pH Dependence of T2 for Hyperpolarizable 13C-Labelled Small Molecules Enables Spatially Resolved pH Measurement by Magnetic Resonance Imaging

Hyperpolarized 13C magnetic resonance imaging often uses spin-echo-based pulse sequences that are sensitive to the transverse relaxation time T2. In this context, local T2-changes might introduce a quantification bias to imaging biomarkers. Here, we investigated the pH dependence of the apparent transverse relaxation time constant (denoted here as T2) of six 13C-labelled molecules. We obtained minimum and maximum T2 values within pH 1–13 at 14.1 T: [1-13C]acetate (T2,min = 2.1 s; T2,max = 27.7 s), [1-13C]alanine (T2,min = 0.6 s; T2,max = 10.6 s), [1,4-13C2]fumarate (T2,min = 3.0 s; T2,max = 18.9 s), [1-13C]lactate (T2,min = 0.7 s; T2,max = 12.6 s), [1-13C]pyruvate (T2,min = 0.1 s; T2,max = 18.7 s) and 13C-urea (T2,min = 0.1 s; T2,max = 0.1 s). At 7 T, T2-variation in the physiological pH range (pH 6.8–7.8) was highest for [1-13C]pyruvate (ΔT2 = 0.95 s/0.1pH) and [1-13C]acetate (ΔT2 = 0.44 s/0.1pH). Concentration, salt concentration, and temperature alterations caused T2 variations of up to 45.4% for [1-13C]acetate and 23.6% for [1-13C]pyruvate. For [1-13C]acetate, spatially resolved pH measurements using T2-mapping were demonstrated with 1.6 pH units accuracy in vitro. A strong proton exchange-based pH dependence of T2 suggests that pH alterations potentially influence signal strength for hyperpolarized 13C-acquisitions.


S1: Concentration dependence of T2 for [1-13 C]pyruvate and [1-13 C]acetate
pH titration of stock solutions involves addition of small volumes of acids and bases, which increases the overall volume of the stock solution and therefore reduces the concentration of the dissolved 13 C-labelled compound. In addition, during injection of these 13 C-labelled compounds after hyperpolarization, heterogeneous distribution of the bolus leads to local concentration differences in tissue. Therefore, the concentration dependencies of T2 were assessed ( Figure S1). [1-13 C]pyruvate shows a monotonic increase of T2 from higher towards lower concentrations, with a two-fold increase in T2 from 250 mM to 50 mM. Acetate shows scattering of T2 at lower concentrations, with a two-to six-fold increase in T2 values at concentrations below 250 mM.
For both molecules, proton exchange might be slowed down at lower concentrations [1], which can most likely be explained by the lower ability to form dimers at higher dilution, therefore rendering hydrogen bonds with the carboxyl groups less effective in contributing to T2 relaxation. Also, for [1 -13 C]acetate molecules, it was observed that concentrations below 250 mM result in the distance between hydrated acetate ions becoming too large to still allow hydrogen-bond mediated interaction [2]. This increased distance between acetate-water clusters potentially reduces T2 relaxation. Consequently, and much like the pH-induced changes in T2, this strong variation limits the applicability of these compounds for pH imaging in vivo by T2 mapping of their hyperpolarized states. increasing magnetic field at moderately acidic (pH 2 -4) and slightly alkaline (pH 7 -9) pH.

S3: Voxel-wise fitting of echo signal decay curves for T2-mapping of [1-13 C]acetate using RARE
For generation of T2-maps, intensities of echo images were plotted versus effective echo time (160 ms per echo image) and fitted with a mono-exponential function with offset ( Figure S3) by minimizing the sum-of-squared residuals between the data points and the fit curve. Fitting was performed in voxels where the initial echoes exceeded a signal-to-noise peak ratio of 20.
All fits showed qualitatively good agreement of the data with the applied model.
Supplementary Figure S3. Fitting of a single voxel echo decay extracted from echo images curve versus the effective echo time. For representation purposes, signal from echoes at later time points (echo time > 50 s) are not shown in the plot but were included in the fitting process.
Acquired data sets showed good agreement with fit curves for all voxels included in the T2-map shown in Figure 4 c.

S4: Titration protocols
For titrations at 7 T, exemplary titration protocols are listed in the following tables. For each titration step, the resulting pH, the resulting concentration, the resulting ion concentration (either Na + or Cl -) as well as the added volume of acid or base relative to the previous titration step is listed:

S5: Error Estimation for T2 and pH measurements
To assess the uncertainty of the measured T2 and pH values, an experimental series as The results from all measurements are listed in the following two tables:  Figure S4 a).
However, sample #3 showed an elevated T2 relaxation time constant, which might be attributed to a slightly elevated pH compared to samples #1 and #2. Nevertheless, sample pH stayed almost constant for all samples during the measurement as indicated by the small differences between pH measurements before and after the T2 measurements ( the observed drifts might be the main reason for the observed data scattering in Figure 2 a.
Overall, the results from this experimental series reflect the challenges in T2 measurements under varying pH conditions explaining the data scattering as observed in Figure 2, especially for acetate in the pH range 7.11 -9.22.
(a) (b) Figure S4: In summary, these experiments demonstrate that CPMG-acquisitions allow individual measurement of T2 relaxation time constants with two significant digits after the comma in cases where the sample pH is stable. In these cases, where the pH is sufficiently stable for repeated measurements, such as for pyruvate, the standard deviations from iterative measurements did not exceed 0.05 s. However, larger uncertainties arise from the sample preparation, the resulting pH value and pH changes over time. Here, even for samples with stable pH values, such as for pyruvate, multiple preparations of independent sample cause variations in T2 leading to an overall standard deviation of 0.33 s. In contrast, for acetate, pH drifts of roughly 0.1 s/min in observed T2 values due to drifts in pH also limit the precision of the reportable data points. However, a general statement on the errors on T2 measurement covering all compounds is not possible, as it is determined by the uncertainty in pH which varies between < 0.05 and > 1 pH unit for different compounds. Following the analysis here, we report T2 values throughout the manuscript with an uncertainty of 0.1 s.