the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Modelling and correcting the impact of RF pulses for continuous monitoring of hyperpolarized NMR
Gevin von Witte
Matthias Ernst
Sebastian Kozerke
Abstract. Monitoring the build-up or decay of hyperpolarization in nuclear magnetic resonance requires radio-frequency (RF) pulses to generate observable nuclear magnetization. However, the pulses also lead to a depletion of the polarization and, thus, alter the spin dynamics. To simulate the effects of RF pulses on the polarization build-up and decay, we propose a first-order rate-equation model describing the dynamics of the hyperpolarization process through a single source and a relaxation term. The model offers a direct interpretation of the measured steady-state polarization and build-up time constant. Furthermore, the rate-equation model is used to study three different methods to correct for the errors introduced by RF pulses: (i) a 1/ cosn θ correction, which is only applicable to decays, (ii) an analytic formula to correct for the build-up and decay times and (iii) a newly proposed iterative, self-consistent correction. The corrections are first tested in low signal-to-noise ratio (SNR) simulations (SNR around 40 for 2.5° pulses), predicting accurate results (±10 % error) up to 25° pulses. The correction methods are then tested on experimental data obtained with dynamic nuclear polarization (DNP) using 4-oxo-TEMPO in 1H glassy matrices, resulting in high SNR acquisitions (around 1000 for 2.4° pulses). It is experimentally demonstrated that the rate-equation model allows to obtain build-up times and steady-state polarization (enhancement) even for large RF flip angles (25°) during build-up yielding results within ±10 % error when compared to data acquired with small RF flip angles (< 3°). For decay experiments, corrections are shown to be accurate for up to 12° RF flip angles with discrepancies to the simulations attributed to the low experimental acquisition SNR. In conclusion, corrections based on a rate-equation description offer fast and accurate estimations of achievable polarization levels and build-up time constants in hyperpolarization experiments for a wide range of samples.
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Gevin von Witte et al.
Status: final response (author comments only)
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CC1: 'Comment on mr-2023-5', Norbert Mueller, 27 Apr 2023
Comment on the preprint (https://doi.org/10.5194/mr-2023-5) of
„Modelling and correcting the impact of RF pulses for continuous monitoring of hyperpolarized NMR“
by Gevin von Witte, Matthias Ernst, and Sebastian Kozerke
I just want to add a comment relating to the experimental approaches for monitoring hyperpolarization in NMR. Some time ago in collaboration with other labs my research group investigated the potential of spin noise detection for monitoring buildup of hyperpolarization (see references at the end of this text). Given that the buildup of hyperpolarization is a slow process, in many cases, spin noise measurements should be possible concurrently to the buildup. While being much less sensitive than pulsed excitation based approaches (but sensitivity should not be an issue here) spin noise measurements appear to be virtually non-invasive and will also work for negative polarization, where a pulse might trigger coherent emission (M/RASER). At high polarization levels both pulse and noise based approaches are of course subject to feedback effects involving the rf-receiver circuit, i.e. radiation damping. So the circuit’s quality factor may have an impact on the build-up rates determined by either method. This may be of relevance in the context of this preprint and thus might be considered by the autors.
I apologize if this comment contains too much self-promotion.
Pöschko MT, Peat D, Owers-Bradley J, and Müller N. (2016) Use of Nuclear Spin Noise Spectroscopy to Monitor Slow Magnetization Buildup at Millikelvin Temperatures, ChemPhysChem 17, 3035-3039. https://doi.org/10.1002/cphc.201600323
Pöschko MT, Vuichoud B, Milani J, Bornet A, Bechmann M, Bodenhausen G, Jannin S, and Müller N. (2015) Spin Noise Detection of Nuclear Hyperpolarization at 1.2K, ChemPhysChem 16, 3859-3864. https://doi.org/10.1002/cphc.201500805
Citation: https://doi.org/10.5194/mr-2023-5-CC1 -
AC1: 'Reply on CC1', Gevin von Witte, 02 May 2023
Dear Mr. Müller,
Thank you for you comment. We did not think of the idea for spin noise measurements during the course of the project and specifically were unaware of its performance under dDNP conditions (as the measurements presented in the manuscript). We will update the discussion of the manuscript under consideration to include spin noise measurements as a non-invasive approach to measure the hyperpolarization build-up and decay, contrasting the approach we presented consisting of RF pulses with a subsequent correction.Citation: https://doi.org/10.5194/mr-2023-5-AC1
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AC1: 'Reply on CC1', Gevin von Witte, 02 May 2023
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RC1: 'Comment on mr-2023-5', Anonymous Referee #1, 02 May 2023
The authors discuss corrections for errors introduced by the rf pulses during polarization build-up monitoring of experiments typically encountered in dissolution DNP. Depending on the flip angle of the readout pulses, a certain amount of polarization is lost which not only reduces the steady-state polarization to be reached, but also affects the apparent build-up or decay rates.
In the introduction, a clear and easily comprehendible recap of the rate equations for the build-up dynamics is presented, and the basis for the iterative rf pulse correction algorithm is derived. In the beginning of the methods section the other pulse correction methods are presented (from my perspective these could have been already introduced in the preceding section), and the experimental procedure is explained in sufficient detail. The weakest point of the paper, however, is the presentation of the actual results. Particularly the experimental results (but to some degree also the simulation results) are only referred to as presented in the respective figures and tables, but no practically no explanation of the results is given. Here, I would have expected a more extensive presentation in the text, where the reader is guided through the rather large set of data in figs. and tables 2 and 3. From my perspective, a figure should support the presentation of the results in the text, and not be left alone to the reader to perform the interpretation on their own. In the discussion, the authors touch important points which could lead to the observed results or introduce errors, and in the conclusions a relatively short summary is given.
Besides the above general criticism I have another more detailed question about the validity of the rate equation approach. The independence of buildup and decay rates which form the basis of Eq. (1) have been derived for solid effect DNP, where an additional polarization injection pathway is driven by microwave irradiation. Turning off the microwaves would then effectively set k_W to 0, leaving us only relaxation with k_R back to thermal equilibrium. Besides others, Shimon et al. (Phys. Chem. Chem. Phys., 2012, 14, 5729) have shown that under similar conditions, cross effect or thermal mixing may also be active. For these DNP mechanisms, polarization injection and relaxation cannot be separated as the nuclear polarization is always coupled to an electron polarization difference (or spectral gradient). Thus, the relaxation term should be small compared to k_W and turning off microwave irradiation would only modulate A to a value near thermal equilibrium, while k_W is unaffected. How would this affect the herein presented method? Can you make an estimate which DNP mechanism is dominant? From the observed difference in tau_bup and tau_rec, the assumption of having more or less independent injection and relaxation pathways seems obvious, but I am still wondering what cause some admixture of the other DNP mechanism (CE/TM) would have in the analysis.
In conclusion, the manuscript should be of high interest for the magnetic resonance community. It is These points should be addressed before publication. Besides the above-mentioned shortcomings, it is of high scientific value and quality, and should be publishable in MR after minor revision.
Minor remarks: the use of the multiplication sign is inconsistent, and oftentimes spaces after the degree symbol are either missing or repeated.
Citation: https://doi.org/10.5194/mr-2023-5-RC1 -
RC2: 'Comment on mr-2023-5', Anonymous Referee #2, 07 May 2023
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2023-5/mr-2023-5-RC2-supplement.pdf
Gevin von Witte et al.
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Model code and software
Model code for the experimental RF correction Gevin von Witte https://gitlab.ethz.ch/gvwitte/rfcorrection
Gevin von Witte et al.
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