Health risk assessment of fluctuating concentrations using lognormal models

A mathematical model is proposed for assessing health risk rates of fluctuating concentrations. Each time-averaged concentration may be regarded as a dose that, when applied to the dose-response curve, produces a risk of an adverse effect. A theoretical derivation shows that the dose-response pattern is a cumulative lognormal curve because of the diversity of the individuals in the exposed population. Similarly, the concentration pattern is a log-normal distribution because of the diversity of emission sources and dispersive processes. The health risk is produced by the overlapping of the right tail of the concentration distribution and the left tail of the dose-response curve. The evaluation of the joint probability in this region has been performed by numerical integration by computer in terms of two generalized parameters. One represents the geometric standard deviation of the concentration distribution relative to that of the dose-response curve, and the other represents the distance between the geometric mean concentration and the concentration producing an adverse response in 50% of the exposed population. These results are presented graphically and in tabular form. If the two parameters of the dose-response curve are known, the health risk of the concentration pattern may be calculated conveniently for any geometric mean and geometric standard deviation values.