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.

[1]  Byong-kyu Shin.  A simple quasi-analytical method for the deconvolution of Voigtian profiles. , 2014, Journal of magnetic resonance.

[2]  L. Petrakis.  Spectral line shapes: Gaussian and Lorentzian functions in magnetic resonance , 1967 .

[3]  D Regulla,et al.  From dating to biophysics--20 years of progress in applied ESR spectroscopy. , 2000, Applied Radiation and Isotopes.

[4]  H. Swartz,et al.  Implantable resonators--a technique for repeated measurement of oxygen at multiple deep sites with in vivo EPR. , 2010, Advances in experimental medicine and biology.

[5]  Samuil I︠A︡kovlevich Pshezhet︠s︡kiĭ.  EPR of free radicals in radiation chemistry , 1974 .

[6]  R. J. Nicolalde,et al.  In Vivo EPR For Dosimetry. , 2007, Radiation measurements.

[7]  Benjamin B Williams,et al.  Clinical electron paramagnetic resonance (EPR) oximetry using India ink. , 2010, Advances in experimental medicine and biology.

[8]  Harold M. Swartz,et al.  Black Magic and EPR Oximetry , 2005 .

[9]  C. Rhodes,et al.  Radicals on surfaces , 1995 .

[10]  Colin Mailer,et al.  Spectral fitting: The extraction of crucial information from a spectrum and a spectral image , 2003, Magnetic resonance in medicine.

[11]  P. Atkins,et al.  The structure of inorganic radicals : an application of electron spin resonance to the study of molecular structure , 1967 .

[12]  Rizwan Ahmad,et al.  Application of magnetic field over-modulation for improved EPR linewidth measurements using probes with Lorentzian lineshape. , 2006, Journal of magnetic resonance.

[13]  N. Khan,et al.  Cerebral oxygenation of the cortex and striatum following normobaric hyperoxia and mild hypoxia in rats by EPR oximetry using multi-probe implantable resonators. , 2011, Advances in experimental medicine and biology.

[14]  W. Bernhard,et al.  Radiation Effects: ESR and ENDOR Analysis , 1977 .

[15]  Y. Frapart,et al.  EPR and electrochemical quantification of oxygen using newly synthesized para-silylated triarylmethyl radicals , 2015, Free radical research.

[16]  N. Khan,et al.  Repetitive tissue pO2 measurements by electron paramagnetic resonance oximetry: current status and future potential for experimental and clinical studies. , 2007, Antioxidants & redox signaling.

[17]  D. Collison,et al.  Electron paramagnetic resonance of d transition metal compounds , 1992 .

[18]  J. Buckey,et al.  EPR spectrometer for clinical applications , 2005, Magnetic resonance in medicine.

[19]  Steven G Swarts,et al.  Clinical EPR: unique opportunities and some challenges. , 2014, Academic radiology.

[20]  L. Berliner.  In vivo EPR (ESR) : theory and application , 2003 .

[21]  C. Poole,et al.  Electron spin resonance: A comprehensive treatise on experimental techniques , 1983 .

[22]  Galen Wood Ewing,et al.  Analytical instrumentation handbook , 1990 .

[23]  Sushil K. Misra,et al.  Multifrequency electron paramagnetic resonance : theory and applications , 2011 .

[24]  N. Yordanov.  Electron Magnetic Resonance of Disordered Systems (EMARDIS – 91): Proceedings of the International Workshop , 1991 .

[25]  J. Zweier,et al.  Large-scale synthesis of a persistent trityl radical for use in biomedical EPR applications and imaging. , 2007, Bioorganic & medicinal chemistry letters.

[26]  H. Halpern,et al.  Electron spin relaxation of triarylmethyl radicals in fluid solution. , 2001, Journal of magnetic resonance.

[27]  S. Eaton,et al.  Multifrequency EPR of four triarylmethyl radicals , 2005 .

[28]  B. Bales.  A simple, accurate method of correcting for unresolved hyperfine broadening in the EPR of nitroxide spin probes to determine the intrinsic linewidth and heisenberg spin exchange frequency , 1980 .

[29]  A. Smirnov,et al.  Rapid Quantitation from Inhomogeneously Broadened EPR Spectra by a Fast Convolution Algorithm , 1995 .

[30]  J. Hyde,et al.  Pseudo field modulation in EPR spectroscopy , 1990 .

[31]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[32]  B H Robinson,et al.  Linewidth analysis of spin labels in liquids. I. Theory and data analysis. , 1999, Journal of magnetic resonance.

[33]  Rizwan Ahmad,et al.  Theory, instrumentation, and applications of electron paramagnetic resonance oximetry. , 2010, Chemical reviews.

[34]  B. Armstrong.  Spectrum line profiles: The Voigt function , 1967 .

[35]  Byong-kyu Shin.  An Analytical Method for the Deconvolution of Voigtian Profiles , 2016 .

[36]  Nghia Tran Duc,et al.  Estimation of spectrum parameters for Quantitative EPR in the derivative limit , 2017, 2017 International Conference on Advanced Technologies for Communications (ATC).

[37]  Ann Barry Flood,et al.  Electron Paramagnetic Resonance Dosimetry for a Large-Scale Radiation Incident , 2012, Health physics.

[38]  S. Eaton,et al.  Relaxation Times of Organic Radicals and Transition Metal Ions , 2002 .

[39]  Arthur Schweiger,et al.  EasySpin, a comprehensive software package for spectral simulation and analysis in EPR. , 2006, Journal of magnetic resonance.

[40]  B. Bales.  Correction for inhomogeneous line broadening in spin labels, II , 1982 .

[41]  J. Zweier,et al.  Reaction of superoxide with trityl radical: implications for the determination of superoxide by spectrophotometry. , 2004, Archives of biochemistry and biophysics.

[42]  Hugo D. Wahlquist,et al.  Modulation Broadening of Unsaturated Lorentzian Lines , 1961 .

[43]  Jiancheng Fang,et al.  On-Site Synchronous Determination of Coil Constant and Nonorthogonal Angle Based on Electron Paramagnetic Resonance , 2020, IEEE Transactions on Instrumentation and Measurement.

[44]  S. Eaton.  Electron Paramagnetic Resonance: Elementary Theory and Practical Applications , 1995 .

[45]  B H Robinson,et al.  Linewidth analysis of spin labels in liquids. II. Experimental. , 1999, Journal of magnetic resonance.

[46]  C. Tsallis,et al.  Statistical-mechanical foundation of the ubiquity of Lévy distributions in Nature. , 1995, Physical review letters.

[47]  J. Buckey,et al.  Clinical applications of EPR: overview and perspectives , 2004, NMR in biomedicine.

[48]  L. Potter,et al.  Optimization of magnetic field sweep and field modulation amplitude for continuous-wave EPR oximetry. , 2011, Journal of magnetic resonance.