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The development of hyperpolarized tracers has been limited by short nuclear polarization lifetimes. The dominant relaxation mechanism for many hyperpolarized agents in solution arises from intramolecular nuclear dipole-dipole coupling modulated by molecular motion. It has been previously demonstrated that nuclear spin relaxation due to this mechanism can be removed by storing the nuclear polarization in long-lived, singlet-like states. In the case of N2O, storing the polarization of the nitrogen nuclei has been shown to substantially increase the polarization lifetime. The feasibility of utilizing N2O as a tracer is investigated by measuring the singlet-state lifetime of the N2O when dissolved in a variety of solvents including whole blood. Comparison of the singlet lifetime to longitudinal relaxation and between protonated and deuterated solvents is consistent with the dominance of spin-rotation relaxation, except in the case of blood.
The utility of hyperpolarized MRI tracers is often limited by their longitudinal relaxation rates which are usually quite fast with respect to in vivo circulation, uptake, and metabolism (1-3). These rates are typically determined by intramolecular dipolar interactions. As has been previously shown (4-5), exchange-antisymmetric singlet spin states of pairs of isotopically-identical nuclei are immune to intra-pair dipolar relaxation. Other intra- and inter-molecular mechanisms can be greatly reduced by populating a singlet-like state as well (6-8); thus, storage of nuclear polarization of a molecule in singlet-like states can lead to polarization lifetimes which are dramatically longer than the longitudinal spin polarization lifetime of the individual nuclear spins. For example, the singlet lifetime (TS) of nitrous oxide (15N2O) dissolved in DMSO-d6 was measured to be 26 min (5). In this study, we report measurements of doubly-enriched 15N2O TS in a variety of solvents including fresh whole blood in order to shed light on the mechanism of singlet state relaxation and to determine if the singlet state lifetimes in vivo can be sufficiently long to warrant the development of 15N2O or an analogous agent as an MRI tracer.
The mechanism for populating the singlet state by field cycling can be understood if the total Hamiltonian for the system is constructed. The Hamiltonian of two coupled spins in a magnetic field is given by:
Where I1, I2 are the two nuclear spins, γ denotes their gyromagnetic ratio, B is the magnetic field, J the scalar coupling between the nuclei, and δ1 and δ2 are the respective chemical shifts of the two nuclei. In low magnetic field, the scalar coupling dominates the interaction and the eigenstates of the system are well described by the familiar singlet-triplet basis:
Here |↑> describes a spin aligned with the magnetic field, and |↓> opposed to it. |S0> denotes the singlet state with total spin I=0, and |Tμ> the μ azimuthal angular momentum projection of the triplet state with total spin I=1.
In sufficiently high field, the chemical shift difference between the nuclei dominates the scalar coupling interaction and the eigenstates are described as:
Adiabatic transport of the system from high field to low field results in a transfer of quantum level populations from one eigenbasis to the other, described as(9):
where J and γ have the same sign and δ1- δ2 >0. (|S0 and |T0 change places in eq. 4 otherwise). This transfer is reversible. Thus selectively populating the |↓↑> state in a high magnetic field, and adiabatically transferring the system to a region of low magnetic field results in an increased population of |S0> in low field. Similarly, the behavior of the singlet population in low magnetic field may be deduced by adiabatic transport back to high magnetic field, followed by excitation of the magnetization using a non-selective pulse and measurement of the NMR signal (9-10). We note that although the singlet state has no magnetic moment, conversion into the |↓↑> state by adiabatic transport to an imaging-strength magnetic field results in distinct, anti-phase NMR lines and makes it a suitable agent for high-sensitivity MRI. One can imagine in vivo administration of N2O by injection after first dissolving the gas in suitable a solvent, in a manner similar to previous work with hyperpolarized 129Xe (11.12). N2O is utilized as a test molecule to demonstrate the effectiveness of singlet states in preserving polarization in solution. In a clinical setting a different molecule would likely be administered.
Doubly 15N-labeled N2O gas (98%+ 15N fraction, Cambridge Isotope Laboratories, Inc.) was dissolved in various solvents in 5-mm NMR tubes (0.38 mm and 0.77 mm wall thickness, Wilmad Glass). With the exception of blood, solutions were deoxygenated under N2 prior to introduction of N2O. Non-metallic needles and tubing were utilized during the degassing procedure in order to prevent leaching of metal ions into the sample tube. Additionally, 100 μM EDTA was added to aqueous solutions (H2O and D2O) as a metal-ion chelating agent. N2O was introduced in a two step process; The gas was released from a lecture bottle into a glass pumping manifold with a calibrated volume. A section of the NMR tube was then placed in contact with liquid N2 using a custom dewar (see Fig. 1). This condensed the N2O gas into the cold section of the NMR tube and the amount of gas condensed was monitored using a pressure gauge on the calibrated volume. The tube was then flame-sealed, and the custom dewar was removed. The tube was allowed to warm up to room temperature, and inverted several times, after which the dissolved N2O was in equilibrium with a gas pressure of 7–25 bar, estimated using the calibrated pressure drop, the volume of the sealed tube, and published N2O solubilities. For the experiments involving blood, heparinized rat blood (drawn from the tail vein of Sprague-Dawley rats) was used. All animal experiments were carried out under a protocol approved by the University of Pennsylvania Institutional Animal Care and Use Committee. After loading the blood into an NMR tube, a small section of blood (~6 mm tall) was separated from the bulk of the blood by a few centimeters of an air bubble to serve as a cold plug. This section was frozen using the custom dewar by placing liquid N2 in contact with the NMR-tube wall to reduce freezing and possibly lysing the bulk of the blood sample (~100 mm tall) during the N2O filling process. To elucidate relaxation in other environments of interest for in vivo studies, experiments were also performed on rat blood plasma samples and goose fat. The plasma solution was extracted by pipette from centrifuged rat blood, prior to introduction of N2O. The goose fat was purchased from a local food store. It was introduced into the NMR tube with a spatula and collected at the bottom by melting the fat with an hairdryer. The tube was then fused with a J-young valve and attached to the manifold. The sample was frozen in a liquid-N2 bath and N2O frozen on top of the fat. The J-Young valve was closed and the sample flame-sealed while frozen. After thawing the sample was shaken to favor the N2O dissolution in the fat.
NMR experiments were performed on a Varian 11.7 Tesla vertical bore system. After the sample was fully thermally relaxed to the 11.7 T field, the N2O singlet state was populated using a two-step process. First, a selective long (3.3 ms) square π pulse centered on the NMR frequency of the terminal 15N spectral doublet was applied. The pulse length was chosen to have a spectral node (the eleventh) at the frequency of the adjacent central 15N doublet, enabling selective excitation of the terminal 15N nucleus. The terminal nucleus was chosen for selective inversion to minimize repolarization effects upon re-insertion of the sample into the vertical bore magnet due to its longer T1. For the experiments carried out in the blood sample the singlet lifetime was additionally measured by selectively inverting the central 15N nucleus. TS was consistent irrespective of which 15N nucleus was inverted.
Subsequent adiabatic transport of the NMR tube by hand from the bore of the 11.7-T magnet to the center of a custom built low-field μ-metal shielding cylinder (8.75″ diameter, 17.5″ length, with the top of the shielding can removed) increased the population of the m=0 singlet state relative to the triplet state populations. The transfer of the sample out of the bore of the magnet into the magnetic shields requires approximately 10s, and the field in the μ-metal shield is approximately 1mG. The dynamics of the spin states during transfer is accurately described as an adiabatic transport process because the transit time is much longer (a factor of 80) than the reciprocal of the N-N J-coupling (9,13). See (Eq. 5).
After a predetermined time interval the sample was reintroduced into the bore of the 11.7-T magnet. A hard, non-selective π/2 pulse was applied to both nuclei to determine their polarization. The procedure was repeated after a wait of 5 times the longer of the two individual nuclear T1's. This allowed the sample to attain steady-state thermal polarization between measurements. The data was analyzed by fitting to the two Lorentzian doublets of inverse phase and unequal amplitude. The model included a correction for the small amount of re-polarization of the nitrogen nuclei as they were reintroduced into the magnet. Singlet state (anti-phase) amplitude was quantified as the difference between the doublet amplitudes, after the correction was applied. Accurate determination of the singlet lifetime required many long-delay data points which exhibited correspondingly low SNR. Systematic error in overestimating the amplitude of the peaks utilizing the Lorenztian fit was reduced by integrating correlations between points in the spectra separated by the well-measured J coupling prior to fitting to a single Lorentzian lineshape; that is, each doublet in the spectrum S(f) with splitting J and center freqnecy f0 was characterized by an integral I over a region δ J:
The sign was chosen to be opposite for the two doublets and only spectra exhibiting clear antiphase behavior was used. This correlation avoids difficulty in phasing low-signal spectra and, unlike the magnitude spectrum, averages to zero in the absence of signal. Where signal levels allowed direct comparison to the more commonly employed Lorentzian fit to phased spectra, the results were found to be consistent. A standard inversion-recovery experiment was performed both preceding and following the singlet lifetime measurements. The T1's correspond to the time-constant for inter-conversion among uncorrelated product states. We note that the blood darkened visibly during the 4-6 hour duration of the experiments despite the sealed tube, although there was no apparent change in either T1 or TS.
Sample selectively inverted spectra after re-insertion into the magnet are shown in (Fig. 2), along with the time-course of polarization decay in inversion-recovery measurements (Fig. 3) and decay of the difference in signal amplitudes for the two 15N sites in singlet experiments (Fig. 4). Decay curves are fit to a bi-exponential representing the more rapid triplet interconversion and the slower singlet decay. Table 1 summarizes these results. Of particular note is the similarity between time-constants in deuterated and protonated water. This strongly suggests that intermolecular dipole interactions do not contribute significantly to relaxation of the singlet state in aqueous solution. With the exception of the measurements in blood and goose fat, the ratio of TS/T1 is quite constant, and is consistent with the assumption that the differing spin-rotation couplings of the two nuclei are the dominant contributor to both singlet and T1 relaxation. The theoretically predicted ratio depends on the ratio of spin-rotation tensors r = Cc/Ct for the central and terminal 15N sites (5):
The expected TS/T1 based on Eq. 7 is 11.4 (5), which agrees well with the measured ratio for solvents excluding the whole blood, goose fat and blood constituents. The agreement with the predicted TS/T1 further suggests spin-rotation coupling is a significant source of relaxation (5).
The ratio of the longitudinal relaxation times of the central and terminal nitrogen at high field can also be calculated under the assumption that the individual 15N nuclear spin relaxation is dominated by spin rotation (5,8,14):
This ratio is expected to be 1.8 in the case of nuclear spin relaxation arising solely from spin rotation interaction. Table 1 shows that the relaxation of N2O in the solvents studied in this work are consistent with this estimate, indicating a significant fraction of the total relaxation rate is likely due to the spin rotation interaction. The relaxation ratio in (Eq. 7) holds for the spin-less solvent carbon disulfide. This further suggests that interaction of the nitrous oxide with the spin of the solvent does not significantly contribute to the overall relaxation.
The measurements in blood do not fit in this pattern, however. The singlet lifetime of N2O in blood exceeds the average nuclear T1 by a factor of ~21, indicating that another mechanism, likely paramagnetic centers in hemoglobin or another blood component, dominate relaxation. To the extent that the local fields of these paramagnetic components operate at long range and influence both 15N nuclei equally, singlet-triplet conversion is suppressed, potentially explaining the large ratio of TS to T1 in the case of blood. It is, however, unexpected that the ratio of the T1's in the blood sample was 1.7, which is close to the value of 1.8 predicted by a dominance of relaxation by the spin rotation mechanism (Table 1).
The relaxation of the singlet state was also studied among the two major blood constituents, plasma and hemoglobin, which together account for approximately 65% of blood mass. The singlet lifetime in plasma is 9.3 min. The T1's of the central and terminal Nitrogen at 2 mT are 0.6, and 0.7 min, and 0.7 and 1.3 min at 7.04 T respectively. The deviation of the ratio of the central to terminal nitrogen lifetime from 1.8 at low field indicates that the dominant relaxation mechanism in plasma may be interaction with paramagnetic impurities.
Regardless of the relaxation mechanism, the unusually long TS relative to T1 provides an opportunity for longer-duration in vivo imaging experiments in which the agent is allowed to distribute in the body at low field and is imaged after re-introduction into the MRI scanner, in a manner analogous to the experiments described here. Although N2O or another agent would be subject to in vivo T1 relaxation once in the imaging field, intracellular or lipid-dissolved agent may exhibit a longer T1 compared to that measured here in blood. Measurement in goose fat yielded a T1 of 0.4, and 1.0 minutes and a singlet lifetime of 9.9 min.
The singlet spin-state lifetime of doubly enriched 15N2O in blood is sufficiently long-lived to warrant its further investigation as a potential MRI tracer. The lifetimes of this state in various solvents have been measured and are consistent with relaxation dominated by differing spin-rotation couplings of the two 15N nuclei in water and alcohol, and by strong paramagnetic sites in blood. These residual relaxation mechanisms may be further reduced in agents in which the spin-rotation couplings of the nuclear pair are similar, and the close approach to paramagnetic blood components is minimized. Further analysis of the effect of individual blood components on relaxation of the singlet state is ongoing, as are attempts to hyperpolarize nitrous oxide in the dissolved phase.
The authors would like to acknowledgement financial support from the Leverhulme Trust (UK) and EPSRC (UK). We would also like to thank Marina Carravetta and Rishad Mazitov for technical assistance.
|T1||Upper case Roman ‘tee’, subscript ‘one’|
|TS||Upper case Roman ‘tee’, subscript upper case roman ‘S’|
|I1||Upper case Roman ‘eye’, subscript ‘one’|
|I2||Upper case Roman ‘eye’, subscript ‘two’|
|γ||lowercase Greek gamma|
|δ1||lowercase Greek delta, supscript ‘one’|
|δ2||lowercase Greek delta, supscript ‘two’|
|π||lowercase greek ‘pi’|
||S0>||vertical line, Upper case ‘es’, subscript ‘zero’, right angle bracket|
||↑>||vertical line, upward pointing arrow, right angle bracket|
||↓>||vertical line, downward pointing arrow, right angle bracket|
|‘one’ over than sign, square root sign, ‘two’|
||T1>||vertical line, Uppercase roman ‘tee’, subscript ‘one’, right angle bracket|
||T0>||vertical line, Uppercase roman ‘tee’, subscript ‘zero’, right angle bracket|
||T-1>||vertical line, Uppercase roman ‘tee’, subscript ‘minus one’, right angle bracket|
||Tμ>||vertical line, Uppercase roman ‘tee’, subscript lowercase greek mu, right angle bracket|
|Iz||Uppercase roman ‘eye’, subscript uppercase roman ‘zee’|
|μ||lowercase greek ‘mu’|
|↔||double arrow pointing both left and right|
|much much greater than sign|
|Ttransit||Uppercase roman ‘tee’, subscript roan ‘tee arr aye en es eye tee’|
|1/Jik||‘one’, over than sign, Upper case Roman ‘jaye’, subscript lowercase ‘eye’ ‘kay’|
|½||‘one’ over than sign ‘two’|
|Cc||Upper case Roman ‘cee’, subscript roman lowercase ‘cee’|
|Ct||Upper case Roman ‘cee’, subscript roman lowercase ‘tee’|
|T1c||Upper case Roman ‘tee’, subscript ‘one’ ‘cee’|
|T1t||Upper case Roman ‘tee’, subscript ‘one’ ‘tee’|