Modeling exposure phases

INTRODUCTION 210 STATUS OF RESIDENTIAL MODELS 211 EXPOSURE PHASES IN RESIDENTIAL EXPOSURE 212 Mixing and Loading Phase 212 Application Phase 212 Post-Apphcation Phase 213 MODEL CONCEPTS FRAMEWORKS 214 Mass-Balanced Air Qnality Model 214 Fngacity Model 215 Flnid Dynamics Model 216 MODEL CONCEPTS SOURCES AND SINKS 216 Sonrce Evaporation of Pesticides 216 Vapor-Pressnre-Driven Evaporation 216 Chinn Evaporation 217... 

These models often incorporate intermediate biomarker responses. Consequently, trial simulations driven by PK models, rather than more traditional dose-response relationships, will enable more detailed simulations. For example, exposure differences due to interactions, inclusion of special populations, or from dosing regimen or formulation changes may be explored with the PK models driving PD responses. This will place additional emphasis on the modeler to develop reliable PK models using Phase 1 and 2 data that translate into the patient population. Appropriate consideration of covariates, as discussed later, will be an important part of this development. 

As an example, it may be supposed that in phase 1 there is a constant finite resistance to mass transfer which can in effect be represented as a resistance in a laminar film, and in phase 2 the penetration model is applicable. Immediately after surface renewal has taken place, the mass transfer resistance in phase 2 will be negligible and therefore the whole of the concentration driving force will lie across the film in phase 1. The interface compositions will therefore correspond to the bulk value in phase 2 (the penetration phase). As the time of exposure increases, the resistance to mass transfer in phase 2 will progressively increase and an increasing proportion of the total driving force will lie across this phase. Thus the interface composition, initially determined by the bulk composition in phase 2 (the penetration phase) will progressively approach the bulk composition in phase 1 as the time of exposure increases. 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

A model developed by Leksawasdi et al. [11,12] for the enzymatic production of PAC (P) from benzaldehyde (B) and pyruvate (A) in an aqueous phase system is based on equations given in Figure 2. The model also includes the production of by-products acetaldehyde (Q) and acetoin (R). The rate of deactivation of PDC (E) was shown to exhibit a first order dependency on benzaldehyde concentration and exposure time as well as an initial time lag [8]. Following detailed kinetic studies, the model including the equation for enzyme deactivation was shown to provide acceptable fitting of the kinetic data for the ranges 50-150 mM benzaldehyde, 60-180 mM pyruvate and 1.1-3.4 U mf PDC carboligase activity [10]. 

Activation of the catalyst is usually performed by exposure to a co-catalyst, namely an aluminum alkyl. The model catalysts were successfully activated by trimethylalumimun (TMA) and triethylaluminum (TEA), commonly used for this purpose. The compounds were dosed from the gas phase either at room temperature for a prolonged time or for a much shorter time at a surface temperature of 40 K. Nominal 3400 L of TMA or TEA were exposed at room temperature. The chemical integrity of the co-catalyst was verified by IR spectroscopy of condensed films grown at low temperature on the substrates. The spectra were typical for condensed and matrix isolated species [119]. 

Fate and exposure analyses. The multimedia transport and transformation model is a dynamic model that can be used to assess time-varying concentrations of contaminants that are placed in soil layers at a time-zero concentration or contaminants released continuously to air, soil, or water. This model is used for determining the distribution of a chemical in the environmental compartments. An overview of the partitioning among the liquid, solid and/or gas phases of individual compartments is presented in Fig. 7. The exposure model encompasses... 

Emissions of DEHP during use of the cushion vinyl floor covering appear to have a negligible contribution in the total weighted score. However, the assessment of the impact of the DEHP emission on human health is based on a characterization model that is developed for outdoor emissions, Usetox. The emission of DEHP during the use phase of the floor covering is indoors and therefore fate and the human exposure... 

Zygourakis (1990 Zygourakis and Markenscoff, 1996) developed a discretized model in which cells are assigned a degradation time, upon exposure to solvent, based on their identity as either drug, polymer, solvent, or void. The initial distribution of cells can be modeled after the microstructure of the polymer matrix and multiple phases are explicitly accounted for. The solution is found numerically. 

Exposure pathways were estimated using the modified soil module of the MSCE-POP model (http //www.msceast.org). At present the scheme is complemented with the fraction of dissolved organic matter (/doc) and with the fraction of the chemical non-equilibrium adsorbed by solid phase (/n0n-equii) or low available with individual degradation rate. The scheme of a pollutant distribution between different soil components is shown in Figure 16. 

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