Multi-axis fields boost SABRE hyperpolarization

Abstract

The inherently low signal-to-noise ratio of NMR and MRI is now being addressed by hyperpolarization methods. For example, iridium-based catalysts that reversibly bind both parahydrogen and ligands in solution can hyperpolarize protons (SABRE) or heteronuclei (X-SABRE) on a wide variety of ligands, using a complex interplay of spin dynamics and chemical exchange processes, with common signal enhancements between 10³ and 10⁴. This does not approach obvious theoretical limits, and further enhancement would be valuable in many applications (such as imaging mM concentration species in vivo). Most SABRE/X-SABRE implementations require far lower fields (μT-mT) than standard magnetic resonance (>1T), and this gives an additional degree of freedom: the ability to fully modulate fields in three dimensions. However, this has been underexplored because the standard simplifying theoretical assumptions in magnetic resonance need to be revisited. Here, we take a different approach, an evolutionary strategy algorithm for numerical optimization, multi-axis computer-aided heteronuclear transfer enhancement for SABRE (MACHETE-SABRE). We find nonintuitive but highly efficient multiaxial pulse sequences which experimentally can produce a sevenfold improvement in polarization over continuous excitation. This approach optimizes polarization differently than traditional methods, thus gaining extra efficiency.

Keywords: hyperpolarization; magnetic resonance; optimal control.

Fig. 1.

Spectra of thermally polarized and hyperpolarized ¹⁵N-pyridine (cyan) and ¹⁵N-acetonitrile (blue). MACHETE produces an order of magnitude improvement in signal over SABRE-SHEATH (${\epsilon }_{\mathit{MACHETE}}/{\epsilon }_{\mathit{SHEATH}}$) at optimal field conditions. Significant improvement over SABRE-SHEATH is observed for both the ES optimized MACHETE pulse with $A_z<0$ and the $A_z<0$ variant.

Fig. 2.

Exchange interactions in SABRE with an Ir catalyst (prototype three-spin “Y configuration” model). Parahydrogen, a target ligand (here ¹⁵N-acetonitrile), and a stabilizing coligand (here ¹⁴N-pyridine) exchange at the equatorial sites to form transient spin coupling networks for polarization transfer. In the actual catalyst, the two axial positions have ligands (commonly IMes for one position, an exchangeable ligand for the other). This is also a good model for hyperpolarization of natural abundance ligands. The results are also applicable to the case of two bound polarizable ligands, such as concentrated ¹⁵N-pyridine, which we call the “X configuration” case.

Fig. 3.

(A) Coherent evolution (ignoring any exchange) in the SABRE-SHEATH experiment at the optimal magnetic field for polarization transfer (0.6 μT). Initially, only the S_Hα and S_Hβ states are populated, but at later times the average population of the α states (dashed) is modestly higher than the β states (solid). (B) On the ligand spin, these population dynamics lead to oscillations of the polarization back and forth, which are averaged out by the exchange on short timescales. (C) Over longer timescales, this leads to excess α population in solution. For the simulations with exchange, $k_L=20 {\mathrm{s}}^{-1}$, $k_H=1 {\mathrm{s}}^{-1}$, and $T_{1,L}=22.5 \mathrm{s}$.

Fig. 4.

SABRE using circularly polarized fields. (A) The matching condition to generate hyperpolarization with a circularly polarized transverse magnetic field of equal amplitude to the $B_z$ field is given by the condition ${\omega }_{\mathit{rf}}=\left({\gamma }_H+{\gamma }_H\right)B_z\pm ϵ$, slightly offset from the double quantum frequency. (B) Frequency sweep of the circularly polarized field holding $B_z=15 \mathrm{\mu }\mathrm{T}$ and $B=14.9 \mathrm{\mu }\mathrm{T}$. (C) Sweep of $B_z$ using $B=14.9 \mathrm{\mu }\mathrm{T}$ and ${\omega }_{\mathit{rf}}/2\pi =579 \mathrm{Hz}$.

Fig. 5.

MACHETE-SABRE pulse sequence and experimental setup. (A) The pulse shape optimized to use excitation with two shaped magnetic fields: a transverse magnetic field (that we denote $B_x$) and a longitudinal magnetic field, $B_z$, along which polarization is stored. Specific details as to the pulse parameters are detailed in the SI Appendix. After 50 s of simulations, the MACHETE-SABRE sequence generates an approximately 10-fold improvement over SABRE-SHEATH. (B) Spin trajectories of ¹⁵N (cyan) and ¹H (light purple) under 10 periods of the MACHETE-SABRE pulse sequence. While the z magnetization of the target nucleus is largely preserved for this sequence, which is required to preserve the generated hyperpolarization once the target dissociates, the proton magnetization is rapidly modulated.

Fig. 6.

Population flow in (A) SABRE-SHEATH, (B) the ES optimized MACHETE shape with $A_z<0$, and (C) the MACHETE shape with $A_z<0$. In SABRE-SHEATH, population flows out of both singlet states into both target state as well as off-target states, making it a relatively inefficient process. In contrast, the ES optimized MACHETE shape selectively generates population transfer between a single pair of states ($|S_H{\alpha }_L\rangle \to |T_H^{+}{\beta }_L\rangle$) while still preserving population in the $|S_H{\beta }_L\rangle$ state. Similarly, applying the MACHETE shape with $A_z<0$ completely depletes the $|S_H{\beta }_L\rangle$ state and distributes population into $|T_H^{+}{\alpha }_L\rangle$, $|T_H^0{\alpha }_L\rangle$, and $|T_H^{-}{\alpha }_L\rangle$. Exchange is suppressed in these calculations.

Fig. 7.

The performance of SABRE experiments varies depending on timescale, where mediation of back-pumping was first accomplished with (A) the coherently-pumped SABRE-SHEATH experiment. (B) Compared to SABRE-SHEATH, the coherently pumped SABRE-SHEATH variant prevents losses from over-driving the system and losing polarization. Despite not generating as much polarization as either SABRE-SHEATH or the coherently pumped variant over timescales of a few exchange events, the MACHETE-SABRE sequence outperforms any other sequence substantially at long times.

Fig. 8.

MACHETE signal enhancement over SABRE-SHEATH for both ¹⁵N-acetonitrile and ¹⁵N-pyridine at various field conditions. For the $A_z<0$ shape, $B_x$ sweeps (A) were conducted with constant $B_z=-14.10\mathrm{\mu }\mathrm{T}$ while $B_z$ sweeps (B) were conducted with constant $B_x=4.25\mathrm{\mu }\mathrm{T}$ for both acetonitrile and pyridine. The $A_z<0$ sweeps were conducted at different fields for both model systems. For the $A_z<0 B_x$ sweeps (C), ¹⁵N-acetonitrile held a constant $B_z=-13.70\mathrm{\mu }\mathrm{T}$ while ¹⁵N-pyridine used $B_z=-16.00\mathrm{\mu }\mathrm{T}$. Similarly, for the $B_z$ sweeps (D), ¹⁵N-acetonitrile used a constant $B_x=1.25\mathrm{\mu }\mathrm{T}$ while ¹⁵N-pyridine held $B_x=2.00\mathrm{\mu }\mathrm{T}$ MACHETE hyperpolarized signal (blue for ¹⁵N-acetonitrile and cyan for ¹⁵N-pyridine) demonstrated improvement over optimal SABRE-SHEATH (gray) at numerous field conditions. Experimental data are represented by points while simulation data are shown as solid lines.