Increased CEST specificity for amide and fast exchanging amine protons using exchange-dependent relaxation rate

Abstract

Chemical exchange saturation transfer (CEST) imaging of amides at 3.5 ppm and fast exchanging amines at 3 ppm provides a unique means to enhance the sensitivity for detecting e.g., proteins/peptides and neurotransmitters, respectively, and hence can provide important information on molecular composition. However, despite the high sensitivity compared to conventional magnetic resonance spectroscopy (MRS), CEST in practice often has relatively poor specificity. For example, CEST signals are typically influenced by several confounding effects including direct water saturation (DS), semi-solid non-specific magnetization transfer (MT), the influence of water relaxation times (T_1w) and nearby overlapping CEST signals. Although several editing techniques have been developed to increase the specificity by removing DS, semi-solid MT, and T_1w influences, it is still challenging to remove overlapping CEST signals from different exchanging sites. For instance, the amide proton transfer (APT) signal could be contaminated by CEST effects from fast exchanging amines at 3 ppm and intermediate exchanging amines at 2 ppm. The current work applies an exchange-dependent relaxation rate (R_ex) to address this problem. Simulations demonstrate that: (1) slowly exchanging amides and fast exchanging amines have distinct dependences on irradiation powers; and (2) R_ex serves as a resonance-frequency high-pass filter to selectively reduce CEST signals with resonance frequencies closer to water. These characteristics of R_ex provide a means to isolate the APT signal from amines. In addition, previous studies have shown that CEST signals from fast exchanging amines have no distinct features around their resonance frequencies. However, R_ex gives Lorentzian lineshapes centered at their resonance frequencies for fast exchanging amines and thus can significantly increase the specificity of CEST imaging for amides and fast exchanging amines.

Graphical abstract

We applied an exchange-dependent relaxation rate R_ex to enhance CEST specificity for imaging amide and fast exchanging amine protons. Results show that R_ex can correct the shift of CEST peaks in the CEST imaging of fast exchanging amines, and the subtraction of two R_ex with a low and a high power (ΔR_ex) can successfully remove influences from nearby CEST signals in APT imaging.

INTRODUCTION

Chemical exchange saturation transfer (CEST) is a MRI contrast mechanism for indirectly detecting low-concentration solute molecules with enhanced sensitivity by saturating the solute protons and measuring subsequent changes in the water signal (1). Previously, CEST has been used to detect various endogenous metabolites and macromolecules, such as proteins/peptides (2), creatine (3–6), glutamate (7–12), glucose (13–16), myo-inositol (17), glycogen (18), glycosaminoglycan (19), and lactate (20). Some CEST effects are also sensitive to proton chemical exchange rates and pH (2,21,22). Amide proton transfer (APT) is one widely used form of CEST effect arising from protein backbone amides which resonate at 3.5 ppm from water, and has been used in a range of applications including studies of solid tumors (23–27), ischemic stroke (28–31), and multiple sclerosis (32). Recently, CEST imaging of fast exchanging amines has also been reported. This CEST effect is centered at around 3 ppm from the water resonance which may originate from glutamate amine (7,33) and protein lysine amine (34,35) protons, and which has potential applications in neurological diseases including Alzheimer’s disease (8,9), Huntington’s disease (10), epilepsy (11), psychosis spectrum (36), and dopamine deficiency (12).

However, although CEST significantly increases the sensitivity for detecting metabolites compared to magnetic resonance spectroscopy (MRS), its specificity in practice is relatively poor: first, CEST can be diminished by non-specific background effects including direct water saturation (DS) and semi-solid magnetization transfer (MT) effects; second, CEST signals may depend on longitudinal relaxation time constant of water (T_1w); third, CEST signals from different molecular species overlap. These non-specific factors often vary in pathological tissues, and thus reduce the specificity of CEST for imaging molecular composition. The development of methods to enhance the specificity of CEST imaging is thus important for practical applications.

In order to identify the effect of exchange at a specific frequency, CEST imaging usually acquires a Z-spectrum by employing RF irradiation pulses over a certain range of frequencies, and the normalized water signals are then analyzed as a function of irradiation frequency (37). Previously, several approaches have been developed to process Z-spectra to isolate the CEST effects from other non-specific signals. For example, an asymmetric analysis (MTR_asym) of the Z-spectrum has been used to remove non-specific background signals by assuming that they are symmetric about water. However, in biological tissues, the semi-solid MT is asymmetric, and there are also upfield, relayed nuclear Overhauser enhancement (rNOE) effects (38). Therefore, MTR_asym does not accurately report specific information on composition, so to avoid some of these confounding factors, other approaches such as, an extrapolated semi-solid MT reference (EMR) approach (39–41), a Lorentzian difference (LD) analysis (42,43), and a three-point method (21,44) etc. have been developed. To further increase the specificity of CEST metrics, an inverse subtraction method that takes account of variations in T_1w, named apparent exchange-dependent relaxation (AREX), was also developed (45–47). Distinct from conventional subtractions of reference and label signals, which can remove only some non-specific background signals, this inverse subtraction can remove a broader range of interactions between CEST and background signals (45).

However, despite these improvements, it is still challenging to remove overlapping CEST signals from nearby exchanging sites. In APT imaging, which is usually performed at relatively low irradiation powers (e.g. 1 μT), nearby intermediate-exchanging amines at 2 ppm may contribute to CEST effects at 3.5 ppm. In addition, our previous study (48) showed that the contributions of fast exchanging amines to CEST signals at 3 ppm are significant even at low irradiation powers, which affect a broad spectral region that overlaps with the APT spectrum centered around 3.5 ppm. Although a multiple-pool Lorentzian fit may potentially separate such overlapping signals (49–53), our study (48) also indicated that fast exchanging amines do not produce Lorentzian lineshapes in CEST spectra, which induces errors to spectral fittings. In CEST imaging of fast exchanging amines, which is usually performed at relatively high irradiation powers (e.g. > 3 μT), the CEST peak shifts, which makes it difficult to identify specific CEST effects (7,54).

In this paper, we apply an exchange-dependent relaxation rate (R_ex) for quantifying CEST effects to overcome some of these limitations. R_ex was first introduced by Trott and Palmer (55), and later Jin et al. (56) showed that R_ex can be obtained from CEST Z-spectra in simple model (solute and water) phantoms. More recently, Zaiss et al. (45–47) defined a slightly different R_ex and showed that this R_ex can be obtained from AREX and can be applied in more complex model (solute, semi-solid component, and water) systems and in vivo. Note that these two definitions of R_ex can be exchangeable with a factor (square of irradiation power/square of irradiation frequency offset). In the rest of this article, we name R_ex defined by Zaiss et al. as R′_ex to avoid any confusion. Since AREX is more suitable to process in vivo CEST data, we obtain R_ex from the AREX metric by accounting for the irradiation power. The R_ex reduces the influences of overlapping CEST signals for APT imaging and provides Lorentzian lineshapes centered at their resonance frequencies (56) for fast exchanging amines, and thus can significantly enhances the CEST detection specificity compared with several previous quantification methods (21,38–40,42–44).

METHODS

The magnetization transfer ratio (MTR) is here defined as the difference between a labelled signal (S_lab(Δω)) and a reference signal (S_ref(Δω)) normalized by a control signal (S₀) (37),

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

where Δω is the RF frequency offset from the water resonance frequency.

The metric AREX was defined as (47),

$$\mathit{AREX}(\mathrm{\Delta }\omega )=(\frac{S_0}{S_{\mathit{lab}}(\mathrm{\Delta }\omega )}-\frac{S_0}{S_{\mathit{ref}}(\mathrm{\Delta }\omega )})R_{1\mathit{obs}}(1+f_{\mathrm{m}})=\frac{R_{\text{ex}}^{\prime }(\mathrm{\Delta }\omega )}{{cos}^2\theta }$$ (2)

where

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

R_1obs is the apparent water longitudinal relaxation rate, f_m is the semi-solid component concentration, and ω₁ is the irradiation power.

R′_ex(Δω) for fast exchanging pools can be described by (57),

$$R_{\text{ex}}^{\prime }(\mathrm{\Delta }\omega )\approx f_s{k}_{sw}\frac{\delta {\omega }_{\mathrm{s}}^2}{\underset{a-\mathit{peak}}{\underbrace{{\omega }_1^2+\mathrm{\Delta }{\omega }^2}}}\frac{{\omega }_1^2}{{\omega }_1^2+(R_{2s}+k_{sw})k_{sw}+{(\mathrm{\Delta }\omega -\delta {\omega }_{\mathrm{s}})}^2{k}_{sw}/(R_{2s}+k_{sw})}$$ (3)

where f_s is the solute concentration, k_sw is the exchange rate between solute and water protons, δω_s is the difference between the water and solute resonance frequencies, and R_2s is the solute transverse relaxation rate. The ‘a-peak’ is close to 1 when the irradiation pulse is near the solute resonance frequency, and thus it has weak influence on CEST signals with narrow peaks which could be from slow exchanging pools (e.g. amide) and intermediate exchanging pools (e.g. amine at 2 ppm) at low ω₁. For this reason, the slow and intermediate exchanging pools, that have been described by following Eq. (4), could be also roughly described by Eq. (3).

$$R_{\text{ex}}^{\prime }(\mathrm{\Delta }\omega )\approx f_s{k}_{sw}\frac{{\omega }_1^2}{{\omega }_1^2+(R_{2s}+k_{sw})k_{sw}+{(\mathrm{\Delta }\omega -\delta {\omega }_{\mathrm{s}})}^2{k}_{sw}/(R_{2s}+k_{sw})}.$$ (4)

Note that Eq. (4) is a Lorentzian function, whereas Eq. (3) is not.

Here, we normalize AREX by the irradiation power expressed as the square of tan θ, where tan²θ = ω₁²/Δω².

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

Eq. (5) shows that after normalization by the square of tangent theta, R_ex can be obtained from AREX. CEST lineshapes in Eq. (5) are Lorentzian for both slow and fast exchanging regimes. Specifically, for slow exchanging amide pools for which k_sw (e.g. 30 s⁻¹ (2)) is much less than typical ω₁ (e.g. 1 μT (44,48,52,58,59)), R_ex inversely depends on ω₁² and is expected to approach 0 at high ω₁; by contrast, for fast exchanging pools for which k_sw (e.g. 5000 s⁻¹ (7,33–35)) is much greater than ω₁ (e.g. 3.6 μT (7)), R_ex is approximately independent of ω₁². This is different from AREX which gradually increases at higher ω₁ for slow exchanging pools, and is proportional to ω₁² for fast exchanging pools. These characteristics of R_ex provide an opportunity to isolate slow exchanging amide protons from fast exchanging amine signals. The subtraction of R_ex acquired at a high ω₁ from that at a low ω₁ yields.

$$\mathrm{\Delta }{R}_{ex}(\mathrm{\Delta }\omega )=R_{ex}{(\mathrm{\Delta }\omega )|}_{\mathit{low}}-R_{ex}{(\mathrm{\Delta }\omega )|}_{\mathit{high}}$$ (6)

The contributions from fast exchanging pools are relatively independent of irradiation powers, and hence are removed in the subtraction. Therefore, ΔR_ex provides a means to detect slow exchanging pools selectively. In addition, both R_ex and ΔR_ex are proportional to δω_s², which serves as a resonance-frequency high-pass filter to reduce the influences of other CEST signals with resonance frequency closer to water. This in turn enhances the detection of APT at the higher frequency offset 3.5 ppm. Because MTR, AREX, R_ex and ΔR_ex were obtained by several ways including simulations and fitting simulated or measured Z-spectra, different subscripts were used to distinguish the obtaining methods.

Numerical simulations

Two types of numerical simulations were performed. First, in order to study the different dependences on ω₁ and Δω of slow and fast exchanging pools, simulations of two-pool (amide and water or fast exchanging amine and water) models and one-pool (water) model were performed. The two-pool model simulations were used to create labelled signals, and the one-pool model simulations were used to create reference signals for further quantification. The corresponding metrics are named MTR_simu, AREX_simu, and R_{ex_simu} respectively. Second, to mimic realistic tissues, simulations were performed of a six-pool (amide, intermediate and fast exchanging amines, water, rNOE, and semi-solid component) model and another two-pool (semi-solid component and water) model. The six-pool model simulations were used to create labelled signals, and the two-pool (semi-solid component and water) model simulations were used to create simulated reference signals. Fitted reference signals were also obtained from the following fitting approaches on the six-pool model simulated Z-spectra. Comparisons between the fitted reference signals and the simulated reference signals were performed to evaluate the fitting accuracy. The sequence parameters for the simulations are the same as those used in MR experiments in vivo (see below), and the tissue parameters are tabulated in Table 1. R_1obs was obtained by using Eq. (7) according to Ref (47),

Table 1.

Parameters for the multiple 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 (δω). Water content is set to be 1.

	water	amide	intermediate exchanging amine	fast exchanging amine	NOE(−3.5)	Semi-solid
f	1	0.001,0.0015, 0.002	0.0005	0.0025, 0.005, 0.0075	0.005	0.06,0.09, 0.12
K (s−1)	-	30, 50, 70	500	3000, 5000, 7000	25	15, 25, 35
T1 (s)	1, 1.5, 2	1.5	1.5	1.5	1.5	1.5
T2 (ms)	40, 60, 80	2	15	15	1	0.015
δω (ppm)	0	3.5	2	3	−3.5	−2.3a

^aRef (68)

$$R_{1\mathit{obs}}\approx (R_{1w}+f_m{R}_{1m})/(1+f_m)$$ (7)

where R_1w=1/T_1w and R_1m is the semi-solid component longitudinal relaxation rate.

The coupled Bloch equations can be written as $\frac{d\mathbf{M}}{dt}=\mathbf{AM}+{\mathbf{M}}_0$, where A is a matrix for the corresponding model. The components of the water and solute magnetizations are each described by three coupled equations. The semi-solid pool has a single coupled equation representing the z component, with a Lorentzian absorption lineshape (49). All numerical calculations of the CEST signals were obtained by integrating the differential equations through the sequence using the ordinary differential equation solver (ODE45) in MATLAB 2013b (Mathworks, Natick, MA, USA).

Animal preparation

All animal experiments were approved by the Institutional Animal Care and Usage Committee of Vanderbilt University. Five healthy rats were included in this study. All rats were immobilized and anesthetized with a 2%/98% isoflurane/oxygen mixture during data acquisition. Respiration was monitored to be stable, and a constant rectal temperature of 37°C was maintained throughout the experiments using a warm-air feedback system (SA Instruments, Stony Brook, NY, USA).

MRI

All measurements were performed using a Varian DirectDrive^™ horizontal 9.4T magnet with a 38-mm Litz RF coil (Doty Scientific Inc. Columbia, SC, USA). CEST measurements were performed by applying a continuous wave (CW) irradiation with irradiation duration of 5 s and ω₁ of 1 μT and 3.6 μT before acquisition. Since AREX can only process steady-state CEST signals (45), the 5 s irradiation is performed to ensure that the spin system goes to steady state. Z-spectra with ω₁ of 1 μT were acquired with Δω from −4000 Hz to −2500 Hz with a step size of 500 Hz (−10 ppm to −6.25 ppm with a step size of 1.25 ppm at 9.4 T), −2000 Hz to 2000 Hz with a step size of 50 Hz (−5 ppm to 5 ppm with a step size of 0.125 ppm at 9.4 T), and 2500 Hz to 4000 Hz with a step size of 500 Hz (6.25 ppm to 10 ppm with a step size of 1.25 ppm at 9.4 T). Z-spectra with ω₁ of 3.6 μT were acquired with Δω from −6500 Hz to −3500 Hz with a step size of 500 Hz (−16.25 ppm to −8.75 ppm with a step size of 1.25 ppm at 9.4 T), −2000 Hz to 2000 Hz with steps of 50 Hz (−5 ppm to 5 ppm with a step size of 0.125 at 9.4 T), and 3500 Hz to 6500 Hz with a step size of 500 Hz (8.75 ppm to 16.25 ppm with a step size of 1.25 at 9.4 T). Control images were acquired with Δω of 100,000 Hz (250 ppm at 9.4 T). The acquisition of a Z-spectrum for each power takes roughly 20 mins. R_1obs and f_m were obtained using a selective inversion recovery (SIR) quantitative MT method (60). Specifically, a 1-ms inversion hard pulse was applied to invert the free water pool and the subsequent longitudinal recovery times were set to be 4, 5, 6, 8, 10, 12, 15, 20, 50, 200, 500, 800, 1000, 2000, 4000, and 6000 ms. Spin-echo Echo Planar Imaging (SE-EPI) was used for the readout followed by a saturation pulse train to shorten the total acquisition time as described previously (61). A constant delay time of 3.5 s was set between the saturation pulse train and the next inversion pulse. The SIR quantitative MT takes roughly 6 mins. Before data acquisition, shimming was carefully performed so that the root mean square (RMS) deviation of B₀ was less than 5 Hz. All images were obtained using a single-shot SE-EPI acquisition with triple references for phase correction and matrix size 64 × 64 and field of view 30 mm × 30 mm.

Data analysis

For six-pool model simulations and experiments, to avoid the effects of rNOE and asymmetric MT, we used the EMR method (39–41) to fit reference signals for quantifying CEST signals, and derived the metrics as MTR_EMR, AREX_EMR, R_{ex_EMR}, and ΔR_{ex_EMR}, respectively. Specifically for the EMR, CEST data with Δω from −6500 Hz to −3500 Hz and 3500 Hz to 6500 Hz and ω₁ of 3.6 μT, and with Δω from −4000 Hz to −2500 Hz and 2500 Hz to 4000 Hz and ω₁ of 1.0 μT were fitted to a two-pool MT model (APPENDIX) (54). The reference signals in an offset range from −5 ppm to 5 ppm were then estimated using the fitted parameters and used for calculating the above metrics. Due to the relatively homogenous B₁ field in rat brains, ω₁ used to calculate the tangent theta were from nominal values. We also used the three-point method to quantify APT signals and the asymmetric analysis method to quantify CEST signals from fast exchanging amines, and compared them with EMR. Specifically, the average of two CEST signals at 3 and 4 ppm in Z-spectrum was used as reference signal for the three-point method and the signal on the opposite site of water was used as reference signal for the asymmetric analysis method. Their corresponding R_ex metrics were named R_{ex_3pt} and R_{ex_asym}, respectively. To evaluate the accuracy of R_ex from these approaches, R_ex for amide, fast exchanging amine, and the sum of three pools (amide, intermediate and fast exchanging amine) were also calculated using Eq. (5) and used as standard values. For animal studies, region of interests (ROIs) were chosen from the whole rat brains. All data analyses were performed using MATLAB 2013b (Mathworks, Natick, MA, USA).

RESULTS

Simulated MTR, AREX, and R_ex for slow exchanging amides and fast exchanging amines

We got MTR_simu, AREX_simu, and R_{ex_simu} with different ω₁ and Δω using the two-pool (amide and water or fast exchanging amine and water) model simulations, and results are shown in Fig. 1 and Fig. 2, respectively. For slow exchanging amides, MTR_simu (Fig. 1a) increases with ω₁ when it is smaller than 1.5 μT, and decreases at higher ω₁. This non-monotonic dependence may be caused the competitive effects of ω₁ and DS. After correcting for the DS effect by the inverse analysis, AREX_simu (Fig. 1c) increases continuously with ω₁. Different from both MTR_simu and AREX_simu, R_{ex_simu} (Fig. 1e) for slow exchanging amides decreases significantly with ω₁ (R_{ex_simu} value at 3.5 μT is roughly 10% of that at 1 μT). For fast exchanging amines, both MTR_simu (Fig. 1b) and AREX_simu (Fig. 1d) increase with ω₁ in our simulation range. In contrast, R_{ex_simu} (Fig. 1f) of fast exchanging amines is independent of ω₁. This simulation result is in agreement with the predictions of Eq. (5), and demonstrates that the subtraction of the two R_ex values acquired with a high and a low ω₁ may remove the influence of fast exchanging amines in APT imaging.

FIG. 1.

Simulated MTR_simu, AREX_simu, and R_{ex_simu} values at 3.5 ppm for slow exchanging amides (a, c, and e) and at 3 ppm for fast exchanging amines (b, d, and f), respectively, vs. ω₁. ω₁ is the irradiation power. The parameters used in simulation were shown in bold in Table 1.

FIG. 2.

Simulated MTR_simu, AREX_simu, and R_{ex_simu} spectra for slow exchanging amides (a, c, and e) and for fast exchanging amines (b, d, and f), respectively, with ω₁ of 1 μT and 3.6 μT. The parameters used in simulation were shown in bold in Table 1.

Fig. 2 shows the spectra of these metrics. For slow exchanging amides with ω₁ of 1 μT, the deviation of the R_{ex_simu} peak lineshape (Fig. 2e) caused by the tangent theta normalization is negligible compared with the MTR_simu peak lineshape (Fig. 2a) and the AREX_simu peak lineshape (Fig. 2c). This result is in agreement with our analysis that the ‘a-peak’ does not influence CEST peaks of slow and intermediate exchanging pools greatly, and thus Eq. (3) can model CEST peaks of slow to fast exchanging pools. For fast exchanging amines, both the central frequency and the lineshape of MTR_simu peaks (Fig. 2b) depend on ω₁, suggesting that MTR may misinterpret CEST effects. This agrees with previous reports that MTR_asym peaks for fast exchanging pools depend on multiple sequence parameters and cannot be used to identify an effect of exchange at a specific frequency (40,46). Even using AREX to improve specificity (Fig. 2d), the CEST peaks have no distinct features around their resonance frequency offsets. In contrast, R_{ex_simu} peaks (Fig. 2f) have Lorentzian lineshapes centered at 3 ppm without dependence on ω₁.

Fitting references using EMR

Fig 3 shows results of simulating the six-pool model and the measured Z-spectra from rat brains and their corresponding EMR fitted reference spectra with ω₁ of 1 μT and 3.6 μT. The simulated reference spectra using two-pool (semi-solid component and water) model simulations are also provided in Fig. 3a and 3c. The match of the fitted reference spectra (S_ref) and the simulated reference spectra indicates the success of the fitting approach. In Fig. 3b and 3d, the match of the Z-spectra and the corresponding fitted reference spectra beyond 5 ppm and −5 ppm also suggests the success of the fitting approach in animals (Sup. Fig. S1 shows that the residuals of the EMR fitting are very small). Table 2 lists the fitted semi-solid MT parameters and simulation parameters in the six-pool model simulations. Note that the fitted parameters are very close to the simulation parameters. Table 3 lists the fitted semi-solid MT parameters in the animal experiments.

FIG. 3.

Six-pool (amide, intermediate exchanging amine, fast exchanging amine, rNOE, semi-solid MT, and water) model simulated Z-spectra (S_lab) and corresponding EMR fitted reference spectra (S_ref) (a, c) using values in bold in Table 1, and experimental Z-spectra (S_lab) and corresponding EMR fitted reference spectra (S_ref) on five healthy rat brains (b, d) with ω₁ of 1 μT (a, b) and 3.6 μT (c, d), respectively. Two-pool (water and semi-solid component) model simulated reference spectra were also shown in (a, c) for comparison with S_ref spectra. Note that S_ref spectra are covered by the simulated reference spectra, indicating the success of the fitting approach. Error bars in (b, d) represent the standard deviations across subjects.

Table 2.

Fitted semi-solid MT parameters and the simulation parameters in the six-pool model simulations using values in bold in Table 1.

	kmw (s−1)	T2m (μs)	kmwfmT1w	δωm (ppm)
Fitted	26.9833	16.423	3.5466	−2.0315
simulation	25	15	3.375	−2.3

Table 3.

Fitted semi-solid MT parameters for the whole brain in the animal experiments.

n=5	kmw (s−1)	T2m (μs)	kmwfmT1w	δωm (ppm)
Fitted	17.5 ± 3.1	41 ± 4.1	3.0 ± 0.4	−1.4 ± 0.1

Fitted MTR, AREX, R_ex, and ΔR_ex from simulated Z-spectra with the presence of multiple exchanging pools

For simulations with ω₁ of 1 μT, the APT signal at 3.5 ppm in the MTR_EMR spectrum (Fig. 4a) overlaps with nearby CEST signals. These nearby overlapping signals are still present in the AREX_EMR spectrum (Fig. 4b). However, the intermediate exchanging amine signal at 2 ppm becomes relatively weak in the R_{ex_EMR} spectrum (Fig. 4d) and the ΔR_{ex_EMR} spectrum (Fig. 4e). This result is also in agreement with the expectation from Eq. (5) that R_ex has a resonance-frequency high-pass filter effect. Fig. 4d shows that the R_{ex_EMR} spectrum with ω₁ of 3.6 μT roughly matches the baseline of that with ω₁ of 1 μT. Fig. 4e shows the ΔR_{ex_EMR} spectrum in which both the nearby intermediate exchanging amine at 2 ppm and the fast exchanging amine at 3 ppm are successfully reduced. Fig. 4d also shows that R_{ex_EMR} spectrum is a Lorentzian lineshape centered at its resonance frequency and roughly matches the calculated R_ex using Eq. (5) for the sum of three pools (amide, intermediate exchanging amine, and fast exchanging amine). The difference between R_ex using Eq. (5) for the sum of three pools and the fast exchanging amine pool is the contributions from the amide and the intermediate exchanging amine which cause ~11% error for quantifying the fast exchanging amine. Fig. 4e also shows that R_{ex_EMR} has ~17% error for quantifying amide compared with R_ex using Eq. (5) for amide. Similar conclusion can be also drawn from simulations with other tissue parameters listed in Table 1 (data not shown).

Fig. 4.

Fitted MTR_EMR (a), AREX_EMR for slow exchanging amides (b), AREX_EMR for fast exchanging amines (c), R_{ex_EMR} (d), and ΔR_{ex_EMR} (e) spectra from the six-pool model simulations using values in bold in Table 1. Calculated R_ex using Eq. (5) for the sum of three pools (amide, intermediate exchanging amine, and fast exchanging amine) and fast exchanging amine and R_ex using Eq. (5) for amide were also shown in (d) and/or (e), for comparison with the fitted metrics.

Fig. 5 shows several R_ex metrics and/or ΔR_ex metric with varied tissue parameters. Note that R_{ex_EMR} is significantly larger than R_ex using Eq. (5), but R_{ex_3pt} is significantly smaller than R_ex using Eq. (5) for slow exchanging amides. However, ΔR_{ex_EMR} is more close to R_ex using Eq. (5) than other two metrics. Also note that both R_{ex_EMR} and R_{ex_asym} are close to R_ex using Eq. (5) for fast exchanging amines, although R_{ex_EMR} is larger and R_{ex_asym} is smaller than R_ex using Eq. (5).

Fig. 5.

R_ex and/or ΔR_ex with varied amide and fast exchanging amine concentrations (a, b), amide-water and fast exchanging amine-water exchange rates (c, d), T_1w (e, f), T_2w (g, h), f_m (i, j), and k_mw (k, l). Each set of parameters was varied with other parameters remaining at the values in bold in Table 1. 1 μT and 3.6 μT powers are used for getting R_ex for slow exchanging amides and fast exchanging amines, respectively.

Experimental MTR, AREX, R_ex, and ΔR_ex

Fig. 6 shows experimental results from rat brains. Similar to the simulations in Fig. 4, the APT signal at 3.5 ppm acquired with ω₁ of 1 μT overlaps with nearby CEST signals in the MTR_EMR spectrum (Fig. 6a), but can be successfully isolated from nearby CEST signals in the ΔR_{ex_EMR} spectrum (Fig. 6e). In addition, the CEST peak acquired with ω₁ of 3.6 μT shows no distinct feature around its resonance frequency offset in the AREX spectrum (Fig. 6c), but shows a clear peak centered at around 3 – 4 ppm in the R_{ex_EMR} spectrum (Fig. 6d). Considering some contributions from APT at 3.5 ppm (around 10% of that acquired with ω₁ of 1 μT based on Fig. 1e) and the range of resonance frequencies of endogenous fast exchanging amines and hydroxyls in biological tissues (0.6 – 3 ppm) (7,13,17), the CEST peaks acquired with ω₁ of 3.6 μT may center at around 3 ppm and thus could originate from glutamate amines (7,33) and/or protein lysine amine protons (34,35) which have resonance frequencies at around 3 ppm. Fig. 7 shows maps of R_{ex_EMR} at 3 ppm with ω₁ of 3.6 μT (predominated by the contrast from fast exchanging amine) and ΔR_{ex_EMR} at 3.5 ppm (predominated by the contrast from amide) from a representative rat brain.

Fig. 6.

Measured MTR_EMR (a), AREX_EMR for amides (b), AREX_EMR for fast exchanging amines (c), R_{ex_EMR} (d), and ΔR_{ex_EMR} (e) spectra on five healthy rat brains. Error bars represent the standard deviations across subjects.

Fig. 7.

Maps of R_{ex_EMR} at 3 ppm with ω₁ of 3.6 μT (a) and ΔR_{ex_EMR} at 3.5 ppm (b) from a representative rat brain

DISCUSSION

In this paper, we show that R_ex provides unique features to separate slow exchanging amides from fast exchanging and nearby intermediate exchanging amines and to correct central frequency offset in CEST imaging of fast exchanging pools. Together with EMR fitting to get the reference signal, we applied R_ex in imaging animal brains. This in turn significantly improves the detection specificity of CEST imaging for more accurate quantification of molecules.

The influences of fast exchanging pools have not been comprehensively investigated in APT imaging. However, our results in Fig. 6d show that contributions from fast exchanging amines at 3.5 ppm are roughly 64 % of those from amides at 3.5 ppm with ω₁ of 1 μT, suggesting that they may be a major source of errors in quantifying amide protons. These contaminations would be stronger at relatively higher ω₁, which can be shown from the CEST spectra acquired with ω₁ of 3.6 μT in Fig. 6a and 6d. Contaminations from intermediate exchanging amines at 2 ppm in APT imaging may not be significant at 9.4 T, but would be stronger at lower field strength. Another CEST peak at around 2.7 ppm, which cannot be easily observed in the MTR_EMR and AREX_EMR spectra with ω₁ of 1 μT in Fig. 6a and 6b, can be clearly shown in the R_{ex_EMR} and ΔR_{ex_EMR} spectra in Fig. 6d and 6e. This peak is buried by the two nearby CEST signals from amides at 3.5 and amines at 2 ppm, and thus is overlooked. However, with the reduction of signals from amines at 2 ppm in the R_{ex_EMR} and ΔR_{ex_EMR} spectra, it can be easily observed. This signal at 2.7 ppm is as narrow as those of amides and intermediate exchanging amines at 2 ppm and thus should be from slow or intermediate exchanging pools. According to previous phantom experiments (7,62), it may originate from phosphocreatine which has a resonance frequency at around 2.7 ppm.

Although previous studies suggest the CEST signal at 3 ppm acquired with high ω₁ using MTR_asym originates from glutamate, the reported central frequency of the MTR_asym peak is not at 3 ppm, but at 2 ppm (7). Our MTR_EMR spectrum with ω₁ of 3.6 μT in Fig. 6a also shows a central frequency at around 2 ppm. It has been reported that the central frequency quantified by MTR depends on multiple sequence and tissue parameters, and thus MTR provides false CEST peaks (54,56). Therefore, based only on CEST measurements, it is challenging to identify the resonance frequencies of the exchanging pools and thus the molecular origin of the CEST signals. The AREX_EMR spectrum acquired with ω₁ of 3.6 μT in Fig. 6c does not show any distinct feature, and thus is not appropriate to identify the resonance frequency of exchanging pools. However, the R_{ex_EMR} spectrum in Fig. 6d suggests that this CEST effect with ω₁ of 3.6 μT measures both fast exchanging amines at around 3 ppm and some minor contributions from amides at 3.5 ppm. Hydroxyl-water exchange effects may influence the MTR_asym spectra, but not the R_ex spectrum because they are closer to the water line (<1 ppm) and thus can be reduced by the resonance-frequency high-pass filter of R_ex. This in vivo result is also in agreement with previous R_ex study on phantoms that R_ex can provide distinct feathers for fast exchanging CEST signals (56). The difference between R_ex using Eq. (5) for the sum of three pools and the fast exchanging amine pool in Fig. 4d suggests that this method can not remove contaminations from amide and intermediate exchanging amine for quantifying fast exchanging amine. However, this contamination is minor at high power based on our simulations. The measured R_{ex_EMR} on rat brains is 28.3 ± 3.7 s⁻¹ (Fig. 6d), and the simulated R_ex with f_s of 0.005 is 60.81 (Fig. 4d). Therefore, we can estimate that the concentration of fast exchanging amines in brain should be roughly an order of magnitude higher than the glutamate concentration. This suggests that protein lysine amines at 3 ppm may be a major contribution (34,35).

In this paper, the EMR method was used to estimate reference signal in a complex tissue model. A previous study (63) indicates that, in order to get reliable fittings of the semi-solid MT parameters, multiple RF powers are necessary. Therefore, we used Z-spectra acquired with two RF powers to fit semi-solid MT parameters in the current work. In other studies (39–41,54,63), several independent semi-solid MT model parameters including T_1w/T_2w were obtained by fitting CEST data to Eq. (A1). However, our fitting of simulated data indicates that T_1w/T_2w can not be fitted accurately and this inaccuracy leads to errors to the extrapolated signals near water frequency in our study (Sup. Table. S1 and Sup. Fig. S2). This may be due to the different sampling scheme or ω₁ that used for fitting the semi-solid MT model parameters. Interestingly, we found that two different approaches, i.e. (1) fitting of four independent semi-solid MT model parameters (k_mw, T_2m, k_mwf_mT_1w, Δ_m) with a roughly estimated T_1w/T_2w value, or (2) direct fitting of five parameters (k_mw, T_2m, k_mwf_mT_1w, T_1w/T_2w, Δ_m) with a limited fitting boundary of T_1w/T_2w, lead to similar accuracy in the estimation of other CEST parameters and extrapolated MT reference signals. Sup. Table. S2–S3 and Sup. Fig. S3–S4 indicate a successful EMR fitting with four independent parameters and an input of 0.8 times and 1.2 times of T_1w/T_2w value, respectively. Sup. Table S4 and Sup. Fig. S5 indicate a successful EMR fitting with five independent parameters and a limited fitting boundary ranging from 0 to 1.2 times of T_1w/T_2w value. In normal rat brains at 9.4 T, T_1w and T_2w distributions are in a limited range. So we obtained T_1w/T_2w value of 45 from literature survey (44) and fitted four independent semi-solid MT model parameters in the animal study in this paper. In pathologies with significant variations of T_1w and T_2w, they can be measured and included in the fittings as constants on a voxel basis. More interestingly, we find that ΔR_ex is not significantly influenced by the inaccurate fitting of T_1w/T_2w, possibly because that the subtraction of two R_ex removes the fitting errors. Previous studies (64,65) indicate that the semi-solid pool in biological tissue has super-Lorentzian absorption lineshape. However, their studies also show that MT signals with frequency offsets roughly less than 16 ppm can still be fitted well by Lorentzian lineshape. In addition, another study (49) indicates that the semi-solid MT effect near water resonance can be modeled as Lorentzian lineshape. To avoid the singularity in the super-Lorentzian fitting, we used Lorentzian lineshap for the MT fitting. Here we choose sampling points from −16.25 ppm to −8.75 ppm and 8.75 ppm to 16.25 ppm with ω₁ of 3.6 μT and from −10 ppm to −6.25 ppm and 6.25 ppm to 10 ppm with ω₁ of 1 μT for fitting the semi-solid MT parameters. For the sampling points with ω₁ of 3.6 μT, farther offsets were set to avoid the possible contaminations from fast exchanging amines which are more significant at higher powers. Both experiments in Fig. 6d and simulations in Fig. 4d show that R_ex with ω₁ of 3.6 μT is higher than that with ω₁ of 1 μT near 5 ppm. These unmatched curves also cause the negative ΔR_ex values near 5 ppm in both Fig. 6e and Fig. 4e. This may be due to that our sampling points for fitting the semi-solid MT are contaminated by fast exchanging amines. Further studies require optimization of these sampling points. In the current study, this fitting error near 5 ppm is far from amide at 3.5 ppm and fast exchanging amine at 3 ppm and thus does not have significant influence on our quantifications. Since 1 μT and 3.6 μT RF irradiation powers have been previously used in detecting CEST signals from amides (44,66) and fast exchanging amines (7), respectively, we evaluated these two powers here. Further studies are necessary to optimize the powers for better sensitivity and specificity.

For quantitative CEST data analyses, it is important to estimate reference signals accurately in order to isolate the true chemical exchange effects from other confounding effects including MT and DS. Unfortunately, there is currently no perfect method for this purpose. In the current work, the EMR approach (39–41) was used for fitting reference signals, but our analysis indicates that the EMR is still not robust. Note that the R_ex method introduced here is not limited to the EMR method. Some other methods, such as LD (42,43) and Lorentzian fitting (48), may be combined with R_ex as well to evaluate reference signals, although the accuracy of these methods at high powers has not been comprehensively investigated either. Further development of methods for obtaining more accurate reference signals may increase the in vivo application of R_ex.

Although R_ex and ΔR_ex can significantly increase specificity, it has several drawbacks. First, ΔR_ex has reduced signal to noise ratio (SNR) due to the removal of CEST signals from fast exchanging amines. Further studies may be performed to increase the acquisition efficiency. For instance, the SNR could be increased and the acquisition time could be reduced through optimizing the sampling scheme. In this paper, although dense sampling of Z-spectra was performed to show clear CEST profiles, less sampling points between −5 to 5 ppm and multiple acquisitions at 3.5 ppm could significantly reduce the total acquisition time, increase the SNR for imaging amide, and keep showing a rough CEST profile from fast exchanging amine. Second, R_ex and/or ΔR_ex requires acquisitions with two ω₁, which lengthen the total acquisition time. Third, the tangent theta is sensitive to B₁ error. For example, there will be 19% error in R_ex when B₁ has 10% error. However, B₁ mapping as well as CEST acquisitions with multiple ω₁ have already been used in clinical scanners to increase the specificity of CEST imaging (67). Here, we did not measure B₁ since it is relatively homogenous using animal volume coil. But in situations where B₁ is relatively inhomogeneous, B₁ mapping is also required. Here, our study is focused on 9.4 T and two specific ω₁. The relative contribution from amides and fast exchanging amines on other fields and ω₁ require further studies.

CONCLUSION

Our results show that R_ex can correct the shift of CEST peaks from fast exchanging amines and ΔR_ex can successfully remove influences from nearby CEST signals in APT imaging. This significantly enhances the detection specificity of CEST imaging to amide and fast exchanging amine protons.

Abbreviations used

CEST

chemical exchange saturation transfer

MRS

magnetic resonance spectroscopy

APT

amide proton transfer

MT

magnetization transfer

MTR

magnetization transfer ratio

DS

direct water saturation

LD

Lorentzian difference

T_1w

water longitudinal relaxation time

R_ex

exchange-dependent relaxation rate

MTR_asym

MTR asymmetry analysis

AREX

apparent exchange-dependent relaxation

rNOE

relayed nuclear Overhauser enhancement

k_sw

solute-water exchange rate

f_m

semi-solid MT pool concentration

f_s

solute concentration

R_1obs

apparent water longitudinal relaxation rate

CW

continuous wave

SNR

signal to noise ratio

APPENDIX

Eq. (A1) gives the two-pool MT model,

$$\frac{\mathrm{S}}{S_0}=\frac{\frac{1}{T_{1m}}(k_{mw}{f}_m{T}_{1w})+R_{\mathit{rfm}}+\frac{1}{T_{1m}}+k_{mw}}{(k_{mw}{f}_{\mathrm{m}}{T}_{1w})(R_{\mathit{rfm}}+\frac{1}{T_{1m}})+[1+{(\frac{{\omega }_1}{2\pi \mathrm{\Delta }\omega })}^2(\frac{T_{1w}}{T_{2w}})](R_{\mathit{rfm}}+\frac{1}{T_{1m}}+k_{mw})}$$ (A1)

where k_mw is the exchange rate between semi-solid and water protons; T_2w is the transverse relaxation time of water pool; T_1m and T_2m are the longitudinal and transverse relaxation times of the semi-solid pool, respectively; R_rfm is the RF absorption rate, which depends on the absorption lineshape, g_m(2πΔω) through the relationship ${\mathrm{R}}_{\mathit{rfm}}={\omega }_1^2\pi g_m(2\pi \mathrm{\Delta }\omega )$,

$$g_m(2\pi \mathrm{\Delta }\omega )=\frac{1}{\frac{\pi }{T_{2m}}(1+T_{2m}^2{(\mathrm{\Delta }\omega -\delta {\omega }_{\mathrm{m}})}^2)}$$ (A2)

where δω_m is the central resonance frequency of semi-solid pool. Four independent semi-solid MT model parameters (k_mw, T_2m, k_mwf_mT_1w, δω_m) were obtained by fitting CEST data to Eq. (A1), based on the nonlinear least squares fitting approach, using the Levenberg-Marquardt algorithm. In the fitting, T_1m was set to 1 s (39,40). T_1w/T_2w was calculated using the simulation parameters for all simulation studies and set to be 45 for all animal studies. The T_1w/T_2w value in animals was obtained by literature survey (44). Table A1 lists the starting points and boundaries of the fit of semi-solid MT model parameters.

Table A1.

Starting points and boundaries of MT model parameters.

	Start	Lower	Upper
kmw (s−1)	25	0	100
T2m (μs)	16	1	100
kmwfmT1w	2	0	10
δωm (ppm)	0	−3	3