Simplified and scalable numerical solution for describing multi-pool chemical exchange saturation transfer (CEST) MRI contrast

https://doi.org/10.1016/j.jmr.2010.05.004Get rights and content

Abstract

Chemical exchange saturation transfer (CEST) imaging is sensitive to dilute labile proton and microenvironment properties such as pH and temperature, and provides vital information complementary to the conventional MRI methods. Whereas the Bloch equations coupled by exchange terms (i.e., Bloch–McConnell equations) have been utilized to quantify 2-pool CEST contrast, it is tedious to extend the Bloch–McConnell equations to describe CEST contrast beyond four saturation transfer sites. Hence, it is necessary to develop a scalable yet reasonably accurate numerical solution to describe the complex multi-pool CEST contrast. It is postulated here that the multi-pool CEST contrast can be quantified by modifying the classic 2-pool model. Although the direct exchange among labile proton groups is often negligible, labile protons may be coupled indirectly through their interaction with bulk water protons, which has to be quantified. The coupling term was solved empirically, and the proposed simplified solution was shown in good agreement with the conventional simulation. Moreover, the proposed solution is scalable, and can be easily extended to describe multi-pool CEST contrast. In sum, our study established a simplified and scalable, yet reasonably accurate numerical solution, suitable for quantitatively describing multi-pool CEST contrast.

Introduction

The indirect detection mechanism of chemical exchange saturation transfer (CEST) MRI confers it with an enormous sensitivity enhancement so that dilute labile proton and microenvironment properties such as pH and temperature can be estimated [1], [2]. Specifically, CEST contrast is approximately proportional to the labile proton concentration and exchange rate, hence, provides information that complements the conventional imaging methods [3], [4], [5], [6]. For instance, CEST MRI is capable of measuring metabolites and their byproducts such as glucose, glycogen and lactate [7], [8], [9]. In addition, amide proton transfer (APT) imaging, a specific form of CEST MRI, is pH dependent and remains promising for detecting ischemic tissue acidosis beyond the commonly used perfusion and diffusion scans [10], [11], [12], [13], [14]. Nevertheless, CEST MRI contrast is complex; it not only varies with labile proton concentration, exchange rate and relaxation time, but also depends on the experimental parameters such as the magnetic field strength, RF power, duration and scheme [15], [16], [17], [18], [19]. In addition, when there are multiple exchangeable proton groups within a single CEST system, quantitative description of CEST contrast becomes even more complex [13], [20], [21], [22], [23]. Moreover, semisolid macromolecular magnetization transfer (MT) and nuclear overhauser effect (NOE)-mediated saturation transfer may also become non-negligible for in vivo CEST MRI, particularly so if large RF irradiation power is applied [22], [24], [25], [26], [27].

Mathematical models have been developed to describe CEST contrast [27], [28], [29], [30], [31]. Specifically, an empirical solution based on the 2-pool exchange model provides simple yet reasonably accurate quantification of CEST contrast [15], [19]. The solution has also been modified to describe in vivo pH-weighted APT imaging of acute ischemia [31]. While on the other hand, Bloch equations coupled with exchange terms (Bloch–McConnell equations) can also numerically simulate 2-pool chemical exchange, and has been recently extended for quantifying 3-pool and 4-pool CEST contrast [27], [30]. However, conventional Bloch–McConnell equations are not easily scalable, and it is somewhat tedious to apply it to describe multi-pool CEST contrast beyond three labile proton groups. While on the other hand, over ten saturation transfer sites have been identified in biological systems, and therefore, it is necessary to develop a simplified solution for describing complex multi-pool CEST contrast [13], [22], [23], [32].

To address this need, our study investigated whether the multi-pool CEST contrast can be simulated using the commonly used 2-pool exchange model. It is important to note that because the direct RF saturation should be taken into account only once, multi-pool CEST Z-spectrum cannot be obtained by simply superimposing multiple Z-spectra estimated independently. Fortunately, the direct RF saturation can be quantified using a single set of Bloch equations [30], [33]. In addition, whereas direct exchange among labile proton groups is negligible due to their dilute concentration, labile protons may be coupled indirectly through their saturation transfer with bulk water protons. Particularly, when the RF irradiation amplitude becomes comparable with their chemical shifts, multiple labile protons may be simultaneously saturated, thus, compete for CEST contrast. As a result, simple linear superposition of individual CEST contrast will overestimate the multi-pool CEST contrast. Our study here derived the coupling term and developed a simplified solution, based on the classic 2-pool model, to quantify multi-pool CEST MRI contrast. We first confirmed that the proposed method is in good agreement with the conventional multi-pool CEST simulation using a representative 3-pool CEST system. We then showed that the proposed method is scalable and can be easily extended to simulate multi-pool CEST contrast with only minimal modification. In summary, the proposed numerical solution method provides simplified yet reasonably accurate modeling of multi-pool CEST contrast, suitable for quantifying complex CEST contrast.

Section snippets

Theory

Bloch–McConnell equations are often used to describe CEST contrast, and for a representative 2-pool chemical exchange, we have [28], [30],Mwx/tMwy/tMwz/tMsx/tMsy/tMsz/t=-kwsΔωw0ksw00Δωw-kws-ω10ksw00-ω1-kws00kswkws00-kswΔωs00kws0Δωs-ksw-ω100kws0-ω1-kswMwxMwyMwzMsxMsyMsz-Mwx/T2wMwy/T2w(Mw0-Mwz)/T1wMsx/T2sMsy/T2s(Ms0-Msz)/T1sin which Mwx,y,z and Msx,y,z are the x, y and z magnetization components for bulk water and labile protons, respectively, with T1,2w and T1,2s being their

Materials and methods

Numerical simulation was conducted in Matlab 7.4 (Mathworks, Natick MA). The coupling term was first derived, and the proposed simplified solution was compared with the conventional numerical solution using a representative 3-pool CEST model. We assumed that the T1 and T2 for bulk water are 3 s and 100 ms, respectively, and being 1 s and 15 ms for two dilute labile protons. In addition, the chemical shifts for two labile protons were set to be 4 and 5 ppm, for the magnetic field strength of 4.7 T (200

Results

Fig. 1 compares the proposed scalable solution with the conventional simulation of multi-pool CEST contrast. The conventional simulation (Fig. 1a) utilizes multiple sets of Bloch equations coupled by the exchange terms, with each set representing a single labile proton group [28]. The Bloch matrix size, for a general N-saturation transfer sites, is 3 N by 3 N (O(N2)). In comparison, the proposed simplified solution utilizes multiple 2-pool models, with a correction term that takes into account of

Discussion

This study developed a simplified numerical solution for describing multi-pool CEST contrast. The proposed method is scalable, and can be easily extended to describe CEST imaging of a large number of labile protons, potentially useful for quantifying in vivo CEST applications [13], [22]. Whereas for the representative 3-pool CEST contrast, the computation time of the proposed method is comparable with that of conventional solution (∼0.2 s, Dell Dimension 9100), the advantage in computation time

Conclusion

A flexible numerical solution based on the classic 2-pool exchange model was developed to describe multi-pool CEST contrast, in good agreement with the conventional numerical simulation method. The proposed method is scalable and can be easily extended to describe CEST contrast of a large number of saturation transfer sites. As such, our work may facilitate quantitative understanding of complex CEST contrast, complementing the conventional numerical simulation methods.

Acknowledgments

This study was supported in part by Grants from AHA/SDG 0835384N, NIH/NIBIB 1K01EB009771-01 and NIH/R21NS061119-02.

References (37)

  • S. Aime et al.

    Pushing the sensitivity envelope of lanthanide-based magnetic resonance imaging (MRI) contrast agents for molecular imaging applications

    Acc. Chem. Res.

    (2009)
  • S. Aime et al.

    A paramagnetic MRI-CEST agent responsive to lactate concentration

    J. Am. Chem. Soc.

    (2002)
  • S. Zhang et al.

    A paramagnetic CEST agent for imaging glucose by MRI

    J. Am. Chem. Soc.

    (2003)
  • P.C.M. van Zijl et al.

    MRI detection of glycogen in vivo by using chemical exchange saturation transfer imaging (glycoCEST)

    Proc. Natl. Acad. Sci.

    (2007)
  • E. Liepinsh et al.

    Proton exchange rates from amino acid side chains-implication for image contrast

    Magn. Reson. Med.

    (1996)
  • S.W. Englander et al.

    Hydrogen exchange

    Annu. Rev. Biochem.

    (1972)
  • P.C.M. van Zijl, N. Goffeney, J.H. Duyn, L.H. Bryant, J.W.M. Bulte, The use of starburst dendrimers as pH contrast...
  • J. Zhou et al.

    Using the amide proton signals of intracellular proteins and peptides to detect pH effects in MRI

    Nat. Med.

    (2003)
  • Cited by (51)

    • Quantitative MR relaxation using MR fingerprinting with fractional-order signal evolution

      2021, Journal of Magnetic Resonance
      Citation Excerpt :

      Recently, the application of fractional calculus into the water T1rho relaxation [35] has been reported that provided a possibility of applying the fractional approach to T1rho MR fingerprinting [36,37]. Other, It is possible to apply the fractional approach to the CEST-MRF [38,39] to improve the detection of chemical exchange saturation transfer (CEST) signal due to the influence of T1 relaxation to CEST signal [40,41]. Dictionary size grows exponentially as the number of tissue parameters (i.e the dictionary dimension) is increased which can quickly result in prohibitively large dictionaries that require extensive computational resources to process [42].

    • 7T CEST MRI: A potential imaging tool for the assessment of tumor grade and cell proliferation in breast cancer

      2019, Magnetic Resonance Imaging
      Citation Excerpt :

      Therefore, different methods for Z-spectrum analysis that can separate these effects should be considered [34]. Also, future methodological developments that would enable a description of multi-pool CEST contrast may be potentially useful for quantifying in vivo CEST applications [35]. In addition, it is still challenging to remove overlapping CEST signals from different neighboring exchanging sites.

    View all citing articles on Scopus
    View full text