Hierarchical maximum likelihood estimation for time-resolved NMR data

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.