In vivo pH mapping with omega plot-based quantitative chemical exchange saturation transfer (CEST) MRI

Abstract

Purpose:

Chemical exchange saturation transfer (CEST) MRI is promising to detect dilute metabolites and microenvironment properties, which has been increasingly adopted in imaging disorders such as acute stroke and cancer. However, in vivo CEST MRI quantification remains challenging because routine asymmetry analysis (MTR_asym) or Lorentzian decoupling measures a combined effect of the labile proton concentration and its exchange rate. Therefore, our study aimed to quantify amide proton concentration and exchange rate independently in a cardiac arrest-induced global ischemia rat model.

Methods:

The amide proton CEST (APT) effect was decoupled from tissue water, macromolecular magnetization transfer, nuclear overhauser enhancement, guanidinium, and amine protons using the Image Downsampling Expedited Adaptive Least-squares (IDEAL) fitting algorithm on Z-spectra obtained under multiple RF power levels, before and after global ischemia. Omega plot analysis was applied to determine amide proton concentration and exchange rate simultaneously.

Results:

Global ischemia induces a significant APT signal drop from intact tissue. Using the modified omega plot analysis, we found that the amide proton exchange rate decreased from 29.6 ± 5.6 to 12.1 ± 1.3 s⁻¹ (P < 0.001), while the amide proton concentration showed little change (0.241 ± 0.035 % vs. 0.202 ± 0.034 %, P = 0.074) following global ischemia.

Conclusion:

Our study determined the labile proton concentration and exchange rate underlying the in vivo APT MRI. The significant change in the exchange rate but not the concentration of amide proton demonstrated that the pH effect dominates the APT contrast during tissue ischemia.

Introduction

Chemical Exchange Saturation Transfer (CEST) MRI is sensitive to the interaction between the labile and bulk tissue water protons, providing an informative imaging contrast (1,2). CEST MRI has been applied to investigate acute stroke (3–6), tumor (7–11), neurological disorders (12–14), osteoarthritis (15), and muscle physiology (16,17), etc. However, the commonly used magnetization transfer (MT) asymmetry analysis (MTR_asym) provides a mixed contrast, with contaminations from neighboring exchangeable proton pools, nuclear overhauser enhancement (NOE), and macromolecular MT effects (18–21). Moreover, the CEST measurement depends on radiofrequency (RF) irradiation amplitude and duration, T₁ and T₂ (22). As such, quantitative CEST (qCEST) analysis that fully characterizes the CEST system helps elucidate the underlying tissue changes. There has been continuous effort to model the CEST MRI through Bloch-McConnell equations (22,23), spinlock solutions (24–26), and saturation time and power dependence analyses (27–29) to determine labile proton ratio and exchange rate (30–35). Notably, Dixon et al. proposed an omega plot approach (36). Sun et al. demonstrated a spillover-corrected omega plot analysis for quantifying diamagnetic CEST (DIACEST) systems (35). The omega plot was further extended with inverse CEST analysis (26) and multi-RF power-based ratiometric analysis (37–39) and also adapted for pulsed saturation as compared to the ideal case of continuous wave saturation (40). Nevertheless, in vivo omega plot is challenging due to multipool contributions (41,42).

Our study aimed to extend the omega plot and quantify the endogenous amide proton transfer (APT) MRI. Specifically, multipool Lorentzian fitting provides accurate CEST quantification, particularly at low irradiation powers (43–47). Recently, we demonstrated an Image Downsampling Expedited Adaptive Least-squares (IDEAL) algorithm, which improves the fitting robustness (47,48). Our current study chose a global ischemia rat model to test the in vivo qCEST analysis. We obtained densely sampled Z-spectra under multiple RF amplitudes and decoupled the multipool CEST effects, particularly the amide proton signal at 3.5 ppm, using the IDEAL algorithm. We then applied the omega plot and determined the labile amide proton concentration and exchange rate before and immediately after global ischemia.

Methods

Animal Stroke Model

The experiments were approved by the Institutional Animal Care and Use Committee. Adult male Wistar rats were anesthetized with 1.5–2.0% isoflurane/air mixture. A global ischemia model was induced by a lethal dose of potassium chloride (KCl) injection through the right femoral artery. MRI scans were performed on six animals (N=6) before and after global cerebral ischemia. Heart rate and blood oxygen content (SpO₂) were monitored throughout the experiment. The body temperature was maintained within its physiological range with a circulating warm water jacket positioned around the torso.

MRI

All scans were performed on a 4.7 Tesla small-bore MRI scanner (Bruker Biospec, Erlangen, Germany) with a dual RF coil setup to achieve a homogeneous B₁ field and sensitive detection. Multi-slice MRI (5 slices, slice thickness/gap=1.8/0.2 mm, field of view=20×20 mm², image matrix=48×48) was acquired with echo planar imaging (EPI). Z-spectra were obtained from −6 to 6 ppm with intervals of 0.05 ppm and a continuous wave RF irradiation at power levels of 0.25, 0.35, 0.5, and 1 μT. We set the relaxation time to 2.5 s with the primary RF saturation duration and secondary RF saturation duration being 2.5 s and 0.5 s, respectively, and therefore an equivalent repetition time (TR) = 7.5 s, echo time (TE) = 24 ms, one average, and the scan time was 34 min per Z-spectrum (49). The water saturation shift referencing (WASSR) map was collected with an RF irradiation power level of 0.5 μT (TR/TS=1.5/0.5 s) for frequency offsets ranging between ±0.5 ppm with intervals of 0.05 ppm. Also, T₁-weighted images were acquired using inversion recovery EPI, with seven inversion times ranging from 250 ms to 3,000 ms (TR/TE = 6.5 s/15 ms, 4 averages, scan time=3 min); T₂-weighted spin echo images were obtained with two TE of 30 and 100 ms (TR = 3.25 s, 16 averages; scan time=2 min) (50).

Data Analysis

Data were analyzed in MATLAB (MathWorks, Natick, MA). The T₁ map was obtained with the mono-exponential fitting of the signal as a function of the inversion time $I_i=I_0\left[1-\left(1-\eta \right)e^{-T{I}_i/T_{1w}}\right]$, where η is the inversion efficiency and TI_i is the i^th inversion time (51). T₂ map was calculated as $T_2=\frac{T{E}_2-T{E}_1}{\text{ln}\left(I\left(T{E}_1\right)/I\left(T{E}_2\right)\right)}$, where I(TE_1,2) are T₂-weighted signals obtained at two echo times (TE= 30 and 100 ms). A series of post-processing steps were performed on the Z-spectral images. Briefly, CEST images were coregistered using SPM12. B₀ field inhomogeneity was corrected using the WASSR, and Z-spectral images were normalized by the signal without RF irradiation (I₀) (52,53). The Z-spectra at each RF irradiation level was flipped as 1-I/I₀ and fitted using the IDEAL fitting approach (47,48), which uses a globally averaged Z-spectrum for initial fitting. The initial fitting results are then used as initial values for subsequent fitting of substantially downsampled images. The resolution of downsampled images is increased iteratively and fitted with the results from the previous downsampled images as new initial values until the desired image resolution is reached. A seven-pool Lorentzian model including water (0 ppm), semisolid macromolecular MT (−2 ppm), amide (3.5 ppm), amine (2.75 ppm), guanidinium (2 ppm), and NOE effects (−1.6 ppm and −3.5 ppm) was applied (46,54–56). The Z-spectrum was described as a sum of multiple Lorentzian functions as

$$1-\frac{I}{I_0}={\sum }_{i=1}^{N=7}\frac{A_i}{1+4{\left(\frac{\omega -{\omega }_i}{{\sigma }_i}\right)}^2}$$ [1]

where ω is the frequency offset from the water resonance, A_i, ω_i and σ_i are the amplitude, frequency offset, and linewidth of the CEST peak for the i^th proton pool, respectively.

Because the CEST effect is susceptible to direct RF saturation (spillover) (35), the RF spillover effect was accounted for by calculating the inverse CEST difference (26) as,

$${\mathit{\text{CESTR}}}_{ind}=\frac{1}{Z_{\mathit{\text{label}}}}-\frac{1}{Z_{ref}}=\frac{1}{Z_{ref}-\mathit{\text{CESTR}}}-\frac{1}{Z_{ref}}$$ [2]

where Z_ref is the reference signal. With a 90° excitation pulse, the RF spillover can be described by

$$Z_{ref}=\frac{\left(1-e^{-\left(TR-T_s\right)\cdot R_{1w}}\right)\cdot e^{-R_{1\rho }\cdot T_s}+\frac{R_{1w}\cdot co{s}^2\theta }{R_{1\rho }}\cdot (1-e^{-R_{1\rho }\cdot T_s})}{1-e^{-TR\cdot R_{1w}}}$$ [3]

where R_1ρ is the longitudinal relaxation rate in the rotating frame (R_1ρ = R_1w · cos²θ + R_2w · sin²θ), TR is the repetition time, Ts is the saturation times, R_1w and R_2w are the experimentally obtained longitudinal and transverse relaxation rates of bulk water, and θ = atan (ω₁/Δω) with ω₁ and Δω being the RF irradiation level and offset. Based on the modified omega plot analysis (57,58), the relationship between 1/CESTR_ind and $1/{\omega }_1^2$ can be described by linear regression as

$$\frac{1}{{\mathit{\text{CESTR}}}_{ind}}\approx \frac{R_{1w}}{f_r\cdot k_{sw}}+\frac{k_{sw}\cdot \left(k_{sw}+R_{2s}\right)\cdot R_{1w}}{f_r\cdot k_{sw}}\cdot \frac{1}{{\omega }_1^2}$$ [4]

Both the labile proton exchange rate (k_sw) and ratio (f_r) can be solved as

$$k_{sw}=\frac{\sqrt{R_{2s}^2+4C_1/C_0}-R_{2s}}{2}$$ [5.a]

$$f_r=\frac{R_{1w}}{C_0\cdot k_{sw}}$$ [5.b]

where C₀ and C₁ are the intercept and slope of the omega plot analysis, respectively, and the transverse relaxation rate of labile protons of amides (R_2s) was set to 100 s⁻¹ (59). Due to the strong correlation between T₁ and water content (60,61), fr was corrected by normalizing the postmortem fr to the ratio of T₁ between postmortem and live brain. The IDEAL approach was implemented for omega plot analysis, where parametric maps of k_sw and f_r were obtained by two-parameter fitting of the iteratively less downsampled spillover-corrected CEST images using Eq. [4]. Then the measured labile proton exchange rate (k_sw) can be used to estimate the pH map by the formula previously derived by Zhou et al. (18):

$$pH=6.4+lo{g}_{10}^{k_{sw}/5.57}$$ [6]

The k_sw and f_r were measured from the parametric maps with a region of interest (ROI) over the brain tissue, excluding the ventricles. The statistical analysis was performed using a two-tailed Student’s t-test.

Results

Figure 1 shows Z-spectra averaged across all brain voxels of 6 rats before and after global ischemia at B₁ levels of 0.25, 0.35, 0.5, and 1 μT. It has been shown that a moderate B₁ level (i.e., ≤ 1 μT) maximizes the APT signal contrast between the ischemic and normal tissue (31). The APT effect at 3.5 ppm downfield from the water resonance (Fig. 1, dashed line) was observed at all B₁ levels in the normal brains, which decreased following global ischemia. Also, the guanidinium CEST signal change can be observed after global ischemia, particularly at lower B₁ levels (≤ 0.5 μT). The pH-dependency of amide and guanidinium CEST effects are opposite to each other, consistent with that of Jin et al. (62). Because guanidinium is closer to the bulk water resonance, it is more susceptible to B₀ field inhomogeneity, particularly when a weak B₁ field is used. Hence, our current work focused on quantifying the amide proton signal.

Figure 1.

CEST Z-spectra averaged across all brain voxels before and after global ischemia. Mean with shaded standard deviation are shown (N = 6). Most notable are CEST effect changes at 3.5 ppm (APT) and 2 ppm (guanidinium) CEST effects.

Figure 2a shows the multipool Lorentzian fitting of the whole brain-averaged flipped Z-spectra (1-I/I₀) at representative B₁ levels of 0.25, 0.5, and 1.0 μT, respectively, from a representative rat before (blue) and after global ischemia (red). Figure 2b compares the residual Z-spectra, obtained by subtracting the fitted water and MT curve from the raw flipped Z-spectra, with the decoupled CEST effects of amide, amine, guanidinium, and NOE pools from the normal and ischemic brain. Multi-pool CEST effects were found at 3.5, 2.75, 2, −1.6, and −3.5 ppm of the water- and MT-subtracted Z-spectra. These fitting results of the globally averaged Z-spectra were subsequently used as inputs for the IDEAL fitting. The histograms of the fitted parameters for amide protons from a representative rat were shown in Figure S1.

Figure 2.

a) Multi-pool Lorentzian fitting of the whole brain-averaged Z-spectra at three representative B₁ of 0.25, 0.5, and 1 μT before (solid lines) and after global ischemia (dotted lines). The saturation transfer effect from amide protons (3.5 ppm) can be decoupled from other pools, including amine (2.7 ppm), guanidinium (2.0 ppm), NOE (−1.6 ppm), NOE (−3.5 ppm), as well as direct water saturation and MT. b) The fitted water and MT effects were subtracted from the raw Z-spectra, which shows amide, amine, guanidinium, and NOE signals change between normal and ischemic tissues at different B₁ levels.

Figure 3 shows the in vivo omega plots of the inverse of CESTR_ind vs. $1/{\omega }_1^2$. The CESTR_ind effect was obtained from multipool Lorentzian fitting of the globally averaged Z-spectrum and corrected for RF spillover. The goodness of linear regression (R²) of omega plots was above 0.95 before and after global ischemia. Amide proton k_sw and f_r were determined from the omega plot (Eqs. 5a and 5b). Table 1 summarizes the T₁, k_sw, and f_r of amide protons from 6 animals. In addition to significantly increased T₁ (P=0.007), we found that the amide proton exchange rate calculated from the globally averaged Z-spectrum decreased substantially and significantly from 29.6 ± 5.6 to 12.1 ± 1.3 s⁻¹ (P<0.001) following global ischemia. In comparison, the labile amide proton content did not show significant changes (0.241 ± 0.035% vs. 0.202 ± 0.034%, P=0.074).

Figure 3.

The omega plot analysis of 1/APT effect versus $1/{\omega }_1^2$. The APT effect obtained from multipool Lorentzian fitting of the averaged Z-spectrum was corrected for RF spillover before omega plot analysis. Mean ± standard deviation from 6 animals before and after global ischemia was shown. The goodness of fit (R²) from the linear regression was above 95%.

Table 1.

Comparison of T₁, the exchange rate (k_sw), and the relative labile proton ratio (fr) of amide protons before and after global ischemia (N = 6). k_sw and fr values reported were from both omega plot on APT decoupled from globally averaged Z-spectrum and from IDEAL-based omega plot analysis on APT maps fitted using the IDEAL approach. Given a strong correlation between T₁ and water content, the contribution of change in water proton towards f_r has been normalized by T₁. Mean ± standard deviation values were shown. Student’s t-tests were performed between live and postmortem conditions in the same brains with p values <0.05 denotes a statistically significant difference.

	Live		Postmortem		P-value
T1 [s]	1.56 ± 0.012		1.65 ± 0.058		0.007
	Globally averaged APT	IDEAL fitted APT	Globally averaged APT	IDEAL fitted APT	Globally averaged APT	IDEAL fitted APT
ksw [s−1]	29.6 ± 5.6	29.9 ± 14.2	12.1 ± 1.3	11.2 ± 1.3	<0.001	0.009
fr × 10−3	2.42 ± 0.35	2.50 ± 0.30	2.02 ± 0.34	1.90 ± 0.40	0.074	0.034

Figure 4 shows representative maps of the T₁, amide proton concentration, exchange rate, goodness of fit (R²) of the omega plot, and pH before (Figs. 4a) and after global ischemia (Figs. 4b). The effect of global ischemia on k_sw but not f_r can also be observed in Figure 4. Similar to the findings from the omega plot on APT decoupled from globally averaged Z-spectrum (Table 1), parametric fitting maps showed k_sw reduced from 29.9 ± 14.2 to 11.2 ± 1.3 s⁻¹ (P=0.009) (Table 1) after global ischemia with a marginal yet significant change in the labile proton concentration (0.25 ± 0.03 vs. 0.19 ± 0.04 %, P=0.034) (Table 1). The averaged R² values from the goodness of fit maps were 0.89 ± 0.11 and 0.85 ± 0.15 for before and after global ischemia, respectively.

Figure 4.

Representative maps of the T₁, relative labile proton ratio (f_r) of amide protons, exchange rate (k_sw) of amide protons, corresponding goodness of fit (R²) of the omega plot analysis, and pH before (Figs. 4a) and after global ischemia (Figs. 4b).

Discussion

Our study combined the omega plot analysis with multipool Lorentzian decoupling and IDEAL fitting algorithms, and solved the brain amide proton concentration and exchange rate following global ischemia. Our results concluded that reduced amide exchange rate, not its concentration, is the dominating factor in APT contrast for ischemia, confirming its pH sensitivity.

The amide proton exchange rates determined from the globally averaged data in our study, which are 29.6 ± 5.6 s⁻¹ and 12.1 ± 1.3 s⁻¹ before and after global ischemia, respectively, are in excellent agreement with those reported by Zhou et al. (28.6 ± 7.4 s⁻¹ and 10.1 ± 2.65 s⁻¹, respectively) (18). It is helpful to point out that Zhou et al. (18) used water exchange spectroscopy while our study used a modified in vivo omega plot analysis. Moreover, they observed no change in amide signal intensity from the exchange spectra in the first 2 hours postmortem. Our study found a negligible/marginal effect of ischemia on amide proton concentration during the initial hours after ischemia. Our study determined an amide concentration of 122 mM, which is in reasonable agreement with 100 ± 8 mM, derived from a dual 2-pool model (31). Although both derived concentrations were higher than that reported by Zhou et al. (i.e., 71.9 mM), this is likely because the original work of Zhou et al. used a pulse-APT MRI scheme (18), which slightly underestimates the APT effect than that of using CW-APT MRI (63,64). Altogether, these multi-site studies have been reasonably consistent results. The global ischemia is a relatively straightforward model, shedding light on the origin of in vivo CEST MRI. The qCEST framework can be further applied to characterize the contrast mechanism in disorders like tumors, which may have significant changes in pH and amide proton concentration.

We maintained animals on a heating pad, and the rectal temperature was monitored and recorded throughout the imaging session. Nevertheless, there might be a gradual brain temperature drop following global ischemia, which could cause a non-uniform T₁ change (65). However, we did not perform serial T₁ mapping after global ischemia, which might help characterize the extent. It will be helpful to apply the modified omega plot to analyze focal ischemia animal models, in which the tissue temperature variation shall be smaller than global ischemia. It’s worth discussing the effect of the temperature drop after global ischemia on chemical exchange rate. The temperature records showed no more than 3°C dropped following global ischemia under the pad heating condition. It has been reported that a temperature change range of 1–3 °C would not significantly alter the exchange rate compared with the effect of pH, indicating the change of the chemical exchange rate after ischemia is dominated by pH(18). In the brains before global ischemia, a relatively uniform amide proton concentration is found, consistent with our prior study (48). Previously, we found that the T₁-normalized CEST effects (6) for the intact brain white matter and grey matter are about equal for APT while significantly different in MT contrast asymmetry and NOE effects (48). Indeed, this magnitude difference between NOE and MTC asymmetry is not pH-specific. Importantly, because the intact white matter and gray matter have little pH difference (within 0.05), the amide proton exchange rate and hence, the labile amide concentration shall be reasonably uniform across the brain (66).

Our study used relatively weak saturation powers for APT MRI of ischemia (0.25 −1 μT), which is desired for fitting multipool CEST effects for subsequent omega plot (21). The four saturation powers were selected so that the corresponding $1/{\omega }_1^2$ values are reasonably evenly spaced on the omega plot to achieve a robust linear regression. It’s worth mentioning that a systemic B₁ calibration was performed to correct systematic B₁ error at different power levels in omega plot analysis. Because of the relative size between the rodent brain and RF volume transmit coil, the B₁ inhomogeneity is within 5% (67)and hence no pixel wise correction was performed because relatively uniform B₁. The good linear relationship from the in vivo omega plot supports adequate B₁ homogeneity. In addition to the APT effect, we were able to resolve amine (2.7 ppm) and guanidinium (2.0 ppm) effects (4,22). However, the intermediate to fast exchange rate of amine and guanidinium protons may limit the applicability of the omega plot to quantify them at 4.7 Tesla. Also, the typical range of RF saturation powers optimized for APT MRI may not capture intermediate and fast exchanging protons. On the other hand, the CEST effects overlap significantly when B₁ is over 1 μT, making decoupling more difficult. qCEST MRI at the high field may provide improved spectral resolution to fully characterize multipool CEST MRI effects. Finally, we need to point out that the robustness of omega plot analysis relies on the multipool Lorentzian decoupling of the exchanging protons and, therefore, the signal-to-noise ratio (SNR). Thus, the decreased APT effect after global ischemia makes the fitting more susceptible to physiological and thermal noises than normal conditions. Not surprisingly, the goodness of fit (R²) from the omega plot after global ischemia is slightly less than that before ischemia (95% vs. 100%). This fitting uncertainty is likely due to the multipool fitting error propagation. Nevertheless, numerical fitting under the condition of high SNR (e.g., global fitting) provides a more robust quantification of the in vivo APT MRI.

Conclusion

Our study documented the decreased exchange rate but not proton concentration of amide protons after cerebral ischemia. The significant change in amide exchange rate indicates the APT contrast is dominated by pH change during ischemia, suitable for mapping tissue acidosis.