Sample timing and mathematical considerations for modeling breath elimination of volatile organic compounds

Real-world exposure measurements are a necessary ingredient for subsequent detailed study of the risks from an environmental pollutant. For volatile organic compounds, researchers are applying exhaled breath analysis and the time dependence of concentrations as a noninvasive indicator of exposure, dose, and blood levels. To optimize the acquisition of such data, samples must be collected in a time frame suited to the needs of the mathematical model, within physical limitations of the equipment and subjects, and within logistical constraints. Additionally, one must consider the impact of measurement error on the eventual extraction of biologically and physiologically relevant parameters. Given a particular mathematical model for the elimination kinetics (in this case a very simple pharmacokinetic model based upon a multiterm exponential decay function that has been shown to fit real-world data extremely well), we investigated the effects on synthetic data caused by sample timing, random measurement error, and number of terms included in the model. This information generated a series of conditions for collecting samples and performing analyses dependent upon the eventual informational needs, and it provided an estimate of error associated with various choices and compromises. Though the work was geared specifically toward breath sampling, it is equally applicable to direct blood measurements in optimizing sampling strategy and improving the exposure assessment process.