Variability issues in determining the concentration of isoprene in human breath by PTR-MS

This paper deals with variability issues connected with the proton transfer reaction-mass spectrometry (PTR-MS) measurements of isoprene concentration. We focus on isoprene as an abundant and widely studied compound in human breath. The variability caused by the measurement process is described by the within-sample distribution. Thus, based on the formula for computing isoprene concentration that reflects the principle of the PTR-MS, a theoretical model for the within-sample distribution of isoprene concentration is suggested. This model, which assumes that the distribution is proportional to a quotient of two independent Poisson-distributed random variables, is then confronted with empirical distributions obtained from 17 breath samples collected from a healthy individual within a month. (In each sample, isoprene concentration was determined 97 times.) The empirical within-sample distributions are also compared to normal and log-normal distributions. While those seem to be satisfactory approximations, the theoretical model is found suitable only in 10 out of 17 breath samples. We also comment on the stability of samples during the measurement process in the PTR-MS instrument and, for the sake of comparison, determine the within-sample and the within-subject variability of isoprene concentrations in our data. The respective geometric standard deviations are 1.01 and 1.29.