14 Apr 2023
 | 14 Apr 2023
Status: a revised version of this preprint is currently under review for the journal MR.

Modelling and correcting the impact of RF pulses for continuous monitoring of hyperpolarized NMR

Gevin von Witte, Matthias Ernst, and 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.

Gevin von Witte et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Comment on mr-2023-5', Norbert Mueller, 27 Apr 2023
    • AC1: 'Reply on CC1', Gevin von Witte, 02 May 2023
  • RC1: 'Comment on mr-2023-5', Anonymous Referee #1, 02 May 2023
  • RC2: 'Comment on mr-2023-5', Anonymous Referee #2, 07 May 2023

Gevin von Witte et al.

Model code and software

Model code for the experimental RF correction Gevin von Witte

Gevin von Witte et al.


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Short summary
Hyperpolarization methods offer the possibility to overcome the inherent sensitivity limits of nuclear magnetic resonance (NMR) given by the thermal Boltzmann spin distribution. The radio-frequency (RF) pulses to monitor the hyperpolarization process alter it by depleting the created magnetization. Possible corrections are simulated with a rate-equation model containing a single source and relaxation rate. The accuracy is demonstrated experimentally, enabling the use of larger flip angles.