Magnetic resonance without magnets: explained

Have you ever done MRI? If yes, you probably remember, it is not the most pleasant experience. MRI is claustrophobic, loud, and takes a long time. The main reason for these problems — high magnetic fields. Would it be cool to avoid them? Why can’t we simply do MRI without magnetic fields?

It turns out, we can do it though it is not that simple…

To understand why high magnetic fields are needed to obtain magnetic resonance images, we need to understand the principles of signal detection and the concept of polarization.

Some atomic nuclei possess a property called spin and, therefore, produce magnetic fields. These nuclei can simply be visualized as tiny magnets (magnetic dipoles) swirling in space as their hosts — molecules — move, rotate or vibrate depending on the physical state of the chemical system they comprise (solid, liquid or gas).

In the absence of external fields, nuclear spin orientations are random:

By placing the spins in high magnetic fields, one can align them in the same direction, creating “polarization”:

The level to which spins are polarized in the picture above is extremely exaggerated. In reality, even in the very high magnetic fields of modern magnetic resonance spectrometers and imaging scanners (thousands of times higher than the Earth’s magnetic field), nuclear spin polarization is only a fraction of percent. Complete (100%) polarization is also possible. However, instead of placing spins in high fields, it is practically more feasible to use a different approach. Physicists and chemists came up with several creative techniques to create extremely high polarization or hyperpolarization. Techniques based on chemical reactions (such as parahydrogen-induced polarization) are my favorite ones since they don’t require magnetic fields at all (in reality, polarization in such techniques can still be magnetic-field-dependent but the requirements are very modest).

Now about detection. Nuclear magnetism can be detected in several ways. I will talk about two ways and both of them are named after a brilliant physicist Michael Faraday.

The first detection technique is the so-called inductive detection. If spins are polarized and brought to the magnetic field perpendicular to the polarization axis, collective nuclear magnetization will start oscillating about the field axis. This phenomenon is called Larmor precession and it is a general result of classical physics (no quantum mechanics is necessary to explain it but quantum mechanics brings more fun). Oscillating magnetization can be picked up by a coil (solenoid) and a voltage across the coil terminals (electromotive force) will be generated according to Faraday’s law of induction:

Collective nuclear spin magnetization (M) is rotating about the magnetic field (B0). When a pre-polarized (or, simply speaking, pre-magnetized) sample is placed in such a field, M starts oscillating and its z-component generates an oscillating voltage across the coil’s terminals according to the Faraday’s law.

The problem is that it is really hard to construct magnets that produce high magnetic fields. Moreover, these fields need to be very uniform to be suitable for magnetic resonance purposes. This is why bores of MRI scanners are usually small – this way engineers achieve higher magnetic field homogeneity over the active volume.

The conventional logic of MRI engineers is straightforward: by using higher magnetic fields (1) we achieve higher nuclear spin polarization (indeed, polarization scales linearly with the applied field B0) and (2) we increase sensitivity of the detection (the voltage generated in the coil by Faraday’s law is linearly proportional to the oscillation frequency which, in turn, proportional to B0). Therefore, conventional MRI signal scales as a square of the magnetic field. Higher the field is — bigger the magnet should be, and we already reached the limits of our engineering capabilities to make the highest magnetic fields that are stable and uniform.

Now imagine that we already have high polarization produced without magnetic fields, for example, via chemical reactions mentioned above. Therefore, the signal is only linearly proportional to the magnetic field strength and even low magnetic fields can be used to produce high-quality images.

Recently my students and I played with MRI at the Earth’s magnetic field (compare 50 micro-Tesla vs. several Tesla of conventional MRI scanners). In our experiments, we simply bubbled a gas through a solution containing the required ingredients and picked up the signal by a coil:

Bubbling para-H2 gas through a solution containing a “polarizable” substrate and a SABRE catalyst.

The gas that we used is parahydrogen (para-H2) and the enhanced nuclear polarization in solution is the result of Signal Amplification By Reversible Exchange (SABRE) effect. This effect is a remarkable consequence of the interplay between chemical kinetics and nuclear spin dynamics. Unfortunately, explaining it here, in this post, would require many more words and even some math 🙂 But the main point is simple: bubbling the gas through the solution results in high nuclear polarization and, therefore, high MRI contrast. Without bubbling the gas, magnetic nuclei are oriented randomly and the signal is too low to be detected.

MRI of a SABRE solution at the Earth’s magnetic field (left) when para-H2 gas is bubbled and (middle) when the gas supply is ceased. (Right) Proton Nuclear Magnetic Resonance (NMR) spectrum of the solution at the Earth’s magnetic field.

This idea of avoiding magnetic fields can be extended even further. Indeed, if we don’t need a magnetic field to generate polarization, can we detect nuclear spin signals completely without magnets? This somewhat weird idea (magnetic resonance without magnets) is, in fact, one of the most outstanding achievements in magnetic resonance of the last decade. It was pioneered by chemists and physicists from UC Berkeley (laboratories of Alex Pines and Dmitry Budker).

It turns out that very weak magnetic signals can be detected by atomic magnetometers. These magnetometers use vapor cells, glass containers filled with the vapor of alkali metal. Atoms of alkali metals have unpaired valence electrons. Since electrons are tiny magnets in the same way as their nuclear brothers, they can also be polarized, this time by lasers. Properties of a laser beam passing through such polarized “electronic gas” can be modulated if electrons are subjected to additional magnetic fields. This is called the Faraday effect and it is a second way of detecting magnetic resonance signals. In a nutshell, electrons “feel” the magnetic fields around them in a very sensitive way, even if these fields are generated by nuclear spins from a sample placed on top of a vapor cell:

Magnetization (M) generated in a sample can be detected by atomic magnetometers. The most sensitive magnetometers operate at a near-zero magnetic field. Signal can be detected by lasers due to the Faraday effect using a variety of polarimetry schemes.

The end result of this signal detection scheme is the same as before – the voltage is generated and picked up, this time by a photodetector. If magnetic fields coming from the sample are time-dependent, the voltage is time-dependent as well and it can be converted into a spectrum containing useful chemical information about the sample.

You might wonder where this all can be applied? Well, it is worth mentioning Faraday here again:

I personally feel that MRI without magnets is not only possible but necessary. However, it will obviously not replace the conventional approach but will rather complement it. One may imagine sensitive magnetometers and Earth’s-field MRI applied to study chemicals at a large scale, to investigate processes taking place inside big industrial chemical reactors. Indeed, the Earth is the best magnet for these purposes – it is extremely homogeneous on the scale that we need. Nullifying magnetic fields (to produce zero field) is another option – remarkably, the sensitivity of atomic magnetometers is maximized at the near-zero-field conditions. It is hard to predict the direction that future will take but one thing is clear – magnetic resonance is entering a new era. So you better stay tuned! 😉

Further reading

https://chemrxiv.org/articles/Zero-Field_Nuclear_Magnetic_Resonance_of_Chemically_Exchanging_Systems/7658372

https://aip.scitation.org/doi/abs/10.1063/1.5003347

https://www.nature.com/articles/nphys1986

https://onlinelibrary.wiley.com/doi/abs/10.1002/cphc.201402607

https://pubs.acs.org/doi/abs/10.1021/ac501638p

https://www.sciencedirect.com/science/article/abs/pii/S1090780717301659

Monday Morning Effect

Friday evening. While his friends had already met in the Pub on Shattuck Avenue to celebrate a happy hour, UC Berkeley’s Ph.D. student Henry Bryndza was still in the Lab. He wanted to finish preparation of his samples so that he could come over on Monday morning to focus on the NMR measurements, not worrying about sample preparations. In order to suppress chemical reactions which could have started in his samples over the weekend, Henry put them in the liquid nitrogen dewar (T=-196oC).

Henry was working in the Laboratory of Robert Bergman, a renowned UC Berkeley professor who has made a significant contribution to the organic and metallorganic chemistry. Bergman and Bryndza were studying Fischer–Tropsch reactions using exemplary Cobalt and Iridium catalysts [1].

When he came back on Monday, Henry started to observe very interesting phenomena. 1H NMR spectra of the samples he took in the morning showed very weird “negative” NMR peaks (Figure 1). Moreover, the intensity of these peaks decreased day after day during the week when Henry tried to repeat the experiments and completely disappeared by the end of the week [2]. Henry was confused and decided to repeat his measurements. Surprisingly, this phenomenon was not observed every single time but was definitely the strongest on Mondays. Bergman and Bryndza decided to jestingly call this a “Monday phenomenon”; this was the beginning of what was known later as Parahydrogen-Induced Polarization (PHIP).

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Figure 1. “Pseudo-CIDNP” observed in 1H NMR spectra during hydrogenolysis reactions of Cobalt alkylidyne complexes. Adapted from [3].

Bryndza and Bergman asked for help from many NMR specialists, including NMR expert Professor Alex Pines from UC Berkeley and Professor Joachim Bargon from the University of Bonn [2]. The last one was known for the discovery of so-called chemically-induced dynamic nuclear polarization (CIDNP). The CIDNP effect is usually manifested as positive and negative NMR signals (very similar to those observed in Henry’s experiments) for the reactions taking place via radical intermediates. After contacting Bargon and other CIDNP specialists, weird results were interpreted as “pseudo-CIDNP” in hydrogenation reactions [3]. However, it was clear that CIDNP-based explanation was at least not complete, first, because of the very unusual suggestion of radical pairs in the studied hydrogenation reactions and, second, because of the lack of convincing simulations supporting the observed phenomena. Moreover, it by no means explained why the effect was the strongest on Mondays and why it was only observed in the laboratory of Robert Bergman.

This “Monday morning” puzzle remained unresolved until the International Society of Magnetic Resonance meeting in Rio de Janeiro in June 1986. There, during an evening session, Professor Daniel Weitekamp from Caltech presented his “thought experiment” of using parahydrogen (para-H2) as a source of enhancing NMR signals. The concept and the expected results were immediately published in Physical Review Letters [4]. The experimental demonstration conducted by a Weitekamp’s Ph.D. student Russ Bowers followed in July, and brilliantly supported all theoretical predictions (Figure 2) [5].

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Figure 2. First experimental demonstration of a PASADENA experiment. The characteristic PHIP multiplets are seen on the right. Adapted from [5].
Bowers and Weitekamp called their experiment PASADENA (Parahydrogen And Synthesis Allow Dramatically Enhanced Nuclear Alignment) to glorify the location of their institute (Caltech is located in Pasadena, CA). After their publication, it immediately became obvious that PASADENA is, in fact, a correct explanation of “Monday phenomenon” of Bryndza and Bergman. Indeed, the low-temperature storage of NMR tubes over the weekend partially converted normal hydrogen into para-H2. The conversion was not complete, but it was enough to observe antiphase lines in 1H NMR spectra (Figure 1). The PASADENA effect and discovered later effect ALTADENA (Adiabatic Longitudinal Transport After Dissociation Engenders Net Alignment) were collectively given the name PHIP (Parahydrogen-Induced Polarization) [6].

Now let’s talk about physical principles of this effect. As we discussed before, due to the absence of a net nuclear magnetic moment, para-H2 itself does not produce an NMR signal. However, this single nuclear spin state implies that, in a sense, it is cold. Indeed, a comparable degree of spin ordering is obtainable at equilibrium only at temperatures of a few mK and magnetic fields of several Tesla [7]. The brilliance of Wetekamp’s idea was to introduce magnetic inequivalence to release this potential signal by connecting the singlet to the triplet states. This would require chemistry, but simple bond cleavage would not suffice. A singlet state of two protons is a relationship of one spin relative to the other and this order would be dissipated if the pair were split and mixed with an ensemble of other such products. Rather, it is necessary that the pair have a special relationship even after being distinguished by magnetic inequivalence. This is called a “pairwise” hydrogen addition and can be realized in hydrogenation reactions in the presence of homogeneous catalysts. To see how it works, let’s take as an example the simplest situation and imagine that a chemical reaction leads to the association of para-H2 with a molecule not containing magnetic nuclei.

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Figure 3. Schematic diagram of the PASADENA experiment: parahydrogen (para-H2) reacts with an unsaturated molecule forming a reaction product where two nascent para-H2 atoms occupy chemically inequivalent positions. Energy level diagrams and corresponding 1H NMR spectra are shown in the bottom. Thick blue rectangles indicate overpopulated energy levels.

The two-spin system of the hydrogen molecule gives rise to four nuclear spin energy levels. As we described before, three of these energy levels correspond to orthohydrogen, the state with total nuclear spin 1 (triplet state), whereas the remaining fourth energy level corresponds to parahydrogen (singlet state), the state with zero total nuclear spin (Figure 3). Transitions between singlet and triplet spin states are forbidden by symmetry and the spin 0 parahydrogen is NMR-silent.

Now, the incorporation of para-H2 into an asymmetric molecule breaks the symmetry of the singlet spin state. For simplicity, I will consider only the PASADENA experiment, the case where hydrogenation reaction is performed at a high magnetic field (wherein the chemical shift difference between the two para-H2-nascent protons is much greater than the spin-spin coupling J between them). In this situation, the population of the singlet spin state αββα (numerical factor is omitted) of para-H2 is immediately transferred to the population of spin states αβ and βα of the formed spin system.

This can be understood as follows. Because of the chemical reaction, two H atoms from para-Hsuddenly end up in a different molecular environment. This leads to a collapse of the nuclear spin wavefunction αββα into one of the two states, αβ or βα, each with 50% probability. Next, it is easy to deduce from the energy level diagram that the NMR spectrum of the produced in such a manner molecule will contain four peaks grouped in two antiphase multiplets (Figure 3), exactly what was observed in the experiments of Bryndza (Figure 1) and Bowers (Figure 2). The key requirement is that both hydrogen protons from the para-H2 molecule are added together without significant competition from exchange reactions. This is a property of many, but not all, hydrogenations.

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Figure 4. Hydride region of PHIP-enhanced 1H NMR spectra showing
negative-positive multiplets for products formed when RhI(CO)(PMe3)2 reacts with para-H2 in the absence (a) and presence (b) of styrene [8].
The assignment of the peaks to particular transitions depends on the sign of the J-coupling between the para-H2-nascent hydrogens. When J-coupling is positive, PASADENA multiplets are positive-negative; if J-coupling is negative, the spectral appearance is opposite. This feature is very useful for studying hydrogenation reaction intermediates. Normally, organic molecules possess positive J-couplings between protons; and J-couplings between them are negative in case of metal hydrides. Therefore, in a complex reaction involving many intermediates, it becomes possible to distinguish low-concentration hydrides (possessing negative-positive multiplets) from organic reaction products (Figure 4).

It is also important to realize that PHIP can lead to 100% nuclear spin polarization of the reaction product. In the case of PASADENA experiment, 100% population of para-His split into just two energy levels, making transitions from these levels enhanced by orders of magnitude compared to the thermal case. Theoretically, if all para-Hmolecules are transferred to products in a pairwise manner and relaxation loses are minimized, the reaction product can acquire 100% spin polarization. This would, of course, require an additional step to transfer spin order from αβ and βα into the state αα but this can be readily realized using a simple RF pulse sequence.

Enormous NMR signal enhancements and unique spectroscopic signatures made PHIP a very useful tool in chemistry for more than 25 years to elucidate hydrogenation reaction mechanisms, study metalorganic hydride complexes, and catalysis [6]. However, PHIP can be also used in a very different context. Imagine a suitable molecular precursor which can become a naturally occurring metabolite after hydrogenation. This metabolite can be produced in seconds, with a very high level of nuclear polarization, injected into a living organism and a metabolism of that organism can be monitored by magnetic resonance spectroscopy (MRS) and magnetic resonance imaging (MRI). Today PHIP, and its sister technology SABRE (Signal Amplification By Reversible Exchange) allow to efficiently hyperpolarize dozens of biologically relevant molecules on nuclei such as 1H, 13C, 15N, 19F, 29Si, 31P, 119Sn etc. But this is a story for a separate blog post! 🙂

It is important to emphasize that only the connection between nuclear spin and rotational degrees of freedom allows this unique situation to take place. Indeed, the fact that the nuclear spin state can be overpopulated simply by cooling is a remarkable quality inherent only to the small hydrogen molecule. Indeed, even though other molecules can have the similar connection between rotational and nuclear spin states (N2, F2 etc.), larger moments of inertia will make overpopulating these states much more challenging task (because of the lower temperature requirements). Moreover, it is very challenging to keep these molecules in the gas state at low temperatures, and the simple rule of making a total wavefunction be a product of individual wavefunctions will no longer hold true. So, it is more likely that hydrogen molecule is the only example when the rules of spin statistics and Pauli’s principle can lead to the nuclear spin hyperpolarization.

What excites me about this story is how a purely thought experiment, on the one hand, and a weird experimental phenomenon, on the other hand, emerged into a new discipline and a remarkable tool to study chemical reactions. Moreover, more exciting applications of the para-H2-based hyperpolarization techniques are expected to emerge in biomedicine. I really wish there were more Monday morning effects in science! Who knows but maybe someone today has come to a lab to look at a weird result which will form a new field of study tomorrow.

 

References

[1] J. Bargon. Chance Discoveries of Hyperpolarization Phenomena. eMagRes, 2007.

[2] Private conversations with Robert Bergman and Alex Pines.

[3] P. F. Seidler, H. E. Bryndza, J. E. Frommer, L. S. Stuhi, R. G. Bergman. Synthesis of Trinuclear Alkylidyne Complexes from Dinuclear Alkyne Complexes and Metal Hydrides. CIDNP Evidence for Vinyl Radical Intermediates In the Hydrogenolysis of These Clusters. Organometallics, 1983, 2 (11), 1701-1705.

[4] C. R. Bowers, D. P. Weitekamp. Transformation of Symmetrization Order to Nuclear-Spin Magnetization by Chemical Reaction and Nuclear Magnetic Resonance. Phys. Rev. Lett., 1986, 57 (21), 2645-2648.

[5] C. R. Bowers, D. P. Weitekamp. Parahydrogen and Synthesis Allow Dramatically Enhanced Nuclear Alignment. J. Am. Chem. Soc., 1987, 109 (18), 5541-5542.

[6] J. Natterer, J. Bargon. Parahydrogen-Induced Polarization. Prog. Nucl. Magn. Reson. Spect. 1997, 31, 293-315.

[7] D. Weitekamp. Sensitivity Enhancement Through Spin Statistics. Encyclopedia of Magnetic Resonance, 2007.

[8] S. Colebrooke, S. Duckett, J. Lohman, R. Eisenberg. Hydrogenation studies involving halobis(phosphine)-rhodium(I) dimers: Use of parahydrogen-induced polarisation to detect species present at low concentration. Chem. Eur. J., 2004, 10, 2459–2474.