Correction for artifacts induced by B0 and B1 field inhomogeneities in pH-sensitive chemical exchange saturation transfer (CEST) imaging

Authors

  • Phillip Zhe Sun,

    Corresponding author
    1. Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, Massachusetts, USA
    • Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129
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  • Christian T. Farrar,

    1. Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, Massachusetts, USA
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  • A. Gregory Sorensen

    1. Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, Massachusetts, USA
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Abstract

Chemical exchange saturation transfer (CEST) imaging provides an indirect detection mechanism that allows quantification of certain labile groups unobservable using conventional MRI. Recently, amide proton transfer (APT) imaging, a variant form of CEST imaging, has been shown capable of detecting lactic acidosis during acute ischemia, providing information complementary to that of perfusion and diffusion MRI. However, CEST contrast is usually small, and therefore, it is important to optimize experimental conditions for reliable and quantitative CEST imaging. In particular, CEST imaging is sensitive to B0 and B1 field, while on the other hand; field inhomogeneities persist despite recent advances in magnet technologies, especially for in vivo imaging at high fields. Consequently, correction algorithms that can compensate for field inhomogeneity-induced measurement errors in CEST imaging might be very useful. In this study, the dependence of CEST contrast on field distribution was solved and a correction algorithm was developed to compensate for field inhomogeneity-induced CEST imaging artifacts. In addition, the proposed algorithm was verified with both numerical simulation and experimental measurements, and showed nearly complete correction of CEST imaging measurement errors caused by moderate field inhomogeneity. Magn Reson Med, 2007. © 2007 Wiley-Liss, Inc.

Chemical exchange saturation transfer (CEST) imaging provides a sensitivity enhancement mechanism that allows for indirect detection of exchangeable protons from mobile proteins and peptides, in which selective irradiation of labile protons attenuates the bulk water signal through saturation transfer (1–4). Because chemical exchange is often pH-dependent, CEST imaging can be sensitive to microenvironment pH (2, 5–9). Indeed, it has been shown that lactic acidosis during acute ischemia can be detected through amide proton transfer (APT) MRI, a particular variant of CEST imaging that utilizes labile amide protons from endogenous proteins and peptides (9, 10). Because tissue pH is closely correlated with glucose metabolism during acute stroke, CEST imaging might eventually serve as an informative imaging marker complementary to commonly used perfusion and diffusion MRI (10, 11).

For labile protons whose chemical shift is well separated from that of the bulk water, the CEST contrast (proton transfer ratio [PTR], to specify CEST imaging using proton exchange) can be described using a two-pool exchange model consisting of a small pool (s) for labile solute protons and a large pool (w) representing bulk water protons (12–14). The saturation transfer process is usually quantified using the magnetization transfer ratio (MTR = 1 − Ssat/S0), by comparing bulk water signal with and without RF irradiation of labile protons. However, if RF irradiation power is not negligible in comparison with the chemical shift difference between labile protons and bulk water protons (Δωs), there will be direct RF saturation of water signal (spillover effects), making the derived MTR nonspecific to the saturation transfer process. As a result, an MT asymmetry analysis is often applied to compensate for such RF spillover effects, wherein the label image is subtracted from a reference scan, with RF irradiation applied at the labile frequency (Δωs) and reference frequency (−Δωs), respectively (15). Because the irradiation RF pulses for label and reference scans are symmetric around the bulk water resonance, RF spillover effects are approximately equal and can be suppressed by MTR asymmetry (MTRasym) analysis (16, 17). However, in the presence of severe B0 inhomogeneity, the label and reference scans are no longer symmetric about the water resonance, and consequently, the asymmetry analysis cannot remove the spillover effects, and instead, it will introduce a B0 inhomogeneity-dependent MTR offset. Such an MTR offset, if not properly accounted for, may cause nonnegligible errors in quantitative CEST imaging. In addition, for in vivo CEST imaging, there is also inherent magnetization transfer (MT) between semisolid macromolecules and bulk water (18–20), which are also dependent on the local magnetic fields (21–23). Given that commonly obtainable endogenous CEST imaging contrast is only a few percent, it is crucial to correct for field inhomogeneity-induced measurement errors for quantitative CEST imaging.

Because z-spectrum records bulk water signal while the irradiation RF is swept around the bulk water resonance, the maximal CEST contrast is reached when the labeling RF pulse is on resonance with the labile proton frequency. In the presence of B0 field inhomogeneity, the RF irradiation frequency at which the CEST contrast is maximal is shifted according to the local field per voxel. As a result, the B0 inhomogeneity-induced measurement errors can be compensated for by interpolating the z-spectrum for the maximal CEST contrast. However, it may take very long experiment time to acquire a z-spectrum with very fine frequency interval, and therefore, the interpolation approach is not suitable to study dynamic diseases such as acute stroke. In this study, we developed a correction algorithm that enables compensation of field-inhomogeneity induced measurement errors in CEST imaging with commonly used three-point CEST scan (label, reference, and control scan). We first quantified the dependence of PTR on B0 and B1 fields using a classic two-pool chemical exchange model and developed a correction algorithm that can compensate for field inhomogeneity-induced errors in CEST imaging. We then showed that the proposed algorithm can correct measurement errors in numerically simulated CEST imaging. Moreover, we characterized a tissue-like gel phantom using numerical fitting of a three-pool exchange model, and verified the proposed algorithm using a tissue-like pH phantom.

THEORY

Pool Chemical Exchange

The CEST contrast mechanism is typically described using a two-pool exchange model, which provides a simple yet reasonably accurate representation of the saturation transfer process. For very long RF irradiation, the PTR can be shown to be equal to (17):

equation image(1)

where PTRmax is the maximal PTR, given by equation image, α is the labeling coefficient, σ is the spillover factor, ksw,ws are the chemical exchange rates from labile proton to bulk water and vice versa, r1w,s = R1w,s + kws,sw, r2w,s = R2w,s + kws,sw, in which R1w,s and R2w,s are the intrinsic longitudinal and transverse relaxation rates of bulk water and labile groups, respectively. For slow to intermediate chemical exchange, the labeling coefficient is equal to equation image, here equation image, equation image, and ω1 is the irradiation RF power. In the presence of field inhomogeneity, however, the labeling coefficient is modulated because the off resonance RF pulse is less efficient in saturating the exchangeable protons, and can be shown to be,

equation image(2)

where Δω is the frequency difference between the labeling RF and the labile proton resonance. For a labeling pulse on resonance with labile protons (i.e., Δω = Δωs), the labeling coefficient can be shown to be equal to that derived by Zhou et al. (24).

In order for the MT asymmetry (MTRasym) analysis to compensate for RF spillover effects, the label and reference scan must be symmetric around the water resonance so that we have MTRasym ≈ PTR. In the presence of B0 inhomogeneity, MTRasym is equal to the difference of images acquired at the mismatched “label” and “reference” frequencies (Fig. 1a) as,

equation image(3)

where PTR′ represents PTR without B0 field inhomogeneity-induced MTR offset, and ΔMTR is the MTR offset caused by mismatched asymmetry analysis. It is important to note that PTR′ is modulated from the true PTR because the labeling coefficient and spillover factor are also RF field–dependent.

Figure 1.

a: Numerically-simulated z-spectra using a two-pool exchange model (B1 = 1 μT). The solid black line represents a z-spectrum and its corresponding asymmetry curve. In the presence of B0 field inhomogeneity, the “label” and “reference frequencies” are shifted by the same amount (flabel, fref vs. flabel′, fref′). An averaged z-spectrum with B1 field range between 1 ± 0.5 (42.6 ± 21.3 Hz) is shown by the dotted line, which nearly overlaps with the ideal z-spectrum. In addition, the dashed line represents a z-spectrum with B0 field inhomogeneity equally spaced within 0 ± 0.5 ppm (0 ± 200 Hz) around the bulk water resonance. b: MTRasym at 1.9 ppm (circles) as a function of the B1 field inhomogeneity. The corrected PTR is shown in gray solid line. c: MTRasym at 1.9 ppm for the asymmetry analysis by subtracting the “label” scan from that of the “reference” scan as a function of the B0 offset from bulk water resonance. It shows that MTRasym (black solid line) deviated significantly from simulated results under the condition of homogeneous B0 field (open circles). The MTR offset computed from Eq. [4] is shown by the black dashed line. PTR′ (gray dashed line) was obtained by subtracting the MTR offset from MTRasym and it agreed well with simulated data (circles). In addition, the fully compensated PTR (gray solid line) is nearly equal to the ideal CEST contrast of 16% across B0 field inhomogeneity.

For long continuous wave (CW) RF irradiation, the residual magnetization along the z-axis is given as equation image, where T1w, T2w are apparent longitudinal and transverse relaxation times for bulk water, and ΔωRF is the frequency offset between the RF irradiation pulse and bulk water resonance (14). ΔMTR can be derived by taking the difference between bulk water signals with the RF irradiation applied at the apparent “reference” ((Δωref = −Δωs + Δω)) and “label” ((Δωlabel = Δωs+Δω)) frequencies, respectively, and is equal to

equation image(4)

With MTR offset solved, the fully compensated PTR can be derived by taking into account the field inhomogeneity-induced modulation of the labeling coefficient and spillover factor as (17),

equation image(5)

where η is the modulation factor, and can be derived from Eq. [1] as,

equation image(6)

where α(B1,Δω) and σ(B1,Δω) are labeling coefficient and spillover factor for RF power of B1 and at B0 offset Δω from the labile proton resonance, respectively. In sum, the compensated PTR is given as,

equation image(7)

Pool Chemical Exchange

Because in vivo CEST imaging is susceptible to concomitant conventional MT effects and RF spillover effects, it may take a three-pool exchange model in order to properly describe the in vivo CEST contrast (25, 26); on the other hand, solutions for such a multipool exchange model are very complex while providing little insight (18). Fortunately, given that the transverse relaxation times for labile protons and semisolid macromolecules are very different (27), CEST contrast in the presence of concomitant MT effects can be accounted for by modifying the solution derived from the two-pool exchange model.

The three magnetization pools (bulk water, labile protons, and semisolid macromolecules) can be partitioned into two two-pool models: bulk water with labile protons (first two-pool), and bulk water with semisolid macromolecules (second two-pool), with negligible direct exchange between labile protons and macromolecules (28, 29). The solution for the first two-pool model has been derived elsewhere (16, 17, 29). For the second two-pool model, because the transverse relaxation time of semisolid macromolecules is very short (∼10–15 μs) (18), MTR asymmetry analysis can suppress symmetric MT effects and MTRasym is not sensitive to B0 field inhomogeneity. As a result, the bulk water signal can be quantified using the formula I = equation image by Eng et al. (14), where the apparent relaxation time constants (T1wm, T2wm) can be shown to be equal to equation image, in which T1,2w is the intrinsic water relaxation time constant, αMT is the labeling coefficient defined in Eq. [3], and fMT and kMT, are the proton ratio and exchange rate from the semisolid macromolecule pool to bulk water, respectively. Because MTRasym for semisolid macromolecular MT is not sensitive to moderate B0 field inhomogeneity, the correction algorithm can be modified so that the conventional MT effects can be included by adjusting the apparent transverse relaxation time of bulk water.

MATERIALS AND METHODS

Phantom Preparation

A 3% agarose solution (w/w) was prepared by adding agarose (Sigma Aldrich, St. Louis, MO, USA) to filtered and deionized water (MilliPore, Billerica, MA, USA). The solution was heated to boiling and then immersed in a water bath set at 46°C (Cole-Parmer, Vernon Hills, IL, USA). After 15 min, the agarose solution was transferred into a 50-ml Falcon tube; creatine (Sigma Aldrich) was added to reach the concentration of 50 mM. The pH of the solution was then titrated to 6.5 at 46°C (EuTech Instrument, Singapore). For the dual pH phantom, additional gel solution was prepared (60 mM creatine in 3% agarose) following the same procedure. The solution was then transferred into a 15-ml Falcon tube, which was inserted into a 50-ml Falcon tube filled with the same gel solution. The pH for the inner tube was titrated to 5.9 while the pH of the exterior tube remained at 6.5 at 46°C. Phantoms were removed from the water bath and left at room temperature to solidify before experiments.

MRI and Data Processing

All images were acquired on a 9.4 T Bruker Biospec Imager (Bruker Biospin, Billerica, MA, USA). The RF power was calibrated using multiple preexcitation pulses ranging from 10° to 180° before the regular spin-echo acquisition. In addition, the main field (B0) was shimmed using Fastmap (30). Image readout was single-shot spin-echo echo planar imaging (EPI) (slice thickness = 3 mm, field of view = 50 × 50 mm, imaging matrix size = 64 × 64, TR = 15,000 ms, TE = 20 ms, and acquisition bandwidth = 267,000 Hz). T1 images were acquired using an inversion-recovery sequence with a global adiabatic inversion pulse (eight inversion intervals [TI] from 100 to 6000 ms and number of averages (NA) = 2). The T2 map was derived from five separate spin-echo images with echo times of 30, 40, 50, 60, and 80 ms (TR = 10,000 ms, NA = 2). The B0 map was obtained by acquiring five phase images with off-centered echo times (τ) of 0.25, 0.5, 1, 1.75, 2.5, and 3 ms. The B1 map was obtained using the double angle method (DAM) proposed by Stollberger and Wach (31). The CEST imaging comprised acquisition of three z-spectra from −1500 Hz to 1500 Hz with an offset interval of 50 Hz (TR = 15,000 ms, time of saturation [TS] =7500 ms, and NA = 1) at RF power of 0.4, 1, and 2 μT. Afterward, the first-order shimming gradient along the y axis was reduced by 4%, and two z-spectra were measured with RF irradiation power of 0.4 and 1 μT. For the dual-pH phantom, B0, B1, T1, and T2 maps and CEST z-spectra were acquired as described previously. In addition, three-point CEST imaging was performed with an irradiation pulse applied at ±750 Hz, in addition to a control scan (TR = 15,000 ms, TS = 7500 ms, TE = 20 ms, and NA = 8). The RF power used was 1 μT (42.6 Hz). Moreover, the shimming gradient along the y-axis was also varied by 4% to evaluate the proposed correction algorithm.

All images were processed in MATLAB (Mathworks, Natick, MA, USA). z-Spectra were obtained by normalizing RF-irradiated images by the control map, and plotted against the irradiation RF offset. The MTRasym map was computed by taking the difference between the label and reference images. Absolute T1 and T2 maps were derived by least square fitting of image intensity against the inversion delay and echo time, respectively. The B0 map was derived by linearly fitting the obtained phase map against the off-centered echo time (τ) using,

equation image(8)

where γ is the gyromagnetic ratio and ϕ is the unwrapped phase. The B1 map was calculated using

equation image(9)

where I1 and I2 are image intensities with excitation flip angles of 60° and 120°, respectively; τ is the duration of the excitation pulse. The PTR map was corrected using Eq. [7] based on the measured B0 and B1 field map, as well as T1 and T2 values.

Numerical Simulation

A simulated z-spectrum using the two-pool exchange model is shown in Fig. 1a (black line), with the following parameters: T1w = 3000 ms, T2w = 50 ms, T1s = 1000 ms, T2s = 15 ms, ksw = 50 s−1, and f = 1:200. The simulated labile proton frequency is 1.9 ppm (± 760 Hz) and the RF irradiation power is 1 μT (42.6 Hz).

The experimentally obtained z-spectrum with the RF power of 1 μT (42.6 Hz) was numerically fit using a modified routine for three-pool exchange model from Woessner et al. (28) with six independent variables: the transverse relaxation rates for bulk water (T2w) and CEST labile protons (T2s), and the chemical exchange rate (ksw, kmw) and concentration of the CEST and semisolid macromolecule protons (fs, fmt). Other parameters used were: T1w = 3 s, T1s = 1 s, T1mt = 1 s, T2mt = 15 μs, and Δωs = 1.875 ppm (750 Hz). The fitting takes about 6 s using an office PC with an Athelon Dual-core CPU.

RESULTS

A simulated z-spectrum using a two-pool exchange model (black line) is shown in Fig. 1a. The dip at 1.9 ppm (760 Hz) (flabel) represents the CEST contrast. The MTRasym was symmetric around the labile proton frequency, with its peak intensity being 16.6%. In Fig. 1a, the dotted line represents an averaged z-spectrum with RF power being 1 ± 0.5 μT (42.6 ± 21.3 Hz), which nearly overlapped with the ideal z-spectrum. On the other hand, B0 inhomogeneity induces significant changes in both the z-spectrum and the corresponding asymmetry curve. The dashed line in Fig. 1a represents a simulated z-spectrum with B0 offsets equally spaced within ±0.5 ppm (200 Hz) of bulk water resonance. Although the z-spectrum for negative frequencies showed little variation, significant artifacts can be observed around the labile proton frequency. For instance, in the presence of a B0 field error of 0.5 ppm (200 Hz), the “label” and “reference” scan will be applied at 1.4 ppm (560 Hz) and −2.4 ppm (−960 Hz) rather than at the ideal label and reference frequencies, namely ±1.9 ppm (760 Hz), and consequently the measured MTRasym is a superposition of the field inhomogeneity-modulated CEST effect and MTR offset. Figure 1a shows that in the presence of severe B0 inhomogeneity, MTRasym was significantly broadened and attenuated, with the peak CEST contrast decreased from 16.6% to 8.1%. In addition, B0 inhomogeneity causes RF irradiation applied at bulk water resonance to be equivalent to off-resonance saturation of bulk water for voxels with nonnegligible B0 offset, and therefore, the bulk water signal at the center frequency was no longer fully saturated, with a minimal value of 10.2%.

Figure 1b shows MTRasym at 1.9 ppm (760 Hz) as a function of the RF irradiation field. It initially increased with the B1 field, and reached its maximal value of 16.6% at about 0.7 μT (29.8 Hz). However, MTRasym decreased as RF powers continued to increase, similar as those observed by Sun et al. (17). The modulation factor from Eq. [6] can correct for such B1 artifacts (gray line), reducing the variance of the measured MTRasym (i.e., from 15.1 ± 1.4% to 15.6 ± 0.4%). Figure 1c shows MTRasym (6.8 ± 10.4 %) in the presence of a B0 field inhomogeneity of ±0.5 ppm (200 Hz) (black solid line). The open circles represent the simulated ideal PTR with homogenous B0 field. The large deviation of MTRasym from PTR shows that if B0 inhomogeneity is not accounted for, MTRasym will not be equal to PTR. For instance, at a B0 offset of −0.5 ppm (200 Hz), the derived MTRasym is actually negative, being −13.5%. MTRasym increased with better B0 homogeneity up to 16.6% at 0 ppm (i.e., homogeneous B0 field). For positive B0 field errors, however, MTRasym showed a complex pattern; it decreased initially but recovered after reaching a trough at 0.2 ppm (80 Hz). In addition, the gray dashed line represents the MTR offset (ΔMTR) caused by the asymmetry analysis of mismatched label and reference scans, as computed from Eq. [4]. The derived PTR′ showed excellent agreement with the simulated ideal PTR′ (circles). Moreover, by accounting for the modulation factor of the labeling coefficient and spillover factor, the compensated PTR is equal to 15.6 ± 1.3% (gray solid line), significantly improved from the directly measured MTRasym.

Shown in Fig. 2a are three z-spectra and their corresponding MTRasym from a phantom with minimal B0 field inhomogeneity (2 ± 9 Hz [mean ± SD]), with the RF irradiation power being 0.4 μT (17 Hz), 1 μT (42.6 Hz), and 2 μT (85.2 Hz), respectively. At weak and moderate RF powers (i.e., 0.4 and 1 μT), a prominent CEST peak can be observed, while the CEST contrast was significantly attenuated by concomitant spillover effects at high RF power (i.e., 2 μT) (17). To properly model the system, the z-spectrum with irradiation power of 1 μT was numerically fit using a three-pool exchange model. The bulk water T1 was measured to be 3 ± 0.02 s; therefore, T1w = 3 s was used for the simulation. T2 for bulk water was measured to be 39 ± 0.8 ms. Because short T2w is likely due to magnetization coupling of bulk water protons with semisolid macromolecules; T2w was assigned as an independent variable for fitting. In addition, the longitudinal relaxation time for labile proton was assumed to be 1 s (4, 17). Moreover, representative semisolid macromolecular relaxation times were used: T1mt = 1 s and T2mt = 15 μs (23). The parameters obtained from fitting were ksw = 125 s−1, fs = 1:742, T2s = 8.5 ms, kmt = 48 s−1, fmt = 1:48, and T2w = 48 ms. To validate the derived parameters, z-spectra for RF powers of 0.4 and 2 μT were computed using the fitted results; which showed good agreement with the experimentally obtained z-spectra, suggesting that the derived parameters should be able to adequately describe the spin system. Z-Spectra acquired after adjusting the y axis shimming gradients showed that the CEST contrast was severely broadened and attenuated (Fig. 2b), much like the simulated z-spectra with B0 inhomogeneity. In addition, the water signal at 0 ppm with an RF irradiation power of 0.4 μT was not zero, but 26.9 % of the control scan, attesting to severe B0 inhomogeneity.

Figure 2.

Experimentally measured z-spectra from a phantom containing 3% agarose (w/w) and 50 mM creatine at pH of 6.5. a: z-Spectra acquired with homogeneous B0 field (2 ± 9 Hz) at three RF irradiation powers: 0.4, 1 and 2 μT. The z-spectrum at the intermediate RF power (i.e., 1 μT) was numerically fit using a three-pool exchange model (black solid line). The z-spectra of the 0.4 and 2 μT RF powers were computed based on the derived parameters (gray dotted lines) and showed good agreement with experimental measurements. b: z-Spectra acquired in the presence of nonnegligible B0 field inhomogeneity (24 ± 65 Hz) with two RF powers; 0.4 and 1 μT. It shows that the CEST contrast was significantly attenuated and broadened, similar to those observed in the simulated z-spectrum with B0 inhomogeneity (Fig. 1a).

After readjustment of y-axis shimming gradient, the B0 inhomogeneity was measured to be 24 ± 65 Hz and varied linearly along the y-axis (Fig. 3a). The normalized B1 map was found to be 100 ± 6%. The good B1 homogeneity is consistent with the observation that the pattern of MTRasym artifacts does not resemble B1 field distribution. The measured MTRasym was minimal at negative offsets, and increased to its maximal at close to the center frequency (i.e., minimal B0 field errors). With positive B0 offset, MTRasym showed little change, likely because the reduction of CEST contrast was partially compensated by the increased MTR offset. The modulation factor from Eq. [6] was nearly 1 at the center, and increased for large B0 field offsets. Such a pattern can be attributed to the fact that for a reasonably homogeneous B1 field, the labeling coefficient is modulated by the ratio of the offset and the apparent relaxation rate (Δω/P), and therefore resembles the spatial distribution of B0 map. The compensated PTR image showed significant improvement over the MTRasym map, especially for voxels with negative B0 offsets. The residual variation in PTR map is likely caused by cumulated errors from multiparameter fitting and residual magnetization coupling between CEST and conventional MT effects. Figure 3b shows how the proposed algorithm corrected MTRasym toward the fully-compensated PTR, with MTRasym, ΔMTR, PTR′, and PTR scatter-plotted against the B0 inhomogeneity per voxel. The MTRasym (red dots) decreased almost linearly with the B0 field for negative offsets, but showed very minor change for positive offsets. The MTRasym was 12 ± 4% (mean ± SD). By compensating MTRasym with ΔMTR (black dots), the obtained PTR′ (green dots) became nearly symmetric around the water resonance, indicating that the B0 inhomogeneity-induced MTR offset had been largely corrected. Moreover, by accounting for the modulation factor, the fully compensated PTR (blue dots) was obtained to be 15 ± 2%, comparable to 17 ± 1% measured under the condition of homogeneous B0 field.

Figure 3.

a: Illustration of the proposed correction algorithm that compensates field inhomogeneity-induced CEST measurement errors based on field mapping. The B0 map shows a linear variation after readjusting the shimming gradient along the y axis (24 ± 65 Hz), whereas the B1 map is reasonably homogeneous (100 ± 6%). The MTR offset (ΔMTR) varies linearly with the B0 field inhomogeneity. The modulation factor was about 1 for voxels with homogeneous field (center line), but increased to nearly 5 for voxels with large B0 field inhomogeneity. The measured MTRasym map shows severe heterogeneity, sharing the pattern of the B0 field map. After compensating for the MTR offset and the modulation factor using the proposed correction algorithm, the obtained PTR map shows reasonably homogeneous CEST contrast across the phantom. b: A scatter-plot of MTRasym, ΔMTR, PTR′, and PTR against the B0 field is shown in red, black, green, and blue dots, respectively. The MTRasym decreased almost linearly with the B0 field of negative offsets, but showed relatively minor change for positive offsets. The PTR′ was approximately symmetric around the labile proton resonance, indicating that the B0-induced MTR offset (ΔMTR) had been largely compensated for. Moreover, by accounting for the modulation factor, the fully-compensated PTR showed significantly improved CEST contrast with reduced variance.

The proposed correction algorithm was further evaluated using a dual tissue-like pH phantom with pH being 5.9 and 6.5 for the inner and outer tube, respectively (Fig. 4). The relaxation times were about equal, with T1 and T2 being 3.1 ± 0.03 s, 41.2 ± 0.7 ms, and 3.1 ± 0.03 s, 40.2 ± 1.2 ms for the inner and outer tubes, respectively. The B1 field was reasonably homogeneous (100 ± 7%). The B0 inhomogeneity for the inner and outer tubes was −6 ± 7 Hz and −4 ± 13 Hz, with the measured MTRasym being at 12.3 ± 0.8% and 21.8 ± 1.1%, respectively. Thus, a CEST contrast of 9.5% is associated with the pH difference of 0.6 unit. After varying the shimming gradient, the B0 field mapping was repeated and found to be −13 ± 34 Hz and −5 ± 81 Hz for the inner and outer tubes, respectively. Concomitantly, their MTRasym decreased to 9.2 ± 3% and 11.9 ± 8%, respectively, and pH induced CEST contrast was only 2.7%. It shows that pH induced CEST contrast decreases significantly in the presence of B0 inhomogeneity. Using the proposed correction algorithm and parameters derived from the single gel phantom, the PTR of the inner and outer tubes were compensated to be 11.7 ± 0.9% and 21.7 ± 2.8%, respectively. The corresponding CEST contrast was 10%, significantly higher than that prior to correction (2.7%) and in very good agreement with that derived with homogeneous B0 field (9.5%). This demonstrated that the proposed algorithm can effectively compensate for field inhomogeneity-induced artifact in CEST imaging (Table 1).

Figure 4.

Experimentally measured MTRasym and field error-compensated PTR maps from a dual-gel phantom of different pH. a: Illustration of the dual pH phantoms, with pH for the inner and outer tube being 5.9 and 6.5, respectively. b: MTRasym map after readjustment of the shimming gradient, the contrast between the two tubes decreased to 2.7%. In contrast, the compensated PTR was 10%, suggesting that the proposed correction algorithm can indeed significantly reduce field inhomogeneity-induced artifacts in CEST imaging (c).

Table 1. CEST Imaging of a Dual-Gel Phantom of Different pH (5.9 vs. 6.5)*
 pH = 5.9 (inner tube)pH = 6.5 (outer tube)ΔCEST (1.9 ppm)
  • *

    With good B0 shimming, a contrast of 9.5% can be obtained for a pH difference of 0.6 unit. With moderate B0 field errors, the measured MTRasym decreased significantly while the variation increased enormously. In fact, the pH induced CEST contrast dropped to 2.7%. Using the proposed correction algorithm, the CEST contrast was corrected to be 10%, in close agreement with the “ideal” CEST contrast measured at good field homogeneity.

With good shimming   
 B0 (Hz)−3 ± 7−4 ± 13 
 MTRasym (%)12.3 ± 0.821.8 ± 1.19.5
With altered shimming   
 B0 (Hz)−13 ± 34−5 ± 81 
 MTRasym (%)9.2 ± 3.011.9 ± 7.62.7
Altered shimming with correction   
PTR (%)11.7 ± 0.921.7 ± 2.810.0

DISCUSSION

Although CEST imaging has been shown to provide information complementary to that of conventional MRI for characterizing pathologies such as acute stroke and cancer, there have been some concerns about its sensitivity to field inhomogeneity, particularly for in vivo imaging at high magnetic field. For instance, using relaxation time constants from Stanisz et al. (27), the MTRasym offset (ΔMTR) introduced by a 50-Hz B0 field error can be estimated using Eq. [4] to be 19% and 6% for field strengths of 1.5 and 3T, respectively, at the amide proton frequency (3.5 ppm) for an RF irradiation power of 1 μT (42.6 Hz). In addition, B1 field strongly depends upon coil design, and homogeneous B1 field over a large imaging volume becomes challenging at very high magnetic field strengths. Therefore, proper compensation of field inhomogeneity-induced errors in CEST imaging should improve the accuracy of quantitative CEST imaging (29).

It has also been shown that B0 inhomogeneity-induced measurement errors in CEST imaging can be compensated for by interpolating the z-spectrum using high-order polynomials and adjusting the measurements per voxel (24). However, such an approach requires measurements with fine frequency intervals, and as such, can become very time consuming and may not be practical for studying dynamic processes such as acute stroke. In comparison, the algorithm described in this study requires only a MTRasym map with additional scan of B0 and B1 field map, while providing reasonable correction for typical field inhomogeneity (within 100 Hz). In the presence of very severe B0 errors, however, the RF labeling coefficient can be very low (i.e., α [Δω] << 1) and the proposed correction algorithm may not be able to provide satisfactory compensation. Given that the labeling coefficient increases with RF irradiation power, it may be advantageous to apply the irradiation pulse at an RF power above the optimal level. However, doing so may introduce additional spillover effects, attenuating CEST contrast (17, 29). On the other hand, if time permits acquisition of CEST images with a very fine frequency interval over the complete range of B0 field errors, the interpolation algorithm may still compensate for field inhomogeneity artifacts.

In this study, the conventional MT contribution was accounted for by modifying the solution obtained from a two-pool exchange model rather than by directly solving a three-pool exchange model. This approach is justified because the typical transverse relaxation time for semisolid macromolecules is very short (∼10–15 μs), making conventional MT imaging insensitive to commonly encountered B0 inhomogeneity. For instance, for the typical RF power used for CEST imaging (∼1 μT) and within an offset of 100 Hz, the labeling coefficient for a semisolid macromolecule pool varies by less than 0.1%. Therefore, the asymmetry analysis can fully suppress conventional MT effects. However, the MT between semisolid macromolecules and bulk water shortens the apparent transverse relaxation time of bulk water, causing a change in the spillover effects, which must be taken into account. It is worthwhile to mention that the in vivo conventional MT effects are not fully symmetric around the bulk water resonance, and therefore, the correction algorithm may need further modification and beyond the scope of this study (32).

The fact that CEST contrast is not very sensitive to B1 inhomogeneity is consistent with our previous study showing that RF irradiation power plateaus briefly for maximal CEST contrast, and a small deviation from the optimal power should not significantly affect the CEST contrast (17). Although the B1 field is reasonably homogeneous in our experiments, the modulation factor is still not negligible, especially at voxels with large B0 offsets. This is so because the labeling coefficient varies with both B0 and B1 field inhomogeneity, as does the modulation factor (see Eq. [6]). The spillover factor, on the other hand, showed very little change with field errors, likely because only moderate RF power was used (1 μT [42.6 Hz]). In addition, MTRasym showed less reduction for positive B0 offsets, which can be attributed to the fact that MTR offset is larger for positive B0 offsets, which partially compensates for the reduced CEST contrast. However, such compensation varies with experimental conditions and CEST agents, and should not be interpreted as representing an advantage over negative field inhomogeneities.

The phantom used in this study contains 3% agarose in order to model conventional MT effects incurred in tissue, similar to phantoms used by Henkelman et al. (23). Indeed, numerical fitting using a two-pool exchange model showed poor results (data not shown). In contrast, three-pool numerical fitting showed good agreement with measured z-spectrum. Although several parameters were either measured or chosen based on representative values from other studies, the fitting of our three-pool model still had six independent variables, making the derived parameters susceptible to fitting errors. In addition, the fitting is sensitive to initial guess of chemical exchange rate. However, we have shown that the computed z-spectra agreed reasonably well with experimental results for two additional RF irradiation powers (i.e., 0.4 and 2 μT), indicating that the numerical fitting should be able to adequately describe the investigated tissue-like phantoms. Moreover, the labile amide proton concentration can be estimated to be within 1:1100 and 1:455, with a mean value of 1:778 (33). In comparison, the labile proton frequency obtained from fitting is 1:742, in excellent agreement with the estimation. Furthermore, the signal-to-noise ratio (SNR) of CEST images at 1.9 ppm for RF power of 1 μT was 217, while we found that that the mean MTRasym from the whole phantom did not change significantly until SNR decreased below 30 by systematically varying random Gaussian noise added to images during postprocessing (data not shown). Hence, the SNR of our experimentally measured z-spectrum is sufficiently high for properly fitting the z-spectrum.

CONCLUSIONS

In this study, we showed that CEST imaging measurement errors induced by field inhomogeneity can be decomposed into two components: a modulated PTR and a MTR offset caused by MTR asymmetry analysis of mismatched label and reference scans. A correction algorithm was proposed that can compensate for typical B0 and B1 field inhomogeneity-induced errors in CEST imaging, which only requires the commonly used three-point CEST scan and field mapping. The algorithm was verified with both numerical simulation and experimental measurements from tissue-like pH phantoms. Further evaluation of the algorithm showed that it corrected CEST contrast of a tissue-like pH phantom from 2.7% to 10%, which was nearly identical to the direct measurement of 9.5% under the condition of homogeneous magnetic field. In sum, the correction algorithm proposed in our study provides fast compensation for field inhomogeneity induced measurement errors in CEST imaging.

Acknowledgements

We thank Dr. Donald Woessner and Dr. Dean Sherry from University of Texas at Dallas for kindly sharing their simulation routines with us.

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