccurate due to inhomogeneities. However, we anticipate that advances in hardware will mitigate these inhomogeneities, which would support the proposed optimization strategy [55]. Given possible concomitant tissue changes in relaxation and semisolid magnetization transfer effects, it helps to estimate the target of the system (i.e., $R_{1\rho }$) of interest before optimization, such as pathological tissue, normal tissue, or their contrast. Fortunately, such information could be obtained either directly from a priori measurements under the long repetition and saturation time scan condition or postprocessing QUASS reconstruction approach [56]. The knowledge gained from this study also helps the optimization of multi-slice [57-59] and three-dimensional CEST MRI [60-62]. Although our study focused on the optimization of spin echo CEST MRI, the framework can be extended to optimize gradient echo CEST MRI, which will introduce additional parameters of interest, such as the flip angle. Nevertheless, rigorous optimization and quantification could boost the CEST MRI sensitivity to facilitate in vivo CEST MRI to detect subtle changes in metabolites.

Conclusions

Our study establishes a workflow to predict optimal scan conditions toward maximizing the CEST sensitivity per unit of time, and the derivations were confirmed with both numerical simulation and phantom scans. The optimized CEST acquisition further benefits from the QUASS postprocessing, hence improving both the sensitivity and accuracy of CEST MRI. This approach holds the potential for facilitating the translation and adoption of CEST MRI, where quantitative molecular imaging needs to be conducted within tight time constraints.

Highlights.

• There is a strong interdependency between optimal repetition time and RF duty cycle for maximizing CEST MRI sensitivity per unit of time.

• A workflow has been established to improve CEST optimization and quantification by combining the spinlock model that describes the CEST signal evolution and the quasi-stead-state (QUASS) approach that reconstructs the equilibrium CEST signal.

Appendix

The MTR asymmetry can be described by

$$MT{R}_{asym}(\eta ,TR,R_{1w},R_{1\rho }^{\pm })=\frac{(1-e^{-R_{1w}\cdot Td})\left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^{-}{R}_{1\rho }^{+}}\left(R_{1\rho }^{+}(1-e^{-R_{1\rho }^{-}\cdot Ts})-R_{1\rho }^{-}\left(1-e^{-R_{1\rho }^{+}\cdot Ts}\right)\right)}{1-e^{-R_{1w}\cdot TR}}$$ (A.1)

For the optimization of the asymmetry efficiency calculation ($\frac{MT{R}_{asym}(\eta ,TR,R_{1w},R_{1\rho }^{\pm })}{\sqrt{TR}}$); we apply the quotient rule, which states that the quotient rule and have $\frac{\partial \frac{u(x)}{v(x)}}{\partial x}=\frac{{\mathrm{u}}^{\prime }\cdot \mathrm{v}-\mathrm{u}\cdot {\mathrm{v}}^{\prime }}{{\mathrm{v}}^2}$. We define

$$u=(1-e^{-R_{1w}\cdot Td})\left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^{-}{R}_{1\rho }^{+}}\left(R_{1\rho }^{+}(1-e^{-R_{1\rho }^{-}\cdot Ts})-R_{1\rho }^{-}(1-e^{-R_{1\rho }^{+}\cdot Ts})\right)$$ (A2.a)

and

$$v=(1-e^{-R_{1w}\cdot TR})\cdot \sqrt{TR}$$ (A2.b)

Their derivates could be calculated as,

$$u^{\prime }=R_{1w}(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts})\left((1-\eta )e^{-R_{1w}\cdot Td}+\eta co{s}^2\theta \right)-\eta (1-e^{-R_{1w}\cdot Td})\left(R_{1\rho }^{-}{e}^{-R_{1\rho }^{-}\cdot Ts}-R_{1\rho }^{+}{e}^{-R_{1\rho }^{+}\cdot Ts}\right)$$ (A3.a)

and

$$v^{\prime }=\frac{\partial I_0(TR)\cdot \sqrt{TR}}{\partial R_{1\rho }}=\frac{1+e^{-R_{1w}\cdot TR}(2R_{1w}TR-1)}{2\sqrt{TR}}$$ (A3.b)

We have the MTR asymmetry sensitivity efficiency derivate against TR as

$$\frac{\partial \frac{MT{R}_{asym}}{\sqrt{TR}}}{\partial TR}\propto \begin{array}{c}\hfill 2\cdot (1-e^{-R_{1w}\cdot TR})\cdot \left[\begin{array}{c}\hfill R_{1w}\cdot \left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)(Td\cdot e^{-R_{1w}\cdot Td}+Ts\cdot co{s}^2\theta )\hfill \\ \hfill -Ts\cdot (1-e^{-R_{1w}\cdot Td})\left(R_{1\rho }^{-}{e}^{-R_{1\rho }^{-}\cdot Ts}-R_{1\rho }^{+}{e}^{-R_{1\rho }^{+}\cdot Ts}\right)\hfill \end{array}\right]\hfill \\ \hfill -[1+e^{{-R}_{1w}\cdot TR}(2R_{1w}\cdot TR-1)]\left[\begin{array}{c}\hfill (1-e^{-R_{1w}\cdot Td})\cdot \left(e^{-R_{1\rho }^{-}\cdot Ts}-e^{-R_{1\rho }^{+}\cdot Ts}\right)\hfill \\ \hfill +\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^{+}{R}_{1\rho }^{-}}\left(R_{1\rho }^{+}-R_{1\rho }^{-}+R_{1\rho }^{-}{e}^{-R_{1\rho }^{+}\cdot Ts}-R_{1\rho }^{+}{e}^{-R_{1\rho }^{-}\cdot Ts}\right)\hfill \end{array}\right]\hfill \end{array}$$ (A4)

The optimal TR against the RF duty cycle can be calculated based on $R_{1w}$ and $R_{1\rho }^{\pm }$.

More generally, the CEST scan can be optimized as a function of $R_{1\rho }$. In this case, the normalized saturated CEST signal is given by

$$\frac{I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{I_0(TR,R_{1w})}=\frac{(1-e^{-R_{1w}\cdot Td})e^{-R_{1\rho }\cdot Ts}+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }}(1-e^{-R_{1\rho }\cdot Ts})}{1-e^{-R_{1w}\cdot TR}}$$ (A.5)

The function to optimize the signal sensitivity per unit of time is approximated by $\frac{I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{I_0(TR,R_{1w})\cdot \sqrt{TR}}$. We again applied the quotient rule and took its derivative against $R_{1\rho }$. We define

$$u=I^{sat}(TR)=(1-e^{-R_{1w}\cdot Td})e^{-R_{1\rho }\cdot Ts}+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }}(1-e^{-R_{1\rho }\cdot Ts})$$ (A.6a)

and

$$v=I_0(TR)\cdot \sqrt{TR}=(1-e^{-R_{1w}\cdot TR})\cdot \sqrt{TR}$$ (A.6b)

Their derivates could be calculated as,

$$u^{\prime }=\frac{\partial I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{\partial R_{1\rho }}=\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^2}\left(e^{-R_{1\rho }\cdot Ts}(1+R_{1\rho }\cdot Ts)-1\right)-Ts\cdot e^{-R_{1\rho }\cdot Ts}(1-e^{-R_{1w}\cdot Td})$$ (A7.a)

and

$$v^{\prime }=\frac{\partial I_0(TR,R_{1w})\cdot \sqrt{TR}}{\partial R_{1\rho }}=0$$ (A7.b)

We have the saturated signal intensity sensitivity efficiency derivate against TR as

$$\frac{\partial \frac{I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{I_0(TR,R_{1w})\cdot \sqrt{TR}}}{\partial R_{1\rho }}=\frac{R_{1w}co{s}^2\theta \left(e^{-R_{1\rho }\cdot Ts}(1+R_{1\rho }\cdot Ts)-1\right)-R_{1\rho }^2\cdot Ts\cdot e^{-R_{1\rho }\cdot Ts}(1-e^{-R_{1w}\cdot Td})}{R_{1\rho }^2\cdot (1-e^{-R_{1w}\cdot TR})\cdot \sqrt{TR}}$$ (A.8)

We take the derivative of $\frac{\partial \frac{I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{I_0(TR,R_{1w})\cdot \sqrt{TR}}}{\partial R_{1\rho }}$ gainst TR to maximize the signal efficiency per unit of time. We have

$$\frac{\frac{\partial \frac{I^{sat}(\eta ,TR,R_{1w},R_{1\rho })}{I_0(TR,R_{1w})\cdot \sqrt{TR}}}{\partial R_{1\rho }}}{\partial TR}\propto \begin{array}{c}\hfill \left(1-e^{-R_{1w}\cdot (1-\eta )\cdot TR}-\frac{R_{1w}co{s}^2\theta }{R_{1\rho }}\right)+\frac{R_{1w}co{s}^2\theta }{\eta \cdot TR\cdot R_{1\rho }^2\cdot e^{-R_{1\rho }\cdot \eta \cdot TR}}\cdot (1-e^{-R_{1\rho }\cdot \eta \cdot TR})\hfill \\ \hfill -2\left[\begin{array}{c}\hfill \left((1-e^{-R_{1w}\cdot (1-\eta )\cdot TR})\left(1-R_{1\rho }\cdot \eta \cdot TR\right)+R_{1w}\cdot TR\cdot (\eta co{s}^2\theta +(1-\eta )e^{-R_{1w}\cdot (1-\eta )\cdot TR})\right)\hfill \\ \hfill -\frac{R_{1w}\cdot e^{-R_{1w}\cdot TR}}{1-e^{-R_{1w}\cdot TR}}\left(TR\cdot (1-e^{-R_{1w}\cdot (1-\eta )\cdot TR})+\frac{R_{1w}co{s}^2\theta }{R_{1\rho }^2}\left(\frac{1-e^{-R_{1\rho }\cdot \eta \cdot TR}}{\eta \cdot e^{-R_{1\rho }\cdot \eta \cdot TR}}-R_{1\rho }\cdot TR\right)\right)\hfill \end{array}\right]\hfill \end{array}$$ (A.9)