Modeling/simulation validation

The PBPK model for a chemical substance is developed in four interconnected steps (1) model representation, (2) model parametrization, (3) model simulation, and (4) model validation (Krishnan and Andersen 1994). In the early 1990s, validated PBPK models were developed for a number of toxicologically important chemical substances, both volatile and nonvolatile (Krishnan and Andersen 1994 Leung 1993). PBPK models for a particular substance require estimates of the chemical substance-specific... 

PBPK and classical pharmacokinetic models both have valid applications in lead risk assessment. Both approaches can incorporate capacity-limited or nonlinear kinetic behavior in parameter estimates. An advantage of classical pharmacokinetic models is that, because the kinetic characteristics of the compartments of which they are composed are not constrained, a best possible fit to empirical data can be arrived at by varying the values of the parameters (O Flaherty 1987). However, such models are not readily extrapolated to other species because the parameters do not have precise physiological correlates. Compartmental models developed to date also do not simulate changes in bone metabolism, tissue volumes, blood flow rates, and enzyme activities associated with pregnancy, adverse nutritional states, aging, or osteoporotic diseases. Therefore, extrapolation of classical compartmental model simulations... 

Modeling and validation require the close cooperation of all parties involved in the project. Further success factors in simulation modeling include adequate planning experience, special experience with simulation tools, and the ability to think in abstract structures. 

Mechanism-based PK/PD modeling and validation. This involves the four distinct steps of building PK model, building PD model, linking PK and PD models, and simulation of treatment regimens or trials for useful prediction. 

Because the reaction in a CL requires three-phase boundaries (or interfaces) among Nafion (for proton transfer), platinum (for catalysis), and carbon (for electron transfer), as well as reacfanf, an optimized CL structure should balance electrochemical activity, gas transport capability, and effective wafer management. These goals are achieved through modeling simulations and experimental investigations, as well as the interplay between modeling and experimental validation. 

Only deterministic models for cellular rhythms have been discussed so far. Do such models remain valid when the numbers of molecules involved are small, as may occur in cellular conditions Barkai and Leibler [127] stressed that in the presence of small amounts of mRNA or protein molecules, the effect of molecular noise on circadian rhythms may become significant and may compromise the emergence of coherent periodic oscillations. The way to assess the influence of molecular noise on circadian rhythms is to resort to stochastic simulations [127-129]. Stochastic simulations of the models schematized in Fig. 3A,B show that the dynamic behavior predicted by the corresponding deterministic equations remains valid as long as the maximum numbers of mRNA and protein molecules involved in the circadian clock mechanism are of the order of a few tens and hundreds, respectively [128]. In the presence of molecular noise, the trajectory in the phase space transforms into a cloud of points surrounding the deterministic limit cycle. 

Tronconi et al. [46] developed a fully transient two-phase 1D + 1D mathematical model of an SCR honeycomb monolith reactor, where the intrinsic kinetics determined over the powdered SCR catalyst were incorporated, and which also accounts for intra-porous diffusion within the catalyst substrate. Accordingly, the model is able to simulate both coated and bulk extruded catalysts. The model was validated successfully against laboratory data obtained over SCR monolith catalyst samples during transients associated with start-up (ammonia injection), shut-down (ammonia... 

The model was validated against heavy duty and passenger car diesel engine test bench experiments. A good correlation was obtained between ESC and ETC experiments and simulation with 0 and 0.5% NO2 NO ratios and a virtual oxidation catalyst. The virtual oxidation catalyst model was realized by placing an oxidation catalyst model in front of the SCR catalyst. 

To test the validity of Eqs. (25) and (31), we have performed simulations of groove relaxation under evaporation-condensation dynamics and numerical integration of (31). Below we describe briefly the model simulated and present data for the averaged surface profile and the lifetime of the top terrace during relaxation. Details of this study will be reported elsewhere. 

Future areas of development Include theoretical formulation of source/receptor models and validation tests with real and simulated data. 

Altogether, the data reported in this section indicate a very good predictive quality of the model simulations this implies in the first place that the SCR kinetics estimated over powdered catalyst were successfully validated at this bigger scale. However, the excellent agreement between monolith data and model predictions based on intrinsic kinetics also confirms the accurate model description of physical phenomena, specifically external and intraporous mass transfer, which were not significant in the microreactor runs over the powdered catalyst, but played an important role in the monolith runs, as pointed out by the direct comparison in Fig. 44. 

In the model of Csanady et al. (1996), the biochemical parameters for butadiene in rats and mice were obtained by fitting model simulations to in-vivo data of Bolt et al. (1984) and Kreiling et al. (1986). The biochemical parameters for epoxybutene were identical to those of Johanson and Filser (1993, 1996). This model accurately predicted experimental data on epoxybutene. The most advanced models are those of Csanady etal. (1996) and Sweeney et al. (1997), since they can simulate both epoxybutene and diepoxybutane as metabolites of butadiene. The tissue blood partition coefficients for diepoxybutane were estimated by Csanady et al. (1996) to have a value of 1 for all tissues. Sweeney et al. (1997) obtained tissue blood partition coefficients from in-vitro measurements (Table 23). Both models yielded good predictions for mice and rats for both metabolites. For humans, no measured data have been reported against which the predictions could be validated. In addition, the model of Csanady et al. (1996) predicted accurately the measured haemoglobin adduct levels (Osterman-Golkar etal., 1993 Albrecht et al., 1993) of epoxybutene in rodents following exposure to butadiene. None of the models published has included the fonnation and elimination of epoxybutanediol. 

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