Abstract
Chemical exchange saturation transfer (CEST) is one of the contrast mechanisms in magnetic resonance imaging (MRI) and has been used to detect dilute proteins through the interaction between bulk water and labile solute protons. Amide proton transfer (APT) MRI has been developed for imaging diseases such as acute stroke. Moreover, various CEST agents have been explored to enhance the CEST effect. The contrast mechanism of CEST or APT MRI, however, is complex and depends not only on the concentration of amide protons or CEST agents and exchange properties, but also varies with imaging parameters such as radiofrequency (RF) power and magnetic field strength. When there are multiple exchangeable pools within a single CEST system, the contrast mechanism of CEST becomes even more complex. Numerical simulations are useful and effective for analyzing the complex contrast mechanism of CEST and for investigating the optimal imaging parameter values. In this chapter, we present the basics of CEST or APT MRI and a simple and fast numerical method for solving the time-dependent Bloch-McConnell equations for analyzing the behavior of magnetization and/or contrast mechanism in CEST or APT MRI. We also present a method for analyzing the behavior of magnetization in spin-locking CEST MRI.
Keywords
- Bloch-McConnell equations
- numerical solution
- chemical exchange saturation transfer (CEST) MRI
- amide proton transfer (APT) MRI
- spin-locking
1. Introduction
Chemical exchange saturation transfer (CEST) is one of the contrast mechanisms in magnetic resonance imaging (MRI) [1] and has been increasingly used to detect dilute proteins through the interaction between bulk water protons and labile solute protons [2, 3, 4]. Amide proton transfer (APT) MRI has been developed for imaging diseases such as acute stroke and cancer, and is now under intensive evaluation for clinical translation [5, 6]. APT MRI is a particular type of CEST MRI that specifically probes labile amide protons of endogenous mobile proteins and peptides in tissue [5, 6]. In addition to APT MRI [5, 6], useful CEST MRI contrast for clinical imaging can be generated from amine protons [7], hydroxyl protons [8], glycosaminoglycans [9], and glutamate [10], as well as from changes in creatine and lactate concentrations [11]. Glucose and iopamidol have been used as exogenous CEST agents that have been administered to patients [12, 13]. Moreover, various CEST agents have been energetically developed to detect the parameters that reflect tissue molecular environment such as hydrogen ion exponent (pH) and/or to enhance the CEST effect [14].
In CEST or APT MRI, the exchangeable proton spins are saturated, and the saturation is transferred upon chemical exchange to the bulk water pool [1, 15]. As a result, a large contrast enhancement in bulk water can be achieved. The contrast mechanism of CEST or APT MRI, however, is complex and depends not only on the concentration of amide protons or CEST agents, relaxation, and exchange properties but also varies with imaging parameters such as radiofrequency (RF) power and magnetic field strength [15]. When there are multiple exchangeable pools within a single CEST system, the contrast mechanism of CEST becomes all the more complex [16]. Numerical simulations are useful and effective for analyzing the complex CEST contrast mechanism and for investigating the optimal imaging parameter values [17, 18]. In order to perform extensive numerical simulations for CEST or APT MRI, it requires the development of a simple and fast numerical method for obtaining the solutions to the time-dependent Bloch-McConnell equations.
In this chapter, we present the basics of CEST or APT MRI and a simple and fast numerical method for solving the time-dependent Bloch-McConnell equations for analyzing the behavior of magnetization and/or contrast mechanism in CEST or APT MRI. We also present it in SL CEST MRI.
2. Bloch-McConnell equations in the presence of CEST
2.1. Two-pool chemical exchange model
A two-pool chemical exchange model is illustrated in Figure 1 . A and B in Figure 1 represent the pools of bulk water protons and labile solute protons, respectively. The time-dependent Bloch-McConnell equations for the two-pool chemical exchange model in CEST or APT MRI are expressed as [17, 18].
where superscripts a and b show the parameters in pool A and pool B, respectively. For example,
The differential equations given by Eq. (1) can be combined into one vector equation (homogeneous linear differential equation) [18]:
where
and
For simplicity, we assume that the RF pulse is applied along the x-axis of the rotating frame, that is,
where
In the case of
where
and
where
The solution of Eq. (2) with
where
It should be noted that mass balance imposes the following relationship between the exchange rates (
and
2.2. Three-pool chemical exchange model
Figure 3
illustrates a three-pool chemical exchange model in which pool a represents the bulk water pool. In this case,
and
respectively.
The solutions of other multi-pool chemical exchange models such as an hour-pool chemical exchange model are described in Ref. [20].
2.3. Calculation of Z-spectrum, MTRasym, and PTR
The CEST effect has usually been analyzed using the so-called Z-spectrum [18]. The Z-spectrum is given by the following equation:
where
The magnetization transfer asymmetry (MTRasym) analysis has been performed using the following equation [18]:
Instead of MTRasym, the following equation for proton transfer ratio (PTR) has also been used for analyzing the CEST effect [18]:
where
Figure 4(a)
shows Z-spectra as a function of offset frequency (Δ
In the above simulations, we assumed that
The peaks at 0 Hz (0 ppm) and 1192.8 Hz (4 ppm) in
Figure 4
derived from pool A and pool B, respectively. As shown in
Figure 4(a)
and
Figure 4(b)
, Z-spectra changed largely depending on the saturation time and
Figure 5
shows cases for the three-pool chemical exchange model (
Figure 3
) consisting of bulk water (pool A) and two labile proton pools (pool B and pool C). In these cases, we assumed that
Figure 5(a)
shows Z-spectra as a function of Δ
Figure 6(a)
shows the MTRasym values given by Eq. (19) as a function of
Figure 7(a)
shows the PTR values given by Eq. (20) as a function of
In this study, we presented a simple equation for solving the time-dependent Bloch-McConnell equations, in which our previous method [18] and the approach presented by Koss et al. [19] were combined. Our method can be easily expanded to multi-pool chemical exchange models by modifying the matrix
As previously described, the so-called Z-spectrum has usually been used to analyze the CEST effect [18]. The Z-spectrum is obtained by plotting the z magnetization component of bulk water protons (
2.4. Calculation of R
1ρ
and R
2ρ
The longitudinal relaxation rate in the rotating frame (
The transverse relaxation rate in the rotating frame (
Figure 8
shows the common logarithm of
Figure 9
shows the common logarithm of
As described above,
As shown in
Figure 8
,
3. Spin-locking CEST MRI
3.1. Principle of spin-locking
Longitudinal relaxation time in the rotating frame (
As pointed out by Jin et al. [27], the SL approach is useful for improving the signal-to-noise ratio (SNR) in CEST MRI. Furthermore, Kogan et al. [28] demonstrated that a combination of the CEST and SL approaches is useful for detecting proton exchange in the slow-to intermediate-exchange regimes.
As earlier described, the Bloch-McConnell equations for the two-pool chemical exchange model ( Figure 1 ) in the rotating frame with the same frequency as that of the RF-pulse irradiation is given by Eq. (2) [18, 29]. The solution of Eq. (2) can be given by [18]
Figure 10
illustrates the image of the pulse sequence with SL. We assume that the SL pulse (frequency:
where
The
Thus, the magnetization vector after flipping back to the z-axis [
Note that Ω and
where
3.2. Calculation of T
1ρ
where
The approximate solution for
where
Figure 11
shows an example of the three-dimensional plots of the magnetization vector in pool A in the two-pool chemical exchange model (
Figure 1
).
Figure 11(a)
and
11(b)
show cases without and with SL, respectively. In these cases, the relaxation time constants were assumed to be
When
In this study, we developed a simple and fast method for calculating the magnetization vector in SL CEST MRI, in which a simple matrix equation was derived for solving the time-dependent Bloch-McConnell equations in SL MRI [Eq. (25)] and the
As previously described, when
Although we treated the two-pool chemical exchange model (
Figure 1
) for analyzing
4. Correction of B0 and B1
As previously described, the CEST effect has usually been analyzed using MTRasym [Eq. (19)] or PTR [Eq. (20)]. However, these parameters are susceptible to the B0 inhomogeneity of the static magnetic field. When there exists the B0 inhomogeneity, the spillover effect is no longer symmetric. Furthermore, the B1 inhomogeneity of the RF pulse may also cause spatial variation in labeling efficiency and spillover factor [35]. Apart from the efforts in improving magnetic field inhomogeneities using hardware-based methods, such as parallel transmit technologies [36], post-processing algorithms have been developed for field inhomogeneity correction [37, 38].
Kim et al. [37] showed that direct water saturation imaging allows measurement of the absolute water frequency in each voxel, allowing proper centering of Z-spectra on a voxel-by-voxel basis independent of spatial
A B1-correction of CEST contrasts is crucial for the evaluation of data obtained in clinical studies at high field strengths with strong B1-inhomogeneities. To correct for the B1 inhomogeneity, a B1 map is acquired for correction of Z-spectra using either a calibration [39] or an interpolation approach [40]. Singh et al. [39] developed an approach for
The comprehensive methods like simultaneous mapping of B0 and B1 fields [35, 41], and model-based correction algorithm, [42] have also been developed to improve the accuracy of MTRasym or PTR.
Acknowledgments
This work was supported, in part, by a Grant-in-Aid for Challenging Exploratory Research (Grant No. 25670532) from the Japan Society for the Promotion of Science.
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