Version 1
: Received: 16 April 2024 / Approved: 16 April 2024 / Online: 16 April 2024 (15:52:25 CEST)
How to cite:
Bortolotti, V.; Conte, P.; Landi, G.; Lo Meo, P.G.M.; Nagmutdinova, A.; Spinelli, G.V.; Zama, F. Robust Algorithms for the Analysis of Fast Field Cycling Nuclear Magnetic Resonance Dispersion Curves. Preprints2024, 2024041055. https://doi.org/10.20944/preprints202404.1055.v1
Bortolotti, V.; Conte, P.; Landi, G.; Lo Meo, P.G.M.; Nagmutdinova, A.; Spinelli, G.V.; Zama, F. Robust Algorithms for the Analysis of Fast Field Cycling Nuclear Magnetic Resonance Dispersion Curves. Preprints 2024, 2024041055. https://doi.org/10.20944/preprints202404.1055.v1
Bortolotti, V.; Conte, P.; Landi, G.; Lo Meo, P.G.M.; Nagmutdinova, A.; Spinelli, G.V.; Zama, F. Robust Algorithms for the Analysis of Fast Field Cycling Nuclear Magnetic Resonance Dispersion Curves. Preprints2024, 2024041055. https://doi.org/10.20944/preprints202404.1055.v1
APA Style
Bortolotti, V., Conte, P., Landi, G., Lo Meo, P.G.M., Nagmutdinova, A., Spinelli, G.V., & Zama, F. (2024). Robust Algorithms for the Analysis of Fast Field Cycling Nuclear Magnetic Resonance Dispersion Curves. Preprints. https://doi.org/10.20944/preprints202404.1055.v1
Chicago/Turabian Style
Bortolotti, V., Giovanni Vito Spinelli and Fabiana Zama. 2024 "Robust Algorithms for the Analysis of Fast Field Cycling Nuclear Magnetic Resonance Dispersion Curves" Preprints. https://doi.org/10.20944/preprints202404.1055.v1
Abstract
Fast Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment.
This study focuses on a \textit{model-free} approach, representing the NMRD profile $R_1$ as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework.
Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analysing NMRD profiles.
These include: (1) \nameUpe, utilizing locally adapted $L_2$ regularization; (2) \nameL, based on $L_1$ penalties; and (3) a hybrid approach combining locally adapted $L_2$ and global $L_1$ penalties. Each method's regularization parameters are determined automatically, according to the Balancing and Uniform Penalty principles.
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Our contributions include the implementation and experimental validation of the \nameUpe{} and \nameUp{} algorithms, and the development of a "dispersion analysis" technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios.
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Keywords
Fast Field-Cycling (FFC) NMR relaxometry; Model-free approach to NMR Dispersion profiles; MuPen and L1 regularization algorithms.
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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