Quantitative chemical exchange sensitive MRI using irradiation with toggling inversion preparation (iTIP)

Abstract

Chemical exchange (CE) sensitive MRI contrast acquired with an off-resonance irradiation pulse is affected by other relaxation mechanisms, such as longitudinal and transverse relaxations. In particular, for intermediate chemical exchanges, the effect of transverse relaxation often dominates CE contrast. Since water relaxation rates can change significantly in many pathological conditions or during physiological challenge, it is crucial to separate these relaxation effects in order to obtain pure CE contrast. Here we proposed a novel acquisition scheme in which a toggling inversion pulse is applied prior to the off-resonance irradiation. By combined acquisition of irradiation images with and without an inversion pulse at both the labile proton frequency and the reference frequency, longitudinal and transverse relaxation contributions are cancelled; and the quantification of CE parameters, such as the exchange rate and the labile proton concentration, can be simplified. Furthermore, the CE mediated relaxation rate can be readily determined with a relatively short irradiation pulse and without approaching the steady state, therefore, reducing the limitations on hardware and specific absorption rate requirements. The signal characteristics of the proposed method are evaluated by numerical simulations and phantom experiments.

Introduction

Chemical exchange (CE) sensitive MRI provides valuable information on tissue pH and metabolite, protein and peptide concentrations; and has been applied to preclinical study of cartilage degeneration, stroke, and tumor (1–9). Previous CE-MRI methods mostly explore labile protons in the slow exchange regime, i.e. the exchange rate, k, between water and labile protons is much smaller than their chemical shift, δ(k/δ ≪ 1) (1,3,9–13). Recently, there are growing interests in the study of hydroxyl-water exchange (7,14,15) and amine-water exchange (16,17) processes, in which CE is close to the intermediate exchange (IMEX) regime (e.g., ~0.3 < k/δ < ~3). Compared to slow exchange cases, the IMEX contrast has very different properties and is more difficult to characterize. For example, the specificity of labile protons decrease with increasing k, and the optimal imaging contrast is often achieved at the transient state without a long irradiation pulse (16).

During an off-resonance irradiation pulse, the effective B₁ field in the rotating frame is tilted away from the Z-axis and, thus, the measured water signal is affected by both R₁ and R₂ relaxations (18,19). Specifically, with a relatively high irradiation pulse power (B₁) tuned to the IMEX process (16,20), as will be shown later, the CE contrast will be greatly affected by the R₂ relaxation, and also the magnetization transfer (MT) effect due to immobile macromolecules. Since water R₂ and/or R₁ may change significantly in many pathological conditions (2,16,21), it is critical to separate these relaxation effects from pure CE contrast. To simplify the quantification of CE, Sun recently proposed a ratiometric analysis approach that utilizes a long irradiation pulse to obtain steady state signals for purposes of normalization and separating R₁ and R₂ effects (22). One practical issue is that a long irradiation pulse of several seconds is often limited by MR hardware capability and specific absorption rate (SAR) restrictions, especially at high magnetic field strengths and large B₁ power levels needed for IMEX applications. Moreover, in these applications, the steady state signal can be very low and leads to quantification errors using ratiometric normalization.

In this study, we propose a novel acquisition method, dubbed irradiation with toggling inversion preparation (iTIP), to remove the R₁ and R₂ contributions in CE sensitive imaging, and to simplify the quantification of CE parameters. Numerical simulations and phantom experiments were performed to examine the signal characteristics and to validate our theoretical predictions.

Theory

Optimized irradiation time versus the steady state signal

When the populations of two exchangable proton pools are highly unequal, i. e. p_A ≫ p_B, where p_A and p_B are the relative populations of water and labile solute protons (p_A + p_B = 1), respectively, the relaxation rate R_1ρ can be expressed as (23):

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

where θ = arctan(ω₁/Ω),Ω is the frequency offset from water and ω₁ is the Rabi frequency (=γ·B₁) of the irradiation pulse. The exchange-mediated relaxation rate is

$$R_{ex}=\frac{p_A·p_B·{\delta }^2·k}{{(\delta -\mathrm{\Omega })}^2+{\omega }_1^2+k^2}\approx \frac{p_B·{\delta }^2·k}{{(\delta -\mathrm{\Omega })}^2+{\omega }_1^2+k^2},$$ [2]

assuming p_A≈ 1 and R₂ − R₁ ≪ k.

Fig. 1A shows the pulse sequence for the proposed iTIP approach, where a toggling inversion pulse is applied preceding an off-resonance spin-locking (SL) module. When the inversion pulse is toggled “off”, the 1^st radiofrequency (RF) pulse in an ideal SL experiment flips the water magnetization by an angle θ to the $B_{1,\text{eff}}(=2\pi \sqrt{{\mathrm{\Omega }}^2+{\omega }_1^2}/\gamma )$ direction, such that it will be “locked” during the subsequent irradiation pulse and will decay with the relaxation rate R_1ρ (Fig. 1B). In practice, the flip angle may not be accurate and is assumed to be a different angle, φ, here. Thus, the magnetization precesses around B_{1, eff} with an angle θ − φ (Fig. 1B), and the chemical exchange saturation transfer (CEST) acquisition scheme corresponds to the case of φ = 0 (24). In most circumstances, the component perpendicular to the B_{1, eff} direction dephases quickly due to inhomogeneities in B₁ and B₀ and can be ignored. After the spin-locking pulse with duration of TSL, the magnetization parallel to the B_{1, eff} direction (red arrow) is flipped back by the 2^nd φ-pulse for imaging (Fig. 1C). The normalized magnetization can be expressed as (16):

$$M_{SL}(\mathrm{\Omega })\equiv S(\mathrm{\Omega })/S_0=C^2·e^{-R_{1\rho }·\mathit{TSL}}+S_{SS}·C·(1-e^{-R_{1\rho }·\mathit{TSL}})$$ [3]

where the normalized steady state signal is S_SS = R₁ · cosθ/R_1ρ, C = cos(θ − φ) equals 1 for ideal SL and cosθ for CEST. The TSL value for optimized CE contrast can be derived from Eq. [3]. Assuming C = 1, we have (16)

Fig. 1. Pulse sequence and magnetization trajectories.

(A) Pulse sequence for the Irradiation with Toggling Inversion Preparation (iTIP) approach. A spin-locking (SL) module is applied following a toggling inversion pulse, indicated by a red dashed square. The super- and subscripts of an RF pulse denotes its phase and transmitter frequency, respectively. Water magnetization differs at the initial condition with inversion pulse toggled “off” (B–C) and “on” (D–E). In either case, the water magnetization is flipped by a φ pulse and then “locked” by an SL pulse with frequency offset Ω, a Rabi frequency of ω₁ and a spin-locking time (TSL). Consequently, the water magnetization (red arrow) precesses around B_1,eff by an angle (θ - φ), relaxes with time constant R_1ρ (B, D), and reaches the same steady state if TSL is sufficiently long. For finite TSL in the transient state, the magnetization is larger than the steady state in (C), whereas it is smaller than the steady state in (E). Following the SL pulse, the 2^ndφ pulse flips the magnetization (red arrow) back toward the Z-axis for imaging (green arrow). The image readout is EPI in this example, but can be replaced by other fast acquisition methods.

$${\mathit{TSL}}_{\mathit{optimal}}({\omega }_1)=\frac{1}{R_{1\rho }-R_{1}cos\theta }=\frac{T_{1\rho }}{(1-S_{SS})}$$ [4]

Note that the T_1ρ value is always between T₁ and T₂ (Eq. [1]). Thus, the CE contrast will be maximized at a long TSL if S_SS is high, i.e. a high steady state (HSS) condition, which is mostly seen with very small θ as in slow exchange applications, and at a short TSL if S_SS ≪ 1, i.e. a low steady state (LSS) condition, which often occurs for IMEX applications.

Magnetization and asymmetric analysis for the iTIP approach

In Eq. [3], M_SL(Ω) is dependent on R₁, R₂, R_ex as well as ω₁ and TSL, and it is difficult to separate R_ex from R₁ and R₂. In the iTIP approach, when the inversion pulse is toggled “on”, the water magnetization will still be “locked” by the B_{1, eff}, and will recover from the negative magnetization by the same R_1ρ to the same steady state (Fig. 1D). The normalized magnetization can be expressed as:

$$M_{\mathit{iSL}}(\mathrm{\Omega })=-\alpha ·C^2·e^{-R_{1\rho }·\mathit{TSL}}+S_{SS}·C·(1-e^{-R_{1\rho }·\mathit{TSL}}),$$ [5]

where α is the inversion efficiency that equals 1 for ideal inversion. The difference between the “on” and “off” preparation yields:

$$M_{\mathit{iTIP}}(\mathrm{\Omega })\equiv \frac{[M_{SL}(\mathrm{\Omega })-M_{\mathit{iSL}}(\mathrm{\Omega })]}{2}=\frac{(1+\alpha )}{2}·C^2·e^{-R_{1\rho }·\mathit{TSL}}$$ [6]

The difference is halved in Eq. [6] for sensitivity comparison with M_SL, because the number of acquired images is doubled in M_iTIP. The CE contrast is often assessed from the difference between M_SL measured at the labile proton frequency δ (label frequency) and at the reference frequency of −δ, which is referred to as the asymmetry analysis (20):

$${\mathit{SLR}}_{\mathit{asym}}(\mathrm{\Omega }=\delta )\equiv M_{SL}(-\delta )-M_{SL}(\delta )$$ [7]

Similarly, we have

$${\mathit{SLR}}_{\mathit{iTIP},\mathit{asym}}(\mathrm{\Omega }=\delta )\equiv M_{\mathit{iTIP}}(-\delta )-M_{\mathit{iTIP}}(\delta )$$ [8]

Beside the widely used absolute asymmetry defined by Eq. [7] (similar to MTR_asym, the magnetization transfer ratio asymmetry of CEST applications), several studies have adopted a relative asymmetry, where the differential signal is normalized by the signal at the reference frequency instead of S₀ (7,17,24,25):

$${\mathit{Rel}}_{\mathit{asym}}(\mathrm{\Omega }=\delta )\equiv \frac{M_{SL}(-\delta )-M_{SL}(\delta )}{M_{SL}(-\delta )}$$ [9]

Quantification of the exchange-mediated relaxation rate

R_1ρ can be obtained by a mono-exponential fitting of TSL in iTIP data using Eq. [6], or by fitting of regular SL data using Eq. [3]. To remove the R₁ and R₂ contribution, we subtract the R_1ρ of the reference frequency (−Ω) from the R_1ρ at a frequency offset of Ω:

$$\begin{array}{l}{R}_{1\rho ,\mathit{asym}}(\mathrm{\Omega })\equiv R_{1\rho }(\mathrm{\Omega })-R_{1\rho }(-\mathrm{\Omega })=\frac{1}{\mathit{TSL}}·ln\frac{M_{\mathit{iTIP}}(-\mathrm{\Omega })}{M_{\mathit{iTIP}}(\mathrm{\Omega })}\\ =[R_{ex}(\mathrm{\Omega })-R_{ex}(-\mathrm{\Omega })]·\frac{{\omega }^2}{{\omega }^2+{\mathrm{\Omega }}^2}\end{array}$$ [10]

From Eq. [10], the major advantage of the iTIP approach over the conventional SL approach is that R_{1ρ, asym} can be obtained from iTIP data with a single TSL measurement. When Ω = δ,

$$R_{1\rho ,\mathit{asym}}(\mathrm{\Omega }=\delta )=p_{B}k·\frac{1}{1+\frac{k^2}{{\omega }_1^2}}·\frac{1}{1+\frac{{\omega }_1^2}{{\delta }^2}}·\frac{1}{1+\frac{{\omega }_1^2+k^2}{4{\delta }^2}}$$ [11]

which is only dependent on the exchange parameters p_B and k and does not have R₁ and R₂ relaxation terms, and is also independent of the inversion efficiency α and the flip angle φ.

Materials and Methods

Numerical Simulations

Numerical simulations were performed in Matlab^® 7.0 using Bloch-McConnell Equations. A three-compartment exchange was simulated, where the water pool exchanges with a labile solute proton pool and an immobile proton pool, and the relative population for each compartment is P_w, P_S, and P_im (P_w + P_S + P_im = 1), respectively. Note that in the theory section only water and solute proton populations were considered, thus the relative population can be converted as p_A = P_w/(P_w+P_S), and p_B = P_S/(P_w+P_S). The MT effect between water and bound protons associated with immobile macromolecules was modeled as a super-Lorentzian function (26,27), and incorporated into the Bloch-McConnell Equations following the work of Li et al (10). Without loss of generality, we assumed a chemical shift between water and the labile protons of δ = 1 ppm (400 Hz or 2515 rad·s⁻¹ at 9.4 T), an exchange rate of k = 1250 s⁻¹ (i.e., k/δ = 0.5), and C = α = 1. Two irradiation pulse powers were chosen in the simulation to compare signal properties with HSS and LSS conditions. An HSS condition will be reached with ω₁ = 40 Hz and R₂ = 1 s⁻¹, and an LSS condition with ω₁ = 160 Hz and R₂ = 15 s⁻¹. To examine the signal characteristics of iTIP as a function of TSL, the M_SL, M_iSL, M_iTIP, SLR_asym, SLR_{iTIP, asym}, and Rel_asym were calculated for ω₁ = 160 Hz (1000 rad·s⁻¹). Due to the B₁-tuning effect, this pulse power would be most sensitive to CE rate around 1000 s⁻¹ (16). At each TSL, R_1ρ and R_{1ρ, asym} were calculated using Eq. [6] and [10], respectively. As a qualitative example, the R_1ρ and R_{1ρ, asym} dispersions with an ω₁ range of 10 to 800 Hz were also simulated for quantification of exchange parameters. All other parameters used in the simulation were listed in Table 1.

Table 1.

Parameters used in three-compartment simulation of Bloch-McConnell Equations

Description	Parameter	values
Water pool
Longitudinal relaxation rate	R1w	0.5 s−1 (0.8 s−1)
Transverse relaxation rate	R2w	15 s−1 (1 s−1, 4 s−1)
Relative population	Pw	1 – PS – Pim
Labile solute proton
Longitudinal relaxation rate	R1S	= R1w
Transverse relaxation rate	R2S	= R2w
Chemical shift from water	δS	1 ppm
Relative population	PS	0.003
Exchange rate with water	k	1250 s−1
Immobile proton
Longitudinal relaxation rate	R1, im	= R1w
Transverse relaxation rate	R2, im	10 μs*
Chemical shift from water	δim	0
Relative population	Pim	0 (0.05)
Exchange rate with water	kim	50 s−1*

Several values were varied (shown in parenthesis) to evaluate the effect of those parameters.

^*from reference (38).

MR experiments

All MR experiments were performed at room temperature on a 9.4 T Varian system. A 3.8-cm diameter volume coil (Rapid Biomedical, Ohio, USA) was used for excitation and reception. Magnetic field homogeneity was optimized by localized shimming over the volume of interest to yield a water spectral linewidth within 9–15 Hz. B₁ fields were mapped for calibration of the transmit power (28), B₀ maps were measured by gradient-echo echo-planar imaging (EPI) with multiple echo times, R₁ maps were measured by an inversion recovery sequence, and R₂ maps were measured by an on-resonance spin-locking sequence with ω₁ = 4000 Hz to suppress the chemical exchange contributions (16). MR images were acquired using the iTIP scheme (Fig. 1A). After the preparation pulses, images were collected by single-shot spin-echo EPI with a field of view of 40 mm × 40 mm, a slice thickness of 5 mm, matrix size of 64 × 64, and a post-imaging recovery time of 15 s. Control scans were acquired at Ω = 300 ppm for normalization of M_SL.

Three types of metabolite phantoms were imaged. Metabolite solutions were prepared and transferred into 9 mm I.D. cylinders and multiple cylinders were bundled together for iTIP imaging studies. To obtain M_iTIP maps, SL images with inversion preparation “off” and “on” were acquired sequentially. Three SL imaging studies were:

1. 50 mM myo-Inositol (Ins, cyclohexane-1,2,3,4,5,6-hexol, C₆H₁₂O₆) was dissolved in phosphate buffered saline (PBS) (pH = 7.4), and 0.025, 0.05, 0.075, and 0.1 mM MnCl₂ was added to modulate both R₁ and R₂. Ins has hydroxyl protons with a chemical shift of ~0.93 ppm from water and an exchange rate of about 1250 s⁻¹, thus k/δ≈ 0.53 and is in the IMEX regime (29). The iTIP images at Ω = 0.95 and −0.95 ppm were acquired with ω₁ = 100 Hz and 160 Hz, and TSL values from 0 to 4 s.

2. To modulate water R₂ and also introduce the magnetization transfer effect, 50 mM Ins was dissolved in PBS (pH = 7.4), and mixed in 0.5, 1, 2 and 3% agar. The mixtures were heated to 90–95°C in a water bath for 2–3 minutes, cooled down to 60°C and transferred to plastic cylinders to solidify. The iTIP images at Ω = 0.95 and −0.95 ppm were acquired with ω₁ = 100 Hz and 160 Hz, and TSL values from 0 to 1.5 s.

3. 50 mM Creatine (Cr, 2-(Methylguanidino)ethanoic acid, C₄H₉N₃O₂) was dissolved in PBS and titrated to pH = 7.4, 7.7, 8.05, and 8.4. Cr has exchangeable guanidine protons (i.e., NH₂ − C&#x0030D; = NH) at 1.9 ppm from the water resonance (30). These pH values were selected so that the exchange will be close to the IMEX regime. At lower pH values, the exchange between water and Cr guanidine protons is in the slow exchange domain, and has been thoroughly studied by Sun et al. using CEST models (22,31,32). The iTIP images were acquired at Ω = 1.9 and −1.9 ppm. Off-resonance R_1ρ dispersion was measured using twelve ω₁ values of approximately 85, 107, 135, 170, 214, 270, 340, 428, 540, 680, 857, and 1080 Hz. For each power level, iTIP images were acquired with twelve TSL values. Because R_1ρ increases with ω₁, the range of TSL varied accordingly, e. g. from 0 to 3 s for small ω₁ of 85 Hz and from 0 to 0.4 s for 1080 Hz. In addition, on-resonance R_1ρ dispersion was measured using ω₁ value of approximately 125, 177, 250, 353, 500, 707, 1000, 1414, 2000, 2828, and 4000 Hz.

Data analysis

To obtain M_iTIP, pair-wise subtraction between SL images with inversion pulse “on” and “off” were performed in k-space before the image reconstruction. R_1ρ maps were calculated from fitting of multi-TSL data to Eq. [6], and R_{1ρ, asym} maps were calculated from M_iTIP maps at each TSL using Eq. [10]. For quantitative analysis, a region of interest (ROI) with minimal B₀ heterogeneity (< 3 Hz) was selected from each sample. The R_{1ρ, asym} dispersion data were fitted to Eq. [11] to determine the chemical exchange parameters p_B and k. To fit the on-resonance R_1ρ dispersion data, Eqs. [1] and [2] were used with θ = 90°.

Results

M_SL versus M_iTIP

Fig. 2 shows the simulated iTIP signals for the HSS case (small ω₁ and R₂), and for the LSS case (large ω₁ and R₂). The HSS case (Fig. 2A–C) requires long irradiation of more than 5 s to approach the steady state for both the label (Fig. 2A, black) and reference frequencies (red), where the steady states are the same for SL with the inversion pulse “off” (solid lines) and “on” (dashed lines). In the LSS case (Fig. 2D–F), MR signals decay quickly with TSL and reaching the steady state much faster than the HSS case because of larger R_1ρ values (Fig. 2D). In both HSS and LSS cases, M_iTIP signals (shown in logarithms scale, Fig. 2B and 2E) are monoexponential functions of TSL, from which R_1ρ can be easily calculated. In the HSS condition (Fig. 2C), SLR_asym is maximized at TSL approaching the steady state, whereas SLR_{iTIP, asym} peaks at a shorter TSL and is much smaller than SLR_asym. In the LSS condition (Fig. 2F), the peaks of both SLR_asym and SLR_{iTIP, asym} are reached at short TSL values of ~ 0.35 s. SLR_{iTIP, asym} is still less than SLR_asym, but their difference is small.

Fig. 2. Simulated results of the iTIP approach.

Normalized magnetization (M_SL) with inversion pulse “off” and “on” (A, D), M_iTIP at the label and reference frequencies in the logarithmic scale (B, E), and asymmetrical spin-locking ratios, SLR_asym and SLR_{iTIP, asym} (C, F) were simulated as a function of TSL. A small irradiation pulse power and a small R₂ value lead to high steady state signals (left column), and a high pulse power and a large R₂ lead to low steady state signals (right column). Other parameters used were δ = 1 ppm (400Hz or 2515 rad·s⁻¹), labile proton concentration P_S = 0.003, R₁ = 0.5 s⁻¹, k = 1250 s⁻¹.

To compare simulation and experimental results, iTIP data of 50 mM Ins were obtained in 0.05 mM MnCl₂ (Fig. 3A–C) and in 2% agar (Fig. 3D–F). The former sample has smaller R₂ and no MT effect. Thus, the steady state signals for ω₁ = 100 Hz are relatively high and require a long irradiation pulse (Fig. 3A). The M_iTIP values decay monoexponentially with TSL, except for a few long TSL values with Ω = δ in which M_iTIP becomes very low and is dominated by noise (Fig. 3B). SLR_{iTIP, asym} is significantly smaller than SLR_asym (Fig. 3C), similar to the simulation results of the HSS condition in Fig. 2C. For the Ins in agar phantoms, the steady state signals for ω₁ = 160 Hz are very small due to large R₂ and MT effects (Fig. 3D). The imaging contrast is maximized with a short irradiation pulse for both SLR_{iTIP, asym} and SLR_asym, and the peak SLR_{iTIP, asym} is only slightly smaller (~15%) than that of SLR_asym (Fig. 3F), similar to the simulation results of the LSS condition in Fig. 2F.

Fig. 3. Experimental iTIP results of 50 mM myo-Inositol with high (A–C) and low steady state conditions (D–F).

The normalized signal was measured with anω₁ = 100 Hz irradiation pulse for Ins in PBS with 0.05 mM MnCl₂ (left column), and with a 160 Hz pulse for Ins in 2 % agar (right column). In both cases, magnetization with inversion “on” and “off” reached the same steady states, and M_iTIP decayed monoexponentially with TSL, except for a few data points when the M_iTIP becomes very low and dominated by noise (B). Similar to the simulated data in Figure 2, the left column data reached a high steady state and SLR_{iTIP, asym} was significantly smaller than SLR_asym for long TSL values (C), while the right column data reached a low steady state, and the peak SLR_{iTIP, asym} was only slightly smaller than the peak SLR_asym (F).

R_{1ρ, asym} is independent of R₁ and R₂

Computer simulations were performed to determine the effect of R₁, R₂, and P_im on CE contrast indices, for an ω₁ = 160 Hz pulse. SLR_asym, SLR_{iTIP, asym} and Rel_asym are all sensitive to R₁, R₂ and P_im except for short TSL values (Fig. 4A–4C). Specifically, in both SLR_asym and SLR_{iTIP, asym}, the optimal TSL values decrease significantly with increasing R₂ and P_im. The relative asymmetry (Fig. 4C) minimizes the dependence on R₁, R₂ and P_im for TSL < ~0.3 s, which is wider than the range for absolute asymmetry (TSL < 0.1 s, Fig. 4A), but not for larger TSL values. In contrast, R_{1ρ, asym} is not dependent on R₁, R₂ and TSL (Fig. 4D). Note that R_{1ρ, asym} was determined at every TSL value with Eq. [10]. The R_{1ρ, asym} for P_im = 0.05 is about 5% larger than that for P_im = 0, because for a two-site exchange in Eq. [2], p_B = P_S/(P_w+P_S) = P_S/(1−P_im) increases with P_im.

Fig. 4. Independence of R_{1ρ, asym} on R₁, R₂ and MT effects: simulations.

The TSL-dependent SLR_asym (A), SLR_{iTIP, asym} (B), Rel_asym (C), and R_{1ρ, asym} (D) were simulated for five R₁, R₂ and P_im combinations. Other parameters used were δ = 1 ppm, P_S = 0.003, ω₁ = 160 Hz, and k = 1250 s⁻¹. In (D), all four lines with P_im = 0 were overlapping and displayed with different thickness.

To experimentally demonstrate the insensitiveness of R₁ and R₂ to R_{1ρ, asym}, the R₁, R₂, SLR_asym Rel_asym, and R_{1ρ, asym} maps were obtained from 50 mM Ins in four different concentrations of MnCl₂ (upper row, Fig. 5) and agar (bottom row, Fig. 5). Both R₁ and R₂ increase with the MnCl₂ concentration, whereas R₂ and P_im increase with agar concentrations. For a short TSL of 0.25 s, the CE contrasts measured with SLR_asym and Rel_asym are relatively insensitive to changes in R₁, R₂ and P_im. At a longer TSL of 1.0 s, both SLR_asym and Rel_asym are dependent on R₁, R₂ as well as P_im, and are inversely correlated with R₂ and P_im. In contrast, for both TSL values, the dependence on R₁ and R₂ is removed in the R_{1ρ, asym} maps acquired using the iTIP approach. Whereas a small P_im dependence is expected for R_{1ρ, asym} from simulation, no significant contrast was observed among the samples, suggesting that the difference of P_im may be too small to be detectable in these agar samples. The insensitiveness of R_{1ρ, asym} on agar concentration also suggests that the exchange rate is not affected by the addition of MT effect in these phantoms.

Fig. 5. Independence of R_{1ρ, asym} on R₁, R₂ and MT effects: phantom experiments.

For 50mM Ins samples in PBS with MnCl₂ (upper row), both R₁ and R₂ are sensitive to the MnCl₂ concentration (denoted in the R₁ map). For 50 mM Ins in agar mixture (bottom row), only R₂ is sensitive to the agar concentration (denoted in the R₁ map), whereas R₁ is insensitive. SLR_asym and Rel_asym maps measured with an ω₁ = 160 Hz pulse are almost independent on MnCl₂ and agar concentrations for TSL = 0.25 s, but not for a longer TSL of 1.0 s. For all phantoms, the R_{1ρ, asym} map measured by the iTIP approach appear similar.

Quantification of exchange parameters using R_{1ρ, asym} dispersion

Exchange parameters p_B and k can be determined from R_{1ρ, asym} dispersion (R_{1ρ, asym}(Ω = δ) vs. ω₁ plot) with Eq. [11]. The simulated off-resonance R_1ρ dispersion increases with R₂ and P_im at both the label (Fig. 6A, black) and reference frequencies (red). However, the R_{1ρ, asym} eliminates these dependences and gives a dispersion which is only related to exchange parameters p_B and k (Fig. 6B).

Fig. 6. R_1ρ dispersions simulated at the label and the reference frequencies.

R_1ρ dispersions are highly dependent on R₂ and P_im (A). Such dependence can be removed in the R_{1ρ, asym} dispersion (B).

This approach is experimentally tested. The R_1ρ dispersions of Cr phantoms with four pH values were measured by the iTIP approach at both Ω = 1.9 and −1.9 ppm (Fig. 7A and 7B). R_{1ρ, asym} was calculated from R_1ρ of label and reference frequencies (Fig. 7C). The control PBS phantom has the same R_1ρ value for 1.9 and −1.9 ppm and was cancelled in the R_{1ρ, asym}, as expected. The exchange rate and labile proton population were obtained by fitting the R_{1ρ, asym} dispersions (Eq. [11]). For comparison, the on-resonance R_1ρ dispersions of these phantoms were obtained in order to calculate the exchange parameters (Fig. 7D). The two fitting procedures of R_{1ρ, asym} and on-resonance R_1ρ dispersions give similar results of the exchange rate, which increases with pH as expected for a base-catalyzed amine-water proton exchange (Fig. 7E). For on-resonance SL, p_B and k cannot be determined separately in the slow exchange regime (20), which is the case for the pH = 7.4 and 7.7 phantoms, so their p_B values were set to be same as the pH = 8.05 sample (indicated by the stars in Fig. 7F). The fitted p_B slightly increases with pH in the R_{1ρ, asym} results and also in the on-resonance R_1ρ dispersion of pH = 8.05 to 8.4. This may be due to the different exchange rates of ηNH₂ and εNH protons in Cr (33), leading to small errors in our calculations that assumed a single rate constant.

Fig. 7. Off- and on-resonance R_1ρ dispersion measurements of Creatine phantoms, and exchange parameter determinations.

Off-resonance R_1ρ dispersions were measured at 1.9 ppm (A) and −1.9 ppm (B) for PBS only and 50 mM Creatine in PBS with 4 different pH values (indicated in B). The R_{1ρ, asym} dispersion (C) was obtained from the difference of (A) and (B) which removes the R₁ and R₂ effects. The on-resonance R_1ρ dispersion increased with pH for these phantoms (D). The fitted results of k (E) and p_B (F) obtained from the dispersions show that R_{1ρ, asym} and on-resonance R_1ρ are in reasonable agreement. At low pH values (7.4 and 7.7), k and p_B cannot be determined separately from on-resonance R_1ρ dispersion, so their p_B was chosen to be the same as at pH = 8.05 (indicated by asterisks).

Discussion

The absolute asymmetry signal (SLR_asym or MTR_asym) has been widely used as a convenient indicator of CE contrast in the slow exchange regime. In the IMEX regime, however, SLR_asym is much more sensitive to other relaxation effects, thus it is no longer a good index for quantitative CE imaging. For instance, the SLR_asym obtained for an R₂ and MT effect similar to in vivo conditions can be more than 10 times smaller than that of an aqueous solution (cyan versus black curves for TSL > 0.8 s, Fig. 4a), and the optimal TSL that maximizes SLR_asym is much shorter for the former than the latter. Therefore, care should be exercised when comparing SLR_asym or MTR_asym measured under different conditions. In a previous study of IMEX metabolites including glutamate and glucose, we reported that the frequency offset of the SLR_asym peak shifts with pH as well as with labile proton concentrations (29). Although the relative asymmetry, as defined in Eq. [9], can alleviate some of these problems at short TSL values, our results of current and previous studies show that the asymmetry of exchange-mediate relaxation rate (R_{1ρ, asym} or R_{ex, asym}) would be most suitable for quantitative CE imaging in the IMEX regime.

Our proposed iTIP approach can simplify quantitative CE imaging in two ways. (1) Multi-TSL measurements with long TSL values approaching the steady state are necessary for accurate fitting of R_1ρ using Eq. [3] (or Eq. [5]). Using iTIP, M_iTIP is a mono-exponential function of R_1ρ that reduces the fitting parameters, so that R_1ρ can be determined more accurately and with shorter TSL. (2) The CE contrast acquired by an off-resonance irradiation is affected by R₁ and R₂. These relaxation effects are canceled out in R_{1ρ, asym}, which simplify the quantification of exchange parameters. In fact, R_{1ρ, asym} can be readily obtained from iTIP data at a single TSL value, and also without the necessity to acquire a control scan (300 ppm in this study) for normalization. This is clearly advantageous over conventional off-resonance irradiation approaches that require multiple TSL values because data acquisition time is greatly shortened.

Technically, the iTIP quantification of R_1ρ is independent of the flip angle in the SL preparation (Eq. [6]), and thus can be acquired with the conventional CEST scheme. It is also insensitive to inversion efficiency and theoretically can be acquired with a toggling saturation pulse or any two pulses with different initial magnetizations. While our simulation and phantom experiments mainly targeted IMEX process, the iTIP approach can also be applied to slow exchange applications. Because the iTIP contrast is greatly reduced at a long irradiation time (Fig. 2C and 3C), it would be best suitable for IMEX studies where the contrast is optimized at the transient state, or for slow exchange studies where a long irradiation pulse is unavailable because of hardware or SAR limitations.

Off-resonance irradiation with a preceding inversion preparation has been suggested or applied in MT and CEST studies (24,34–37). In MRI, Mangia et al. showed that the combination of MT-weighted images acquired with and without inversion preparation improves the quantification accuracy of MT rate (36). Vinogradov et al. applied an inversion pulse before irradiation of labile protons to obtain positive CEST imaging contrast, which was smaller in magnitude than conventional CEST that gives negative contrast (37). Indeed, our simulation and experimental results also showed that the CE contrast is reduced with the inversion preparation “on” for the HSS condition (Fig 2A and 3A), but the loss of iTIP contrast becomes very small for LSS cases.

Although both on-resonance R_1ρ and R_{1ρ, asym} are sensitive to the IMEX process, R_{1ρ, asym} can also be tuned to slow chemical exchange using low B₁, unlike on-resonance R_1ρ (20). On the other hand, the asymmetry analysis of R_{1ρ, asym} greatly reduces the sensitivity when the exchange rate is near the fast exchange regime (k ≫ δ, see Eq. [11]), for which on-resonance R_1ρ may be more sensitive. Besides this difference in sensitivity regimes, iTIP quantification of IMEX using R_{1ρ, asym} dispersion has a few advantages. For example, (1) R_{1ρ, asym} can be acquired selectively for a specific type or a certain group of labile protons in contrast to on-resonance R_1ρ, which has contributions from all relaxation pathways. (2) A lower ω₁ is necessary for quantification of exchange parameters because off-resonance irradiation increases the effective B₁ (see Fig. 7), which alleviates the burden on hardware and SAR limitations. (3) R_{1ρ, asym} dispersion (Eq. [11]) cancels the R₂ term and, therefore, has fewer fitting parameters. (4) As mentioned earlier, R_{1ρ, asym} can be obtained with a single TSL for each ω₁ value and, therefore, reduces the acquisition time.

Only one labile proton pool is considered in this proof-of-principle study. In vivo there are many different IMEX protons, and some of them are similar in frequency offset. Since the specificity of labile protons are inversely dependent on the linewidth of $R_{\text{ex}}(=\sqrt{{\omega }_1^2+k^2}$, from Eq. [2]), it would be very difficult to distinguish two populations of labile protons if the linewidths of R_ex for both species are comparable or larger than the chemical shifts between them. Due to this intrinsic limitation of off-resonance irradiation approaches, the in vivo quantification of IMEX may only be achieved for a group-average of labile protons with similar chemical shifts and exchange rates, e. g. amine- or hydroxyl-groups.

Similar to the problems encountered in CEST studies, in vivo quantification using R_{1ρ, asym} is also susceptible to B₀ and B₁ inhomogeneities as well as the intrinsic asymmetry of the MT effect from immobile macromolecules (38). Both variations in B₀ and B₁ will lead to error in the exchange-mediate relaxation rate (Eq. [1] and [2]), and the former will also cause error in the calculation of R_{1ρ, asym} and incomplete cancelation of R₁ and R₂. To alleviate the inhomogeneous B₀ problem, iTIP images may be acquired at multiple offsets around the label and reference frequencies for B₀ correction if a severe B₀ shift is present. Similarly, a B₁ calibration procedure may be performed to correct the R_{1ρ, asym} quantification error caused by B₁ inhomogeneity (39). Further simulations and modeling studies are necessary to evaluate the effect of MT asymmetry on R_{1ρ, asym} and its dispersion, and whether it can be minimized by adjusting irradiation parameters.

Conclusions

In the IMEX regime, CE contrast is greatly affected by other relaxation effects. With the proposed iTIP approach, R_{1ρ, asym} (or similarly, R_{ex, asym}), which removes the R₁ and R₂ relaxation effects, is readily determined, and the quantification of chemical exchange parameters can be simplified. In addition, the iTIP approach is insensitive to inversion efficiency and flip angle for SL, and does not rely on long irradiation pulses. Therefore, this novel acquisition method can be very useful for slow to intermediate exchange or high-field CE applications.