Hyperpolarization

 

Introduction

 

The alignment or spins or the polarization of spins at a given magnetic field and temperature is described by the Boltzmann distribution under the thermal equilibrium. It is noted that equilibrium nuclear spin polarization is only 10-6 (1 in the million) to 10-5 at conditions of human body temperature and Bo of several Tesla. This means that only 1 in the million of 100.000 spins is aligned with the magnetic field. A state of increased alignment or polarization of spins far beyond thermal equilibrium conditions is termed hyperpolarization.

 

There are different techniques that can mediate hyperpolarization which include transfer of polarization between nuclear spins and from electron spins to nuclear spins (ref.: https://en.wikipedia.org/wiki/Hyperpolarization_(physics)

 

If we wish to induce polarization transfer from electron spins to nuclei spins when the electron spin system is in thermal equilibrium, we need to excite electron spins to resonance by irradiation at a frequency close to the corresponding electron paramagnetic resonance (EPR) frequency, which is in the microwave range. Techniques that mediate hyperpolarization include (ref.): Dynamic nuclear polarization, Spin exchange optical pumping and Parahydrogen induced polarization.

 

 

 

Dynamic nuclear polarization

 

Dynamic Nuclear Polarization consists of different mechanisms, among which prominent is the Overhauser effect (OE) (or nuclear Overhauser effect). The Overhauser effect was demonstrated in 1953, when Albert Overhauser showed that nuclei of metals would be polarized, if the system was irradiated with conditions mediating electron spin resonance of the conducting electrons (Overhauser 1953). It is necessary to have saturating ERP conditions i.e. an almost equal population in each of the two spin states, for example ms = ± ½. The phenomenon is due to electron-nucleus cross-relaxation based on their hyperfine coupling. 

 

Relevant passages can be found at the thesis by Jan G. Krummenacker, section 2.3 “Dynamic Nuclear Polarization” e-page 8 and e-page 25.

 

A video on Dynamic Nuclear Polarization from the AMES National Lab (affiliated with the U.S. Dept. of Energy) at the link https://youtu.be/s4pXADCtXxY mentions: "Instead of irradiating the nuclei we use microwaves to excite the electron, which means we can take spectra about ten thousand times faster. Not only that, but we can now study materials which will previously completely out of the reach of NMR."

 

 

Figure 1: Video on Dynamic Nuclear Polarization from the AMES National Lab (affiliated with the U.S. Dept. of Energy) (https://youtu.be/s4pXADCtXxY)

 

 

The scientific literature refers to the Overhauser-Pound family of Double Resonances. One of the most important developments following magnetic resonance was the double resonance, which consists of exciting one resonant transition of the system while observing another. The first double resonance experiment performed was by Pound R. on the Na23 resonance of NaNO3. He found that by saturating one transition, he was increasing the intensity of the others. The experiment by Overhauser A. that led to the discovery of the Overhauser effect contributed in the rapid development of the field. 

 

An important relevant historical experiment was performed by G. Feher who named it “Electron-Nuclear Double Resonance Spectroscopy” (ENDOR). ENDOR is considered to represent a pulsed ERP technique. A similar technique is “Electron Electron Double Resonance” (ELDOR). The following text presents a theoretical section from patent US4719425 which analyses double resonance effects ENDOR and ELDOR in the frame of a setting that is relevant to the detection of neural activity. 



 

[Note] A note on double resonance effects ENDOR and ELDOR 

 

A theoretical section is copied below from patent US4719425 (with minor modifications).

 

"Nuclei with a total magnetic moment μ placed in a magnetic field H(m) have an interaction energy described by the Hamiltonian:

Ĥ = μ * H(m)

 

Assuming the field to be in the z-direction, the eigenvalues of energy are

E = γ(p) * ħ * H(z) * m      with m = I, I-1 ,..., -I

 

where γ(p)=gyromagnetic ratio, ħ=Planck's constant and m=angular momentum

 

For hydrogen which has I=1/2 and m =1/2 , a -1/2 transition between these two states has an energy of

ΔE= γ(p)* ħ * H(z)

 

or frequency associated with transition

ω = 2πf = γ(p) * H(z)

 

The factor γ(p) (note: gyromagnetic ratio) for hydrogen nucleus (proton) is equal to 2.6753 * 108 radian sec-1 Tesla-1. For a single electron in external magnetic field (spin S=1/2) the same formalism holds, but the gyromagnetic factor γ(e) is equal to 1.7576 * 10-8 radian sec-1 Tesla-1 or 657 times higher, owing to the much lesser mass of the electron. 

 

In a hydrogen atom we have a nucleus with spin I=1/2 coupled to an electron with a spin of S=1/2. The Hamiltonian for such a system is

 

H= γ(e)* ħ * H(z) * S(z) + AI.S - γ(n)* ħ * H(z) * I(z)

 

where A is a measure of coupling between the two spins. The expression is valid for the electron in the ground i.e. non-excited state.

 

In so called strong field approximation i.e. when  * S(z) + AI.S - γ(n)* ħ * H(z) * I(z) the Hamiltonian becomes 

H= γ(e)* ħ * H(z) * S(z) + AI.S - γ(n)* ħ * H(z) * I(z)(6) 

and the energy eigenvalues are then 

E=γ* ħ * H(z) * M  + A m(I) m (S) - γ(n)* ħ * H(z) m(I) m (S)= ±1/2 m(I) = ±½

 

There are four possible transitions in such a system, which are shown in FIG. 2. Symbol ± means ms =+1/2, mτ =-1/2 etc.

 

FIG. 2 is an energy level diagram showing the allowed transitions for a hydrogen atom in an external magnetic field H(z). 

 

The resonant frequencies for electronic and nuclear transitions are correspondingly:

We = γ(e)Hz + A/h MI

Wn = γ(n)Hz + A/h MS

 

There exists an Overhauser-Pound Family of Double Resonances (as described by Slichter in Principles of Magnetic Resonance, 2nd ed. Springer Velas, Berlin, 1978). In the nuclear Overhauser effect, one observes the change in the integrated intensity of the NMR absorption of a nuclear spin as a result of the concurrent saturation of another NMR resonance.

 

FIG. 2 shows an energy level diagram for S=1/2 and I=1/2 showing the transitions being `pumped` or excited and observed transitions. We and Wn are nuclear and electronic relaxations. 

 

In Electron Nuclear Double Resonance (ENDOR) transitions 1-2 or 4-3 are pumped. In Electron Electron Double Resonance (ELDOR) transition 2-3 is pumped. The observed transition is 4-1. In the simple NMR the same transition is excited and its relaxation observed (4-3) or (1-2). If in addition another transition (e.g. 2-3 or 1-4) is excited, than the intensity of levels will be changed and change in intensity and apparent change in the relaxation rate will manifest itself in the monitored NMR transition, so if the ESR `pumping` generator is amplitude modulated including pulsing on and off, this modulation will be transferred to the NMR signal. The limiting case of amplitude modulation is on-off pulsing. It may be expected that if the ESR pumping generator is frequency modulated instead of amplitude modulated, and if the frequency deviation is sufficiently high, it will have the same effect on the NMR signal."

 

 

 

 

Figure 2: Figures from patent US4719425


 

Spin exchange optical pumping

 

3He and 129Xe are hyperpolarized using a technique termed spin-exchange optical pumping (SEOP). An alkali metal such as caesium or rubidium is irradiated with circular polarized light to excite its electrons. The term optical pumping is linked to the use of optical radiation for increase of energy levels. Via collisions, angular momentum is transferred from the alkali metal electrons to the noble gas nuclei. 129Xe is used in human clinical applications.


 

Parahydrogen induced polarization 

 

National MagLab researchers (ref.) have shown that nanoparticles can be used to catalyse polarization from parahydrogen to hydrogen in water. This important discovery can be used for contrast agents.


 

 

 

2D-NMR - Magnetization Transfer - Homonuclear and Heteronuclear Techniques - "Inverse" NMR

 

The Overhauser effect mentioned previously, constitutes a case of magnetization transfer through space due to the physical proximity of nuclei. It represents a through-space correlation technique used in two dimensional NMR (2D-NMR) spectroscopy, termed NOESY for “Nuclear Overhauser effect spectroscopy”. In 1D-NMR we provide a pulse (sequence) and then we acquire a spectrum. In 2D-NMR we provide a pulse (sequence), we wait for time t, we acquire a spectrum and then we repeat (pulse/acquisition) by incrementing time t. The obtained data are analyzed with a 2D Fourier transform (ref.). 

 

There exist NMR spectroscopy techniques which measure magnetization transfer through bonds. Firstly, we distinguish homonuclear through-bond correlation methods, where magnetization transfer occurs between nuclei of the same type through J-coupling of nuclei connected by up to a few bonds. By J-coupling we refer to influences between spins (FB). Example methods are COSY, TOCSY and INADEQUATE.

 

Secondly, we distinguish heteronuclear through-bond correlation methods, where magnetization transfer occurs between nuclei of the different. Examples are HETCOR, HSQC and HMBC. 

 

Heteronuclear techniques may study magnetization transfer between the hydrogen nucleus (proton) and another nucleus termed "heteronucleus" (for "another nucleus"). The HETCOR technique records the heteronucleus spectrum. For historical reasons, the techniques that record the proton spectrum instead of the heteronucleus spectrum are termed "inverse" NMR spectroscopic techniques.

 

Inverse spectroscopy was developed to study insensitive nuclei (such as 13C or 15N) using a high-sensitivity nucleus typically 1H, which is usually detected with high sensitivity.