Quasi-steady-state chemical exchange saturation transfer (QUASS CEST) MRI analysis enables T₁ normalized CEST quantification - Insight into T₁ contribution to CEST measurement

Abstract

Chemical exchange saturation transfer (CEST) MRI depends not only on the labile proton concentration and exchange rate but also on relaxation rates, particularly T₁ relaxation time. However, T₁ normalization has shown to be not straightforward under non-steady-state conditions and in the presence of radiofrequency spillover effect. Our study aimed to test if the combined use of the new quasi-steady-state (QUASS) analysis and inverse CEST calculation facilitates T₁ normalization for improved CEST quantification. The CEST signal was simulated with Bloch-McConnell equations, and the apparent CEST, QUASS CEST, and the inverse CEST effects were calculated. T₁-normalized CEST effects were tested for their specificity to the underlying CEST system (i.e., labile proton ratio and exchange rate). CEST experiments were performed from a 9-vial phantom of independently varied concentrations of creatine (20, 40, and 60 mM) and manganese chloride (20, 30, and 40 μM) under a range of RF saturation amplitudes (0.5–4 μT) and durations (1–4 s). The simulation showed that while T₁ normalization of the apparent CEST effect was subject to noticeable T₁ contamination, the T₁-normalized inverse QUASS CEST effect had little T₁ dependence. The experimental data were analyzed using a multiple linear regression model, showing that T₁-normalized inverse QUASS analysis significantly depended on creatine concentration and saturation power (P<0.05), not on manganese chloride concentration and saturation duration, advantageous over other CEST indices. The QUASS CEST algorithm reconstructs the steadystate CEST effect, enabling T₁-normalized inverse CEST effect calculation for improved quantification of the underlying CEST system.

Graphical Abstract

1. Introduction

Chemical exchange saturation transfer (CEST) provides a sensitive mechanism for the detection of dilute labile protons, including amide [1–4], guanidinium [5–10], and hydroxyl [11, 12] protons. CEST MRI has also been applied to map microenvironment properties such as pH and mobile protein content in disorders of acute stroke [13–21], renal injury [22–26], and tumor [27–34]. It is worth noting that the CEST MRI effect reflects the balance between two competing processes: the water signal decrease due to its exchange with saturated labile protons and signal increase due to longitudinal relaxation recovery [35]. As such, the CEST effect depends not only on the labile proton ratio and exchange rate, often parameters of interest, but also on the bulk water T₁ relaxation [36–39]. However, the correction of T₁ contribution has been controversial in CEST imaging due to the complex multiple overlapping CEST, nuclear Overhauser enhancement (NOE), and magnetization transfer (MT) effects [40–42]. As such, a phantom study to systematically evaluate the complex phenomenon is necessary.

The inverse CEST analysis has been shown to compensate for the direct RF saturation effect, which provides improved quantification of the underlying CEST systems [43–45]. However, the CEST-weighted MRI effect approaches its steady state exponentially following the spin-lock relaxation rate, and rarely are experiments performed under fully relaxed and RF saturation steady-state [46–48]. For CEST MRI scans that do not use sufficiently long saturation time and relaxation delay, the CEST-weighted signal is highly dependent on the RF saturation time, relaxation delay, and T₁, complicating the downstream CEST quantification [49]. Indeed, studies showed that the T₁ normalization is complex, particularly so under the conditions of non-steady-state and in the presence of concomitant RF saturation effects [40–42]. A quasi-steady-state (QUASS) CEST MRI was recently developed that reconstructs the steady-state from experimental CEST scans under not sufficiently long saturation time [50, 51]. Although the QUASS CEST solution is valid for describing in vivo CEST MRI, additional work is needed to examine T₁ contribution [52]. Briefly, Zhang et al. showed that QUASS APT signal remains steady with respect to different saturation time (Ts) and relaxation delay (Td), with and without T₁ normalization. Yet, it provided no insights if the T₁ normalization is valid. Our study aimed to investigate the T1 contribution in CEST MRI systematically. In short, Bloch-McConnell simulation was performed with serially varied T₁, RF saturation power, and duration to test if T₁ normalized-CEST MRI indices provide a specific measurement of the underlying CEST system [53]. Experimentally, a 9-vial phantom with serially varied manganese chloride and creatine concentrations was used to test if T₁-normalized QUASS CEST MRI is specific to creatine concentration, independent of T₁ and RF saturation time. This study lays the foundation for future studies to investigate the in vivo CEST contrast mechanisms.

2. Theory

QUASS CEST MRI has been recently proposed to account for the finite saturation time and relaxation delay on the steady-state CEST MRI signal. Briefly, building on the spin-lock theorem [46, 47], the measurable CEST MRI signal can be described as [48]

$$\frac{I_{\mathit{\text{sat}}}^{\mathit{\text{app}}}(\Delta \omega )}{I_0^{\mathit{\text{app}}}}=\frac{\left(1-e^{-R_{1w}\cdot Td}\right)e^{-R_{1\rho }\cdot Ts}+\frac{R_{1w}}{R_{1\rho }}\mathit{\text{co}}{s}^2\theta \left(1-e^{-R_{1\rho }\cdot Ts}\right)}{1-e^{-R_{1w}\cdot (Ts+Td)}}$$ (1)

where ${\text{I}}_{\text{sat}}^{\text{app}}$ and ${\text{I}}_0^{\text{app}}$ are the saturated and unsaturated scans, respectively, obtained under a given set of Ts and Td. R_1w is the bulk water longitudinal relaxation rate, and $\theta =\mathit{\text{atan}}\left(\frac{\gamma B_1}{\Delta \omega }\right)$, where γ is the gyromagnetic ratio, B₁ and Δω are the amplitude and offset of the RF saturation with respect to the bulk water resonance. As the apparent CEST signal approaches its steady state monotonically, the spin-lock relaxation rate R_1ρ can be numerically solved from Eq. 1, provided that T_1w, Td, and Ts are known.

With R_1ρ solved, the QUASS CEST Z signal can be calculated as

$${\left(\frac{I_{\mathit{\text{sat}}}(\Delta \omega )}{I_0}\right)}^{\mathit{\text{QUASS}}}=\frac{R_{1w}}{R_{1\rho }}\mathit{\text{co}}{s}^2\theta$$ (2)

The inverse CEST asymmetry effect can be derived as

$$\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}},\mathit{\text{ QUASS}}}={\left(\frac{I_0}{I_{\mathit{\text{sat}}}(\Delta \omega )}\right)}^{\mathit{\text{app}},\mathit{\text{ QUASS}}}-{\left(\frac{I_0}{I_{\mathit{\text{sat}}}(-\Delta \omega )}\right)}^{\mathit{\text{app}},\mathit{\text{QUASS}}}$$ (3)

For the QUASS CEST effect, we have

$$\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}\approx \frac{f_r\cdot k_{sw}\cdot \alpha }{R_{1w}}\cdot \frac{1}{\mathit{\text{co}}{s}^2\theta }$$ (4)

in which α is the labeling efficiency, being $\frac{{\omega }_1^2}{{\omega }_1^2+k_{sw}\cdot \left(R_{2s}+k_{sw}\right)}$, where f_r and k_sw are the labile proton fraction ratio and exchange rate, respectively, and ω₁ = 2πγB₁. For B₁ amplitude substantially smaller than labile proton chemical shift, we have cos²θ ≈ 1. As such, the T₁-normalized inverse QUASS effect can be shown to be

$$R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}\approx f_r\cdot k_{sw}\cdot \alpha$$ (5)

, which depends on the labile proton ratio, exchange rate, and labeling efficiency.

3. Experiment

Simulation

CEST MRI was simulated for a typical CEST echo planar imaging (EPI) sequence using a classical 2-pool exchange model in MATLAB 2019a (Mathworks, Natick, MA) [54]. To simulate the T₁ effect on the CEST measurement, the bulk water T_1w was varied from 1 to 2 s with intervals of 0.1 s, with representative bulk water T_2w of 100 ms, and labile proton T_1s and T_2s of 1 s and 15 ms. Typical labile proton fraction ratio and exchange rate were simulated, being 1:1000 and 100 s⁻¹, respectively. The labile proton chemical shift was set at 1.9 ppm for the magnetic field strength of 7 T, and Z-spectra were simulated from −3 to 3 ppm with intervals of 0.05 ppm. For the simulation, we varied Ts and Td concurrently (i.e., Ts=Td) from 1 to 4 s in increments of 0.5 s, and RF saturation power B₁ from 0.5 to 4 μT with intervals of 0.5 μT. We calculated CESTR^app, $\mathit{\text{CEST}}R{}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$, CESTR^QUASS, and $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$ at 1.9 ppm and their corresponding T₁-normalized indices.

Phantom

We prepared a 9-vial phantom with serially varied manganese chloride (MnCl₂) and creatine (Cr) concentrations. Briefly, pH buffer solution at 6.86 was prepared by adding one pack of pH buffer powder (KD Tech, Shenzhen, China), ordered from Amazon, to 250 ml deionized water. MnCl₂ was added to buffer solution at concentrations of 20, 30, and 40 μM (i.e., [MnCl₂]). Creatine was then added to each MnCl₂ solution at concentrations of 20, 40, and 60 mM (i.e., [Cr]). pH was found to be 6.86 after MRI experiments. The mixed solution was transferred into 9 NMR tubes and inserted into a phantom holder, filled with 1% agarose gel (Supplementary Figure 1). The phantom solidified overnight before the imaging experiment.

MRI

MRI experiments were conducted using a 7 T Bruker MRI scanner (Bruker Biospec, Ettlingen, Germany) with a volume RF transceiver (ID=72 mm) at room temperature. We used single-shot spin echo EPI readout (slice thickness = 5 mm, a field of view (FOV) = 48 × 48 mm, image matrix = 96 × 96, bandwidth = 247 kHz with its echo time (TE) being 43 ms). The CEST experiments had two dummy scans and 2 signal averages. The label and reference saturation offsets were set at ±1.9 ppm from that of the bulk water resonance. The RF saturation power was varied from 0.5, 1, 1.5, 2, 3 to 4 μT, and for each B₁ amplitude, the Td and Ts were varied together from 1, 1.5, 2, 3, and 4 s. We maintained Td=Ts, so the overall RF duty cycle is 50%. The B₀ field inhomogeneity was determined with water saturation referencing (WASSR) MRI [55] between ± 0.2 ppm with intervals of 0.025 ppm (B₁ = 0.5 μT, Td/Ts=1.5/0.5 s, and scan time = 36 s). The B₁ field inhomogeneity was mapped by varying the flip angle (FA) of a pre-saturation pulse before the EPI, from 10° to 250° with intervals of 10° (repetition time (TR) /TE =10 s /46 ms, and scan time = 4 min 10 s). T₁–weighted inversion recovery images were acquired with 6 inversion times ranging from 100 to 3000 ms (relaxation delay/TE =7.5 s/43 ms, 2 averages, and scan time = 2 min 23 s).

Data Analysis

The bulk water T_1w was solved using least-squares fitting of the signal intensity $(I=I_0\left|1-\beta \cdot e^{-\frac{TI}{T_{1w}}}\right|)$ as a function of the inversion time (TI), in which β accounts for the inversion efficiency [56]. The B₀ field inhomogeneity map was determined from the WASSR scan [55]. The B₁ field inhomogeneity map was determined by fitting the signal intensity as a function of the pre-pulse FA as (I = I₀ |1 – α · (1 – β · cos(C₀ + C₁ · FA))|), in which free parameters α and β account for post-label delay and relaxation recovery, with C₀ and C₁ being the offset and scaling factors of the B₁ field, respectively. R_1ρ was solved from Eq. 1 with the measured $\frac{I_{\mathit{\text{sat}}}^{\mathit{\text{app}}}(\Delta \omega )}{I_0^{\mathit{\text{app}}}}$, T_1w and scan parameters of Ts and Td, and the QUASS Z signal was calculated from Eq. 2. The CEST effect was calculated using the conventional apparent CEST asymmetry effect (i.e., $\mathit{\text{CEST}}{R}^{\mathit{\text{app}}}=\frac{I_{\mathit{\text{ref}}}}{I_0}-\frac{I_{\mathit{\text{label}}}}{I_0}$), inverse apparent CEST asymmetry effect (i.e., $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}=\frac{I_0}{I_{\mathit{\text{label}}}}-\frac{I_0}{I_{\mathit{\text{ref}}}}$), QUASS CEST asymmetry effect (i.e., $\mathit{\text{CEST}}{R}^{\mathit{\text{QUASS}}}={\left(\frac{I_{\mathit{\text{ref}}}}{I_0}\right)}^{\mathit{\text{QUASS}}}-{\left(\frac{I_{\mathit{\text{label}}}}{I_0}\right)}^{\mathit{\text{QUASS}}}$), and the inverse QUASS CEST asymmetry effect (i.e., $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}={\left(\frac{I_0}{I_{\mathit{\text{label}}}}\right)}^{\mathit{\text{QUASS}}}-{\left(\frac{I_0}{I_{\mathit{\text{ref}}}}\right)}^{\mathit{\text{QUASS}}}$). The T₁-normalized CEST effect was calculated for CESTR^app, $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$, CESTR^QUASS, and $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$. We tested CEST indices (CESTR^app, $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$, CESTR^QUASS, and $\mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$) and T₁-normalized CEST indices (R_1w · CESTR^app, $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$, R_1w · CESTR^QUASS, and $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$) using a multiple linear regression model. Because the labeling efficiency depends on B₁, it was treated as a categorical variable, and the independent variables were [Cr], [MnCl₂], Ts, and B₁. In short, we had ${\text{y}}_{\text{i}}={\beta }_0+{\beta }_1{[\text{Cr}]}_{\text{i}}+{\beta }_2{\left[{\text{MnCl}}_2\right]}_{\text{i}}+{\beta }_3{[\text{Ts}]}_{\text{i}}+{\sum }_{j=1}^5{\beta }_{j+3}I\left[B_{1i}=a_j\right]+{ϵ}_i$, with i indexing scan per B₁ level, β_j being coefficients, ϵ_i being the residual error, and a₁ = 1, a₂ = 1.5, a₃ = 2, a₄ = 3, a₅ = 4 μT and I[B_1i = a_j] denoting the indicator function. Note that B_1i was treated as a categorical variable with a reference level of 0.5 μT.

4. Results

The effects of Ts and B₁ on the apparent and QUASS CEST MRI measurements were simulated. Briefly, Supplementary Figure 2A shows 10 apparent Z-spectra (B₁=0.5 μT (red), 1 μT (blue), 2 μT (green), 3 μT (black) and 4 μT (cyan)) under two representative Ts of 1 s (short, dash-dotted) and 4 s (long, solid). We assumed Ts=Td. The apparent Z-spectra (Supplementary Figure 2A), asymmetry spectra (Supplementary Figure 2B), and inverse asymmetry spectra (Supplementary Figure 2C) depend strongly not only on the RF irradiation power but also on Ts. Supplementary Figure 2D shows QUASS Z-spectra. Note that Z-spectra overlapped for different Td and Ts. Similarly, the asymmetry QUASS spectra (Supplementary Figure 2E) and the inverse asymmetry spectra (Supplementary Figure 2F) confirmed the QUASS algorithm’s effectiveness for reconstructing the steady-state CEST MRI signal.

The CEST effects were simulated as bulk water T₁ and RF saturation power. The apparent CESTR (Figure 1A), inverse apparent CESTR (Figure 1B), QUASS CESTR (Figure 1C), and inverse QUASS CESTR (Figure 1D) were simulated under Ts of 1 s. We assumed Td=Ts. It is worth noting that the apparent CEST effects display a weak relationship with T₁. In comparison, there is a relatively prominent T₁ effect on the QUASS and inverse QUASS CESTR. The CEST effects were also simulated under Td and Ts of 4 s. Notably, the apparent CESTR (Figure 1E) and inverse apparent CESTR (Figure 1F) were higher than the corresponding CEST measurements under Ts and Td of 1 s due to more prolonged saturation transfer. In comparison, QUASS CESTR (Figure 1G) and inverse QUASS CESTR (Figure 1H) showed little change with respect to Td and Ts, evidencing that the QUASS algorithm has corrected the transient saturation and relaxation effects.

Figure 1.

Simulation of the effect of the bulk water T₁ and RF saturation level (B₁) on the CEST MRI measurement for two representative saturation times of 1 and 4 s. A) The apparent CEST effect as a function of T₁ (1–2 s with intervals of 0.1 s) and B₁ (0.5–4 μT with intervals of 0.5 μT) for a short Ts (Td) of 1 s. B) The inverse apparent CEST effect as a function of T₁ and B₁ (Ts (Td) =1 s). C) The QUASS CEST effect as a function of T₁ and B₁ (Ts (Td) =1 s). D) The inverse QUASS CEST effect as a function of T₁ and B₁ (Ts (Td) =1 s). E-H) As A-D, but with Ts=Td=4 s. For the simulation, we varied T_1a from 1 to 2 s with intervals of 0.1 s, B₁ from 0.5 to 4 μT with intervals of 0.5 μT, and Ts (Td) from 1 to 4 s with intervals of 0.5 s. We used T_2a=100 ms, T_1b=1s, T_2b=15 ms, f_r=1:1000 and k_sw=100 s⁻¹.

Figure 2 evaluates the simulated T₁ dependence of the CEST measurements. Figure 2A shows CESTR under 5 representative B₁ levels (0.5 μT (red), 1 μT (blue), 2 μT (green), 3 μT (black) and 4 μT (cyan)) under two representative Ts (Td) of 1 s (short, dash-dotted) and 4 s (long, solid). The CEST effects increase with Ts (Td) as well as the bulk water T₁. Similarly, the apparent inverse CESTR (Figure 2B), QUASS CESTR (Figure 2C), and inverse QUASS CESTR (Figure 2D) increase with T₁. T₁ normalization was tested for all four CEST indices. Specifically, T₁-normalized apparent CESTR (Figure 2E), T₁-normalized inverse apparent CESTR (Figure 2F), T₁-normalized QUASS CESTR (Figure 2G) showed unsatisfactory T₁ correction. Importantly, T₁-normalized inverse QUASS CESTR (Figure 2H) demonstrated satisfactory T₁ correction in that the measurement showed little dependence with T₁, with the maximal relative deviation from the mean within 0.5% per B₁ level. Notably, ${\text{R}}_{1\text{w}}\cdot {\text{CESTR}}_{\text{ind}}^{\text{QUASS}}$ increased with B₁ due to the increased saturation efficiency at higher B₁.

Figure 2.

Simulation of T₁ dependence of common CEST indices. A) The apparent CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. B) The corresponding inverse apparent CEST effect. C) The QUASS CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. D) The inverse QUASS CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. E) The T₁-normalized apparent CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. F) The T₁-normalized inverse apparent CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. G) The T₁-normalized QUASS CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels. H) The T₁-normalized inverse QUASS CEST effect as a function of T₁ for representative Ts (Td) and B₁ levels.

The experimental CEST results were evaluated as functions of B₁ and Ts (Td). The measured T_1w were 1.69 ± 0.04 s, 1.43 ± 0.04 s and 1.27 ± 0.04 s for MnCl₂ concentrations of 20, 30, and 40 μM, respectively. These values cover the typical tissue T₁ at 7T. The CESTR^app and CESTR^QUASS maps are shown as a function of B₁ (Supplementary Figures 3 A and B) for a typical Ts of 2 s. We had Ts=Td. Because of the slow and intermediate chemical exchange rates, the labeling efficiency plateaus when the exchange rate is about the same as the optimal B₁ amplitude. The observation that the CEST effect peaked at an intermediate B₁ of 1.5 μT suggests an intermediate guanidinium proton exchange rate of creatine at near-neutral pH. For a representative B₁ of 1.5 μT, CESTR^app and CESTR^QUASS maps are shown as a function of Ts (Supplementary Figures 3 C and D). While both the apparent and QUASS CEST effects displayed dependency on the creatine and manganese chloride concentrations, only the apparent CEST effect depended on Ts. We tested T₁ normalization for apparent and QUASS CEST MRI. T₁-normalized CESTR^app and CESTR^QUASS maps were shown as a function of B₁ (Supplementary Figures 4 A and B) for a typical Ts (Td) of 2 s. The CEST effect peaked at an intermediate B₁ of 1.5 μT. Importantly, T₁-normalized CESTR^app and CESTR^QUASS maps are shown as a function of Ts (Supplementary Figures 4 C and D). Whereas T₁-normalized CESTR^app steadily increased with Ts (Td), T₁-normalized CESTR^QUASS remained unchanged for the full range of Ts.

Although $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$ (Figure 3A) showed dependence on manganese chloride and creatine concentrations and B₁, $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$ (Figure 3B) had little dependence on manganese chloride concentration. Similarly, $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$ (Figure 3C) increased with saturation time while $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$ (Figure 3D) remained stable. We evaluated T₁-normalized CEST effects and their inverse calculations as functions of manganese chloride and creatine concentrations, Ts, and B₁. For a representative B₁ of 1.5 μT, the apparent CEST indices without (R_1w · CESTR^app, Figure 4A) and with inversion ($R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{app}}}$, Figure 4B) showed a strong dependence on the creatine concentration and Ts (Td), and to a less degree, manganese chloride concentration. In comparison, the QUASS CEST indices without (R_1w · CESTR^QUASS, Figure 4C) and with inversion ($R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$, Figure 4D) showed little variation with Ts (Td) and manganese chloride concentration (i.e., [MnCl₂]), advantageous over the apparent CEST MRI. Overall, the multiple linear regression provided a robust description of all CEST indices (Table 1). The adjusted R² for T₁-normalized CEST indices is significantly higher than those without T₁ normalization (2 sample t-test, P<0.01). Notably, $R_{1w}\cdot \mathit{\text{CEST}}{R}_{\mathit{\text{ind}}}^{\mathit{\text{QUASS}}}$ only showed significant dependence on [Cr], not on [MnCl₂] or Ts (Td), suggesting that it is specific to the underlying CEST system.

Figure 3.

Experimental demonstration of apparent and QUASS CEST MRI maps. A) The T₁-normalized inverse apparent CEST effect as a function of B₁ for a representative Ts (Td) of 2 s. B) The T₁-normalized inverse QUASS CEST effect as a function of B₁ for a representative Ts (Td) of 2 s. C) The T₁-normalized inverse apparent CEST effect as a function of Ts (Td) for a representative B₁ of 1.5 μT. D) The T₁-normalized inverse QUASS CEST effect as a function of Ts (Td) for a representative B₁ of 1.5 μT.

Figure 4.

Evaluation of T₁-normalized CEST MRI effects as functions of creatine and manganese chloride concentrations. A) The T₁-normalized apparent CEST effect as a function of creatine and manganese chloride concentrations for a representative B₁ of 1.5 μT for 5 Ts (Td) from 1, 1.5, 2, 3, and 4 s. B) The corresponding T₁-normalized inverse apparent CEST effect as a function of creatine and manganese chloride concentrations for Ts (Td) from 1, 1.5, 2, 3, and 4 s. C) The T₁-normalized QUASS CEST effect as a function of creatine and manganese chloride concentrations for a representative B₁ of 1.5 μT for Ts (Td) from 1, 1.5, 2, 3, and 4 s. D) The corresponding T₁-normalized inverse QUASS CEST effect as a function of creatine and manganese chloride concentrations for Ts (Td) from 1, 1.5, 2, 3, and 4 s. The T₁-normalized QUASS effects, with and without inversion, showed little dependence on Ts (Td) when compared to the apparent CEST effects.

Table 1.

Quantification of CEST indices (i.e., CESTR^app, CESTR^QUASS, ${\text{CESTR}}_{\text{ind}}^{\text{app}}$ and ${\text{CESTR}}_{\text{ind}}^{\text{QUASS}}$), and their T₁ normalization with a multiple linear regression model being ${\text{y}}_{\text{i}}={\beta }_0+{\beta }_1{[\text{Cr}]}_{\text{i}}+{\beta }_2{\left[{\text{MnCl}}_2\right]}_{\text{i}}+{\beta }_3{[\text{Ts}]}_{\text{i}}+{\sum }_{j=1}^5{\beta }_{j+3}I\left[B_{1i}=a_j\right]+{ϵ}_i$, with i indexing scan per B₁ level, β_j being coefficients, ϵ_i being the residual error, and a₁ = 1, a₂ = 1.5, a₃ = 2, a₄ = 3, a₅ = 4 μT and I[B_1i = a_j] denoting the indicator function. Note that B_1i was treated as a categorical variable with a reference level of 0.5 μT. (SE: standard error, * P<0.05 and ** P<0.0001)

	${\widehat{\beta }}_0$ Estimate (SE)	${\widehat{\beta }}_1$ Estimate (SE)	${\widehat{\beta }}_2$ Estimate (SE)	${\widehat{\beta }}_3$ Estimate (SE)	${\widehat{\beta }}_{4-8}$ Estimates (SE)	Adjusted R2
CESTRapp (%)	−2.91 ** (0.32)	0.12 ** (0.00)	−0.05 ** (0.01)	1.13 ** (0.05)	3.08 **, 3.89 **, 4.02 **, 3.19 **, 2.28 ** (0.20)	0.89
CESTRQUASS (%)	−3.68 ** (0.21)	0.08 ** (0.00)	0.02 ** (0.00)	0.76 ** (0.03)	2.12 **, 2.67 **, 2.77 **, 2.18 **, 1.55 ** (0.13)	0.90
${\text{CESTR}}_{\text{ind}}^{\text{app}}\left(\%\right)$	−6.37 ** (0.49)	0.17 ** (0.01)	−0.05 ** (0.01)	1.80 ** (0.08)	3.55 **, 4.84 **, 5.54 **, 6.13 **, 6.87 ** (0.31)	0.89
${\text{CESTR}}_{\text{ind}}^{\text{QUASS}}\left(\%\right)$	−6.59 ** (0.33)	0.12 ** (0.00)	0.04 ** (0.01)	1.22 ** (0.06)	2.44 **, 3.33 **, 3.82 **, 4.22 **, 4.74 ** (0.21)	0.89
R1w ⋅ CESTRapp (%/s)	1.18 ** (0.26)	0.15 ** (0.00)	−0.11 ** (0.01)	0.08 (0.04)	4.16 **, 5.10 **, 5.02 **, 3.42 **, 1.82 ** (0.16)	0.95
R1w ⋅ CESTRQUASS (%/s)	−1.41 ** (0.15)	0.11 ** (0.00)	−0.00 (0.00)	0.06 * (0.03)	2.85 **, 3.48 **, 3.43 **, 2.32 **, 1.23 ** (0.10)	0.96
${\text{R}}_{1\text{w}}\cdot {\text{CESTR}}_{\text{ind}}^{\text{app}}\left(\%/\text{s}\right)$	−0.88 * (0.43)	0.23 ** (0.00)	−0.14 ** (0.01)	0.11 (0.07)	5.00 **, 6.78 **, 7.60 **, 8.14 **, 8.76 ** (0.27)	0.94
${\text{R}}_{1\text{w}}\cdot {\text{CESTR}}_{\text{ind}}^{\text{QUASS}}\left(\%/\text{s}\right)$	−3.70 ** (0.25)	0.16 ** (0.00)	0.01 (0.01)	0.07 (0.04)	3.42 **, 4.63 **, 5.20 **, 5.57 **, 6.01 ** (0.16)	0.95

5. Discussion

This study expanded Zu et al. to demonstrate that the non-steady-state CEST measurement can be processed with the QUASS algorithm and, combined with the inverse calculation, enables robust T₁ correction for a broad range of RF saturation amplitudes [42]. Indeed, the multiple linear regression model offers compelling evidence that the T₁-normalized inverse QUASS CEST effect is specific to the underlying CEST system, not dependent on the bulk water T₁ and RF saturation time, improving the specificity of quantitative CEST imaging.

The experiment varied both B₁ and Ts/Td dimensions to evaluate their effects on the CEST measurement. Because the scan time would have been excessively long if Z-spectra were obtained, the study performed 3-point CEST scans (control, label, and reference scans). The phantom had satisfactory shimming, which made the expedited experimental design equivalent to the Z-spectral acquisition approach. The study interleaved WASSR and 3-point CEST scans to ensure that the field drift, if present, can be adjusted accordingly. The field inhomogeneity ranged from −0.2 ± 1 and 0.1 ± 1 Hz for the duration of the experiment, showing little drift. The satisfactory field homogeneity and stability allowed us to collect 3-point CEST scans to demonstrate the advantage of T₁-normalized QUASS post-processing. Also, our study used the same pH buffer solution for all vials, so their exchange rates remained the same [57]. Such a phantom design simplified the evaluation in that the CEST effect should be proportional only to creatine concentration to investigate the impact of B₁, Ts, and [MnCl₂] on CEST quantification. The findings were compelling because the T₁-normalized inverse QUASS CEST effect showed a linear dependence on [Cr] while its Ts (Td) and [MnCl₂] dependencies were not significant. Although the resulted CEST effect still depended on B₁, this observation had been well understood in that the labeling efficiency increases with B₁ [35, 58]. Additional work is needed to advance in vivo CEST quantification. One major issue is that biological tissue has multiple partially overlapping CEST effects and semisolid macromolecular magnetization transfer (MT) of vastly different exchange rates, which need to be isolated reliably before T₁ correction of QUASS CEST MRI can be performed [59, 60]. Also, tissue T₁ depends on water content, which might affect how to account for T₁ contribution during in vivo CEST imaging properly. It is helpful to point out that simulation and phantom studies provide tremendous insights into the contrast mechanism, quantification, and new post-processing routines when appropriately designed. A mechanistic work that thoroughly elucidates the relationship between T₁ and CEST measurements under different RF saturation amplitude, saturation time, and relaxation delay lays the foundation for evaluating the complicated T₁ effect in quantitative CEST imaging in vivo.

6. Conclusions

This study demonstrated that the combined use of QUASS analysis and inverse Z spectral calculation makes it feasible to perform accurate T₁ normalization in CEST MRI. The T₁-normalized inverse QUASS CEST index accurately depicted the underlying CEST system (labile proton ratio and exchange rate) and labeling efficiency, not confounded by the bulk water T₁, saturation time, and relaxation delay, promising for quantitative CEST MRI analysis.

Highlights.

• T₁ normalization of the apparent CEST effect was subject to noticeable T₁ contamination.

• The quasi-steady-state (QUASS) CEST algorithm reconstructs the steady-state CEST effect, enabling T₁-normalized inverse CEST effect calculation for improved quantification of the underlying CEST system.