Towards the complex dependence of MTR_asym on T_1w in amide proton transfer (APT) imaging

Abstract

Amide proton transfer (APT) imaging is a variation of chemical exchange saturation transfer (CEST) MRI which has shown promise in diagnosing tumor, ischemic stroke, multiple sclerosis, and traumatic brain injury etc. Specific quantification of APT effect is crucial for the interpretation of APT contrast in pathologies. Conventionally, magnetization transfer ratio with asymmetric analysis (MTR_asym) has been used to quantify APT effect. However, some studies indicate that MTR_asym is contaminated by water longitudinal relaxation time (T_1w) and thus it is necessary to normalize T_1w in MTR_asym to obtain specific quantification of APT effect. Until now, whether to use MTR_asym or the T_1w normalized MTR_asym is still under debate in the field. In this paper, the influence of T_1w on the quantification of APT was evaluated through theoretical analysis, numerical simulations, and phantom studies for different experimental conditions. Results indicate that there are two types of T_1w effects (T_1w recovery and T_1w-related saturation) which have inverse influences on the steady-state MTR_asym. In situations with no or weak direct water saturation (DS) effect, there is only T_1w recovery effect and MTR_asym linearly depends on T_1w. In contrast, in situations with significant DS effects, the dependence of MTR_asym on T_1w is complex, which is dictated by the competition of these two T_1w effects. Therefore, by choosing appropriate irradiation powers, MTR_asym could be roughly insensitive to T_1w. Moreover, in non-steady-state acquisitions with very short irradiation time, MTR_asym is also roughly insensitive to T_1w. Therefore, for the steady-state APT imaging at high fields or with very low irradiation powers where there are no significant DS effects, it is necessary to normalize T_1w to improve the specificity of MTR_asym. However, on clinical MRI systems (usually low fields or non-steady-state acquisitions), T_1w normalization may not be necessary when appropriate sequence parameters are chosen.

Graphical Abstract

MTR_asym from two creatine samples with pH 6.3 (mimicking amide) with different T_1w shows that it has complex dependencies on T_1w. The steady-state MTR_asym (a) are sensitive to T_1w at relatively lower powers, but are roughly insensitive to T_1w at relatively higher powers. The non-steady-state MTR_asym (dashed line in (b)) are relatively insensitive to T_1w compared with the steady-state MTR_asym with the same powers (solid line in (b)).

INTRODUCTION

Chemical Exchange Saturation Transfer (CEST) is a sensitivity enhancement mechanism that has shown great potentials in imaging molecules in millimolar range (1–3). In CEST imaging, an irradiation RF pulse is applied at the frequency offset of exchangeable protons of solute molecules and the subsequent chemical exchange between those saturated protons and water protons reduces the magnitude of the measured water signal. Because water is significantly more abundant than the solutes, the detection sensitivity to exchanging protons by measuring water signal is magnified. Previously, CEST effects have been observed for a number of endogenous and exogenous molecules (4–12), and have been found to be sensitive to tissue pH (13,14). Amide proton transfer (APT) is an important application of CEST imaging, which detects the chemical exchange between backbone amide protons of proteins/peptides and water protons (14). In the last decade, APT has been applied to diagnose tumors (5,15–18), ischemic stroke (19–22), multiple sclerosis (23), and traumatic brain injury (24,25).

However, CEST is an indirect method to detect solute molecules or pH through measurements of water signals, and thus depends on multiple other tissue parameters including direct water saturation (DS), semi-solid magnetization transfer (MT), and water longitudinal relaxation time (T_1w). Those non-exchange related factors may vary in pathologies, which reduces the specificity of CEST imaging and may lead to misinterpretations. To remove contaminations from these factors, a reference signal that ideally has the same contributions from DS and semi-solid MT effects, but without chemical exchange, is required to compare to the exchange-labeled signal. Conventionally, the difference in the label and reference signals normalized to a control signal with no saturating pulses, termed CEST ratio (CESTR), was used to quantify the CEST effect. The CESTR was also named magnetization transfer ratio with asymmetric analysis (MTR_asym) when the reference signal is obtained from the offset frequency symmetric about the water resonance (3). However, CEST, DS, and non-specific MT effects have mutual interactions, and do not add linearly (26). Thus CESTR cannot fully remove the DS and MT effects (26–28). Recently, Zaiss et al. introduced an alternative analysis of CEST data, which subtracts the reciprocals of the label and reference signals obtained in steady state and normalize water longitudinal relaxation time (T_1w), to address the non-specificities associated with CESTR. This method is termed apparent exchange-dependent relaxation (AREX) (26–28), and its specificity has been previously evaluated through simulations, phantom, and animal studies (26,29,30).

Although AREX is specific, it requires special hardware for long-time RF irradiation as well as measurement of water longitudinal relaxation time (T_1w=1/R_1w) which lengthen the total imaging time. Therefore, CESTR, as a simple and effective metric to remove most of the influence (0^th order effect) from DS and semi-solid MT effects, is still widely used especially in clinical applications (31–35). However, the T_1w normalization in AREX and a previous defined CESTR under weak saturation pulse approximation (3) suggest that CESTR depends on T_1w. This raises a concern whether there is a need to normalize T_1w in CESTR.

Here, the influence of T_1w on CESTR quantification of APT was evaluated through theoretical analysis, numerical simulations, and phantom studies for different experimental conditions. This study will provide insights into the specificity of APT imaging and guide MRI researchers and radiologists to choose appropriate CEST quantification metrics.

THEORY

Steady-state CESTR under an approximation of weak saturation pulse and complete saturation

CESTR is defined by (3),

$$CESTR(\mathrm{\Delta }\omega )=\frac{S_{ref}(\mathrm{\Delta }\omega )-S_{lab}(\mathrm{\Delta }\omega )}{S_0}$$ (1)

where Δω is the RF frequency offset from water resonance frequency. S_lab(Δω), S_ref(Δω), and S₀ are the label, reference, and non-irradiated control signals, respectively. A previous study indicates that CESTR can be described by the following Eq. (2) under an approximation of weak saturation pulse and complete saturation, and also with spin system in steady state (3),

$$CESTR(\mathrm{\Delta }\omega )=\frac{{\text{f}}_s{k}_{sw}}{R_{1w}+{\text{f}}_s{k}_{sw}}$$ (2)

where f_s and k_sw are the solute concentration and exchange rate, respectively. The steady-state acquisition can usually be obtained with RF irradiation time (t_p) > 5T_1w. For slow exchanging pool (f_sk_sw < R_1w), Eq. (2) could be approximated by,

$$CESTR(\mathrm{\Delta }\omega )=\frac{{\text{f}}_s{k}_{sw}}{R_{1w}}$$ (3)

Eq. (3) suggests that T_1w normalization is required in CESTR to obtain specific quantification of exchanging effect. However, under this weak saturation pulse approximate, there is no DS effect, and thus both Eq. (2) and Eq. (3) may be too simple to provide a correct T_1w dependence for in vivo CESTR.

Steady-state CESTR with DS and semi-solid MT effects

Zaiss et al. (26,27) have shown that water, chemical exchange, and semi-solid MT effects acquired in steady state can be described simultaneously by superimposing their rotating frame relaxations (when the exchanging solute concentration is much less than 1),

$$R_{1p}(\mathrm{\Delta }\omega )\approx R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{cest}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m)$$ (4)

where R_1ρ(Δω), R^cest_ex(Δω), and R^MT_ex(Δω) are water longitudinal relaxation, chemical exchange, and semi-solid MT effects in the rotating frame, respectively; f_m is the semi-solid component concentration. R^cest_ex(Δω), R_eff, and R_1ρ(Δω) can be described by the following Eq. (5), Eq. (6), and Eq. (7), respectively,

$$R_{ex}^{cest}(\mathrm{\Delta }\omega )=\frac{f_s{k}_{sw}{\omega }_1^2}{{\omega }_1^2+(R_{2s}+k_{sw})k_{sw}+{(\mathrm{\Delta }\omega -\mathrm{\Delta })}^2{k}_{sw}/(R_{2s}+k_{sw})}$$ (5)

$$R_{\text{e}ff}=R_{1w}{\text{cos}}^2\theta +R_{2w}{\text{sin}}^2\theta$$ (6)

$$R_{1p}(\mathrm{\Delta }\omega )\approx \frac{S_0{R}_{1\text{o}bs}}{S^{ss}(\mathrm{\Delta }\omega )}$$ (7)

with

$${\text{cos}}^2\theta =\frac{\mathrm{\Delta }{\omega }^2}{{\omega }_1^2+\mathrm{\Delta }{\omega }^2};{\text{sin}}^2\theta =\frac{{\omega }_1^2}{{\omega }_1^2+\mathrm{\Delta }{\omega }^2}$$

where ω₁ is the RF irradiation power; R_2w (1/T_2w) and R_2s (1/T_2s) are the transverse relaxation rate of water and solute, respectively; Δ is solute resonance frequency; S^ss(Δω) is the steady-state CEST signal which represents either S_lab(Δω) or S_ref(Δω); R_1obs is the apparent water longitudinal relaxation rate in the presence of semi-solid MT effect, which can be obtained by (R_1w + f_mR_1m)/(1+f_m) in which R_1m is the longitudinal relaxation rate of the semi-solid component (26). Here, R^cest_ex can be looked as the product of f_s, k_sw, and labeling efficiency (27), which can represent pure CEST effect that depends only on solute exchanging parameters and sequence parameters but not non-specific tissue parameters. By substituting R_1ρ(Δω) in Eq. (4) with Eq. (7), and expanding it in powers of R^cest_ex(Δω), we can obtain,

$$\begin{array}{l}{S}^{ss}(\mathrm{\Delta }\omega )\approx \frac{S_0{R}_{1\text{obs}}}{R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m)+R_{ex}^{cest}(\mathrm{\Delta }\omega )}\\ \approx \frac{S_0{R}_{1\text{obs}}}{R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m)}-\frac{S_0{R}_{1\text{obs}}{R}_{ex}^{cest}(\mathrm{\Delta }\omega )}{{(R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m))}^2}+\cdot \cdot \cdot \end{array}$$ (8)

In APT imaging in biological tissues, R^cest_ex is much less than R_eff (Sup. Table S1 shows the calculated R^cest_ex with complete saturation (=f_sk_sw) and R_eff for different experimental conditions using Eq. (5) and Eq. (6), respectively, with parameters mimicking amide and tissue water). Therefore, the first two items of the series in Eq. (8) dominate S^ss. Assuming R^cest_ex(Δω) is zero in the reference signal, we can obtain S_ref in steady state,

$$S_{ref}(\mathrm{\Delta }\omega )\approx \frac{S_0{R}_{1\text{obs}}}{R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m)}$$ (9)

By further substituting Eq. (1) with Eq. (8) and Eq. (9), we can derive CESTR for a more complex model with DS and semi-solid MT effects,

$$\text{C}ESTR(\mathrm{\Delta }\omega )\approx \frac{R_{1\text{obs}}{R}_{ex}^{cest}(\mathrm{\Delta }\omega )}{{(R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{MT}(\mathrm{\Delta }\omega )/(1+f_m))}^2}\approx \frac{1}{R_{1\text{obs}}}{(\frac{S_{ref}}{S_0})}^2{R}_{ex}^{cest}(\mathrm{\Delta }\omega )$$ (10)

From Eq. (8) and Eq. (10), we find that CESTR only removes the 0^th order term, but not higher order terms of the non-exchange related factors, which thus still depends on DS and semi-solid MT effects. Eq. (10) also provides an approximate model for the steady-state CESTR signal which shows the relationship between CESTR and the pure CEST effect quantified by R^cest_ex.

Dependence of the steady-state CESTR with DS effect on R_1w.

To be simple, we ignore the semi-solid MT effect in Eq. (10). Then we substitute Eq (10) with Eq. (6), replace R_1obs with R_1w, and obtain,

$$CESTR(\mathrm{\Delta }\omega )\approx \underset{{\text{T}}_{1w}\text{ recovery}}{\underbrace{\frac{1}{R_{1\text{w}}}}}{(\underset{{\text{T}}_{1w}-\text{related saturation}}{\underbrace{\frac{{\omega }_1^2+\mathrm{\Delta }{\omega }^2}{\frac{R_{2\text{w}}}{{\text{R}}_{1w}}{\omega }_1^2+\mathrm{\Delta }{\omega }^2}}})}^2{R}_{ex}^{cest}(\mathrm{\Delta }\omega )$$ (11)

Eq. (3) suggests that there is a T_1w scaling effect under an approximation of weak saturation pulse. Since there are no DS and semi-solid MT effects in Eq. (3), the CESTR in Eq. (3) should be determined only by the decrease of water signal due to chemical exchange and the recovery of water signal due to T_1w. Thus we name this T_1w effect in Eq. (3) as T_1w recovery effect here. Furthermore, since T_1w recovery exists in all spin systems, it should also present when there are DS and semi-solid MT effects. Therefore, the first item in Eq. (11) should represent the T_1w recovery effect. By comparing Eq. (11) with Eq. (3), we find that except the T_1w recovery effect, there is another T_1w effect which indirectly influences CESTR through the DS effect. Here, we name this T_1w effect as T_1w-related saturation effect. From Eq. (11), we also know that the two T_1w effects have inverse influences on CESTR, which may result in different T_1w dependence as that given by Eq. (3). The two competing T_1w effects suggest that T_1w normalization may not be generally required in CESTR. Eq. (11) also suggests that except R_1w, the DS effect also depends on R_2w and Δω/ω₁.

Dependence of the non-steady-state CESTR on R_1w

The non-steady-state CEST signals (t_p << 5T_1w) with long recovery time (t_rec > 5T_1w, t_rec is the recovery time between the end the acquisition module and the beginning of next RF irradiation pulse) were previously described by (27,36),

$$\frac{S^{\text{nss}}(\mathrm{\Delta }\omega )}{S_0}=(1-\frac{{\text{S}}^{ss}}{{\text{S}}_0})\text{exp}(-R_{1\rho }{t}_{\text{p}})+\frac{{\text{S}}^{ss}}{{\text{S}}_0}$$ (12)

where S^nss is the water signal acquired in the non-steady-state CEST imaging.

In some non-steady-state CEST imaging especially in clinic, both t_p (usually from 200 ms to 1000 ms) and t_rec (~2 s) are less than 5T_1w (31–35). As a result: (1) the control scan will obtain a non-equilibrium signal (S_unsat) which is less than S₀; (2) the initial signal before the RF irradiation (S_i) is not equal to S₀ (37). In this case, Eq. (12) becomes,

$$\frac{S^{\text{nss}}(\mathrm{\Delta }\omega )}{{\text{S}}_{unsat}}=(\frac{{\text{S}}_{\text{i}}}{{\text{S}}_{unsat}}-\frac{{\text{S}}^{ss}}{{\text{S}}_{unsat}})\text{exp}(-R_{1\rho }{t}_{\text{p}})+\frac{{\text{S}}^{ss}}{{\text{S}}_{unsat}}$$ (13)

Eq. (13) can be rewritten as

$$\frac{S^{\text{nss}}(\mathrm{\Delta }\omega )}{{\text{S}}_{unsat}}=((\frac{{\text{S}}_{\text{i}}}{{\text{S}}_{\text{0}}}-\frac{{\text{S}}^{ss}}{{\text{S}}_{\text{0}}})\text{exp}(-R_{1\rho }{t}_{\text{p}})+\frac{{\text{S}}^{ss}}{{\text{S}}_{\text{0}}})\frac{{\text{S}}_{\text{0}}}{{\text{S}}_{unsat}}$$ (14)

When t_p << 1/R_1ρ,

$$\frac{S^{\text{nss}}(\mathrm{\Delta }\omega )}{{\text{S}}_{unsat}}=(\frac{{\text{S}}_{\text{i}}}{{\text{S}}_{\text{0}}}-(\frac{{\text{S}}_{\text{i}}}{{\text{S}}_{\text{0}}}(R_{eff}(\mathrm{\Delta }\omega )+R_{ex}^{\text{MT}}(\mathrm{\Delta }\omega ))-R_{1w}+\frac{{\text{S}}_{\text{i}}}{{\text{S}}_{\text{0}}}{R}_{ex}^{cest}(\mathrm{\Delta }\omega ))t_{\text{p}})\frac{{\text{S}}_{\text{0}}}{{\text{S}}_{unsat}}$$ (15)

By assuming R^cest_ex(Δω) is zero in the reference scan, the non-steady-state CESTR can be derived as,

$$CESTR(\mathrm{\Delta }\omega )\approx \frac{S_i}{S_{unsat}}{R}_{ex}^{cest}(\mathrm{\Delta }\omega )t_{\text{p}}$$ (16)

When t_rec > 5T_1w, S_i = S_unsat = S₀. Then CESTR = R^cest_ex(Δω)t_p which is independent of T_1w. When t_rec < 5T_1w and because t_p << 5T_1w, S_i ≈ S_unsat < S₀. Then, CESTR could be also roughly independent of T_1w.

METHODS

Numerical simulations

Numerical simulations were used to evaluate these two competing T_1w effects and to validate the approximate model given in Eq. (10) and Eq. (11). Two-pool (solute and water) model numerical simulations were performed with a continuous wave (CW) CEST sequence with a series of ω₁ (1 μT, 2 μT, 3 μT, 4 μT, and 5 μT) and T_1w (0.5 s, 1 s, 1.5 s, 2 s, and 2.5 s). The irradiation time is 8 s for steady states and 0.5 s for non-steady states. Table 1 lists the simulation parameters mimicking APT imaging. All CESTR were calculated by using the asymmetric analysis. So in following sections, we use MTR_asym to represent CESTR.

Table 1.

Parameters for the two-pool model numerical simulations with pool concentration (f), exchange rate (k), longitudinal relaxation time (T₁), transverse relaxation time (T₂), and resonance frequency offset for each pool (Δ_r). Water content is set to be 1.

	f	k (s−1)	T1 (s)	T2 (ms)	Δr (ppm)
Solute	0.001	50	1.5	15	-
Water	1	-	0.5, 1, 1.5, 2, 2.5	50	0

(a) To study the T_1w recovery effect in Eq. (10) and Eq. (11) separately, we plotted the steady-state MTR_asym vs. T_1w with Δω set to be 100ω₁ to satisfy the condition of ω₁ << Δω. We also plotted 1/R_1w vs. T_1w in the same figure and scaled it for comparison with the curve of MTR_asym vs. T_1w.

(b) To study the T_1w-related saturation effect in Eq. (10) and Eq. (11) separately, we plotted the steady-state MTR_asym·R_1w vs. T_1w with: (1) Δω set to be 10ω₁, 5ω₁, and 2ω₁ with T_2w of 50 ms, respectively; (2) T_2w set to be 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁ of 5, respectively. The product of MTR_asym and R_1w was used to remove the T_1w recovery effect so that it only shows the T_1w-related saturation effect. (S_ref/S₀)² vs. T_1w was also plotted in the same figure and scaled for comparison with the curve of MTR_asym·R_1w vs. T_1w. (S_ref/S₀)² was obtained through numerical simulations with RF offset symmetric about the water resonance against CEST effects.

(c) To study how the two T_1w effects in Eq. (10) and Eq. (11) influence the steady-state MTR_asym, we plotted the steady-state MTR_asym vs. T_1w with: (1) Δω set to be 10ω₁, 5ω₁, and 2ω₁ with T_2w of 50 ms, respectively; (2) T_2w set to be 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁ of 5, respectively.

(d) To study whether the approximate model of MTR_asym in Eq. (10) is valid, we compared the steady-state MTR_asym with (S_ref/S₀)²R^cest_ex/R_1w for different experimental conditions, in which the steady-state MTR_asym and (S_ref/S₀)² were from simulations, and R^cest_ex was calculated using Eq. (5) with the same parameters as those in the simulation.

(e) To study the dependence of the non-steady-state MTR_asym in Eq. (16) on T_1w, we plotted the non-steady-state MTR_asym vs. T_1w with: (1) Δω set to be 10ω₁, 5ω₁, and 2ω₁ with T_2w of 50 ms, respectively; (2) T_2w set to be 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁ of 5, respectively. t_p was 0.5 s for the non-steady-state acquisition. For the simulation of the non-steady-state acquisition with short recovery time, t_rec was 1.5 s and the Z component of water signal before recovery was set to 0 by assuming a 90° excitation for the readout.

The coupled Bloch equations can be written as $\frac{d\mathbf{M}}{dt}=\mathbf{A}\mathbf{M}+{\mathbf{M}}_0$, where A is a 6 × 6 matrix for the two-pool model. The water and solute pools each has three coupled equations representing their x, y, and z components. All numerical calculations of CEST signals integrated the differential equations through the sequence using the ordinary differential equation solver (ODE45) in MATLAB 2014a (Mathworks, Natick, MA, USA).

Sample preparation and MRI

Two creatine samples served to evaluate the dependence of MTR_asym on T_1w. Creatine was added to phosphate-buffered saline (PBS) solution to reach a concentration of 100 mM, and the pH of the solution was titrated to 6.3 by using NaoH/HCl. The solution was then transferred into two tubes. 0.075 mM and 0.05 mM MnCl₂ were added to the two tubes (samples #1 and #2), respectively, to vary T_1w. At room temperature and with pH of 6.3, creatine is in the slow exchange regime (38,39). The resonance frequency offsets of creatine amines and protein amides are at around 1.9 ppm and 3.5 ppm, respectively. So the Δ of creatine at 4.7 T (380 Hz) is close to that of amide at 3 T (447 Hz). Therefore, experiments on creatine at 4.7 T can be used to mimic amide at clinical 3 T.

All measurements on creatine samples were performed at a Varian 4.7 T MRI system with a 38-mm Doty coil (Doty Scientific Inc. Columbia, SC, USA) for both transmission and reception. CEST measurements were performed by applying a CW RF irradiation before free induction decay (FID) acquisition. An 8-s irradiation pulse was performed for steady-state acquisitions, and a 0.5-s irradiation pulse was performed for non-steady-state acquisitions. TR was 10 s for both the steady-state acquisition and the non-steady-state acquisition. S_lab, S_ref, and S₀ were acquired with RF offsets at 1.9 ppm, −1.9 ppm, and 500 ppm, respectively. MTR_asym was calculated using Eq. (1). T_1w were obtained using an inversion recovery sequence. T_2w were obtained using a multiple echo sequence.

RESULTS

T_1w recovery effect and T_1w-related saturation effect

Fig. 1 shows the simulated steady-state MTR_asym vs. T_1w for the condition of ω₁ << Δω (no DS effect). Note that the curves of MTR_asym vs. T_1w match the curve of 1/R_1w vs. T_1w, indicating that MTR_asym linearly depends on T_1w, which confirms the presence of the T_1w recovery effect. Fig. 2 shows the simulated steady-state MTR_asymR_1w vs. T_1w for a series of Δω/ω₁ (with DS effect) and T_2w. Note that different from Fig. 1, MTR_asymR_1w in Fig. 2 inversely depends on T_1w, suggesting the presence of other T_1w effects. Also note that the curves of MTR_asymR_1w vs. T_1w match the curve of (S_ref/S₀)² vs. T_1w, indicating that MTR_asymR_1w may depend on DS effect regulated by T_1w, which confirms the presence of T_1w-related saturation effect. It was also found that both MTR_asymR_1w and (S_ref/S₀)² values are smaller for lower Δω/ω₁ values (see Fig. 2a-2c) and shorter T_2w values (see Fig. 2d-2i), suggesting that MTR_asymR_1w also depends on DS effect regulated by Δω/ω₁ and T_2w.

FIG. 1.

Steady-state MTR_asym vs. T_1w for ω₁ << Δω (Δω/ω₁=100) with a series of ω₁ (solid lines) as well as 1/R_1w vs. T_1w (dotted line). Note that the lines with different ω₁ are indicated by different colors, which overlap. Also note that the solid lines and the dotted line overlap.

FIG. 2.

Steady-state MTR_asymR_1w vs. T_1w for Δω/ω₁=10, 5, and 2 with T_2w of 50 ms (a-c), as well as for T_2w = 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁=5 (d-i). Solid lines represent the simulated MTR_asymR_1w, and the dotted line represents the simulated (S_ref/S₀)². Note that the lines with different ω₁ are indicated by different colors, which overlap. Also note that the solid lines and the dotted line overlap.

Dependence of the steady-state MTR_asym on T_1w with DS effect.

Fig. 3 shows the simulated steady-state MTR_asym vs. T_1w for a series of Δω/ω₁ and T_2w. Note that the curves of MTR_asym vs. T_1w are relatively flat in Fig. 3b and Fig. 3e-3h, suggesting that the two competing T_1w effects may result in the rough independence of MTR_asym on T_1w by choosing appropriate sequence parameters. In Fig. 3a and 3i, MTR_asym increases with T_1w which is due to that the T_1w recovery effect dominates the T_1w-related saturation effect when Δω/ω₁ is relatively higher or T_2w is relatively longer and thus the DS effect is relatively weaker. In Fig. 3c and 3d, MTR_asym decreases with T_1w which is due to that the T_1w-related saturation effect dominates the T_1w recovery effect when Δω/ω₁ is relatively lower or T_2w is relatively shorter and thus the DS effect is relatively greater. Fig. 4 shows the measured steady-state MTR_asym from two creatine samples with different T_1w. Note that the steady-state MTR_asym increases with T_1w with lower ω₁, but becomes roughly insensitive to T_1w with higher ω₁.

FIG. 3.

Steady-state MTR_asym vs. T_1w for Δω/ω₁=10, 5, and 2 with T_2w of 50 ms (a-c), as well as for T_2w = 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁=5 (d-i). Note that the lines with different ω₁ are indicated by different colors, which overlap.

FIG. 4.

Measured steady-state MTR_asym from two creatine samples with different T_1w. T_1w and T_2w were measured to be (0.9 s and 88 ms) and (1.2 s and 132 ms) for sample #1 and #2, respectively.

An approximate model of MTR_asym

Fig. 5 shows the simulated steady-state MTR_asym and (S_ref/S₀) ²R^cest_ex/R_1w vs. T_1w and ω₁ for a series of Δω/ω₁ values and T_2w. The curves of MTR_asym match the curves of (S_ref/S₀)²R^cest_ex/R_1w very well for all experimental conditions, confirming the approximate model in Eq. (10).

FIG. 5.

Steady-state MTR_asym (red) and (S_ref/S₀)²R^cest_ex/R_1w (blue) vs. T_1w for Δω/ω₁=10, 5, and 2 with T_2w of 50 ms (a-c), as well as for T_2w = 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁=5 (d-i).

Dependence of the non-steady-state MTR_asym on R_1w

Fig. 6 shows the simulated non-steady-state MTR_asym with full recovery (t_p = 0.5 s) vs. T_1w for a series of Δω/ω₁ values and T_2w, respectively. Fig. 7 shows the simulated non-steady-state MTR_asym with short recovery time (t_p = 0.5 s, t_rec = 1.5 s) vs. T_1w for a series of Δω/ω₁ values and T_2w, respectively. Note that the curves of MTR_asym vs. T_1w are relatively flat for all experimental conditions, indicating that MTR_asym is roughly independent of T_1w for the non-steady-state irradiation with very short irradiation time, which confirms Eq. (16). Fig. 8 shows the measured MTR_asym from two creatine samples with different T_1w. Note that although the steady-state MTR_asym increases with T_1w at relatively low ω₁, the non-steady-state MTR_asym acquired with the same ω₁ is roughly insensitive to T_1w.

FIG. 6.

Non-steady-state MTR_asym with full recovery vs. T_1w for Δω/ω₁=10, 5, and 2 with T_2w of 50 ms (a-c), as well as for T_2w = 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁=5 (d-i). Note that the lines with different ω₁ are indicated by different colors, which overlap.

FIG. 7.

Non-steady-state MTR_asym with short recovery time vs. T_1w for Δω/ω₁=10, 5, and 2 with T_2w of 50 ms (a-c), as well as for T_2w = 10 ms, 30 ms, 50 ms, 70 ms, 100 ms, and 150 ms with Δω/ω₁=5 (d-i). Note that the lines with different ω₁ are indicated by different colors, which overlap.

FIG. 8.

Measured steady-state (solid lines) and non-steady-state (dashed lines) MTR_asym from two creatine samples with different T_1w. T_1w and T_2w were measured to be (0.9 s and 88 ms) and (1.2 s and 132 ms) for sample #1 and #2, respectively.

DISCUSSION

Our study suggests that there are two inverse T_1w effects (T_1w recovery effect and T_1w-related saturation effect) for the steady-state MTR_asym. The competition of the two T_1w effects results in the complex dependence of MTR_asym on T_1w, which is different from that given by Eq. (2) or Eq. (3) under weak saturation pulse approximation. Since T_1w-related saturation effect depends on ω₁, MTR_asym could be adjusted to be roughly insensitive to T_1w by choosing appropriate ω₁. In addition, we show that the non-steady-state MTR_asym acquired with very short irradiation time is also roughly insensitive to T_1w.

In addition to Fig. 1, Fig. 3a shows positive dependence of the steady-state MTR_asym on T_1w, which suggests that the T_1w recovery effect may dominate T_1w-related saturation effect when there are no significant DS effects at high fields or with low irradiation powers. Therefore, in these situations, it is necessary to use T_1w normalization to increase the specificity of MTR_asym. Actually, previous studies at high fields have indicated that T_1w normalization is necessary for obtaining specific MTR_asym in APT imaging (26,29,30). In contrast, Fig. 3b shows roughly flat curves, which suggests that the two T_1w effects are comparable at relatively low fields. For amides at 3.5 ppm at 3 T, ω₁ of 2 μT can satisfy the condition of Δω/ω₁=5 used in Fig. 3b and thus can make the MTR_asym roughly insensitive to T_1w. In previous APT imaging at 3 T (40), ω₁ from 1 μT–3 μT were traditionally used. Therefore, it may not be necessary to normalize T_1w to remove the influence from T_1w in some of these previous studies on clinical MRI systems.

Although AREX is equal to the pure CEST effect quantified by R^cest_ex (26,29,36), the relationship between MTR_asym and the pure CEST effect has not been evaluated. Eq. (10) provides an approximate model for MTR_asym which provides insight into its contrast sources. Eq. (10) also suggests that MTR_asymR_1w/(S_ref/S₀)² could be a simple metric to remove the influence from T_1w and to obtain relatively purer CEST effects. Simulations in Sup. Fig. S1 show that MTR_asymR_1w/(S_ref/S₀)² is independent of T_1w and is roughly equal to R^cest_ex except for very strong DS effects. Please note that although we use a two-pool model simulation (Fig. 5) to evaluate Eq. (10), it can be extended to more complex tissue models by inspecting the definition of S_ref. Simulations in Sup. Fig. S2 confirm Eq. (10) in a three-pool (solute, semi-solid, and water) model. In biological tissues, T_1w also influences R^MT_ex and thus affects both S_ref and MTR_asym according to Eq. (9) and Eq. (10). Studies on the influence of T_1w on MTR_asym through the semi-solid MT effect are also necessary. However, although the analytical equation for R^MT_ex has been given previously (26), its dependence on T_1w is complex. Here, we ignored the semi-solid MT effect in the theoretical analysis, but provided the three-pool model simulated MTR_asymR_1w and MTR_asym vs. T_1w in Sup. Fig. S3 and Fig. S4, respectively. Different from the two-pool model simulated MTR_asym for higher Δω/ω₁ (Fig. 3a) or longer T_2w (Fig. 3i) which depends on T_1w, the add of semi-solid MT effect makes MTR_asym in these two conditions relatively insensitive to T_1w. Previously, an empirical MTR_asym equation for a two-pool model with DS effect has been also provided (41). Sup. Fig. S5 compares MTR_asym in Eq. (10), the empirical MTR_asym equation, and the numerical simulated MTR_asym. It was found that the empirical MTR_asym equation matches the numerical simulated MTR_asym better than the MTR_asym in Eq. (10), suggesting that the empirical MTR_asym equation is more accurate than the MTR_asym in Eq. (10). However, the empirical MTR_asym equation is very complex and is not as straightforward as the MTR_asym in Eq. (10) to study the dependence of MTR_asym on T_1w and DS effect.

In addition to Eq. (1), MTR_asym was also defined to be (S_ref(Δω)-S_lab(Δω))/S_ref(Δω) (42,43) which can be looked as the product of (S_ref(Δω)-S_lab(Δω))/S₀(Δω) and S₀(Δω)/S_ref(Δω). Here we name this definition as MTR^’_asym. By substituting this definition with Eq. (10), we can obtain,

$$\begin{array}{l}MT{R^{\prime }}_{asym}(\mathrm{\Delta }\omega )\approx {\text{MTR}}_{\text{asym}}\frac{S_0}{S_{ref}}\approx \frac{1}{R_{1\text{w}}}\frac{S_{ref}}{S_0}{R}_{ex}^{cest}(\mathrm{\Delta }\omega )\\ \begin{array}{ccc}& & \end{array}\approx \frac{1}{R_{1\text{w}}}\frac{{\omega }_1^2+\mathrm{\Delta }{\omega }^2}{\frac{R_{2\text{w}}}{{\text{R}}_{1w}}{\omega }_1^2+\mathrm{\Delta }{\omega }^2}{R}_{ex}^{cest}(\mathrm{\Delta }\omega )\end{array}$$ (17)

Eq. (17) indicates that MTR^’_asym also has two competing T_1w effects, but the influence from the T_1w-related saturation effect on MTR^’_asym is relatively weak compared with its influence on MTR_asym. Therefore, it should require higher ω₁, and thus greater DS effect, for MTR^’_asym to be roughly insensitive to T_1w. Sup. Fig. S6 and Fig. S7 show the simulated MTR^’_asymR_1w and MTR^’_asym vs. T_1w, respectively, which confirms our expectation. In addition, our analysis is based on CW RF irradiation. For pulsed-RF irradiation, short RF irradiation pulses may also increase the DS effect, which may enhance the T_1w-related saturation effect.

Heo et al. (44) have also studied the dependence of CESTR on T_1w for different ω₁ through numerical simulations, and found similar complex dependences: the CESTR at 3.5 ppm increases with T_1w under lower ω₁, but is roughly insensitive to T_1w or even decreases with T_1w under relatively higher ω₁. However, this study did not give an explanation for these complex dependences. Our results about the two competing T_1w effects can explain these complex dependences and guide researchers and radiologists to choose appropriate quantification metrics. Previously, Jokivarsi et al. (45) showed a strong correlation between MTR_asym and pH in ischemic stroke. However, Sun et al. (45) showed that the correlation between MTR_asym/T_1w and pH is stronger than that between MTR_asym and pH in ischemic stroke. Based on our study, choosing an appropriate CEST quantification metric should consider the relative contributions of the two T_1w effects for specific experimental conditions.

Fig. 6 and Fig. 8 suggest that the non-steady-state MTR_asym with very short RF irradiation time and long recovery time is roughly insensitive to T_1w effect. This may be due to the different dynamics of chemical exchange, T_1w recovery, and T_1w-related saturation effects. Based on the Bloch equations with exchange terms (3), the water signal depends on three terms including the chemical exchange term (M_zwk_ws, where M_zw is the water Z magnetization and k_ws is the rate of exchange from water to solute protons, and in which we ignore the small back exchange), T_1w recovery term (R_1w(M_0w – M_zw), where M_0w is the equilibrium water magnetization), and water saturation term (ω₁M_yw, where M_yw is the water Y magnetization). In a short time after the irradiation, both M_zw – M_0w and M_yw are very small, but M_zw is large. Thus chemical exchange dominates other two T_1w effects, and as a result MTR_asym is insensitive to T_1w. Fig. 7 suggests that the non-steady-state MTR_asym with very short RF irradiation time and short recovery time is also roughly insensitive to T_1w effect. This may be due to that the dependences of the labeled signal, the reference signal, and the non-equilibrium control signal on T_1w are roughly the same, and thus could be cancelled. However, when equilibrium control signal is used, the non-steady-state MTR_asym with very short RF irradiation time and short recovery time is still influenced by T_1w (Sup. Fig. S8).

Although steady-state MTR_asym can be adjusted to be roughly insensitive to T_1w, the direct subtraction of the label and reference signals cannot remove the higher order effect of the influence from the semi-solid MT effect. In situations, such as tumor, where there is significant change of semi-solid MT effect (46), MTR_asym may be still contaminated by the semi-solid MT effect. Variation of T_1w is usually associated with multiple physiological parameters such as water content. A recent paper indicates that the increase of T_1w could be mostly eliminated by the increase of water content in tumors (47). This study is important for interpretation of contrast mechanism in many CEST applications. In this paper, we ignore this dependence and only studied the specificity of MTR_asym to solute concentration from a perspective of theory.

CONCLUSION

We show that MTR_asym has different dependences on T_1w at high fields, low fields, and with steady-state or non-steady-state acquisitions. For some previous studies on clinical MRI systems with appropriate sequence parameters, the steady-state MTR_asym may be roughly insensitive to T_1w; For non-steady state acquisitions with very short RF irradiation time, MTR_asym is also roughly insensitive to T_1w.

Abbreviations used

CEST

chemical exchange saturation transfer

APT

amide proton transfer

MT

magnetization transfer

MTR

magnetization transfer ratio

MTR_asym

magnetization transfer ratio with asymmetric analysis

AREX

apparent exchange-dependent relaxation

DS

direct water saturation

R_1ρ

water longitudinal relaxation rate in the rotating frame

R^cestex

chemical exchange effect in the rotating frame

R^MTex

semi-solid magnetization transfer effect in the rotating frame