Parameter Estimation for Quantitative EPR Spectroscopy

Electron paramagnetic resonance (EPR) is a spectroscopy and imaging method based on detecting the spin resonance of electrons. EPR is particularly suited for detecting and quantifying free radicals and biological markers of oxidative stress, for which it is the only quantitative imaging method at the moment. Its application in clinical contexts is a major challenge because of the lack of standardized procedures for estimating the measurement quality. Previous work analyzed the Lorentzian model of single-line EPR spectra in the derivative limit. For the general case, a modified acquisition procedure called overmodulation improves the signal-to-noise ratio (SNR). This article studies single-line EPR spectra with Lorentzian line shape under overmodulation and proposes maximum likelihood estimates (MLEs) as well as formulas for the expected relative error. The results are validated with simulated spectra and in vitro experimental results. The computed relative error is shown to be a good estimate of the observed instrumental variation.