Parsimonious basis selection in exponential spectral analysis.

Area of Science:

• Pharmacokinetics and Systems Biology
• Mathematical Modeling
• Signal Processing

Background:

• Sums of decaying real exponentials (SDREs) model time-varying processes and mass transport in biological systems.
• Exponential Spectral Analysis (ESA) uses exponential basis functions (EBFs) to estimate SDRE parameters, but faces challenges in selecting EBFs and rate constants.
• Non-uniqueness in ESA parameters hinders statistically meaningful comparisons of time series data.

Purpose of the Study:

• To develop a method for selecting the optimal number and rate constants of EBFs in ESA.
• To address the inherent non-uniqueness problem in ESA parameter estimation.
• To enable statistically meaningful comparisons of time series data using physically relevant parameters.

Main Methods:

• Model selection criteria were used to determine basis dimension, considering approximation error and parameter redundancy.
• Parameter redundancy was estimated through simulations across multiple noise realizations.
• A constrained Cramér-Rao lower bound was derived for ESA parameters.
• The developed Parsimonious Exponential Spectral Analysis (PESA) algorithm was applied.

Main Results:

• PESA effectively ameliorates the non-uniqueness issue in ESA parameters.
• The algorithm enables statistically sound comparisons of time series data based on significant parameters.
• PESA was successfully applied to analyze radiotracer retention in a rabbit heart model.

Conclusions:

• PESA provides a robust approach for analyzing SDRE models and comparing time series data.
• The method enhances the interpretability and statistical validity of parameter estimation in pharmacokinetic and biological modeling.
• PESA facilitates more meaningful comparisons of physiological processes, such as radiotracer dynamics.