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Hierarchical maximum likelihood estimation for time-resolved NMR data.

Lennart H Bosch1, Pernille R Jensen2, Nico Striegler3

  • 1Institute of Theoretical Physics, Ulm University, 89081 Ulm, Germany.

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|March 4, 2026
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Summary
This summary is machine-generated.

This study introduces a novel Bayesian hierarchical model for metabolic monitoring and reaction rate estimation using hyperpolarized NMR technology. The new method enhances precision and minimizes uncertainty in quantitative analysis, outperforming existing techniques.

Keywords:
Hierarchical modelHyperpolarizationNitrogen-VacancyTime resolutionTime-domain analysis

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Metabolic Pathway Analysis
  • Quantitative Chemical Analysis

Background:

  • Accurate metabolic monitoring and reaction rate estimation are crucial for hyperpolarized NMR technology.
  • Current two-stage analysis methods suffer from uncertainty propagation errors.

Purpose of the Study:

  • To develop a novel Bayesian hierarchical model for enhanced quantitative analysis in hyperpolarized NMR.
  • To improve precision and minimize uncertainty in metabolic monitoring and reaction rate estimation.

Main Methods:

  • A Bayesian hierarchical model was developed, intrinsically propagating uncertainties.
  • The method was analytically reduced to a least-squares optimization problem, extending Variable Projection (VarPro).
  • The approach was validated using two experimental setups: conventional high-field NMR and a microscale NMR with Nitrogen-Vacancy centers.

Main Results:

  • The proposed Bayesian approach demonstrated improved estimation accuracy compared to traditional Fourier methods.
  • The method showed operational advantages over two-stage VarPro procedures.
  • Enhanced precision and minimal uncertainty were achieved by operating on the full dataset.

Conclusions:

  • The novel Bayesian hierarchical model offers a superior approach for quantitative analysis in hyperpolarized NMR.
  • This method effectively addresses limitations of current two-stage procedures, improving accuracy and uncertainty management.
  • The approach is broadly applicable to other estimation scenarios with similar data structures, such as time-resolved photospectroscopy.