Annals of Occupational Hygiene Advance Access originally published online on April 29, 2009
Annals of Occupational Hygiene 2009 53(4):409-424; doi:10.1093/annhyg/mep017
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Bayesian Modeling of Exposure and Airflow Using Two-Zone Models
1 Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455, USA
2 Workplace Safety Insurance Board, Toronto, M5V 3J1 Ontario, Canada
3 Department of Environmental Health Sciences, University of Alabama at Birmingham, Birmingham, AL 35294, USA
4 Division of Environmental Health Sciences, University of Minnesota, Minneapolis, MN 55455, USA
* Author to whom correspondence should be addressed. Tel: 612-626-5428; fax: 612-626-4837; e-mail: ramac002{at}umn.edu
Mathematical modeling is being increasingly used as a means for assessing occupational exposures. However, predicting exposure in real settings is constrained by lack of quantitative knowledge of exposure determinants. Validation of models in occupational settings is, therefore, a challenge. Not only do the model parameters need to be known, the models also need to predict the output with some degree of accuracy. In this paper, a Bayesian statistical framework is used for estimating model parameters and exposure concentrations for a two-zone model. The model predicts concentrations in a zone near the source and far away from the source as functions of the toluene generation rate, air ventilation rate through the chamber, and the airflow between near and far fields. The framework combines prior or expert information on the physical model along with the observed data. The framework is applied to simulated data as well as data obtained from the experiments conducted in a chamber. Toluene vapors are generated from a source under different conditions of airflow direction, the presence of a mannequin, and simulated body heat of the mannequin. The Bayesian framework accounts for uncertainty in measurement as well as in the unknown rate of airflow between the near and far fields. The results show that estimates of the interzonal airflow are always close to the estimated equilibrium solutions, which implies that the method works efficiently. The predictions of near-field concentration for both the simulated and real data show nice concordance with the true values, indicating that the two-zone model assumptions agree with the reality to a large extent and the model is suitable for predicting the contaminant concentration. Comparison of the estimated model and its margin of error with the experimental data thus enables validation of the physical model assumptions. The approach illustrates how exposure models and information on model parameters together with the knowledge of uncertainty and variability in these quantities can be used to not only provide better estimates of model outputs but also model parameters.
Keywords: Bayesian statistics • exposure assessment • indoor air modeling • industrial hygiene • Markov chain Monte Carlo • two-zones modeling • worker's exposure
Received October 3, 2008; in final form February 26, 2009