Improving Standardization and Accuracy of In vivo Omega Plot Exchange Parameter Determination using Rotating-Frame Model-Based Fitting of Quasi-Steady-State (QUASS) Z-spectra

Abstract

Purpose:

While Ω-plot-driven quantification of in vivo amide exchange properties has been demonstrated, differences in scan parameters may complicate the fidelity of determination. This work systematically evaluated the use of quasi-steady-state (QUASS) Z-spectra reconstruction to standardize in vivo amide exchange quantification across acquisition conditions and further determined it in vivo.

Methods:

Simulation and in vivo rodent brain CEST data at 4.7 T were fit with and without QUASS reconstruction using both multi-Lorentzian and model-based fitting approaches. pH modulation was accomplished both in simulation and in vivo by inducing global ischemia via cardiac arrest. Amide parameters were determined via Ω-plots and compared across methods.

Results:

Simulation showed that Ω-plots using multi-Lorentzian fitting could underestimate the exchange rate, with error increasing as conditions diverged from the steady state. In comparison, model-based fitting using QUASS estimated the same exchange rate within 2%. These results aligned with in vivo findings where multi-Lorentzian fitting of native Z-spectra resulted in an exchange rate of 64 ± 13 s⁻¹ (38 ± 16 s⁻¹ after cardiac arrest), while model-based fitting of QUASS Z-spectra yielded an exchange rate of 126 ± 25 s⁻¹ (49 ± 13 s⁻¹).

Conclusion:

The model-based fitting of QUASS CEST Z-spectra enables consistent and accurate quantification of exchange parameters through Ω-plot construction by reducing error due to signal overlap and non-equilibrium CEST effects.

Introduction

Chemical Exchange Saturation Transfer (CEST) MRI has emerged as a sensitive imaging technique to characterize the chemical exchange (CE) kinetics between the labile protons of certain metabolites of interest and bulk water (1). The exchange between saturated labile and bulk water protons attenuates bulk water proton magnetization (2). Z-spectra measurement provides valuable information about the dynamics of such exchanges (3–11). pH-sensitive CEST imaging has been demonstrated through focal ischemia models (12–22), globally ischemic brain (23–26), and ischemic muscle (27). In particular, ischemic tissue suffers heterogeneous hemodynamic, metabolic, and structural changes, and therefore, pH-sensitive MRI complements commonly used perfusion and diffusion MRI for refined demarcation of graded ischemic insult (17,28–38). Substantial effort has been devoted to improving the sensitivity and specificity of pH measurement, including minimization of the non-pH specific MT asymmetry baseline or use of the difference in pH sensitivity between amide and guanidino CEST effects (34,35,39–42).

It is worth noting that the reported exchange properties, even for the most well-studied amide proton transfer (APT) MRI, have large discrepancies between studies (4,42,45–48). In addition, endogenous in vivo CEST signals are complex, resulting from a multitude of partially overlapping peaks, and spectral fitting has been adopted to model in vivo CEST data (29,43,44). Multiple Lorentzian fitting (Multi-Lorentzian) has been commonly adopted (49–53), which utilizes a linear combination of Lorentzian curves to fit the Z-spectra, such as direct water saturation, semisolid magnetization transfer (ssMT), relayed nuclear Overhauser enhancement (rNOE) and chemically exchanging protons. However, the utilization of a linear combination depends on an assumption of mutual independence between pools in the Z-domain (i.e., an assumption that concomitant effects on the Z-spectra can be linearly separated), which may result in notable error, particularly when exchange peaks have excessive overlap (49). The feasibility of using fitted peaks from multi-Lorentzian fitting to calculate exchange parameters has previously been demonstrated at 4.7 T in rodents before and after cardiac arrest (26). In that study, Z-spectra were fit to the multi-Lorentzian model, and the peak heights obtained were used to construct Ω-plots (54–57), which utilize the relation between CEST signal and saturation power to determine CEST pool fraction and exchange rates. Voxel-wise exchange rates were then used to generate pH maps through a previously established exchange rate-pH calibration curve. However, the previous study assumed data were at a steady state, which could be susceptible to notable errors when scans were not performed under proper equilibrium conditions (8). Recently, quasi-steady-state (QUASS) postprocessing has been established to transform the experimental data into the desired equilibrium CEST effects (9,14,58–62). QUASS has already been shown to improve the quantification of exchange parameters through Ω-plot analysis in vitro (63). Furthermore, steady-state approximation through QUASS has also enabled the application of the rotating frame-based model to multiple pool fitting of CEST Z-spectra (64,65). This rotating-frame model-based fitting, or model-based fitting for short, improves the accuracy of CEST quantification by fitting peaks in the inverse-Z domain. Inverse-Z domain fitting has also been used with a combined Lorentzian and polynomial fit in order to account more generally for broad background effects (29,66–69). Such an inverse-Z domain analysis is preferred because, under the equilibrium condition, either directly acquired experimentally or reconstructed with postprocessing, it can linearize multi-pool contributions.

In this work, we investigate the multi-Lorentzian fitting and the rotating-frame model fitting with and without QUASS postprocessing to quantify in vivo amide proton properties. Through simulation, we examined the effect of departure from steady-state conditions on spectral fitting and the feasibility of using QUASS to standardize spectral quantification. We investigated the exchange quantification by comparing exchange parameters determined under blind fitting using both the multi-Lorentzian and the rotating-frame models to the simulated ground truth. We further quantified exchange parameters in rodent brains before and after cardiac arrest. Finally, we demonstrated the application of model-based fitting of QUASS spectral data in an exemplary rodent to confirm the feasibility of generating reliable exchange parameter maps in vivo.

Methods

Simulations

CEST signals at 4.7T with concomitant and partially overlapping effects at similar offsets as observed in vivo were simulated by Bloch-McConnell Equations (70,71), including amide protons (3.5 ppm), guanidino protons (2.0 ppm), phosphocreatine protons (2.6 and 2.0 ppm), rNOE protons, ssMT protons, and free water protons. Simulation parameters of each proton pool are summarized in Supplementary Table 1, partially based on literature values for creatine and phosphocreatine (72). Z-spectra were simulated with saturation times and relaxation delays in combinations of 2, 3, 5, and 10 s with B₁ = 0.25, 0.35, 0.50, and 1.00 μT between −6 and 6 ppm with intervals of 0.05 ppm.

Animal Preparation

A total of 6 adult male Wistar rats (Charles River Laboratory, Wilmington, MA) were studied with the approval of the local Institutional Animal Care and Use Committee. The animals were anesthetized with isoflurane (1.5–2.0%) in a mixture of O₂ and air gases, maintaining total O₂ concentration at ~30%. The core temperature was controlled and measured at 37.2 ± 0.5°C with a rectal probe by using a circulating warm water jacket positioned around the torso. Global ischemia was induced by a lethal dose of potassium chloride injection through the right femoral artery. Brain imaging was performed before and after global ischemia.

MRI Experiments

All MR experiments were performed on a Bruker Biospec 4.7 T small-bore MRI scanner (Billerica, MA, USA) with a dual RF coil setup to achieve a homogenous B₁ field and sensitive detection. The volume transmitter coil has a relative B₁ uniformity within 5% across the brain. B₁ was adjusted to correct for default calibration inaccuracy. Magnetic field homogeneity was optimized by Mapshim. Multi-slice EPI readout was performed with the following imaging parameters: matrix size = 48 × 48, a field of view = 20 × 20 mm, slice thickness/gap = 1.8/0.2 mm (5 slices), readout time = 60 ms and volume TR/TE = 8.5 s/24 ms. Z-spectra were acquired before and after inducing cardiac arrest from −6 to 6 ppm with intervals of 0.05 ppm using continuous wave RF saturation at B₁ = 0.25, 0.35, 0.50, and 1.00 μT, using a CEST MRI sequence with interleaved RF irradiation and image readout. The relaxation delay time was set to 2.5 s, with the primary and secondary RF saturation duration being 3.5 s and 0.5 s, respectively (scan time = 34 min per Z-spectrum) (3). T₁-weighted images were acquired using inversion recovery EPI, with 7 inversion times ranging from 250 ms to 3000 ms (TR/TE = 6.5 s/15 ms, 4 averages, scan time = 3 min); and T₂-weighted spin echo images obtained with 2 TE of 30 and 100 ms (TR = 3.25 s, 16 averages; scan time = 2 min).

Data Processing

All data were analyzed with in-house developed MATLAB code (MathWorks, Natick, MA). The ${\mathrm{T}}_1$ map was obtained with the mono-exponential fitting of the signal (${\mathrm{I}}_{\mathrm{i}}$) as a function of the inversion time $I_i=I_0·\left[1-(1-\eta )·e^{{-TI}_i/T_{1w}}\right]$, where $\mathrm{\eta }$ is the inversion efficiency, and $\mathrm{T}{\mathrm{I}}_i$ is the ith inversion time. A series of postprocessing steps were performed on the Z-spectra images. CEST images were co-registered using SPM12 (https://www.fil.ion.ucl.ac.uk/spm/). B₀ field inhomogeneity was corrected using WASSR (73), and Z-spectra images were normalized by the signal without RF irradiation (${\mathrm{I}}_0$). Quasi-steady-state (QUASS) Z-spectra was generated by calculating the rotating-frame relaxation (R_1ρ) as previously reported (14). The native Z-spectra ($Z_{app}$) and QUASS Z-spectra ($Z_{QUASS}$) were fit to either a multi-Lorentzian model (49):

$$Z_i=1-{\sum }_{i=1}^N\frac{A_i}{\left(1+4{\left(\frac{\mathrm{\Omega }-{\delta }_i}{{\sigma }_i}\right)}^2\right)}$$ [1]

or to a rotating-frame model (64):

$$Z_i=\frac{1}{1+\frac{R_{2w}}{R_{1w}}·{\tan }^2\theta +{\sum }_{i=1}^N\frac{A_i/(R_{1w}{\cos }^2\theta )}{\left(1+4{\left(\frac{\mathrm{\Omega }-{\delta }_i}{{\sigma }_i}\right)}^2\right)}}$$ [2]

where ${\mathrm{A}}_{\mathrm{i}}$ is amplitude, ${\mathrm{\sigma }}_{\mathrm{i}}$ is linewidth, and ${\mathrm{\delta }}_{\mathrm{i}}$ is the chemical shift for the ith pool, and fit parameters are ${\mathrm{R}}_{1\mathrm{w}}$ normalized (i.e., ${\mathrm{A}}_{\mathrm{i}}/{\mathrm{R}}_{1\mathrm{w}}$ or ${\mathrm{R}}_{2\mathrm{w}}/{\mathrm{R}}_{1\mathrm{w}}$); initial seed values were set according to Supplementary Table 2 with boundary conditions being 90% and 110% of the seed. The fit was iterated, taking the fitted parameters as the new seed, and walking the parameters (with 90%–110% bounds) until they arrived at stable values. Using the fitted parameters across powers, the exchange parameters were determined by spillover-corrected omega plot fitting (57,63) between $1/{\mathrm{\omega }}^2$ and $\mathrm{C}\mathrm{E}\mathrm{S}{\mathrm{T}}_{\mathrm{i}}^{-1}$:

$${{CEST}_i}^{-1}=b_0+b_1·{\omega }^{-2}$$ [3]

where: $k_{ex,i}=\frac{\sqrt{{R_{2s}}^2+4·b_1/b_0}-R_{2s}}{2},f_i=R_{1w}/\left(k_{ex,i}·b_0\right)$, CEST signal or ${CEST}_i=A_i$ for multi-Lorentzian fittings and ${CEST}_i=A_i/\left(R_{1w}·{\cos }^2\theta \right)$ for model-based fitting, the transverse relaxation rate of labile protons of amides (${\mathrm{R}}_{2\mathrm{s}}$) was set to 100 s⁻¹, ${\mathrm{k}}_{\mathrm{e}\mathrm{x},\mathrm{i}}$ is the exchange rate for the ith pool, and $f_{\mathrm{i}}$ is the molecular fraction for the ith pool. The IDEAL fitting approach (26,74) was then applied with both fitting models to calculate exchange parametric maps across the whole brain.

Results

Traditional Lorentzian and Model-based Z-spectra Fitting of Simulated CEST Z-spectra with varying Saturation Times and Relaxation Delays

A simulation was performed of a representative multi-pool exchange generating Z-spectra (circles) with saturation times (T_sat) and relaxation delays (T_rec) of T_sat/T_rec = 2 s (black), 3 s (red), 5 s (blue), and 10 s (cyan) which were independently fit (lines) under conditions blind to the true exchange parameter values used in the simulation in order to examine the effect of these saturation parameters on the resilience of fitting with the models used in Lorentzian and Model-based fitting (Fig. 1). Equivalent T_sat and T_rec were chosen as examples to demonstrate the disparity between parameters which are closest and furthest away from steady-state conditions. In addition, QUASS Z-spectra were calculated for T_sat/T_rec = 2 s (magenta) and plotted on the same plots for comparison. As expected, for the Z-spectra simulated for the simple system at pH 7.0, increasing the saturation time and relaxation delay improved the fidelity of the CEST peaks, particularly for the amide peak, which becomes larger compared to the background as the saturation time increases (Fig. 1a). For the 2 ppm peak, this trend is less conspicuous as direct saturation also increases along with saturation time. Employing QUASS for the Z-spectra at T_sat/T_rec = 2 s results in a spectrum that nears the spectrum simulated using the longest T_sat/T_rec = 10 s (gold standard equilibrium Z-spectrum), as expected.

Fig. 1. 7-pool simulation of CEST signal using varying saturation time (T_sat) and relaxation delays (T_rec) with multi-Lorentzian Fitting and rotating frame model based-fitting of native and QUASS Z-spectra at pH 7.0 and 6.5.

(A) Simulated Z-spectra at pH 7.0 are shown (open circles) using T_sat/T_rec of 2 s (black), 3 s (red), 5 s (blue), 10 s (cyan), and 2 s with QUASS reconstruction (magenta) along with the fit (solid lines) using multi-Lorentzian fitting. (B) Residuals for pH 7.0 are shown in stacked plots between simulated Z-spectra and fitted Z-spectra using the multi-Lorentzian model for native Z-spectra (solid lines) and QUASS reconstructed Z-spectra (dotted lines) using T_sat/T_rec of 2 s (black), 3 s (red), 5 s (blue), and 10 s (cyan). (C) Z-spectra at pH 7.0 were also simulated and fit using rotating frame model-based fitting along with their (D) fitting residuals. (E) Z-spectra at pH 6.5 were simulated and fitted using multi-Lorentzian fitting along with (F) fitting residuals. (G) The same simulated Z-spectra at pH 6.5 were fit using model-based fitting along with (H) fitting residuals.

Nonetheless, using the multi-Lorentzian models appears to reasonably fit the Z-spectra despite the short saturation and delay (Fig. 1a), with the largest residual (Fig. 1b) occurring close to water resonance. The maximal absolute residuals for T_sat/T_rec = 2 s, 3 s, 5 s, and 10 s are 1.8%, 0.9%, 0.5%, and 0.5%, respectively. Conversely, the maximal absolute residual for QUASS data using any T_sat/T_rec is 0.5% comparable to that of the T_sat/T_rec = 10 s. Fitting using the model-based approach also reasonably fits the data (Fig. 1c). As the rotating-frame model is predicated on an assumption of steady-state, the maximal absolute residuals (Fig. 1d) for T_sat/T_rec = 2 s and 3 s are slightly higher at 2.4% and 1.2%, respectively. However, the maximal absolute residual for T_sat/T_rec above 5 s and the QUASS data using any T_sat/T_rec are smaller at 0.3% for 5 s and 0.2% for both QUASS and 10 s. Simulations for the system at a reduced pH of 6.5 (Fig. 1e) exhibited reduced peaks at 2.6 and 3.5 ppm, while the peak at 2.0 ppm showed better definition compared to the pH 7.0 Z-spectra (Fig. 1a). The trends with respect to saturation lengths and relaxation delays, however, behaved similarly. Multi-Lorentzian fitting exhibited minimal residuals (Fig. 1f) for T_sat/T_rec = 2 s, 3 s, 5 s, and 10 s of 1.7%, 0.9%, 0.4%, and 0.4%, respectively, with 0.4% using any T_sat/T_rec under QUASS. Model-based fitting (Fig. 1g) also exhibited comparable results with fitting residuals (Fig. 1h) for T_sat/T_rec = 2 s, 3 s, 5 s, 10 s being 2.4%, 1.2%, 0.2%, and 0.1%, respectively, with 0.1% using any T_sat/T_rec under QUASS.

Exchange Parameter Determination using Ω-Plot Analysis of Multi-Lorentzian and Model-based Fit Simulated Z-spectra with varying Saturation Times and Relaxation Delays

To investigate the potential of using the fitted curves from multi-Lorentzian and model-based analysis, spillover corrected Ω-plots were constructed from fitted amplitudes at 3.6 ppm determined from data simulated using T_sat/T_rec = 2 s, 3 s, 5 s, 10 s (Fig. 2). At pH 7.0, the Ω-plots of the multi-Lorentzian fitted amplitude vs. 1/ω² fitted well by linear regression (${\stackrel{-}{R}}^2=0.988$ for QUASS T_sat/T_rec = 2 s) (Fig. 2a). The pH 7.0 Ω-plots constructed from using model-based fitting method also exhibit high linearity (${\stackrel{-}{R}}^2=0.999$ for QUASS T_sat/T_rec = 2 s) approaching the fitted curves determined from QUASS reconstructed Z-spectra as T_sat and T_rec become longer (Fig. 2b). Fitted exchange rates (k_ex) are larger at lower times for T_sat and T_rec since the slope-to-intercept ratio is larger compared to the steady-state for multi-Lorentzian fitting and model-based fit curves (Fig. 2c). Parameters determined from data reconstructed through QUASS remain comparatively consistent across all T_sat and T_rec at values converging with parameters determined from standard Z-spectra as T_sat and T_rec become excessively long. This finding demonstrates the fidelity of quantification using QUASS data regardless of the T_sat and T_rec used for imaging. There is a large underestimation in the k_ex calculated using equilibrium data fit by multi-Lorentzian fitting as opposed to model-based fitting, considering the ground truth k_ex for this proton was 130 s⁻¹. In f_amide, there was underestimation in both model-based and multi-Lorentzian values compared to the true value of 0.045% with larger error in multi-Lorentzian values (Fig.2d). These values also approach QUASS values with increasing T_sat and T_rec. For the Ω plots using Z-spectra data simulated for pH 6.5 (Fig. 2e–h), linearity holds up well due to the dependence of ssMT on power with ${\stackrel{-}{R}}^2=0.988$ for QUASS values using multi-Lorentzian fitting (Fig. 2e). For model-based fitting (Fig. 2f), steady-state and QUASS Z-spectra fit well under the rotating-frame model and generated Ω-plots with good linearity (${\stackrel{-}{R}}^2=0.999$), preserving the integrity of exchange parameter determination. Again, from these Ω-plots, the equilibrium k_ex is underestimated using the CEST signal from the multi-Lorentzian fit as compared to model-based fitting, which comes close to the ground truth of 50 s⁻¹ at pH 6.5 (Fig. 2g). In this case, calculated k_ex quickly increases as T_sat and T_rec become too short. On the other hand, f_amide decreases as T_sat and T_rec become shorter, perhaps due in part to the inverse relationship with k_ex (Fig. 2h).

Fig. 2. Exchange parameter determination through Ω-plots constructed using amide pool parameters extracted from multi-Lorentzian and Model-Based Fitting of simulated native and QUASS Z-spectra.

(A) Ω-plots of CEST_i⁻¹ (solid circles) from multi-Lorentzian fitting versus (γB₁ [rad])⁻² from native Z-spectra at pH 7.0 using T_sat/T_rec of 2 s (black), 3 s (red), 5 s (blue), 10 s (cyan), and 2 s with QUASS reconstruction (magenta) with linear fit (lines). (B) Ω-plots of CEST_i⁻¹ from model-based fitting versus (γB₁)⁻² from native and QUASS Z-spectra at pH 7.0. (C) Exchange rates (k_ex) calculated across various T_sat/T_rec from Ω-plots of native (black) and QUASS (red) Z-spectra at pH 7.0 fit with multi-Lorentzian (dashed) or model-based (solid) fitting. (D) Amide proton fraction (f_amide) calculated across various T_sat/T_rec from Ω-plots of native and QUASS Z-spectra at pH 7.0 fit with multi-Lorentzian or model-based fitting. (E) Ω-plots of CEST_i⁻¹ from multi-Lorentzian fitting versus (γB₁)⁻² from native and QUASS Z-spectra at pH 6.5. (F) Ω-plots of CEST_i⁻¹ from model-based fitting versus (γB₁)⁻² from native and QUASS Z-spectra at pH 6.5. (G) Exchange rates (k_ex) calculated across various T_sat/T_rec from Ω-plots of native and QUASS Z-spectra at pH 6.5 fit with multi-Lorentzian or model-based fitting. (H) Amide proton fraction (f_amide) calculated across various T_sat/T_rec from Ω-plots of native and QUASS Z-spectra at pH 6.5 fit with multi-Lorentzian or model-based fitting.

Fig. 3 shows heat maps of relative error with respect to the ground truth for exchange parameters determined from multi-Lorentzian and model-based fitting using Z-spectra simulated with various saturation times and relaxation delays. As the figure shows, the determination of exchange parameters is highly dependent upon these acquisition parameters, particularly for saturation time. However, at both pHs, exchange parameter determination is much more consistent when the steady state is approximated through QUASS reconstruction. We can also see that for both pH, exchange rates determined using CEST signals from multi-Lorentzian fitting tend to have a consistent error across different saturation times, which is consistently more erroneous than using CEST signals from model-based fitting. On the other hand, for amide proton fraction, multi-Lorentzian fitting exhibits a higher error at pH 7 than pH 6.5, while model-based fitting exhibits a consistent error at both pH values, comparable to multi-Lorentzian at 6.5. As a result, QUASS fitting improves the consistency of calculated values, while model-based fitting increases the accuracy of the determined exchange parameters as well as consistency across pH.

Fig. 3. Heatmaps of relative error in exchange parameters calculated from simulations across various combinations of saturation time (T_sat) and relaxation delays (T_rec) with multi-Lorentzian Fitting and rotating frame model based-fitting of native and QUASS Z-spectra at pH 7.0 and 6.5.

(A) The exchange rate (k_ex) was calculated from simulated native and QUASS Z-spectra at pH 7.0 using multi-Lorentzian or model-based fitting across various combinations of T_sat and T_rec. (B) Amide proton fraction (f_amide) calculated from simulated native and QUASS Z-spectra at pH 7.0 using multi-Lorentzian or model-based fitting across various combinations of T_sat and T_rec. (C) The exchange rate (k_ex) was calculated from simulated native and QUASS Z-spectra at pH 6.5 using multi-Lorentzian or model-based fitting across various combinations of T_sat and T_rec. (D) Amide proton fraction (f_amide) calculated from simulated native and QUASS Z-spectra at pH 6.5 using multi-Lorentzian or model-based fitting across various combinations of T_sat and T_rec.

Model-based Fitting of Whole Brain-averaged CEST Z-spectra in Rat Brains before and after Cardiac Arrest-induced Global Ischemia (n=6)

The whole brain-averaged native and QUASS Z-spectra were fit to the rotating-frame model before and after cardiac arrest across RF powers (Fig. 4). The disparity between the native (black) and QUASS Z-spectra (red) at 0.25 μT (Fig. 4a) indicates that the saturation time used here is not sufficient to reach equilibrium. Nonetheless, the rotating-frame model (solid lines) fits very well with native Z-spectra (black circles, Z_app) as well as QUASS Z-spectra (red circles, Z_QUASS) with minimal residuals (maximal absolute residual was 0.74% for Z_app and 1.10% for Z_QUASS). The better-established multi-Lorentzian model also performed comparably (results shown in Supplementary Fig. 2).

Fig. 4. Rotating-frame model-based fitting of native and QUASS Z-spectra from rodents before and after cardiac arrest (n = 6).

(A) A close-up of mean native (black) and QUASS (red) Z-spectra (open circles) using 0.25 μT saturation averaged over whole-brain ROIs before cardiac arrest and fit with rotating-frame model-based fitting (solid lines) with the fitting residuals below. (B) A close-up of amide (blue) and guanidino (red) peaks along with the −3.5 ppm rNOE peak (brown) of mean native (dotted lines) and QUASS (solid lines) Z-spectra using 0.25 μT saturation obtained from whole-brain ROIs before cardiac arrest. (C) Mean native and QUASS Z-spectra with model-based fit and (D) individual peaks using 0.25 μT saturation averaged over whole-brain ROIs after cardiac arrest. (E) Mean native and QUASS Z-spectra with model-based fit and (F) individual peaks using 1.0 μT saturation averaged over whole-brain ROIs before cardiac arrest. (G) Mean native and QUASS Z-spectra with model-based fit and (H) individual peaks using 1.0 μT saturation averaged over whole-brain ROIs after cardiac arrest.

At the power of 0.25 μT, curve-fitting utilizing the rotating-frame model generated individual curves for amide (1.06 ± 0.18% [mean ± SD] /1.18 ± 0.12% for Z_app/Z_QUASS) and rNOE at −3.5 ppm (2.44 ± 0.46%/2.74 ± 0.25% for Z_app/Z_QUASS) with reasonable consistency across animals (Fig. 4b). However, for guanidino, the curves expressed considerably higher volatility for fitting in both native and QUASS Z-spectra (1.71 ± 1.30%/1.75 ± 1.55% for Z_app/Z_QUASS). This may be attributed to the proximity to water resonance resulting in a lower signal as well as the relatively higher exchange rate for guanidino protons, which result in much broader, less defined CEST peaks. The reduced definition in peak shape makes it increasingly difficult to separate from ssMT and bulk water signals (shown in Supplementary Fig. 3), reducing certainty in guanidino quantification. After cardiac arrest, the peak at 2.0 ppm in both Z_app and Z_QUASS spectra became better defined while the amide peak was reduced (Fig. 4c). Nonetheless, the rotating-frame model fits the Z-spectra well with a relatively low fitting residual (maximal absolute residual was 0.77% for Z_app and 1.15% for Z_QUASS). However, though model-based fitted curves for amide (0.69 ± 0.19%/0.78 ± 0.11% for Z_app/Z_QUASS) exhibited peak reduction for both Z-spectra, guanidino reduced in peak for Z_app (1.56 ± 0.59%) and increased in peak for Z_QUASS (1.83 ± 0.57%) after ischemia (Fig. 4d) showing considerable volatility at this power. On the other hand, the peaks for rNOE at −3.5 ppm from both Z-spectra exhibited an increase (3.79 ± 0.89%/3.87 ± 0.63% for Z_app/Z_QUASS), which could be from incomplete fitting. At a higher power of 1.0 μT, the Z-spectra and metabolite curves before (Fig. 4e–f) and after cardiac arrest (Fig. 4g–h) exhibit model-based fitting with smaller residual differences than those at the lower power. Compared to 0.25 μT, the difference between Z_app and Z_QUASS is slightly closer at 1.0 μT since the increased power has pushed the system closer to the steady state within the same saturation time. Model-based fitting of Z-spectra at this power exhibits smaller residuals than at 0.25 μT (maximal absolute residual was 0.39% for Z_app and 0.53% for Z_QUASS before ischemia and 0.40% for Z_app and 0.57% for Z_QUASS after ischemia). The calculated fitted peaks at 1.0 μT for amide, guanidino, and rNOE_{-3.5 ppm} before ischemia were 6.06 ± 0.62%/7.03 ± 0.62%, 10.32 ± 1.40%/12.08 ± 1.53%, and 9.39 ± 0.81%/10.51 ± 1.77%, respectively. At this power, amide and guanidino peaks reduced after cardiac arrest to 1.95 ± 0.86%/2.07 ± 0.83% and 5.93 ± 1.67%/6.70 ± 1.43%, while the rNOE_{-3.5 ppm} peak increased to 12.71 ± 0.97%/14.42 ± 2.08%.

Determination of k_ex and f_amide through spillover-corrected Ω-plots from Whole Brain-averaged CEST Z-spectra Fit with Multi-Lorentzian and Model-based Fitting (n=6)

The RF spillover-corrected Ω-plots were constructed to determine exchange parameters using the fitted data for whole brain-averaged Z-spectra (Fig. 5). The Ω-plots using the fitting parameters from multi-Lorentzian fitting of native Z-spectra (Fig. 5a) show resemblance to the plots from simulated data in Fig.2a and 2e. The Ω-plots from the multi-Lorentzian fitting of native Z-spectra before cardiac arrest show relative linearity across all powers (${\stackrel{-}{R}}^2=0.964\pm .043$) similar to the data simulated in Figure 2 at pH 7.0. After cardiac arrest, the Ω-plots show strongly reduced linearity for certain animals (${\stackrel{-}{R}}^2=0.686\pm .328$) at pH 6.5. With the application of multi-Lorentzian fitting to QUASS Z-spectra (Fig. 5b), there is improved linearity (${\stackrel{-}{R}}^2=0.965\pm .065$ before cardiac arrest and ${\stackrel{-}{R}}^2=0.913\pm .097$ after cardiac arrest).

Fig. 5. Exchange parameter determination through Ω-plots constructed using amide pool parameters extracted from multi-Lorentzian and Model-Based Fitting of mean native and QUASS Z-spectra from whole-brain Z-spectra of rodents before and after cardiac arrest (n = 6).

(A) Ω-plots of CEST_i⁻¹ (solid circles) from multi-Lorentzian fitting versus (γB₁ [rad])⁻² from mean native Z-spectra from rodents before (black) and after (red) cardiac arrest. (B) Ω-plots of CEST_i⁻¹ (solid circles) from multi-Lorentzian fitting versus (γB₁ [rad])⁻² from mean QUASS Z-spectra from rodents before and after cardiac arrest. (C) Ω-plots of CEST_i⁻¹ (solid circles) from model-based fitting versus (γB₁ [rad])⁻² from mean native Z-spectra from rodents before and after cardiac arrest. (D) Ω-plots of CEST_i⁻¹ (solid circles) from model-based fitting versus (γB₁ [rad])⁻² from mean QUASS Z-spectra from rodents before and after cardiac arrest. (E) Box plots of exchange rates (k_ex) calculated from Ω-plots of native and QUASS Z-spectra with multi-Lorentzian or model-based fitting before (black) and after (red) cardiac arrest. The black asterisk (*) indicates a significant difference (p<0.05) from Wilcoxon signed rank tests among parameters before cardiac arrest, and the red asterisk indicates significance after cardiac arrest, while bracketed asterisks ([*/*]) indicate a significant difference between a parameter before and after ischemia. (F) Bland Altman plot comparing the agreement between k_ex calculated between multi-Lorentzian fitting of native Z-spectra and model-based fitting of QUASS Z-spectra for data before (black) and after (red) cardiac arrest. The bounds represent the 95% confidence intervals. (G) Box-plots of amide proton fraction (f_amide) calculated from Ω-plots of native and QUASS Z-spectra with multi-Lorentzian or model-based fitting before and after cardiac arrest. (H) Bland Altman plot comparing the agreement between f_amide calculated between multi-Lorentzian fitting of native Z-spectra and model-based fitting of QUASS Z-spectra for data before (black) and after (red) cardiac arrest with 95% confidence intervals.

The Ω-plots using the fitting parameters from the model-based fitting of native Z-spectra (Fig. 5c) exhibited strong linearity before cardiac arrest (${\stackrel{-}{R}}^2=0.964\pm .032$) with moderately reduced linearity in Ω-plots after cardiac arrest (${\stackrel{-}{R}}^2=0.817\pm .152$). QUASS Z-spectra for model-based fit Ω-plots (Fig. 5d) generates curves with slightly improved linearity before cardiac arrest (${\stackrel{-}{R}}^2=0.976\pm .031$) and after cardiac arrest (${\stackrel{-}{R}}^2=0.871\pm .039$). While Ω-plots before cardiac arrest resulted in points with relatively low variation across animals, Ω-plots after cardiac arrest resulted in points with significantly increased variability, which may be attributed to both reduced CEST sensitivity as well as increased difficulty in controlling environmental conditions for animals post-mortem.

Box-plot analysis of exchange rates calculated from Ω-plots of amide peaks from curve fitting (Fig. 5e) reveals ranges for calculated exchange rates before ischemia (64 ± 13 for Z_app and 61 ±11 s⁻¹ for Z_QUASS using multi-Lorentzian fitting and 122 ± 34 s⁻¹ for Z_app and 126 ± 25 s⁻¹ for Z_QUASS using Model-based fitting, Table 1). After the induction of cardiac arrest, calculated exchange rate drops (38 ± 16 s⁻¹ for Z_app and 50 ± 18 s⁻¹ for Z_QUASS using multi-Lorentzian fitting and 52 ± 21 s⁻¹ for Z_app and 49 ± 13 s⁻¹ for Z_QUASS using Model-based fitting, Table 1). Using the Wilcoxon signed-rank test to examine statistical differences, the differences between exchange rates calculated from the multi-Lorentzian fitting of either Z_app or Z_QUASS were shown to be significantly disparate from the exchange rates calculated from the model-based fitting of either Z_app or Z_QUASS (p < 0.05) before cardiac arrest. There was a clear statistical difference between ante-mortem and post-mortem values (p < 0.05) with each fitting method except multi-Lorentzian fitting of Z_QUASS, which had unstable post-mortem exchange rates. Bland-Altman analysis between exchange rates based on amide peaks from multi-Lorentzian fitting of apparent native Z-spectra and exchange rates based on amide peaks from the model-based fitting of QUASS Z-spectra (Fig. 5f) revealed a clear systematic bias on average 35.75 s⁻¹ in favor of model-based fitting. Moreover, there was a trend of increasing bias with increasing exchange rates. As the difference across methods changed with the calculated exchange rate, the apparent random error was broad (S.D. = 30.53); however, there was no evidence of outliers.

Table 1:

Mean and standard deviation (S.D.) parameters obtained from the whole brain in rodents before and after cardiac arrest (n=6)

Parameters			Ante-Mortem		Post-Mortem
			Mean	S.D.	Mean	S.D.
Water Relaxation		T1 (s)	1.71	0.17	1.83	0.42
		T2 (ms)	55.9	0.81	51.6	0.91
Multi-Lorentzian	Z app	kex (s−1)	63.9	13.3	37.7	15.7
		famide (%)	0.027	0.003	0.021	0.005
	Z QUASS	kex (s−1)	61.1	11.1	49.9	17.6
		famide (%)	0.032	0.005	0.021	0.007
Model-based	Z app	kex (s−1)	121.6	34.2	51.6	21.2
		famide (%)	0.035	0.003	0.021	0.006
	Z QUASS	kex (s−1)	126.0	24.8	48.7	13.3
		famide (%)	0.040	0.004	0.026	0.008

The amide fractions calculated from Ω-plots of amide peaks from curve fitting (Fig. 5g) were also relatively stable before global ischemia (2.7 ± 0.3 × 10⁻⁴ for Z_app and 3.2 ± 0.5 × 10⁻⁴ for Z_QUASS using multi-Lorentzian fitting and 3.5 ± 0.3 × 10⁻⁴ for Z_app and 4.0 ± 0.5 × 10⁻⁴ for Z_QUASS using model-based fitting, Table 1) with increased variability after cardiac arrest (2.1 ± 0.5 × 10⁻⁴ for Z_app and 2.1 ± 0.7 × 10⁻⁴ for Z_QUASS using multi-Lorentzian fitting and 2.1 ± 0.6 × 10⁻⁴ for Z_app and 2.6 ± 0.8 × 10⁻⁴ for Z_QUASS using model-based fitting, Table 1). There were statistical differences among calculated amide proton fractions for Z_app using multi-Lorentzian fitting and amide proton fraction using model-based fitting for either Z_app or Z_QUASS before global ischemia, and only model-based fitting using either Z_app or Z_QUASS generated a clear statistical difference between proton fractions before and after cardiac arrest (p < 0.05). Bland-Altman analysis between amide fraction from Lorentzian fitting of apparent native Z-spectra and model-based fitting of QUASS Z-spectra (Fig. 5h) revealed a systematic bias of 0.4 × 10⁻⁴ in favor of model-based fitting with limited trend. The apparent random error for the amide fraction was also broad (S.D. = 0.6 × 10⁻⁵). However, there was no specific evidence of glaring outliers.

Multi-slice In vivo Parametric Maps of an Exemplary Rodent before and after Cardiac Arrest-induced Global Ischemia from Voxel-based Ω-plots of QUASS CEST signals from Multi-Lorentzian and Model-based Fitting using IDEAL

Fig. 6 shows multi-slice parametric maps from voxel-by-voxel Ω-plots from Lorentzian and Model-based fitting of QUASS CEST data using IDEAL at multiple powers for an exemplary rodent before (Fig. 6a) and after (Fig. 6b) cardiac arrest-induced global ischemia. As expected, the k_ex maps calculated using multi-Lorentzian fittings were lower than those computed using model-based fitting. While there appeared to be some gray/white matter contrast in the exchange rate maps, comparison with T₁ maps reveals the contrast to differ from longitudinal relaxation, particularly for the maps calculated using model-based fitting. This shows that QUASS reconstruction has performed well in removing T₁ contributions to the signal(75). Similarly, f_amide maps were higher using model-based fitting when compared to maps calculated using multi-Lorentzian fitting. However, f_amide maps from multi-Lorentzian fittings showed significantly more correlation with T₁ maps. In contrast, f_amide maps from model-based fitting showed relatively uniform contrast across the entire brain. After cardiac arrest (Fig. 6b), despite the possible reduction in temperature, T₁ maps showed minor change across brain tissue aside from the drop in T₁ in the ventricles. The maps for k_ex calculated using both multi-Lorentzian fitting and model-based fitting showed sharp drops after the induction of global ischemia through cardiac arrest. Similarly, both f_amide maps from multi-Lorentzian fitting and model-based fitting showed global decreases post-mortem. However, in both maps, there appear to be regions that are abnormally high due to fitting errors. Despite their appearing on f_amide maps with model-based fitting as well, the frequency of these voxels is significantly reduced using model-based fitting.

Fig. 6. Multi-slice parametric maps for an exemplary rodent before and after cardiac arrest.

(A) T₁ maps with k_ex and f_amide maps calculated with the multi-Lorentzian or model-based fitting of QUASS Z-spectra before cardiac arrest. (B) T₁ maps with k_ex and f_amide maps calculated with the multi-Lorentzian or model-based fitting of QUASS Z-spectra after global ischemia.

Discussion

Our study demonstrated QUASS reconstructed Z-spectra, along with model-based spectral fitting, improves the accuracy of exchange parameter quantification with Ω-plot determination. Our simulation results have shown that using QUASS Z-spectra improved the fidelity and standardization of parametrization results across varying saturation and acquisition conditions. Moreover, they demonstrate systematic differences in the determined exchange rate as well as labile proton fraction with fitting parameters determined through the multi-Lorentzian fitting. On the other hand, utilizing parameters determined through model-based fitting based on the rotating-frame model resulted in exchange parameters that followed quite closely with the ground truth in simulation. Our in vivo results concur with our simulations, demonstrating a systematic difference between fitting using the multi-Lorentzian model versus the rotating-frame model, which results in consistently lower exchange rates using multi-Lorentzian fitting. Interestingly, unlike the simulations, there was also a clear systematic difference in proton fractions calculated using the multi-Lorentzian model versus the rotating-frame model. This is likely due to the increased underestimation of the Lorentzian peaks due to the presence of overlapping ssMT pool in vivo.

Our results provided some insight into one potential contributing factor to the broad range of exchange rates reported in the literature (4,42,45–48), from about 30 to 300 s⁻¹. With the complexity of the amide signal as a composite of a myriad of differing amide signals, as well as the derivation of our results from curve fitting, it may be difficult to conclude a definitive answer to the exchange rate of amides. However, our calculated exchange of 126 s⁻¹ was comparable with the range of reported exchange rates, improving quantification with CEST MRI sequence and QUASS postprocessing. Nonetheless, our results have demonstrated an underestimation when exchange parameter quantification is performed using parameters conventionally extracted in the Z-domain, such as standard Lorentzian peaks. Quantification will likely benefit from using CEST signals quantified in at least the inverse Z-domain, such as model-based fitting, or utilizing other 1/Z metrics, e.g., R_ex (76), MTRR_ex (77), or AREX (78).

Peak extraction performed directly from Z-spectra suffers from the fact that concomitant effects are not directly separable in the Z-domain. While approximate separation may be useful for relative comparison, precise quantification suffers particularly at lower fields such as 4.7 T (not to mention 3T), where spectral proximity of adjacent peaks is detrimental. Conversely, these adjacent effects are linearly separable in R_ex while under the steady-state (which underlines the importance of the usage of QUASS), R_ex can be analytically related to 1/Z, enabling facile quantification of individual CEST peaks. However, direct fitting in R_ex comes with challenges as in vivo derivations of R_ex tend to deviate as offset frequency diverges from water resonance. Alternatively, MTRR_ex and AREX, which relate with each other by R₁ and relate to R_ex by tan²ϑ approaches a singularity at water resonance, which also complicates direct fitting. Thus, 1/Z fitting has been carried out indirectly by fitting Z to models in the denominator, thereby circumventing the singularity issue that has been employed by the rotating-frame model-based fitting used in the current paper and by Polynomial and Lorentzian Line-shape Fitting, which focuses on specific peaks and relegates other sources to the background(64,67). While applying 1/Z fitting in forms such as using the rotating-frame model does solve the coupling issue of concomitant exchanges and should be broadly applicable to other exchanges such as the guanidino peak, it still cannot solve the sensitivity issue due to direct saturation of background water which affects proper quantification of peaks in close proximity to water resonance. As a result, there is a large error in the guanidino peak, particularly before cardiac arrest, which obfuscates proper quantification and makes it difficult to compare to the post-mortem condition properly. Due to this, this study focuses primarily on the amide peak, which has sufficient resolution compared to water resonance. However, proper quantification of guanidino exchanges may be feasible at higher field strengths that benefit from increased spectral resolution.

A limitation of the current study is the post-mortem dynamics that may occur during acquisition after cardiac arrest. While relaxation conditions such as T₁ remain relatively consistent, similar to that demonstrated by Fagan et al. (79), temperature was controlled via heated air to further minimize relaxation differences. The larger concern is changes to the proteome. In fact, there have been reports that rapid proteolysis after death impacts the integrity of cellular proteins (80,81), which would have a significant effect on amide concentration. These dynamic changes may be the source of the unexpected concentration drop measured in amides after global ischemia, as well as the increased variability in post-mortem quantification. From our results, model-based fitting of QUASS data described a statistically significant difference, dropping from 47.7 mM to 30.8 mM (calculated by assuming the total proton concentration is dominated by the 111 M concentration of water protons). Proteolysis of amides may potentially increase fast amines, which, however, are too fast to quantify, particularly at the current field strength. With the conclusion of this study, there is a need to recalibrate the correlation of pH and exchange rate for in vivo amides to ensure that calibration with exchange rates determined in the rotating frame can be matched with pH determined through MR spectroscopy (82–87) as the difference in exchange parameter quantification is certain to have a profound effect on pH calibration. Furthermore, future studies are needed to confirm whether this methodology can provide consistent results at differing field strengths and whether a higher field can enable proper quantification of peaks that are closer to direct water saturation, such as the guanidino peak and the smaller phosphocreatine peak, which have exchange parameters that are still under contention(42,88–92).

Conclusion

While Z-domain peak fitting with the multi-Lorentzian approach could be a source of error that may lead to underestimation in the quantification of CEST exchange effects, model-based fitting of QUASS CEST Z-spectra enables consistent and accurate quantification of exchange parameters through Ω-plot construction by reducing error due to signal overlap and non-equilibrium CEST effects. Therefore, QUASS-boosted quantitative CEST analysis could be a powerful tool for advancing in vivo CEST quantification and ultimately may enable precise pH and protein content mapping in multiple diseases.