Modelling the human olfactory stimulus-response function

Two models, derived from the equations of Michaelis-Menten and Hill, were adapted to olfaction. Their ability to model human olfactory stimulus-response relationships was compared with that of the classical laws of Fechner and Stevens. First, these four models were systematically compared on data available in the literature concerning 20 pure odorous compounds. At the lower concentrations of the odorous compound, the model of Stevens was found to be as good as the model of Hill. However, when the concentration range was extended further and included the concentration at half the maximum intensity, the model of Hill was found to be better. Second, the four models were tested on different parts of a true stimulus-response sigmoid curve with 5% noise added. The comparison confirmed the results obtained when experimental data were used. Third, the hypothesis that the psychophysical response is the sum of sigmoidal responses generated at the more peripheral parts of the olfactory system was examined, assuming a binomial distribution of receptor affinities. Within a very large range of variation in their characteristics, the sums of several sigmoids are indeed correctly modelled by Hill equations with exponents reflecting the distribution of receptor affinities.