Systematic reduction of mechanistic models for efficient use in population exposure assessments
S.W. Wang, M. Ouyang, P.G. Georgopoulos (EOHSI, UMDNJ - R.W. Johnson Medical School and Rutgers University)
Complex mechanistic environmental and biological models, required for comprehensive exposure assessments, are often very computationally demanding. In performing population (i.e. distribution-based) exposure assessments, large numbers of simulations employing these mechanistic models are often required to obtain the population exposure estimates for the pollutant of concern, in order to account for location as well as age, gender, and other demographic and physiological variability within a population. Therefore, the computing time and resources can be prohibitively expensive or infeasible. For example, the computing time for performing a regional photochemical air quality model (e.g., CMAQ/Models-3) simulation over the Ozone Transport Assessment Group (OTAG) domain (eastern United States) typically takes 12 hours on a SUN ULTRA SPARC-4 workstation for each day of the simulation period. For this reason, population exposure assessments often utilize simpler, empirical formulations, and many (over-)simplifying assumptions. A desirable alternative, however, consists of deriving simple, computationally efficient substitutes to the comprehensive process models ("Fast Equivalent Models") through a formal, systematic process of mathematical model reduction that considers and retains essential characteristics of input-output relationships in the original model.
The systematic reduction of both environmental and biological transport and fate models is demonstrated here through application of the High Dimensional Model Representation (HDMR) technique. As one example, a reduced model is constructed for aerosol inhalation dosimetry in the MENTOR (the Modeling Environment for Total Risk studies) framework; this model incorporates anatomic, metabolic, and physical characteristics for different ages and gender to calculate dosages for different regions of the respiratory tract in members of a specified population. The application of the HDMR method is based on expressing selected model output variables (e.g., accumulated PM dose estimate for an individual) as an expansion of correlated functions consisting of model input variables (e.g., physical characteristics of the individual and PM exposure). The HDMR expansion can then be used as the reduced model to directly and efficiently calculate a PM dose estimate based on the inputs. Compared to solving the dynamic dosimetry equations, the calculation of an HDMR expansion is very fast, since its operation only involves very rapid and stable algebraic manipulations.
Evaluation and refinement of reduced models is demonstrated also here, through the application of multivariate analysis techniques, including SVD (singular value decomposition) and PCA (principal component analysis). SVD and PCA are used to identify patterns in the differences between original and reduced model outputs. The results help to identify any undesirable bias in the estimates of the reduced model. Refined reduced models are then developed to eliminate the bias, at the cost of more computation time if necessary. This procedure allows to achieve a favorable balance between accuracy and efficiency of the reduced model.