# Possible Applications of Dissolution Dynamic Nuclear Polarization in
Conjunction with Zero- to Ultralow-Field Nuclear Magnetic Resonance

Danila A. Barskiy<EMAIL_ADDRESS>Institut für Physik, Johannes
Gutenberg Universität Mainz, 55128 Mainz, Germany,
Helmholtz Institut Mainz, 55128 Mainz, Germany,
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany  John W.
Blanchard  Institut für Physik, Johannes Gutenberg Universität Mainz, 55128
Mainz, Germany,
Helmholtz Institut Mainz, 55128 Mainz, Germany,
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany  Dmitry
Budker  Institut für Physik, Johannes Gutenberg Universität Mainz, 55128
Mainz, Germany,
Helmholtz Institut Mainz, 55128 Mainz, Germany,
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany  Department
of Physics, University of California, Berkeley, CA 94720-7300 USA  Quentin
Stern  Univ Lyon, ENS Lyon, UCBL, CNRS, CRMN UMR 5082, F-69100, Villeurbanne,
France  James Eills  Institut für Physik, Johannes Gutenberg Universität
Mainz, 55128 Mainz, Germany,
Helmholtz Institut Mainz, 55128 Mainz, Germany,
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany  Stuart J.
Elliott  Molecular Sciences Research Hub, Imperial College London, London W12
0BZ, United Kingdom  Román Picazo-Frutos  Institut für Physik, Johannes
Gutenberg Universität Mainz, 55128 Mainz, Germany,
Helmholtz Institut Mainz, 55128 Mainz, Germany,
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany  Antoine
Garcon  Helmholtz-Institut Mainz, 55099 Mainz, Germany  Johannes Gutenberg-
Universität Mainz, 55128 Mainz, Germany  Sami Jannin  Univ Lyon, ENS Lyon,
UCBL, CNRS, CRMN UMR 5082, F-69100, Villeurbanne, France  Igor V. Koptyug
Laboratory of Magnetic Resonance Microimaging, International Tomography Center
SB RAS, Institutskaya Street 3A, 630090 Novosibirsk, Russia

###### Abstract

The combination of a powerful and broadly applicable nuclear hyperpolarization
technique with emerging (near-)zero-field modalities offer novel opportunities
in a broad range of nuclear magnetic resonance spectroscopy and imaging
applications, including biomedical diagnostics, monitoring catalytic reactions
within metal reactors and many others. These are discussed along with a
roadmap for future developments.

##  1 Introduction

Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) has emerged from
the far corner of NMR exotica and is becoming a relatively well established
subfield of NMR on its own Blanchard and Budker (2016a); Blanchard et al.
(2021). While for high-field NMR, hyperpolarization often represents a
“luxury” of having enhanced signals, it is an absolute necessity for ZULF NMR
where signals vanish in the absence of hyperpolarization. It is, therefore,
not surprising that the progress in ZULF NMR techniques and applications has
paralleled developments in hyperpolarization Eills et al. (2023). In fact,
essentially all hyperpolarization techniques have by now been used with ZULF
NMR Theis et al. (2011, 2012); Barskiy et al. (2019); Picazo-Frutos et al.
(2023); Chuchkova et al. (2023).

At first glance, dissolution dynamic nuclear polarization (dDNP) is not an
obvious technique to use with ZULF NMR. In fact, $d$DNP usually involves
relatively complex setup based on a high-field magnet and cryogenics, so it
would seem to negate potential advantages of ZULF NMR such as portability,
relative simplicity and low cost. Nevertheless, in this article111The paper is
based on the discussions prior to February 2022 and projects initiated at that
time., we argue that a “marriage” of $d$DNP and ZULF NMR makes a lot of
practical sense, given the growing availability of $d$DNP in preclinical and
clinical contexts, the ability to hyperpolarize nearly arbitrary small
molecules, and the compatibility of the two techniques with _in vivo_ studies
due to their non-invasiveness Jannin et al. (2019); Blanchard et al. (2021).

###  1.1 What is ZULF NMR?

ZULF-NMR experiments are performed at low bias magnetic fields, so that
internal molecular interactions between spins are larger than interaction
between the spins and the external field Blanchard and Budker (2016b). In most
of the ZULF NMR apparatus today, detection is accomplished with spin-exchange
relaxation-free (SERF) magnetometers Tayler et al. (2017). At the heart of
such a magnetometer is a glass cell containing atomic vapor, for example Rb,
K, or Cs Budker and Romalis (2007), heated to 150-180 oC to ensure
sufficiently high concentration of the alkali metal in the gas phase. Since
the magnetic field from a polarized sample scales as $1/r^{3}$ (where $r$ is a
distance between the sample and the vapor cell), the vapor cell is typically
positioned as close as possible to the sample. Commercial magnetometers are
currently available and the surface of such sensors remains relatively cool
(40 oC) on the outside Put et al. (2021).

The sensor and the sample are enclosed in a magnetic shield. The shield
separates the ZULF region from the environmental magnetic fields (the Earth
magnetic field, AC-line induced fields, etc.). External fields are typically
attenuated by a factor of 105-106, while the residual fields are further
reduced with a set of magnetic-field coils mounted inside the shield Xu et al.
(2006).

###  1.2 Why $d$DNP?

Dissolution dynamic nuclear polarization (dDNP) is one of the key
hyperpolarization methods used to enhance NMR signals of molecules in the
solution-state Ardenkjær-Larsen et al. (2003). DNP works by applying a
microwave field (with frequency set near-resonance with electron Zeeman
transitions) to the solid-state sample kept at a high magnetic field
containing molecules to be polarized and the source of electrons, typically,
stable radicals like TEMPO van den Brandt et al. (2004) or trityl Shankar
Palani et al. (2023) (although other sources are known as well). The
dissolution step involves fast injection of hot water and transfer of the
hyperpolarized sample to a detection apparatus.

Over the last two decades, $d$DNP has emerged as a major player in various
subfields of magnetic resonance, particularly, metabolic imaging using
13C-detected MRI (i.e., in the context of chemical shift imaging and single
voxel spectroscopy) Kurhanewicz et al. (2011). It is therefore reasonable to
explore opportunities provided by generality and widespread availability of
$d$DNP for novel ZULF NMR/MRI applications.

Combining ZULF with $d$DNP makes even more sense in the current context, where
there are ongoing efforts towards benchtop $d$DNP setups and with several
teams working on making hyperpolarization generated by low-temperature off-
site transportable over long distances Ji et al. (2017); El Daraï et al.
(2021); Capozzi (2022); Steiner et al. (2023), with dissolution taking place
remotely on-site, therefore possibly turning hyperpolarization in the near
future into a consumable. The production of large quantities of hyperpolarized
substrates on demand in a single site and the delivery of those hyperpolarized
molecules on-site might end-up in overall lower costs and higher availability.

###  1.3 The purpose of this paper

There have already been first reports of the combination of $d$DNP with ZULF
NMR. In Barskiy et al. (2019), a portable ZULF-NMR apparatus was taken to the
University of California San Francisco (UCSF) hospital where a $d$DNP machine
was available. Zero-field spectrum of $d$DNP-hyperpolarized [2-13C]-pyruvic
acid was recorded, demonstrating feasibility of the $d$DNP/ZULF-NMR
combination.

Recent works Picazo-Frutos et al. (2023); Mouloudakis et al. (2023)
demonstrated ZULF-NMR detection of [13C]-sodium formate, [1-13C]-glycine,
[2-13C]-sodium acetate, and [1–13C]-pyruvate with dDNP-provided signal
enhancements of up to 11,000 compared to thermal prepolarization at 2 T
Elliott et al. (2021). Relaxivity of 0.3 s-1mM-1 was found for the TEMPOL
radicals used in the $d$DNP process resulting in ZULF-NMR line broadening of
100 mHz per mM of the radical. These results show that, despite the presence
of the radicals, $d$DNP can be used as a universal hyperpolarization tool for
ZULF-NMR applications. Further improvements will be possible in the near
future to produce radical-free hyperpolarized solutions with heterogeneous
sample formulations El Daraï and Jannin (2021).

In this paper, we discuss potential future applications of $d$DNP in
conjunction with ZULF NMR, focusing on directions where such a combination may
be particularly advantageous.

##  2 Applications of $d$DNP in ZULF NMR

###  2.1 Complex Environments and NMR of mixtures

In conventional high-field NMR, the main source of chemical information is
chemical shift wherein the applied magnetic field is partially shielded by
molecular electrons, giving rise to a shift in the nuclear Larmor frequency.
Because differences between chemical shifts corresponding to different
chemicals are proportional to the applied magnetic field, high-resolution
high-field NMR measurements require extremely homogeneous magnetic field and
highly homogeneous samples. Any heterogeneity leads to susceptibility-induced
magnetic field gradients that broaden nuclear spin resonance lines, reducing
the resolution–and thus chemical specificity–of the NMR spectrum.

Unfortunately, many (if not most) important real-world materials and devices
are inherently heterogeneous, including, for example, energy-storage devices
and catalytic chemical reactors. While direct, non-destructive in situ and/or
operando measurements would be of tremendous value for understanding such
systems, real samples and devices pose numerous challenges for traditional
spectroscopic methods: in addition to the heterogeneity-based problems for
NMR, many such devices are optically and RF-opaque and must remain fully
sealed for practical safety considerations.

Fortunately, a significant advantage of operating at zero magnetic field is
that the resulting NMR spectra are almost entirely unaffected by the magnetic
susceptibility of the sample environment. In fact, zero-field NMR experiments
on heterogeneous samples routinely feature sub-Hz resonance linewidths
Blanchard et al. (2015); Tayler et al. (2018). Also, because low-field NMR
involves frequencies much lower than in the high-field case, the skin effect
becomes negligible (for example, the RF penetration depth of a 1 kHz signal
into stainless steel is $>1$ cm).

Apart from (or in addition to) the challenges of measurements in complex
environments, another challenge is chemical analysis of complex mixtures with
a representative example being the analysis of impurities in food and
beverages.

###  2.2 Wine and spirits testing

The $d$DNP/ZULF-NMR spectroscopy can be used to screen for methanol content
and other impurities in alcoholic beverages. This is of importance because
methanol poisoning is a major cause of injury and death in Eastern European
and Asian countries Giovanetti (2013); Lee et al. (2014); there is a general
need to test for counterfeit and bootlegged products. Additional motivation
may be that a similar method can be used for the detection of liquid poisons
and explosives that escape nuclear-quadrupole-resonance (NQR) based screening.
High polarization available with $d$DNP is good for developing the technique
and building up a library of relevant ZULF-NMR spectra.

ZULF NMR spectra are generally vastly different for different molecules, with
line widths much narrower than the major peak separation. This potentially
facilitates analyte discrimination, even in low-cost instruments.

ZULF NMR spectra of ethanol extracted from a vodka sample (bought at a
supermarket) was recently studied, where alcohol was hyperpolarized using
parahydrogen Dyke et al. (2022). In particular, $J$-coupling transitions
corresponding to [13C]-methanol, [1-13C]-ethanol and [2-13C]-ethanol in both
13C-isotopically enriched and natural-abundance samples were observed after
employing the relayed version of the signal amplification by reversible
exchange (SABRE) hyperpolarization (Fig. 1) Iali et al. (2018). Interestingly,
different lines in $J$-spectra showed different relaxation behavior,
highlighting opportunities for a combined use of hyperpolarization and
relaxometry for chemical identification. Fast Laplace-transform methods could
be envisioned for obtaining 2D-spectra containing spectroscopic, relaxation,
and diffusion information Telkki (2018).

Figure 1: ZULF NMR spectrum of the sample containing ethanol (750 mM)
extracted from vodka and methanol (750 mM) at natural isotopic abundance with
benzylamine (250 mM) and Ir catalyst (12 mM). The spectrum was observed
following 1500 scans (each scan required 10 s of parahydrogen bubbling in a
field of 19 mT at 5 bar and 60 sccm). The peaks of methanol at 140 and 280 Hz
represent $J_{\rm CH}$ and $2J_{\rm CH}$, and the cluster of peaks surrounding
210 Hz arise from the AX2 spin system of [1-13C]-ethanol (1.5$J_{\rm CH}$,
$J_{CH}=140$ Hz). Peaks for [2-13C]-ethanol are visible around 255 Hz,
although markedly less clear than those of the other ethanol isotopomer; (*)
denotes peak from an unknown source. Reproduced with permission from Ref. Dyke
et al. (2022).

Despite SABRE-relay being a convenient way of polarizing molecules containing
exchangeable protons, it is still not as universal as $d$DNP as shown recently
with the hyperpolarization of complex mixtures such as cancer or plant
extracts to biological fluids Dey et al. (2022); Dumez et al. (2015). High
levels ($>$5%) of heteronuclear polarization using SABRE approach are yet to
be demonstrated. Therefore, $d$DNP remains a primary method for universal
hyperpolarization and ZULF NMR detection.

The spectrum of 13C-methanol has two peaks at 140 and 280 Hz. The spectrum of
1-13C-ethanol has peaks at near-zero frequency and around 200-220 Hz. The
spectrum of 2-13C-ethanol has peaks at near-zero frequency, at around 120-130
Hz, and around 230-260 Hz. Overlap between the signals for ethanol and
methanol should be small. However, the tails of the ethanol peaks may still be
significant relative to the methanol signals if using a realistic samples
(hopefully, with low methanol concentration).

When evaluating whether the $d$DNP/ZULF NMR analysis is the best way to go in
practice, one also need to consider that what we have discussed so far is
effectively a destructive analysis method, as the bottle has to be opened and
the contents mixed with radicals and dissolution solvent. If, however, the
analysis is a part of the production process, testing can be performed in
real-time. One also needs to compare the $d$DNP/ZULF NMR against gas
chromatography–mass spectrometry, another approach in which the sensor can be
portable, and sensitive.

We suggest further research on $d$DNP/ZULF NMR on ethanol and methanol which
are good standard materials with well-understood spectra, which should lead to
optimization of the analysis and extension to other possible impurities.

###  2.3 NMR of mixtures (liquids, adsorbed gases) in porous materials

An important task of NMR spectroscopy is to analyze (quantify) the composition
of a mixture of fluids confined in a porous solid material.

There are numerous situations and processes which involve liquids or gases
adsorbed/absorbed in porous materials, such as filtration of liquid mixtures,
chromatographic separation, chemical (e.g., heterogeneous catalytic)
reactions, transport of fluids in building materials and rock cores, etc.
Analyzing the mixture composition in real time may be required as it may
change in space and time because of adsorption, chemical transformation, etc.
This can be potentially extended to adsorbed gases, but $d$DNP of gases
Vuichoud et al. (2016); Comment et al. (2010) can be challenging as the
relaxation rates are very much enhanced by spin rotation.

Hyperpolarization is generally required for such experiments because the
porosity of solid materials is lower than unity, which reduces the amount of
liquid in the sample under study, particularly for materials with low values
of the specific pore volume. In this respect, $d$DNP is a most universal
hyperpolarization technique at present, which can be used to polarize a broad
range of fluids suitable for such studies.

Figure 2: 1H NMR spectra of a 1:1 mixture of $\alpha$-methylstyrene (AMS;
left) and its hydrogenation product cumene detected for bulk liquid (a) and
liquid permeating a porous catalyst pellet (b,c). Spectrum (b) was detected
with spatial resolution. The number of acquisitions was eight (a,c) or two
(b). Reproduced with permission from Ref. Koptyug et al. (2002).

NMR spectra of fluids filling the pore space of porous solids are inevitably
significantly broadened and distorted, with the main reason being the
susceptibility mismatch between the involved liquid, solid, and gaseous (e.g.,
in partially saturated porous solids) phases which leads to large local
gradients of the applied magnetic field when conventional NMR spectroscopy or
imaging is performed (Fig. 2).

Performing NMR experiments at lower magnetic fields (e.g., benchtop NMR
systems) does not entirely solve the problem; while local field gradients
become lower, the frequency separation of the NMR lines with different
chemical shifts decreases as well, and thus no gain in spectral resolution is
achieved this way. ZULF NMR, on the other hand, is advantageous in this
respect since no (or very low) applied magnetic field means that no field
gradients are present in the sample (Fig. 3), while at the same time chemical
information is derived from the spin-spin couplings which are independent of
magnetic field instead of chemical shifts.

###  2.4 NMR of heterogeneous catalytic reactions

Another promising direction related to the application of NMR spectroscopy is
to monitor over time the conversion of substrates to products on porous solid
catalysts. The general motivation for this is provided by the notion that NMR
analysis of the reacting mixture is essential in characterizing the activity
and selectivity of heterogeneous catalysts which are their most important
characteristics from the point of view of industrial applications. In this
context, hyperpolarization of nuclear spins Eills et al. (2023) is essential
for providing sufficient detection sensitivity for such experiments. In
particular, as the concentrations of molecules vary in time during a catalytic
reaction, high levels of initial hyperpolarization can help characterize the
early (low concentration of products) and late stages of the reaction (low
concentrations of a starting substrate). Furthermore, high levels of spin
polarization may provide a unique possibility to detect short-lived reaction
intermediates that are present in low concentrations during the reaction,
which would be a tremendous asset for studying the underlying reaction
mechanisms. In this respect, utilization of $d$DNP for spin hyperpolarization
is essential as this technique currently outperforms other hyperpolarization
approaches in terms of its much wider scope of potential reactants that can be
hyperpolarized, and also often in terms of the achievable spin
hyperpolarization levels.

When it comes to the availability and quality of spectroscopic information,
ZULF NMR is expected to have significant advantages over other NMR detection
schemes because the application of any sizeable magnetic field results in its
significant inhomogeneity for samples comprising both solid (catalysts and
adsorbates) and fluid (reactants, products, solvent) phases. While such
applications have not been demonstrated yet, their feasibility can be
envisioned based on the successful application of $d$DNP to polarizing
reactants to study homogeneous catalytic hydrogenation Boeg et al. (2019) and
implementation of ZULF NMR to monitor the formation and consumption of
hyperpolarized reaction products produced in sequential homogeneous
hydrogenation of an alkyne with parahydrogen Burueva et al. (2020).

Figure 3: (a-b) Single-scan NMR spectra recorded using atomic magnetometer and
(c-d) $T_{1}$ relaxation data recorded at a magnetic field of 0.634 $\mu$T
(corresponding to 1H Larmor frequency of 27 Hz) for n-heptane in (a+c) bulk
liquid and (b+d) imbibed into Q–15 porous silica. Reproduced with permission
from Ref. Tayler et al. (2018).

###  2.5 NMR spectroscopy and imaging of a model catalytic reactor

Industrial (including catalytic) reactions often use high pressures and
temperatures and thus reactors to implement such processes are often made of
metals. Such reactors cannot be studied with conventional NMR/MRI. While it is
possible to use different materials for constructing an NMR-compatible model
reactor, this may not be suitable or realistic as non-traditional materials
may affect reactor performance, for instance, because the heat transport in
exothermic or endothermic reactions may be altered. Similar to the studies of
heterogeneous catalytic processes addressed in the previous section, $d$DNP is
necessary to provide adequate detection sensitivity, while ZULF NMR is
required to achieve the necessary spectroscopic resolution. In addition, of
primary importance in such studies is the fact that metal containers are not
transparent to radiofrequency electromagnetic fields used for sample
excitation and signal detection in conventional NMR/MRI because the
penetration depth of rf field into metals is limited by the skin depth which
is too small at conventional NMR frequencies (the MHz range). This problem is
eliminated in ZULF NMR which does not use radiofrequency fields, opening the
door for _operando_ reactor studies under harsh reaction conditions. Such
spectroscopic (and potentially imaging) experiments are thus deemed feasible.
Recent developments of fast transfer and injection devices for $d$DNP, based
on liquid pumps operating at pressures up to 40 bars Ceillier et al. (2021),
would readily provide way to supply these reactors with hyperpolarized
solutions even under high pressure conditions.

###  2.6 Utilization and exploration of long-lived spin states

Another promising strategy is the production of long-lived spin states (LLSS)
with $d$DNP and their observation with ZULF NMR. The utility of LLSS is in
prolonging the useful time window for the observation of enhanced NMR signal
Levitt (2019); Stevanato et al. (2015); Sonnefeld et al. (2022), enabling
obtaining NMR spectra with higher SNR and the study of slower physical and
chemical processes than what is possible with hyperpolarized substances for
which the lifetime of NMR signal enhancement is governed by the conventional
$T_{1}$ nuclear spin-relaxation times. Dissolution DNP has already
demonstrated the ability to efficiently produce LLSS of not totally symmetric
molecules Vasos et al. (2009), which is not universally possible with other
hyperpolarization techniques. In addition, the preparation of LLSS with
dissolution DNP ensures a major gain in SNR when such states are detected in
NMR experiments. At the same time, many molecules that do not exhibit
properties of LLSS in high magnetic fields may do so under ZULF NMR conditions
because of the strong coupling of nuclear spins, and not only between nuclei
of the same type but also between different nuclei Emondts et al. (2014). At
the same time, the correlated state of a spin system containing, for example,
1H and 13C nuclei, can be easily read out using ZULF NMR.

Relaxation of nuclear spin order at low magnetic fields may be affected by
chemical exchange in the case of molecules containing exchangeable chemical
groups, for example, protons (especially in conditions when $J$-coupling
between the polarized nucleus and an exchanging group matches the chemical
exchange rate). Studying relaxation dynamics and understanding which of the
chemical pathways may lower the available hyperpolarization is therefore
warranted. Since accelerated relaxation of chemically-exchanging systems is
expected to occur at near-zero-field, it is reasonable to study these effects
by ZULF NMR. Furthermore, the possibility to “decouple” the rapidly exchanging
group from the target spin system by applying magnetic field pulses is
attractive because it can in principle prolong the lifetime of
hyperpolarization Alcicek et al. (2021).

###  2.7 Drug screening by $d$DNP-ZULF NMR

Pharmaceutical industry is in constant search for new methods to detect
interactions between small molecules and biomolecules and NMR plays an
important role in this field. Drug screening is an essential step of drug
discovery that consists of testing a library of compounds as possible binders
for a target protein (or another biomolecule). It requires reliable assays
able to detect weak interactions between a small organic molecule and a large
biomolecule, for which NMR is a technique of choice. However, the low
sensitivity of NMR forces researchers to use large amounts of expensive
proteins and work at high concentrations that sets a limit to the contrast
between the bound and free state. $d$DNP has been proven as a means of
overcoming these limitations Kim and Hilty (2019) by allowing to decrease the
ligand and protein concentrations.

In a $d$DNP-ZULF NMR experiment, one would hyperpolarize a small molecule
(“the spy”) that is known to bind weakly to the protein and first detect it
using ZULF NMR in the absence of protein. The experiment would be then
repeated by injecting the hyperpolarized spy in a protein solution preloaded
in the ZULF spectrometer. The relaxation (or, alternatively) coherence time of
the spy is likely to be severely affected by binding (by changing rotational
correlation time as well as by interactions with deuterons in the protein).
Further experiments would be conducted adding competitor molecules to the
protein solution. If the competitor binds to the protein, the hyperpolarized
ligand will not bind and will thus (partially) recover the coherence time it
has in the free state, which reveals the binding of the competitor. This type
of “competition experiment” is common in drug screening.

Detection at high field, although feasible, is not straightforward. In the
case of experiments where 1H or 19F spins are detected, field inhomogeneity
after injection (due to the uncertainty of injected volume produced by $d$DNP
and microbubbles) causes large broadening. This limitation is expected to
disappear at low field. Importantly, the relaxation contrast between bound and
free form of a small molecule prepared in a LLSS is likely to be stronger at
low fields Kowalewski and Maler (2019).

If the sensitivity is no longer the limitation, the concentrations can be set
so as to have the optimal contrast. Among the possible proteins for such
studies are heavy trans-membrane proteins that tend to aggregate so they
cannot be kept in solution during the typical times required with standard
thermal equilibrium NMR (typically 20 minutes). As a consequence, conventional
NMR cannot always be used as it requires accumulation of scans.

Figure 4: Zero-field $J$-spectra of (a) [1-13C]-glycine, (b)
[2,3-13C2]-fumarate, and (c) [1-13C]-D-glucose. In (a,b), top pictures show
experimental spectra after averaging (1024 scans) and the bottom spectra are
simulations obtained in Mathematica using the SpinDynamica package. (25) In
(c), the spectrum is a result of 2000 averages. The peak at 180 Hz denoted by
asterisk is due to the residual magnetic field at the power-line harmonic
leaking into the magnetic shielding. Reproduced with permission from Ref. Put
et al. (2021).

###  2.8 Expanding the library of ZULF-NMR spectra

For future practical applications, particularly, in the biomedical field, it
will be useful to collect high-quality ZULF-NMR spectra of a number of small
biomolecules (Fig. 4) Blanchard et al. (2020a); Put et al. (2021). In the
first round, the focus could be on molecules/metabolites that are already
under investigation for use as hyperpolarized sensors in vivo for high-field
MRI. The existing knowledge about these systems will help to evaluate the
relative advantages and disadvantages of the ZULF approach. Another bonus is
that some of these systems are already approved or are in the process of
certification for use with patients. One should note that strategies of
accelerating DNP hyperpolarization buildup such as 1H-13C and 1H-15N cross-
polarization enable satisfactory heteronuclear polarization only in a few tens
of minutes.

Experimental data on ZULF NMR spectra are complementary to theoretical
evaluations Hogben et al. (2011) and serve to determine or validate the values
of $J$-couplings Wilzewski et al. (2017) as well as various assumptions that
enter the calculations of spin dynamics (e.g., the rates of relaxation and
chemical exchange).

The acquisition of a substantially large number of spectra can be facilitated
by modern automation techniques (robotic arms, microfluidics, remote control
of the experiment, machine learning, etc.). Since it is easier to produce
large homogeneous region of the low magnetic field (compared to high field),
massive automated screening of different molecules could be employed at the
same time Ajoy (2023). Some of the important metabolites such as
[1-13C]-pyruvate, [1-13C]-lactate, [1-13C]-fumarate, [1-13C]-malate, etc. have
already been studied by ZULF NMR Barskiy et al. (2019); Put et al. (2021);
Eills et al. (2022); Knecht et al. (2021); Theiss et al. (2023). Other
molecules, in particular, 15N-labelled compounds such as 15N-choline,
15N-phosphocholine, 15N-histidine, 15N-histamine, 15N-proline,
15N-trimethylglutamine among others, can be of interest to metabolomics, thus,
their ZULF NMR investigation is warranted. It is anticipated that the presence
of low-gamma 15N nuclear sites may increase relaxation times of the observable
transitions at ultralow fields, enabling a number of applications. One may
need to pay careful attention to pH during polarization and/or detection to
avoid exchange-related accelerated relaxation.

Until now, ZULF NMR has been mostly limited to either high-concentration
solutions (often solvents), or parahydrogen-polarized molecules. With $d$DNP
one have the possibility to collect ZULF spectra for many more classes of
molecules by achieving polarization levels high enough to see them at
biologically relevant concentrations. Besides adding to the library of ZULF
NMR spectra, this is the first step towards eventual _in vivo_ imaging at zero
field (see below).

###  2.9 ZULF-NMR Molecular Imaging

The goal of molecular imaging is to visualize, characterize, and quantify
particular molecular species within intact subjects (such as materials,
chemical reactors etc.) and organisms non-invasively and in real time
Gallagher (2010).

Dissolution DNP is an enabling technique for _in vivo_ metabolic imaging
Kurhanewicz et al. (2011), while ZULF NMR can be used to measure metabolites
provided the signals are sufficiently enhanced by hyperpolarization Barskiy et
al. (2019). Thus, the combination of the two techniques appears to be both
feasible and beneficial. Indeed, for metabolites present in complex
environments all of the attractive features discussed in Sec. 2.1 are directly
relevant.

Magnetic resonance imaging (MRI) is an important (if not the main) application
of conventional NMR, and it is interesting to explore what can be done in the
realm of ZULF. In order to realize ZULF MRI, one needs to contend with the
issue of concomitant gradients. According to Maxwell’s equations, linear
magnetic field gradients satisfy

$\frac{\partial B_{z}}{\partial z}=-\frac{\partial B_{x}}{\partial
x}-\frac{\partial B_{y}}{\partial y}\,.$ (1)

While in high field, the influence of the transverse components (on the right-
hand side) is typically negligible, this is not the case at ZULF conditions.

There are are several approaches currently being pursued to address the
concomitant-gradient issue at ZULF, including:

  1. (i)

Imaging with sensor arrays. This approach is similar to magnetoencephalography
(MEG), but offers additional spectroscopic information. While the inverse
problem of reconstructing the source-magnetization distribution is ill-posed,
information from a sensor array provides a rich input to modern
analysis/reconstruction tools based on machine learning.

  2. (ii)

“Sweet-spot-scanning”. Consider a quadrupolar field produced, for example,
with an anti-Helmholtz coil pair. In this geometry, the field is zero at the
center, and increases everywhere else. Thus, only a part of the sample
sufficiently close to the center where the ZULF conditions are satisfied yield
a coherent zero-field signal, while the rest of the sample would produce
homogeneously broadened background. The “sweet spot” can be moved around to
interrogate different parts of the sample and create its molecular image.
Because one would only be measuring a part of the total sample, it is
imperative to start out with a lot of signal, which highlights the role of
hyperpolarization in general and $d$DNP in particular. Note that more
elaborate field configurations can be considered such as arrays of
quadrupoles, which could allow simultaneous measurements at multiple field
zeros to speed-up the imaging.

  3. (iii)

Fourier imaging. Concomitant gradients are a problem at ultralow fields, but
not so at higher fields. Correspondingly, spatial encoding can be achieved by
applying a gradient on top of the field of the “DC” magnetic-field pulse used
to initiate the ZULF-NMR signal. This approach resembles Hoult’s “Rotating-
frame zeugmatography” Hoult (1979) or Transmit Array Spatial Encoding (TRASE)
Sharp and King (2010).

###  2.10 Dual-modality magnetoencephalography (MEG) and metabolic
$J$-spectroscopy

ZULF NMR spectra can be collected using same or similar devices as currently
employed for MEG (see, for example, Ref. Boto et al. (2018)). Detection of
metabolic signatures associated with cognitive processes together with MEG
could open new ways to better understand the human brain, for instance, by
detecting metabolic changes associated with brain activity. A combination of
ZULF NMR with MEG for simultaneous mapping of the brain activity and brain
chemistry could be used for detecting abnormalities and improving our general
understanding of cognition.

Dissolution DNP is currently a leading hyperpolarization modality for clinical
applications and, more likely, will remain to be so. Optically pumped
magnetometers (OPMs) are small, do not require cooling systems and can rival
superconducting cryogenic quantum interference devices (SQUIDs) in terms of
sensitivity Boto et al. (2018). At the same time, magnetic signals generated
by hyperpolarized nuclei can be conveniently detected at zero field.

Let us estimate the sensitivity of OPM-based detection of $d$DNP-polarized
molecules given the approximate parameters available with current setups. Let
us assume injection of 40 mL into a human patient of an aqueous buffer
containing $C=300$ mM [1-13C]-pyruvate with 13C polarization of $P=40$ %.
Assuming 5 l of blood in a patient (and the fact that hyperpolarized bolus is
redistributed within the blood reservoir in $\sim$20 s UPTON and HUANG (1993))
and 100 mL of blood at a given moment of time in the head, let us calculate
13C nuclear magnetization in a patient’s head given hyperpolarized bolus is
uniformly redistributed within the body without loss of hyperpolarization.

Magnetization ($M$) of such a bolus is

$M=\frac{\gamma_{\rm C}\hbar}{2}CP\approx 6\cdot 10^{-8}{\rm\frac{A}{m}},$ (2)

where $\gamma_{\rm C}$ is gyromagnetic ratio of 13C nucleus and $\hbar$ is
Plank’s constant. This magnetization generates a magnetic field measured with
the OPM at the surface of the head (assuming magnetization is spread out
inside the head uniformly, which is a crude approximation) at a distance
$R=10$ cm from the center of the head:

$B=\frac{\mu_{0}M}{2\pi R^{3}}=10\,{\rm pT},$ (3)

This is plenty of signal since OPMs with $\sim$5 fT/Hz1/2 sensitivity are now
commercially available Blanchard et al. (2020a). In reality, relaxation during
the transfer, injection, and distribution of the hyperpolarized material, as
well as non-uniform distribution of polarization across the volume of the
studied subject etc. will result in lower available signal. However, we point
out that not 13C magnetization but rather heteronuclear spin coherence can be
detected with ZULF NMR. Its signal is proportional to the difference between
gyromagnetic ratios of the participating nuclei and the lifetime can exceed
conventional $T_{1}$ relaxation of individual spins Emondts et al. (2014),
thus, even more signal can be expected than provided in the estimation above.

Another possible application is studying metabolic transformations in muscles
during exercise/rest in order to reveal and quantify metabolic changes
associated with muscle activity. High-field MRI (with $d$DNP) can be used but
it is limited to only a few muscle groups due to the small motion range
restricted in conventional NMR scanners. We are aware of only one study that
did it on calves muscles UPTON and HUANG (1993). Future zero-field NMR
wearable spectrometers will be ideally suited for such studies.

###  2.11 Production and Detection of Nuclear Spin Isomers

Nuclear spin isomers (NSIs) have been explored in the context of fundamental
spin physics, chemistry Chapovsky and Hermans (1999), and even astronomy Curl
Jr et al. (1966). Here we suggest producing NSIs by means of $d$DNP and
measuring their lifetimes with ZULF NMR.

Currently, there is no way to obtain large quantities of NSIs for molecules
other than hydrogen (for the latter, the well-known spin isomer, parahydrogen,
is routinely produced Farkas (1935)). Current techniques for NSI enrichment
employ laser cooling Chapovsky and Hermans (1999) and Stern-Gerlach spin-
separation devices Wennerström and Westlund (2012). These methods cannot yield
sufficiently large quantities of NSIs since only several milliliters can be
stored in a flask or a tank, while larger quantities are desirable for both
research and applications.

$d$DNP is universal hyperpolarization technique and allows high ($>$50%)
polarization levels. SABRE can be used for polarizing NH3 Iali et al. (2018)
but sufficiently high and reproducible polarization levels ($>5$ %) have not
been demonstrated as of yet. The advantage of ZULF NMR for NSI detection is
that the spectra will directly show the distribution of NSIs via the intensity
of $J$-spectral lines (a chemical step inducing molecular symmetry breaking
would be necessary in some cases). Another advantage of ZULF NMR is the fact
that modular spectrometers can be easily optimized for various chemical
manipulations (which can be necessary in some cases to observe spin dynamics)
Simultaneous ZULF detection of NSI with IR/Raman spectroscopy could also be
envisioned.

###  2.12 Developing Decoupling Sequences for ZULF NMR

One of the unique advantages of ZULF NMR is that the technique is, in
principle, capable of detecting spin-spin couplings that are “truncated” in
high-field NMR. However, practical realization of this advantage requires the
ability to suppress larger “background” interactions, which can be
accomplished with rank-selective pulse sequences to decouple terms in the
Hamiltonian of different rank. An example is decoupling the rank-2 dipole-
dipole interactions so that they do not overwhelm the antisymmetric rank-1 $J$
coupling in an oriented sample Llor et al. (1995a, b); King et al. (2017);
Blanchard et al. (2020b).

###  2.13 Searches for dark matter and exotic spin-gravity coupling

Figure 5: Nuclear spin energy levels and NMR spectra of 13C-formic acid
measured in three different field conditions. (A) At zero magnetic field, the
$F=1$ levels are degenerate, resulting in a spectrum exhibiting a single peak
at the $J$-coupling frequency. (B) In the presence of a DC magnetic field
$B_{z}\approx 50$ nT, the $m_{F}=\pm 1$ degeneracy is lifted. The spectrum
exhibits two split $J$-resonances. The splitting is equal to $\hbar
B_{z}(\gamma_{\rm C}+\gamma_{\rm H})$. The asymmetry of the resonances is due
to the influence of the applied field on the response characteristics of the
atomic magnetometer. (C) Addition of an oscillating magnetic field along
$B_{z}$ modulates the $m_{F}=\pm 1$ energy levels, resulting in sidebands
located at $J/2\pi\pm B_{z}(\gamma_{C}+\gamma_{H})/2\pi\pm\omega_{AC}$ with
amplitude proportional to the modulation index: $A_{s}\propto B_{\rm
AC}(\gamma_{\rm C}+\gamma_{\rm H})/(2\omega_{\rm AC})$. Reproduced with
permission from Ref. Garcon et al. (2019)

ZULF NMR has been proven to be a powerful technique with potential to detect
ultralight bosonic fields hypothesized to be constituents of galactic dark
matter responsible for about 80% of galactic mass that appears to be
“invisible” apart from its gravitational pull. This was accomplished in the
cosmic-axion spin-precession experiments (CASPEr) Wu et al. (2019); Garcon et
al. (2019) that searched for axion-like particles (ALPs) and dark-photon (DP)
dark-matter particles. If those particles were to exist, they should induce
phase and frequency modulation/shifts of the well-defined ZULF-NMR spectra of
small molecules through their interaction with nuclear spins. However, the
interaction between ALPs and nuclear spins is predicted to be feeble and
hyperpolarization of nuclear spins needs to be employed to enable competitive
sensitivity. We note that CASPEr-ZULF experiments take advantage of the
“intramolecular comagnetometry” to distinguish the sought-after effect from
systematics Ledbetter et al. (2012); Wu et al. (2018).

We propose to utilize $d$DNP techniques to polarize nuclear spins prior to the
acquisition, potentially improving the sensitivity by five orders of magnitude
compared to the experiments proposed in Refs. Wu et al. (2019); Garcon et al.
(2019), thus, enhancing the dark matter detection potential. Detection of dark
matter via a non-gravitational interaction would resolve one of the biggest
mysteries of modern physics by uncovering the nature this phenomenon.

Hyperpolarization is necessary to perform dark-matter NMR searches, as the
signals we aim to observe are extremely weak. $d$DNP is currently the most
general method, enabling hyperpolarization on the widest range of spin
targets. ZULF NMR atomic magnetometers are among the most sensitive sensors
for signals in the 0-500 Hz frequency range. This places ZULF NMR as promising
method to search for ALPs and DPs within this range for which only a few
experiments exists even though the existence of ALPs and DPs in this range is
well motivated (see, for example, Wei et al. (2023) and references therein).

Another important fundamental-physics application of ZULF NMR with
hyperpolarized samples is the search for a possible coupling of nuclear spins
to gravity (the Hamiltonian term proportional to $\vec{S}\cdot\vec{g}$ with
$\vec{S}$ being the spin and $\vec{g}$–the local acceleration due to gravity)
Ledbetter et al. (2012); Jackson Kimball et al. (2017); Wu et al. (2018). Such
an interaction would violate several fundamental symmetries; however, it is
hypothesized in certain theories of gravity and represents an important probe
into the connection between gravity and quantum mechanics Jackson Kimball et
al. (2023); Zhang et al. (2023).

Consideration for practical realization of $d$DNP-ZULF-NMR fundamental physics
experiments include ensuring repeatable and stable supply of hyperpolarized
material with continuous (automated) data acquisition to enable multi-shot
averaging, calibration, and auxiliary experiments to identify and control for
systematic errors.

##  3 Conclusions and outlook

The a-priori non-obvious combination of $d$DNP hyperpolarization with ZULF NMR
can, indeed, be advantageous in a broad range of practical applications
including but certainly not limited to the ones discussed above. The
particularly powerful aspects of this combination include the ability to
hyperpolarize a broad range of samples, insensitivity to sample
inhomogeneities, and the ability to conduct spectroscopic measurements and
imaging within conducting (e.g., metal) containers. In the medical context,
one can benefit from the availability of $d$DNP infrastructure at hospitals
Ardenkjaer-Larsen (2016), the relative simplicity, compactness and portability
of ZULF-NMR devices Blanchard et al. (2020a); Put et al. (2021). These
features of ZULF NMR are likely to be augmented in the near future when more
compact magnetometers based on color centers in diamond Zheng et al. (2019)
come into use. It is our hope that this overview will serve as a “roadmap” to
stimulate developments in this area.

##  4 Acknowledgements

We thank Prof. Blümich for his interest in our work and helpful advice he has
given us over the years. ZULF-NMR imaging was extensively discussed with Dr.
Nataniel Figueroa Leigh.

##  5 Declarations

###  5.1 Ethical Approval

Not applicable.

###  5.2 Competing interests

The authors declare that they have no conflict of interest.

###  5.3 Authors’ contributions

All authors contributed ideas. DAB and DB wrote the final text. All authors
reviewed the manuscript.

###  5.4 Funding

This work was supported in part by the DFG/ANR grant BU 3035/24-1; DAB
acknowledges financial support from the Alexander von Humboldt Foundation in
the framework of Sofja Kovalevskaja Award; QS, SJE, and SJ thank the ENS-Lyon,
the French CNRS, Lyon 1 University, the European Research Council under the
European Union’s Horizon 2020 research and innovation program (ERC Grant
Agreements No. 714519/HP4all and Marie Skłodowska-Curie Grant Agreement No.
766402/ZULF), and Bruker Biospin; IVK thanks the Russian Science Foundation
(grant #22-43-04426).

###  5.5 Availability of data and materials

This manuscript is a roadmap paper as such it reviews the current status of
the work in this area and proposes future directions.

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