Live magnetic observation of parahydrogen hyperpolarization dynamics

Abstract

Hyperpolarized nuclear spins in molecules exhibit high magnetization that is unachievable by classical polarization techniques, making them widely used as sensors in physics, chemistry, and medicine. The state of a hyperpolarized material, however, is typically only studied indirectly and with partial destruction of magnetization, due to the nature of conventional detection by resonant-pickup NMR spectroscopy or imaging. Here, we establish atomic magnetometers with sub-pT sensitivity as an alternative modality to detect in real time the complex dynamics of hyperpolarized materials without disturbing or interrupting the magnetogenesis process. As an example of dynamics that are impossible to detect in real time by conventional means, we examine parahydrogen-induced ¹H and ¹³C magnetization during adiabatic eigenbasis transformations at [Formula: see text]T-field avoided crossings. Continuous but nondestructive magnetometry reveals previously unseen spin dynamics, fidelity limits, and magnetization backaction effects. As a second example, we apply magnetometry to observe the chemical-exchange-driven ¹³C hyperpolarization of [1-¹³C]-pyruvate-the most important spin tracer for clinical metabolic imaging. The approach can be readily combined with other high-sensitivity magnetometers and is applicable to a broader range of general observation scenarios involving production, transport, and systems interaction of hyperpolarized compounds.

Keywords: NMR; adiabaticity; hyperpolarization; optical magnetometry; parahydrogen.

Fig. 1.

Hyperpolarization boosts the NMR signals of chemicals and materials, enabling a range of applications from medical diagnostics to particle physics, but the process of exciting the signals for magnetic detection is slow and is destructive to the hyperpolarized state. Additionally, detector saturation typically precludes simultaneous spin-driving and signal detection, necessitating indirect detection via multiple “hyperpolarize–observe” cycles. Direct detection using optical magnetometry allows “live” hyperpolarization dynamics to be observed nondestructively, even in the presence of driving fields.

Fig. 2.

Direct observation of magnetogenesis in nuclear-spin-hyperpolarized molecules. (A) Hyperpolarized fumarate is formed by reducing [1–¹³C]-acetylenedicarboxylic acid with paraenriched H₂, and a $\mathrm{\mu }$T magnetic field sweep (either linear or constant adiabaticity) is applied for scalar-to-vector order conversion. After magnetogenesis, the nuclear spin vector order may be toggled up and down along the $z$ axis by a series of $\pi$ pulses, or excited with a pulse of tip angle $\theta \ne \pi$ to produce oscillating transverse magnetization. (B) A solenoid coil supplies the sweep field, and an alkali-vapor OPM (in the solenoid’s exterior rather than interior field to maximize operating range) is used for detection. Both are located inside a multilayer magnetic shield. The OPM’s sensitive axis is tilted $\sim$30 ^° away from the solenoid axis to be sensitive to both longitudinal ($z$) and transverse ($x$ and $y$) fields produced by the sample. (C) Typical OPM pickup signals during a 50 nT to 2 $\mathrm{\mu }$T field sweep: (purple) stray field of the solenoid field during the sweep; (red) stray field of hyperpolarized [1–¹³C]-fumarate (1 mL, 60 mM). Magnetization toggling before and after the field sweep is performed using composite $\pi$-pulses (90_X 180_Y 90_X) selective to ¹H, and spaced at 0.1 s intervals. After stopping at 6 s the magnetization persists as a stationary state in the solenoid field. The simplified state energy diagrams show population exchange during the adiabatic sweep, leading to a magnetized state. To the Right, the [1–¹³C]-fumarate $J$-coupling parameters are shown. These were used, within the specified errors, for all subsequent simulations.

Fig. 3.

Experimental (color) and simulated (gray) magnetic field profiles for different magnetogenesis cases. (A) OPM signals detected during a linear 0 to 2 $\mathrm{\mu }$T field sweep for the trans and cis isomers of [1–¹³C]-butenedicarboxylate. The applied field sweep is the same for both molecules, but vastly different magnetogenesis dynamics occur due to different $J$-couplings (trans³$J_{\text{HH}}=$ 15.7 Hz, ²$J_{\text{CH}}=$ 5.94 Hz, and ³$J_{\text{CH}}=$ 3.4 Hz; cis³$J_{\text{HH}}=$ 12.2 Hz, ²$J_{\text{CH}}=$ 13.4 Hz, and ³$J_{\text{CH}}=$ 2.6 Hz). The weaker maleate (cis) signal arises from its lower concentration, due to the slower chemical reaction. (B) OPM signals detected during constant-adiabaticity (CA) field sweeps of differing total duration. These profiles are smoother than for uniform field sweeps, although additional low- and high-frequency oscillations are apparent. (C) OPM signals under a field inversion from $-2$ to $+2$ $\mathrm{\mu }$T. Vastly different profiles from those in (A and B) are observed, with an initial negative magnetization build-up followed by a rapid inflection yielding positive magnetization. Simulations represent the total magnetization produced by the 3 spins, vertically scaled to fit the experimental data; the same vertical scaling is applied to each set of panels in (B and C). In (A), phenomenological relaxation is included in the simulated profiles, where $T_1$ and $T_2$ are given in SI Appendix. (D) 3D (Bloch sphere) representation of magnetogenesis trajectories for [1–¹³C]-fumarate during the 0 to $+2$ $\mathrm{\mu }$T sweeps. Spin states $|S_0\alpha \rangle$ and $|T_{+1}\beta \rangle$ as defined in the main text form a near-isolated two-level subspace that undergoes population inversion during sweeps through the anticrossing field. Magnetization is proportional to the vertical distance from the north pole. CA sweeps yield higher-fidelity inversion than the linear sweep, and the beat features are clearly visualized as “cycloid arcs”; these arcs correspond to the high-frequency magnetization oscillations seen in panel (B).

Fig. 4.

Reversibility of the magnetogenesis process. Magnetizing (0 $\mathrm{\mu }$T to 2 $\mathrm{\mu }$T) and demagnetizing (2 $\mathrm{\mu }$T to 0 $\mathrm{\mu }$T) sweeps are performed repeatedly with a 100 ms pause at 2 $\mathrm{\mu }$T with continuous detection throughout. Top: Applied $B_z$ magnetic field profiles and a simulation of the total nuclear magnetization for [1–¹³C]-fumarate for three different sweep durations (0.5 s, 1 s, 2 s). Center: Experimental data showing the magnetic field produced by samples of [1–¹³C]-fumarate subjected to the field sweeps, at different levels of ¹³C isotopic enrichment (2.2%, 20%, 99%); the gray filled region denotes simulation. Bottom: Simulated magnetization trajectories for sweeps between 0 $\mathrm{\mu }$T and 1.986 $\mathrm{\mu }$T in the absence of additional fields, such as the sample’s internal field. The sphere diagrams show selected regions of the trajectory in the $\{|S_0\alpha \rangle$, $|T_{+1}\beta \rangle \}$ two-level subspace at the beginning and center of the profiles, in red and blue, respectively. Fitted exponential decay time constants for the simulated profiles are between 16 s and 22 s (SI Appendix). The Inset for the 20% isotopic labeling, 1 s result shows that a different magnetization trajectory (in both experiment and simulation) is observed when the $B_z$ field during the 100 ms pauses is set to 2.05 $\mathrm{\mu }$T.

Fig. 5.

Time dependence of the ¹H and ¹³C resonance frequencies in [1–¹³C]-fumarate after magnetization following a 0 to 2 $\mathrm{\mu }$T field inversion. Left: The pulse sequence employs short periods of magnetization toggling followed by a small-tip-angle pulse ($\theta \sim$10 ^°) to excite free-precession NMR signals. Right: Fourier transforms of the individual signal transients for ¹³C-enriched and natural-abundance [1–¹³C]-fumarate, showing the ¹³C and ¹H signal regions separately at 13 to 29 Hz and 78 to 93 Hz. For natural-abundance [1–¹³C]-fumarate, the signals are fixed over time at the predicted resonance frequencies, but for the ¹³C-enriched sample, the signals exhibit an exponentially decaying drift over time, arising from the sample’s internal field. Colored signals are vertically scaled by a factor 0.01 relative to the gray signals.

Fig. 6.

Magnetometry during SABRE-SHEATH polarization. (A) An experiment to probe ¹³C magnetization accumulation in 1 mL, 60 mM [1-¹³C]-pyruvate at 350 nT by employing brief intervals of ¹³C toggling at 4 $\mathrm{\mu }$T. Parahydrogen bubbling was switched on and off to alternate between periods of polarization buildup and decay. Plot markers represent the average measured magnetization during a toggling interval, and the raw magnetometer signal during the toggling interval is shown Above (in red) for selected data points (mean signal difference between spin-up and spin-down toggling regions). (B) Optimization of the SABRE-SHEATH field dependence for the polarization of both ¹H and ¹³C in [1-¹³C]-pyruvate. Parahydrogen was bubbled continuously, and the magnetic field was fixed for an 8 s polarization period at the field $B^{\prime }$ followed by NMR signal excitation and detection at 4 $\mathrm{\mu }$T. In the Upper plots representative ¹³C and ¹H spectra are shown. In the Lower plots, the integral of the absolute-mode NMR peaks in the specified frequency range is plotted against the polarizing field $B^{\prime }$. The Inset shows the pulse sequence used to collect the ¹H and ¹³C spectra, where $B^{\prime }$ was varied. The solid curves are the best-fit sums of two Lorentzian curves of equal amplitude but different sign, centered at $+1$ and $-1$ times the center field shown.