Background and Purpose

Proton exchange is the fundamental mechanism underpinning CEST MRI contrast, and it has been reported that mapping of the proton exchange rate (k_ex) may help the clinical diagnosis of stroke and cancer [1, 2]. Our preliminary study has demonstrated that omega plotting with direct saturation (DS) signal removed can be used to map the exchange rate in healthy brains in vivo [3]. However, omega plot based on steady-state saturation assumption may lead to long scanning time and potential high SAR deposition, limiting it from clinical applications. Here we propose a novel method with induced saturation-transfer-recovery steady states (iSTRESS) to measure k_ex with low saturation power, short duration, and hence negligible SAR deposition.

Theoretical considerations and methods

Continuous RF saturation on a metabolite’s chemical shift frequency reduces its signal. For an RF with the power B₁, the saturation efficiency, $$$α$$$, can be approximated as [4-7]: $$α= \frac{(γB_1)^2}{(γB_1)^2+(k_{ex})^2 }{\phantom \cosin} (1)$$
in which $$$\gamma$$$ is the nuclear gyromagnetic ratio (42.58 Hz/µT for proton).
Proton exchange between the metabolite and bulk water pool transfers a portion of saturated protons to the water pool and cause its signal to reduce. The rate of signal loss in the water pool due to the exchange with the saturated protons from the metabolite’s pool depends on the exchange rate, the relative proton density ($$$f$$$), as well as the saturation efficiency: $$R_{exch}=k_{ex}×f×α{\phantom \cosin} (2)$$
Concurrently, the signal of water pool protons recovers back towards its equilibrium value due to the inherent spin-lattice relaxation (T₁-recovery) process with the rate of $$$\left(1-\frac{M_{Z,ss}^A}{M_{Z,eq}^A}\right)R_1^A$$$, where $$$M_{Z,ss}$$$ and $$$M_{Z,eq}$$$ are the steady-state and the equilibrium magnetization respectively, and $$$R_1=1/T_1$$$. In a saturation transfer recovery steady-state (STRESS) (Fig.1), when the signal loss due to the proton exchange balances the signal gain due to the T₁ recovery, the signal stays at a steady-state value. Therefore, under STRESS we have $$\frac{M_{Z,ss}^A}{M_{Z,eq}^A}×R_{exch} =\frac{M_{Z,ss}^A}{M_{Z,eq}^A}×k_{ex}×f×\frac{(γB_1)^2}{(γB_1)^2+(k_{ex})^2 }=\left(1-\frac{M_{Z,ss}^A}{M_{Z,eq}^A}\right)R_1^A{\phantom \cosin} (3)$$ where $$$M_{Z,ss}$$$, $$$M_{Z,eq}$$$, $$$R_1^A$$$, and $$$B_1$$$ are either known or measurable parameters. In this equation relative proton density of the two pools, $$$f$$$, and the exchange rate, $$$k_{ex}$$$, are the only two parameters to be determined. When using two saturation powers $$$B_{11}$$$ & $$$B_{12}$$$ to create two STRESS conditions, $$$f$$$ and $$$R_1^A$$$ can be canceled out and the exchange rate, $$$k_{ex}$$$, directly calculated from the following equation. $$k_{ex}^2=\frac{(γB_{11})^2×(γB_{12})^2×Mz,eq×(Mz,ss_1-Mz,ss_2)}{(γB_{12} )^2×Mz,ss_2×(Mz,eq-Mz,ss_1 )-(γB_{11} )^2×Mz,ss_1×(Mz,eq-Mz,ss_2))}{\phantom \cosin} (4)$$
Reaching two different steady states, theoretically requires long saturation durations, such as 10 s, which may induce unbearable SAR deposition in clinical applications. This problem can be overcome alternatively by noticing that 1) to calculate $$$k_{ex}$$$ from Eq.4 the only required parameters are the initial and final values of the magnetization for two $$$B_1$$$’s, and 2) the process of how the steady states are reached is not important, as eventually, it is an equilibrium when the two rates (saturation and T₁ recovery) cancel each other. These enable one to induce the steady-states and to measure the exchange rate, in much shorter saturation times and negligible SAR deposition.
We developed a novel iSTRESS sequence as shown in Fig.2, in which an excitation RF pulse flips the magnetization by a small flip angle ($$$β$$$) followed by a short saturation pulse (ms to 0.5 s) to maintain a steady-state magnetization after the flip. To determine the saturation power ($$$B_{11}$$$ or $$$B_{12}$$$) for each iSTRESS condition, B₁ is varied and the corresponding MR signals are measured to ensure that steady-state signal is maintained.

Method

We have programmed the novel iSTRESS sequence in a 9.4T preclinical MRI scanner (Agilent Technologies, Santa Clara, CA) and performed initial validation based on simulations and scanning of phantoms at varied pH. To validate the accuracy of the derived equation for calculating the exchange rate, we performed simulations with two-pool Bloch-McConnell equations and compared the determined k_ex from Eq.4 with the actual input k_ex. In vitro protein solution phantoms (20% w/w BSA in PBS, n=3) at varied pH (6.2, 6.6, 7.0 & 7.4) were scanned with iSTRESS protocol. The flip angles were β=10^o & 20^o. For each five Z-spectra were acquired, one right after the flip pulse and four with saturation duration= 0.5 s and saturation powers (B1=0, 25,50 & 100 Hz), and frequency offsets ranging from -6 to +6 ppm, +15.6 & +39.1 ppm. M_z at +2.75 ppm was used for the exchange rate analysis.

Results

In the simulations, strong linear relationships with R² = 0.999 were found between the input and calculated values as in Fig.3. In the phantom study, the calculated exchange rate showed an increase in k_ex with increasing pH (Fig.5), as expected [8].

Discussion and conclusion

In this work, we proposed a novel method to induced saturation-transfer-recovery steady states for determining k_ex with low saturation power, short duration, and hence negligible SAR deposition. Our analytic approach was validated with simulations and imaging phantoms. The acquisition time for collecting the parameter was shortened from ~10s to ~2s. In conclusion, this study shows great promise for in vivo proton exchange rate imaging and its clinical applications.

Acknowledgements

This work was supported by NIH grants R21EB023516, R01AG061114, and R21AG053876.

References

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