1. Introduction
Since the introduction of dissolution dynamic nuclear polarization in 2003 [
1], several hyperpolarized
13C-labelled biomolecules have been applied in preclinical [
2] and clinical studies [
3], establishing new ways to generate magnetic resonance imaging (MRI) contrast. The metabolic conversion of [1-
13C]pyruvate to its downstream metabolites [1-
13C]lactate, [1-
13C]alanine and
13C-bicarbonate has been investigated as an imaging biomarker for the detection and evaluation of various pathologies such as cancer [
4], inflammation [
5], and related changes in pH [
6], as well as the functionality of various organs, such as the heart [
7], liver [
8], or kidney [
9], and of perfusion [
10]. Metabolically inert compounds such as
13C-urea and [
13C,
15N
2]urea have also been introduced, enabling the assessment of perfusion and kidney function from signal intensity maps [
9]. Hyperpolarized
13C-labelled molecules can also be used as sensors of physicochemical properties by exploiting changes in longitudinal and transverse relaxation times or chemical shift, e.g., for the detection of metal ion concentrations [
11] or pH [
6,
12].
To sense these properties, the initially created hyperpolarized longitudinal magnetization must be excited in MRI experiments, thereby converting the longitudinal magnetization into transverse magnetization. This transverse magnetization then precesses about the static magnetic field axis while decaying exponentially with a time constant T2, known as the transverse relaxation time constant. This decay mainly occurs because the individual spins, composing the net transverse magnetization, experience microscopic field fluctuations over time. These fluctuations induce small changes in the spins’ Larmor frequencies, thereby causing the spins to lose synchrony over time, i.e., to dephase, decreasing the measurable net signal.
T2 limits preparation and acquisition time and thereby influences the achievable spectral and spatial resolution and signal strength; therefore, a long T2 is desirable for hyperpolarized 13C-MRI experiments. Nevertheless, T2 weighting or direct measurement of T2 can also be exploited to generate contrast in hyperpolarized 13C-MRI, whereby dependencies of T2 on biomarkers such as pH might be of interest for in vivo applications.
However,
T2 measurements involve acquisitions at multiple echo times that lead to additional dephasing beyond
T2. This includes spins diffusing between refocusing pulses [
13] and imperfect refocusing [
14], potentially leading to a mixture of
T1 and
T2 decay. The measured
T2 is thus an apparent transverse relaxation time constant (
Appendix A). Despite this discrepancy, the term
T2 is used in the following when reporting results, while explicitly stating here that apparent
T2 relaxation times are meant.
Changes in the apparent transverse relaxation time, as demonstrated by
T2-mapping for hyperpolarized
13C-urea [
15], have been shown to detect alterations of tissue oxygenation [
16], protein content [
16], viscosity [
17] or restricted diffusion due to cellular uptake [
17]. Furthermore,
T2 measurements in hepatocellular carcinoma showed differences in
T2 between healthy and tumor tissue for [1-
13C]alanine and [1-
13C]lactate [
18], with further heterogeneity in
T2 indicated by the necessity of multi-exponential fitting of the transverse magnetization decay curves of healthy [
15,
17,
19] and tumor tissue [
19,
20].
Many approaches for the assessment of metabolism using hyperpolarized magnetic resonance spectroscopy and imaging rely on the acquisition of spin echoes and are inherently sensitive to
T2, such as point-resolved spectroscopy (PRESS) [
18,
21], fast spin echo [
16,
22,
23], double spin echo [
8,
24], multi-echo spin echo [
20], or balanced steady-state free precession (bSSFP) sequences [
9,
15,
17,
25,
26]. However, to the best of our knowledge, the sensitivity of these sequences to alterations of
T2 and heterogeneity in
T2 within the imaged object has so far not been considered for the calculation of metabolic conversion rates. This is especially important for sequences that employ echo times on the time scale of the
T2 relaxation constants of the metabolites being imaged.
Consequently, the
T2 relaxation time constants of several commonly imaged biomolecules, such as [1-
13C]pyruvate [
19,
20,
25,
27,
28], [1-
13C]lactate [
18,
19,
20,
25,
27], [1-
13C]alanine [
18,
19],
13C-urea [
15], [
13C,
15N
2]urea [
15,
16,
17],
13C-bicarbonate [
19,
26], bis-1,1-(hydroxymethyl)-1-
13C-cyclopropane-
2H
8 (HP001) [
27] or [1-
13C]acetate [
26] have been measured at various magnetic field strengths; in vivo for various organs or diseases, or in vitro for various viscosities or media. In addition to those influencing factors, further parameters that are altered in vivo, such as tissue [
29] or blood [
30,
31,
32] buffer capacity and pH [
33,
34], might affect
T2 but have not yet been explored.
In this work, the pH dependence of the T2 relaxation time constant of several 13C-labelled biomolecules that are commonly used for hyperpolarized magnetic resonance imaging is investigated. For the two compounds with the strongest pH dependence of T2 in the physiological pH range, namely, [1-13C]pyruvate and [1-13C]acetate, further factors influencing T2 are examined, including concentration, temperature, buffer capacity, and salt concentration. Furthermore, T2 mapping is used to generate images with strong pH-based contrast in buffer-free aqueous solutions using [1-13C]acetate as a pH sensor.
3. Discussion
In this work, pH was shown to strongly influence T2 relaxation time constants of 13C-labelled hyperpolarizable biomolecules which are commonly imaged in vivo.
[1-
13C]acetate at 14.1 T showed a minimum of
T2 around pH values close to its p
Ka at 14.1 T. This can be explained by the fast proton exchange of the carboxyl proton in the vicinity of this pH [
41,
42]. The slope of the titration curve close to this minimum
T2 was slightly flattened towards basic pH values. At pH values close to the p
Ka = 6.81 of water at 37 °C [
36], fast proton exchange at the carboxyl group of acetate with non-dissociated water based on the Grotthuss mechanism might take place. Furthermore, the Grotthuss mechanism, describing the exchange of protons between H
2O molecules, might be most efficient at the mentioned pH, with the exchange rate having spectral density at the Larmor frequency of [1-
13C]acetate. These effects likely shortened the
T2 values of acetate in the pH range similar to the water p
Ka. The higher absolute
T2 values in the basic compared to the acidic regime may be explained by the deprotonated state having one less proton to mediate relaxation via dipole–dipole-interactions. However, acetate ions might still act as weak bases, consequently exhibiting proton exchange with water up to pH 10. Beyond this pH, the acetate ions cannot deprotonate water molecules and
T2 reaches a plateau. At 7 T, there is a weaker sensitivity to pH changes at neutral to slightly basic pH (pH 7–9) compared to 14.1 T, which might be explained by proton exchange with water of the acetate carboxyl group having more spectral density at this Larmor frequency. However,
T2 values at 7 T are generally higher compared to 14.1 T, most likely caused by decreased chemical shift anisotropy effects at lower field. Temperature appears to only have a minor effect on
T2. This, together with
T2 being similar to
T1 [
35], indicates that the correlation time of acetate is relatively short due to relatively fast molecular tumbling. This tumbling rate further increases towards higher temperatures, as indicated by the slight increase in
T2 values for increasing temperatures. Salt ions also appear to only slightly shorten
T2, because an increased concentration of the diamagnetic Na
+-ions induced additional dipolar relaxation mechanisms [
43,
44]. In contrast, diluting the [1
−13C]acetate solution to a concentration lower than 250 mM appears to alter
T2 similarly to variations induced by pH, because here the mean distance between hydrated acetate ions in solution becomes too large to still allow hydrogen bond-mediated interactions that potentially enhance
T2 relaxation [
45].
Low
T2 values of [1-
13C]pyruvate at strongly basic pH values are most likely explained by base-mediated keto-enol tautomerism [
46], where rapid conformational exchanges and subsequent reactions to para-pyruvate enhance relaxation. At neutral pH values, proton exchange at the carboxyl group might be enhanced by rapid hydroxy–hydronium exchange reactions of water, similar to the observations for [1-
13C]acetate. This assumption is supported by the observation of decreased
T2 values in the same pH range with added buffer, where rapid proton exchange with buffer molecules might occur, thereby potentially inducing additional relaxation via proton exchange between buffer molecules and [1-
13C]pyruvate molecules [
47]. At strongly acidic pH values, close to pyruvate’s p
Ka, fast proton exchange and hydration of the molecule to pyruvate-hydrate further shorten
T2 [
48]. The difference in magnitude between the basic global maximum and the local maximum in the weakly acidic regime can be explained by the increased proton concentration at acidic pH, which enhances dipolar relaxation pathways. Regarding the local minimum of the
T2 relaxation time constant at pH 6, proton exchange with water might lead to the observed reduction in
T2. However, this does not fully explain the minimum being at a more acidic pH than the neutral point of water. Further theory models and simulations beyond the scope of this work might be helpful to explain this observation. Regarding [1-
13C]pyruvate concentration and salt ion concentration, the observations for [1-
13C]pyruvate are similar to [1-
13C]acetate and can be explained similarly. As for the temperature dependence of
T2, [1-
13C]pyruvate shows an exponential decrease with higher temperature, in contrast to [1-
13C]acetate. Normally, the temperature-dependent molecular tumbling and the related correlation time would lead to an increase in
T2. However, the decrease might rather be explained by the hydration process of [1-
13C]pyruvate in the pH regime chosen for temperature dependence measurements of
T2. Here, an increased temperature potentially increases the hydration rate of pyruvate [
49], and the rapid exchange of water molecules between the pyruvate and the bulk water pool might lead to a reduced
T2 relaxation time, to a sufficient degree to exceed the increase in
T2 due to faster tumbling.
The global
T2 maximum of [1-
13C]lactate at strongly acidic pH values can be explained by protonated lactic acid molecules forming dimers, rendering the carboxyl proton inaccessible for exchange reactions [
50]. At neutral pH, hydrogen bonding of the deprotonated carboxyl group of [1-
13C]lactate to the intramolecular hydroxyl group and surrounding water molecules might be most efficient [
51], explaining the global minimum of
T2. Towards more alkaline pH values, this effect seems to decrease, together with reduced proton concentration, leading to an increase in
T2. At even stronger basic pH regimes, the formation of lactate–metal complexes with added Na
+-ions and deprotonation of the hydroxy group (p
Ka = 15.8) start to decrease
T2 [
52,
53].
For [1-13C]alanine, pH milieus close to the pKa of an amine or carboxyl group of this molecule allow fast proton exchange, which appears to be an effective T2 relaxation pathway. Furthermore, the overall decrease in T2 from basic to acidic pH might be explained by susceptibility to the surrounding hydronium ion concentration. In addition, the existence of the amphoteric ion across a wide range of pH values causes the charge distribution in the molecule to be potentially perturbed by dipolar interactions with the charged hydronium ions, thereby promoting T2 relaxation.
For 13C-urea, inability to exchange protons with its environment result in T2 values being almost inert to variations in pH. The low absolute value of T2, compared to other investigated 13C-labelled compounds, can be explained by the strong quadrupolar relaxation induced by 14N nuclei.
For the pH range where [1,4-13C2]fumarate is dissolvable in water, shortened T2 values are seen at pH values near the pKa of its carboxyl groups, where fast proton exchange at both carboxyl groups occurs, as well as potential influence of proton exchange with water around pH 7. For alkaline pH values, T2 reaches its maximum as the molecule exhibits as symmetric double deprotonation with limited ability for the formation of hydrogen bonds due to the high concentration of surrounding hydroxyl ions.
Together, the findings in this work are consistent with fast proton exchange being an effective
T2 relaxation pathway, because measured
T2 values decreased strongly in these regimes for proton-exchanging molecules. In this context, buffers contribute to proton exchange processes [
47] because the addition of TRIS-buffer or measurements in whole blood, which contains phosphate- and bicarbonate-buffers, were shown to exhibit decreased
T2 compared to unbuffered aqueous solutions. Notably, for all of the proton-exchanging molecules investigated here, their
T2 values were below 50% of their pH-dependent maxima in the vicinity of the p
Ka of water, which has its neutral point at pH 6.81–7.15 [
36], for 16–37 °C. Instead, global and local
T2 maxima for all titration curves, excluding
13C-urea, were located at moderate to strongly acidic or basic pH. This suggests that water might also act as a proton exchange enhancing moiety, or that it has an increased ability to form hydrogen bonds with the investigated biomolecules [
48,
54,
55] in pH regimes close to its neutral point, which enhances relaxation.
Apart from this strong pH dependence of
T2 relaxation time constants, temperature, concentration and salt ion concentration dependence were investigated to determine their influence on
T2 under conditions close to an in vivo setting. For NaCl concentrations in vivo, ranging at most from 120 mM to 180 mM and normally at 150 mM, a rather low variation of
T2 was observed for [1-
13C]pyruvate and [1-
13C]acetate. Temperature variations between 35 °C and 39 °C also appeared to have a limited effect on the
T2 of [1-
13C]pyruvate and [1-
13C]acetate. However, concentration dependence of
T2 had a strong effect on in vivo
T2 measurements, where local accumulation and dilution of the tracer, governed by perfusion, might dominate observed variations in
T2. Therefore, in addition to pH, concentration variations might be of crucial influence when mapping
T2 in vivo [
15].
T2 relaxation time constants of
13C-labelled biomolecules have already been measured at various field strengths from 3 T to 9.4 T [
16,
25], within different solvents in vitro [
15], and in vivo in several organs [
15,
16,
18,
19,
25,
28]. Previously reported
T2 values of
13C-urea [
15], [1-
13C]pyruvate [
25] and [1-
13C]acetate [
26] show reasonable agreement with the results from this study, when taking field strength differences and uncertainties in pH and temperature into account. However, in the literature,
T2 measurements in vivo show considerably shortened relaxation times, typically not exceeding a few seconds for most compounds [
19,
25,
27], except for [
13C,
15N
2]urea (
T2 in vivo up to 11 s [
15]). Additionally, multi-compartment relaxation behavior is observed, requiring multi-exponential fitting [
15,
17,
19,
20].
While reduced
T2 in vivo compared to in vitro results might be attributed to protein content, oxygenation of hemoglobin [
16] and metabolic conversion [
18], the presence of multiple
T2 compartments within tumor tissue [
20] might also be related to sub-resolution heterogeneity in pH. Interestingly, comparison of measurements between healthy and tumor tissue showed prolonged relaxation times in the latter for [1-
13C]pyruvate, [1-
13C]lactate and [1-
13C]alanine [
18,
28], while shorter
T2 values were observed in diseased kidneys compared to healthy ones for [
13C,
15N
2]urea [
17]. For
13C-urea, this was attributed to alterations in tissue oxygenation. For tumor tissue, changes in pH might also contribute to these observed differences. For acidic cancer types, this should be further considered when using spin echo-based sequences, such as bSSFP or RARE, for the imaging of hyperpolarized [1-
13C]pyruvate, [1-
13C]lactate and [1-
13C]alanine, because pH-based prolongation or shortening of the transverse magnetization signal decay might introduce bias to the quantification of metabolic conversion. Simultaneous mapping of pH [
6] using hyperpolarized
13C-bicarbonate as a metabolic product of [1-
13C]pyruvate or pH mapping by an additional injection of hyperpolarized [1,5-
13C
2]zymonic acid [
12] or iopamidol together with chemical exchange saturation transfer (CEST) MRI [
56] might be a helpful tool for the estimation of such influences.
Despite these potentially strong effects of pH on existing hyperpolarized 13C-MRI imaging quantification approaches, direct application of T2 mapping of the investigated compound for pH mapping in vivo appears challenging because of the strong influence of concentration on T2 relaxation.
In this work, slight deviations between
T2 values being measured by a non-localized CPMG train compared to values derived from
T2 mapping could be observed. Here, potentially larger
B1 inhomogeneities and worse shimming for the 3-phantom-geometry might explain these observations. In blood, additional relaxation mechanisms, e.g., caused by paramagnetic deoxyhemoglobin, might have a stronger effect on
T2 than pH. In addition, for injected
13C-labelled compounds, large amounts might flow into and out of the imaged volume and contribute to the measured signal, such that refocusing of the magnetization after a certain echo time, and therefore reliable measurement, might be difficult [
18]. Nevertheless, for aqueous solutions of known composition, such as quality control in human hyperpolarized
13C imaging studies [
3], pH control might be realized directly inside the magnet bore via NMR-based
T2 measurements, thereby potentially speeding up the preparation time.
To further investigate the role of water for proton exchange-mediated relaxation processes, titration curves in different solvents or in solvents with varying water content are required. In order to quantify the potential influence of the pH dependence of T2 for measurements of hyperpolarized 13C-labelled metabolites in vivo, tissue pH-targeting therapies using acetazolamide or bicarbonate can be used together with hyperpolarized 13C imaging to examine changes in metabolite quantification due to pH alterations.