Global sensitivity analysis

A global sensitivity analysis was performed for the lead concentration in the arterial blood model (Fig. 7) over the simulation period for each parameter. Parameters considered for the sensitivity analysis are listed in Table 8 (Annex 1). The magnitude of sensitivity is shown by relative sensitivity index. It was observed that the most influential parameter is the porosity of the sediment of the river (phi sed)... 

Fig. 7 A global sensitivity analysis for lead concentration in arterial blood...

Regarding the global sensitivity analysis, the results indicate that the variation of the model output is highly sensitive to the variations of parameters used in fish and root compartments. The higher concentration of Pb in fish than in potato, leaf, root, milk, and beef (Fig. 6) reflects that the variation of the model output is more sensitive to variations of fish parameters than of potato, leaf, root, milk, and beef parameters. 

However, as a general observation, this study demonstrated the feasibility of the integrated modeling approach to couple an environmental multimedia and a PBPK models, considering multi-exposure pathways, and thus the potential applicability of the 2-FUN tool for health risk assessment. The global sensitivity analysis effectively discovered which input parameters and exposure pathways were the key drivers of Pb concentrations in the arterial blood of adults and children. This information allows us to focus on predominant input parameters and exposure pathways, and then to improve more efficiently the performance of the modeling tool for the risk assessment. 

The global sensitivity analysis methods address the problem of the precise calculation of the uncertainty of the model output as a result of uncertainties in parameters. These methods can handle any large uncertainty in the input parameters. More refined techniques include the determination of the extent of the uncertainty in output as a result of the uncertainty of each parameter. 

A. Saltelli, T. Homma and T.H. Andres, A New Measure of Importance in Global Sensitivity Analysis for Model Output. Proceedings of 6th Joint EPS/APS International Conference on Physics and Computing (1994) pp. 511-514. 

T. Homma T. and A. Saltelli, Importance Measures in Global Sensitivity Analysis of Nonlinear Models, Rel. Eng. Syst. Safety 52 (1996) 1-17. 

C. Kontoravdi, S.P. Asprey, E.N. Pistikopoulos, A. Mantalaris, 2005. Application of global sensitivity analysis to determine goals for design of experiments An example study on antibody-producing cell cultures. Biotechnology Progress, 21, 1128-1135. 

TABLE 35.2 Effect of Uncertainty Level on the Estimate of Trial Power Using a Global Sensitivity Analysis for the Zidovndine Analog Efficacy Trial Simnlation... 

Carrero, E., Queipo, N., Pintos, S. and Zerpa, L. (2007) Global sensitivity analysis of alkaline-surfactant-polymer enhanced recovery processes. /. Pet. Sci. Eng., 58( 1-2), 30-42. 

McRae, G. J., Tilden, J. W., and Seinfeld, J. H. (1982) Global sensitivity analysis - a computational implementation of the Fourier Amplitude Sensitivity Test (FAST), Computers and Chem. Engineering. 6, 15-25. 

Borgonovo, E., G. Apostolalds, S. Tarantola, and A. Saltelli (2003). Comparison of global sensitivity analysis techniques and importance measures in PSA. Reliability Engineering and System Safety 79, 175-185. 

Global sensitivity analysis allows investigating the relationship between uncertainty in the inputs of a computational model and the uncertainty in the output. So-called variance-based techniques are based on a decomposition of the variance in ie model output into components each depending on just one input variable, components each depending on two variables and so forth. Correspondingly, the output variance can be decomposed into contributions each coming from only one input variable ( first order effects ), from just two variables ( second order ), etc. A major drawback of the available algorithms (FAST(Saltelli et al. 

Saltelli, A., S. Tarantola, and K. Chan (1999). A quantitative, model independent method for global sensitivity analysis of model output. Technometrics 41, 39-56. 

Sobol , 1., S. Tarantola, D. Gatelli, S. Kucherenko, and W. Mauniz (2007). Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering System Safety 92, 957-960. 

ABSTRACT Several EU PAMINA project partners have applied different Sensitivity Analysis (SA) techniques to analytical models as well as to a simplified, though representative, PA model. The aims of the exercise were to investigate the performance of different techniques in the presence of features such as (lack of) linearity, (lack of) monotony, interactions, etc. to check the importance of sample size to compare different options within a given S A technique to cross-compare the results obtained using different teehniques and to get a better understanding of the rationale behind every available technique and about their capabilities and shortcomings. This paper presents and discusses some results on the tests of global sensitivity analysis performed with variance-based sensitivity indicators. 

Saltelli, A. et al. 2008. Global Sensitivity Analysis. Chichester Wiley. 

Saltelli, A., Tarantola, S. Chan, K. 1999. A Quantitative, Model Independent Method for Global Sensitivity Analysis of Model Output. Technometrics 41(1) 39-56. 

Wagner, H.M. (1995) Global sensitivity analysis. Operations Research, 43 (6), 948-969. 

Equation (5.4) provides us the local sensitivities. A global sensitivity analysis can be calculated using the square of the sum of the normalized sensitivity matrix... 

An advanced detailed non-hnear computation model of the mobile antinoise wall has been used. The computation model of the motorcar has been selected from the database of test vehicle models. The analysis has been carried out using a specially developed procedure. Fulfilling certain specified criteria, the computer analysis substitutes the actual impact test of the vehicle crashing into the restraint system. Following the results of computations, the construction details of the mobile noise damping wall structure have been properly modified. Advanced is a method of global sensitivity analysis that allows us to analyze the higher order interaction effects. 

Moment-Independent Global Sensitivity Analysis Methods... 

In most uncertainty studies published so far (see e.g. Brown et al. (1999), Turanyi et al. (2002), Zsely et al. (2005), Zador et al. (2005a, b, 2006a) and Zsely et al. (2008)), where the uncertainties of the rate coefficients were utilised, the uncertainty of k was considered to be equal to the xmcertainty of the pre-exponential factor A. This implies that the uncertainty of parameters E and n is zero, which is an unrealistic assumption. In a global sensitivity analysis study of a turbulent reacting atmospheric plume, Ziehn et al. (2009a) demonstrated the importance of uncertainties in EIR for the reaction N0 + 03 = N02 + 02. In this case for the prediction of mean plume centre line O3 concentratiOTis, the sensitivity to the assumed value for EIR was almost a factor of 20 higher than that of the A-factor, based on input parameter uncertainty factors provided by the evaluation of Androulakis (2004, 2004). However, in this case the parameters of the Anhenius expression for the chemical reactions considered were allowed to vary independently. In fact, the characterisation of the joint uncertainty of the Arrhenius parameters is important for the reahstic calculatiOTi of the uncertainty of chemical kinetic simulation results as will be discussed in the next section. 

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