Modeling of uncertainty associated with dose-response curves as applied for probabilistic risk assessment in laser safety

In laser safety, dose-response curves describe the probability for ocular injury as a function of ocular energy, and are often used to quantify the risk for ocular injury given a certain level of exposure to laser radiation. In principal, a dose-response curve describes the biological variation of the individual thresholds in a population. In laser safety, a log-normal cumulative distribution is generally assumed for the dose-response curve, for instance, when Probit analysis is performed. The log-normal distribution is defined by two parameters, the median, called ED50 and the slope. When animal experiments are performed to obtain dose-response curves for laser induced injury, ecperimental uncertainty such as focussing errors as well as variability within the group of experimental animals, such as inter-individual variability of obsorption of the ocular media, can influence the shape of the dose-response curve.

We present simulations of uncertainties and cariabilities that show that the log-normal dose-response curve as obtained in a animal experiments can grossly overestimate the probability for ocular damage for small doses. It is argued that the intrinsic slope for an individual's dose response curve is rather steep, even for retinal injury, however, the dose-response curve for a group or population can be broader when there is inter-individual variability of parameters which influence the threshold. the quantitative results of the simulation of the grouping of individual dose-response curves can serve as basis to correct potentially biased dose-response curves as well as to characterize the uncertainty associated with the ED50 and the slope of the dose-response curve. A probabilistic risk analysis model, which accounts for these uncertainties by using Monte-Carlo simulation, was developed for retinal laser injuries from pulsed lasers with wavelengths from 200 nm to 20mu m, and the interpretation of the results are discussed on the basis of example calculations.