Estimation of pO₂ distribution in EPR oximetry

Electron paramagnetic resonance (EPR) oximetry, using oxygen-sensing implant such as OxyChip, is capable of measuring oxygen concentration in vivo - a critical tissue information required for successful medical treatment such as cancer, wound healing and diabetes. Typically, EPR oximetry produces one value of the oxygen concentration, expressed as pO₂ at the site of implant. However, it is well recognized that in vivo one deals with a distribution of oxygen concentration and therefore reporting just one number is not representative_a long-standing critique of EPR oximetry. Indeed, when it comes to the assessment of radiation efficacy one should be guided not by the mean or median but the proportion of oxygenated cancer cells which can be estimated only when the whole oxygen distribution in the tumor is known. Although there is a handful of papers attempting estimation of the oxygen distribution they suffer from the problem of negative frequencies and no theoretical justification and no biomedical interpretation. The goal of this work is to suggest a novel method using the empirical Bayesian approach realized via nonlinear mixed modeling with a priori distribution of oxygen following a two-parameter lognormal distribution with parameters estimated from the multi-implant single component EPR scan. Unlike previous work, the result of our estimation is the distribution with positive values for the frequency and the associated pO₂ value. Our algorithm based on nonlinear regression is illustrated with EPR measurements on OxyChips equilibrated with gas mixtures containing four values of pO₂ and computation of the proportion of volume with pO₂ greater than any given threshold. This approach may become crucial for application of the EPR oximetry in clinical setting when the sucsess of the treatment depends of the proportion of tissue oxygenated.