Spin-locking vs. chemical exchange saturation transfer MRI for investigating chemical exchange process between water and labile metabolite protons

Abstract

Chemical exchange saturation transfer (CEST) and spin-locking (SL) experiments were both able to probe the exchange process between protons of non-equivalent chemical environments. To compare the characteristics of the CEST and SL approaches in the study of chemical exchange effects, we performed CEST and SL experiments at varied pH and concentrated metabolites with exchangeable amide, amine, and hydroxyl protons at 9.4 T. Our results show that: i) On-resonance SL is most sensitive to chemical exchanges in the intermediate exchange regime and is able to detect hydroxyl and amine protons on a millimolar concentration scale. Off-resonance SL and CEST approaches are sensitive to slow-exchanging protons when an optimal SL or saturation pulse power matches the exchanging rate, respectively. ii) Offset frequency-dependent SL and CEST spectra are very similar, and can be explained well with an SL model recently developed by Trott and Palmer. iii) The exchange rate and population of metabolite protons can be determined from offset-dependent SL or CEST spectra or from on-resonance SL relaxation dispersion measurements. iv) The asymmetry of the magnetization transfer ratio (MTR_asym) is highly dependent on the choice of saturation pulse power. In the intermediate exchange regime, MTR_asym becomes complicated and should be interpreted with care.

Introduction

Recently, there has been an increasing number of in vivo studies that have utilized the chemical exchange (CE) effect to probe the tissue microenvironment and provide novel imaging contrasts that are not available from conventional MRI techniques. Most of these studies adopted either a chemical exchange saturation transfer (CEST) or a spin-locking (SL) approach to detect contrast in tissue pH or the population of labile protons, which have a Larmor frequency different from water. Ideally, a CE-sensitive imaging contrast should have good sensitivity and vary monotonically with pH and linearly with labile proton concentration. The CE contrast is determined by many parameters, such as the exchange rate between water and labile protons (k_ex), the difference in their Larmor frequencies (δ), the populations of the exchangeable protons, water T₁, and the magnetic field strength (B₀), etc. The CE effect in MRI is also highly sensitive to a ratio of k_ex to δ. k_ex/δ, which indicates the chemical exchange kinetics, is usually divided into three regimes: slow (k_ex/δ≪1), intermediate (k_ex/δ ∼ 1), and fast exchange (k_ex/δ≫1). CEST techniques are mostly applied at the slow or slow to intermediate exchange regime (1,2), while the CE is often assumed to occur at the fast exchange regime for SL applications (3,4).

In CEST studies that are based upon endogenous contrast, selective off-resonance irradiation of labile protons of protein or peptide side chains attenuates the water signal via exchange between these labile protons and bulk water. The signal intensity as a function of irradiation frequency, often referred to as the Z-spectrum, can be expressed by the magnetization transfer ratio (MTR):

$$\mathit{\text{MTR}}(\Omega )=\stackrel{M_{\text{CEST}}(\Omega )}{}/\underset{M_0}{}$$ [1]

where Ω is the frequency offset with respect to water. In practice, the conventional non-CE magnetization transfer effect and direct water saturation (or the so-called spillover effect) also affect the Z-spectrum, and these effects are assumed to be symmetrical around the water resonance frequency. To minimize these non-CE contributions, CEST contrast in MRI is usually extracted from two images— one acquired with off-resonance irradiation on the targeted labile proton and the other as a control with opposite offset frequency from the water (5). The normalized differential image, usually referred to as the asymmetry of MTR (MTR_asym), is described as

$${\mathit{\text{MTR}}}_{\mathit{\text{asym}}}(\Omega )=\mathit{\text{MTR}}(-\Omega )-\mathit{\text{MTR}}(\Omega ),$$ [2]

which is sensitive to the CE effect. Previous endogenous CEST contrast is mostly based on protons in slow-exchanging regimes and has been applied in many pathological studies. For example, the amide proton transfer (APT) approach, which is based upon the exchange between amide protons of protein side chains and water, has been utilized to study tumor or stroke (5-7). At neutral pH, amide protons typically have a chemical shift of around 3.5 ppm (1400 Hz or 8800 rad/s at 9.4 T) from water, and the exchange rate with water proton is on the order of 100 s^-1 (8). Recently, endogenous CEST contrast has been also observed on faster-exchanging protons, where, for example, hydroxyl-based CEST approaches were reported to provide information on the concentration of glycogen as well as glycosaminoglycans (9,10). These hydroxyl protons have chemical shifts of 1-3 ppm from water and exchange rates on the order of 700-15000 s^-1 (1,8); thus, the exchange is close to the intermediate regime for 3 T (1 ppm = 128 Hz or 802 rad/s) or even 9.4 T.

The CE effect can also be studied by an SL approach, where water magnetization is first flipped away from the Z-axis and then spin-locked by either an on- or off-resonance B₁ radiofrequency (RF) pulse. During the applied spin-locking pulse, the water magnetization decays with the spin-lattice relaxation time in the rotating frame (T_1ρ), which is sensitive to molecular fluctations with a frequency that is close to the Rabi frequency of the SL pulse, ω_{1, SL} (= γB_{1, SL}). SL contrast has been utilized to characterize cartilage degradation (11-13), tumors (14-17), stroke (18,19), and neurodegenerative diseases (20,21). The T_1ρ dependence on ω_{1, SL}, referred to as the T_1ρ dispersion, has also been applied in pathological studies (16,19,22). It was reported in protein phantoms that the CE effect contributes significantly to the T_1ρ dispersion in the ω_{1, SL} range below a few kHz (11,23). Previous SL studies of CE effects were often explained by theoretical models with fast exchange approximation (3,4). This assumption has hindered the application of SL approaches to slow- and intermediate-exchange protons, which are widely present in biological tissues. Recently, Trott and Palmer proposed a theoretical description to explain the CE contribution to the relaxation rate R_1ρ (= 1/T_1ρ) when the populations of two exchanging proton pools are highly unequal (24). Under such asymmetric population (AP) approximation, the expression of CE contribution to R_1ρ can be simplified and applied beyond the fast exchange limit (24). The AP assumption holds for most in vivo chemical exchange applications, because water is the dominant pool; thus, the Trott and Palmer model may be applicable to in vivo SL studies.

The aims of this work are: i) to examine the characteristics of SL and CEST contrast for chemical exchanges in the slow-, intemediate-, and fast-exchange regimes, and ii) to explain experimental data with Trott and Palmer's AP model. On-resonance R_1ρ dispersion, offset-dependent SL spectra, and CEST Z-spectra measurements were performed at varied pH and concentrated metabolite phantoms with typical exchangeable proton groups found in vivo, including amide, hydroxyl, and amine protons.

Theoretical backgrounds

The pulse sequence for an SL experiment is illustrated in Fig. 1A, where the super- and sub-scripts of an RF pulse denote its phase and transmitter frequency, respectively. The spin-locking pulse has a Rabi frequency (SL frequency) ω_{1, SL} and is applied on the Y-axis at a frequency offset Ω; thus, in the rotating frame, the effective SL field $B_{1,\mathit{\text{eff}}}=\sqrt{{\omega }_{1,\mathit{\text{SL}}}^2+{\Omega }^2}/\gamma$ (Fig. 1B). To achieve SL, the water magnetization is first flipped by the θ degree pulse to the Y-Z plane, then spin-locked by B_{1, eff} for duration of TSL, and then flipped back to the Z-axis for imaging. During TSL, the water magnetization is locked at an angle θ = arctan(ω_1,SL / Ω) from the Z-axis and decays with R_1ρ, the spin-lattice relaxation rate in the rotating frame (Fig. 1C). Provided that the spin relaxation is dominated by single-exponential decay, R_1ρ can generally be expressed as:

Fig. 1.

(A) The pulse sequence diagram used for the SL and CEST experiments contains an SL or CEST preparation pulse and a spin-echo EPI acquisition. The super- and sub-scripts of an RF pulse denote its phase and transmitter frequency, respectively. For SL, the water magnetization is first flipped by a hard pulse and then locked by an SL pulse with a Rabi frequency of ω_{1, SL} (=γB_{1, SL}) and a duration of TSL. The hard pulse following the SL pulse flips the magnetization back to the Z-axis. For CEST, the saturation pulse has a Rabi frequency of ω_{1, CEST} and a duration of TST (saturation time). (B) With an off-resonance B_{1, SL} or B_{1, CEST} pulse applied at the frequency offset Ω, the water magnetization in the rotating frame experiences an effective B_{1, eff} that has an angle θ with the Z-axis. (C) In an SL experiment, the water magnetization M₀ was flipped to the B_{1, eff} direction and was spin-locked by B_{1, eff}. (D) In a CEST experiment, the magnetization precesses around B_{1, eff}.

$$R_{1\rho }=R_1\cdot {\text{cos}}^{\text{2}}\theta +(R_2+R_{\mathit{\text{ex}}})\cdot {sin}^2\theta ,$$ [3]

where R₁ is the longitudinal relaxation rate of water and R₂ is the intrinsic water transverse relaxation rate in the absence of chemical exchange. A special case is when Ω = 0 and θ = 90°, which is the on-resonance SL. For two-site exchange between A and B with different magnetic environments (representing water and labile non-water protons, respectively), the population (p) of each site and the exchange rate constant (k) satisfy p_A k_A = p_B k_B. Using population-averaged values of R₁ and R₂ for protons in the two sites and assuming that the populations of the two sites are highly asymmetric (p_A ≫ p_B), the Bloch-McConnell equation can be solved and the chemical exchange-related relaxation rate in an SL experiment, with Ω and ω_{1, SL} as experimental variables, can be written as (24)

$$R_{\mathit{\text{ex}}}(\Omega ,{\omega }_{1,\mathit{\text{SL}}})=\frac{p_B\cdot {\delta }^2\cdot k_{ex}}{{(\delta -\Omega )}^2+{\omega }_{1,SL}^2+k_{\mathit{\text{ex}}}^2},$$ [4]

where δ is the chemical shift of the labile proton relative to water, k_ex = k_A + k_B is the exchange rate between the two proton pools, and p_A ≈ 1 is assumed. Note that the frequency offset is expressed relative to the Larmor frequency of water, and some notations are different from those in the original reference of Trott and Palmer (Ω and k_ex correspond to ω_rf and k, respectively). R_ex reaches a peak at Ω = δ. The parameters of interest, p_B, k_ex, and δ, can be obtained by fitting R_ex with Eq. [4]. To this end, two SL approaches are adapted; change in ω_1,SL with fixed Ω, and change in Ω with fixed ω_1,SL.

SL measurements as a function of ω_1,SL can be performed at Ω = 0 (on-resonance SL) or Ω = δ. For on-resonance SL (Ω = 0),

$$R_{\mathit{\text{ex}}}\text{(}{\omega }_{\text{1},\text{SL}}\text{)}=\frac{p_B\cdot k_{\mathit{\text{ex}}}}{1+{({\omega }_{1,SL}/\delta )}^2+{(k_{\mathit{\text{ex}}}/\delta )}^2}.$$ [5]

The SL relaxation rate is

$$R_{1\rho }=R_2+R_{\mathit{\text{ex}}}=R_2+\frac{p_B\cdot k_{\mathit{\text{ex}}}}{1+{({\omega }_{1,\mathit{\text{SL}}}/\delta )}^2+{(k_{\mathit{\text{ex}}}/\delta )}^2}.$$ [6]

The on-resonance R_1ρ dispersion data can be fitted to ω_{1, SL} to obtain p_B and k_ex in addition to R₂ and δ. If δ is known, k_ex can also be inferred from the linewidth of the R_ex(ω_{1, SL}) Lorentzian-shaped curve (R_ex vs. ω_{1, SL} plot): full width at half maximum $(\text{FWHM})=\sqrt{k_{\mathit{\text{ex}}}^2+{\delta }^2}$. In the case of k_ex/δ_B≪1, however, p_B and k_ex cannot be separately determined from on-resonance R_1ρ dispersion. Another SL offset frequency of particular interest is the Larmor frequency of the labile proton B (Ω = δ), for which

$$R_{\mathit{\text{ex}}}({\omega }_{1,\mathit{\text{SL}}})=\frac{p_B\cdot k_{\mathit{\text{ex}}}}{{({\omega }_{1,\mathit{\text{SL}}}/\delta )}^2+{(k_{\mathit{\text{ex}}}/\delta )}^2}$$ [7]

SL experiments can also be performed as a function of offset frequency (Ω) with a fixed ω_{1, SL}, similar to a CEST Z-spectrum. The magnetization at a spin-locking time (TSL), with repetition time → ∞, is

$$\frac{M(\Omega )}{M_0}=\frac{(R_2+R_{\mathit{\text{ex}}}){sin}^2\theta \cdot exp\left\{-[(R_2+R_{\mathit{\text{ex}}}){sin}^2\theta +R_1{cos}^2\theta ]\cdot \mathit{\text{TSL}}\right\}+R_1{cos}^2\theta }{(R_2+R_{\mathit{\text{ex}}}){sin}^2\theta +R_1{cos}^2\theta },$$ [8]

When TSL is sufficiently long, the magnetization reaches steady state. An SL ratio (SLR) can be described, similar to MTR of CEST studies (see Eq. [1]), as

$$\mathit{\text{SLR}}(\Omega )=\frac{M_{\mathit{\text{SL}}}(\Omega )}{M_0}=\frac{R_1{cos}^2\theta }{(R_2+R_{\mathit{\text{ex}}}){sin}^2\theta +R_1{cos}^2\theta },$$ [9]

Ω-dependent SLR spectrum will be referred to as the SL Z-spectrum for comparison with the CEST Z-spectrum. Similar to MTR_asym (see Eq. [2]), the CE-related contrast can be obtained from the asymmetry of the SLR; i.e., the normalized differential signal acquired from opposite frequency offsets with respect to water:

$${\mathit{\text{SLR}}}_{\mathit{\text{asym}}}(\Omega )=\mathit{\text{SLR}}(-\Omega )-\mathit{\text{SLR}}(\Omega )$$ [10]

In off-resonance SL studies with varying Ω, R_ex can be obtained by rearranging Eq. [9] from an SL Z-spectrum:

$$R_{\mathit{\text{ex}}}(\Omega )=(1/\mathit{\text{SLR}}-1)\cdot \frac{{\Omega }^2}{{\omega }_{1,\mathit{\text{SL}}}^2}\cdot R_1-R_2.$$ [11]

Ω-dependent R_ex can be used for fitting k_ex and p_B from Eq. [4]. The exchange rate k_ex can also be inferred from the linewidth of the R_ex Lorentzian-shaped curve (R_ex vs. Ω-plot): $\text{FWHM}=\sqrt{k_{\mathit{\text{ex}}}^2+{\omega }_{1,SL}^2}$. To compare CEST results with the SL approach, an effective R_{ex, CEST} may be constructed from the CEST Z-spectra, similar to Eq. [11]:

$$R_{\mathit{\text{ex}},\mathit{\text{CEST}}}(\Omega )=(1/\mathit{\text{MTR}}-1)\cdot \frac{{\Omega }^2}{{\omega }_{1,\mathit{\text{CEST}}}^2}\cdot R_1-R_2$$ [12]

If R_{ex, CEST} (Ω) is similar to R_ex(Ω) (at ω_{1, CEST} = ω_{1, SL}), k_ex can be inferred from FWHM of the R_{ex, CEST} vs. Ω plot and also determined using Eq. [4].

Materials and Methods

MR experiments of metabolite phantoms

All MR experiments were performed at room temperature on a 9.4T/31-cm magnet (Magnex, UK), interfaced to a Unity INOVA console (Varian). The actively shielded 12-cm-diameter gradient insert (Magnex, UK) operates at a maximum gradient strength of 40 gauss/cm and a rise time of 120 μs. A 3.8-cm-diameter volume coil (Rapid Biomedical, Ohio) was used for excitation and reception. Metabolite solution (see below) was transferred into a 9-mm I.D. syringe, and three or four syringes were inserted together into the coil for imaging. Magnetic field homogeneity was optimized by localized shimming over a ∼20 × 20 × 6 mm³ volume to yield a water spectral linewidth that was typically 10 Hz or less. The imaging parameters were: a field of view = 24 mm × 24 mm, matrix size = 64 × 64, and slice thickness = 5 mm. Before the SL and CEST experiments, a T₁ map was obtained using an inversion-recovery sequence. In addition, the B₁ field was also mapped for calibration of the transmit power (25). With our volume coil, the B₁ map showed fairly good spatial homogeneity: the variation of B₁ was less than 10% across all pixels within the samples (data not shown).

For SL and CEST experiments, the chemical exchange contrast was first generated by the SL or CEST preparation (Fig. 1A); then the residue magnetizations in the X-Y plane were dephased with crushing gradients; and finally, images were acquired with a spin-echo echo-planar imaging (EPI) technique using an echo time (TE) of 42 ms. For on-resonance R_1ρ dispersion experiments, SL was either achieved with the sequence shown in Fig. 1A for Ω = 0 or with an adiabatic SL pulse sequence (25); the results were highly similar and are not distinguished here. R_1ρ dispersion was measured for 10 ω_{1, SL} values of approximately 1110, 1570, 2220, 3140, 4440, 6280, 8880, 12560, 17760, and 25120 rad/s. At each ω_{1, SL}, 14 TSL values, ranging between 0 and 330 ms, were acquired with a repetition time (TR) of 8 s and a TE of 42 ms. For CEST and SL Z-spectra measurements, images were collected within ±10 ppm of the water resonance, with the Rabi frequency of a 4-s SL or CEST saturation pulse (ω_{1, SL} or ω_{1, CEST}) = ∼1100 rad/s, and the repetition time was 18 s. At each offset frequency, the SL flip angle θ was adjusted according to θ = arctan(ω_1,SL / Ω). For the calculation of SLR and MTR, control M₀ images were acquired at the offset frequencies of ±300 ppm.

Three sets of MRI phantom experiments were performed:

• Experiment I: on-resonance R_1ρ dispersion and CEST studies of nicotinamide and glucose with different concentrations. To evaluate whether SL and CEST contrast is sensitive to chemical exchanges in the slow- and intermediate-exchange regimes and to labile proton concentrations, 20, 50, 100, and 200 mM nicotinamide (Nic) and glucose (Glc) were dissolved in 1× phosphate-buffered saline (PBS) and titrated to pH of 7.4. As described in Introduction, the amide and hydroxyl protons are expected to be in the slow- and intermediate-exchange regimes, respectively. On-resonance R_1ρ dispersions and CEST Z-spectra were obtained.

• Experiment II: on-resonance R_1ρ dispersion and CEST studies of glutamate with various pH values. To systematically study the exchange rate dependence of SL and CEST measurements, 50 mM glutamate (Glu) was dissolved in PBS and titrated to pH values of 3.1, 3.8, 4.5, 5.2, 5.9, 6.4, 6.9, 7.4, 7.9, 8.4, 9.1, and 9.8. The chemical shift between the amine (−NH₂) proton and water is 3.0 ppm (2). On-resonance R_1ρ dispersions and CEST Z-spectra were obtained.

• Experiment III: SL and CEST Z-spectra of nicotinamide and glucose with different pH values. To compare the Z-spectra of SL and CEST, 100 mM Nic was dissolved in PBS and titrated to pH values of 7.4, 7.8, and 8.4, and 100 mM Glc was dissolved in PBS and titrated to pH values of 5.6, and 7.0. SL and CEST Z-spectra were obtained at ω₁ of ∼1100 rad/s, and on-resonance R_1ρ dispersions were also measured with varying ω_{1, SL}.

Data analysis and numerical simulations

For each ω_{1, SL}, on-resonance R_1ρ maps were calculated by pixel-wise fitting of multi-TSL data to monoexponential signal decay with respect to TSL. One 5 × 5 mm² region of interest was selected for each sample, where all data were averaged. The CEST and off-resonance SL contrasts were estimated by calculating MTR_asym and SLR_asym using Eqs. [2] and [10], respectively. To obtain k_ex, p_B, and R₂, the on-resonance R_1ρ dispersion data were fitted to Eq. [6], assuming a chemical shift of 1.2 ppm for glucose hydroxyl protons and 3.0 ppm for glutamate amine protons (2), respectively. Glucose hydroxyl protons have more than one CEST peak (9); for simplicity, we used only one chemical shift for data fitting in this work. Note that δ is expressed in rad/s unit for the fitting of on-resonance R_1ρ dispersion data to match with k_ex and ω₁ but is expressed in ppm units for CEST or SL Z-spectra, following the literature.

Experiment I

For glucose, the chemical exchanging parameters (k_ex, δ, p_B, and R₂), determined from on-resonance R_1ρ dispersions, were used to simulate SLR_asym using Eqs. [8] to [10] for comparing with the experimental MTR_asym, and an effective R_{ex, CEST} was constructed from the CEST Z-spectra using Eq. [12] with measured R₁ and fitted R₂. To simulate SLR_asym of Nic, a δ of 3.4 ppm (8545 rad/s) and k_ex of 100 s^-1 were assumed (8), and R_{ex, CEST} was constructed using measured R₁ and assumed R₂ (see results). Then, the FWHM was obtained from fitting R_{ex, CEST} to a Lorenztian lineshape, excluding data points close to the water resonance frequency (see results below).

Experiment II

In all Glu pH phantoms, p_B should be constant, while k_ex is varied. Note that k_ex and p_B cannot be determined separately from on-resonance R_1ρ dispersion data for samples when k_ex/δ ≪1. Thus, p_B of Glu were first fitted with a δ of 3.0 ppm (7540 rad/s) from pH phantoms that gave the largest R_1ρ dispersions (averaged from pH = 6.9, 7.4, and 7.9 samples, see results below). Then, k_ex was determined with a fixed p_B for all pH phantoms. Similar to the data processing of Experiment I, SLR_asym was simulated and the linewidth of the R_{ex, CEST} was calculated. To study the dependence on the chemical exchanging kinetics, on- and off-resonance R_1ρ (Ω = 0 and δ) were also simulated with δ = 3.0 ppm, p_B = 0.0014, R₁ = 0.35 s^-1, and R₂ = 0.5 s^-1 as a function of k_ex/δ for a few selected values of ω_{1, SL}.

Experiment III

SL Z-spectra and SLR_asym were directly compared with the CEST Z-spectra and MTR_asym.

Results

Experiment I: R_1ρ and CEST effects of amide and hydroxyl protons

Fig. 2 shows the on-resonance R_1ρ dispersions, CEST Z-spectra, and MTR_asym for Nic (Figs. 2A-C) and Glc (Figs. 2D-F) phantoms with varying concentrations. As a control, the PBS solution was used (black squares), and no CE-related R_1ρ dispersion or MTR_asym was observed. For Nic samples with slow-exchanging amide protons, the R_1ρ dispersion is very small in the whole ω_{1, SL} range (Fig. 2A). In contrast, the CEST effect is apparent at the left side of the Z-spectra, where the MR signal dips at 3.4 ppm, more significantly with increasing Nic concentration (Fig. 2B). The spectra on the right side with negative frequency offset are independent of Nic concentration and overlap well with PBS, indicating minimal chemical exchanging effects. MTR_asym spectra had an increasing peak at 3.4 ppm with concentration (Fig. 2C) but was not symmetric around the peak. There is a plateau region in the 0.5–2 ppm range (arrow), which was also reported in a previous CEST study for amide protons (26).

Fig. 2.

On-resonance R_1ρ dispersion, CEST Z-spectra, and the MTR_asym lineshapes for Nico (A-C) and Glc (D-F) samples with varied concentrations in PBS. The data of a pure PBS sample are also shown for comparison (black data points). For Nic with slow-exchanging amide protons, the R_1ρ dispersion is small (A), but the CEST contrast is significant (B), and a well-defined MTR_asym peak appears at around 3.4 ppm for all concentrations (C). A plateau is observed in MTR_asym in the frequency offset range of 0.5 ppm to 2 ppm (black arrow). For Glc with faster-exchanging hydroxyl protons, the R_1ρ dispersion is large and increases linearly with Glc concentration (D). The CEST Z-spectra (E) appear much broader compared to the Nic samples. The MTR_asym peak offset shifts, and the peak magnitude shows a non-linear dependence with concentration (F).

Unlike Nic, Glc samples with a faster exchanging hydroxyl group show large R_1ρ dispersions, where R_1ρ decreases with the SL frequency ω_{1, SL} (Fig. 2D). R_1ρ at each SL frequency increases almost linearly with Glc concentration. The signal drops in the CEST Z-spectra become very broad, and the exchange effect extends to negative frequency offsets, where the signals of Glc samples are much lower as compared to PBS (Fig. 2E). Since the exchanging effect presents on both sides of the water resonance, some CEST contrast would be sacrificed when two MTR signals of opposite frequency offset are subtracted for MTR_asym. The peak of MTR_asym spectra shifts towards a larger frequency offset with increasing Glc concentration (Fig. 2F).

In same metabolite phantoms with different concentrations, we expect a linear increase in p_B with concentration but a constant k_ex. Since large on-resonance R_1ρ dispersions were only observed in the Glc samples, p_B, k_ex, and R₂ of glucose were obtained by fitting R_1ρ dispersion data to Eq. [6] with a fixed δ of 1.2 ppm (3016 rad/s) for glucose hydroxyl groups (see Fig. 3A-C). The fitted p_B is proportional to Glc concentration (r²=0.9994) (Fig. 3A). The fitted k_ex and R₂ increase slightly with Glc concentration, probably due to the simplification of using a single chemical shift in our data fitting (Fig. 3B-C). It has been reported in a recent CEST study that the OH groups of Glc have three chemical exchange peaks with different frequency offsets (1 to 3 ppm from water) (9). Note that the measured R₁ is almost independent of the Glc concentration (Fig. 3C). For Glc samples in the intermediate-exchanging regime, the peak intensity of MTR_asym at 1.1 ppm does not monotonically increase with concentration (Fig. 3D). In contrast, for Nic samples in the slow-exchanging regime, the peak magnitude of MTR_asym at 3.4 ppm increases with concentration in a nearly linear manner.

Fig. 3.

(A-C) Fitted results of the on-resonance R_1ρ dispersion data as a function of Glc concentration, assuming δ = 1.2 ppm (3016 rad/s). The fitted p_B is proportional to the Glc concentraion (A). Fitted k_ex (B) and R₂ (C) increase with concentration, whereas the measured R₁ only increases weakly with concentration (C). (D) For Nic and Glc, the MTR_asym peaks, obtained at 3.4 ppm for Nic and 1.1 ppm for Glc, were normalized. MTR_asym does not increase linearly with metabolite concentrations, especially for Glc.

Experiment II: SL and CEST at varying chemical exchange rate by changing pH

The chemical exchange rate between amine (−NH₂) protons and water was systematically varied by changing pH values in 50-mM Glu samples. At lower pH, a slower exchange rate between two proton pools is expected. Significant on-resonance R_1ρ dispersion was observed for samples with intermediate pH values (5.9 ≤ pH ≤ 7.9); the R_1ρ dispersion peaked at a pH of ∼7.4 but was small for both very high and low pH values (Fig. 4A-B). The half widths of R_1ρ dispersion decreased with pH values (arrows in Fig. 4A-B). In the CEST experiments, the Z-spectra of Glu samples with pH = 9.1 and 9.8 were narrow and symmetric around the water frequency (Ω = 0) (Fig. 4C), similar to the PBS data in Fig. 2E. When pH decreased, Z-spectra became broader initially, increased the asymmetry around the water frequency (pH = 8.4 − 7.4, Fig. 4C), and then had an increased dip at 3.0 ppm (Fig. 4D). MTR_asym spectra were broad at pH = 7.4 and 6.9, and its peak shifted to 3.0 ppm for pH ≤ 6.4. The shapes of the MTR_asym spectra were similar for pH ≤ 5.2 but not symmetric around the 3-ppm peak (Fig. 4E-F).

Fig. 4.

On-resonance R_1ρ dispersion (A and B), CEST Z-spectra (C and D), and MTR_asym lineshapes (E and F) for 50-mM Glu samples with varied pH. R_1ρ dispersion is large for intermediate pH values but small for very high or low pH. The half width of the R_1ρ dispersion decreases with pH (circles and arrows). The CEST Z-spectra are narrow and symmetric for high pH values (9.1 and 9.8); becomes broad and increasingly asymmetric for intermediate pH values; and shows a sharp dip at 3.0 ppm for low pH values. For pH ≤ 5.9, the MTR_asym peaks at 3.0 ppm and the peak magnitude only reduces slightly with pH. For higher pHs, MTR_asym lineshape becomes broad and the peak shifts to a smaller frequency offset and decreases in magnitude.

Fig. 5A shows the k_ex of Glu with pH ≤ 8.4, determined by fitting on-resonance R_1ρ dispersions with a p_B of 0.00135 ± 0.0001 (n = 3), obtained from pH = 6.9, 7.4, and 7.9 data. As expected in a base-catalyzed exchange process, k_ex decreases with pH, similar to recent CEST measurements of amide protons (26). Given a δ of 3 ppm (7540 rad/s), pH = 6.4 to 7.9 samples can be roughly ascribed to the intermediate-exchange regime, whereas samples with pH ≤ 5.9 and pH ≥ 8.4 are in the slow- and fast-exchange regimes, respectively. These results indicate that on-resonance R_1ρ dispersion is most sensitive to the intermediate-exchange regime but much less to fast and slow exchanges (see Fig. 4A and 4B). In contrast, CEST with a relatively low ω_{1, CEST} is sensitive to slow to intermediate exchanges but more to slow exchanges (see Fig. 4C and 4D).

Fig. 5.

(A) Fitted k_ex as a function of pH for 50-mM Glu samples, assuming δ = 7540 rad/s (3 ppm). (B) For Glu samples with varying pHs, the MTR_asym at frequency offset of 3 ppm is plotted as a function of the fitted k_ex, which shows a peak around k_ex / δ ∼ 0.1 at the slow-exchange regime. The peak k_ex is ∼1100 s^-1 and matches with the frequency of the applied saturation power (1100 rad/s). (C and D) Simulation of on- and off-resonance (R_1ρ/p_Bδ) as a function of k_ex/δ for selected ω_{1, SL}/δ values, assuming δ = 3 ppm, p_B = 0.0014, R₁ = 0.35 s^-1, and R₂ = 0.5 s^-1. On-resonance R_1ρ can only be tuned to the intermediate chemical exchange process with a small ω_{1, SL} and a faster exchange with a higher ω_{1, SL} (C). In contrast, off-resonance (Ω = δ) R_1ρ can be tuned to slow, intermediate, and fast exchanges with small, intermediate, and large ω_{1, SL} values, respectively (D).

The k_ex values obtained from on-resonance SL were plotted against the MTR_asym of 3 ppm (Fig. 5B). MTR_asym is maximal at a k_ex/δ of ∼0.1 (in the slow exchange regime) and at a k_ex of ∼1100 s^-1 (pH = 5.9), which matches well with the Rabi frequency of the applied saturation pulse ω_{1, CEST} (∼1100 rad/s). To compare the characteristics of on- and off-resonance SL, R_1ρ on the resonance of water (Ω = 0) and labile proton (Ω = δ) were simulated as a function of k_ex/δ at a few selected ω_{1, SL} (Fig. 5C and 5D), with assumptions of R₁ = 0.35 s^-1, R₂ = 0.5 s^-1, δ = 3.0 ppm, and p_B = 0.0014. Although different parameters can change R_1ρ values, the features of R_1ρ vs. k_ex/δ curves remain. Note that R_1ρ and ω_{1, SL} were scaled by p_Bδ and δ, respectively. For on-resonance SL (Fig. 5C), the R_1ρ peak starts from the intermediate-exchange regime for very small ω_{1, SL} and shifts to faster exchanges with increasing ω_{1, SL}. Thus, on-resonance SL is less sensitive to slow chemical exchanges as compared to intermediate exchanges. For off-resonance SL with Ω = δ (Fig. 5D), R_1ρ can be made to be sensitive to different k_ex values by variation of ω_{1, SL}, and the peaks appear at k_ex = ω_{1, SL}. The maximum R_1ρ is reached at an intermediate exchange domain with an intermediate SL frequency (ω_{1, SL} = k_ex = δ). This simulation can be understood as a tuning of R_1ρ to certain k_ex values when there is a wide distribution of k_ex values. In contrast to on-resonance SL, off-resonance R_1ρ with a small ω_{1, SL} can be tuned to slow exchanges, where a faster CE contribution is suppressed. For example, for our Glu data with ω_{1, SL} = 1100 rad/s (which were obtained from Glu with a pH of 5.9), δ = 3 ppm (7540 rad/s), and ω_{1, SL}/δ = 0.14, the peak of the R_1ρ curve (solid black) appears at k_ex/δ ∼ 0.14 in the slow-exchange regime.

Experiment III: Similarity of SL and CEST Z-spectra

The SL Z-spectra (solid lines in Fig. 6A and D) of the Nic, Glc, and PBS samples were compared with the corresponding CEST Z-spectra (dashed lines). These two spectra match very well except at small frequency offsets (see Insets). SLR at a given offset is always higher than MTR. For example, for Nic at pH = 7.4 (6A) and PBS (6D), 7% and 13% of the MR signal remained after a 4-s on-resonance SL pulse (Ω = 0), respectively, while the CEST signals were zero due to the direct water saturation effect. The MTR_asym and the SLR_asym spectra (Figs. 6B and 6E) also show high similarity. The difference between MTR_asym and SLR_asym spectra close to 0 ppm was small, indicating that the subtraction of MTR between opposite offset frequencies is indeed an effective approach to cancel the majority of the spillover effect in CEST Z-spectra. In the SLR_asym and MTR_asym of Nic samples, there is a shift of the peak from 3.4 ppm to 2.6 ppm (arrows) with increasing pH from 7.8 to 8.4. In both the SLR_asym and MTR_asym spectra of the Glc samples, more than one −OH peak can be discerned (for pH = 5.6, arrows), similar to a previous report (9). To compare with off-resonance SL and CEST data, on-resonance R_1ρ dispersions were plotted in Figs. 6C and 6F. The R_1ρ dispersion in Nic and Glc increases significantly with pH due to an increase of k_ex from slow- to intermediate-exchange regimes.

Fig. 6.

SL Z-spectra (solid) and CEST Z-spectra (dashed), the SLR_asym (solid) and MTR_asym (dashed) lineshapes, and on-resonance R_1ρ dispersions for Nic (A-C) and Glc (D-F) samples with varied pH in PBS. SL and CEST spectra match well for large frequency offsets, and a small difference is observed when close to the water resonance (A and D). Insets: the enlarged SL and CEST Z-spectra show that the CEST signals are smaller than those of SL due to direct water saturation. SLR_asym and MTR_asym also match well for all samples (B and E), and more than one peak is detected for both Nic and Glc (arrows). On-resonance R_1ρ dispersions of both Nic and Glc are very sensitive to pH (C and F).

Simulated SLR_asym spectra vs. experimental MTR_asym spectra

The similarity in the SL and CEST Z-spectra suggests that the experimental CEST data may be explained by Trott and Palmer's SL model. SLR_asym values (lines) were simulated with the parameters obtained from on-resonance R_1ρ dispersions for Glu and Glc (Fig. 7A and 7B) or assumed values for Nic (Fig. 7C) and compared with experimental CEST MTR_asym data (data points). The Nic on-resonance R_1ρ dispersion data cannot be fitted robustly due to its low sensitivity (see Fig. 2A). Overall, the match between simulated SLR_asym and experimental MTR_asym is very good, indicating that the CEST Z-spectra can be explained by the SL model.

Fig. 7.

Simulated SLR_asym spectra (line) are compared with the experimental MTR_asym (squares) for 50-mM Glu samples with varied pH (A) and for Glc (B) and Nic (C) samples with varied concentrations. In (A) and (B), the parameters used for the simulation of SLR_asym were obtained by the fitting of on-resonance R_1ρ dispersion. In (C), k_ex of 100 s^-1 and δ_B of 3.4 ppm (8545 rad/s) were assumed for Nic samples.

Effective R_ex obtained from CEST Z-spectra

On-resonance R_1ρ dispersion provides one way of characterizing the chemical exchange process that is well suited for the intermediate-exchange regime. However, it is difficult to apply to a slow-exchange regime because of reduced sensitivity, and it is also difficult to distinguish from multiple exchanging sites with different chemical shifts. Alternatively, R_ex can be obtained from SL Z-spectra (Eq. [11]) or CEST Z-spectra (Eq. [12]). Unlike CEST Z-spectra (see Fig. 4C-D), the R_{ex, CEST} of Glu samples with varied pH showed a peak at 3 ppm (Fig. 8A). The data close to water resonance were not reliable because of the direct water saturation effect and thus were excluded. The broadening of the R_{ex, CEST} curve is sensitive to exchange rates; the FWHM of the Lorentzian shape is highly correlated with $\sqrt{{\omega }_{1,\mathit{\text{CEST}}}^2+k_{\mathit{\text{ex}}}^2}$(Fig. 8B), where k_ex is the fitted exchange rate from on-resonance R_1ρ dispersion data (Fig. 5A) and the applied ω_{1, CEST} = 1100 rad/s. This indicates that k_ex can be obtained from CEST Z-spectra (more accurately R_{ex, CEST}).

Fig. 8.

(A) Effective R_{ex, CEST}, defined in Eq. [12], was calculated from the CEST Z-spectra of 50-mM Glu samples with pH between 3.1 and 7.4. The linewidth of R_{ex, CEST} decreases with pH, and the peak of R_{ex, CEST} is reached for the pH = 5.9 sample. The data at frequency offsets close to zero were excluded because of the direct water saturation effect. (B) The linewidths of R_{ex, CEST} in (A) were fairly close to those fit from the on-resonance R_1ρ dispersion data. Effective R_{ex, CEST} was also calculated for Nic (C) and Glc (D) samples with four concentrations. The peak of R_{ex, CEST} increases linearly with metabolite concentration (E).

When the linewidth of R_{ex, CEST} is constant (i.e., k_ex constant), the peak amplitude of R_ex is proportional to the labile proton population. Fig. 8C-D shows the R_{ex, CEST} converted from Nic and Glc CEST Z-spectra data with four concentrations (see Fig. 2B and 2E). Although R₂ has not been calculated for Nic samples, on-resonance R_ex is minimal when ω_{1, SL} ≫ δ and p_Bk_ex <1 s^-1 (see Eq. 5 and Fig. 7C). Therefore, R₂ can be approximated well with the measured R_1ρ at a large ω_{1, SL}. The averaged R_1ρ is 0.48 ± 0.02 s^-1 (n = 4) at ω_{1, SL} = 25120 rad/s (Fig. 2A), so we used R₂ = 0.5 s^-1 for simplicity. The R_{ex, CEST} values of Nic and Glc show a peak at 3.4 ppm and 1.1 ppm, respectively. The peak magnitude of R_{ex, CEST} increases with concentration almost linearly for both Nic and Glc (Fig. 8E). The averaged FWHM of R_{ex, CEST} for the four Glc is 4272 ± 628 s^-1, and consequently, k_ex is estimated to be 4147 s^-1 for a ω_{1, CEST} of 1100 rad/s, slightly smaller than k_ex = 4680 ± 390 s^-1 (n = 4, from Fig. 3B) obtained from the on-resonance R_1ρ dispersion data. Nic samples give an averaged R_{ex, CEST} FWHM of 1156 ± 125 s^-1, which is not much larger than the applied ω_{1, CEST}, indicating that k_ex is very small. To accurately determine slow k_ex, it is necessary to use a small ω_{1, CEST}, similar to or less than k_ex.

Discussion

Both on- and off-resonance SL approaches can be applied to studies of chemical exchange. While on- and off-resonance SL is sensitive to intermediate exchanges, off-resonance SL can also be tuned to slow exchanges by adjusting ω_{1, SL} (Fig. 5C and 5D). At high magnetic fields, such as 9.4 T, the on-resonance SL is more sensitive to hydroxyl and amine proton exchanges than amide protons, whereas off-resonance SL experiments with a low irradiation power are more sensitive to amide protons. Hence, the parameters of the SL technique, such as the SL pulse power and SL frequency offset, can be adjusted to provide optimal contrast and probe information of the tissue microenvironment for specific applications. When multiple exchangeable protons exist, such as in vivo, it would be difficult to determine the source of a CE contrast in on-resonance SL. Off-resonance SL experiments may be selective to certain types of exchanging protons within the slow-exchange domain, such as the amide protons, by locking the water magnetization on that specific Larmor frequency. However, the interpretation of the observed CE contrast should remain cautious, because other intermediate- or fast-exchanging protons (even if with a different Larmor frequency) can still contribute, due to their broad R_ex spectrum.

Since off-resonance SL is similar to CEST, CEST spectra can be used to measure slow- to intermediate-exchange processes and can be explain approximately with the SL theoretical model. This is plausible, because both techniques measure the same chemical exchange phenomena, with slightly different experimental approaches (Fig. 1A). During the long off-resonance RF pulse common to both approaches, the water magnetization experiences an effective B₁, tilted at an angle θ = arctan(ω₁ / Ω) from the B₀ direction. With the SL technique, water magnetization is first flipped to and then locked to the B_{1, eff} direction. In a CEST experiment, without the initial flip, the magnetization along the B_{1, eff} direction relaxes with a time constant T_1ρ, and the component perpendicular to the B_{1, eff} oscillates and decays with a time constant T_2ρ (27). Thus, a CEST experiment can be considered an off-resonance SL with imperfect spin-locking: the water spins are pseudo-locked to B_{1, eff}, precessing on the surface of a cone with a half angle of θ (Fig. 1D). Such a pseudo-SL can be a good approximation as long as θ is very small; i.e., ω_{1, CEST} ≪ Ω. Thus, to study the chemical exchange effects, the SL technique is more versatile and can be applied to a frequency offset close to water and also for on-resonance cases.

SL and CEST results of simple metabolite phantoms can be explained well using Trott and Palmer's AP model. Previous SL models mostly assumed a fast exchange limit hence could not be applied to slower-exchanging protons. The exchange-related relaxation rate under fast exchange approximation is (24):

$$R_{ex}(\Omega ,{\omega }_{1,SL})=\frac{p_B\cdot {\delta }^2\cdot k_{ex}}{{\Omega }^2+{\omega }_{1,SL}^2+k_{ex}^2},$$ [13]

Thus, p_B and δ cannot be determined separately, so the application is further limited. One simplification taken in Trott and Palmer's model is to use population-averaged values of R₁ and R₂ for protons of the two exchanging sites and ignore their differences, which may affect the accuracy in the estimation of k_ex and p_B if such differences are significant. Nevertheless, this SL model is quite useful and can be applied to slow-, intermediate-, and fast-exchanging regimes, enabling quantification of CE parameters. The AP model is also compatible with current CEST models. For example, if the SL pulse is applied on the labile proton (Ω = δ), under the conditions k_ex≪ ω_{1, SL} and R₂ ≪ R_ex, the steady state solution equation [9] can be simplified to:

$$\frac{M(\Omega ={\delta }_B)}{M_0}=\frac{1}{1+p_B\cdot k_{ex}\cdot T_1}$$ [14]

which is equivalent to the steady state solution obtained from the CEST experiment (Eq. 23 in (28)). From Eq. [9], one can also find that

$$\frac{M_0}{M_{\mathit{\text{offset}}}}-1=\frac{R_2+R_{\mathit{\text{ex}}}}{R_1}\cdot \frac{{\omega }_1^2}{{\Omega }^2},$$ [15]

If the SL pulse is applied on the labile proton and under the assumption R₂ ≪ R_ex, the equation above can be converted to

$$\frac{M_{\mathit{\text{offset}}}}{M_0-M_{\mathit{\text{offset}}}}=\frac{R_1{k}_{\mathit{\text{ex}}}}{p_B}\cdot \left(\frac{1}{k_{\mathit{\text{ex}}}^2}+\frac{1}{{\omega }_1^2}\right),$$ [16]

which is identical to the omega-plot equation derived by Dixon et al. (29).

To quantify the concentration of labile non-water protons or the pH of a tissue microenvironment in conventional CEST approaches, McMahon et al. (26) and Sun (30) performed CEST experiments with several different ω_{1, CEST} values and fit the experimental results to the CEST model with a number of assumed parameters. McMahon et al. (26) also proposed to measure the MTR as a function of saturation time and fit to theoretical models. Dixon et al. proposed another method to measure the exchange rate and labile proton population. From Eq. [16], a plot of M_offset / (M₀ − M_offset) at a labile proton frequency vs. $1/{\mathit{\omega }}_1^2$ gives the k_ex for the X-intercept and the product of k_ex and p_B for the slope. The frequency offset of the targeted labile proton should be known in all these methods.

Our results show that the effective relaxation rate R_{ex, CEST}(Ω), converted from the CEST Z-spectra data, is well suited for the characterization of chemical exchanges in slow and intermediate regimes. Because a complete Z-spectrum is used for data fitting, a priori knowledge of frequency offset of the labile proton is unnecessary. R_{ex, CEST} is proportional to the labile proton population in both slow- and intermediate-exchange regimes, and R_{ex, CEST} peak intensity increases with labile proton concentration. The linewidth of R_{ex, CEST} is closely related to exchange rates and, consequently, pH. Note that for in vivo applications, confounding effects such as magnetization transfer effects from large solid-like macromolecules, also affect the Z-spectra; hence, the extraction and analysis of R_ex become much more complicated.

The asymmetrical MTR analysis from the CEST Z-spectra provides a convenient measure of chemical exchange contrast and has been proven to be successful in the slow-exchange regime, but it should be noted that MTR_asym is not a monotonic function of k_ex or pH; for example, it can increase or decrease with k_ex depending on the choice of saturation pulse power. Under our condition, MTR_asym peaks at k_ex = ω_{1, CEST}; therefore with decreasing k_ex; MTR_asym will decrease for k_ex < ω_{1, CEST} but increase for k_ex > ω_{1, CEST}. Thus, the saturation pulse power should be carefully chosen if MTR_asym is used as a biomarker to detect in vivo pH changes. A similar issue has also been pointed out in a previous CEST study with numerical simulations (26). In the intermediate-exchange regime, the interpretation of MTR_asym is highly complicated. i) The peak offset of MTR_asym shifts with varying labile proton concentrations and pHs, making it hard to interpret the data. ii) Because MTR_asym is essentially a measure of imaging contrast, it cannot be higher than 100% (9). With increasing concentrations of labile protons, MTR_asym does not increase linearly in the slow-exchange regime, but this problem becomes more severe in the intermediate-exchange regime, where it can even decrease at small frequency offsets. iii) If the CEST Z-spectrum is broad and the CE contrast extends to negative offset frequencies beyond the water resonance frequency (see Fig. 2E), the subtraction method for the MTR_asym may lead to a significant loss of sensitivity, especially at smaller frequency offsets (see Fig 2E vs. 2F).

One difficulty of in vivo applications of endogenous chemical exchange contrast is its limited sensitivity. The reported MTR_asym of amide proton transfer at 3.5 ppm is about 2% for 1.5 T and 4% for 3 T (5,31). To enhance the chemical exchange sensitivity, a larger exchange rate, a larger difference in the Lamor frequencies of exchanging protons, and a higher magnetic field are favorable. Based on our results, 1 mM glucose and glutamate can contribute up to an on-resonance R_1ρ of 0.07 and ∼0.1 s^-1, repesctively. With an SL B₁ of a few hundred Hz and a continuous wave spin-locking pulse length of 50 ms (close to the the T_1ρ of brain cortical tissue at 9.4 T (25,32)), this relaxation rate would translate to a signal change of 0.35-0.5%, which could be well detectable by many in vivo experiments.

Conclusions

To compare the characteristics of on- and off-resonance SL and CEST experiments, metabolite phantoms were studied in the slow-, intermediate-, and fast-exchanging regimes and with varied concentrations. The off-resonance SL approach exhibits similar results as the CEST experiment when the direct water saturation effect is small. On-resonance SL is mostly sensitive to intermediate proton exchanges, whereas off-resonance SL and CEST experiments can be tuned to slow-exchanging protons using a low-power SL or saturation pulse. SL and CEST data can be explained well using Trott and Palmer's model with asymmetric population approximation. From the CEST Z-spectra, an effective exchange relaxation rate, R_ex, can be constructed and can be used to quantitatively characterize the chemical exchanging process. The conventional parameter MTR_asym provides an easy measure of chemical exchange contrast, but unlike R_ex, it is not a monotonic function of exchange rate (and pH); its application in the intermediate-exchange regime becomes problematic.