Base Model Development

Base model development proceeded from a 1-compartment model (ADVAN1 TRANS2) estimated using first-order conditional estimation with interaction (FOCE-I) in NONMEM (Version 5.1 with all bug fixes as of April 2005). All pharmacokinetic parameters were treated as random effects and residual error was modeled using an additive and exponential (sometimes called an additive and proportional) error model. Initial values for the fixed effects were obtained from the literature (Xuan et al., 2000) systemic clearance (CL) of 4.53 L/h and volume of distribution (VI) of 27.3 L. Initial values for the variance components was set to 32% for all, except the additive term in the residual error which was set equal to 1 mg/L. The model successfully converged with an OFV of 20.141. The results are shown in Table 9.4. 

All models were fit using FOCE-I. Data are reported as estimate (standard error of the estimate).R denotes model minimized successfully but with R-matrix singularity. (A) denotes additive residual error term. (E) denotes exponential residual error term. 

a 2-compartment model (ADVAN3 TRANS4) was then fit to the data. Initial values were taken from the literature (Winslade et al., 1987) 5 L/h for CL, 17 L for VI, 1 L/h for intercompartmental clearance to the peripheral compartment (Q2), and 94 L for the peripheral compartment (V2). BSV was set to 70% for CL and 32% for all remaining pharmacokinetic variance terms. The exponential component of the residual error was set to 23% while the additive component was set to 1 mg/L. Optimization minimized successfully with an OFV of —6.280 (Table 9.4). R-matrix singularity was observed which indicated that the model was overparameterized. The 2-compartment fit was a significant improvement in the goodness of fit compared to the 

1- compartment model based on the LRT (26.42 on four degrees of freedom, p 0.0001). Even though the model had R-matrix singularity, near zero variance components were retained in the model since it is better to have an overparameterized covariance matrix than a restrictive, underparameterized one. Hence, model reduction will occur after the covariate model is developed. 

Lastly, a 3-compartment model (AD VAN 11 TRANS4) was then fit to the data. There were no literature values for fits to a 3-compartment model so initial values were guessed 4 L/h for CL, 15 L for VI, 2 L/h for Q2, 8 L for V2, 0.01 L/h for intercompartmental clearance to the deep compartment (Q3), and 10 L for the volume of the deep compartment (V3). The model successfully minimized with an OFV of — 14.368 but exhibited R-matrix singularity (Table 9.4). The model was not a significant improvement over the 2-compartment model (LRT = 8.09 on 4 degrees of freedom, p = 0.088). 

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The physiologically based model developed by Willman et al. [53, 54], for the prediction of both rat and human Fibs, was shown to be predictive for the human situation if passively transported compounds were studied. In their study, they used a semiempirical formula for the prediction of human permeability trained with a set of 119 passively transported drugs that did not show solubility or dissolution rate-limited absorption. 

The results presented so far in this section correspond to the regime of fully developed riser flow. Kuipers and van Swaaij (1996) applied the KTGF-based model developed by Nieuwland et al. (1996b,c) to study the effect of riser inlet configuration on the (developing) flow in CFB riser tubes and found that the differences in computed radial profiles of hydrodynamic key variables (i.e., gas and solids phase mass fluxes) rapidly disappear with increasing elevation in the riser tube. 

Ingestion exposures can be estimated using the Dietary Exposure Evaluation Model (DEEM), a computer-based model developed by Novigen Sciences, Inc. to estimate dietary intake of chemical residues (California Environmental Protection Agency 2007). The outputs from this model include estimates of dietary exposure over multiple averaging times so that both acute and chronic exposures can be considered. Exposures can also be considered on a population or individual level. The... 

Application to Test Case The DCPN-based model developed for the Test Case of land vs line-up CATC alert is too lengthy to be included in this paper therefore, we restrict to a list of Agents and... 

The ideas on which the methodology is founded are not new if separately considered (e.g., the usage of patterns, models composition, component based model development). Nevertheless, they are integrated and applied to the quantitative evaluation of physical vulnerability leading to an original way of addressing this problem. 

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